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MATERIALS RESEARCH SOCIETY SYMPOSIUM PROCEEDINGS VOLUME 296
Structure and Properties of Energetic Materials •
Symposium held November 30-December 2, 1992, Boston, Massachusetts, U.S.A.
Z4 EDITORS:
Donald H. Liebenberg U.S. Office of Naval Research Arlington, Virginia, U.S.A.
Ronald W. Armstrong University of Maryland College Park, Maryland, U.S.A.
John J. Gilman Lawrence Berkeley Laboratory Berkeley, California, U.S.A.
MATERIALS RESEARCH SOCIETY Pittsburgh. Pennsylvania
93 6 14
0z23
=
This work was supported in part by the Office of Naval Research under Grant Number N00014-93-1-0147. The United States Government has a royalty-frce license throughout the world in all copyrightable material contained herein.
Single article reprints from this publication are available through University Microfilms Inc., 300 North Zeeb Road, Ann Arbor, Michigan 48106 CODEN: MRSPDH Copyright 1993 by Materials Research Society. All rights reserved. This book has been registered with Copyright Clearance Center. Inc. For further information, please contact the Copyright Clearance Center, Salem, Massachusetts. Published by: Materials Research Society 9800 McKnight Road Pittsburgh, Pennsylvania 15237 Telephone (412) 367-3003 Fax (412) 367-4373 Library of Congress Cataloging in Publication Data Structure and properties of energetic materials : symposium held November 30December 2, 1992. Boston. Massachusetts, U.S.A. / edited by Donald H. Liebenberg. Donald WV. Armstrong. and John J. Gilman p. cm.-(Materials Research Society symposium proceedings. ISSN 0272-9172 : N. 296) Includes bibliographical references and indexes. ISBN 1-55899-191-3 1. Explosives-Congresses. 1. Liebenberg. Donald H. If. Armstrong, 'John Joseph) IV. Series: Materials Research Ronald W. III. Gilman, Job.Am proceedn, , v. 296. Society s'-), 93-12847 TP270.AIS77 1993 CIP 662'.2-dc2O Manufactured in the United States of America
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*
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:
Contents PREFACE
ix
ACKNOWLEDGMENTS
xi
MATERIALS RESEARCH SOCIETY SYMPOSIUM PROCEEDINGS
xii
PART 1: STRUCTURE AND STABILITY *MOLECU[AR STRUCTURE AND PERFORMANCE OF HIGH EXPLOSIVES James q1.Stine
3
*RECENT ADVANCES IN THE THERMAL DECOMPOSITION OF CYCLIC NITRAMINES Richard Behrens, Jr. and Suryanarayana Bulusu
13
*MOLECULAR COMPOSITION, STRUCTURE, AND SENSITIVITY OF EXPLOSIVES Carlyle B. Storm and James R. Travis
25
ENERGY TRANSFER DYNAMICS AND IMPACT SENSITIVITY Laurence E. Fried and Anthony J. Ruggiero
35
RELATIONSHIP BETWEEN RADIATION STABILITY AND MOLECULAR STRUCTURE OF NITRAMINE EXPLOSIVES James J. Pinto
41
THIN FILM INFRARED LASER PYROLYSIS STUDIES OF THERMAL DECOMPOSITION MECHANISMS IN NITRAMINE PROPELLANTS Ted R. Botcher and Charles A. Wight
47
NITROGEN RADICALS FROM THERMAL AND PHOTOCHEMICAL DECOMPOSITION OF AMMONIUM PERCHLORATE. AMMONIUM DINITRAMIDE, AND CYCLIC NITRAMINES M.D. Pace
53
PART 1I: DEFORMATION, FRACTURE, AND INITIATION *ENERGY LOCALIZATION AND THE INITIATION OF EXPLOSIVE CRYSTALS BY SHOCK OR IMPACT C.S. Coffey
63
*THE IMPORTANCE OF STERICALLY HINDERED SHEAR IN DETERMINING THE SENSITIVITY OF EXPLOSIVE CRYSTALS Jerry 1. Dick
75
FRACTURE SURFACE TOPOGRAI-,IY OF OCTOL EXPLOSIVES M. Yvonne D. Lanzeroni, James J. Pinto. and Allan Wolfe
81
THE ELECTRON-BEAM SENSITIVITY OF BINARY METAL AZIDES Patrick J. Herley and William Jones
87
COMPARISON OF DEFORMATION AND SHOCK REACTIVITY FOR SINGLE CRYSTALS OF RDX AND AMMONIUM PERCHLORATE H.W. Sandusky. B.C. Beard, B.C. Glancy. W.L. Elban. and R.W. Armstrong
D.t.J/Or
*Invited Paper
[VYC QUAL•'
'.•••
'/
93
..odes
MOLECULAR MODELING OF SLIP SUPPOSED TO OCCUR IN THE SHOCK INITIATION OF CRYSTALLINE PETN James P. Ritchie
99
INTERPRETING DROP-WEIGHT IMPACT RESULTS IN TERMS OF DEFORMATION DEPENDENT INITIATION CRITERIA P.J. Baker and A.M. MeIlor
107
HOT SPOT HEATING FROM IMPURITIES AND VACANCIES IN A CRYSTALLINE SOLID UNDER RAPID COMPRESSION D.H. Tsai
113
PART III: SHOCK PHENOMENA *DISSOCIATIVE PHASE TRANSITIONS, SPLIT SHOCK WAVES, RAREFACTION SHOCKS, AND DETONATIONS C.T. White, D.H. Robertson. M.L. Elert, J.W. Mintmire. and D.W. Brenner *FEMTOSECOND SPECTROSCOPY OF CHEMICALLY REACTIVE SOLIDS: A METHODOLOGY Weaning Wang. Marc M. Wefers. and Keith A. Nelson *EXPLOSION OF DROPS IMPACTING NON-WETTING RIGID SURFACES Clarence Zener and Dennis Prieve
123
129 141
AB INITIO STUDY OF ELECTRONIC STRUCTURE OF RDX MOLECULAR CRYSTAL Guang Gao. Ravindra Pandey. and A. Barry Kunz
1-19
MOLECULAR DYNAMICS SIMULATIONS OF SHOCKS AND DETONATIONS IN A MODEL 3D ENERGETIC CRYSTAL WITH DEFECTS Lee Phillips
155
MOLECULAR DYNAMICS SIMULATIONS OF SHOCK-DEFECT INTERACTIONS IN TWO-DIMENSIONAL NONREACTIVE CRYSTALS Robert S. Sinkovits. Lee Phillips, Elaine S. Oran. and Jay P. Boris
161
MOLECULAR LEVEL STUDY OF INSENSITIVE AND ENERGETIC LAYERED AND INTERCALATED MATERIALS Richard D. Bardo
167
OVERVIEW: HIGH SPEED DYNAMICS AND MIODELLING AS IT APPLIES TO ENERGETIC SOLIDS J. Covino. S.A. Finnegan. O.E.R. Heimdahl. A.J. Lindfors. and J.K. Pringle
173
DELAYED INITIATION IN A MODEL ENERGETIC MATERIAL D.H. Robertson. D.W. Brenner. and C.T. White
183
PART IV: CRYSTALS: GROWTH AND BEHAVIOR *ELFCTRONIC EXCITATIONS PRECEDING SHOCK iNITIATION IN EXPLOSIVES J. Sharma and B.C. Beard
189
*PRESSURE/TEMPERATURE/REACTION PHASE DIAGRAMS FOR SEVERAL NITRAMINE COMPOUNDS T.P. Russell. P.J. Miller. G.J. Piermarini. and S. Block
199
*Invited Paper
vi
THE GROWTH AND PERFECTION OF SINGLE CRYSTALS OF TRINITROTOLUENE (TNT) Hugh G. Gallagher and John N. Sherwood
215
ATOMIC FORCE MICROSCOPY OF AMMONIUM PERCHLORATE Minsun Yoo, Seokwon Yoon, and Alex De Lozanne
221
ENERGETIC CRYSTAL-LATTICE-DEPENDENT RESPONSES R.W. Armstrong. H.L. Ammon, Z.Y. Du, W.L. Elban. and X.J. Zhang
227
THE MOLECULAR AND CRYSTAL STRUCTURES OF POLYCYCLIC ENERGETIC MATERIALS Richard Gilardi
233
NTO POLYMORPHS Kien-yin Lee and Richard Gilardi
237
GROWTH AND DEFECTS OF EXPLOSIVES CRYSTALS Howard H. Cady
243
PART V: STATICS, KINEMATICS, AND DYNAMICS *SURFACE CHEMICAL CHARACTERIZATION METHODS APPLIED TO ENERGETIC MATERIALS B.C. Beard and J. Sharma *SURFACE CHEMISTRY OF ENERGETIC MATERIALS AT HIGH TEMPERATURE Thomas B. Brill
257
269
QUANTUM DYNAMICAL STUDIES OF THE DECOMPOSITION OF ENERGETIC MATERIALS Herschel Rabitz and Eduardo Vilallonga
281
CORRELATION TIME FOR POLYMER CHAIN MOTION NEAR THE GLASS TRANSITION IN NITROCELLULOSE J.R.P. Jayakody. S. Bulusu. and R A Marino

287
HOT SPOT HISTORIES IN ENERGETIC MATERIALS A.M. Mellor. D.A Wiegand. and K.B. Isorn
291
EXPERIMENTAL STUDY AND MODEL CALCULATIONS OF METAL COMBUSTION IN AIIAP UNDERWATER EXPLOSIVES Philip 1. Miller and Raafat H. Guirguis
299
DETONATION STUDIES IN DISPERSED SOLID PARTICULATE EXPLOSIVES USING HIGH SPEED TIME-RESOLVED HOLOGRAPHY Michael J. Ehrlich. James W Wagner. Jacob Friedman. and Heinrich Eggnart
305
REACTION KINETICS OF METALLIZED EXPLOSIVES Hermenzo D. Jones and Frank J. Zerilh
311
PART VI: PROCESSES, PERFORMANCE. AND PROPELLANTS *COMBUSTION SYNTHESIS OF COMPOSITL M.'.TERIALS J.J. Moore *INTERRELATIONSHIP BETWEEN SOLi j PROPELLANT COMBUSTION AND MATERIALS BEHAVIOR Kenneth K. Kuo. Thomas A. Litzinger. and Wen H Hsieh *invited Paper vii
319
331
LABORATORY TESTING AND CONSTITUTIVE MODELING OF COAL INCLUDING ANISOTROPY Dar-Hao Chen, Musharraf M. Zaman, and Anant R. Kukreti
349
TIME LAG DIFFUSION METHOD FOR A SOLID PROPELLANT EMITTING GASES James K. Baird and Jenn-Shing Chen
355
ENERGETIC MATERIALS IN CERAMICS SYNTHESIS J.J. Kingsley and L.R. Pederson
361
INFRARED FIBER OPTIC DIAGNOSTIC FOR SOLID PROPELLANT COMBUSTION J. Wormhoudt and P.L. Kebabian
367
LASER-BASED SENSITIVE DETECTION OF ENERGETIC MATERIALS G.W. Lemire, J.B. Simeonsson, and R.C. Sausa
373
SHOCKED ENERGETIC MOLECULAR MATERIALS: CHEMICAL REACTION INITIATION AND HOT SPOT FORMATION M.D. Fayer. Andrei Tokmakoff. and Dana D. Dlott
379
AUTHOR INDEX
385
SUBJECT INDEX
387
viii
Preface This was the first Symposium on Energetic Materials held at a Materials Research Society Mee.ng. Energetic materials are substances that undergo exothermic chemical reaction in response to some stimulus and react in time scales leading to combustion, explosion, and/or detonation (millisec to femtosec). Energetic materials represent a multibillion dollar industry for both commercial and military uses. These are among the earliest of man-made classes of materials. Their historical role in the development of nations has been enormous. Land clearing, railroad and highway construction, and mining continue as important though not exclusive uses. The space program is enabled by energetic materials. While many of the energetic materials in current use were developed in the previous century, a recent renaissance by synthetic chemists has brought forward new
compounds. The response of these new materials to stimuli that cause initiation or
transition from combustion to detonation and the response of energetic materials generally to a variety of new uses (such as for air bags in automobiles where the environmental conditions and longer term storage stability questions must be carefully assessed) have led to increased interest in understanding the fundamental mechanisms for initiation and decomposition and also to new methods for quality and safety assurance tests. Understanding the sensitivity to known stimuli such as impact or heating, the routes of chemical decomposition, and the theoretical techniques that can describe these processes is a fertile field of current research addressed in this Symposium. Relations between the molecular structure and the defect structures and initiation and decomposition, properties of new materials, experimental tests and new methods for probing at the microscopic level, and theoretical progress were the main topics. The commonality with studies of other materials using many similar experimental techniques, especialiv in the area of defect and the special features of the subpicosecond time scale for reactions and deeL. -position both in experiments and molecular dynamics simulations provides a strong bond with other materials research. The organizers hope that these proceedings will further strengthen those bonds. Donald H. Liebenberg Ronald W. Armstrong John J. Gilman March 1993
IX
Acknowledgments The organizers acknowledge with thanks the efforts of Professor R. Roy and members of the Materials Research Society boards to provide a forum for the discussion of energetic materials. The support staff of MRS significantly helped this Symposium run smoothly, and encouraged the timely receipt of papers included in these proceedings. The Chairs of the Sessions are to be especially thanked for their help in the review process in addition to keeping the sessions on time and providing opportunity for stimulating discussions of the papers. These Chairs were: R. Lieb, R. Doherty, M. Berman, R. Simpson, H. Cady, W. Faust, C. Capelnos, J. Oxley, J. Covino, and J. Dienes. The organizers acknowledge the support of Richard Miller and dhe Office of Naval Research and the response of the energetic materials community in providing an important set of papers describing current research results and future directions. We hope this Symposium has added to the breadth of materials science included in the Materials Research Society charter.
Xi
Acknowledgments The organizers acknowledge with thanks the efforts of Professor R. Roy and
members of the Materials Research Society boards to provide a forum for the discussion of energetic materials. The support staff of MRS significantly helped this Symposium run smoothly, and encouraged the timely receipt of papers included in these proceedings. The Chairs of the Sessions are to be especially thanked for their help in the review process in addition to keeping the sessions on time and providing opportunity for stimulating discussions of the papers. These Chairs were: R. Lieb, R. Doherty, M. Berman, R. Simpson, H. Cady, W. Faust, C. Capellos, J. Oxley, J. Covino, and J. Dienes. The organizers acknowledge the support of Richard Miller and ihe Office of Naval Research and the response of the energetic materials community in providing an important set of papers describing current research results and future directions. We hope this Symposium has added to the breadth of materials science included in the Materials Research Society charter.,
Xi
MATERIALS RESEARCH SOCIETY SYMPOSIUM PROCEEDINGS
Volume 258-Amorphous Silicon Technology--1992, M.J. Thompson, Y. Hamakawa, P.G. LeComber, A. Madan, E. Schiff, 1992, ISBN:. 1-55899-153-0 Volume 259-Chemical Surface Preparation, Passivation and Cleaning for Semiconductor Growth and Processing, R.J. Nemanich, C.R. Helms, M. Hirose, G.W. Rubloff, 1992, ISBN: 1-55899-154-9 Volume 260-Advanced Metallization and Processing for Semiconductor Devices and Circuits II, A. Katz, Y.I. Nissim. S.P. Murarka, J.M.E. Harper, 1992, ISBN: 1-55899-155-7 Volume 261-Photo-Induced Space Charge Effects in Semiconductors: Electro-optics, Photoconductivity, and the Photorefractive Effect, D.D. Nolte, N.M. Haegel, K.W. Goossen, 1992, ISBN: 1-55899-156-5 Volume 262-Defect Engineering in Semiconductor Growth, Processing and Device
Technology, S. Ashok, J. Chevallier, K. Sumino, E. Weber, 1992, ISBN: 1-55899-157-3 Volume 263-Mechanisms of Heteroepitaxial Growth, M.F. Chisholm, B.J. Garrison, R. Hull, L.J. Schowalter, 1992, ISBN: 1-55899-158-1 Volume 264-Electronic Packaging Materials Science VI, P.S. Ho, K.A. Jackson, C-Y. Li, G.F. Lipscomb, 1992, ISBN: 1-55899-159-X Volume 265-Materials Reliability in Microelectronics II, C.V. Thompson, J.R. Lloyd, 1992, ISBN: 1-55899-160-3 Volume 266-Materials Interactions Relevant to Recycling of Wood-Based Materials. R.M. Rowell, T.L. Laufenberg. J.K. Rowell, 1992, ISBN: 1-55899-161-1 Volume 267-Materials Issues in Art and Archaeology III, J.R. Druzik, P.B. Vandiver, G.S. Wheeler, 1. Freestone, 1992, ISBN: 1-55899-162-X Volume 268-Materials Modification by Energetic Atoms and Ions, K.S. Grabowski, S.A. Barnett, S.M. Rossnagel, K. Wasa, 1992, ISBN: 1-55899-163-8 Volume 269-Microwave Processing of Materials Ill. R.L, Beatty, W.H. Sutton, M.F. Iskander, 1992, ISBN: 1-55899-164-6 Volume 270-Novel Forms of Carbon, C.L. Renschler, J. Pouch, D. Cox, 1992, ISBN: 1-55899-165-4 Volume 271-Better Ceramics Through Chemistry V. M.J. Hampden-Smith, W.G. Klemperer, C.J. Brinker, 1992. ISBN: 1-55899-166-2 Volume 272-Chemical Processes in Inorganic Materials: Metal and Semiconductor Clusters and Colloids, P.D. Persans. J.S. Bradley, R.R. Chianelli. G. Schmid, 1992, ISBN: 1-55899-167-0 Volume 273-Intermetallic Matrix Composites II. D. Miracle, J. Graves, D. Anton. 1992, ISBN: 1-55899-168-9 Volume 274-Submicron Multiphase Materials. R. Baney. L. Gilliom, S.-A. Hirano. H. Schmidt, 1992, ISBN: 1-55899-169-7 Volume 275--Layered Superconductors: Fabrication. Properties and Applications, D.T. Shaw, C.C. Tsuei, T.R. Schneider. Y. Shiohara, 1992. ISBN: 1-55899-170-0 Volume 276-Materials for Smart Devices and Micro-Electro-Mechanical Systems. A.P. Jardine, G.C. Johnson, A. Crowson. NI. Allen. 1992, ISBN- 1-55899-171-9 ;',..-'ne 277-hM,.- .aolecular Host-Guest Complexes: Optical, Optoelectronic, and Photorefractive Properties and Applications. S.A. Jenekhe, 1992, ISBN: 1-55899-172-7 Volume 278--Computational Methods in Materials Science, J.E. Mark, M.E. Glicksman, S.P. Marsh. 1992. ISBN: 1-55899-173-5
MATERIALS RESEARCH SOCIETY SYMPOSIUM PROCEEDINGS Volume 279-Beam-Solid Interactions-Fundamentals and Applications, M.A. Nastasi, N. Herbots, L.R. Harriott, R.S. Averback, 1993, ISBN: 1-55899-174-3 Volume 280-Evolution of Surface and Thin Film Microstructure, H.A. Atwater, E. Chason, M. Grabow, M. Lagally, 1993, ISBN: 1-55899-175-1 Volume 28 1- Semiconductor Heterostructures for Photonic and Electronic Applications, D.C. Houghton, C.W. Tu, R.T. Tung, 1993, ISBN: 1-55899-176-X Volume 282-Chemical Perspectives of Microelectronic Materials IlI, C.R. Abernathy, C.W. Bates, D.A. Bottling, W.S. Hobson, 1993, ISBN: 1-55899-177-8 Volume 283-Microcrystalline Semiconductors-Materials Science & Devices, Y. Aoyagi, L.T. Canham, P.M. Fauchet, L. Shimizu, C.C. Tsai, 1993, ISBN: 1-55899-178-6 Volume 284-Amorphous Insulating Thin Films, J. Kanicki, R.A.B. Devine, W.L. Warren, M. Matsumura, 1993, ISBN: 1-55899-179-4 Volume 285- Laser Ablation in Materials Processing-Fundamentals and Applications, B. Braren, J. Dubowski, D. Norton, 1993, ISBN: 1-55899-180-8 Volume 286-Nanophase and Nanoconiposite Materials, S. Komarneni, J.C. Parker, G.J. Thomas, 1993, ISBN: 1-55899-181-6 Volume 287- Silicon Nitride Ceramics-Scientific and Technological Advances. I-W. Chen, P.F. Becher, M. Mitomo. G. Petzow, T-S. Yen. 1993, ISBN: 1-55899-182-4 Volume 288-High-Temperature Ordered Intermetallic Alloys V, I. Baker, J.D. Whitteriberger, R. Darolia, M.H. Yoo, 1993, ISBN: 1-55899-183-2 Volume 289-Flow and Microstructure of Dense Suspensions, L.J. Struble, C.F. Zukoski, G. Maitland, 1993. ISBN: 1-55899-184-0 Volume 290-Dynamics in Small Confining Systems. J.M. Drake, D.D. Awschalom, J. Klafter, R. Kopelman, 1993, ISBN: 1-55899-185-9 Volume 291-Materials Theory and Modelling. P.D. Bristowe, J. Broughton, J.M. Newsam, 1993. ISBN., 1-55899-186-7 Volume 292-Biomolecular Materials. S.T. Case, J.H, Waite, C. Vines'. 1993. ISBN: 1-55899-187-5 Volume 293-Solid State Ionics III, G-A. Nazri, I-NI. Tarascon, NI. Armand, 1993. ISBN: 1-55899-188-3 Volume 294-Scientific Basis for Nuclear Waste Management XVI. C.G. Interrante. R.T. Pabalan, 1993. ISBN: 1-55899-189-1 Volume 295-Atomic-Scale Imaging of Surfaces and Interfaces. D.K. Biegelson. D.S.Y. Tong, D.J. Smith, 1993. ISBN: 1-55890-190-5 Volume 296-Structure and Properties of Energetic Materials, R.W. Armstrong. J.J. Gilman, 1993, ISBN: 1-55899-191-3 Prior MareriaLs Researdi .Socicei .svmipowu~n Prioceedgtm:% available hi conztamm!z Maiuitwl% Rcwarih Socicgi
PART I
Structure and Stability
3
MOLECULAR STRUCTURE AND PERFORMANCE OF HIGH EXPLOSIVES JAMES R. STINE, Explosives Technology, Group M-1, MS C920, Los Alamos National Laboratory, Los Alamos, NM 87545.
ABSTRACT Empirical methods have been developed to predict density and heat of formation of proposed high explosives. These methods are parameterized in terms of molecular constituents consisting of atoms in particular bonding environments. These methods, along with the atomic composition of the molecule, are then used in an empirically based method to predict the performance of the explosive. Together, these methods form a unified mechanism of relating molecular structure to explosive performance. Indeed, this effort, along with the synthesis effort at Los Alamos, have led to the identification of a new class of high-nitrogen molecules that may prove to be high performance explosives. INTRODUCTION The goal of the high explosives synthesis effort at Los Alamos has been to synthesize an organic high explosive that has the performance of HMX (one of our best performing explosives in general use) but at the same time has the insensitivity of TATB (our most insensitive high explosive). Although numerous efforts at Los Alamos, and indeed throughout the explosives community in general, have tried to achieve this goal, few new explosives have ever made been considered for weapon systems. If we take a glance at the synthesis history of the explosives of military interest1, we immediately see that most all of them were first synthesized in the late 1800s. The fact that synthesis efforts since this time, and particularly during the past 40 years, have not been able to realize the goal given above, was one of the reasons for the development of the methods described here. Table I. History of the Synthesis of Explosives of Military Interest Nitroguanidine Tetryl TNT TATB PETN RDX
1877 1879 1880 1888 1894 1899
One common element of nearly all of the synthesis efforts du-' he last fhis has resu,.ed in the C,.: synthesis of many polynitroaromatics, with TATB and TNT as notable examples. But, are these explosives qualitatively different from one another? To help answer this question, we developed simple empirical methods to help indicate how each molecular constituent affected an explosive's performance, In addition 40 years has been the nitration of a carbon skel. -
Mat. Res. Soc. Symp Proc. Vol. 296
1993 Materials Research Society
to being developed as predictive tools, the primary goal of these methods is to help guide the synthesis effort by providing insight as to what constituents were beneficial to high performance and which ones were not. These methods would then complement the computer methods developed over the years in predicting properties of proposed explosives. The empirical methods developed were concerned with density and heat of formation of the proposed explosive. Certainly, in the past, these factors have been recognized as playing an important part in the performance of an explosive. However, many synthesis efforts have had as their primary goal the synthesis of high density organic molecules instead of high performance molecules. The thought here is that the three factors of density, heat of formation, and atomic composition must all be considered when relating molecular structure to performance. Of the three factors, atomic composition has received the least emphasis. In the sections below, we discuss the three empirical methods as related to the factors given above, and then relate them to performance. DENSITY One method for predicting density was developed by Stine2 in 1981. This method assumed that the volume of a molecule in the unit cell of a crystal (which in this case includes some of the void volume) is a sum of the volumes of the molecular constituents. In this case, the molecular constituent is the atom in its particular bonding environment. Thus, for example, one constituent would be a carbon atom with four single bonds, designated C(1,1,1,1), or if two of the bonds were in a ring system designated C(1,1,-1,-1). Another constituent being a carbon with a double bond and two single bonds, C(2,1,1). Table II lists all of the different constituents possible for carbon, hydrogen, nitrogen, oxygen molecules, where 1, 2, or, 3 represent a single, double, or triple bond, and -5 designates an aromatic bond. A negative value indicates that the bond is part of a ring system. Values for the constituent volumes were derived from over 2000 organic molecules with known crystal structures. A histogram of the errors between the observed and calculated densities for these 2000 compounds indicates that the calculated value is within ,-4% of the observed value. Of course only a few of the 2000 compounds were explosives, but when this method was applied to over 300 organic explosives synthesized at Los Alamos, a similar standard deviation was obtained. Of interest here are the contributions of each constituent to the density, which are also listed in Table II. It can be seen that almost all of the carboncontaining constituents contribute a relatively low value to the density, except for C(-1,-I,-1,-1) and C(1,-1,-1,-I) whose bonds are involved in multiple ring systems. That is, to be high density, the carbons must be a part of a cage-type or spiro-type structure. However, almost all of the nitrogen and oxygen atoms contribute a high value to the density. Thus for a high density compound one would want to eliminate the carbon and hydrogen atoms in favor of nitrogen and oxygen atoms.
5
Table II. Constituent Volumes for the Prediction of Density Definition H(1) bonded to a Carbon H(1) bonded to an aromatic Carbon H(1) bonded to a Nitrogen H(1) bonded to an Oxygen C(1,1,1,1) C(1,1,-1,-1) C(1,-1,-1,-1) C(-1,-1,-1,-1) C(2,1,1) C(1,-1,-2) C(2,-1,-1) C(-1,-1,-2) C(1,-5,-5) C(-1,-5,-5) C(-5,-5,-5) C(3,1) or C(2,2) N(2,2,1) N(1,1,1) N(1,-1,-1) N(-1,-1,-1) N(-5,-5) N(2,1) N(-1,-2) N(3) O(1,1) 0(-1,-i) 0(2)
Volume
Density
A3
g/cm3
5.981 7.499 5.199 0.366 13.390 11.709 9.755 9.673 14.565 13.288 12.654 10.410 12.094 10.618 10.370 16.579 10.368 9.234 9.798 8.759 12.268 14.488 11.941 15.599 12.178 12.172 12.754
0.278 0.221 0.319 4.536 1.486 1.702 2.042 2.060 1.368 1.499 1.575 1.914 1.647 1.876 1.921 1.202 2.242 2.517 2.372 2.654 1.895 1.605 1.947 1.490 2.181 2.183 2.063
HEAT OF FORMATION A method similar to that developed for density was developed for predicting the heat of fcrmation of a proposed explosive 3 . Here, however, it is important to specify the type of atom bonded to the atom of concern. Thus, for example, a carbon bonded to two other carbons, a hydrogen, and a nitrogen would be designated by C(Ci, C1, H1, N1). Also of importance to the heat of formation is the contribution of ring strain. Here we only consider ring strain in rings consisting of three, four, or five atoms. Values for the constituent heats of formation were derived from measured heats of formation of over 1100 organic compounds 4 . As opposed to similar existing methods for estimating the heat of formation of a molecule, this method has a much smaller set of constituents, and the constituent heat of formation is based on a larger set of empirical data. A histogram of the errors between the observed and calculated values indicates a standard deviation of about 10 kcal/mole. Here aga, --. method indicates which molecular constituents contribute a pusitive amount to the overall heat of formation and which contribute a negative amount. It now becomes evident, that a particular molecular constituent might contribute in a positive way to the density, but a negative amount to the heat of formation.
6
ATOMIC COMPOSITION One aspect of performance that has not received as much consideration as density and heat of formation is the role of atomic composition. Our first consideration was to determine in what regions of atomic composition space did most existing explosives lie. We know, for example, that RDX (C3 H 6 N6 0 6 ) and HMX (C4 H 8 N 8 0 8 ) have the same performance if they are pressed to the same density. Thus, the absolute number of each atom making up the molecule is not of importance, but rather their relative amounts. Hence, we can arbitrarily 'normalize' the molecular formula, CaHbNcOd, to CAHBNCOD such that A+B+C+D=I. That is A=a/(a+b+c+d), etc. Thus RDX and HMX would have the same relative formula. Now we wish to represent ui~e relative composition of any organic (carbon, hydrogen, nitrogen, oxygen) molecule graphically. Just as an equilateral triangle can be used to represent the fractional composition for a three component system, a tetrahedron can be used to represent the relative fractions for a four component system. That is, a tetrahedron has the property that the sun. of the four distances from an internal point to each of the four sides is a constant. Thus, the relative composition of any organic molecule can be represented by a point inside a tetrahedron whose corners represent carbon, hydrogen, nitrogen, and oxygen. This tetrahedron is shown in Figure 1.
N
'0
C
H
Figure 1. Composition tetrahedron for representing the relative amounts of carbon, hydrogen, nitrogen and oxygen in any organic mole, . The ideal products in a detonation are water, carbon dioxide, and nitrogen. These molecules are represented by points on the line connecting hydrogen and oxygen, the line connecting carbon and oxygen, and t*Ae apex,
7
respectively. These three points then define an 'oxygen balance plane,' in which any point lying in this plane is said to have sufficient oxygen to convert the carbon to CO 2 and the hydrogen to H 2 0. Over 300 explosives molecules were found in the literature that had been synthesized over the past 40 years. The normalized formulas for each of these explosives is plotted in Figure 2. Also seen in this figure is the oxygen balance plane. It is readily seen that most all of these explosives lie within a cluster that is characterized by high carbon - low oxygen content. Included in this cluster are explosives such as TATB, TNT, DATB, HNS, TNB, etc. These are basically low performing explosives because most of the carbon ends up as solid carbon in the form of soot. One molecule somewhat outside of this cluster is HMX, one of the best performing explosives. This indicates that perhaps molecules with as much as or greater nitrogen content might be a promising region for high performing explosives.
LAX-112
J4
Oxygen '
carbor
HVarone-
igure 2. Composition tetrahedron showing the location of over 300 known explosives.
8
One molecule that consists of just nitrogen atoms is octaazacubane, N8 , (Figure 3) and is of interest to demonstrate the performance expected for a pure nitrogen molecule 5 . The predicted heat of formation for this molecule using ab initio methods is 530 kcal, and the predicted density using the above mentioned density prediction method, is 2.65 g/cm 3 . These values yield a predicted detonation velocity (using the TIGER code with the BKW equation of state) of over 15 km/s and a CJ-pressure of 157.2 GPa. In fact, even if the real density differed substantially from that predicted and was found to be only 1.90 g/cm 3 , and the real heat of formation found to be only 200 kcal/mole, the predicted detonation velocity would be 10.4 km/s and the CJ-pressure would be 50.1 GPa. These values are still substantially greater than those for HMX, namely 9.14 km/s and 40.5 GPa, respectively.
N
N N NI N
N NI N
Figure 3. Molecular structure of octaazacubane. PERFORMANCE The density, heat of formation, and atomic composition can now be integrated into an empirical method for predicting the performance of a proposed explosive. The approach taken here is an extension of a method first developed by Urizar 6 at Los Alamos in 1947. In his method, he assumed that the detonation velocity of a mixture of explosives is the sum of the detonation velocities of the constituents weighted by their respective volume fractions. He also allowed for the contribution of voids to the overall detonation velocity by assigning a 'characteristic velocity' and including its contribution to the sum. Thus, for a mixture of n components we have, D=XviDi
i=1.n
(1)
where D is the detonation velocity. Here we extended his method 7 to pure compounds by making the additional assumption that the detonation velocity of a pure compound and that of a mixture are identical if the densities, heats of formation, and atomic compositions are the same. Hence these properties of the pure compound could be simulated by an appropriate mixture of explosives with known densities. I- : of formation, and molecular formulas. Thus for a pure .-xj.o.ive with the kaolecular formula CaHbNcOd, we would need a basis set of five explosives, and the addition of voids to simulate the six parameters of carbon, hydrogen, nitrogen, and oxygen content, density, and heat of formation. Equation 1 then becomes,
9
(2)
D =Do + p(aa + i3b +It+ 8d + hAHf) / M,
where Do is the characteristic velocity of a void, p is the density in g/cm 3 , AHf is the heat of formation in kcal/mole, and M is the molecular weight o.f the pure compound. Do, a, j3, y, 8, and h are constants whose values were obtained by a least-squares analysis to detonation velocity, density, and heat of formation data for 22 pure explosives. This analysis yielded, a=
-13.85
8=
=
3.95
h=
1=
37.74
Do =
68.11 0.6917
3.69
The calculated and observed values are plotted in Figure 4 for these 22 explosives. 9.5
9.0.
E i
6.0 of0
7.5
7.0
6.5 6.5
7.0
7.5
8.0
8.5
9.0
9.5
D(obs) (km/s) Figure 4. Plot of the detonation velocities of 22 p-re explosive,: calculated using Equation 2 as a functioih o. 'he observed detonation velocities. The straight line is the ideal case where the calculated value is equal to the observed value.
10
It is clear from the above values that carbon is detrimental to a high detonation velocity because a is negative, but nitrogen and oxygen make a positive contribution because P, X,and 8 are all positive. Here again, we are led to the conclusion that high nitrogen explosives should give good performance. These data indicate that perhaps high nitrogen molecules would be high performance explosives. One compound, first synthesized at Los Alamos 8 in 1986, is a high nitrogen molecule that does not contain any nitro groups. The structure of this molecule is shown in Figure 5.
NH2
NH2 Figure 5. Molecular structure of the high nitrogen explosive, TZX This explosive was predicted to have a detonation velocity about the same as that of HMX. Enough material was then synthesized to perform sensitivity and performance tests. It was found to have an impact sensitivity about like that of TNT, which is a relatively insensitive high explosive. Although it is not as insensitive as TATB, it is one of the few known explosives that has both a relatively good performance and good sensitivity. SMALL-SCALE TESTING TZX is just one of the first high nitrogen molecule to be synthesized and its performance properties are still being tested. As was mentioned at the beginning, one must consider all factors when evaluating what molecular constituents are important contributors to performance. Although we have demonstrated that high nitrogen content is an important contributor to performance, so are density and heat of formation, and it must not be over emphasized. Indeed, these factors must be considered simultaneously when evaluating their contribution related to a particular molecule. The results now are very encouraging that perhaps a single molecule can be both an insensitive and a high performing explosive. However, further tests must be performed on new molecules that do not lie in the cluster forme' the majority of existing explosives. This presents a problem, in that many of the standard sensitivity and performance tests require large amounts of material, usually kilograms at the very least. It is usually a Herculean task tbr the bench chemist to produce these quantities of material, and hence most explosives
11
synthesized in the past simply did not have any sensitivity of performance tests past those required for handliitg small quantities of material. 8.5
PBX9407 (RDX/FPC461) 8.4
8.3-
E
S 8.2 8.1
C
8.0
.g
7.9
0
D 2.2708 +3.5193 (rho)
7.87.7'
7.6
1.50
1.55
1.60
1.65
1.70
1.75
1.80
Density (g/cc) Figure 6. Detonation velocity as a function of density produced in a single PolyRho shot. The rate stick consisted of 1/2 inch diameter pellets. To help bridge the gap between the bench chemist and the firing site engineer, various small-scale tests are being developed at Los Alamos to measure such things as detonation velocity, failure diameter, reaction zone thickness, and sensitivity to shock. These tests require a total of 50-100g of material - a quantity that is able to be synthesized in a laboratory. One such test, requiring about 25-30g of material is the PolyRho test. This is a performance test for measuring the detonation velocity over a range of densities. Pellets, 1/2 inch in diameter and 1/2 inch in length are pressed to different densities. A rate stick is assembled from these pellets where the pellets are placed in the rate stick according to their density. The fix-st pellet is next to the detonator and is the least dense and the last pellet is the most dense. Foil switches are placed between the pellets and an oscilloscope is used to record the arrival times of the detonation wave at each of these switches. From this data and the heights of the individual pellets one can calculate the detonation
12
velocity over each of the pellets and hence obtain detonation velocity as a function of density. One such plot is shown in Figure 6. This test along with the other existing and proposed small-scale performance and sensitivity tests form a basis for obtaining valuable screening information to help aid in designing new explosives and selecting existing explosives for particular programmatic goals. CONCLUSIONS Efforts related to the development of simple empirical predictive methods have interacted with the synthesis effort at Los Alamos to identify a new class of molecules that may prove useful as high-performing insensitive explosives. One member of this new class has been synthesized and tested. However, high nitrogen content is just one of the factors that influence performance and, like density and heat of formation, should not be sole consideration. Indeed, it is imperative that all of the factors be considered simultaneously because there are very few molecular constituents that contribute in a positive way to each of these factors. The interaction between theory and synthesis has led to the realization that perhaps the elusive explosive we have been looking for may have an atomic composition and molecular structure quite different than that of most all known explosives. We now have some guidelines as to what molecular geometries to look for. REFERENCES 1. Encyclonedia of Exnlosives and Related Items, edited by B. T. Fedoroff (Picatinny Arsenal, Dover, 1960). 2. J. R. Stine, Prediction of Crystal Densities of Organic Explosives by Group Additiyiky, Los Alamos National Laboratory Report, LA-8920 (1981). 3. J. R. Stine and J. F. Kramer, in 26th JANNAF Combustion Meeting Proc., Vol. II, pp 53-56, CPIA Publication 529 (1989). 4. J. B. Pedley, R. D. Naylor, and S. P. Kirby, Thermochemical Data of Organic Comp~uns, 2nd ed. (Chapman and Hall, London, 1986). 5. R. Engelke and J. R. Stine, J. Phys. Chem., 94, 5689 (1990). 6. B. M. Dobratz and P. C. Crawford, LLNL Explosives Handbook - Properties of Chemical Explosives and Explosive Simulants, Lawrence Livermore National Laboratory UCRL-52997 (1985). 7. J. R. Stine, J. Energetic Materials, 8, 41 (1990). 8. M. D. Coburn, (private communication).
13
RECENT ADVANCES IN THE THERMAL DECOMPOSITION OF CYCLIC NITRAMINES
RICHARD BEHRENS, JR.* AND SURYANARAYANA BULUSU** *Sandia National Laboratories, Combustion Research Facility, Livermore, CA 94551 ** Energetic Materials Division, U.S. Army, ARDEC, Dover, NJ 07801-5001
ABSTRACT The effects of physical properties and molecular conformation on the thermal decomposition kinetics of several cyclic nitramines are examined and compared to the decomposition of RDX. The compounds used in the study are: octahydro-1,3,5,7-tetranitro1,3,5,7-tetrazocine (HMX), hexahydro-l-nitroso-3,5-dinitro-s-triazine (ONDNTA), 1,3,5trinitro- 1,3,5-triazacycloheptane (TNCHP), and 2-oxo- 1,3,5-trinitro- 1,3,5-triazacyclohexane (K6). The decomposition pathways of HMX in the liquid phase are similar to the four parallel decomposition pathways that control the decomposition of RDX in the liquid phase. The products formed during the thermal decomposition of ONDNTA arise from multiple reaction pathways. The identities and temporal behaviors of the ONDNTA decomposition products are discussed. TNCHP is thermally stable in the liquid phase. The decomposition products from TNCHP are formed via multiple reaction pathways. One decomposition pathway for TNCHP is through its mononitroso intermediate. TNCHP does not form a stable product that is analogous to oxy-s-triazine (OST) formed in RDX or the smaller ring fragments formed in the liquid-phase decomposition of HMX. K6 is less thermally stable and the decomposition mechanism is much simpler than that of RDX, HMX and TNCHP. The thermal decomposition of K6 occurs between 150 and 180 0C. The products formed during the decomposition of K6 are mainly CH 20 and N20 with minor amounts or HCN, CO, NO, and NO 2.
INTRODUCTION The cyclic nitramines hexahydro-1,3,5-trinitro-s-triazine RDX (I) and octahydro-1,3,5,7tetranitro-1,3,5,7-tetrazocine HMX (II) N02
0 2N,
N
0 2N'N
NNN. N, N0
(I)
NO 2
2
0 2N'
N
NO
2
(II)
are energetic ingredients that are used in various propellants and explosives. Understanding the complex physicochemical processes that underlie the combustion of these materials can lead to methods for modifying propellant and explosive formulations in order to obtain better ignition, combustion, or sensitivity properties. The motivation for understanding the thermal decompositior -r'-esses of these materials is threefold. First, in solid-propellant combustion, thermal de,.-:.r.pusition processes that occur in the condensed phase determine both the amount of heat released on the surface of a burning propellant and the identity and rates ot production of the lower molecular weight species that are the reactants in the gas-phase flame. These processes control the bum rates of solid propellants. Second, in both propellants and explosives it is important to understand the mechanisms that control the stability of these materials when they are subjected to elevated temperatures, electrostatic discharge, impact or shock. The response of energetic materials in munitions to these stimuli determine their Mat. Res. Soc. Symp. Proc. Vol. 296. '1993 Materials Research Society
14
degree of safety when subjected to abnormal environments such as fire. Third, an understanding of the molecular processes that control the response of energetic materials to these various stimuli will provide insight into the molecula.'properties that control the relative stability of these materials. This, in turn, will provide guidance for the synthesis of new, more stable, energetic materials. Thus, the goal of our work is to understand how the molecular conformation, physical properties and molecular structure affect the thermal decomposition processes in energetic materials. Since RDX and HMX are two cyclic nitramines used extensively in explosive and propellant formulations, our initial work 1 -4 has focused on understanding the decomposition mechanisms of these two materials in the solid and liquid phases. To extend our knowledge of cyclic nitramine decomposition, we are currently studying the decomposition of an intermediate formed during the decomposition of RDX and several other cyclic nitramines with molecular conformations and physical properties different from RDX and HMX. In this paper we present the following: a summary of the thermal decomposition pathways for RDX in the liquid and solid phases; the results from our studies on the thermal decomposition of liquid-phase HMX, hexahydro-l-nitroso-3,5-dinitro-s-triazine (ONDNTA) (i11), 1,3,5trinitro-l.3,5-triazacycloheptane (TNCHP) (IV), and 2-oxo-1,3,5-trinitro-1,3,5triazacyclohexane (K6) (V); a comparison of these results with those of RDX. NO
ON 02N
~`ý (1I1)
NO,
N02
II
r )N NO 2
I N O2 N 02
N Ci1
(IV)
NN 2
2
O N,
O*.C'
NN
02 WN N-ýýN ~N0
2
(V)
EXPERIMENTAL Instrument description The simultaneous thermogravimetric modulated beam mass spectrometry (STMBMS) apparatus is used to conduct the thermal decomposition experiments. The apparatus and the basic data analysis procedure have been described previously. 5. 6 This instrument allows the concentration and rate of formation of each gas phase species in a reaction cell to be measured as a function of time by correlating the ion signals at different m/z values measured with a mass spectrometer with the force measured by a microbalance at any instant. In the experimental procedure, a small sample (-10 mg) is placed in an alumina reaction cell that is then mounted on a thermocouple probe that is seated in a microbalance. The reaction cell is enclosed in a high vacuum environment ( < 10-11 torr) and is radiatively heated by a bifilarwound tungsten wire on an alumina tube. The molecules from the gaseous mixture in the reaction cell exit through a small diameter (0.0025 cm in these experiments) orifice in the cap of the reaction cell, traverse two beam-defining orifices before entering the electronbombardment ionizer of the mass spectrometer where the ions are created by Collisions of 20 eV electrons with the different molecules in the gas flow. The background pressures in the vacuum chambers are sufficiently low to eliminate significant scattering between molecules from the reaction cell and background molecules in the vacuum chambers. The different nVzvalue ions are selected with a quadrupole mass filter and counted with an ion counter. The gas flow is modulated with a chopping wheel and only the modulated ion signal is recorded. The containment time of gas in the reaction cell is a function of the orifice area, the free volume within the reaction cell, and the characteristics of the flow of gas through the orifice. For the reaction cell used in the ey',n'nents, the time constant for exhausting gas from the cell is small (-3 2 cec) compareu :t 1,e duration of the experiments ( >-I0(W sec). Note that the containment u-ne of gas within the reaction cell is short once the gas molecules are in the free volume of the cell, but it may be much longer if the gas is trapped in the condensed-phase of the material within the cell.. For reactions in the liquid phase, such as those with RDX, the lighter molecular weight gases (i.e., N20) will be released from the liquid rapidly whereas for reactions that occur in the solid phase even these lower molecular weight gaseous products may be trapped for longer periods of time.
14
degree of safety when subjected to abnormal environments such as fire. Third, an understanding of the molecular processes that control the response of energetic materials to these various stimuli will provide insight into the molecular properties that control the relative stability of these materials. This, in turn, will provide guidance for the synthesis of new, more stable, energetic materials. Thus, the goal of our work is to understand how the molecular conformation, physical properties and molecular structure affect the thermal decomposition processes in energetic materials. Since RDX and HMX are two cyclic nitramines used extensively in explosive and propellant formulations, our initial work'- 4 has focused on understanding the decomposition mechanisms of these two materials in the solid and liquid phases. To extend our knowledge of cyclic nitramine decomposition, we are currently studying the decomposition of an intermediate formed during the decomposition of RDX and several other cyclic nitramines with molecular conformations and physical properties different from RDX and HMX. In this paper we present the following. a summary of the thermal decomposition pathways for RDX in the liquid and solid phases; the results from our studies on the thermal decomposition of liquid-phase HMX, hexahydro- 1-nitroso-3,5-dinitro-s-triazine (ONDNTA) (111), 1,3,5trinitro-1,3,5-triazacycloheptane (TNCHP) (IV), and 2-oxo-1,3,5-trinitro-1,3,5triazacyclohexane (K6) (V); a comparison of these results with those of RDX. NO I
02 N
O NN N NN2 N402 (III)
NO I 2
N O2N >-• N Ci12 (I V)
NO, I '
NNCNO NO
2
0 2N
NO
N, N402
(V)
EXPERIMENTAL Instrument description The simultaneous thermogravimetric modulated beam mass spectrometry (STMBMS) apparatus is used to conduct the thermal decomposition experiments. The apparatus and the basic data analysis procedure have been described previously. 5 ,6 This instrument allows the concentration and rate of formation of each gas phase species in a reaction cell to be measured as a function of time by correlating the ion signals at different m/z values measured with a mass spectrometer with the force measured by a microbalance at any instant. In the experimental procedure, a small sample (-10 mg) is placed in an alumina reaction cell that is then mounted on a thermocouple probe that is seated in a microbalance. The reaction cell is enclosed in a high vacuum environment ( < 10-11 torr) and is radiativeiv heated bv a bifilarý wound tungsten wire on an alumina tube. The molecules from the gaseous mixture in the reaction cell exit through a small diameter (0.0025 cm in these experiments) orifice in the cap of the reaction cell, traverse two beam-defining orifices before entering the electronoombardment ionizer of the mass spectrometer where the ions are created by collisions of 20 eV electrons with the different molecules in the gas flow The background pressures in the vacuum chambers are sufficiently low to eliminate significant scattering between molecules from the reacuoni cell and background molecules in the vacuum chamhers. The difterent n/zvalue ions are selected with a quadrupole mass filter and counted with an ion counter The gas flow is modulated with a chopping wheel and only the modulated ion signal is recorded. The containment time of gas in the reaction cell is a function of the orifice area, the free volume within the reaction cell, and the characteristics of the flow of gas through the orifice For the reaction cell used in the ey',nnents, the time constant for exhausting gas from the cell is small (-3 2 efc) comparet, .,' •iie duration of the experiments ( >-~1X0) sec). Note that the containment utne of gas within the reaction cell is short once the gas molecules are in the free volume of the cell, but it may be much longer if the gas is trapped in the condensed-phase of the material within the cell. For reactions in the liquid phase, such as those with RDX, the lighter molecular weight gases (ie., N20) will be released from the liquid rapidly whereas for reactions that occur in the solid phase even these lower molecular weight gaseous products may be trapped for longer periods of time.
15
Sample preparation. The cyclic nitramines used in the experiments were prepared according to previously published methods for ONDNTA, 7 TNCHP, 8 and K6.9 The K6 sample was obtained from P. Pagoria of LLNL. The samples were characterized by NMR and IX measurements. Data analysis The data analysis procedures used for identifying the pyrolysis products and determining their rates of formation have been described previously.5.6.I0 For the qualitative comparisons of the differences in the decomposition behavior between RDX and HMX, TNCHP, and K6 only the temporal behaviors of the ion signals associated with the various decomposition products, and not the gas formation rates for each product, are presented in this paper. RESULTS AND DISCUSSION Our previous work has examined the decomposition of HMX in the solid phasel, 2 and RDX in both the solid and liquid phases. 3,4 For RDX decomposition in the liquid phase, we have found that it decomposes by the following four reaction pathways: OST +
H20
NO 2
H2CN
+
ONDNTA
N20
+
+
NO +
+
NO 2
2 N20
m N20 +
-
CH 20
+
NO 2
+ 2 CH 20
CH 2 G
+
(P1)
other
+
NH2CHO
(P2)
(P3)
(P4).
Reaction pathway P1 is first order in RDX and accounts for approximately 30% of the total decomposition. Using 2 H, 13C, 15 N, and 180 isotopic analogues of RDX in isotopic scrambling and deuterium kinetic isotope experiments (DKIE). we have shown that oxy-striazine (OST) is formed directly from RDX and hydrogen atom transfer is involved in the rate determining step. The other products formed in this reaction path are NO, H2 0, and NO 2 . This reaction pathway involves the elimination of HONO, leaving the RDX ring intact.
0
OH
NO I
NO
I OST structures
(VI)
NO (VII)
Reaction pathway P2 is also first order in RDX and accounts for approximateN - of the total decomposition. In this pathway the C-N bonds of the i,DA .noecule eventually rupture, leading to the formation of N20 and CH20. However, this does not necessarily imply that C-N bond rupture is the first step in this thermal decomposition pathway, since N-N bond rupture followed by subsequent bond breaking of the resulting radicai is also consistent with our results.
I'
16
Reaction pathway P3 involves the decomposition of RDX via a mononitroso-RDX (ONDNTA) intermediate (VI). Decomposition via this pathway accounts for approximately 30% of the total decomposition. CH2 0 and N20 are major products formed via the ONDNTA intermediate during the decomposition of RDX. Reaction pathway P4 involves the autocatalytic decomposition of RDX and accounts for approximately 30% of the total RDX decomposition. The main decomposition products formed via this channel are also CH2 0 and N20. Although the catalyst has not been identified, possible candidates for the catalyst include several amides (i.e., formamide and Nmethylformamide) and the polyamide residue that forms during the decomposition of RDX. The details of reaction pathway P4 are the least well characterized of the four pathways. Summary of RDX Results To compare the decomposition pathways of the other cyclic nitramines with those of RDX, we first summarize the RDX results. The decomposition pathways of RDX were determined from both the extent of isotope crossover and deuterium kinetic isotope effect (DKIE) in experiments with isotopically labeled analogues of RDX and the temporal behaviors of the gas formation rates of the decomposition products as shown in Figure I (additional results may be found in References 3 and 4). For all of the decomposition products. the gas formation rates rise rapidly as the sample melts at 200°C. For OST, the rate of gas formation rises rapidly as the sample melts and gradually decreases as the RDX sample is depleted. This is characteristic of reaction pathway P1. For ONDNTA, the gas formation rate gradually increases as the sample is depleted. This behavior is due to the increasing vapor pressure of ONDNTA in the reaction cell which in turn is due to the increasing mole fraction of ONDNTA in the sample as the decomposition progresses. The temporal behavioi of ONDNTA characterizes reaction pathway P3. For Nmethylformamide (NMFA), the gas formation rate also gradually increases as the sample is depleted. This bel'avior is also characteristic of the other formamides formed during the
5( 4C
51 . .
. ..
0
8ONDNTA NMF -1*--
6-
I0-I
4
(1)
O 3C. o
2C
80 20
E
CH 02
~ 250_ 1 U)
LL A.
195 200 205 210 215
0
20 0 10F
2 A
2 ssA
195 200 205 210 215 195 200 205 210 215
Temperature ( °C)
Figure 1. Contribuuons of the four primary decomposition pathways to the various products formed during the thermal decomposition of pure RDX. The bold line i-) in all of the graphs represents the total contribution from all of the reaction channels, The bold line (-) in OST represents the . ... ,..ution by reaction pathway P1. The thin dashed (- - ) lines shown in N20. CH20. NO?. and Na,2CHO represent the contributions from reaction pathway P2. The bold dashed liaies
.
-- )
represent the contribution from the ONDNTA decomposition pathway P3. The thin solid lines
(-)
that peak near the highest temperature correspond to the contribution from the catalytic
decomposition pathway P4. The calculated rate of formation of C1t20 is equivalent to the rate of formation of N20. The difference between the calculated and measured rates of formation of CH20 is due to its reaction %iLhin the sample cell.
17
decomposition. The rates of gas formation shown for N 20, CH 2 0 and NO 2 have temporal behaviors that are due to contributions from three of the RDX decomposition pathways. The contribution that increases rapidly as the sample melts and falls off gradually as the sample is depleted arises from reaction pathway P2. The contribution that peaks midway during the decomposition (bold dashed line in Fig. 1) arises from the decomposition of the ONDNTA intermediat, in reaction pathway P3. Finally, the contribution that increases gradually during the decomposition and peaks just prior to complete depletion of the sample is characteristic of the catalytic reaction pathway P4. Liquid-Phase Decomposition of HMX Comparison of the liquid-phase decomposition of HMX to that of RDX will show whether decomposition pathways similar to RDX control the decomposition of HMX or whether the higher melting point of HMX and its decomposition in the solid phase prior to melting alter its decomposition mechanism. The liqr;d-phase decomposition products from HMX that are observed in our experiments include: H 20, HCN, CO, CH 20, NO, N 20, NO 2 , formamide, NMFA, N,N-dimethylformamide, and ONTNTA (VII). In addition, we observe ion signals at m/z values of 70 and 97. Experiments with 2 H, 13C, and 15 N isotopically labeled HMX analogues have shown that the ion signals at these two m/z values correspond to ions with formulas of C 2 N2H2O (70) and C 3N3H3O (97). For RDX, the ion signals at m/z values of 70 and 97 both arise from the OST decomposition product. However, for HMX, differences in the relative intensities of these two ions, in addition to differences in their temporal behaviors in the HMX experiments, show that they arise from two different decomposition products These ion signals clearly arise from thermal decomposition products that are similar to the OST formed during the decomposition of RDX. However, without time-of-flight (TOF) velocity-spectra measurements of these ion signals, it is not possible to determine whether the observed ion signals are molecular ions, and thus have the same formula as the thermal decomposition products, or whether they are daughter ions formed from a decomposition product with a higher molecular weight. In either case, the ion signals at m/z values of 70 and 97 are associated with fragments from the HMX ring formed in a manner similar to reaction pathway P1 for the RDX decomposition. The results shown for the decomposition of HMX in Fig. 2 are consistent with the four decomposition pathways found for the decomposition of RDX. A reaction pathway similar to reaction pathway P1 for RDX produces the HMX-ring fragments that are charactenrzed by the ion signals at m/z values of 70 and 97 shown in Panel b of Fig. 2. These two ion signals first appear when the HMX sample liquefies at approximately 276°C and their signal strength decreases as the HMX sample is depleted. This behavior is similar to that observed for OST formed in the decompositior, of RDX The temporal behavior if the ion signals formed from the monontroso HMX analogue. ONTNTA. (shown in Panel c of Fig. 2) is similar to the temporal behavior of ONDNTA observed in the liquid-phase RDX decomposition Note the increase in the amount of ONTNTA associated with the vertical arrow on the right in Fig. 2. This behavior is similar to that observed for ONDNTA during the decomposition of RDX . One significant difference I '-en the behavior of the monomtroso product in the decomposition of IIMX compared wit. .-. decomposition of RDX is that a much largeer amount of ONTNTA is released from the IIMX sample before it liquefies. As can be seen from Fig. 2. the size of the ]on signal associated with the ONTNTA product does not sho, aisignificant increase as the sample liquefies. This indicates that the decomposition of I lMX to its mononitroso analogue is ,a maJor decomposition pathway in the solid-phasc This, i, similar to the results found or the decomposition of RDX in the solid phase except. tatat ,t the higher temperatures associated with the decomposition of I IMX. the reaction rate tor tie tcmnaton of ONTNTA is greater and a larger fraction of the HtMX sample has decomposed via a reaction pathway similar to pathway P3 prior .o the liquefaction of the ItMX sample The temporal beha,' - - f the ion signals associated with the CIIO0 and N2 0 formed t,',- dccomposi,. - of IIMX after its liquefaction have the same broad type of peaks that were observed for these products in the decomposition of RDX. Both of the ion signals associated with these products show a rapid increase as tile IIMX liquefies and an initial peal, that is correlated with the ion signals associated with the products formed trom the ring of the IIMX molecule. The CH 2 0 and N 2 0 formed later in the decomposition appear to be correlated with the ONTNTA product and also display a temporal behavior that is characteristic of an autocatalvyic decomposition channel similar to patnwav P4 for RDX
18
so L 7ST
0
2
20 C
o-
ýMFA
10(
270
~27427 Temperature (°C)
Figure 2. Ion signals associated with various thermal decomposition products formed during the decomposition of HMX as the sample melts. The sample melts at 276 0C. The signal associated with thermal decomposition fragments formed from the ring (b) only appear in significant quantities as the sample melts. Other products associated with this pathway are indicated by the vertical arrow. on the left. After the sample melts a second set of products that peak later in the decomposition is observed as indicated by the arrow. on the right. These products ame associated with the amides, such as the Nmethylformamide. This behavior is similar to that observed for RDX decomposition in the liquid phase. However, in contrast to the decomposition of RDX, substantial amount of thermal decomposition occurs prior to melting of the sample. Note the relatively large amount of the mononitroso analogue of HMX (ONTNTA) observed prior to meting. The heating rate is 2*C/min. The initial increase in the CH 2 0 and N20 signals after the HMX sample liquefies is also similar to that observed in the decomposition of RDX and associated with decomposition via reaction pathway P2. Fizm the relative s.,es of the ion signals associated with the CH20 and N20 products compared to those associate:.. with the HMY ring fragment ion signals at m/z values of 70 and 97 this would suggest that the relative amount of HMX that decomposes by a pathway similar to P2 compared to pathway P1 is greater for HMX than for RDX. In light of the fact that the decomposition of HMX occurs at a temperature about 70'C greater than RDX, the behavior of CH20 and N20 tends to suggest that reaction channel P2 may become more dominant than reaction pathway P1 at higher temperatures. However, it is also possible that the increase of the CH 20 and N20 signals after the HMX sample liquefies is due to an increase in the decomposition rate of ONTNTA, formed in the solid-phase decomposition. Without further quantification of the HMX results, it is rot possible at this time to determine
exact relative decomposition rates of the various HMX decomposition pathways. Relative Stabilities of RDX. HMX. ONDNTA. TNCHP. and K6
The relative rates of formation of the major thermal decomposition products formed from RDX, HMX, ONDNTA, TNCHP athd I>ý, ace shown as a function of temperature in Figure 3. Both RDX and HMX timompose slowly in the solid phase and exhibit a rapid increase in the decomposition rates upon melting. In comparison to RDX and HMX, both ONDNTA and TNCHP do not undergo the same rapid increase in the decomposition rate upon melting as illustrated in Fig. 3. For ONDNTA, this may be due a slower decomposition rate at the temperature associated with its lower melting point of 168*C. As ONDNTA melts there is already evidence of decomposition. The entire ONDNTA sample has decomposed below
19
200 0C (below the melting poin: of RDX). TNCHP, on the other hand, is quite stable in the liquid phase. TNCHP melts at -170*C but it does not show the first evidence of decomposition until -205 0 C and only starts to decompose at more rapid rates above 240*C. Its decomposition behavior clearly differs from RDX and HMX. The replacement of a methylene group in RDX with a keto group makes the resulting K6 compound less thermally stable as can be seen from Fig. 3. K6 starts to decompose at -150'C and has undergone complete decomposition by 180*C. K6 appears to decompose below its nominal melting point (180'C), although such extensive decomposition below 180 0 C suggests that its melting point is uncertain. Consequently, we do not know at present whether K6 decomposes in the solid or liquid phase. However, it is clear that X6 is the least thermally stable cyclic nitramine ot those used in the present study.
~
CH~CH20
_5 150180210240 270300
Temperature (°C)
0.
1
150180210240270300 150180210240270300
Temperature (0C)
Temperature (OC)
Figure 3. The ion signals associated with various decomposition products formed during the
decomposition of RDX, HMX. ONDNTA, TNCHP, and K6. The heating rate for each expenment was 20C/min. The ion signals are related to the gas formation rates of each decomposiuon product by an undetermined mass spectrometer sensitivity factor. Thus, the ion signals represent only the temporal behavior of each decomposition product and not their relative rates of formation. Thermal Decompogsition of ONDNTA The thermal decomposition of ONDNT A is a complex process that also occurs via multiple pathways. The results presented in this paper cover our initial analysis of the thermal decomposition of ONDNTA and are used to show the qualitative behavior of the decomposition of ONDNTA. Quantification of our results requires further expenments and analysis and will appear at a later date. The mass spectrum of ONDNTA has been presented previously,' At 20 eV, the major ion sigitals are C2 H4 N+ (m/z=42) and C2H4 N2 (NO)NO 2+ (m/z = 132). The mass spectrum of ONDNTA differs from RDX in that the ONDNTA forms most of its daughter ions by loss of fragments from the nng whereas RDX forms more of its daughter ions by loss of substituents on the ring. The products formed during the thermal decomposition of ONDNTA are determined from STMBMS measurements that have been reported previously 11 Two of the major products formed are CH20 and N20. An ion signal measured at m/z=28 also originates from a major decomposition product that may be either N2 , CO, or possibly C2 ti. The fourth major product observed in the decomposition forms an ion signal at m/z=42 that has the formula C2 H4 N+ and is associated with a thermal decomposition product with a mokcular weight less than 60 amu. Since it is less likely that the C2 H4 N radical is a major d'x.omposition product. formation of C2 H5 N by abstraction of a hydrogen atom may be a :,iore reasonable product This species is consistent with the ion signals at m/z = 43 from ONDNTA-ul and n/z = 48 from ONDNTA-d6 formed during the decomposition. This tyve -,f -ng fragment has not been observed as a major product in the thermal dec-mposition o, '...r RDX or HMX. Other products formed dunng the decomposition of ONDNTA include: H120, HICN. NO, NO2 . and HO.,O. Similar to the decomposition of RDX and HMX, three amides are also observed (formamide (m/z=45), N-methylformamide (m/7 = 58,59) and N.Ndimethylformamide (m/z = 73)y. Higher molecular weight products observed during the decomposition include two species. CiN3H3 (m/z = 81) and C 3N3H6 (n/z = 84). in which the ONDNTA ring appears to remain intact. Two other higher mo!ecular weight species that
20
appewa during the decomposition are associated with the ion signals observed at m/z values of 85 and 132. Since the ONDNTA itself forms a large ion signal at m/z =132, it has been difficult to determine the exact molecular weight of the thermal decomposition product that leads to the signal at m/z = 132. If the molecular weight of the product is 132, this would indicate that one of the decomposition pathways of ONDNTA involves elimination of methylenenitramine (CH 2=N-NO 2 ). If C2H 3N30÷ (m/z=85) is a molecular ion, then this thermal decomposition product may be formed by the loss of HONO from C2H-N 4 2 (NO 2)NO (mn/z=132) to form a species such as CH2=N-CH=N-NO. Further TOF velocity spectra measurements and analysis will provide more conclusive findings on these species. The temporal behaviors of the ion signals associated with the ONDNTA thermal decomposition products are consistent with a multiple pathway decomposition mechanism. Figure 4 shows the temporal behaviors of the ion signals associated with the major products formed during an isothermal decomposition of ONDNTA-ul and ONDNTA-d6. In these experiments the sample starts to decompose as it is heated to its isothermal temperature. For a first order reaction in ONDNTA, one expects the ion signals arising from the decomposition products to decrease as the sample size decreases once the sample reaches its isothermal temperature. However, the CH 2 0 and N20 signals continue to increase after the isothermal temperature is attained. This behavior is similar to that observed in the decomposition of RDX in that multiple pathways control the decomposition. This behavior is supported by the temporal behaviors of several ion signals associated with the other decomposition products. As can be seen from Figure 4, the product associated with the ion signal at m/z = 132 appears to be first order in ONDNTA since the signal decreases as the sample is depleted. On the other hand the product associated with the ion signal at m/z =85 slowly increases as the sample is consumed and peaks just before the sample is depleted. Temporal behaviors similar to m/z = 85 are observed for the amide products. The product associated with the ion signal at m/z = 132 may originate directly from a unimolecular decomposition of ONDNTA, whereas, the amides and the products associated with the m/z = 85 signal may arise through either an intermediate or an autocatalytic pathway. As shown in Figure 4a to 4c, the CH 20 and N20 products, along with several lighter products, have temporal behaviors that increase as the sample size decreases and thus probably arise from both a first-order pathway and an intermediate or autocatalytic pathway. The effect of hydrogen transfer in the rate limiting step of the d~fferent decomposition pathways is illustrated by the ion signals associated with the CH20 and N20 products shown in Figure 4a and 4d. In contrast to the temporal behaviors of the CH 20 and N20 signals measured during the decomposition of ONDNTA-ul, the CD 20 and N20 signals measured during the decomposition of ONDNTA-d6 show a fall off as the sample size decreases and is indicative of a first order reaction in ONDNTA. This indicates that the reaction rate of the intermediate/autocatalytic decomposition channel of ONDNTA is much slower for ONDNTA-d6 than ONIDNTA-ul, and thus, the intermediate/autocatalytic channel exhibits a very strong DKIE. One other interesting feature observed in the decomposition of ONDNTA is the evolution of N20 and CH 2 0 as the sample is heated but prior to melting. These peaks occur in the CH 2 0 and N20 signals between 800 and 1500 seconds in Figure 4a and 4d, and evolve over a temperature range from 120 to 170 *C. Contamination of the original sample has been eliminated as an explanation for this peak. Details of the mechanisms controlling each of the decomposition pathways of ONDNTA require a more detailed examination of the ONDNTA data, which is currently underway. Thermal decomposition products from TNCHP TNCHP is more stable in the liquid phase than either RDX or ttMX. The malor products formed in its decomposition are CH 2O and N20. Products formed to a lessor extent include: H20, HCN, NO, and NO 2. Ion signals, representing other decomposition products, are also observed. Further measurements utilizing deuterium labeled TNCHP and TOF -,'-city spectra are underway to determine the identity of the thermal &,-',nicsition produ,. .,admng to these other ion signals. The temporal behaviors of the major ion signals are shown in Figure 5. These results illustrate the increased thermal stabilitv of TNCHP in the liquid phase compared to RDX. The ion signal at m/z = 146 is analogous to the ion signal at m/z = 132 that arises from ONDNTA. Thus, the ion signal at m/z =146 most likely arises from the mononitroso analogue of TNCHP.
21
3
.s
-~30
60~t
.~21l
S20 P:
40 101
1000
0
3000
2000
0
20 0 1000
06C
3000
0
1000
2000
3000
Time (ec)
Tim.(sc)
Time (86C)
E15
2000
3
20 1
C10
0
10 0
2000
1000
3000
4000
0
1000
Time 114K:)
2000 3000
WO0 0
1000
TIMe (10)
2000
3000 4,00
'limfe (slee)
Figure 4. Ion signals associated with thermal decomposition products from ONDNTA. Signals in panels a, b and c are from unlabeled ONDNTA and signals in d, e and f are from ONDNTA-d6. The signals in the left shaded portion of the graphs were recorded during the thermal ramp of the sample and the right shaded portions were recorded at the isothermal temperature listed on each graph. The large oscillations in the ion signals at m/z values of 132 and 136 is due to the large correction factor that was used to subtract the contribution from evaporating ONDNTA at these two m/z values. 20'
N
N20
'15C
NO
wE5 P
5
20
5 HCN
150 175 200 225 250 275300
tJ
-10 Mononltroso C 146+' ' U 5 - MP 150 175 200 225 250 275300
Temperature (OC) Temperature (°C) Figure 5. Ion signals associated with the products formed during the thermal dccomposiuon of TNCHP. The heating rate is 2 °C/mm. In isothermal experiments with TNCHP, the temporal behaviors of the ion signals associated with the decomposition products from TNCHP are indicative of several parallel reaction pathways. The temporal behaviors of several of the products are illustrated in Figure 6. Ion signals associated with processes that are approximately first order in TNCHP are represented by the signals for NO and N02 in Fig. 6 and also include signals that represent FICN. Ion signals associated with intermediate products formed during the thermal decomposition are found at n/z values of 55, 84, 130, and 146. The ion signals at m/z values of 55, 84 and 130 have temporal behaviors similar to that of 146, which probably represents the mononitroso analogue of TNCFIP. This suggests that the ion signals at mlz values of 55, $4 and 130 may be ion dissociation products of the TNCHP mononitroso analogue. TOF velocity spectra signals at these n/z values will resolve whether these signals are ion dissociation products formed in the mass spectrometer or whether they anse from additional thermal decomposition products. A stable product, similar to the formation of OST in the decomposition of is not i'2 observed in the thermal decomposition of TNCHP. This a,.b/,:,y ,o form a decomposition product by stabilizing the nng of the cyclic nitramine may lead to the increased thermal stability nf TNCHP.
22
30
21
C8 OC
'• 0:6
212
4
T~i;
S10
C
0
0 0
2
4
6
8
0
10
2
Time (sec x 103)
4
6
8
10
Timo (sec x 103)
Figure 6. Ion signals associated with the thermal decomposition products from TNCHP. The region in the left shaded panel is the heating portion and the right shaded panel is the isothermal portion of the experiment. The ion signals representing NO and N02 appear to be approximately first order in liquid-phase TNCHP. The ion signals at m/z values of 130 and 146 are associated with an intermediate formed during the thermal decomposition. The ion signals associated with CH20 and N20 probably originate from pathways associated with both the first order process and the decomposition of the intermediate. Thermal decomposition products from K6 The decomposition of K6 is quite different from the other cyclic nitramines used in this study. In addition to its lower thermal stability, K6 also produces fewer and simpler decomposition products. The decomposition products from K6 are mainly CH20, N20 and CO 2 , with minor contributions from HCN, CO, NO and NO 2 . Unlike the other cyclic nitramines used in this study, K6 does not form any amides, mononitroso analogue, or residue. The temporal behaviors of the products formed during the decomposition of K6 are shown in Figure 7. 200
I' -
-
E 150 -
N20, CO
1
/
40
NO-
30
100 -2 CH
'50
20
0
C
,'
'1 o 0
I
Z
HCNI
190 180 170 160 150 190 180 170 160 Temperature (°C) Temperature (-C) Figure 7. Ion signals formed in the mass spectrometer from products formed dunng the thermal decomposition of K6. 150
The decomposition of K6 may be initiated by attack of one of the NO 2 oxygen atoms on the keto group carbon atom leading to the initial elirmnation of CO'2 and followed by the rapid transformation of the remaining fragment into CH 2 0 and N20. The rate of decomp)osition of K6 through this initial four center C-N-N-O complex would appear to be competitive with NN02 bond breaking in that no mononitroso analogue or amide, are observed in th. decomposition of K6. SUMMARY Through the use of measurements of the temporal behaviors of the gas tormation rates of products formed dunng the thermal decomposition of RDX and the analysis of results from DKIE and isotopic scrambling experiments with the 211. 13C, 15N. l •; labeled analogues of RDX, we have previously determined that four different primary reaction pathways control the decomposition of RDX. These pathways consist of 1) the unimolecular decomposition of RDX to form oxv-s-mnazine (OST) through HION() and HNO elimination. 2) the unimolceular decomposition of RDX via the N-NO 2 bond breaking step with the subsequent unraveling of the RDX ring, possibly through the methvlenenitramine intermediate, to form N20 and CH2O, 3) the conversion of RDX to its mononitroso analogue
23
ONDNTA followed by the subsequent decomposition of ONDNTA to predominantly N2 0 and CH 2O, and 4) the catalytic decomposition of RDX by some catalyst formed from the RDX decomposition products. The products associated with the formation of OST exhibit a DKEE and the OST itself shows no evidence of isotopic scrambling of any of the elements in the molecule. Consequently. it appears that the formation of OST involves an intra-molecular hydrogen transfer step that controls the decomposition of RDX in this channel. Just as importantly, the CH2 0 and ONDNTA products do not exhibit a DKIE and thus indicate that the products produced through the channels associated with these products do not involve transfer of hydrogen in the rate limiting step. Through examination of the temporal behaviors of the ion signals associated with the thermal decomposition products from HMX in the liquid phase, it was found that the decomposition of HMX also occurs by multiple decomposition pathways. Ion signals associated with fragments of the HMX ring are observed for the thermal decomposition of HMX in the liquid phase. No molecular ion of an HMX decomposition product that is analogous to OST formed in the decomposition of RDX is observed. The temporal behaviors of several of the HMX decomposition products are approximately first order in HMX, indicating that pathways similar to pathways 1 and 2 observed in the decomposition of RDX are also present in the decomposition of HMX. The mononitroso analogue of HMX, ONTNTA. and its associated decomposition products are also formed during the decomposition. This behavior is similar to that of RDX. In addition. ONTNTA is formed in significant quantities in the solid phase of HMX prior to melting.. However, since HMX melts at a temperature approximately 80 'C higher than RDX, more solid-phase decomposition occurs in HMX. Finally, several amides and a residue are also observed in the decomposition of HMX. Through examination of the temporal behaviors of the ion signals associated with the thermal decomposition products from ONDNTA. the mononitroso analogue of RDX, and its deuterium labeled analogue, it was found that it also decomposes by multiple decomposition pathways. The major products formed in the decomposition of ONDNITA include CH2O. N2 0 and a lower molecular weight product that forms C2 H4 N+ in the mass spectrometer and whose exact identity has not yet been determined.. Several ion signals are associated with decomposition products Jhat exhibit approximately first order behavior in liquid-phase ONDNTA. One higher molecular weight product that exhibits this first order behavior is associated with the ion signal at m/z = 132. One component of the ion signals associated with the CH,2 O and N2 0 products is associated with this first Order process. Another decomposition pathwaN exhibits autocatalytic behavior and has a large deuterium kinetic isotope effect. The resuits on the thermal decomposition of ONDNTA are consistent with the behavior of the ONDNTA intermediate formed in one of the RI)X decomposition pathways The present results on the decomposition of ONDNTA show that more complicated patnways control its decomposition tflan assumned in its patnwav for RDX. 'Ihe decomposition behavior of ONDNTA formed as the intermediate in the deco'mposition of RDX ma actually play at role in the more complicated chemistry associated with the autocatalvtic pathway in RDX. The decomposit,)n of 'rNCHP and K6, two other cyclic nitramine compounds with molecular conformations, similar to those of RDX. has sho%n thle effect of different molecular conformations on the vanous decomposition pathways. Of the tour c~clhc nitramines studied. RDX. HMX. K0. and TNCIIIP. only TNCIIP sho%s significant stabilits' atter mel~ting. Our initial results on thle act.omnosition of TNC'l W1s-ao~k several prnklucz'. tnii exhibit a temporal behavior that is first orocr in liqutid- phase: TNCi II'. lI o'kc' r. there is 11o esidence of an product formecd in thle ae:oinposinon of TNCHPin at is szimilir to cinier O)S' lrined in thec decomposition of RI)X or thle rinc fragments formed in tile (iccotipositIioiltito IIMX Tlhis inability to form it stab.,; vroduct %ith tile rill_- troml tfile ' i nitranitfme intact inaN accoun: '.I nere are ses eral ion signal, bor the increased stabini, of TNCI ll in the iuiuild p associated with decomnosition products fron TlNCIIP tonit inuicate tnat TNC'I l also .O)flfl a mononitroso intermediate tnat controls one of toe decomipo.%ition patn%a% This is similar to esults show that the ieneral stability of Ko is mutch less ifiat the both RDX and IIMD file thermail diecomipositioni of Ko vroiluces oni l '1).-0. N-)() and ,ti- - lue comflount, u KIs lNCo. and No, Quaiitatis c.%. fine adcoifltosition patoways CO, with ntiiior aniounzo t> of KbO appear to bt: less complex than lnoos of RI_)N. MI X a nl'l'Nil ll
24
ACKNOWLEDGMENTS The authors thank M. G. Mitchell and K. A. Morrison for assistance in running the experiments and collecting the data and J. R. Autera for assistance in the synthecis. Research supported in part by the U. S. Army Research Office, U. S. Army ARDEC, and the U. S. Department of Energy. 1 R. Behrens, Jr., J. Phys. Chem., 94, 6706, (1990). 2 R. Behrens, Jr. and S. Bulusu, J. Phys. Chem., 95, 5838, (1991). 3 R. Behrens, Jr. and S. Bulusu, J. Phys. Chem., 96, 8877, (1992). 4 R. Behrens, Jr. and S. Bulusu, J. Phys. Chem., 96, 8891, (1992). 5 a) R. Behrens, Jr., Rev. Sci. Instrum., 58,451, (1986); b) R. Behrens, Jr., 'The Application of Simultaneous Thermogravimetric Modulated Beam Mass Spectrometry and Time-of-Flight Velocity Spectra Measurements to the Study of the Pyrolysis of Energetic Materials.' In 'Chemistry and Physics of Energetic Materials', Bulusu, S. N., Ed.; Proceedings of the NATO Advanced Study Institute, Vol. 309, Kluwer Academic Publishers, Netherlands, 1990, •.327. R. Behrens, Jr., Int. J. Chem. Kinetics, 22, 135, (1990). 7 F. J. Brockman, D. C. Downing, and G. F.Wright, Canadian J. of Research, 27B, 469, (1949). 8 G. S. Meyers and G. F.Wright, Canadian Journal of Research, 27B, 489, (1949). 9 A. R.Mitchell, P. F. Pagoria, C. L. Coon, E. S. Jessop, J. F. Poco, C. M. Tarver, R.D. Breithaupt and G.L. Moody, 'Synthesis, Scale-up, and Characterization of K-6', Univ. of 1Calif Report, UCRL-LR- 109404, February, (1991). 1 R. Behrens, Jr., IntL J. Chem. Kinetics, 22, 159, (1990). 11 R. Behrens, Jr. and S. Bulusu, Proceedings of the 29th JANNAF Combustion Meeting, Langley, Virginia, Chemical Propulsion Information Agency, October, 1992.
I.'-
25
MOLECULAR COMPOSITION, STRUCTURE, AND SENSITIVITY OF EXPLOSIVES
CARLYLE B. STORM AND JAMES R. TRAVIS Explosives Technology and Applications Division, Los Alamos National Laboratory, Los Alamos, NM 87545
ABSTRACT High explosives, blasting agents, propellants, and pyrotechnics are all metastable relative to reaction products and are termed energetic materials. They are thermodynamically unstable but the kinetics of decomposition at ambient conditions are sufficiently slow that they can be handled safely under controlled conditions. The ease with which an energetic material can be caused to undergo a violent reaction or detonation is called its sensitivity. Sensitivity tests for energetic materials are aimed at defining the response of the material to a specific situation, usually prompt shock initiation or a delayed reaction in an accident. The observed response is always due to a combination of the physical state and the molecular structure of the material. Modeling of any initiation process must consider both factors. The physical state of the material determines how and where the energy is deposited in the material. The molecular structure in the solid state determines the mechanism of decomposition of the material and the rate of energy release. Slower inherent reaction chemistry leads to longer reaction zones in detonation and inherently safer materials. Slower chemistry also requires hot spots involved in initiation to be hotter and to survive for longer periods of time. High thermal conductivity also leads to quenching of small hot spots and makes a material more difficult to initiate. Early endothermic decomposition chemistry also delays initiation by delaying heat release to support hot spot growth. The growth to violent reaction or detonation also depends on the nature of the early reaction products. If chemical intermediates are produced that drive further accelerating autocatalytic decomposition the initiation will grow rapidly to a violent reaction. Introduction The relationship between the constitution of an organic explosive and the sensitivity and performance of the material is a question of long standing interest. The subject was first reviewed in 1944.1 It was demonstrated early in the systematic investigation of high explosive properties, using homogeneous mixtures of liquids of continuously varying oxygen balance. that power, detonation velocity, brisance, and sensitivity all increase as the oxygen balance moves towards a product composition of carbon dioxide and water, and then decreases as the explosive becomes overly oxygen rich. t .2 In the late 1950s Kamlet and coworkers began a series of studies that related molecular composition and structure to impact sensitivitv 3-6 in a wide variety of organic explosives. A major interest in these studies was to identify 'trigger linkages' in molecular structures so as to avoid kinetically labile structural components in future synthetic efforts. A variety of other investigations have studied the effect', of such parameters as bond polarities, molecular composition, electronegativit. and Carl decomposition chemistry 7 -21on sensitivity. Sensitivity Testing The sensitivity of an energetic material is always defined relative to a particular test. The test may be designed to give information about a particular hazard situation or to provide more general information implying how !' :rgetic material will behave over a wider range of conditions. T:.,: are -arried out to a.easure the explosives response to energy input from shock, impact, thermal, friction, and electrostatic discharge sources. The number of material, that have been tested under the different categories and how well the tests are characterized varies widely. Shock initiation tests are expensive and require relatively large amounts ot material. The shock initiation tests tend to be well characterized but relatihvel few matenal.. either pure compounds or formulations, have been tested. Drop-weight-impact testing is Mat. Res. Soc. Symp. Proc. Vol. 296. '1993 Materials Research Society
26
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21
Failure diameter (mm)
9
1
32
Reaction zone thickness (mm)
6
0.1
26
Detonation velocity (m/s)
7.76
9.11
30
Gurney energy (MJ/kg)
1.1
1.6
30
Heat of detonation (MJ/kg)
-5.02
-6.78
30
In Table 2 we compare the properties of TATB and cyclotetramethylenetetranitramine (H4X). HMX is the highest performance explosive in use, TATB the most insensitive high performing explosive in use. The detonation velocity of HMX is some 17% greater than that of TATB, the Gurney energy 45% greater, and the heat of detonation 35% greater One reason that TATB performs as well as it does, given the relatively low heat of detoihation, is it', unusually high density, An atom additivity calculation predicts 33 a density of 1.80 g/cm', well below the 1.94 g/cm 3 observed. This large positive density deviation is a consequence of the strong in-plane hydrogen bonding 2 9 observed in the crystal structure. Without this high density the performance of TATB would not be high enough for the material to be of anl practical interest. Even with this large positive deviation in density the material is still well below HMX in all of the figures of merit for performance. However in all measures of sensitivity TATB is vastly better than HMX. Since HMX (nitramine) and TATB (nitroaromatic) are diawn from different structural classes of organic high explosives any comparison of sensitivity to performance involve, apples to oranges analogies. A comparison of TATB properties to materials drawn from a related homologous series is given in Table 1., This comparison speaks to the qu!stion of whether TATB is an unusual outlier in its sensitivity or whether it is behaving as a reasonable
28
began investigations of the possibility of using TATB as an insensitive high explosive (IHE) and extensive studies of the fundamental physical properties of the material. The x-ray crystal structure determination 29 for TATB showed that the material had a high density and unusually strong intra- and intermolecular hydrogen bonding. Since the intensive investigation of TATB began in the 1960s two proposals have been consistently put forward relative to its extreme insensitivity. One is that TATB is a very unusual outlier, insensitive due to a fortuitous combination of as yet unidentified properties. The implication of this approach is that equally unusual outliers may well turn up in other classes of explosives, such as nitramines or nitrate esters, if enough compounds are examined. The second proposal ascribes the insensitivity to the hydrogen bonding in TATB. The implication of this hypothesis is that one should synthesize materials with extensive hydrogen bonding in the search for other IHEs. The question of the performance and sensitivity of TATB is best examined in the context of the properties of other substituted-nitroaromatic high explosives. In Table 1 we give a selection of physical, performance, and sensitivity properties for the nitroaromatic and amninonitroaromatic homologous series and several related compounds. Table 2. A comparison of properties of TATB and HMX. PROPERTY
TATB
HMX
Ref.
Density (g/cm3)
1.938
1.905
30
Thermal conductivity (cal/cm s *C)
1 x 10-3
7 x 10-4
31
Drop-weight impact (50% ht. cm.)
,320
33
30
Small scale gap test, NSWC, (GPa @ 98% TMD)
16.5
2.0
21
Failure diameter (mm)
9
1
32
Reaction zone thickness (mm)
6
0.1
26
Detonation velocity (tms)
7.76
9.11
30
Gurney energy (MJ/kg)
1.1
1.6
30
Heat of detonation (MJ/kg)
-5.02
-6.78
30
In Table 2 we compare the properties of TATB and cyclotetramethylenetetranitramine (HMX). HMX is the highest performance explosive in use, TATB the most insensitive high performing explosive in use. The detonation velocity of HMX is some 17% greater than that of TATB, the Gurney energy 45% greater, and the heat of detonation 35% greater One reason that TATB performs as well as it does, given the relatively low heat of detonation, is it% unusually high density. An atom additivity calculation predicts 33 a density of 1.8() g/cm3. well below the 1.94 g/cm 3 observed. This large positive density deviation is a consequence of the strong in-plane hydrogen bonding 2 9 observed in the crystal structure. Without tils high density the performance of TATB would not be high enough for the material to be of anl practical interest. Even with this large positive deviation in density the material is still well below HMX in all of the figures of merit for performance. However in all measures of sensitivity TATB is vastly better than HNX. Since HMX (nitramine) and TATB (nitroaromatic) are drawn from different structurnd classes of organic high explosives any comparison of sensitivity to performance involve, apples to oranges analogies. A comparison of TATB properties to materials drawn from a related homologous series is given in Table 1. This comparison speaks to the que:stion of whether TATB is an unusual outlier in its sensitivity or whether it is behaving as a reasonable
29
U,4
I--
F-
Uo
o
-ý
in
II-
to
094601
IL)
v-,
'
CD
ZLn
-
U)
U)
0 0z Oi
E01
31
member of the series of compounds it belongs to. Earlier we defined 21 an oxygen balance related Sensitivity Index (SI), similar to that used by Kamlet. 3 '6 In Figure la we show how the shock initiation in the NSWC small scale gap test of trinitrobenzene 34 (TNB)(5), picramide (MATB)(12), 1,3-diamino-2,4,6-trinitrobenzene (DATB)(15) and TATB(18) vary at 90% theoretical maximum density (TMD) as a function of SI. For similar plots at 95% and 98% TMD the series takes on a regular concave upward shape. In all cases TATB sits very much where you would expect it to be based on its oxygen balance in this homologous series. In Figure Ib we compare the drop-weight impact sensitivity of this same series (TNB, MATB, DATB) plus hexanitrobiphenyldiamine (DIPAM)(33) and extrapolate the line to the measured shock sensitivity of TATB. This estimates the drop-weight impact sensitivity of TATB at about 500 cm. The machine used in the Type 12 impact sensitivity measurement only extends to 320 cm. Thus the results are reported as ,320 for any compound that gives no-goes at the maximum height available on the machine. The estimate given by the comparison of the shock initiation to the impact initiation for this series is quite reasonable. That the TATB gets hot enough to react has been demonstrated by impact studies 35 done on heat sensitive film. Although reaction is initiated at a drop height of 320 cm it does not propagate to give a 'go' on the acoustic analyzer. In a similar manner if you plot the SI of the closely related series TNB(5), MATB(12), DATB(15), TATB(18), DIPAM(33), and hexanitrobiphenyl(29) against the impact sensitivities for the series the estimated value of 500 cm for TATB fits well and is quite reasonable. If you now extend that series to the more highly substituted polynitrobenzenes, hexanitrobenzene (1), tetranitrobenzene (3), and pentanitroaniline (4), using the St and impact sensitivity of the first nine materials in Table 1, Figure lc, there is a sharp break in the correlation at TNB(5). However, if you use the heat of detonation (AHdct) as an index for the impact sensitivity all of the related compounds fall on a single regression. This suggests that the mechanism of decomposition of this series is similar or changes gradually as you move
through the series and that the ease of initiation and propagation is controlled by the rate of heat release generated in the hot spots. Insight as to the early mechanism of decomposition of TATB should provide information as to one aspect of :ts insensitivity. Sharma and coworkers 36 '38 have investigated the shock and impact induced early
decomposition of TATB. They have observed several furazan and furoxan compounds resulting from the cyclization of the ortho-aminonitro functional groups, Figure 2. There are several interesting observations relative to the accumulation of these compounds. (a) The furazans and furoxans represent explosives that are known to be or are expected to be much more sensitive than TATB. For instance, the known 5,7-diamino-4.6-dinitrofuroxan observed
in the shock induced decomposition has an impact sensitivity intermediate between TNT and
DATB. (b) The dehydration of the onho-aminonitro functional groups to the furazan or
furoxan function is approximately thermochemically neutral. The formation of water is about 65 kcal/mole exothermic, the furazan or furoxan formation is about the same amount endothermic. (c) The chemical reaction products are chemically benign. Typically an energetic
material will react by generating fuel and oxidizer by separate pathways which combine later to
provide the large, prompt, release of energy. Water has no further role to play in chemical
reactivity and the furazan, furoxan, or similar intermediate has to undergo further decomposition to feed the appropriate pathways. This places a very effective neutral filter in the decomposition mechanism. A mechanism of decomposition that involves a series of consecutive reactions culminating in an explosive reaction is consistent with 45. the observauons of Catalano and Rolon on the thermal decomposition of confined TATII. They observed four separate stages to the evolution of the thermal decomposition. The culminating explosic
reaction is the result of the development of either chain and/or concurrent reactions.
.,ct-induced dccompositon of TATTB arc The early reactions proposed in the shod.- c disfavored by pressure, a titcy .,.sult in the formation of multiple species. It has been suggested by Rogers46, based on solid state deuterium isotope effect studies on the thermal decomposition, that the thermal degradation of TATB involves a positive activation volume. Studies of TATB under high static pressure48 in diamond anvil cells (up to 16 GPa) have shown it to be very stable to pressure effects. The vibrational frequencies show an unusual pressure dependence, ascribed to variations in th: NH 2/N0 2 coupling as the pressure
32
hI CL
z z
a
oM
0
00
z
z~~
0u
C CD
-
OZ
b.
£.
0 C
ht
E
z
o
z
z 0x
size, 10, beyond which the newly created dislocation pair must propagate before the source can create another dislocation pair. The rate at which a single source can create dislocations is --: P
- 4-.
(.;)
The factor of 2 accounts for ti& creativn c. ,asilocation pxt:. I i does not depend strongly on time but rese:'d'Iel: a Step lunuctic:, T(t) ; 7u(t , then tne number of dli-octxon.; ner sourc i•
where the time t is the time from first application ot the shock or impact. These dislocations are expected to bt concentrated on the slip planes that contain the source and lorm a shear band.
66
Combining the above relations, the plastic strain rate from Ns dislocation sources that intercept a unit area is approximately dy -E - 2T(,) 2 VO
dt
bp
(,) N t
(6)
1
The plastic deformation rate given in equation (6) admits two time regimes of interest. These are determined by the time required for a newly created dislocation to move away from its source and encounter an obstacle which forces it to stop. Let LO ne the average distance between the dislocation source and an obstacle, then at early times after the application of a shock or impact when t < Lt/v the plastic strain rate is given by equation (6). However, at later times when t Ž L0/v, the moving dislocations will begin to encounter obstacles and will be forced to stop. For this case the number of moving dislocations approaches a constant and the plastic strain rate is determined by substituting t = 4/v into equation (6) dy__ dt
. 2T(r)vobp,(r)N.Lo 10
(7)
Dislocation Energiy Assume local equilibrium, so that the energy density of a dislocation in a lattice must be the same as the local energy density of the host lattice. During shock or impact the energy will have two components, one due to the shear stress of the shock or impact and the other from the shear stresses arising from the thermal background. Even for high level shocks most of the solid will behave elastically as a Hooke's law solid and most of the shear stress energy of the dislocation core will be elastic energy. The average energy with which a segment of the dislocation core approaches the potential barrier is approximately T2-V
2G
--
2
(8)
where G is the shear modulus, 0 is the temperature and k: is Boltzmann's constant. The thermal energy with which a dislocation segment approaches a potential barrier is just 'd:0. The effect of thermal fluctuations about the mean temperature and the non-linear contribution of the core region to the energy have been ignored. Comparison with Deformation Experiments These results can be compared with the experimental results of Campbell and Ferguson3 who examined the plastic deformation rate in a mild steel for differ;-t applied shear stress levels over a wide range r` t,'ixeratures. .-te material constants were taken as b = 3x10'm, W = .5x10'1m, l1 = 3xl0In, vQ = 5.5x10 3 m/s, G = 7.5x1011dy/cm2 , p = 8.6xlO3 kg/m 3 , U = .5x10 1 3ergs. The number of dislocation sources per unit area was determined in conjunction with the distance, L0 , that a dislocation travels between its source and a blocking obstacle. It was assumed that NULG2 = 1.
67
Taking L0 = 10'4m, the approximate crystal size, then Nf 10m'2 . The mass of a dislocation segment was taken as m z pb , and the volume, V, of the lattice that is perturbed by the presence of the moving dislocation was taken as a cylinderical disk centered at the dislocation core and of height b and radius 7b thus V z 150b 3 . For simplicity, it was assumed that the amplitude of the applied shear stress was large enough so that the source could readily create dislocations allowing p,(7) - 1. Figure (1) shows the predicted behavior of the plastic deformation rate as a function of the applied shear stress for approximately the same temperatures as in the experiments of Campbell and Ferguson. Excert for a less rapid increase in plastic strain rate with increased shear stress at low temperatures and lower shear stress, the predicted behavior contains all of the essential features found in the experimental data. As noted at the outset, the less rapid increase in strain rate at low shear stress levels is due mainly to the use of an idealized square well potential in which the width of the k'arrier is a constant. The correct solution would be to determine the width of the exact potential barrier as a function of the quasi-particle energy and solve the tunneling problem in a way that satisfies the Schrodinger equation and the boundary conditions. A somewhat more realistic potential which gives a better fit to the data is to let the width of the potential barrier be W = W0 (sin(7TE 0 /2E,)) 3, where W0 = .5x10'1 m and E0 is the dislocation segment energy when r 0. 400
3.W K
400
.
.
. ' .
.
.
'
.225 K 300'K
7-300
22
2001
3K
Z300-
22
'1,00 r.W1 S~t•E
(EC•
o
'(E'O 'K•E
0
10.4 10.310-2104
1
10
102
103
104
l05 106
10A 103 10 2 10-1
STRAIN RATE f(SEC*1)
1
10
102 103 10'
JOS 106
STRAIN RATE j (SEC 1)
Figure (1). Plastic strain rate due to tunneling through square well potential barrier, LHS, and half sine wave barrier, RHS, Predictions are indicated by heavy line,. experimental data of Campnell and Ferquson.`
Also
shown
it;
the
The predicted rapid increase in strain rate with applied shear stress that occurs at about y, z 4 . am*' ':- at all temperatures is
due to the tunneling probabil'ity approacning unity as E - U. This behavior is evident in the experiments of Campbell and Ferguson and has been observed in copper and IR brass. The conventional macroscopic constitutive approach is una&- , o account for this rapid increase in plastic sEt... n ate at hly, shear stress levels. At low shear stress levels a nearly non-thermal behavior was observed in the experimental data. In the experiments of Capbell and Ferguson 3 this regime was referred to as region 1. In the present analysis this behavior can be attributed to the presence of low level obstacles in the solid which impede the functioning of
688
the dislocation sources, p 102 Mpa, these obstacles are overcome, p• = 1, and dislocation motion is determined by lattice tunneling. These results can be extended to other materials. The prediction of the dislocation velocity in lithium fluoride crystals compares reasonably well with the experimental measurements of Johnson and Gilman on LiF at several temperatures.4 Finally, this analysis applies to both screw and edge dislocations since the only difference between these is the potential barrier that each type of dislocation must tunnel through. This will only alter the tunneling probability, T, and only for mid range shear stresses. The asymptotic behavior at very high and very low amplitude shear stresses will be the same in both cases as is seen in observations of dislocation velocities.' High Amplitude Shock Loading High amplitude shock loading offers a unique analytical view of plastic deformation because the energy with which the dislocations approach the potential barrier approaches the barrier height, E - U. The plastic strain rate at early times, equation (6), simplifies since the thermal term can be ignored. In these limits the average plastic strain rate is proportional to the fourth power of the applied shear stress. Swegle and Grady have observed that within a few tens of nanoseconds after the onset of a high amplitude shock the plastic strain rate in a number of different materials varied as the fourth power of the stress level. 5 Substituting representative values into equation (6) and the applied shear stress 7 = 2 GPa gives dy.dt = 105 s-'
10'8 s, which is
at t
=
in the range of the experimental data.
Energv Dissipation During Rapid Deformation To understand how energy is dissipated by moving dislocations, observe that the motion of a dislocation through a solid significantly displaces those atoms or molecules located near the core of the moving dislocation. These atoms/molecules can be displaced as much as d/10 or more where d is the lattice constant. Dislocations moving at a speed v encounter the lattice potential at a rate of v/d times per second and in the process disturb the lattice at a frequency of 2rv/d rad/s. The energy of this disturbance is radiated away as phonons. Since in the case of high amplitude shocks v can approach the local sound wave speed, these phonons can have frequencies in excess of 1013rad/s which is sufficient to pump the internal vibrational modes of most molecules this view in some detail and will of interest. We have developed 67 8 briefly review it here. ', Since explosive molecules are complicated affairs having many atomic components (chiefly C, H, N, and 0), it is unlikely that the stress field around the core of a dislocation in such a system will ever be well known. Nor is this necessary in order to obtain workable predictions of energy dissipation and localization in terms of shear modulus and other known physical properties of the crystal. In this spirit, we approximate the stress field -, lh edge dislocation in a lattice composed of expo.o;o'= molecules by the classical expression for the stress field of an edge dislocation in or molecules. The a simple lattice composed of point atoms 6 interaction Hamiltonian can be written as
69
Ax
Gb C(sin+lcos0) ( cosO
H=47EIi'V) -r
d2
-
sine)]
(9)
d,
The shear modulus G provides a measure of the coupling between the dislocation and the lattice. The quantity v is the Poisson ratio, r is the distance from the dislocation core, 8 is the angle between the shear stress and the strain, d, and d2 are the lattice spacings. The energy dissipation rate due to the motion of the core of an edge dislocation moving through a lattice at a velocity v has 7 been determined to be dTN
dE jr(lq + 1) dq +IHI> lIH'Iu> Ij
KdT -
xd.,.
(11) where w = (27rv /d)exp(-T/7.). 0 The first tern of (11) arises from the first order transition pre'b&ility and iF responsible for the dissipation due to low and ,. ! velocity dislocations. Consequently, it reflects the nnergy dissipation rate due to impact and low level shock. '±,e higher order terms are mainly responsible for energy dissipation due to relatively large amplitude shocks, since for these terms to be important resonance must occur, oI., = (El -E- 1.)/h : 1013 rad/s. This requires that the dislocation velocity approach v0 , which
70
only happens when 7 >> To. As resonance is approached, a very rapid increase in the energy dissipation rate occurs. The high number density of optical phonons, centered in a band about w = 2rv/d, the internal of excitation resonant produce multi-phonon vibrational modes of the molecules of the host lattice. At resonance the transition probability between adjacent vibrational levels approaches unity. Only for the more widely spaced lowest vibrational levels are non-resonant conditions likely to occur. Consequently, the energy dissipation-molecular excitation rate for high amplitude shocks will be determined only by the products of these few non-resonant lowest level transition probabilities. This results in an extremely fast process in which energy is transferred directly from the moving dislocations to vibrationally excite and even dissociate the molecules that lie near the path of the dislocation core. The Onset of Reaction What has been developed up to this point applies to both inert and energetic crystalline materials. It is useful to examine the onset of reaction in energetic crystals in the limit where the energy density increases to a critical level, Ec, in at most a very few locations and chemical reaction starts in only a few crystals. The energy density in a shear band due to dissipation by moving dislocations can be obtained by integrating equation (11) with respect to time. Dissipation begins just as the dislocations begin to move, at the yield stress, 7 = 7 . Ignition will occur when this energy density exceeds the critical level, Ec, and the shear bands then become local reaction sites. Assume an energy e 0 is required to cause a molecule to the number density of Early in the ignition, dissociate. dissociated molecules, Nd, is approximately Nd = (E - E,)/e 0 . If each of the reacting molecules releases an amount of energy, u0, and this initial energy release causes few if any additional molecules to react so that no reaction growth occurs, the reaction energy density is approximately U = u 0 (E - E,)/e, where reaction occurs when U > 0. The initial reaction energy in a lightly confined charge is
U(t) 0
e0
2• ( 4=fPG d
eNe
dt +-hfN M
) .7=1
,!
t',tU
3000K) [191. These impacting molten particles may thus act as initiation (nucleating) sites in surrounding material. Notwithstanding this hard landing effect, the method is a viable technique for the generation, as required, of nanosized metal particles at specific locations on the grid in situ in the HRTEM repeatedly. Initially the nascent particles appear to be protected by the evolving nitrogen gas, and subsequent interaction with the vacuum gases can be monitored over a period of time. Further details of these studies will be reported elsewhere [20]. The reason for the absence of explosion/detonation in these materials of known ultrasensitivity is most likely that suggested by Bowden previously for cadmium, lead and silver azides [17). He exploded these azides in a 200 ILA, 75 keV electron beam but concluded that a critical size is required for the hot spot to initiate explosion. He showed that the critical size has to be ca 26-46 pm. Our materials are polycrystalline with the actual microcrystallite size at least several orders of magnitude below this value. Indeed we have deliberately sought out ultrafine particles to prevent such explosions from occurring in the microscope. The behaviour of Pd azide is anomalous. Admittedly it does have one of the lowest M-N bond ionicities (the lowest is Au-N[l]) and it is reportedly extremely sensitive. Notwithstanding we were able to obtain micrographs of this pristine material (Figure 1(b)) and oniy on exposure to an intense focused beam did the material explode. We conclude either that the hot spot is much smaller in this azide or that the dense black material aggregates or packs in such a way as to have a much higher density of material in a ca 1jim clusters studied. ACKNOWLEDGEMENTS Financial support from NATO (award INT890275), NSF (award INT8911940) and VAL-ERO (contract DAJA45-90-C0013) is acknowledged. We appreciated the help given by Dr D A Jefferson.
REFERENCES I. 2. 3. 4. 5. 6. 7. 8. 9. 10 11 12 13
14 15 16. 17. 18. 19. 20.
Energetic Materials, Eds. H.Fair and R. F. Walker, Plenum Press, 1977. K. Dehnicke, J. Inorg. Nucl. Chem., 22, 809 (1965) T. Curtius and A. Darapsky, J Pract Chem., 6.1, 408 (1900) L. Wohler. and F. Martin, Ber. Dtsch. Chem. Ges., 5Q, 586 (1917) L. Wohler and F. Martin, Angew. Chemie, 22 335 (1914) H. P. Fritzer and K. Torkar, Monatsh. Chem., 22, 2333 (1968) R. G. Clem and E. H. Huffman, J. Inorg. Nucl.. Chem., 22, 365 (1965) P. J. Herley and W. Jones, J.Chem. Soc. Farad. Trans., a, 3213 (1992) L. Wohler and F. Martin, Angew. Chemie, 3Q, 33 (1917) D. Forster and W. D. Horrocks, Inorg. Chem., •, 1510 (1966) Y. Mizushima, Tokyo Kogyo Shikensho Hokoku, 529 209 (1964) L. M. Dennis and M. Doan, J. Am. Chem. Soc., 18, 970 (1896) L. Wohler, Angew. Chemie, 5, 294 (1922)
U. Muller and K. Dehnicke, Z. Anorg. Allg. Chem., 350, 113 (1967) N.Wiberg and K. H. Schmid, Chem. Ber., 10W, 741 (1967)
P. J. Herley, N. P. Fitzsimons and W. Jones, in Materials Research Society. Stcimen P r n T .si n Electron Microscopy of Materials Ill, Eds. R. Andert3i.,! YPivman and B. 'fracy, 1992, 2S, 223. F. P. Bowden and K. Singh, Proc. Roy. Soc. A, 1955, 22=, 22. R. Uyeda, in Morphology of Crystals, Ed. I. Sunagawa, Terra Scientific Pub. Co. Tokyo. Part B, Chapter 6 (1987). C. L. Cleveland and U. Landman, Science, 257, 355 (1992). P. J. Herley and W. Jones, to be published.
93
COMPARISON OF DEFORMATION AND SHOCK REACTIVITY FOR SINGLE CRYSTALS OF RDX AND AMMONIUM PERCHLORATE H.W. SANDUSKY*, B.C. BEARD*, B.C. GLANCY*, W.L. ELBAN**, AND R.W. ARMSTRONG*** *Naval Surface Warfare Center, 10901 New Hampshire Ave., Silver Spring, MD 20903 **Loyola College, Dept. of Electrical Engineering and Engineering Science, 4501 N. Charles Street, Baltimore, MD 21210 ***Univ. of MD, Dept. of Mechanical Engineering, College Park, MD 20742 ABSTRACT Deformation of cyclotrimethylenettinitramine (RDX) and ammonium perchlorate (AP) crystals at low strain rates was studied by diamond pyramid (Vickers and Knoop) microindentation hardness testing. RDX is two to three times harder than AP and has relatively limited slip system activity. While both crystals readily crack, cracking did not reduce hardness in RDX but did in AP. Strain fields surrounding the hardness impressions in RDX were extremely localized while in AP they extended well beyond the impressions. Shock experiments were conducted on large (5-9 mm), single crystals in a fluid-filled tank designed to permit high-speed photography and sample recovery. Reaction threshold was obtained by varying the shock pressure entering the crystals. Shock-entry orientation and large hardness impressions were used to alter microstructural responses. High-speed photography showed luminous crack propagation and reaction in both materials and the same slip deformation in AP as from hardness testing. Orientation affected the microstructural response and reaction threshold for AP, and hardness impressions sensitized chemical decomposition far from the impressions. Recovered AP crystals were much more plastically deformed than RDX crystals and were often still transparent in the region opposite shock entry. Recovered RDX crystals, at even the lowest shock pressure of 8.6 kbar, were uniformly white from a high density of fine cracks. RDX reaction threshold was -62 kbar versus 17 to 24 kbar for AP, depending on crystal orientation to the shock wave. INTRODUCTION Several experimental studies have shown that materia! microstructure influences the shock reactivity of energetic crystals. Dick1 determined that reaction was a function of crystal orientation relative to planar shocks in large single crystals of pentaerythritol-tetranitrate (PETN). In addition, Dick 2 found increased shock sensitivity for PETN crystals which had been microscopically damaged with gamma radiation. For two production lots of cyclotetramethylenetetranitramine (HMX) from different manufacturers, Green and James3 observed increased shock sensitivity in HMX/Viton formulations which contained crystals from the lot with the higher concentration of defects. The current work was undertaken to demonstrate that chemical decomposition from shock interaction with relatively defect-free crystals of AP and RDX occurs preferentially at sites of microstructural damage resulting from operative slip and cracking systems. It was also of interest to assess the effect that large strain centers have on the shock reactivity of these materials. EXPERIMENTAL APPROACH Large (>1 cm edge dimensions), optical quality, single crystals of AP and RDX were provided, respectively, by T.L. Boggs of the Naval Air Warfare Center, China Lake, CA and H. Cady of the Los Alamos National Laboratory, Los Alamos. NM. Smaller (approaching 5 mm in size) RDX Mat. Res. Soc. Symp. Proc. Vol. 296. , 1993 Materials Research Society
94
crystals of lesser quality were grown.4 The microstructural response of crystals to quasi-static loads was determined by diamond pyramid (Vickers and Knoop) microindentation hardness testing. The residual impressions were analyzed in detail to yield information about slip and cracking systems, the size and character of the cumulative dislocation strain fields surrounding the impressions, and the effect of cracking on hardness with increasing applied load. Vickers hardness testing wab used in the quasi-static studies on the (001) and (210) cleavage surfaces of AP.5'7 In RDX, Viecers and Knoop indenters were used in similar studies on the (120), (010), and (210) growth surfaces. 4'8.9 It was of interest to determine if the microstructural response of these crystals to the quasi-static loading of the hardness indenter would be similar to the high rates experienced during shock loading. Shock loading experiments were conducted on AP and RDX samples in different orientations, with and without purposely included macroscopic strain centers, and over a range of shock pressures. Since the effect of microstructure on shock reactivity was determined primarily in post-shock analyses, the experimental arrangement was designed for 'soft' recovery of the crystals. The arrangement 5,6 consisted of a closed chamber, mostly filled with mineral oi!, that had ports for backlighting and photography. The shock pressure entering the crystal was controlled by its separation from a Reynolds RP-80 detonator containing -200 mg of explosive. The spherically diverging shock front from the detonator is conceptually similar to hardness testing with a large ball, except that the strain rate for shock loading is orders of magnitude greater. A diverging shock, in contrast to a planar shock, permitted the desired activation of slip and cracking systems. The crystal was supponed on transparent tape, for a clear field of view with the high-speed camera, above a block of oil.soaked foam. Immersion in a fluid and capture of the shocked crystal in foam permitted recovery, even for shock strengths near the reaction threshold. Unlike RDX, HMX, and PETN explosive crystals, threshold reaction in AP would likely quench, allowing recovery of the sample for post-shock analyses. For the shock experiments, AP samples with edge dimensions of 5 to 9 mm were cleaved from larger crystals, whereas RDX samples of similar size were remotely cut using a metallurgical saw and then solvent polished with a mixture of cyclohexanone and acetone. Optical transparcicy of the crystals was advantageous for in-depth viewing during shock passage with an image convener camera recording at rates of 2 to 5 million frames per second. Prior to the shock loading of some crystals, localized regions of increased lattice defects and strain were created by placing Vickers indentations in exterior surfaces. Anumber of shocked crystals were recovered for subsequent microstructural characterization and chemical analysis. Microstructural characterization was performed using hardness testing, light microscopy, and scanning electron microscopy. 5' 7 Bulk decomposition measurements of AP with liquid ion chromatography (LIC) were obtained to determine the reaction threshold. Another crystal with several indentations was shocked near the reaction threshold and cleaved at indentation sites for spatially specific measurements of decomposition in the crystal ir.°erior by means of x-ray photoelectron spectroscopy (XPS). 7 ,10 Chemical etch pitting on another cleaved surface was used to map dislocation densities within the shocked crystal.II XPS measurements were ali.o obtained for shocked RDX crystals, but these had to be broken open to expose the interior. CRYSTAL DEFORMATION AND MICROSTRUCTURAL CHARACTERIZATION For th- (210) and (001) surfaces of AP. details of Vickers impressions and the associated slip and crm,.. ., were shown in transmitted and polarized light micrographs. 6 The ease of p).tir deformation in AP is shown in Figure I with micrographs 6 emphasizing surface relief, viewed with transmitted light that was partially obstructed before entering the crystal. On the (210) surface, there is a (001) crack extending from the upper comer of the impression and a very shallow trough extending in the ±10011 directions far from the impression. Prominent deep
95
o~i
,VHN =
13
(A)(210) Surface
(B)(001) Surface
Fig. 1. Surface relief at Vickers hardness impressions in AP. troughs were found on the (001) surface with large cracks in them. On the (210) surface of RDX, the micrograph of an impression in Figure 2 shows extensive cracking and extremely localized plastic deformation. A micrograph 9 of an impression on the (001) surface of a Holston Class D RDX crystal showed similar behavior. RDX is brittle with limited slip system activity. and, therefore, readily cracks to accommodate
- -
(0 ..i'
[r1oi J
••
•
.
!•
c
:. the indenter. AP is more ductile, exhibiting a -• • larger number of slip systems, but still readily •°• cracks because of dislocation interactions. m For the (210) surface of RDX, the diagonal0.I length of indentations when squared was VHN = 25 kgf/mm2 proportional to the indenter force ; that is, RDnX had constant hardness despite the cracking. 9• Fig. 2. Cracking at a Vickers hardness By comparison, the hardness of the (0)01)5.6 and (20 owbufae the (2l0)• surfaces of AP decreased withimrsonnRD increasing load, e,'pecially for the (21i0) surface. Also. RDX is two to three times as hard as AP. The effect of cracking in AP is to dissipate at least a portion of the strain energy in the vicinity of the impressions, whereas in RDX the strain energyv is stored. SHOCK LOADING AP crystals were subjected to shock entry into both th,. ?! I.and (001) surfaccs. Highspeed photographs in which the (00.., •f'.'-,.,.. was viewed lua owing shock entry, into the {210) surface were shown for shock pressures in the crystal of 16.7 kbar 5 and 24.4 kbar-5; 7. Two experiments were performed at 24.4 kbar because this shock pressure was the reaction threshold determined by LIC on the recovered crystals, as will be discussed. The high-speed photographs showed, although not in each experiment, a luminous shock front, distinct diagonal lines immediately behind the front that were attributed to the primary (100)10011 and secondary
96
(010)[0011 slip systems observed in hardness testing, a moving luminous band that appeared to be a propagating crack, and light in the vicinity of indentations appearing -1 Ps after shock passage that was presumably due to chemical reaction. Several crystals subjected to shock entry into the {210) surface were recovered intact after experiencing pressures as high as 38.5 kbar. These crystals had extensive plastic deformation and clouding near the shock-entry surface that lessened with distance into the crystal. As shown in Figure 3 for a crystal recovered from a shock loading of 24.4 kbar, the bottom section of the crystal (opposite shock entry) remained transparent. Near the shock-entry surface of that crystal, there was a two orders of magnitude increase1 I in dislocation density with a number of large, widely-spaced cracks. The damaged region seen in Figure 3 was outlined in the high-speed photographs 7 immediately after shock passage, thereby indicating the promptness at which the damage occurred relative to the shock loading. High-speed photograph-s of shock entry into the (001) surface of AP, while viewing the (210) surface (orthogonal to the orientation just discussed), showed no microstructural features or luminosity within the crystal during or following shock passage. After the shock exited from the bottom surface of the crystals, there was below each crystal a zone of luminosity attributed to
chemical reaction. The recovered crystals %..recracked apart on (210) planes and also
7 sometimes on (110) or (230) planes, all of which are orthogonal to the shock-entry surface. Also, there was less cloudiness in the recovered crystals compared to those shocked in the other orientation. Thus, the microstructural response and luminous indications of reaction were dependent on crystal orientation. RDX crystals were shock loaded, primarily through either the (100) or (010) surface while viewing the (001) growth surface, over a pressure range of 8.6 to >129 kbar. There was violent reaction only for the crystal in direct contact with the detonator (>129 kbar). For a shock pressure of 129 kbar there was prompt luminosity from reaction and only 9.7% of the crystal was recovered. Two crystals, each having indentations on the (100) shock-entry and (001) viewed surfaces, were shocked at 61.6 kbar and mostly recovered. There was only one small zone of luminosity near the shock-entry surface appearing in the first experiment, and in the second experiment there was light emission from the viewed edge of the (010) side. In both experiments, the luminosity appeared -2 ps after shock passage, and there was no evidence that the late luminosity was associated with the closest impression. In addition to hardness impressions on exterior surfaces, the crystal in the first 61.6 kbar experiment had a predominantly (010) stress crack that was centrally located. This internal flaw did not emit light during shock loading. While shock pressures of 129 and 61.6 kbar are high relative to those causing light emission in shocked AP, they bracket observations 12 by Forbes et al. on RDX single crystals shocked at -100 kbar. These crystals, which were immersed in water and shocked by a 50.8 mm diameter by 50.8 mm long cylinder of 50/50 PETNITNT, showed light emission for 6 gts and what appeared to be reaction, but not instantaneous consumption of the crystals. All of the recovered RDX crystals or fragments were uniformly white throughout from a high density of fine crac,'s, even at the lowest shock pressure of 8.6 kbar. This is illustrated in Figure 4 for a crystal that had been shocked at 16.3 kbar. Rather than the crystal being plastically deformed like AP, the only extensive deformation occurred from the (2101 system of cracks near the shock-entry surface. During the shock loading of this crystal, a luminous crack with the same orientation was observed on high-speed photographs. In all RDX experiments. transmission of backlighting through the crystals ceased immediately after sb,*:* passage, pr. - y due to the creation of the fine crack system observed in the recovered crystals. The opacity of these shocked crystals, in contrast to shocked AP crystals which were still somewhat transparent, allowed only surface observations with the high-speed camera. This was a disadvantage for observing luminosity due to chemical reaction which, as will be discussed, occurred primarily in the interior of the recovered AP crystals.
97
SHOCK PROPAGATION DIRECTION 'SHOCK
PROPAGATION' DIRECTION;:;...
r1101
(001) . ..
,
- -v
.
11201
Fig. 3. Photomacrgtaph of AP crystal after shock loading at 24.4 kbar.
00 0o
Fig. 4. Photomacrograph of RDX crystal after shock loading at 16.3 kbar.
CHEMICAL ANALYSES OF RECOVERED CRYSTALS For AP crystals recovered from shock loading through the [210) surface, LIC measurements were made for chloride, nitrite, nitrate, and chlorate. For a range of shock pressures from 1.0 to 62.5 kbar, only the chloride concentration showed a significant shift, beginning at 24.4 kbar, relative to an unshocked crystal. This reaction threshold was in agreement with the observations of luminosity from the crystals on high-speed photographs. For AP shock loaded through the (001) surface, there was significantly increased concentrations of chloride, nitrite,and nitrate (no measurements for chlorate), for shock pressures of 16.7 and 24.4 kbar. Although there were insufficient experiments to establish a reaction threshold in this orientation, it is less than that for shock entry into the (210) surface. This also correlates with the high-speed photographic observation of luminosity below the crystals after shock passage. The recovered AP crystal shown in Figure 3 had large Vickers impressions placed on two surfaces prior to shock loading at 24.4 kbar, essentially the reaction threshold determined by LIC. There were-two impressions on the viewed (001) surface (denoted in Figure 3) and one on the shock-entry (210) surface. The recovered crystal was cleaved along (210) planes that passed through the impression on the shock-entry surface and the left impression appearing on the viewed surface. With XPS, I mm x I mm areas were analyzed along these previously interior surfaces. The highest level of decomposition (as much as 9.5% perchlorate) was detected 2 to 3 mm below the hardness impression on the shock-entry surface. This position corresponded to the termination of the broad separation in a (001) crack that emanated from the impression. In a comparable location from the shock-entry surface on the other cleaved plane, there was less decomposition, 4.8% perchlorate, associated with shock passage through a lesser damaged region of the crystal. However, further from the shock-entry surface there was as high as 5.5% perchlorate decomposition occurring along slip planes emanating from a (001) surface impression. This is remarkable considering that the shock had significantly attenuated from 24.4 kbar after propagating through -5 min of crystal to reach this region. At a comparable location on the other cleaved plane thcr: was no decomnosition detected. 'r, firs- indication ot reaction in RDX crystals was obtained in XPS measurements in the interi, r of a crystal that had been shocked to 61.6 kbar, correlating with the luminosity recorded on t. .,i-speed photographs. There was significant loss of nitro nitrogen, but the level of reaction was insufficient to observe intermediate products13. such as nitroso or triazine compounds. XPS measurements on the shock-entry surface did not reveal any reaction in the vicinity of a hardness impression placed there prior to shock loading. The fractured zone associated with the hardness
98
impression (similar to that in Figure 2) was not recovered but would have been easily dislodged from the shock loading as well as by any chemical reaction. In contrast to AP, any effect of hardness impressions on enhanced reactivity for RDX was very localized if it occurred at all. CONCLUSIONS Zones of increased defect (dislocation) density enhanced chemical decomposition in relatively defect free, optical quality AP crystals shocked near the reaction threshold (-24 kbar) through the (210) surface. The luminosity in high-speed photographs and differences in bulk decomposition measurements using LIC for two crystal orientations indicated that shock reactivity was microstructurally based. The greatest decomposition was spatially determined, using XPS, to be near the tips of cracks and along slip planes that emanated several millimeters or more from hardness impressions placed in the crystal prior to shock loading. In RDX, the extremely localized increase in defects from hardness impressions and even a large, internal crack in one crystal did not enhance chemical reaction. The detection of decomposition by XPS measurements at 61.6 kbar correlated with observations of luminosity. The combined results, together with the nature of RDX to exhibit only localized deformation even while cracking and to retain deformation energy, suggest that much more extensive pre-shock damage is necessary in RDX for the initiation of dislocation-assisted reaction at lower shock pressures. REFERENCES
1. J.J. Dick, Applied Physics Letters, 44 (9), 859 (1984). 2. J.J. Dick, J. of Applied Physics, 53 (9), 6161 .'982). 3. L.G. Green and E. James, in Fourth Symposium uInternational) on Detonation, (Office of Naval Research, ACR-126, 1965) pp. 86-91, 4. W.L. Elban, J.C. Hoffsommer, and R.W. Armstrong, J.of Materials Science, 19, 552 (1984). 5. H.W. Sandusky, B.C. Glancy, D.W. Carlson, W.L. Elban, and R.W. Armstrong, J. of Propulsion and Power, 7 (4), 518 (1991). 6. W.L. Elban, P.J. Coyne, Jr.. H.W. Sandusky, B.C. Glancy, D.W. Carlson, and R.W. Armstrong, Investigation of the Origin of Hot Spots in Deformed Crystals: Studies on Ammonium Perchlorate and Reference Inert Materials (NSWC NIP 88-178. Naval Surface Warfare Center, Silver Spring, MD, 1988). 7. W.L. Elban, H.W. Sandusky, B.C. Beard, and B.C. Glancy, Investigation of the Origin of Hot Spots in Deformed Crystals: Final Report on Ammonium Perchlorate Studies (NSWCDDITR-92/206, Naval Surface Warfare Center, Silver Spring, MD, to be pnnted). 8. W.L. Elban, R.W. Armstrong, K.C. Yoo, R.G. Rosemeier, and R.Y. Yee. J. of Materials Science, 24, 1273 (1989). 9. R.W. Armstrong and W.L. Elban, Materials Science and Engineenng, AI 11.35 (1989). 10. B.C. Beard, J. Sharma, H.W. Sandusky, B.C. Glancy, and W.L. Elban, Shock Compression of Condensed Matter - 1991, edited by S.C. Schmidt, R.D. Dick, J.W. Forbes. and D.G. Tasker (North-Holland. Amsterdam. 1992) pp. 571-574. 11., B.C. Beard, H.W. Sandusky. B.C. Glancy, and W. L. Elban, J. of Materials Research. to be pnnted. 12. J.W. Forbes, D.G. Tasker, R.H. Granho'., .-. P.K. Gustavson, Shock Compression of Condensed Matter . 'c.ted :,Q by S.C. Suimidt, J.N. Johnson, and L.W. Davison (Elsevier Science Publishers B.V., 1990) pp. 709-712. 13. B.C. Beard. Propellants. hxplosives and Pyrotechnics, 16 (2), 81 (1991). Acknowledgments: Work was supported by the Independent Research Program at Naval Surface Warfare Center and the Office of Naval Research
99
MOLECULAR MODELING OF SLIP SUPPOSED TO OCCUR IN THE SHOCK INITIATION OF CRYSTALLINE PETN
JAMES P. RITCHIE MS-B214, Los Alamos National Laboratory, Los Alamos, NM 87545
ABSTRACT Some molecular modeling of slip using both rigid and flexible molecules of PETN in perfcct. but finite, lattices has been performed. Studies of rigid displacement show slip on (001 ) tc be relatively unhindered. The shock orientation with a maximum resolved shear stress in this direction would, therefore, be expected to be insensitive. Molecular mechanics calculations have also been performed. The results show that it is likely that molecular deformations occur and have an important effect in determining the shear streagth of crystalline PETN. INTRODUCTION Much of the thinking about the elastic and plastic properties of materials is based upon the behavior of inorganic compounds, including metals, their oxides, and ionic solids. These materials differ importantly from common explosives, many of which are organic. Polymers have been intensely studied, but these materials typically lack crystallinity due to their size and in this way also differ from many common organic explosives. We have, consequently. undertaken a study of some of the material properties of common organic explosives in order to determine how they differ from other materials. Dick et al. have observed an orientation dependence of the shock initiation of crystalline pentaerythritol tetranitrate (PETN).' This behavior was attributed to anisotropy of plasticity. It has been proposed that this anisotropy arises from differences in steric hindrance to edge dislocation motion. A simple counting of close contacts occurring during displacement of a rigid lattice along the the slip system of mtximum resolved shear stress was able to distinguish between shock orientations that are insensitive and sensitive. Insensitive orientations give rise to a relatively few number of close contacts during slip. while those that are sensitive encounter more. In that analysis. atom-atom contacts of 1.05 and 0.78 A are obtained for slip systems stimulated by shock orientations classified as relatively insensitive. The actual occurrence of such close atom contacts would result in extremely high energies for plastic deformation in the directions analyzed. It is difficult to reconcile such high energies with the observed shock-insensitivity and would make the suggested occurrence of supercritical shear in PETN2 extremely difficult. This difficulty needs to be overcome to preserve the proposed mechanism. One possibility is that slip occurs rigidly along a path other than that suggested hy Dick. in a fashion that avoids close contacts. Alternatively. the molecule may undergo deformation. PETN is comprised of atoms bonded together by single bond•s, except the terminal oxygenii of the nitro group. Normally, rotation about singlh' bond (a;n occul In the ga.s phas,. %Nith1oil a small cost in energy. For example, the barrier to rotation ,tbont the O-NO 2 bond otl methyl nitrate is estimate(] between 0-7 kcal/mol. from both, theory and experiment.3 iI a nioleculik crystal, however, interactions with neighboring molecules (in aid Indeed do cause tie hindrance of such rotations so that the molecule is essentially frozen in , small neighborhood about -t single configuration. It is therefore possible to obtain an accurate x-ray crystal structure for l'ETN.' During shear. the environment about t! - - lecule changes and rotation of parts of the molecule may become pc--:;' ' .... dramaticai. .,tnge the stress required to produce shear slip. It is desirable to develop a more detailed description of Dick's experiment iii particulai and other crystal behavior, because of the possible insight into initiation mechanisms. it affords. It is the purpose of this paper to consider the possibility of rigid slip along other paths with significant resolved shear stresses. The possibilitv of decreas-ed resistanc' to slip resulting froni molecular deformations has also beei investigated.
Mat. Res. Soc. Symp. Proc. Vol. 296. ' 1993 Materials Research Society
100
RIGID SLIP Because of the complicated shape cf PETN, it was desired to determine if paths that avoid close contacts other than those proposed by Dick exist on the slip planes. This was accomplished using the observed crystal and molecular structure of PETN. 40 The unit cell (shown in Figure 1) was translated to form two blocks comprised of 3x3xl unit cells each. One of the blocks was displaced in stepwise increments along each of the repeat vectors spanning the plane. This procedure gave crystal geometries in which one of the blocks differed from the initial equilibrium configuration by an amount a'v 1 + b*v 2 , where v, and v2 are normal lattice vectors spanning the plane of interest and a and b are fractions between zero an(d one. At each geometry generated in this fashion the closest atom-atom contact between different molecules was calculated and stored. The resulting mesh of values was used to produce contour plots. Figures 2-4 show contour plots of closest contacts for slip on (110). (100). and (101).
View down
o,
e0
0.
-1
..
0o
View down
View down 1I
V 9
pf
V
_
_
_
__
_
_
_
-1
Fi'gure 1. T hree ort hogr,qipi 1(,'1ragcial latt ic
__
_

__.
0
v'., m
.
-10
of
- _. _
_
_
_
_
_
_
_
_
_
0
TSNnit uI ceii and repro•s,•ntatio n of bodh-(cenered
3
101
Rmin on (110) O-
©
AO 0
0!
0
0.2
0.4
0.6
0.8
1
Figure 2. Contour plot of closest atoin-atoni contt Iis etween PET.N molecule.- Im rigid di., placement on (110). The axes represent oni. repeat unit ,i the indicat ed direction. '1 he first
contour encountered from any corner is 2..4 A. Subsequent 'contoursare 0.2 A apart These planes contain the maximum resolved shear sitre.s %ystet, Identified by D)ik. III accord with previous analysis, inspection of Figure 2 shows slip along (I 10)< Ill > results III two close contacts between 1.0 and 1.2 A. Interestingly., a path pa.ssing throughi• thli col, at about 0.25. 0.15 and 0.7, 0.85 can he identified that diflfer, old 'v slight lv from lie proposed patth. ',t would lead to a considerable reduction of sieric hindranC',. li,•, patli re(•ult, li ( lo.wl m tt 1.i of between 1.I and 1.2 A. which is considerabl% long':. tlia. that fo: - Ill .. rILeoroush. Figure 3 shows closest colltacits oI (10(01(.Slip on< W. ) • hllo%'- .1 .iiihlv i,-' colitat I ailll slip on shows tiree. in agreemnenIt with thI. f•r' sil•P .niv %y.tem beinog insen sitive and thw latter sensitive. Again. it is founid that a path pas.ing hlirough appi oxalnl 0.2. 0.71 ditl'e•
onhl -';, t tly from the proposed slhi system and yvel would lead to a significant reduction III stt... 'indrance. This path would result in a closest con tma of betweenl 1.0 and 1.2 : -h' 1 is significantly longer than that of about 0.8 A otherwise. Slip oil is cla.ssiied ;is sel.n,•lv atd a number of close contacts in this direction are encoulntere(d. as showii in Figure:r, :1 'l'h distinction between this direction and is clouded somewhal., however. if dvviat ions are
allowed. Slip to approximately 0.2. 0.5 followed bv slip along results Ili close contact., of between 1.0 anld 1.2 A. nearly the same as that found for ;adeviationi of shII) ('iI 4the < 101 > direction shown
102
Rnin on (100) 1S00
0
04:
0
0
02
0.4
0.6
0.8
1
Figure 3. As in Figure 2. but for displacem'mnt on (100). in the figure is symmetry equivalent) is classified as sensitive. Inspection of Figure .t shows that translation in this direction always results in very close contacts. This is in agreement with previous analysis by Dick. In performing the above calculations it was noticed that a significant spacing between molecules is observed when the crystal lattice is viewed down . 'This is shown in Figure '). This suggests that the slip system (001) should NOT be s.trically hindered. Th'v contour plot of closest approaches on (001) is shown in Figure 6. It shows that rigid silp along results in oi!y a single close contact of slightly less than 1.4 A. This is longer than any of the closest contacts found for any of the other slip systems considered. ('onsideratioli of tli. shock orientations ciassified as sensitive by Dick, namely -001 > and . show there is no resolved shear stress along (001). So including this slip coes not alter previous argumenlts about the shock sensitivity. However, a resolved shea; stress would result in this direction from a shrk parallel '.o I .,;r example. Such oriettations have not beeni studied. Thus•. expeaiine..' .: btudy of an orientation with a maximunm resolved shear str,., on (001 )< 101 > would be a new test of the steric hindrance concept. MOLECULAR MECHANICS An estimate of the repulsion energy for contacts half of normal separations. such as
103
Rrdn on (101) 0V
4®0%
0 0
40 -
0
00 00 0
0
02
0.4
0.6
0.8
1
Figure 4. As in Figure 2. are found in the rigid displacement of PETN. may be made by assuming a R- ` dependence. The resulting factor is about 4000. Assuming an equilibrium repulsion energy on the order of a kcal, the resulting repulsion energy at these close separations would be enormous. Another relevant fact is that the inter-pianar spacing in graphite and TATB. where rigid slip is operative. is 3.35 and 3.29 A. respectively. Consequently. the close contacts found for PETN are far too short to allow for any conception of slip on these planes occurring by rigid displacement. 'This has led to the consideration of the possibility of molecular deformations occurrini during shear. The calculations were performed using the program AMIERB.O It hias a ,molecular mechanics package in it that was used in this work. Briefly. the energv of molecular distortions is calculated using Eq. 1. below.
E-total
SKr(r
rq)2 +
bonds
+
K eiO
-
1 + Cos (11c
0,q
anglrs
I
-+
-
I)
dthedraL.,
',-
[-,
2•]
(+)
104
VMw on
0m-
350 0C. Thus, critical temperatei, is tar initiation criterion. Here critical temperature increases of 150 and 250 0C are examined to looK for possible data trends (only the highest impact velocity cases reached AO = 350 -C). For this criterion the baseline case is perfectly plastic with a yield stress (68.9 MPa or 10,000 psi) and friction constant chosen so final computed sample radii are reasonable at impact velocities used in previous experiments 2 (see Table I). Baseline density and geometry, drop-weight mass, and all impact velocities also correspond to typical experiments-. The anvil is
109
assumed rigid (mass = 10,000 kg), and the sample specific heat is 0.34 cal/g°C (1423 J/kg 0C)i. A second initiation criterion is adiabatic shear banding in the propellant. Winter and Field10 and Moban et al.II both discuss the importance of localized flow in drop-weight impact. For a power law strain and strain-rate material, Staker gives the critical true strain for adiabatic shear12 , which when applied to drop-weight impact is (see Nomenclature)
pm R This critical strain defines a critical thickness for shear band formation at the sample edge where friction causes the largest thermal softening. A simple linear thermal softening model is used here; d•oIdO equals the instantaneous flow stress divided by -300 1C. Below, the effects of varying ni, n2, and K are studied. As before, the baseline case gives reasonable final sample radii when compared with experiment. The different cases are shown in Table II. Thus, two critical conditions are defined for drop-weight impact initiation: a critical temperature for AP decomposition, and a critical thickness for adiabatic shear banding. Model results are discussed below; for a more detailed analysis see the authors' previous paper.-. Table I. Effects of sample thickness, impact velocity, friction, and yield stress on sensitivity of an HTPBIAP propellant sample as determined by work to reach a critical temperature increase. Case
Initial
Impact
Yield Friction
Max.
NoLaver
0.1 mm Laver
Number Thickness Velocity Stress Constant Temp. WS at WS at Wsat W at 1 is Increase Ae = 150TC AO = 250°C AOL = 150C IAOL = 250°C Baseline
(mm)
1
1.16
2 3 4 5
1.00 1.32 1.16
(ms) (Mpa)
m
M
(1)
0.4
297
.--
348 258 122 737
8.4
68.9
j ----L-5.54 12.95
6
8.4
(0)
(U)
(.)
6.83
10.98
6.38
10.90
5.86 7.81 N/A 6.83
9.44 12.40 N/A 10.98
5.83 6.73 N/A 6.38
9.42 12.47 N/A 10.86
34.5
308
6.53
10.58
6.46
10.51
7 8
138 68.9
1.0
283 305
7.18 6.58
1i.54 1().72
9
68.9
0.1
287
7.22
11.44
4.18 3.14 7.21
9.13 7.68 1.41
1
The initial radius is 2.5 mm; drop-weight mass is 367 g, density is 1.83 g/cm 3. For values marked N/A, the sample did not reach he temperature for that case. Table II. Effects of varying material constants and impact velocity on shear banding of a power law strain and strain-rate hardening propellant sample. Case 1i is Baseline
Impact Velocity (m/s)
Strcngth Coefficient K (MPa
11 12 13
5.54 8.40 12.95
23 23 2'-
-ý
I
q.40
15 16
Sirain Exponent Di -0 0.2
Strdin-ratc Exponent D
Final Saimplc Radiu, mm)
Tbhckncss at bandw l. (mm'
Sample Work at1 Banduing (
5.5i 7.2; 9.4i
0.4i 0.4 (0.4.
2.1') 2.44 2.54
.
9.10
0.31
2.18
46
5.72
0.61
2.5t
7.30
0.55
1.82
7.11 5.y(,
0(.38 0.54
2.80 2.78 1.94
nwi
0.12
0.1 0.3
17 18
0.18 .
....
I
09
=R
0..3,
110
CRITICAL TEMPERATURE RESULTS The maximum temperature rise in Table I, AO,w, neglects axial gradients and assumes all drop-weight energy has been transferred to the sample. Actual temperatures are lower since
some energy is lost via elastic vibrations through the machine. AOmax decreases as initial sample thickness increases (Cases 1-3) since the ratio of compression to friction work increases. Also, the work to reach critical sample or layer temperatures increases with thickness. Incontrast to these results, the work per unit sample mass for 0.1 mm layer temperatures decreases with thickness. Thus, data must be analyzed carefully since the actual intrinsic drop-weight initiation probability is only indirectly a function of thickness through loading and loading rate. Layer size affects temperature rise greatly. Figure 2 shows temperature rise histories at the baseline sample edge for 0.05 and 0.1 mnun layers and no layer. For 0.1 mm the temperature returns to that of no layer when the sample thickness equals 2TL. However, for TL = 0.05 mm, the sample is always thicker than 2 TL, so the layer temperature never returns to the no layer case. The AOma= variation with imact velocity (Cases 1, 4, and 5) correlates with the percent consumed results of Baker et al.2 . At the three different velocities of 5.54, 8.4 and 12.95 m/s, the percent of sample reacted was on the order of 5. 50, and 100% respectively 2. From Table I, at 5.54 nm/s A9ma, is almost enough for the onset of AP decomposition; at 8.4 m/s 4A max is about where rapid AP decomposition begins, and at 12.95 m/s AP would decompose vigorously 9. This indicates that friction may explain impact velocity effects on the extent of reaction. The results do not change for 0.1 mm layers since the final thickness is less than 2TL so AOmax = AOL.max.
For friction variations, this model predicts WS to reach a critical temperature increases with
decreasing friction constant. This agrees with critical energy measurements by Coffey et al. for a binder/AP explosive on polished and rough anvils'. As friction decreases, a larger fraction of Ws goes into compression and bulk heating, so more energy is needed to reach critical temperatures. The effect is small when friction heat is distributed uniformly over the thickness, but if focused in layers, as shown by Cases 1,8 and 9 in Table I, friction effects are enhanced. Equation (1) shows a large flow stress effect on deformation, and Cases 1, 6 and 7 show a localization dependent yield stress effect on critical energy. For uniform friction heat, weaker materials have smaller critical energies and are more sensitive, but the effect is reversed for friction localization. Thus, since localization is likely, increased ay increases sensitivity.
400.
0' - -Rapid AP Decomposition (Deflagration) L' 300
S200TL 200STL
=0.05 mm/ 0.1 mm
4,
2
-'-AP
Decomposition T= 2 TL
1l00
00 0
50
100
150
Time after Impact (gis) Figure 2. The effect of layer thickness on hOmav for the baseline case, 1.
111
SHEAR-BANDING
CRITERION RESULTS
Table i1 shows the shear-banding initiation criterion results. Sample thickness and plastic work when flow becomes unstable are reported. Equation (4) indicates that critical strain and, hence, critical thickness, Tc, are functions of deformation. Critical thickness increases as actual thickness decreases; when the two are equal banding occurs. Baker and Mellor5 discuss Eq. (4) and how changing material constants can have the competing sensitivity effects of decreasing critical strain but increasing critical energy. Here we simply highlight those results. For the range of impact velocities chosen, the thickness at shear banding is nearly constant. On the other hand. the energy to cause banding increases with velocity since flow stress increases
with strain rate. Cases 10, 13, and 14 show that increasing strength via K increases Tc by
enhanced thermal softening, but also increases the work to cause banding via an increased flow stress. Similar to increasing K, increasing nj also raises the flow stress; however, unlike K, increasing nj decreases Tc while increasing the sample work for banding (Cases 11, 15 and 16). Thus, a highly strain-hardening material is desirable for low sensitivity based on this criterion. Cases 11, 17 and 18 show the net effect of increasing n2. Increasing n2 is like increasing K in that it increases Tc. Thus the thermal softening effects outweigh the strain-rate effects from the
second term in the denominator of Eq. (4). Also, increasing n2 increases the work required for banding by increasing the flow stress. Consequently, these results indicate that any change in the material constants which raises flow stress will reduce sensitivity based on this criterion. CONCLUSIONS Results from a drop-weight impact sample deformation model were interpreted in terms of two initiation criteria. Effects of sample thickness, friction, yield stress, and impact velocity were studied for a critical temperature criterion, and varying power law material constants was studied for a shear banding criterion. Initiation at a critical specimen thickness corresponding to an AP particle size was analyzed previously 5 and was shown unlikely in view of experimental results 1,2 .
Friction results supported previous experimental data1 by showing increased critical energy when friction was reduced (for a critical temperature criterion). This result was magnified when friction heating was localized. Friction is also important in explaining the percent of sample reacted observations by Baker et al.2; at low velocities the maximum temperature (at the sample edge) is less than the AP decomposition temperature, and at the highest impact velocities the temperature is above the AP deflagration point. With localized friction heating, increasing yield stress decreases the energy required to reach the AP decomposition temperature. Therefore, for a critical temperature criterion, this model predicts a higher strength material has a lower critical energy and, consequently, is more sensitive. However, the trend is reversed when Ihcalization is ignored, and the shear banding criterion predicts that any increase in flow stress decreases sensitivity. This indicates the importance of knowing the hot-spot mechanism for a given scenario. There is no doubt that friction affects the apparent sensitivity in a drop-weight test. The large friction effect may partially explain differing results for identical materials on otherwise identical machines. Also the drop-weight test presents a unique loading on the propellant; strain rates in excess of 104 s-i and strains greater than 500% exist in constrained flow of less than 1 mm thickness. Thus friction causes a large amount of heating in the flow. However, removing friction (a very smooth anvil) may allow crushing of AP in the machine to come into play; this AP cons.'aint between two rigid surfaces would make the drop-weight test unlike any real impact scenario. Therefore, for propellant rankings useful in other scenarios a constant friction coefficient is desirable, but in order to fully understand the drop-weight test some additional basic research is needed. First, a quantitative study of friction effects on propellants with varying particle sizes can be conducted. Second, using samples of homogeneous materials with known mechanical properties similar to propellants, it should be possible with this model to estimate the friction constant of an impact machine, thus providing a means to compare i: y,...t im .hines and interpret data. Third. details will be added to this model to account for sample inhomogeneities and study shear banding in more detail. The improved understanding of the deformation process would facilitate relating critical energy results to other scenarios.
112
ACKNOWLEDGMENTS This work was performed under Contract DAAL03-89-K-0061 with the Army Research Office. The views, opinions, and/or findings contained in this paper are those of the authors and should not be construed as an official Department of the Army position, policy, or decision, unless so designated by other documentation. Program monitor D.M. Mann provided funding
essential to this research. NOMENCLATURE
k
Englih c E K m M n,
: Mass specific heat :Energy : Power law strength coefficient : Friction constant :Mass : Power law strain-hardening exponent
e 9 p a
: True strain : Temperature : Density : Stress
Subscripts
n, : Power law strain-rate exponent
A
r : Radial coordinate R t:: Tune Sample radius T : Sample thickness U : Velocity W : Work
C Critical condition F F:FitoFriction I Internal deformation L : Layer at the sample/machine interface W Drop weight y : Yield
Anvil
REFERENCES 1. C.S. Coffey, DeVost, V.F. and Yergey, B.A., JANNAF Propulsion Systems Hazards Subcommittee Meeting Proceedings (CPIA Publ. 446, I, 1986). 2.
P.3. Baker, Mellor, A.M. and Coffey, C.S., J. Propuls. Power. 8, 578 (1992).
3. C.S. Coffey, DeVost, V.F. and Woody, D.L., JANNAF Propulsion Systems Hazards Subcommittee Meeting Proceedings (CPIA Publ. 477, I, 1988). 4. G.T. Afanas'ev and Bobolev, V.K., Initiation of Solid Explosives by Impact, (Israel Program for Scientific Translations, Jerusalem, 197 1). 5. 6.
PJ. Baker and Mellor, A.M., AIAA Paper 92-3631, 1992. B. Avitzur, Metal Forming: Processes and Analysis, (McGraw-Hill Book Co., New York, 1968).
7. B. Avitzur and Kohser. R.A.. J. Eng. Ind. 100, 421 (1978). 8. C.S. Coffey, Frankel, M.J., Liddiard, T.P. and Jacobs, S.J., Seventh Symposium (International) on Detonation, (NSWC MP 82-334, 1981) pp. 970-975. 9.
P.W.M. Jacobs and Whitehead, H.M., Chem. Rev. 69, 551 (1969).
10. R.E. Wint: - url Field, J.E., Proc. R. Soc. Lond. A 343, 399 (1975). 11. V.K. Mohan, Jyothi Bhasu, V.C. and Field, J.E., Ninth Symposium (International) on Detonation, (II, OCNR 113291-7, 1989) pp. 1276-1283. 12. M.R. Staker. Acta Met. 29, 683 (1981).
113
HOT SPOT HEATING FROM IMPURITIES AND VACANCIES IN A CRYSTALLINE SOLID UNDER RAPID COMPRESSION D. H. TSAI 10400 Lloyd Road, Potomac,MD 20854 ABSTRACT The role of impurity atoms and vacancy defects in the heating of hot spots in a 2D, fcc, monatomic lattice, subjected to rapid, 1D compression, has been studied by means of molecular dynamics. The interaction potential of the impurity atoms, their mass, and size were allowed to differ from those of the atoms in the host lattice. Several configurations of impurity and vacancy clusters were examined. The mechanisms of heating observed here were similar to those found earlier' in a bcc lattice with vacancy defects but without impurities. I. INTRODUCTION In Ref. 1 we discussed the molecular dynamics of structural relaxation around defects (vacancy clusters and slip bands) and its effect on hot spot heating in a 2D. bcc, monatomic lattice when the lattice was rapidly compressed. We found that two mechanisms were responsible for the heating of hot spots. First, since in all systems, in the gas, liquid, or solid phase, the kinetic energy distribution in equilibrium is Maxwellian, there would always be some regions in the system that are hotter than the average. Second. in the condensed phases, particularly the solid phase, rapid compression would often initiate structural relaxation in the system, especially if the system also contained defects. The potential energy released by the relaxation process would be converted locally to kinetic energy, creating hot spots in the relaxing region. The amount of heating was a function of the energy of defect motion. If the strain energy of the defect should be large, then a small change in the strain energy could result in a large amount of heating. The relaxation process, moreover, often would not be confined to the local defects, because the comprf ssion could create defects in other parts of the system. For example, the large shearing stresses from 1D compression could generate a system of slip planes which could propagate from their starting sites. The energy associated with the creation and the relaxation of the new defects would then cause additional heating. Thus hot spots could occur in a much larger region than the immediate neighborhood of the original defects. We have now extended our defect model to include impurity atoms with mass and size different from those of the host atoms. We have also investigated hot spot heating in an fcc lattice which, for central forces, should be more stable than the bcc structure. Because of space limitations, we shall discuss only one set of results here. The model is described in Sec. II. Some of the general results are discussed in Sec. Ill. and the conclusions are summarized in Sec. IV. A fuller account of this work, including a comparison between the fcc and bcc lattices, will be presented elsewhere. II. MODEL Our model was an fcc lattice installed in Cartesian coordinates with the X and Y axes aligned in the [1101 and [T10] directions, respectively, and the Z axis in the 10011 direction. In this arrangement, the ratio of the distances between lattice planes normal to the X and Yaxes and between lattice planes normal to the Z axis would be 1,/2. Our system was 40 lattice planes in the X direction. 20 in the Y direction, anC planes in the Z direction, and periodic boundary conditions were ust iithe X and Ydirections. These lattice planes divided the system into contiguous cells. The position of an atom in a cell was measured from the origin of that cell. and the atom was allowed to move freely across cell boundaries. A cell without any atom in it would be a site of a vacancy. To save computation, it was assumed that all atoms had only in-plane (i.e., 2D) motion in the X-Y planes. and that the motion of corresponding atoms in all (001) face planes and in all (001) body planes, Mat. Res. Soc. Symp. Proc. Vol. 296.
1993 Materials Research Society
114
respectively, was identical. This meant that the forces in the Z direction would exactly cancel, and hence only two (001) planes of the unit cell (400 atoms) need be considered in our system. The interaction potential V= V, between atoms i andj at a distance R=R, was assumed to be a Morse potential: V = AabE {exp[-2a (R-Rab)]-2exp[-a (R-Rab)]} + Bah,.
(1)
Here E 1.0 is the unit of energy anO a =bI 2/0.1. The parameters Aab, Rab and Bab are given below for the different cases listed in Table 1. The subscripts a and b refer either to host Ih or impurity i:
Cases 1-6:
Ai, = 1.0, Ah, = V/2, A, = 2.0,
Rhh = 1.0, Rh, = 1.05, R, = 1.1,
Bhh = 0.015564, Bh, = 0.031077, B, = 0.062012.
(la)
Case 7:
AM = 1.0, Ah, = v/2. A, = 2.0,
Rhh = 1.0, Rh, = 1.0, R, = 1.0,
Bhh = 0.015564, Bh, = 0.022011, B, = 0.031128.
(1b)
The well depth (Ah,) and the atomic size (Rh,) for the h-i interactions were assumed to be intermediate between those of the h-h and i-i interactions. Ba, refers to the amount by which the zero axis of V, eq. (1), was lowered to make V=0 at the cutoff distance R,=1.7. For RtR•, both Vand its derivative were assumed to be zero. The mass of the impurity atoms, M, was assumed to be either unity, the same as the host atoms, or 10. With Rh, Mh, and C all set to unity, the unit of time t=RhV/(Mh/E) was also unity. In addition to impurity clusters the system also could contain other defects such as vacancy clusters. We relaxed the system to a low pressure condition by adjusting the volume. The volume was changed by multiplying the coordinates (XY,Z) of the atoms in the 'normalized' lattice, with lattice planes at (lIv/2, 1/%/2, 1 ) apart, by scale factors (XS,Y, ZS), respectively. The system was then heated, equilibrated, and relaxed again. This process was repeated until an equilibrium state at near-zero temperature and pressure was reached. Each system was then heated to a range of initial temperatures, and after equilibration, these configurations were used as the starting configurations. The system was subjected to rapid 1D compression in the X direction to different volumes by changing X, at a rate which corresponded approximately to planar shock compression.' The energy and stress distributions in the system were recorded at discrete time intervals until a new equilibrium condition under compression was reached. These data were then examined for the development of hot spots. A hot spot was defined here as a region made up of several atoms (or molecules) whose average kinetic energy Ek was higher than the kT of the system. and moreover, the higher Ek was required to have a lifetime of a few periods ot atomic oscillations, so that the region could be said to be thermalized. Table I. Configurations of some of the cases studied. Fcc lattice, interactions as given in eq.( I ). compression=0- 15% in X-direction. Impurities Vacancy cluster lnitial conditions
Cases 2 4 5 6 7
Cluster
Mass None None 1X9 atoms I 1X9 atoms 10 lx9 atoms I 1X9 atoms 10 1x9 atoms 10
in host lattice None I x 10 atoms None None Figg.Ia Fig.la None
A-, (0.7027 0.7020 0.7(144 0.7044 0.7049 0.7048 0.70013
I'M,
Z
EA,
El,()
0.7027 0.7025 0.7041 0.704A 0.7047 0.7047 0.7000
0.7041 0.7043 9.70901
0.0053 0.0049 0.030o 0.0315 0.0292 0.0311 0.0305
-6.193% -6.124 -61•53 ..-52 -6.193 -6.192 -6.296
't•07)()
0./082 0.7082 0.7071
115
III. RESULTS We shall discuss only one representative set of results which we select somewhat arbitrarily from Case 5 in Table 1. We shall also refer to the other cases, but without displaying the actual results. With more data available now than in Ref. 1, we shall attempt to present a more general discussion of hot spot heating from the viewpoint of molecular dynamics. Fig. la shows the lattice configuration of Case 5 before compression, at t=0. The atoms in the two lattice planes of the system are shown as open squares and crosses. A cluster of nine impurity atoms were enclosed in outlines at the center. This cluster was of the size of a unit cell. It was flanked by two vacancy clusters. Fig. lb shows the distribution of the potential energy, E., per atom, at each lattice site, averaged over the atom(s) at that site and those at the four nearest-neighbor sites. Epa is the average of the whole system (dashed outlines), and Epm is the maximum that occurred somewhere in the system. The depression at the center resulted from the impurity cluster. The two humps next to the depression were due to the strain energy of the vacancy clusters. Fig. Ic shows the corresponding distribution of the kinetic energy, Ek, per atom, in equilibrium. Figs. 2a and 2b show the Ep and Ek of the lattice as a function of time t when the lattice 20+
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.
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1 1
.
+ -
x
40
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0
20
1'0
X' 0400
20
1.5-
1.0 (C)
....
0.5
...
0
Y
FIGS. la- Ic. (a) Lattice configuration of Case 5 at t=0. AMh=A,= 1. X,=0.7049, Y,=0.7047, 4,=0.7082. (b) and (c) Ep and Ek distributions at 1=0. Epmý=4.i24.
Epa
-6.194;Eb.=0.084, Ek=O.O30.
I, .
116
-4.0(a) -6.0. Ek 12.0 -k i
.............................................
1.5 0_
4.0
....
.....
.4- Eke
8.0
12.0
16.0 Time 20.0
8.0
12.0
16.0 Time 20.0
S~Ek 1.0 i,_Ekm
(b) 0.t
'... 04.0
FIGS. 2a-2b. Ep and Ek vs. time in the lattice of Fig. la when X, was compressed from 0.7049 to 0.6299 in one unit of time. Epm -3.205, E =-5.199;,E•=0.929,E,ý,=0.337. (Fig. 1) was compressed uniaxially from X,=0.7049 to X,=0.6299 at a uniform rate in the first unit of time. Ep_.and Ep, refer to the equilibrated values of Ep, and Epm between 1= 16 and 1=20. EU and EA, refer to the corresponding values of Ek and EAm. Hot spots in elastic compression During the first part of the compression, just before t=0.7 (Fig. 2), the lattice behaved elastically. We ascertained this by stopping the compression at 1=0.7 and re-expanding it to its initial volume. We found that the lattice then reverted to its initial configuration. In elastic compression, most of the work of compression is stored in the lattice as potential energy, the temperature rise is small, and the lattice configuration remains essentially unchanged. For example, Fig. 2 shows that at t=0.7, E, had changed by about 0.4c whereas Ek had changed only by about 0.001 c. The fcc structure in the present case was rather stable, and could sustain a large ID compression without losing its elastic character, even when the structure contained defects. In all cases, we found that if the structure remained elastic, the rise in Ek due to compression would be small, whether or not the system contained defects, and whether the compresssion was ID or 3D. The hot spots (averaged over eight lattice sites and over 0.4) in these cases were not very hot. being only about 2.5 times the ambient temperature, similar to those found in Ref. I for the perfect bcc lattice. These hot spots clearly were the result of the Maxwellian distribution of the kinetic energy in the system, as was the case in Ref. 1. Anelastic/plastic compression: Hot spots from structural relaxation Figs. 3a-3c show the change in the lattice configuration and the energy distributions at t= 1.0 at the end of compression. In Fig. 3a the lines connecting individual atoms show their displacements at the beginning and end of the time interval 0- 1.0. As Figs. lb and Ic show, the strain energy due to th, vacancy clusters was large compared with the kinetic energy of :he l;:t.;re. These s.-,ural defects also tended to reduce the mechanical strength of the lattiLe in the neighborhood of the defects. If the compression should exceed the strength of the defect configuration, the structure could become locally unstable, at which point it would undergo deformation in an attempt to reduce its potential energy. This would allow more work to be done on the defect region than on other parts of the structure, so that the defect region would become hotter. A second and more important mechanism is that the deformation of the defect structure would lead to the conversion of
,
117
a part of the strain energy to kinetic energy which would then bring about local heating. Since the strain energy was large to begin with, a small change in the strain energy could lead to a large amount of heating. We see an example of these two mechanisms of hot spot heating (viz., by compression and by structural relaxation) in Fig. 2. In the interval between 1=0.7 and 1.0, both Eprn and Ek, increased abruptuy. These changes were accompanied by large atomic motion in the neighborhood of the defect structure in Fig. 3 at 1=1.0. The displacements around the vacancy cluster to the southwest of the impurity cluster, and the accompanying rise in Ek were especially prominent. By t=2.0, the large atomic motion around the vacancy clusters had effectively filled the vacancy sites. When we expanded this lattice to its initial volume at the end of compression, we found that the lattice would not revert to its initial configuration. The compression after 1=0.7 was therefore anelastic or plastic. The two mechanisms of heating operated concurrently. To distinguish them, we could say that if the heating was accompanied by a local increase in Ep, then the hot spot would be from compression; otherwise, it would be from structural relaxation. By this criterion, we 200 0 0 0 0 . 0. O... a,.-*
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118i
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40
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could say that the peak Eb, in Fig. 2b (and in Fig. 3c) at t= 1.0 was due to compression, and the second peak at t=1.4, which occurred to the northwest of the impurity cluster, was due to structural relaxation. By either mechanism, a part of the energy of compression was converted to heating each time a hot spot appeared. Fig. 2b)shows a succession of hot spots. These hot spots heated up the lattice as a whole (Ek, in Fig. 2b), until about t= 10, to an average temperature (Ek•=0.337) considerably above that from elastic compression alone. Pronafation of defects Structural relaxati,•n requires time because it usually involves the coordinated movement of a number of atoms. Also, relaxation in one region would likely disturb the structure in adjoining regions, and this could create new defects which might require further relaxation. For these reasons, we expect that structural rearrangements would generally propagate to other parts of the system, and that it would usually require a long time (compared with sound propagation through the system) to obtain a fully relaxed structure. The energy conversion associated with these relaxation processes would then produce hot spots in other parts of the system. Thus the heated region could be much larger than the original defects. Fig. 4 extends Fig. 3a and shows the aggreg.ate changes in the lattice configuration in the interval 1=0-20. Large displacements had oct ,rred along a number of diagonal planes, reaching across the full width of the system. These complex slip systems resulted from the large shearing stresses from the uniaxial loading. The partially slipped planes tended to group themselves into bands rather than to distribute uniformly. They were observed also in a number of other cases in Table 1, and in Ref. I earlier. They appeared to be a common feature of the lattice rearrangement under ID compression. The extent of the slip system was limited in our model by the periodic boundaries. But slip or partial slip should occur also in larger systems. For these reasons, it seems natural to identif~y these slip planes as the counterpart of the shear bands that are observed in experiments.In Fig. 4, the lattice at t=20 also contained a number dislocations.3•4 These dislocations
did not move easily after they were formed, as was also the case in Ref. 1. In addition to the collapse of vacancy clusters and the formation of shear bands and dislocations, other modes of lattice rearrangement were also observed. For example. in the .•rfect
fcc lat.,.c, orf Case 1,the structure buckled in the Y direction when the system was
.ompressed in the X direction to 0.893 of its initial volume. But the lattice retained its
crystallinity, and the temperature rise was small (E,= changed from 0.030 to 0.043). When the buckled lattice was re-expanded to its initial volume, the system reverted to its original perfect structure. At a still higher compression, to 0.858 of its initial volume, the structure buckled to a greater extent, and there was greater amount of heating. Between 1=4-5 the structure underwent massive rearrangement and became disordered, indicating that local
119
melting had occurred. The temperature change in this case was large (El increased from
0.030 to 0.938). When the partially 'melted' structure was re-expanded to its initial volume, the original crystalline configuration was not restored, at least not in 20 additional time units of computation. Hot spots from impurities: Mass and size defects The impurity cluster in Figs. 1 and 3 may be considered as a 'molecule' embedded in the lattice, inasmuch as the interactions h-h, h-i, and i-i were all different. Our interest in this model was in the energy transfer between the lattice and the 'molecule,' when the lattice was compressed. If we denote the vibrational frequency of an atom by f and the force constant of the interatomic interactions by k, thenf of the host atoms of mass Mh and that of the impurity atoms of massMi, each interactingwith its own kind, would be in the ratios'f f,=(MikhAM, ki)MiI. We verified by separate calculations in Cases 3 and 4 that this was true to about 5% which5 was satisfactory. The vibrational frequency is related to the elastic properties of a lattice: the lattice is stronger the higher its frequency and its elastic constant. Thus the impurity cluster should be mechanically stronger and less compressible than the host lattice when the mass of the impurity atoms was the same as that of the host atoms, and weaker and more compressible when the impurity mass was 10 times larger. Under the same compression, the less compressible cluster should therefore experience smaller increase in temperature. We confirmed this in Cases 3 and 4: The softer impurity cluster in Case 4 experienced larger temperature rise under compression than the stiffer cluster in Case 3, although in both cases there were hotter hot spots from defect movement and structural relaxation elsewhere. At the interface between the impurity cluster and the host lattice, there should be some impedance mismatch which would increase the resistance to energy flow across the interface. But there should also be good thermal contact through the h-i type of interactions. The coupling, moreover, would increase under compression. Thus the impurity cluster should heat up quickly when the host lattice was heated, especially if the cluster was small. We found this to be true even in Cases 5 and 6: Here the vacancies partially separaited the impurity cluster from the host lattice before compression. But good thermal contact was quickly established when the vacancies collapsed under load (Fig. 3a). The energy transfer was in fact aided by the hot spots at these sites. Thus in the various models of Table 1, the impurities clusters never appeared as 'cold' spots, even when the cluster was stiff. These results may be compared with the analysis of Dlott and Faver.6 They postulated that in a molecular solid under shock compression the increased phonon vibrations of the lattice would briefly overshoot the bulk temperature. Subsequently. molecular vibrations would be energized through anharmonic coupling between the lattice and the molecules through the 'doorway' modes. In addition to the different mass, the impurity atoms in Cases 3-6 were also larger than the host atoms (Rob in eq. (Ia)). The larger size had the effect of distorting the lattice structure. For example, Fig. la showed a slight distortion of the host lattice around the impurity cluster. But small misalignments in the lattice structure could have large effects on its strength. We found evidence of this by comparing Cases 4 and 7. in which only the size of the impurity atoms was changed. and both cases contained no vacancies. Under moderate (about 10%) compression, a number of slip planes formed in the lattice of Case 4, similar to Cases 5 and 6 in which the lattice was weakened bv vacancy clusters next to the impurity cluster. In contrast, the lattice of Case 7 deformed primarily through buckiing. similar to the perfect lattice of Case 1. the strongest structure by far in Table 1. Finally, we note that in many cases the impurity cluster underwent large detormation and was grossly distorted when the compression was high. But in the r. : of our investigation we did not observe any break up of the cluste.. e,:'- '-,ienthe structure was partially melted. IV. SUMMARY AND CONCLUSIONS We have discussed some of the results of our molecular dynamical study of hot spots in an fcc lattice under rapid. uniaxiai compression. Our focus has been on the role of structural
F 120
defects and the mechanisms of heating on an atomic scale. The defects included vacancy and impurity clusters of different sizes and geometries. Under elastic compression, most of the work of compression would go into the lattice as increased potential energy, whether or not the lattice contained defects. The temperature rise would be determined principally by the PFTrelation of the perfect lattice, and the rise would be small. In these cases, we found that hot spots developed from the Maxwellian distribution of the kinetic energy. They were about 2.5 times the average temperature of the lattice, and were not very hot. This was similar to the case of the perfect bcc lattice in Ref. 1. When the compression was reversed, and the lattice was allowed to expand to its initial volume, the initial configuration was restored, including the defect structure. This was so even if the compressed lattice had buckled elastically under load. Under larger compression, if the elastic stability of the lattice should be exceeded, the structure could also undergo anelastic or plastic deformation. This kind of deformation could occur in a variety of situations. For example, if the system contained structural defects (vacancies, impurities, etc.) which generally would tend to weaken the mechanical strength of some part of the structure, the weakened part(s) would undergo structural relaxation. The relaxation would release some of the potential energy of the defect structure, and convert it to kinetic energy of the surrounding atoms and local heating. This mechanism of hot spot heating was general, and would operate as long as defects should be present. In this picture, the heating would then be a function of the energy of defect motion, which could be large compared to the temperature of the system. Moreover, structural relaxation in one part of the system could propagate to other parts, and the energy associated with such rearrangements would give rise to other hot spots. Thus the size of a hot spot could be considerably larger than the initial site of structural relaxation. Under uniaxial compression, which would generate large shearing stresses in the whole system, complex systems of slip planes often propagated far from the initial site of structural relaxation. These slip planes would group themselves into bands, which suggest that they could be identified as the shear bands commonly observed in shock wave experiments. The hot spots also heated up the lattice as a whole. Our results showed that the amount of heating, which was large in some cases, depended on such factors as the lattice structure, the nature of the defects and their configuration, the method of compression, etc. These factors affected the response of the model through the different paths of structural relaxation, leading to different end states of partition between the potential and the kinetic energies, and hence different PVT relationships. In view of these results, it might be reasonable to ask whether the differences would persist, and how large they might be, in a more realistic 3D model. These questions require further investigation. ACKNOWLEDGMENTS I thank R.W. Armstrong, L Phillips, B. Rice. S. Trevino and P.K. Tsai for helpful discussions in the course of this work. REFERENCES 1. D.H. Tsai, J. Chem. Phys. 95, 4797 (1991). 2. C.S. Coftey, W. Elban, and S. Jacobs. Proceedings of the 16th JANAF Conference on Combustion, Hampton, VA, 1980. 3. D.H. Tsai, in NA TO ASI Series, edited by S.N. Bulusu (Kluwer, the Netherlands. 1990). Vol. 309, pp. 195-227. 4. F.A. Bandak, D.H. Tsai, and R.W. Armstrong. in Sizock-wa'e and high vera,.:-ra(te phenomena in materiaLv, edited by M.A. Meyers, LE. M., ,-!. K.P. Staudhasimer, (Dekker, New York, 1992), pp. 957-967. 5. C. Kittel, Introduction to solid state physics. 3rd edition, (Wiley, New York. 1967), Chap. 5. 6. D.D. Dlott and M.D. Fayer. J. Chem. Phys. 92. 3798 (1990).
PART m
Shock Phenomena
123
DISSOCIATIVE PHASE TRANSITIONS, SPLIT SHOCK WAVES, RAREFACTION SHOCKS, AND DETONATIONS
C. T. WHITEt, D. H. ROBERTSONt, M. L. ELERTt, J. W. MINTMIREt, and D. W. BRENNERt tTheoretical Chemistry Section, Naval Research Laboratory, Washington, DC 20375 tChemistry Department, U. S. Naval Academy, Annapolis, MD 21402
ABSTRACT We present a comparative study of two different chemically-sustained shock waves. One shows behavior expected from the Zel'dovich, von Neumann, and Doering (ZND) continuum theory of planar detonations. The other exhibits the complexity of a split shock wave resulting from the presence of a polymorphic phase transition. This comparative study demonstrates the importance of carefully considering the high-pressure characteristics of the model in developing potentials for simulating detonations. This comparative study also raises the fascinating possibility of a first-order phase transition accompanying a condensed-phase detonation. INTRODUCTION The shock wave accompanying a detonation typically travels through energetic materials at a velocity between five and ten kilometers per second [1]. This shock wave starts the material flowing a kilometers per second while heating it to thousands of degrees Kelvin and subjecting it to pressures of hundreds of kilobars. This rapid heating and compression of the material in turn causes the exothermic chemical reactions which ultimately sustain the detonation [1-31. Although there have been many theoretical and experimental advances in understanding the macroscopic properties of detonations over the last forty years 11-3]. much work remains to be done to clarify the atomic-scale behavior of shock-induced chemistry in energetic solids [1]. Continuum theories are not designed to treat discrete shock-induced chemistry while the extremely short time and length scales of the processes involved. together with their destructive nature, make experiment difficult and costly, if not currently impossible. In contrast, the picosecond and nanometer length scales of processes at shock fronts make them ideally suited for study using molecular dynamics (MD) simulations[4-11]. Such simulations might also clarify how discrete detonation chernistry relates to properties of planar detonations that can be understood by continuum (hydrodynamic) theories. However. any model of a detonating solid requires some form of energy release to sustain the detonation and so the Lennard-Jones potentials. which are successfully used in MD simulations of nonreactive shocks [.5]. are inadequate. Earlier MD studies have introduced exothermic chemical reactions by using a predissociative potential that incorporates al! $'), chemical energy release into a single bond dissociation e S)].In energt.,. materials, however, exothermicity typically results from in a mc' the reorganization of bonding from weak to strong bonds. Therefore. predissociative potentials do not include sufficient detail to examine the atomic features of shock-induced chemistry. Studies in one dimension [9] showed the promise of employing many-body
Mal. Res. Soc. Symp. Proc. Vol. 296. 11993 Materials Research Society
124
potentials to study chemically-sustained shock waves, but the potential used in that
work was ill-defined in higher dimensions. Recently, we have introduced a new approach based on many-body potentials that not only describes bonding and chemical reaction at the atomic level with well-defined
reactants, products and reaction paths but also allows for efficient computation in MD simulations involving thousands of atoms in two or three dimensions [12]. Simulations in two dimensions proved that this model can support a chemically-sustained shock wave with calculated temperature, pressure, particle flow and shock velocities, and power generation all consistent with macroscopic experimental results and the classic continuum theory of detonations [12]. These studies have also established for the first time a quantitative link between results from MD simulations that follow the individual atomic trajectories and the continuum theory of detonations based on the Navier-Stokes equations. In this paper we present a comparative study of two qualitatively different chemicallysustained shock waves. The two models used in these studies are based on deceptively similar many-body potentials. This comparative study vividly demonstrates that it is not sufficient to focus only on reproducing physically reasonable reactants and products with realistic barriers to reaction in developing many-body potentials for simulating solid-state detonations. Rather, the high-pressure character of the model must also be carefully considered. This comparative study also illustrates the fascinating possibility of a chemically-sustained shock wave accompanied by a dissociative phase transition. MODEL AND METHOD Both Model I and Model 11 used in this comparative study are based on the empirical bond order (EBO) potential form introduced by Tersoff [13] to describe the static properties of silicon but tailored by us in Ref. 12 to describe a simple generic model of an explosive-a model AB molecular solid that when shocked might undergo exothermic chemical reactions to form the more stable A2 and 1, molecular products. In both models formation of the A2 and B2 products releases :1 eV of energy per molecule. It is this release of energy that has tile potential for sustainfing the shock wave. Model I Ila, already been introduced in Ref. 12 and shown there to yield a physically and chemically reasonable model material. The functions used to define Model I1are identical to those used to describe Model I. The parameters entering these functions are also identical in the two models exccpt for the equilibrium bond lengths of the reactant and product diatomic molecules which have been decreased from 0.12 nm in Model I to 0.1 nm in Model II. Because of the form of the EBO potential. this decrease in bond length is accomplished without changing the vibrational ftIeq(Iencie.s of the reactant and prodctic molecules, their equilibrium molecular and cr'stdhlime binding energies. and distan(t' of closest approach between atomis it micare.ý iemigliborhig lilolecimli.e ill t ilt, (oidel.,se'd phase AB crystalline molecular solid. lRea( tion Iarriems ae aim•, isinnar bli ween time 1t, models as are their respective condensed-phase speeds of ,oumid.
MD simulations in two dimensions using bothi immode., are initiat ed Iy i pacti .g a flyer plate at the edge of the semi-infinite model dhatomitc .13 molecular cr'v.St al iitliallx at rest and at near zero teml'pe-sture and )irc - ,fhiis vlyer plate< is composed of several layers of the unreacted energLic A13 molecular solid appropl rale to the mitodel. Hen'e. for Model I a flyer plate composed of Model I material is used. while for Model II a flyer plate composed of Model II material is used. T'he dynanic.- of the atoms in bothli systems are then propagated by integrating Ilamiltoniai'., equation, of motion using a Nordsieck predictor-corrector method [1.11. Periodic l)oundarm conditionls are enforced
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molecules are compressed to the point that they lose their molecular identity but without the large-scale production of molecular products. Although tile density is higher in this dissociative region than in the leading compressional region. the average nearest-
neighbor interatomic separation has actually' increased due to the greater coordination of the atoms. In addition, the dissociative region in Model II is separated from the
products region at the far left of Fig. 1 by a distinct boundary across which the majority of products are abruptly produced. Furthermore, as Fig. 2 shows. Model I1also exhibits a developing flat-topped shock-wave structure rather than the peak and following Taylor wave exhibited by Model I. Although the three boundaries separating the four distance
regions in Model I--like the single boundary in Model I-rapidly stabilize to steady velocities, we have found that these boundaries move at velocities of 7.2. (6.4 and 5.9 km/sec [15]. Hence, the lengths of the icading compressional and dissociat ve regions in Model II enlarge to millimeters in microsecond% Through longer time simulations and varying initial condiitn-is we have verified that the qualitative differences in the cliemically-sustained shock wave, exhibited I v .Model I and Model II are not artifacts of the starting condit ioni but are rat her int rini properl ieof these models. Thus. although IM1odel I and .Model II onlv essentially dilfer at ambient conditions in their bond lengths. these models nevertheless suppoti altogether diflerent chemically-sust P: . ,' shock waves. We have traced the shock-wave splitting present ill Model II to a linst-order polymorphic phase transition accompanied by a volume collapse [l(i6. This volume collapse has been made possible at the temperatures and pressures of lhe chenfically-sustained shock wave in Model 1I by shortening the equilibrium bond lenathlin without changing
127
the intermolecular potential. This polym-orphic phase transition is a dissociative one where the AB diatomic molecular solid transforms to a close-packed material with much higher density but larger average nearest- neighbor interatomic separations. More than 35 years ago the first shock induced polymorphic phase transition was observed [171. An important property of these phase transitions predicted from continuum theory [17-1!)] and observed experimentally 117-19) is the associated compressional shock wave splitting that might occur. If split compressional shock waves are present. then continuum theory predicts [17] that the leading shock front starts the material flowinig bi ingina it to the point of transition while the tr-ansition occurs across thfe second compressional shockfront. This is just the behav'ior (,..served in Model 11. Actually. there are not one but two polymorphic transitions visible in the snapshot of the Model II simulation,. This second transition occurs at the interface between the dissociative zone and the rarefactioni region as the material transforms from the dissociative close-packed phlase to A2 and lB. molecular products. It is this second transition which produces the required behavior in the shock liugoniot for a rarefaction shock wave. This product rarefaction shock front acts as a stcadily moving piston producing the flat-topped shock-wave sitructure't observed in Model 11. In contrast, in Miodel I there is no evidence for either transition and the simulations evolve towards a classic ZIND dectonationi. Shock induced phase transitions accompanied by shock wave splitting are well kiio% ui in energetic materials. The possibility of a dissoitv las rniinidcdb chemicallyv-sustained shock wave is fascinating because this behavior might Yield a miore efficient conversion of chemical energy to uiseful %vork. T'o our knowvledge, liowevem a chemnically-sust ained shock wave accompanied l) a first-order pliasc transit ion has, Yve to be observed. At. a minimium, the resut,i of the coimparat ive stutid> bet 'veeil Model I and Model II demonstrates the importance of carefully coiisideriiig Ilie high-pressure characteristics of the model iiideveloping potentials for -simullatingu condens~ed plia-w detonations. .
SUMMARYV ivr 'l~e(Iht ~ l Ve have presented a comniaratilve SzIItl. of mo (iilia i~u sustainied shlock~ wavc.. one siioxv, l leia~io: eN Ied e(-i Iiil I~ii '. N II~,I IlS~lilt ili 1 detonations. T1hie other exhibiit, I lie eo1II&NplOi ~1.a~splil 'ilmo presence of a polymnorphic phaset-Iansitiun1.
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REFERENCES [1 W. C. Davis, Sci. Am. 256, 106 (1987). [2] Ya. B. Zel'dovich and A. S. Kompaneets. Theory of Detonation, (Academic Press. New York, 1960) and references therein. [3] W. Fickett and W.C. Davis, Detonation, (U. Calf. Press, Berkeley, 1979); WN. Fickett, Introduction to Detonation Theory. (ibid.. 1985) and references therein. [4] B. L. Holian, W. G. Hoover, W. Moran, and G., K. Straub, Phys. Rev. A 22, 2798 (1980>. [5] A. N. Dremin and V. Yu. Mlimenko, Proq. Astronaut. Aeronaut. 75. 253 (1981). [6] A. M. Karo, J. R. Hardy, and F. E. Walker, Acta Astronautica 5, 1041 (1978). [7] D. H. Tsai and S. F. Trevino, J. Chem. Phys. 81, 5636 (1984). [8] M. Peyrard, S. Odiot. E. Oran, J. Boris, and J. Schnur, Phys. Rev. B 33, 2350 (1986); S. G. Lambrakos, M. Peyrard, E. S. Oran, and J. P. Boris. Phys. Rev. B39. 993 (1989). [9] M. L. Elert, D. M. Deaven, D. W., Brenner. and C. T. White. Phys. Rcr. B 39. 1453 (1989). [10] N. C. Blais and J. R. Stine. J. Chem. Phys. 93. 791-1 (1990). [11] D. H. Robertson, D. W. Brenner. and C. T. White. Phys. Rev. Lett. 67. 3132 (1991): C. T. White. D. H. Robertson. and D. WV. Brenner. Physica A 188. 357 (1992). [12] D. W. Brenrer, D. 11. Robertson. M. 1, -,ei t. and C. T. White. (submit/d for publication). [13] J. Tersoff. Phys. Rer. Leit. 56. 632 (19S(). PhY.,. hUl. B 37. 6991 (1988). [14] C. WV. Gear, Numcrical Initial Iahiuc Probhl, , mnOrdinarY DTffercutial Equatoi.,. (Prentice-Hall. Englewood Cliffs. 1971).
115) D. 11. Robertson, D. W. Brenner. M. L. Elci t. and
('.T. While. in Shock ('omprcssion of Condensed Mattfr-1991, S. C. Schmidt. 11. I). 1iclk.. V Forbes. 1). G. Tasker. Eds. (Elsevier Science Publishers B. V.. Amsterdam., 1992). p. 115
[16] C. T. W hite, D. II. Iobertson. I). XV. 3re1i,.ic...MI. .. Ehvtl . and I). V. l 'rciiic,.il Mlicroscoplc SzInulations of ('ompl(x.r
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13. L. I lolian. Eds. (Plenin I'rcs.,. Nexv Noi k. l1192). p. I I.I ;17] S. Mlinshall. Ph!is. hr r'. 98, 271 (1955)1 [18] G. E. Duvall and( 1. A. Graham. 11r. M.llo i',.
49.3'!3 (19771.
n4 [,.qh- (in prrialitri [19] Ya. B. Zel'dox'ici and Yu. P. liaizei. IPhip.,'s of 5;h, Ii %-., and Ne, Yolk. 1966. 1967). Xii',•. Ilhdrodnnainic Phrnoncina.Vol . i - ! 2. f .Xalde.niic
129
FEMTOSECOND SPECTROSCOPY OF CHEMICALLY REACTIVE SOLIDS: A METHODOLOGY WEINING WANG, MARC M. WEFERS, AND KEITH A. NELSON Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139
ABSTRACT An experimental methodology for recording femtosecond time-resolved observations of irreversible change in solids is described. The central problem posed is that the time-dependent evolution must be observed on a single-shot (i.e. real-time) basis since the sample may be permanently altered after each excitation event. Preliminary demonstrations of real-time femtosecond spectroscopic observations are presented. In addition, one-shot data acquisition techniques open up the possibility of excitation intensities that greatly exceed optical damage threshholds of most samples. Since only one excitation pulse is used, cumulative damage mechanisms may be circumvented. Even if the sample is damaged in a single shot, in some cases the events of interest may be observed before damage occurs. The use of timed sequences of high-intensity excitation pulses to drive large-amplitude, coherent lattice vibrations is discussed. If successful, such large-amplitude lattice vibrations could assist ctysta;line chemical reactions or structural phase transitions.
INTRODUCTION Motivation for Real-time Ferntosecornd Specrosop Femtosecond spectroscopy of chemical reactions in gases and liquids has been carried out since the mid-1980's [1). In the simplest cases, optical absorption into an unstable molecular potential energy surface leads to direct photodissociation or rearrangement, and the elementary bond breakage or other chemical process takes place on subpicosecond time scales. If the reacting species is in a condensed medium, the surroundings may influence reaction dynamics considerably. Neighboring molecules may offer mechanical or dielectric resistance to the separation of photofragments, and dissipation of energy from the reactive mode into the nonreactive ('bath') modes of the molecule and its environment may prevent reaction altogether. Time-resolved spectrocopy of liquid-state chemical reactions has revealed substantial solvent effects on chemical reaction dynamics and yield [1,2]. The solid-state environment typical of most energetic materials should be expected to mediate chemical reactivity far more heavily than liquid-state surroundings. Molecular dissociation should be strongly influenced by the repulsive forces of immediate neighbors, or by the possibility of reaction between fragments and their neighbors. An ordered crystalline environment is known to be particularly influential, with reaction dynamics, yields, and branching ratios strongly dependent on the details of crystal structure and quality [3] Chemically reactive crystals are of special interest both because of the high energy density that can be stored and because, from a fundamental point of view, the c-dered environment could facilitate detailed analysis of energy flow between reactive species and their neighbors. Femtosecond spectroscopy of crystalline chemical reactions should reveal much about the sequence of events involved in energy release an%about the microscopic mechanisms of reaction initiation, propagation, and termination. However. the only femtosecond spectroscopic observations of chemically reactive solids reported to date have involved reversible excimer formation reactions in which very low energies (dictated by van der Waals forces) are released [4,5]. .
i:leason for so little solid-state femtosecond spectroscopy is simple: most solii-sa..,
samples cannot be conveniently 'flowed' to remove altered material from further experimenu observation. In examination of chemical reactions in the gas or liquid phase, the sample is flowed so that reaction products resulting from one excitation event (one laser 'shot') are removed before the next laser shot. Data are collected not in a single shot but through many excitation-probe sequences. An excitation pulse initiates photochemical reaction at the zero of time, and a delayed probe pulse is used to monitor reaction progress at some later time. Fresh Mat. Res. Snc. Symp. Proc. Vol. 296 c 1993 Materials Research Society
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material is then introduced into the irradiation volume, and the excitation-probe pulse sequence is repeated with a slightly different delay time. This procedure is continued until the entire process of interest is observed. Each excitation-probe repetition yields a single point on the time axis, and the data are collected point by point. Often many thousands of repetitions (with signal averaging of many repetitions at each delay time) are performed to yield a single timedependent sweep. In this manner the time-dependent evolution of the sample following photoexcitation is recorded 'point by point' along the time axis. This procedure cannot be followed with most solid samples. Only samples of excellent uniformity and optical quality and of large size may be moved after each shot to continuously expose fresh material. If this is not possible, the full time-dependent response must be recorded in a single shot. An experimental apparatus is described below in which multiple probe pulses are pri duced and used to monitor the sample at several different delay times following photoexcitation. Preliminary data will be shown, and current efforts to improve the apparatus will be discussed. pisects for Lar=-amplitde Coherent Phonon Excitation Single-shot data acquisition permits femtosecond time-resolved sp,;ctroscopy to be carried out even when a non-flowab.t sample is permanently altered through photoexcitation. Permanent sample change could be due to a photochemical reaction under study, as discussed above, or due to other processes. Even samples which are not ordinarily photoreactive can be optically altered ('damaged') by a sufficiently intense excitation pulse. Some optical damage mechanisms are dependent on cumulative radiation energy density over an extended time period, while others depend only on peak radiation intensity. In almost all cases the damage mechanism is unclear, with the occurence and extent of damage dependent on not only predictable factors such as optical intensity and wavelength but also on pulse duration, repetition rate, and even the optical phase profile [6]. In general, single-shot spectroscopy should allow examination of samples which are irradiated by excitation pulses whose intensities exceed optical damage threshholds. Cumulative damage mechanisms could be avoided entirely, and even damage which results from high peak intensity may occur on a time scale longer than the one of interest. In the latter case measurements could be recorded before sample deterioration takes place. This opens up the possibility of using intense excitation pulses to excite coherent lattice vibrations (ootic phonons) of large amplitude through impulsive stimulated Raman scattering (ISRS). In ISRS, an ultrashort excitation pulse exerts a sudden ('impulsive') driving force on Raman-active vibrational modes, initiating coherent vibrational oscillations which can then be monitored. Time-dependent observations are made of the crystal lattice at various stages of collective vibrational distortion away from its equilibrium configuration. This is particularly interesting if the lattice vibrational mode plays in important role in chemical or structural rearrangement 17). In organic excimer forming crystals, a lattice mode whose motion brings neighboring molecules toward each other along a likely reaction path was examined through ISRS [8,91. In this case, the mode coincides well with the excited-state reaction coordinate. In ionic crystals which undergo structural phase transitions, 'soft' lattice modes whose motions bring ions from their positions in one phase toward the positions they occupy in a new phase (and which therefore play the role of collective reaction coordinate) were studied [101. In all cases to date, however, the coherent phonon amplitudes (i.e. how far molecules or ions in a crystal were driven through ISRS) were small - on the order of 10-5-104 A. This is much smaller than quantum or mean thermal uncertainties, and so no new chemical or struciural changes were induced. Far higher coherent phonon amplitudes could be reached through the use of more intense excitation pulses with near-resonant wavelengths, but sample damage has prevented this so far. Single-shot detection methods should permit more intense ISRS excitation pulses and should ,.,1,4 considerably higher phonon amplitudes. A complementary experimental approach to higher driven phonon amplitudes through ISRS is the use of multiple excitation pulses to exert a series of 'impulsive' driving forces on a selected mode. This has been demonstrated on both organic and ionic crystals [9,111. A sequence of excitation pulses is timed to match the lattice vibrational period of interest, and each pulse amplifies the coherent vibrational motion induced by pulses before it. This is closely analogous to repetively driving a child on a swing with an appropriately timed series of pushes.
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Multiple excitation pulses, each with intensity below the optical damage threshhold, can result
in improved phonon amplitudes and also improved mode selectivity relative to single pulses. Intense multiple excitation pulses could be used in conjunction with single-shot detection methods.
The production of femtosecond pulse sequences whose timing (and also optical phases) can be controlled is a recent achievement [12]. As described below, femtosecond 'pulse shaping' originally involved the use of optical elements (spatially varying masks) which were permanently fabricated to produce a specified pulse sequence. Any pulse sequences of interest therefore needed to be specified in advance so that the corresponding masks could be manufactu-ed. More recently, multielement liquid crystal displays (LCDs) have been used so that new pulse sequences could be produced at will. We have developed computer algorithms which permit the user to simply specify the desired pulse sequence. The necessary manipulations are then carried out on the LCD such that the pulse sequence is produced. Some illustrative results of the current capabilities will be shown, and the prospects for further development will be described. EXPERIMENTAL Single-shot Detection: Multiple Probe Pulse Apparatus We have constructed a single-shot fermtosecond spectrometer consisting of a series of partial reflectors, delay lines, and other optics such that a single probe pulse is split into sixteen
pulses whose arrival times at the sample are controlled independently. The setup is illustrated in Fig. 1.The apparatus includes several sets of four reflectors whose reflectivities at the probe wavelength are 25%, 33%, 50%, and 100%. This insures reasonable equal intensities of all sixteen probe pulses. The probe pulses are overlapped spatially with the excitation pulse at the sample. The transmitted probe pulses are incident on different regions of a CCD detector and their intensities are measured The CCD detector is equipped with software designed to locate separate 'regions of inteiest' (i.e. separate laser spots) and to carry out simple manipulations of the intensities recorded at pixels within each region. The laser system used to conduct preliminary multiple probe pulse experiments has been described in detail in earlier publications [13]. Briefly, an antiresonant ring dye laser is synchronously pumped by the frequency-doubled output of a cw modelocked Nd:YAG laser. The ouput, centered at 620 nm, is passed through a three-stage amplifier which is pumped by
the frequency-doubled output of a Q-switched, modelocked, and cavity-dumped Nd:YLF laser. The Nd:YAG and Nd:YLF pump lasers are synchronized through the use of a common RF source which drives both of their modelockers. The synchronously amplified output consists of 80-fs, l0-WiJ, 620-nm pulses at a 500-Hz repetition rate. In the preliminary multiple ,..)t pulse experiments, transient birefringence (i.e. optical Kerr effect or OKE) or transient .trso.-ption was measured. In the former case, the excitation pulse was linearly polarized at 450 horn vertical (V). The probe pulses were V polarized, and a horizontal (H) polarizer was placed in front of the CCD detector. In the latter case, the excitation polariztion was varied and there was no polarizer after the sample. Note that in
addition to the individual delay lines for each probe pulse, there is an overall delay line which
changes the timing of all the probe pulses relative to the excitation pulses but not relative to
each other. Data were recorded with several choices of overall delay to check for internal consistency. In addition, data were recorded over periods o1 several hours to check for drift in the spatial alignment of the pulses in the sample or at the CCD detector. Ccrnuter Gerner•a ', r.,f Multiple Excitation Pulses The setup for production of shaped excitation pulse sequences is illustrated in Fig. 2.
The frequency components of a single femtosecond pulse are dispersed by a grating and focussed onto a spatially varying mask. This can be an amplitude mask, which blocks selected
components, or a phase mask, which alters the phases of selected components. The transmitted light is incident o•i a second lens and grating identical to the first and with similar positions and
132
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133
PULSE SHAPING APPARATUS
Grating
Lens
Mask
Lens
Grating
Figure 2: A schematic illustration of the pulse shaping apparatus. An ultrashort pulse is spatially dispersed and collimated by the the first grating and lens. The phase and/or amplitude of differing frequency components are altered at the mask for the desired output pulse. The second grating and lens recombine the shaped pulse. Not shown are half wave plates placed between each pair of lens and grating.
i. K ..
134
orientations relative to the mask. The manipulations of the mask on the frequency profile of the pulse lead to corresponding effects on the temporal profile. With both phase and amplitude masks, the outgoing temporal profile and phase can both be controlled. The original masks were permanantly etched onto glass substrates, and each mask was used to generate a single pulse sequence. In our current setup we have a multielement liquid crystal display (Meadowlark Optics) and driver (Cambridge Research and Instrumentation). The display consists of seventy pixels which are 100 gim wide, including 15 pn 'dead' space. The
computer-interfaced driver applies an ac voltage which orients the liquid crystalline material in the 'live' part of each pixel. The experiments reported below were conducted with the one LCD used as a phase mask. An identical LCD is being incorporated into the system for both phase and amplitude control. The 15-pim dead space in between live pixel areas tends to produce a large peak at the center of the pulsetrains, since about 15% of the light is not under the control of the mask. This effect was taken into account in the algorithms which design the masks. Other limitations include the number of pixels and the spatial resolution (i.e. pixel size). These determine the total temporal range over which a pulse shaped pulse sequence can extend, and the time resolution with which a pulse sequence can be specified. With our apparatus, time resolution of about 85 fs and a total range of about 6 ps should be achievable. The setup includes two 1800 lines/mm holographic gratings (Milton Roy) and two achromatic 15-cm focal length lenses. Also included are two half-wave plates to rotate the polarization from H to V before the mask and back to H after the mask. This is necessary because the gratings and mask require H and V polarizations respectively. The laser system used for multiple-pulse generation is a Titanium:sapphire femtosecond laser pumped by 12 W of the output of a cw argon laser. This commercial system (Coherent), with external prisms, yields 55-fs pulses at 800 nm central wavelength with almost I W of power. The output is used without amplification for pulse shaping. RESULTS MUltiple Probe Pulses
The first one-shot data were optical Kerr effect measurements on carbon disulphide liquid in a 2-mm thick cuvette. Typical data are shown in Fig. 3, along with data recorded in the conventional manner (many shots, with a variably delayed probe pulse). These data were
recorded before the CCD detector was equipped withi the software to do analysis on multiple regions of interest. The integrated intensity readings at each laser spot were recorded by hand to determine the intensity of the corresponding pulse. Differences in probe pulse intesities or in the degrees of overlap between different probe pulses and the excitation pulse were not accounted for. Thus the data show considerable scatter. Nevertheless, the overall temporal response of the sample is represented. The data were reproducible. as illustrated in Fig. 4 which shows an additional one-shot scan recorded with a slightly different 'overall' delay relative to the excitation pulse but with no changes in the relative delays. The response (including scatter, which is primarily due to systematic errors described above) is the same except for the small changes in overall timing. These and other data were recorded over a period of several hours, with no apparent deterioration due to changing spatial overlap of the seventeen pulses. Transient absorption measurements were recorded on an approximately 10(3 M solution of malachite green in ethanol in a 2-mm cuvette. The CCI) detector was equipped with the softwar%. '-a.ribed earlier, and differences in probe pulse intensities were accounted for in the analysis. Differences in the extent of overlap between different probe pulses and the excitation pulse were partially accounted for by measuring the transient absorption of each probe pulse at zero delay time, and normalizing the data appropriately. Typical data are shown in Fig. 5. The data are smoother than those shown in Figs. 3 and 4. presumably because of reduced systematic errors. Remaining systematic error may be reduced with the use of a different excitation wavelength, which eliminates excitation scatter and coherent coupling of varying
135
0.8-
regular
-
a
- 0. 6 . -m-
single shot t=O
'0 0.4.0.2-2
-1
0
1
2 3 4 5 time (ps) Fig.3 Femtosecond single shot experiment: optical Kerr effect in CS2
-
a
0.2-
0.: -2
0
1
single shot t=-66.7fs
.....
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7
regular
-
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6
2 3 time (ps)
.r~
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6
7
Fig.4 Optical Kerr effect in CS2. Same as Fig.3 with excitation pulse delayed by 67 fs 1.2. 1. 0.8.
'* 0.6.
regular single shot
0.6
0.2•I
0-1
0
1
2 3 4 time (ps) FRg.5 Femtosecond single shot pump-probe experiment in malachite green in mathanol
5
136
amounts into the probe spots on the CCD. Additional data recorded from malachite green over periods of several hours and with different 'overall' timing were consistent with that shown. Multiple Excitation Pulses Autocorrelation traces of three representative pulse sequences produced by the LCD mask are shown in Fig. 6. They show distinct temporal profiles with only small amounts of distortion from the specified sequences. We emphasize that only the desired pulse shapes were specified, and the mask needed to produce the pulse shapes was determined and fabricated automatically by the computer and the LCD driver. The algorithms needed to do this will be described subsequently. Our present purpose is merely to illustrate what is currently possible. DISCUSSION AND PROSPECTS Real-rime Femtosecond Spectroscopy The results shown in Figs. 3-5, although preliminary, indicate that this experiment can be conducted on a routine basis even though it involves seventeen spatially overlapped beams and sixteen independently controlled delay times. Clearly the greatest limitation is the small number of points on the time axis. However this can be improved without additional large numbers of beamsplitters, delay lines, etc. The method to be adopted is illustrated in Fig. 7. A fraction of the probe pulse is split off and spectrally narrowed such that its pulse duration reaches several picoseconds. This pulse is used as the (single) probe pulse which is overlapped spatially with the excitation pulse inside the sample. The transmitted probe pulse then carries the temporal information about the sample response. If the experiment were on nanosecond or slower time scales, the transmitted probe pulse would be examined by a fast photodetector and transient digitizing analyzer and the dynamical sample response would be determined directly. In our case the 'reading' of the transmitted probe pulse temporal profile must be done optically. To do this, the transmitted probe, pailse is overlapped spatially inside a nonlinear optical gate (e.g an optical Kerr cell) with the sixteen pulses produced by our multiple beamsplitting apparatus. The transmitted probe pulse temporal profile is determined through measurement (using the CCD detector) of the extent to which each of the sixteen pulses gets through the gate. This approach has several advantages over our current method. First, the probe pulse wavelength could be tuned conveniently without extensive realignment of many beams. For example, the probe pulse (after being split from the pulse which enters the sixteenbeam apparatus) could be frequency-shifted or used to generate a white-light continuum from which desired frequencies could be selected (and amplified if necessary). Second, optical quality of the sample would be somewhat less important since the CCD detector is irradiated by sixteen pulses which never go through the sample but only go through the nonlinear optical gate. Third, the multiple-pulse readout system could be readily modified to yield many more points on the time axis. This is illustrated in Fig. 7. A beamsplitter just before the nonlinear optical gate sends all the beams into another nonlinear optical gate, so the number of total readout pulses goes from 16 to 32. A small retarder (e.g. a thin piece of glass) inserted in the probe beam changes the overall timing of the pulses in the second gate, so that 32 different
times are monitored. This procedure could be continued until all possible space on the CCD detector is used. In practice, at least 32 and probably considerably more spots could fit.
We note that several more 'elegant' approaches to single-shot data acquisition could be tried. For example, a large angle between the cxcitation pulse and a single, cylindrically focussed probe beam could be used. Different, spatially separated regions of the probe beam would then overlap with the sample at different delay times, and the transmitted probe beam could be examined with an array or CCD detector. An analogous procedure could be tried with crossed excitation pulses which form a transient grating and a cylindrically focussed probe
pulse whose parts are diffracted off the grating at dif:- n.,.t delay times 1141. These methods offer many more points on the '..-* ax;, but their tin1.. .olution is limited by the time required for the probe pulse to traverse a distance on the order of the excitation spot size. In practice, the time resolution would almost certainly be poorer than 100 fs. Other possible methods involve introducing a linear frequency chirp in a single probe pulse, then spectrally resolving the
transmitted probe pulse which should have a frequency-to-time correspondence. In this case the distinction between temporal and spectral evolution of the sample may be difficult to make.
137
0.8 z,0.6 .5 0.4
0.2 -8
-4
0
8
4
time iaps Fig. 6a: 1.05 THz pulse train generated by computer controlled LCD mask.
0.8
._z,0. 6. _0.4.0.2-
_______
0-L -6
-3
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36
Fig. 6b: Staggered Pulse Train. The jagged base line is due to depolarization of the beam prior to pulseshaping. This has since been corrected.
1 0.8 2-k (I) C
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____

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-4
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4
Fig. 6c: 0.60 THz Rate Train. Deliberate removal of the peak at t=0 demonstrates complete compensation of the uncontrolled gap regions in the mask.
8
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Picosecond
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16 Transmitted Mixing Pulses To CCD
NLO Gate
16 Fs Mixing Pulses Read Transmitted Ps Probe Pulse
16 Transmitted Mixing Pulses To CCD Figure 7. Illustration of single-shot detection using a single, picosecond probe pulse. The picosecond pulse can be slightly delayed before one NLO gate so that two gates yield 32 different delay times. Additional gates may be used. SAmplifiedFemtosecond
•
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In general, all the methods of which we are aware involve compromises of experimental difficulty, number of points, time resolution, and/or other factors. The method we have chosen is somewhat difficult and limited in the number of points, but permits very good time resolution and straightforward data analysis. Multiple Excitation Pulses Our results thus far encourage us to believe that multiple-pulse femtosecond spectroscopy can soon be carried out at levels of control and convenience comparable to those typical of modem NMR spectroscopy. Improvements currently being prepared include the use of both phase and amplitude LCD masks and fabrication of improved LCD masks with more pixels and considerably smaller 'dead' spaces. Multiple Excitation and Probe Pulses Femtosecond time-resolved spectroscopy of solid-state photochemistry, including photochemistry in energetic solids, can be carried out with single-shot detection methods. For ISRS excitation of large-amplitude vibrational responses, it will be useful to combine multiple excitation pulse and multiple probe pulse techniques. This could permit iterative improvement of the excitation pulse sequence based on the material response observed after each shot. The procedure is illustrated schematically in Fig. 8. At the simplest level, the human experimenter analyzes the sample's response to an excitation pulse sequence, decides what pulse sequence might work more effectively, and instructs the computer to generate the improved pulse sequence. The computer does this through the present algorithms which allow it to design and execute the appropriate mask. However it may prove more effective to remove the human experimenter from the routine interation loop. The analysis of the sample response and the optimization of the excitation pulse sequence could also be largely computerized. This appears futuristic but in fact it is already discussed widely in the context of 'mode-selective chemistry' of isolated molecules in the gas phase. In fact our intentions are also to conduct a sort of modeselective chemistry, but in the crystalline phase. We hope to use intense, near-resonant excitation pulse sequences to drive coherent phonon amplitudes of a substantial fraction ot angstrom. If this proves possible, then new types of chemical or structural rearrangemenets might be driven and monitored in real time through single-shot detection. Optimization of the excitation waveform in the most efficient manner possible (with as little sample loss as possible along the way) will become an important part of the experimental process. Large-amplitude phonon-induced crystalline chemical reactions. if they can be drivei, through ISRS excitation, would permit detailed examination of solid-state chemistr in the ground electronic state. This is most relevant to initiation of chemical change in energeti. materials. In fact the large-amplitude phonon response which we hope to drive could be considered a 'microshock' whose chemical initiation could resemble shock-induced initiation in energetic solids. SUMMARY An experimental methodology for real-time femtosecond spectroscopy. in which observations are made and recorded in a single laser shot, has been described. Preliminary dat.i have been presented %%hich indicate that the approach is viable and can yield reproducibk results. The method used will permit femtosecond time-resolved observations of photochemnic.l reactions in energetic materials. Sonic substantial improvements currently being zmplcmente' have been described. Computerized generation of femtosecond pulse sequences to be used for selective lattice vibrational excitation hqi been illuutr.;., -.Le prospects for excitation of large-amplihtu. coherent lattice vib,aiu,., 1,vich could inauce chemical or structural rearrangements have beei, discussed. These prospects depend on combination of multiple excitation pulse and single-shol detection methodologies.
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ACKNOWLEDGMENTS This work was supported in part by ONR Grant No. N00014-90-J-4070 and by NSF grant no. CHEM-8901722. M.M.W. acknowledges support of an NSERC Predoctoral Fellowship. REFERENCES 1. See for example The Chemical Bond, A.H. Zewail, ed. (Academic Press, 1992). 2. Many examples are presented in G.R. Fleming, Chemical Applications of Ultrafast Sptroa=X (Oxford, 1986). 3. G. R. Desiraju, ed., Organic Solid State Chemistry (Elsevier, 1987).. 4. L.R. Wflliams and K.A. Nelson, J. Chem. Phys. 87, 7346 (1987). 5. T. Tokizaki et al., Proc. of Eighth Int'l Conf. on Ultrafast Phenomena, J.L. Martin, A. Migus, G.A. Mourou, and A.H. Zewail (Springer-Verlag), in press. 6. R Kosloff, A. Dell Hammerich, and D Tannor, Phys. Rev. Lett., submitted. 7. Y.-X. Yan, E.B. Gamble, Jr., and KA. Nelson, J. Chem. Phys. U3, 3591 (1985). 8. S. DeSilvestri, J.G. Fujimoto, E.P. Ippen, E.B. Gamble, Jr., L.R. Williams, and K.A. Nelson, Chem. Phys. Lett. 11f6, 146 (1985). 9. A.M. Weiner, D.E. Leaird, G.P. Wiederrecht, and K.A. Nelson, Science 242, 1317
(1990). 10. T.P. Dougherty et al., Science 25, 770 (1992). 11. G. P. Wiederrecht, T. P. Dougherty, L. Dhar, K. A. Nelson, A. M. Weiner, and D. E. Lcaird, in preparation. 12. A. M. Weiner, D. E. Lcaird, J. S. Patel, and J. R. Wullert, IEEE J. Quan. Elec. 2& 908 (1992). A. M. Weiner, J. P. Heritage, and E. M. Kirschner, J. Opt. Soc. Amer. B, 5 1563 (1988). 13. T.P. Dougherty et al., Phys. Rev. B, submitted. 14. J.T. Fourkas, W. Wang, K.A. Nelson, and R. Trebino, in preparation.
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Explosion Of Drops Impacting Non-Wetting Rigid Surfaces ClarenceZener And Dennis Prieve CarnegieMellon University Pittsburgh,PA 15213
More than 100 years ago Worthington [ 1,21 reported his observations on drops exploding on impacting rigid surfaces they did not wet. Mercury was his favorite fluid, since mercury does not wet most solids. For water drops he had to especially 'smoke' his surfaces to make them non-wetting. In his day high speed photography had not been developed, but he had learned to 'stop' his falling drops by spark illumination. His drops had radii of typically 1 mm, fell from a height of -10 cm and ejected always an even number of spikes, typically -24. These spike, would shoot out from the impacted area at velocities several times higher than the impact velocity. In this paper, we demonstrate that Worthington's reported observations follow directly from the basic physical principles governing fluid flow. As an introduction to our description of why drops explode when they impact non-wetting surfaces, we shall review the physical principles which have lead to our understanding of this explosion. In the 17th century Newton started with the basic relation mass x acceleration = force 11 -f
(I ,
During the 18th century Lagrange gencrahlzed Newton's law to describe the mechanics of a laret. number of interacting masses. d )K di ')t,
)P
_
(2)
Dq,
Here the q1's are the independent variables of the system, K(qI, s,q1 ' s) is the total kinetic energ of the system and P(q' sI 'is the total potential energy of the ,ystem The nineteenth century saw at great advance in understanding the mnechanizct, of fired('
This advance came prinmarily throu,i the introduction of the concept of potentiail flow o1 incompressible fluids. In such flow th• velocity 1i of ev'er% point of the fluid is given by thc gradient of a harmonic function. Thus a hamionic velocity implics U =VO where 0 satisfies the differential equatm,
Mat. Res. Soc. Symp. Proc. Vol. 296.
1993 Materials Research Society
142
v20=0
(4)
The two equations (3) and (4) imply that the fluid behaves as if it were incompressible, V.U=O and curl free VxU=0 Thus harmonic flow implies both zero change in volume and zero energy loss by viscosity. Unfortunately harmonic flow cannot have stationary boundaries. In order to emphasize the difficulty of solving this equation when one boundary is a rigid surface, we quote from Milne-Thomson [3]: 'Not so many years ago the dynamics of a frictionless fluid had come to be regarded as an academic subject incapable of practical application due to the great discrepancy between calculated and observed results.' He then explains how this difficulty was largely removed by the recognition of the Prandtl boundary layer which protects harmonic flow from direct contact with the rigid surface boundaries. In 1985 Rodriguez and Mesler [4] published a paper describing what happens when water drops impact a pond of water. At low impact velocities, small drops bounce off the pond. Large drops float for a while before submerging. On reading of these experiments we suspected that an entrapped air film protected the drop from making direct contact with the water in the pond. This suspicion then lead to the concept that in Worthington's experiments an entrapped air film was protecting his drops from direct contact with non-wetting solid surfaces. If correct, this entrapped air film was performing the role of the Prandtl boundary layer. The low density and low viscosity of the air film in contrast to the Prandtl boundary layer meapt, however, that it would absorb a negligible amount of energy from the drop. This paper gives the results of these thoughts inspired by the observations reported by Rodriguez and Mesler. Analysis With the above background we now attempt to construct the velocity potential of a drop at its instant of impacting a non-wetting rigid surface. Figure 1 presents our first attempt. Here we use symbols as well as pictures of the streamlines which these symbols represent. For the sake of clarity we represent the drop's shape as that of a truncated cylinder rather than as a sphere. Wv, representing the velocity potential at impact, is the sum of two terms. The velocity potential, -Uoz, represents the drop just before impact. The stream lines are a set of uniformly spaced vertical lines. The second velocity potential, i*, represents an initially stationary drop which has just been struck from below by an upward impulse of intensity Uo. The velocity pattern of i* is that specified by the boundary conditions az
Uo at z=0, r~a
(5)
w* = 0 on free surface
(6)
143
-Uo0 z
'*
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av* n
an o• --0
Conservation of kinetic energy requires
fffp[v('e However
- V*)]
ff
[J'p(VxV) (Vy
since
P 2
dV*)dv 0
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Finally we conclude
4
f
*2 a, =
'lost kinetic energ'
Fig. 1. Derivation of 'lost kinetic energy,' using Green's Theorem
Since the stream linLs of V4looked as we thought they should look, we thiought they (lid indeci represent the real stream lines just alter impact. 1o test this nunch. %e transferred x'y to the Ic: side in Fig. 1. took the gradient of both sides, then squared ooth sides, multiplied by the denmii:, p(r). and integrated over all space. observing ho%%e%er. that p vanzlshe', outside the drop Makin, use of Green's theorem. and of the constraints (5ij and (w. we find the integral of the cro-, product term vanishes, leaving
144
2 dV pU20 x drop volume J'ffp(VI)2 d1V +JJfp(V,*)
(7)
Clearly a significant part of the original kinetic energy of the drop is not represented by the velocity potential V. According to Lord Kelvin (1849), we have only found that harmonic function of minimum kinetic energy which satisfies the required boundary conditions. If we wish to know what happened to the drop during impact, we must be able to describe what happened to the 'lost kinetic energy', _ fJfp(V/ *)2 dV. The dilemma we have run into has arisen because of our assumption of zero compressibility. We should have said very small compressibility rather than zero. With this change we now recognr, that our 'lost kinetic energy' is simply the compressive potential energy induced within the drop by its impact. We now have the most remarkable conclusion that whereas the square of the density of the stream lines of Wgives the density of kinetic energy just after impact, the square of the density of the stream lines of i* gives the density of compressive potential energy within the drop just after impact. Wc want to particularly emphasize that the kinetic energy and compressive potential energy are concentrated in the same regions, namely in the lower outer edges of the drop. Clearly the coexistence of a high concentration of kinetic and compressive energy in the same region encircling the drop is an ideal recipe for an explosion. We emphasize that this conclusion is independent of the drop's shape before impact. We now describe a harmonic velocity potential which represents the essential features of a drop impacting a non-wetting surface. O(r,O,z;t) = V(r, z) + 4(r) 0,(r,O,z)
(8)
where r,O,z are the usual cylindrical L.oordinates. The velocity potential W has stream lines as indicated in Fig. ' We have seen that it does not, however, have sufficient kinetic energy to represent our drop after impact. We shall find that the second velocity potential, Jn(Lr-•)e-P15z/a On = cos(no)
aJ5
(9)
a
will, however, supply the missing kinetic energy provided the ratio of sound velocity of drop fluid, C, to the impact velocity Uo is sufficiently high. Towards this end we must find the coefficient q(t). To help visualize the remarkable explosion activated by this second velocity potential, N. we note that q(t) is the amplitude of a perturbation in the radius of the drop rB(O, z,t) -a = q(t)cos(n9)e-Pz/a
here rt1 is the radial distance from the axis to the drop's surface and
(10)
145
q(O)=o
(11)
The primary parameter n is an even integer
repesenting the number of fluid rays emerging from the point of impact. The secondary parameter P has an upper bound limited by
surfaci
tension, and a lower bound of n. The
precise value of P is that which gives the maximum growth rate for n modes (as in ,RPyleigh's analysis of long fluid jets). For water near room temperature, we find n = 24 and f• = 22.I In order to determine q(t), we use (8) and
(9) in (2) to compute the total kinetic energy K, and we use the square of the density of streamlines of W*to compute one contribution to
3600 n
the total potential energy P. Another important rontribution to P is the surface energy, which grows as the area of the drop increases. In the particular case where the fluid sound velocity C is extremely high compared to the impact velocity,
C >> Uo
(12)
the required volume and surface integrals in (2) can be evaluated on the assumption that the drop's surface has not moved significantly before most of the 'lost kinetic energy' has been transferred to the new velocity potential On. In particular, the initial velocity 4(0) is chosen to conserve energy. The differential equation thereby obtained for q(t)
is
T in & UP
I down & out
in & UP
m max
P
LI aij-b4 -cq=O
(13)
P That solution of (13), which satisfies the Fig. 2. boundary condition (11) and conserves kinetic Streamlines a~sociated with p. in one of n energy, is sectors of circle of radius r11 . The (14 streamlines of On are essentially confined q(t) = q, sinh to a thin surface layer. Their low inertia results in a high outward acceleration.
148
The analysis we have adopted leading to (14) is essentially that followed by Rayleigh [5] in his study of the stability of cylindrical columns of water under gravity-free conditions. In his case instability was driven by surface tension. In contrast, in our case instability is driven by the hammer pressure pUoC, which is three orders of magnitude greater than the stagnation pressure at the t'ase of a steady stream of fluid impacting a wetting surface at the velocity Uo. The value of t which we calculate is less than one microsecond. This low value is consistent with the concept that the 'lost kinetic energy' has been absorbed by the O velocity potential before the drop surface has had time to move an appreciable distance. We now review our attempt to find the essential futures of what is happening to a cylindrical drop impacting a non-wetting surface. In our analysis we make one basic assumption: the ratio of sound velocity to impact velocity, C/Uo, is so large that no observable effect would be introduced if C was increased still further. We have found that a consequence of this assumption is that a major part of the kinetic energy of the original drop, but not more than -90%, is associated with an axially symmetric velocity potential, V. We have identified not only the magnitude of this 'missing' kinetic energy (see last line in Fig. 1), but also its spatial distribution, namely that given by ½p(4VOn)2 . This 'missing' kinetic energy has two distinct parts, that containing the square of the vertical velocity, equal to -pUo, and that containing the square of the radial velocity. It is evident from Fig. 1. this second component is absent in the center region near r = 0, but becomes somewhat greater than Uo near r = a. This 'missing' kinetic energy density is therefore at least twice as great near the periphery as at the center. This observation is in agreement with what is found in meteorites striking the earth, namely that the maximum pressure in the .impacting meteorite is much higher at the edges than at the center.16,7] We make one further comparison with prior impact studies. When high velocity solid cylinders impact massive plates, the front part of the cylinder deform in much the same way as if they were, at least temporarily, liquids. This is especially the case where the cylinders are made of metals having a sharp yield stress. Such materials may respond to impact loading where at any one instant deformation is confined to narrow slip bands within which adiabatic deformation results in a local rise in temperature, and thereby a shift of impedance to local increase in deformation rate to the inertia of the material itself. This possibility has recently been explored by Holt and colleagues.[8] Towards this end, they have compared the deformation of impacted cylinders with the deformation calculated by G.I. Taylor.19] We find the deformation represented by our x (see Fig. 3) is essentially the same as the Taylor deformation reported by Holt et al.
147
1.4 1.2
. ............
L.. ... ..

Cahn C 31 Microbalance Manual Lawn Care

........
1.0
U, 0. 8
...........
UO 0.6-
0.2..... 0.0
0.0
0.2
0.4
I
0.6
0.8
1.0
1.2
1.4
zia Fig. 3. Radial impact velocity, VU(a) = dWIr, as a function of the d&stance z from impacted head. U. is impact velocity and a is cylinder radius.
References 1. A.M. Worthington, Proc. Roy. Soc. 2S~, 261 and 498 (1877) and 34,217 (1882). 2. A.M. Worthington, AStudy of Splashes (The MacMillan Co., New York, 1963). 3. L.E. Mfime-Thomson, Theoretical Hydrodynamics (The MacMillan Company, New York, 1968) Preface. 4. F. Rodriguez and R. Mesler, J. Colloid Inierface Sci. 106, 347 (1985). 5. Lord Rayleigh. Proc. Roy. Soc. 219 71 (1879); Theory of Sound (D~over Publications, New York, 1945) Vol. 11. 351-365. 6. Melosh. H.J., Impact Cratering,Oxford University Press, 1989. 7. W. Adler, in Treatise on Material Science and Technology. (ed. by C.M. Preecc. Academic 57 . Press. New York, 1979) Vol. 16, p'1 8. W.H. H~olt et al, (inpress). 9. 0.1. Taylor, Proc.Roy. Soc. A194, 289 (1948).
149
AD INITIO STUDY OF ELECTRONIC STRUCTURE OF RDX MOLECULAR CRYSTAL
GUANO GAO*. RAVINDRA PANDEY AND A. BARRY KUNZ Department of Physics, Michigan Technological University. Houghton, M 49931 * Current address: Depa of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455
ABSTRACT An embedded molecular cluster model is used to study the electronic structure of cyclotuimethylene trniramme(RDX) molecular crystal In this model, a molecular cluster 4escribing a local region of the crystal is treated in the Haree-Fock approximation. The embedding lattice is represented by muldpoles that are determined quantum-mechanically. Cluster-latice orthogonality is achieved by tuansforming canonical orbitals to orbitals which are localized on individual molecular sites by means of a self-consistent localization potential. Results for the free molecule and the perfect crystal demonstrate the domination of three N-NO2 groups on intermoleculr properties. For the defective crystal, results show a significant distortion in the electronic structure caused by local deformations in the lattice that may account for the formation of hot spots.
L INTRODUCTION Cyclotrimethylene trinitramine (RDX) is one of the most important representative energetic materials. A theoretical study of electronic properties of such a material can be expected to produce a fundamental understanding of its detonation behavior at the microscopic level. We note here that a direct relationship between sensitivity and electronic processes in a series of energetic materials (TATB. DATB. MATB and TNB) has been shown by Sharma and Beard [1] using X-Ray Photoelectron Spectroscopy. One of the main problems in describing electronic properties is that these systems often contain more molecules than can be handled by using conventional quantun chemistry methods. An alternative approach is therefore to simulate the crystal by a molecular cluster that contains the local region of intetesL However, in this approach the question of representation of the remaining (embedding) lattice poses the greatest diffculty. Furthermore, the nature of the cluster approach requires (cluster) molecular orbitals to be localized resulting into a very small overlap with the embedding lattice. For ionic crystals, our group has successfully developed the ICECAP methodology that simulates the crystal by a molecular cluster embedded in a shell-model lattice.[2j In the present work, we extend this approach to study electronic properties of energetic materials that are classified as molecular crystals. We will give a brief description of the theoretical model in the next section. Results of the calculations on the RDX molecular crystal will be presented and discussed in Sec. In. 11. THEORETICAL MODEL Embedded cluster appruach (ICECAP) divides a crystal into two regions: cluster (A)and environment (E). In this context, the cluster will be defined as a collection of one or more molecules. By virtue of its finite physical size, the cluster containing the local region of interest is chosen to be larger than the physical extent of the phenomena involved. The cluster Hamiltonian in the BornmOppenheim approximation can be written as : Mat. Res. Soc. Syrp. Proc. Vol 29. p1993 Materials Research Society
150
H1A HAo+ IAE
(1)
where Ho is the Hamiltonian for a free cluster and is IAF the interaction energy between the cluster and its environment HAO and It• can be written as
A h2
AA ze
HAG-Wi~ IAE= -+, A
e
1
AA
I AAZZe2
02
fri -R11
(2)
-+11A -eM 2 += A ,ZtZje2
ZI
EA
2
(3)
where A and E represent summations within cluster and environmeri nespecfively. We use lower case letters to represent electron properties and upper case letters to represent nuclear prpertes. The mass of the electron is m. its charge magnitude e, and its position rt. If spin dependence were neede' then r, would be position and spin coordinate. The nul charge at I is ZI. and the coordinate is RI. In the present study, we have neglected interacton energies within the environment as they are approximately constant relative to the emededcuster. We now introduce Nj to represen the number of electrons associated with atom J. The
inte•ction Hamiltonian (Eq. (3)) can now be written as IAE = VM+VN +Vs Here, VM =-
.
Iri - R
(4)
the Madelung potential due to the presence of ions in the
environment. However, it can be ignored for molecular crystals as Zj = Nj. The interaction potential between the nuclei in the cluster and nuclei and electrons in the envimn t can be written as
A ZZJ e e2
EA Z
VN=I1- IR -Rj I.R 3
ff
(5) 5
Irj- RIt
Under the assumption of a small overlap between molecular orbitals of Cluster (A) and environment (E) region, Eq. (5) is reduces to AE ZI(•Z -NI) e2
1j 1= R - RjI In the absence of any ions in the environment (i.e. ZJ=NJ). we can also neglect the contribution of this term to IAE. Finally, Vs is given as
'V =r-IA ' Ne -i
2
AE
2
r '. '
(7)
where it is defined as the screening potential produced by electrons and nuclei in the environment. For the case of a molecular crystal, we transform confiitvpmioti coordinates of eq. (7) from nuclear-electron representation to me1 -t ai onter-nuclea, z!.ctron representation as follows: A Enm
NK e 2 ri m -MRKI +
juKti
R
icm
AENm
e2
mk
Irsm - rk(8)
151
Here the index m corresponds to amolecule nm is the nw berofatom inthe molecule m. NK is the number of electrons in atom K of the molecule m andNm is the number of electrons in molecule im
We now expand eq. (8) using Taylor's series. This expansion is based on the assumption of a small overlap between molecular orbitals of Cluster (A) and environment (M) regions, so that Rxmc a Transition t Transition
P
0o -50 Y -100£
•
L'Transition
a Transition a Transition > a Transition C Decomposition ->
-100... 20... 36..
-150
0.0
4.0
2.0
10.0
8.0
6.0
12.0
14.0
PRESSURE (CPa) 4A 350 REACTION-PHASE DIAGRAM OF IINIfl' 300sO
manhiAL DICOMPOSOM1 OXCION
S250
-
-
z-oo-*
2 0
-•-
0 7 Ao Transition

207
MgO powder for electrical isolation. The power input to the heater is controlled by a thyristor controller and a silicon-controlled rectifier (SCR) which permits automatic control of heating with proportional, integral and derivative features for the heating rate. Other features which are available include time-proportional heating, temperature overshoot inhibition and direct temperature readout. Temperatures as low as -190 0C can be attained by replacing the removable resistance coil heater with a miniature coiled tube for passage of liquid N2 . Temperature is measured by a chromel-alumel thermocouple with its bead in contact with an Inconel' X750 alloy gasket which confines the sample under pressure. With this system, temperature can be set and automatically maintained to ±1 °C with an estimated accuracy of ±3 0C at 300 0C. A fixed-point calibration method based on the melting point of several pure materials was used to determine this uncertainty [8]. The high-pressure-high-temperature diamond anvil cell can be mounted on a micrometer positioning device for optical polarizing light microscopy. ruby fluorescence pressure measurements. Fourier transform infrared (ETIR) spectroscopy, micro FT-Raman. and energy dispersive X-ray diffraction (EDXD) measurements as described below. Optical Microscopy and Ruby Fluorescence Measurements Optical polarizing light microscopy (OPLM) studies are made with an instrument also used for our ruby fluorescence pressure measurements. This system has been described earlier [5]. A massive micrometer x,y,z positioning device provides the mount for the pressure cell and permits horizontal positioning (x,y) of the sample (or ruby) in the DAC onto the optic axis of the microscope, while permitting vertical motion (z) to focus the sample (or ruby). A tungsten light source is positioned at the bottom of the microscope providing transmission illumination of the sample. This allows visual evaluation of the sample under polarizing light. Structural phase transitions are detected in samples under investigation using OPLM primarily by birefringence changes on single crystals using various pressure transmitting media. e. g.. liquid N,. n-pentane:isopentane (1:1 by volume). and Fluorinert). The use of Fluorinert is limited to samples which are insoluble only in this liquid because its own strong bircfringence does not nromote sharp visual images of the crystals when viewed under polarized light. N-pentane:tsopentanc (1:1 by vol) and liquid N. both permit sharp images of single crystals under poiarized light withl pronounced birefringence effects such as an extreme change in color moving as a wave across the crystal face when a sample undergocs a phase transformation. In some instances, by fine adjustment of the pressure, the transitions can be halted so that both phases arc present simultaneously in the same specimen separated by a sharp demarcation line. The birefringence change and demarcation boundary provide distinct markers for detecting a transition as a function of pressure and temperature. Similarly. ielting (free/ing) as a function of pressure and temperature may be accomplished bw adiusting these parameters sot that both solid and liquid phases are present simultaneousl' A 20 mW CNV He-Cd laser is positioned where the light source ior HII (rellection illumination would normally be located. The I-Ic-Cd laser beam provides the excitation energy for ruby fluorescence. The light image may be transmitted to a television camera I, inserting a movable mirror which contains a very smali circular nonrnated area. Tinoncoated area permits transmission of the fluorescence radiatio to :ý.x monochromator. Therefore. visual observation of the sample and pressure measurement may be accomplished simultaneously. The fluorescence signal is recorded digitally by a diode array detector anti is processed by an IBM' AT computer. Pressure is evaluated by a peak shift calculation or a line-shape modul. Pressure measurements by this technique may be repeated routinely cver.% 3 sec.
208
A
B
ALPHA 1800 F00ItOO 1•O o WAYVWI'ER
0
1Jo
•0
5A
BETA
EPSILON
bli
)e= sio
tiz
1230
ZETA
2o~a
2
57
eso
660
36
2Z
Figures 5A and 5B. Figure 5A shows the infrared absorption spectra of HNIW (A, B, and C) at room temperature and the following pressures: Spectrum A at 0. 16 GPa: Spectrum B at 0.9 GPa: and Spectrum C after lowering the pressure from 0.9 to 0.4 GPa. Figure 5B shows the infrared absorption spectra for ot. 6. f. and P HNIW polymorphs at room temperature and 0.9 GPa showing the differences in the absorption bands among the various phases.
2S~S
209
1.3.-Trinitrohexahvdro-1.3.5-triazine Three solid polymorphs, identified as a, 03, and I were found for RDX. The equilibrium/reaction phase diagram is presented in Figure 6. The determined polymorph stability fields for the three RDX phases are as follows: (I) the stable ambient orthorhombic phase, a, (2) the high pressure phase, y, stable above 3.8 GPa, and (3) the high-temperature and high-pressure phase, P, stable above 2.7 GPa and 225 °C. Between atmospheric pressure and 2.5 GPa, no solid/solid phase transitions are observed for a RDX. a phase melt/decomposition is detected between 215-225 0C up to 2.5 GPa. Between 2.5 and 3.8 GPa at 225 °C, a reversible a-P solid/solid phase transition is detected. a RDX is observed to change to another orthorhombic phase, y, at about 3.8 GPa at room temperature. The a/y phase boundary was found to be essentially temperature independent at 3.8 GPa to 225 *C. Above 225 °C, a unidirectional solid/solid phase transition is observed between y and P RDX up to 7.0 GPa. 03RDX melt/decomposition is detected between 225-275 °C and 2.5-7.0 GPa. The 0 and y RDX phases may be retrieved to ambient temperature at elevated pressures above 3.8 GPa. At room temperature 0 and y RDX transform to a RDX when the pressure is decreased. The y phase reverts to the a polymorph near 3.5 GPa, while the 3polymorph reverts to the a phase as the pressure nears one atmosphere. The thermal decomposition parameters for the a and P polymorphs are as follows: (I) below 2.5 GPa melt/decomposition of a RDX is observed and (2) above 2.5 GPa P RDX melt/decomposition is detected. Furthermore, decomposition of a and P3 phases is observed at temperatures below the melting curve. The rate of thermal decomposition of a RDX increases with increasing pressure between 1.4-2.1 GPa. The AH' for a RDX is equal to 51 Kcal/mol with an AV* of -5.6 cc/mol within the same pressure region [4).
Z0
-
RDX
o0
Liquid
13
i
S2ooJ 1
f5.4
too-
7RDX
a RDX
50'
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
PRESSURE (CPU) Figure 6. Equilibrium phase diagram for RDX showing the stability fields for three solid phases, ce, P and y'and the liquidus or melting point.
210
Ammonium Dinitramide. A preliminary equilibrium phase diagram for ADN is shown in Figure 7. Two
solid ADN phases, a and 03, have been found in the pressure regime up to 10 GPa. The pressure dependence of the melting temperature has been measured. Between atmospheric pressure and 0.9 GPa, melt/decomposition is observed above 95 °C. At room temperature and approximately 2.5 GPa, a solid/solid reversible phase transition between a and 13 ADN polymorphs was detected by OPLM, EDXD and Raman spectroscopy. Identification ADN phase by FTIR spectroscopy was not possible because severe of the high pressure 1P pressure broadening in the infrared absorption spectrum greatly reduced resolution. The temperature dependency of the transition has not been determined. Above 1.0 GPa and 95 *C,melt/decomposition was no longer observed. A solid phase decomposition reaction was detected by a significant change in birefringence in OPLM studies and a corresponding change in the infrared absorption spectra. The solid rearrangement observed at elevated temperatures and pressures has been identified as the conversion of ADN to ammonium nitrate (AN, phase I) and NMO. Confirmation of the high temperature AN phase was done by OPLM studies. Upon formation of AN at high pressure and high temperature, the pressure was then decreased to atmospheric. Then, as the temperature was decreased on the sample, all the known temperature dependent phase transitions between phase I and phase IV of AN were observed at their reported transition temperatures [28]. The decomposition parameters for ADN are as follows: (1) a-ADN melts/decomposes between atm and 0.9 GPa forming AN and N20 and (2) 13-ADN decomposes via a solid/solid rearrangement to AN (phase I) and N20 above 0.9 GPa and 140 *C. These decomposition parameters represent a moderate decomposition rate, i.e., < 5 min. Low temperature, very slow ADN decomposition is also detected at 60 0C at atmospheric pressure [29]. 400 AN MELT/DECOMPOSITION 300
•
Kr• AN S2001)+N20 +
DEC SOLID PHASE REARRANGEMENT S00
too
o0
0
ADN MELT/DEC *
A ...100. 0.0
. . .
.
,
2.0
i.
i
.
*
p . . Ia '*
4.0
AN ADNAN MWITDEC a',' 1
I 1I
I
6.0
I
8.0
I
I
II
*M!
10.0
PRESSURE (CPa)
Figure 7. Preliminary Equilibrium/reaction phase diagram for ADN. indicating the reversible &-ft ADN transition at room temperature. the liquidus or melting point, and the solid state conversion to AN (1)and NO.
211
g.Nitromnitine The equilibrium/reaction phase diagram for p-nitroaniline is shown in Figure 8. Three solid phases for PNA (I, II, and Ill) have been identified. The liquidus of Phase I has been measured from atmospheric pressure to 1.0 GPa and 150-240 *C. During melting the PNA undergoes a chemical reaction, becoming dark and leaving a reddishbrown residue. Between 1.0-4.0 GPa and above 140 °C, a reversible phase transition, I -+II, is detected. Above 245 *C,melting is not observed for phase II. Phase II decomposes above 245 °C between 1.0 and 4.0 GPa. Between 0.0-25 °C at 4.0 GPa, another reversible solid/solid phase transition, I ++I1, has been identified. Thus, in the P, T domain studied, there appears to be three solid forms of p-nitroaniline, I, II, and 1M1. Phases II and 111, upon release of pressure revert to form 1,which is the stable form at ambient conditions of pressure and temperature. The decomposition parameters for PNA are as follows: (1) below 1.0 GPa, I melts and decomposes between 140 and 245 °C, (2) between 1.04.0 GPa and above 245 OC, II decomposes, and (3) above 4.0 GPa and 245 'C, a black amorphous material is formed during decomposition. However, at this time it is not known whether phase II or phase III is decomposing.
400
CHEMICAL REACTION .. ''
',.'300
S_
ZO0
-
--
-
''
SOLID II
I
nSOLID
EO-4
o SOLID I MELT n SOLID Ir' SOLID II SOLID 1 . SOLID III * CHEMICAL REACTION 3.0(CPa)
SOLID III
A
02.0
PRESSURE
4.0
5.0
Figure 8. Equilibrium phase diagram for PNA, indicating the stability fields for the
three known polymorphs (1, II, and IlI), the liquidus or melting point, and the solid state
chemnical reacticn be.'e' 1.0 and 4.0 GPa above 280°C.
ACKNOWLEDGMENTS The authors wish to acknowledge financial support from the U.S. Army Research Office, the Office of Naval Research and the Naval Surface Warfare Center Independent Research Program.
212
REFERENCES
' Certain trade names and or products are mentioned in the text in order to adequately specify the experimental procedure and equipment used. In no case does such identification imply recommendation or endorsement by NIST nor does it imply that the product necessarily is the best available for the purpose. 1. Y. M. Gupta, Shock Compression of condensed Matter, edited by S. C. Schmidt, R. D. Dick, J. W. Forbes, and D. G. Tasker (Proceedings of the American Physical Society Topical Conference, Williamsburg, VA, 1991) pp. 15 and all included references. 2. T. P. Russell, P. J. Miller, G. J. Piermarini, S. Block, J. Phys. Chem, 96, 5509 (1992). 3. T. P. Russell, P. J. Miller, G. J. Piermarini, S. Block, J. Phys. Chem., (in press). 4.
G. J. Piermarini, S. Block, P. J. Miller, The Chemistry and Physics of Energetic Materials, ed. by S. Bulusu, (NATO Advanced Study Institute, 309, Altavilla Milicia, Sicily, September 3-15, 1989), pp. 369-412.
5. Barnett, J. D.; Block, S.; Piermarini, G. J., Rev. Sci. Instrum., 44, 1 (1973). 6.
G. J. Piermarini, S. Block, J. D. Barnett, and R. S. Forman, J. Appl. Phys., 46. 2774 (1975).
7.
Block, S.; Piermarini, G. J., Physics Today. 29, 44 (1976).
8. P. J. Miller, G. J. Piermarini, S. Block. Appl. Spectrosc., 38, 680 (1984). 9.
P. J. Miller. S. Block. G. J. Piermarini. Combustion and Flame, 83, 174 (1991).
10. G. J. Piermarini, S. Block. J. D. Barnett. J. Appl. Phys., 44, 5377 (1973). 11. F. A. Mauer. S. Block. G. J. Piermarini. American Crystallographic Association. Program and Abstracts of Summer Meeting. Boston University. Boston. MA Aug 12-17, Paper G3 (1979). 12. C. E. Weir, E. R. Lippincott, A. Van Valkenburg. and E. N. Bunting. J. Research NBS, 63A. 55 (1959). 13. J. C. Jamieson, A. W. Lawson. N. D. Nachtrieb. Rev. Sci. Instrun.. 30, 1010 (1959). 14. G. J. Piermarini and C. E. Weir. J. Research NBS. 66A. 325 (1962). 15. W. A. Bassett. A. T. Takahashi. and P. W. Stock. Rev. Sci. Instrum.. 38. 37 (1967). 16. H. K. Mao. ar P % Bell. in Canu,.jc Institution of Washington Year Book. 77. 904 (1978). ,.
17. K. R. Hirsh and W. B. Holzapfel. Rev. Sci. Instrumn.. 52, 52 (1974). 18. L. Merrill. and V. A. Bassett, Rev. Sci. Instrum.. 45, 209 (1974).
213
19. T. P. Russell and G. J. Piermarini, presented at the FT-Raman Vibrational Spectroscopy Workshop, Bethesda, MD, May 1992 (unpublished), T. P. Russell and G.J. Piermarini, (to be published). 20. B. C. Giessen and G. E. Gordon, Science, 159, 973 (1968). 21. L. M. Albritton and I. L. Margrave, High Temperatures-High Pressures 4, 13 (1972). 22. B. Buras, J. Staun Olsen, L. Gerward. B. Selmark, and A. Lindegaard Andersen, Acta Cryst., A31, 327 (1975). 23. T. P. Russell, G. J. Piermarini, and S. Block, presented at ONR Workshop on ADN, Arlington, VA, Feb. 1992 (unpublished), T. P. Russell, and G. J. Piermarini, S. Block, (to be published). 24. S. Block and G. J. Piermarini, SPIE, 878. 21 (1988). 25. R. Y. Yee, M. P. Nadler, A. T. Neilson, JANNAF Proceeding, CPIA publication. October 1990. 26. K. J. Kraeutle, JANNAF Proceedings, CPIA publication #498, October 1988. 27. K. J. Kraeutle, JANNAF Proceedings, CPIA publication. November 1990. 28. P. W. Bridgman, Proc. Amer. Acad. Arts Sci. 51. 581 (1916). 29. T. P. Russell, A. W. Stern. W. Koppes, and C. D. Bedford. JANNAF Proceedings. CPIA Publication #593, October 1992.
215
THE GROWTH AND PERFECTION OF SINGLE CRYSTALS OF TRINITROTOLUENE C(NT) HUGH G. GALLAGHER AND JOHN N. SHERWOOD University of Strathclyde, Department of Pure and Applied Chemistry, 295
Cathedral Street, Glasgow GII XL, Scotland, UK. ABSTRACT A study has been made of the crystal growth behaviour and perfection of TNT. Depending on the purity and the solvent used, crystallisation from solution yields material of monoclinic, twinned monoclinic or orthorhombic forms. Of these only the monoclinic form was suitable for detailed study by X-ray topographic techniques. The crystals of the orthorhombic form were too small and imperfect for examination.
Seeded growth from ethyl acetate solution yielded lamellar twinned crystals in
which the twin density was low. Under ideal conditions, relatively perfect samples could be obtained in which the dominant residual growth defects were stacking
faults of Burgers vector b */2 [001] and dislocations. INTRODUCTION
In common with other molecular solids, the physical, chemical and mechanical properties of solid explosives are influenced by lattice defects. It is hardly surprising, therefore, that crystal imperfections are believed to play a role in the
initiation and subsequent decomposition of energetic materials [1]. The impact initiation of crystalline explosives is generally accepted to occur by conversion of the mechanical energy of impact into heat within small volumes of the solid known as hot spots. Several mechanisms involving dislocation slip which occurs during the plastic deformation which accompanies impact have been proposed to explain the formation of these ' hot-spots' [2]. Little is known however about the nature of defects in these materials on which to base reasonable theoretical models. In order to redress this situation, a detailed study of the properties of growth and mechanically induced defects in a number of organic energetic materials has been undertaken [3,4]. The work reported here is an abbreviated description of the initial stages in the assessment of one of these materials trinitrotoluene (TNT) [5]. CRYSTALLISATION OF TNT TNT is known to crystallise in two basic polymorphic forms [6] orthorhombic Pb2 1 a a= 15.005 A, b= 20.024 A. c= 6.107 A monoclinic
P2 1 /c
a= 21.275 A, b= 6.093 A, c= 15.025 A.
,
=
110.230
Depending on the conditions imposed, it is reported -.: a, these may crystallise separately or even simultaneously ab ::on7plex mixed pnase crystals. Despite intensive investigations, however, the conditions for the crystallisation of the various structural modifications have not yet been clearly defined. In order to prepare crystals suitable for examination by X-ray topography, it was necessary first of all to define the nature of polymorphism in TNT crystallised from solution. Mat. Res. Soc. Syrup. Proc. Vol. 296. P19S3 Materials Research Society
216
Crystals of high optical quality were grown from a wide range of organic solvents by the slow evaporation of saturated solutions. The structural nature and perfection of these crystals were systematically determined using various x-ray diffraction techniques. The crystals were found to exist in three basic forms: monoclinic, orthorhombic and twinned monoclinic depending on the crystallising solvent. The crystallisation results are summarised in table 1. Subsequent examination revealed that the orthorhombic polymorph is metastable under ambient conditions and transforms to the monoclinic form over a period of time. On raising the temperature the transformation is instantaneous at 344 K. The monoclinic form was found to be stable up to the melting point, 354 K. The synchrotron radiation source proved to be extremely useful for the characterisation of the twinned and untwinned monoclinic crystals. TABLE I The Influence of Crystallization Solvent on the Morphology of TNT Crystals Solvent Ethylacetate Methanol Toluene Acetone Ethanol Cyclohexanol
Habit* L. N. P. N. N. N.
R. P. R. P. R. P. R. P.
Colour Faint Yellow Dark Amber Yellow Amber Amber Amber
Polymorph
Twinned
Monoclinic Monoclinic Monoclinic Monoclinic Orthorhombic Orthorhombic
Yes/No Yes Yes Yes
-
* L. = Lozenge; N. = Needles; R. = Rods; P. = Plates, SYNCHROTRON X-RADIATION STUDIES OF TWINNING The broad spectral range and low beam divergence available at the UK Synchrotron Radiation Source. Daresbury Laboratory is ideal for the study of twinned structures such as those found in TNT. Due to the large diameter of the beam (2 cm) full crystal Laue diffraction patterns can be taken in which each spot is a full topographic image of the crystal [7]. Since a twinned crystal consists of regions of identical crystallographic structure arranged in different symmetrical l related orientations, then the diffraction pattern record, simultaneously the diffraction pattern of each twin. Where the degree of twinning is low this enables the positions of each twin in the crystal to be identified and at the same time it allows an assessment to be made of the overall defect conce,'.:'ion and configurautm The diffraction patterns of both a twinned and untwinned crystal of the monoclinic phase taken with the synchrotron beam normal to the basal (100) plane are shown in Figure 1. From the symmetry of the pattern for the twinned crystal. the twin law can be defined as 1800 rotation about an axis normal to the (100)
217
Figure I
S
'a
(a) (a)
(b)
.a
Full Crystal Laue Diffraction Patterns of TNT crystals taken using Synchrotron Radiation (a) Untwinned Crystal; (b) Singly twinned Crystal Figure 2
Enlargements of the two twin images circled on Figure I showing the different defect structures in the two lamellae: I. strain due to impurity incorporation; D. dislocations: and S. stacking fault. The upper surface is a fracture surface and not a habit face.
218
plane. To illustrate the detail in the diffraction images, an enlarged pair of twin reflections are shown in Figure 2. These clearly show the differences in the defect structure of the separate twin lamellae. Similar diffraction p,-terns taken of sections of the crystals cut perpendicular to the (100) plane and with the synchrotron beam normal to the (010) plane, provide information on the distribution of the twin layers in depth and thus allow the full characterisation of the specimen. In this way, by study of the varying twin structure of crystals grown under a range of growth conditions, the conditions for the preparation of untwinned crystals can be defined. SINGLE CRYSTAL GROWTH AND PERFECTION Large crystals of the stable monoclinic form of TNT were grown from ethyl acetate solutions by the slow cooling of seeded saturated solutions. Temperature lowering rates lay in the range 0.003 - 0.01 K/hr- 1 over the temperature range 302-309 K. X-ray transmission topography [8] of the crystals showed them to have a characteristic growth induced defect structure in which the overall perfection is determined by the incorporation of residual impurities into the lattice. Regions of high impurity concentration are strained and appear as a dark contrast on the topographs. This is well exemplified by the topographs shown in Figure 2. Several points should be noted -
the lateral growth sectors are highly strained due to the preferential incorporation of the impurities into these sectors compared with the extended growth sectors.
-
the deviations in the trajectory of the boundary between the lateral and the extended growth sectors reflect changes in the relative growth rates of the faces associated with these sectors. One explanation of this is that impurities absorbed onto one of the growing faces inhibits its growth rate. The observation that these changes are frequently accompanied by grov. th banding in the sectors supports this view.
-
linear (dislocations) and planar (stacking faults and twins) defects are generated at solvent inclusions which are trapped in the vicinity of the seed.
The dominant growth defects in high quality crystals of TNT are stacking faults dislocations and twins. In Figure 2. the stacking fault is visible as a wedge shaped area of uniformly dark contrast bordered by well-defined lines of even greater contrast. This type of defect contrast is characteristic of stacking faults bounded by partial dislocations. Occasionally dislocations are observed but they are usually fewer in number than the other defects. Characterisation of the topographic images using the techniques of extinction contrast [81 showed that the predominant strain vector associated with the stacking faults was b [001].
219
ACKNOWLEDGEMENTS We gratefully acknowledge the financial support of this work by the US Office of Naval Research, Washington. REFERENCES I.
i.E. Field, N.K. Bonner, SJ.P. Palmer and S.M. Walley, Phil. Trans. Roy. Soc. A329, 269 (1992)
2.
C.S. Coffey, Phys. Rev. B24, 6984 (1981); C.S. Coffey and SJ. Jacobs, J. Appl. Phys. 52 6991 (1981); C.S. Coffey and R.W. Armstrong, Shock Waves and High Strain Rate Phenomena in Metals, edited by MA. Myers and L.E. Murr (Plenum, NY, 1981) p. 313.
3.
PJ. Halfpenny, KJ. Roberts and J.N. Sherwood, J. Appl. Cryst. 17, 320 (1984); J. Crystal Growth 67, 202 (1984); J. Materials Sci. 19, 1629 (1984).
4.
H.G. Gallagher, PJ. Halfpenny, i.C. Miller and J.N. Sherwood, Phil. Irans. Roy. Soc. A299, 293 (1992).
5.
H.G. Gallagher and J.N. Sherwood, to be published, 1993.
6.
C.R. Duke (private communication).
7.
A.R. Gerson, PJ. Halfpenny, S. Pizzini, R.I. Ristic, KJ. Roberts and J.N. Sherwood, Materials Science and Technology - A Comprehensive Treatment, edited by R. Cahn and E. Lifshin (VCH, Weinheim, 1992) p. 557.
8.
A.R. Lang, Diffraction and Imaging Techniques in Materials Science, edited by S. Amelincx, R. Gevers, G. Rimaut and J. van Landuyt, N. Holland, Amsterdam, 1978) p. 623.
221
ATOMIC FORCE MICROSCOPY OF AMMONIUM PERCHLORATE MINSUN YOO, SEOKWON YOON, AND ALEX DE LOZANNE Department of Physics, University of Texas, Austin, TX 78712-1081, USA ABSTRACT
We have studied the (210) surface of ammonium perchlorate (NH 4 CIO4 ) with an atomic force microscope (AFM) in air. Large scale images show monomolecular steps that are often aligned with major crystalline directions. Surface modification is clearly observed with forces as low as 30 nN, but is usually limited to the bottom and the sides of the field of view, where the tip scans for a long time and where it turns around, respectively. At the molecular scale we have observed structures with substantial order, with minimum lateral sizes of 3 A. The identification of these features is difficult due to the large unit cell of this compound (40 atoms per unit cell), and the lack of perfect order in the images. We use the SARCH/LATUSE program developed by Van Hove and Hermann to analyze this structure. Ammonium perchlorate is hygroscopic; it is therefore possible that surface modification is enhanced by the moisture present in air. Experiments in a dry atmosphere have confirmed this explanation. We have therefore designed and built a UHV (ultra-high vacuum) AFM for these studies. The first images from this instrument are presented here. INTRODUCTION Energetic crystals have been used in many applications for decades, some even have been utilized for centuries. Yet the basic mechanisms for the initiation of the exothermic reaction in these materials is not known. A large amount of empirical data exists, but a detailed understanding of what happens at the molecular level is lacking. Our long term goal is to contribute to this understanding by probing the structure of these materials down to the molecular level, and by attempting to initiate and study reactions within a microscopic volume. Most energetic crystals are insulating; it is therefore not possible to study them with the electron-based microscopies that yield the highest resolution, namely Transmission Electron Microscopy and Scanning Tunneling Microscopy. The Atomic Force Microscope (AFM). invented by Binnig, Quate and Gerber[ 1], is the only instrument that can image insulators with high resolution, in some cases even atomic resolution. We have used the AFM to study crystals of ammonium perchlorate. RDX, and TATB. Thus far the most interesting results have been obtained with ammonium perchlorate, which we present here. CRYSTAL STRUCTURE Ammonium perchlorate (NH 4 CIO 4 . denote~d as AF hereafter) is an insulator with an orthorhombic unit cell of dimensions a=9.202A, b=5.816A, and c=7.449A, and Pnma space group.[2] Each unit cell contains four ammonium ions and four perchlorate ions, as illustrated in fig. 1, for a total of 40 atoms per unit cell. At room temperature the ammonium ions rotate as a single unit about their location in the unit cell.[31 We have used the SARCH/LATUSE program developed by Van Hove and Hermann[4] to analyze this crystal structure. In all our crystal diagrams the ammonium ions are drawn as the largest spheres, followed by medium spheres for the chlorine atoms and small spheres for oxygen
Figure 1. A perspective view of the atoms in a unit cell of NH 4 CIO 4 . The largest spheres ,epresent the rotating ammonium ions, the next largest are chlorine atoms, and the smallest are oxygen atoms. The unit cell dimensions are a=9.202A (to the right), b=5 816A (up). and Four NH 4 C10 4 c=7.449A (out of paper). molecules are contained in the unit cell, for a total of 40 atoms. Figures 1-3 were generated with the SARCH/LATUSE programl4j. Mat. Res. Soc. Symp. Proc. Vol. 29. K,1993 Materials Research Society
222
atoms. Our results for the (100), (010) and (001) projections agree with the diagrams published by Williams et al.[5]. For the sake of brevity we show only the (001) projection in figure 2, since it will be helpful in visualizing the AFM data that follows. We have studied the (210) surface of AP, since it is a natural cleavage plane. It is not known, however, which of the many parallel (210) planes is actually exposed during cleaving. We now discuss which plane is most likely to be exposed. The (210) planes are perpendicular to the plane of figure 2 and they intersect it along the diagonal lines shown. A crystal may cleave along these lines or along any other parallel plane. This structure has ten inequivalent (210) planes (going through the nuclei), with a d spacing of 3.608A. It is difficult to predict which of these planes will be exposed when the crystal is cleaved. A reasonable possibility is that the cleave occurs between planes that have the largest spacing between them and the least number of molecular bonds crossing the plane. The distance between ineq.uivalent (210) planes is, in decreasing order, 0.801A, 0.793A, 0.638A, 0.328A, 0.028A, and 0.010A (the last four spacings occur twice). The diagonal lines in figure 2 are midplanes between planes separated by the largest distance, 0.801A. This is also a good choice for a cleavage plane because there are no strong bonds crossing these planes: all perchlorate ions and all ammonium ions are comp'etely on one side or the other. This is therefore likely to be a weakly bonded plane, which would be most likely to cleave. Taking this plane to be the cleaved surface, we make a (210) projection showing only the atoms within the slab bound by the two equivalent (210) midplanes in figure 2. The thickness of this slab is 3.608A (same as the d-spacing). This slab shows a good symmetry, which we have not observed in any other parallel slabs that we have studied. The depth of the slab is about the deepest that one would expect to see with the AFM, taking into account that the typical lateral spacing of the structure is also about 3 A. For simplicity, a possible surface reconstruction will not be considered here. We note that our result for the (210) projection is different from the one published in ref. 6. The main difference is that they obtained a (210) surface unit cell that is 7.42A along the direction, as one would expect from the crossing of a (210)2 plane 2 through a single bulk unit cell (this gives a length along of (b2+(a/2) )11 = 7.416A). A careful analysis of this geometry, however, shows that the (210) surface unit cell should cross two bulk unit cells along the < 120> direction, thus giving a cell length of 2 x 7.416A = 14.832A. The (210) surface unit cell should therefore be 14.832A along < 120> by 7.449A along , which agrees with the result of the SARCH/LATUSE program.
Figure 2. Projection of the AP crystal along (001). Three unit cells are drawn in each direction. The a-axis (a=9.202A) is horizontal and the b-axis (b=5.816A) is vertical. The two diagonal liner ii-ica,the intersection of two (210) planes (which are perpendicular to the paper) with the p!ane of the figure. The atoms contained between these two planes are projected onto the (210) surface in figure 3. The different atoms are identified as in fig. 1.
iigure 3. Projection of the AP crystal along (210). The axis is horizontal and the c-axis is vertical. The boxes mark two unit cells (14.832A x 7.449A each). The different atoms are identified as in fig. 1.
223
EXPERIMENTAL RESULTS IN AIR The sample was cleaved to expose a fresh (210) face and was immediately imaged in air with a Park Scientific Instruments AFM (SFM-BD2) using a cantilever with dimensions L=1OOpm, w=10tm, and t=0.6,um, and a spring constant of approximately 0.08N/m. Images were obtained in the repulsive mode with a constant lever deflection of 0.52sm, thus yielding profiles with an equal force of approximately 42nN. There may be additional forces between the tip and the sample (e.g. electrostatic, or surface tension of the adsorbed water layer on the tip and the sample); we plan to measure these possible additional forces in the future. Figure 4 shows a representative image of the (210) surface on a scale of 5nm on a side. The usual precautions were taken to ensure the validity of the data, namely changing the image size, the scanning frequency and scanning rotation. The interpretation of these images is complicated by the large size of the unit cell and the possibility of cleaving through various parallel planes. The image in figure 4 has a scale and symmetry similar to the (210) projection in figure 3. Unfortunately, irregularities in the data and the
complexity of the surface unit cell prevent us from making a definite assignment of each
feature in the image at this time. Figure 5 shows very interesting patterns formed by the scanning tip. Trenches are dug around the side edges, where the tip turns around as it scans back and forth, or the top and bottom edges, where the tip scans repeatedly while waiting to take a new image. As larger images are taken in the same area, the trenches created by the previous image are clearly seen. The delpth of the trenches is usually a multiple of the d spacing for (210) planes, namely Nx3.6A. Other natural steps with similar heights are observed to run along nearly straight lines at various angles. The deviations from linearity are probably due to scanner distortion, which is common in images of this size. The angles are likely to be major crystalline directions. Indeed, a comparison with figure 4 shows that the step in the upper right corner runs exactly along one of the atomic (or molecular) rows. Another example is the straight step in the lower half (running 20 degrees counterclockwise from horizontal). The height of all these steps is the same. Finally, the holes in the upper right comer grew as the image was taken, while most of the other features remained unchanged, indicating I that certain regions are more susceptible to mechanical damage. An important parameter in the deformation of the surface is the pressure exerted. Taking the force estimated above (42nN), and estimating the contact area to be the square of the width of the trenches observed (38 rnn), a lower limit for the pressure is about 29 MPa. If the contact area is taken to be nmm2 (assuming contact over one molecule), then the upper limit is about 40 GPa, which is clearly an overestimate (the ultimate strength of steel is 0.4 GPa). Given that the tip modifies the surface, it is difficult to understand how an image with molecular resolution, like Fig. 4, can be obtained. We can only emphasize that such images are obtained immediately after cleaving, and that the surface modification is due to softening caused by adsorbed water, as is discussed in the next section. Furthermore, the understanding of atomic resolution in the AFM, given the large pressures exerted, is still in its infancy.
Figure 4. AFM image taken at constant force of approx. 42nN, with a lateral size of approx. 5 rim.
Figure 5. AFM image taken at constant force of approx. 42nN, with a lateral size of approx. 2prm. Clear evidence of surface modification is observed, as well as natural steps.
224
EFFECTS OF MOISTURE
Now we turn to recent measurements on the effects of ambient moisture on the surface modification of AP. Moisture was controlled by putting silica gel desiccant inside the AFM head before loading the sample. The sample was cleaved with a blade and immediately imaged using a cantilever with dimensions L=100um, w=10am, and t=0.6pm, and a spring constant of approximately 0.08N/m. Images were obtained in the repulsive mode with a constant lever deflection of 0.521tm , thus yielding profiles with an equal force of approximately 42nN. We observed no evidence of surface modification. We then removed the desiccant and continued taking data. Still, there was no surface modification: apparently it takes some time for the surface to absorb water and become soft. We increased the probing force to 0.5,uN by using a lever with k=.21N/m at a deflection of 2.5pum. Eventually we observed surface modification, as shown in the sample image of figure 4. The modification seemed to be a function of the total time that the surface was exposed to moisture, and not related to the increase in force. To confirm this conjecture, we put the desiccant back into the AFM head. Again, no immediate change was seen, as we were still able to modify the surface. Over the period of one hour the ability to modify the surface was lost, indicating that moisture was removed. To further study the effects of moisture we built a simple chamber for the air AFM. The chamber is pumped by a mechanical pump and backfilled with dry nitrogen. The
Figure 6. All three images arc 1.2 jrm on a side and were taken after scanning images of 1/2, 1/4. and 1/8 of this size. Surface modification is observed clearly in the center image. which was taken after exposure to ambient moisture. The centcr of the image shows the areas scanned before this image was taken. The left image was taken with desiccant in the AFM head and a fresh cleave, while the image on the right was taken after the exposure to moisture b,!t with desiccant again present.
Figure 7: AFM images of AP obtained in a dry nitrogen atmosphere. The image on the lelt. which is 1.3 um on a side. shows very interesting steps. while the one on the right v, 13 nm in size and shows molecular resolution.
225
sample was cleaved immediately before mounting in the AFM and pumping down. The surface degradation is no longer observed in dry nitrogen, even two weeks after cleaving the sample. Clear steps are observed on this surface, as shown in Fig. 7a, while molecular resolution is not as clear as before, as shown in Fig. 7b. We have observed other interesting effects on AP surfaces. For example, on a few images there is a popping noise that we have not observed with any other samples. An exciting possible explanation is that the tip causes local decomposition of AP, causing a localized exothermic reaction which kicks the AFM tip off the surface. Further study of these effects will be done in a more controlled environment, namely ultra high vacuum. ULTRA HIGH VACUUM ATOMIC FORCE MICROSCOPE The deleterious effects of water on the surface of AP, as shown above, and the desire to study surface decomposition have motivated us to design and build a UHV AFM. since Furthermore, even if the surface of the commercial instruments are not yet available. sample is not soluble in water (like RDX and TATB), the capillary forces caused by layers of water adsorbed on the tip and sample reduce the force resolution and therefore degrade the spatial resolution of the AFM. We discuss briefly the design philosophy of our UHV A full description will be published AFM and demonstrate that it operates well. elsewhere. The force between the tip and the sample is measured by monitoring the deflection of a microfabricated cantilever that holds the tip, a standard technique in AFM. The deflection is measured by bouncing a laser beam on the cantilever and onto a position sensitive detector.. We use a He-Ne laser outside the UHV chamber, coupled to a single mode optical fiber that goes through a homemade UHV feedthrough into the chamber. The fiber ends with a sharpened cone within 20 pm of the cantilever. We have developed an accurate and very compact positioning device to align the fiber with the cantilever. The sample is scanned in three axes with a standard piezoelectric tube scanner[7]. The coarse approach between the tip and sample is accomplished with a standard tripod of fine-threaded screws. The AFM body hangs inside the UHV chamber from soft springs. A custom window on the side of the chamber allows viewing of the tip and sample area from a distance of only 8 mm, which allows the use of an optical microscope with a high magnification of 400x. The first test and calibration of this instrument was done in air. More recently we have demonstrated operation in vacuum. Figure 8 shows an AFM image obtained in vacuum of a test grating with a period of 1.9 pm. In addition to the clear ripples of the grating. the image has details of imperfections on some ripples, indicating high resolution. Graphite samples will be used in the near future to test for atomic resolution. CONCLUSIONS We have obtained AFM images of the (210) surface of ammonium perchlorate (NH 4 CIOa) ranging from 5 nm to 12 pm in size. We'have observed surface features with a resolution of 3 A. which is the first time for this material. While the size and overall structure is similar to what is expected, based on previous information about the bulk lattice. a definite assignment of features to atoms is not yet possible. Monomolecular steps are Surface observed for the first time. modification is clearly observed, which is almost certainly due to softening of the surface as it absorbs moisture from the air. Tests with desiccant and in a dry nitrogen atmosphere A novel have confirmed this hypothesis. design for a UItV AFM was implemented. This UItV AFM should built and tested achieve higher resolution on ammonium pcrchlorate. TATB. RDX and CI-20.
Figure 8. AFM image obtained with a new UIlV AFM operating in vacuum. The image is 12pm on a side; the grating has a period of 1.9pm and a vertical modulation of 0.5pm.
226
ACKNOWLEDGEMENTS We thank J. Sharma for providing AP samples as well as a wealth of basic information about this material. This work is supported by the U.S. Office of Naval Research (N00014-90-J-1858). REFERENCES [1] [2) [3] [4]
G. Binnig, C. F. Quate, and Ch. Gerber, Phys. Rev. Lett., 56, 930 (1986). R.W.G. Wyckoff, Crystal Structures, vol. 3 (Interscience, New York, 1963) p. 4 8 H.G. Smith and H. A. Levi, Acta Cryst. 15, 1201 (1971). SARCH/LATUSE 3.0, developed by M.A. Van Hove, Department of Chemistry, UC Berkeley, Berkeley, California 94720, USA (BITNET vanhove@LBL) and K. Hermann, Havelmatensteig 21, D-1000 Berlin 22, Fed. Rep. of Germany (BITNET: hermann@vax.hmi.dbp.de) [5] J.O. Williams, J.M. Thomas, Y.P. Savintsev, and V.V. Boldyrev, J. Chem. Soc. All (Inorg. Phys. Theor.), 1757 (1971). [6] P.J. Herley, P.W.M. Jacobs, and P.W. Levy, J. Chem. Soc. All (Inorg. Phys. Theor.), 434 (1971). [71 G. Binnig and D. P. E. Smith. Rev. Sci. Instrum.. 57, 1688 (1986).
227
ENERGETIC CRYSTAL-LATTICE-DEPENDENT RESPONSES R.W. ARMSTRONG*, H.L. AMMON+, Z.Y. DU+, W.L. Elban#, X.J. ZHANG* *Department of Mechanical Engineering or +Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742. #Dept. Engineering Science, Loyola College, Baltimore, MD 21210. ABSTRACT The occurrence )f [100] direction slip on the (021) slip plane of orthorhombic hDX (cyclotrimethylenetrinitramine, (CH2oN.NO 2 ]) is shown to favor the formation of 1,3-dinitroso-5nitro-1,3,5-triazacyclohexane, as detected in drop-weight impact tests at sensitiv.ty height levels near to those measured for Also, the reported observation of deformation initiation. twinning in the chemically-related monoclinic HMX (cyclotetra[CHrN- NO2], ) crystal lattice is methylenetetranitramine, explained on the basis of the greater flexibility of the larger HMX molecule allowing a number of bond rotations that are required to produce a relatively unusual Type II deformation These examples give support to the twinuing structure. consideration that on the molecular level involved in deformation-induced decompositions there may be a direct mechanical force aspect that is additional to the established importance of 'hot spot' heating, say, as described for dislocation pile-up avalanches in RDX. RDX HOT SPOT AND 'BOND-BREAKING' Armstrong,
DEFORMATIONS
Coffey, DeVost ana Elban [1] have given a detailed
description of the generation of hot spots in RDX at the slip band level in individual crystal particles of powder samples subjected to drop-weight impact testing. Hot spots were proposed to occur at dislocation pile-up avalanches that are produced when microslip bands break through blocking obstacles between, or possibly within, the crystals. The hottest spots occur when an
avalanche is released after the microstructural stress intensity Alternatively, RDX and for brittle fracturing is achieved. related energetic crystals are observed experimentally to be plastic flow normally relatively hard and brittle so that little occurs on a macroscopic scale before considerable shattering of
crystals is produced under the action of impact forces leading to
the initiation of fast decomposition. those of a number The strength properties of RDX, relative to of other materials, are illustrated in the microindentation elastic/plastic/cracking results [2] shown in Figure 1 on a An increasing continuous indentation stress/strain basis (33. elastic stiffness for the labelled materials is indicated by the higher ordinate (hardness) stress values of the initial linear Hertzian lines shown at each value of the effective strain defined by the contact-diameter-to-ball-diameter ratio on the Thus RDX is seen to be elastically more abscissa scale. compliant than NaCl. However, tne plastic hardness of RDX, shown in Figure 1 L-*Ii for a nlumber of points on a continuous indentation deformation basis or for the Vickers diamond pyramid
hardness (VHN) value shown at an effective strain of 0.375 for the same range of materials, reveals that RDX is more than twice In addition, the hardness of RDX is shown in as hard as NaCl.
Figure 1 to be relatively high compared to a theoretical cracking Mat. Res. Soc. Symp. Proc. Vol. 296.-1993
Materials Research Society
228
stress that is put at the terminal points for different indenting ball diameters on the RDX and other material elastic loading lines, as evaluated on an indentation fracture mechanics basis. The comparison of properties shows that RDX, though elastically compliant is relatively hard and brittle. 3000
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229
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on
01oo
Fig. 2. Molecular displacements for an edge dislocation in RDX. molecules both near to the dislocation and in the referenc) cell. The (100)(040) dislocation was constructed to explain the first reported observation of (010) slip by Connick and May [5]. Slip for the smaller dislocation Burgers vector along [001) was discounted (4] on the basis of intermolecular blockages occurring in this direction across (OkO). Elban, Armstrong and colleagues (6-9] reported also the prominent occurrence of slip on (021) and (02'1) systems at microindentations in RDX. Figure 3 indicates the intermolecular interactions occurring across the (021) plane spanning two neighboring unit cells. As indicated, 04-02 blockages are produced in this instance for the same favored (1003 slip direction as described for tne (040) slip plane. Here we note that the loss of these particular outcropping atoms will produce the specific dinitroso compound 1,3-dinitroso-5-nitro-l,3,5triazacyclohexane (RO) that has been detected h Hoffsommer, Glover and Elban (103 in drop-weight impact tests at preinitiation drop heights. The RO compound was found to occur in greater amounts than the trinitioso (R) compound. Hoffsommer and Glover (11) also measured the thermal decomposition of liquid RDX to nitroso compounds that were proposed to follow the sequence R03 -• R02 -• RO - R. Behrens and Bulusu [12) have reported the formation of the nitroso R02 compound in condensed phase pyrolysis experiments by removing an NO2 group fro; )X and reacting this with pre-generated NO. I1 ;reviously suggested t*(4] that the [100](040) dislocation shown in Figure 2, involving single H-0 interactions for the (010) slip process, could possibly relate to the formation of ROz. This is now seen clearly to be a weaker interaction than is pointed out here for the dinitroso (RO) case possibly relating to the (100)(021) slip process.
L 230
A
4b
C.
Fig. 3. MOLECLA
Dinitroso-related interactions from (100] (02i)
slip.
FLEXING FOR HMX DEFORMATION TWINS
Cady f[13) has observed that the p-polyorph of HNX (cyclotetramethylenetetranitramine) shows growh twinning on (101 of its P2 1 /n monoclinic structure and also exhibits defrmgation twinning on this same plane. At low stresses, the deformation twinning is reversible. The system presented itself as an interesting case for explaining on the crystal lattice scale why defrmgation twinning should occur for HMX as compared with slip occurring, and then only with difficulty, in the related compound RDX. Even so, Figure 1 shows that the hardness of HMX is about twice as great as that of RDX. Figure 4 shows a stereographic projection plus intermediate and final steps for the defromation twinning process that we propose. As by the twin system specification: K1 , rl, has K1 , been rz= (101)indicated ,(0l, (101) ,[101, respectively, the twinning reasoned to be of relatively unusual type II in which the twinning orientation relationship may be visualized to occur by a rotation of 1800 about the twinning •! direction, followed by a parallel translation. Such twinning has been repnrteud recently in haematite [14). The two-step t%. process ±s indicated 1 n1 :i•c here for the reverse sequence of first a translation paralle] to Fg 3followed by a rotation, as shown in Figure 4 so as to correspond to the physical interactions of HMX molecules traced in the seqence of modeled strctures that are shown for the actual twinning mechanism.
231
•tvL) '16-11011 ViI),
I
I
•
1
1601
[ Position
* **
4: Fig.
(T1PE*)tr
Position A
(T2PE**)tr Kcal/mnol
A
Kcal/mol
0.000
-41.97
0.000
-29.95
0.2C5
-40.91
0.265
-32.4)
0.530
-36.79
0.5)0
-35.91
0.790 1.060
-36.40 -34.19
0.790 1.060
-37.58 -38.06*
1
Type 1 Potential Energy Type 2 Potential Energy Type 2 Potential Energy + 21° rotation of N-N bond 4. Crysta.'ggraphy of Type II
(101)[i101] twinning in HMX.
The Table D •'igure 4 gives the estimated potential energy values for th_..central molecule of the unit cell in the structure, in either the unrotated or 1800 rotated about (101] positions, when subjected to a numer of incremental translations of the upper lattice (15]. Computations were carried out with a potential function extending to 2661 surrounding molecules in accordance with an established program (16]. In the unrotated initial position before displacement, a reference value of -41.97 kcal/mole is obtained for the stable 3-HMX structure, significantly less than the same molecule when rotated. The ,]rotated molecule maintains its relatively lower energ,' until a displacement equivalent to half of the total twinning displacement is achieved, as marked by the bold-print numbers in the Table. Further displacement is shown in the last column of the Table to occur at a lower energy for the molecule in the rotated position. Figure 4 shows in turn that the 1800 rotation
232
for the molecule is achieved by incremental flexing of the Thus, the proposed intramolecular bonds within the molecule. explanation for twinning in HMX, albeit at a greater (hardness) strength level than for RDX is traced to the greater proposed flexibility of the larger HMX molecule. REFERENCES
1. R.W. Armstrong, C.S. Coffey, V.F. DeVost, and W.L. Elban, J. Appl. Phys. 64 (3), 979-984 (1990). 2. R.W. Armstrong and W.L. Elban, presented at 'The Fundamental Physics and Chemistry of the Combustion , Initiation, and Los Alamos National Energetic Materials', Detonation of Laboratory, in print as a Chemical Propulsion Information Agency Publication (1992). 3. B.L. Hammond and R.W. Armstrong, Phil. Mag.
Lett. 57,
41
(1988).
4. R.W. Armstrong and W.L. Elban, in 'ONR Workshop on Energetic Propulsion Chemical Fundamentals', Initiation Material Hopkins 475, (The Johns Agency Publication Information University, Applied Physics Laboratory, Laurel, MD, 1987) p. 177. 5. W. Connick and F.G.J. May, J. Cryst. Growth 5,
65 (1969).
6. W.L. Elban and R.W. Armstrong, in 'Proceedings of the Seventh Symposium (International) on Detonation', (Naval Surface Weapons Center, Silver Spring, MD, 1982) NSWC MP 82-334, pp. 976-985. 7. W.L. Elban, J.C. Hoffsommer and R.W. Armstrong, J. Mater. Sci. 19, 552 (1984). 8. R.W. Armstrong and W.L. Elban, in 'Microindentation Techniques in Materials Science and Engineering', edited by P.J. Blau and and Materials, for Testing Lawn (American Society B.R. Philadelphia, 1985), ASTM STP 889, p. 109. 9. W.L. Elban, R.W. Armstrong, K.C. Yoo, R.G. Rosemeier and R.Y. Yee, J. Mater. Sci. 24, 1273 (1989). 10. J.C. Hoffsommer, Mater. 3, 149 (1985). ii. J.C. (1985).
D.J.
Glover and W.L.
Hoffsommer and D.J.
Glover,
Elban,
Combust.
J.
Flame 59,
12.
R. Behrens and S. Bulusu, J. Phys. Chem. 96 (1992)
13.
H.H. Cady,
14. L.A. (1989).
Energetic 303
in print.
private communication.
Bursill and P. J. Lin, Phil.
15. H.L. Ammon and Z.Y.
Mag.
Lett. 60 (10),
1-10
Du, private communication.
16. W.R. Busing, 'WMIN, A Computer Program to Model Molecules and Crystals in Terms of Potential Functions', (Oak Ridge National Laboratory, TN, 1981) Report 5747.
233
THE MOLECULAR & CRYSTAL STRUCTURES OF POLYCYCLIC ENERGETIC MATERIALS RICHARD GILARDI Laboratory for the Structure of Matter (6030) , The Naval Research Laboratory. Washington, D.C. 20375-5320 USA ABSTRACT Even before the 'Buckey-ball' (or fullerene) era, organic chemists were interested in, and attracted to, the synthesis of compounds containing many rings fused together - especially the symmetric ones. By virtue of their balanced linkages, such compounds may be kinetically stable despite inclusion of massive deviations from normal bond distances and angles. These distortions, in compounds such as cubanes, tetrahedranes, dodecahedranes and prismanes, comprise a storehouse of chemical potential energy known to the chemist as 'strain energy' (unrelated to overall crytal strain discussed in many materials studies). Besides the obvious benefit of including more potential energy in an energetic material, the arrangement of atoms in ring assemblies (rather than chains) leads to a material with a high intrinsic crystal density - a sine qua non for an explosive or propellant. It has long been recognized that the next generation of energetics - better in performance and/or safety - will contain many polycyclic compounds. Hundreds of model compounds were synthesized in the last decade, and their molecular structures identified or verified at the Naval Research Lab. Some of the most promising, beautiful, and unusual ones, including many energetic cubanes, will be discussed. ENERGY-DENSE MATERIALS In 1990, the Department of Defense identified the production of new 'high energy density materials' as one of the 20 technologies 'most critical to our long-term defense' [ 1]. Better materials in this area would enable improvements in performance coupled with increased safety in the next generation of explosives and propellants. To meet these requirements. the Office of Naval Research launched a number of research initiatives which engaged the expertise of researchers from many scientific disciplines, from quantum chemistry to synthetic organic chemistry to rocket engineering. The sudden production of hundreds of new energetic compounds and precursors to energetic compounds by this ONR program provided an opportunity to demonstrate the utility of rapid structural analysis to a s'nthesis program. Each new material in the program was submitted to the Naval Research Laboratory (NRL). There, X-ray analyses quickly corroborated the expected structural formula for most syntheses, but sometimes revealed completely unexpected products. The analyses also indicated the nature and quantity of solvent incorporation (if any) in solid samples, and provided accurate densities of these new materials. In the longer run, the details of the molecular structures furnished by these analyses provide a firm basis for mathematical relations between structure and properties in this class of compounds. DENSITY The explosive power of an explosive, as measured by its detonation pressure. and the utility of a propellant are both greatly enhanced by any increase in the mass density of the compound. Simple algorithms have been developed [21 which statistically relate the densit% of all the known energetic compounds to their structural formulae, and they seem to predict densities of most compounds to within about 3%. It is possible to conceive of many target molecules that are compl-tely. or aln'os: -; -. ,.,teiy. substituted with nitro groups and then s,.h an algorithm. Two of the highest densities predicted so far predict their densit.v WILv, are for the hypothetical target molecules shown in Fig. 1. Both of these molecules are called cage compounds, because the center of the molecule is surrounded by a linked network of rings, like a spherical cage. The molecule on the lcft is called an adamantane. and the one on the right a cubane, after the names of the unsubstituted parent compounds. The nitro-substituted adamantane is made up of module, which resemble the successful explosive RDX. The cubane nucleus has. in addition to Mat. Res. Soc. Symp. Proc. Vol. 296. '1993 Materials Research Society
234
high energy through density and massive nitro substitution, a large inherent strain energy.
Hexanitrohexa-aza-adamantane 0 2N
~
0N/N O2N/
NNN NO2
0 2N
2
N N
Octanitrocubane No 2
0 2N
NO2
NO2
N02 NO2
0 2N
0 2N
NO,
NO2
Predicted Density = 2.0-2.1 g/cc
Predicted Density = 2.0.2.2 g/cc
Figure 1. Two examples of polycyclic target compounds that have yet to be synthesized. STRAIN ENERGY What is strain energy? Molecules generally behave as if their atoms are connected by a flexible sat of connections (called bonds). These bonds can be extended or compressed by
external forces, but tend to assume certain values for their distances and for their inter-bond angles. However, it is impossible to connect some of the more complex ring systems found in these molecules except by forcing some of the bond angles (or, more rarely, distances) to remain at values far from their ideal. Cubanes are close to the top of the list in overall strain energy, for all the carbon bond angles are forced to remain near 90P to maintain closure of its rings, but the preferred bond angle values in this type of compound are 109.50. ENERGETIC CUBANES Three nitro-substituted cubanes, a di-, a tri-, and a tetranitrocubane, have been synthesized at the Univ. of Chicago [3]. All are quite stable. Their crystals were studied at NRL, and their densities were found to be proportional to the number of nitro substituents, namely, 1.66, 1.74 and 1.814 g/cc respectively. The tetranitrocubane is shown in Fig. 2.
'.
Figure 2. A drawing of the molecular structure of 1,3,5,7-tetranitrocubane as it occurs in the crystalline state.
C8
C2
, 03.
-'
o•c
235
The discovery of cubane was first reported [4] and its structure confirmed [5] in 1964. Though it attracted immediate and lasting attention, only a few new cubane compounds were made in the next 20 years. Once a cubane compound was made, it was difficult to transform it without 'zipping open' the strained cage. In the 1980's, new reactions were found which could be used to add new substituents to the cubane cage without destroying it, and a large number of new compounds have since been reported. Figure 3 shows a cubanourea [61 where the cube is fused to an energetic five-membered ring. Figure 4 portrays some novel polycubane compounds analyzed at NRL [7] which may be precursors leading to future energetic materials. 0900
C6
Figure 3. The N,N'-dinitrocubanourea molecule. The crystal density is 1.69 g/cc, and the compound has ample room for further energetic substitution.
P
C
011a
N
•fN11ola
.-
Figure 4. The structures of two polycubyl compounds: phenyltercubyl (top) and cubylcubane (bottom).
11
236
NEW DIRECTIONS A recent article calculated the properties of the 22 possible cubanes made up of carbon
and nitrogen atoms [8]. If existing prediction schemes can be extended to this novel class of molecules, the computations indicate that substitution of four or more of the CH comers by nitrogen atoms leads to compounds denser, and more energetic, than all existing materials. One particularly promising candidate is shown in Figure 5. A search of the crystal structure literature reveals only one example where a nitrogen atom is shared by more than one four-membered (C,N) ring [9], shown in Figure 6. The fact that such a highly strained asymmetric azaprismane is stable enough to undergo an X-ray analysis indicates that the azacubane family may be a powerful source of new energetic materials.
0,
Modelof
S+
12D~~rec
Figure 5. A drawing of a tetraazacubane, where four alternate corners of the cube are replaced by unsubstituted nitrogen atoms; the other four are nitro-substituted.
2 0'
'
Figure 6. A prismane. a cage compound comprised of just 3- and 4-membered rings, with one azasubstituted corner.
References 1. 'Plan for Vital Defense Technologies Issued' (news article). R. Seltzer, Chemical and Engineering News, p. 5, Mar. 26, 1990. 2.
1. R. Stine. Report No. LA-8920 (Los Alamos National Laborator)., Los Alanmo.. NNI 87545, U.S.A.), 1981.
3.
P. E. Eaton. Y. Xiong. and R. Gilardi: 3. Org. Chem., submitted (1992).
4.
P. E. Eaton and T. W. Cole Jr.; 3. Am. Chem. Soc. 86, 962 (1964).
5.
E. B. Fleischer; 3. Am. Chem. Soc. 86, 3889 (1964).
t,.
P. E. Eaton, K. Pramod, and R. Gilardi: 3. Org. Chem. 55, 5746-5750(l1X,J•
7.
R. Gilardi, M. Maggini, and P.. E. Eaton; 3. Am. Chem. Soc. 110, 7232-4 (1988)
8.
R. Engelke; 3. Org. Chenm. 57. 4841-6 (1992).
9.
U. Hees, U. Vogelbacher. G. Michels and M. Regitz: Tetrahedron 45, 3115(1989).
237
NTO POLYMORPHS Kien-yin Lee* and Richard Gilardi** * Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM 87545 ** Laboratory for the Structure of Matter, Naval Research Laboratory, Washington D.C. 20375 ABSTRACT NTO is an explosive of current interest. It has been evaluated as an insensitive component to replace RDX in the bomb fill, and as a major ingredient for the auto air bag system. The crystal structure of the 0 form of NTO has been determined by single-crystal X-ray methods. The unit cell is monoclinic, space group P21/c, with a = 9.326, b = 5.515, c = 9.107 A, 3= 100.77'. There are four molecules in the cell, density 1.878 g/cm 3. Infinite extension of H-bonding in two-dimensional sheets occurs in the monoclinic form. Bond lengths and angles all have normal values. Efforts have been made to determine the crystal structure of a-NTO. However, a structure refined only to R = 17% was obtained, probably due to some kind of twinning about the crystal needle axis. The unit cell is triclinic, space group PL, with a = 5.12, b = 10.30, c = 17.9 A, (x = 106.7', 0 = 97.70, y = 90.20. There are eight molecules in the cell, density 1.92 g/cm 3. Ribbons of NTO molecules formed by a relatively strong network of hydrogen bonds are observed. It was found that a-NTO is the stable, dominating form. A variety of techniques have been chosen to identify the two polymorphs. BACKGROUND 5-Nitro-2,4-dihydro-3H-1,2,4-triazol-3- one, commonly known as NTO is an explosive that was developed at Los Alamos in 1983 as a result of an on-going explosives synthesis program.( 1) It continues to receive attention from both defense and civilian sectors in the United States and abroad as a potential new-generation insensitive high explosive (IHE).(2 ) It has been studied by the Navy as an insensitive component to replace RDX in the bomb fill (3). and as a major ingredient by Morton International, Inc. to replace sodium azide for the auto air bag system.( 4 ) Crystals of NTO were grown to determine the crystal density for performance calculations and for structure confirmation. CRYSTAL STRUCTURE OF P3-NTO CaSt£alli~lfion D-NTO of
form of NTO was obtained by cooling The crystal i'sed to determine the structure of the P3 not aqueous N'It, .;olution. This crystalline form, while maintaining its habit and clarity, does not remain as a single crystal. A re-examination of the crystal after six months period gave no diffrmcon.
Mat. Res. Soc. Symp. Proc. Vol. 296. '1993 Materials Research Society
238
Summar of xnerimen Conditions: Single-crystal X-ray diffraction analysis of 5-nitro-2,4-dihydro-3H- 1,2,4-triazol-3-one. C2H2N40 3 , F.W. = 130.1, monocinic space group P21/c, a = 9.326 (2), b = 5.515(2). c= 9.107(2)MA, 03= 100.77(2)0, V = 460.2(2) A3. Z = 4, pcalc = 1.878 g/cm 3 , ).(MoKo) = 0.7107 A, ig = 0.174 mm-I, F(000) = 264, T= 294*K. A clear colorless 0.08 x 0.2 x 0.32 mm crystal, in the shape of a thick plate, was used for data collection on an automated Siemens R3m/V diffractometer equipped with an incident beam monochromator. Lattice parameters were determined from 25 centered reflections within 30 _ 20 .t, ' lDynamic., of Shock Waves. Explosives, and Detonation.AIAA Progress Series, (Eds. J.R. Bowen. N. Manson, A. K. Oppenheim. and R. J. Soloukhin), Vol. 94, p. 575. 1985. 24 S. R. Wu, Y. C. Lu. K. K. Kuo. and V. Yang, 'Crack Initiation and Propagation in Burning Metalized Propellants.' Eighteenth International PArotechntcs Seminar, The International Pyrotechnics Society. Breckenridge, Colorado. 1992, pp. 985-1003.
348
25 A. F. Belyaev, A. I. Korotkov, A. A. Sulimov, M. K. Sukoyan, and A. V. Obmenin, 'Development of Combustion in an Isolated Pore,' Combustion, Explosion, and Shock Waves, Vol. 5, 1969, pp. 4-9. 26 H. R. Jacobs, W. L Hufferd, and M. L Williams, 'Further Studies of the Critical Nature of Cracks in Solid Propellant Grains,' AFRPL-TR-75-14, 1975. 27 M. M. Athavale, K. C. Hsieh, W. H. Hsieh, J. M. Char, and K. K. Kuo, 'Interaction of Flame Spreading, Combustion, and Fracture of Single-Perforated Stick Propellants Under Dynamic Condition,' Dynamics of Reactive Systems, Part Ih: Modeling and Heterogeneous Combustion, AIAA Progress Series, Vol. 105, (Eds. J.R. Bowen, J.-C. Layer, and R. I. Soloukhin), 1986, pp. 267-290. 28 Y.C. Lu, 'Combustion-Induced Crack Propagation Process in a Solid-Propellant Crack Cavity,' Ph.D. Thesis, The Pennsylvania State University, December 1992. 29 R. A Schapery, 'A Theory of Crack Initiation and Growth in Viscoelastic Media, 1: Theoretical Development,' InternationalJournalofFractureMechanics, Vol. 11, 1975, pp. 141-159. 30 R. A. Schapery, 'Correspondence Principles and a Generalized J integral for Large Deformation and Fracture Analysis of Viscoelastic Media,' International Journal of Fracture,Vol. 25, 1984, pp. 195-223. 31 W.L Hufferd, H. R. Jacobs, and K. L Laheru, 'On the Fracture of Viscoelastic Materials,' CPIA 264, 1975, pp. 339-356.
349
LABORATORY TESTING AND CONSTITUTIVE MODELING OF COAL INCLUDING ANISOTROPY Dar-Hao Chen*, Musharraf M. Zaman**, Anant R. Kukreti*** * Graduate Research Assistant, ** Associate Professor, *** Professor School of Civil Engineering and Environmental Science, University of Oklahoma, Norman, OK 73019 ABSTRACT In this study, the stress-deformation response of coal in the laboratory under threedimensional (3-D) loading conditions similar to those existing in an actual coal mine is investigated, and a constitutive model, including the effects of anisotropy, is developed. The coal samples were obtained from a mine in LeFlore County, Oklahoma, at a depth of approximately 25-30 ft below the ground surface. A High Capacity Cubical Device with servo-controlled independent loading along three axes of a cubical specimen and a computerized data acquisition and monitoring system were used to conduct the tests. A total of 21 tests under 4 different confining pressures and 5 different stress paths were conducted. The influence of the degree of anisotropy was investigated by comparing the transversely isotropic and isotropic idealizations for diffeient stress paths (Triaxial Compression, Triaxial Extension and Simple Shear) at different confining pressures (1,600, 3,200 and 5,600 psi). The experimental results demonstrated that the coal exhibits inherent anisotropy and that it can be treated approximately as a transversely isotropic material. Also, the Young's moduli were found to be dependent on the confining pressure. The experimental data were used to evaluate the material constants associated with the elasto-plastic constitutive model developed in the study. INTRODUCTION As easily mineable reserves deplete, the coal industry must focus its attention on developing innovative techniques to maximize extraction without detrimental effects, such as instability and ground subsidence. To better understand and develop underground mining techniques, it is imperative to study the deformation characteristics and the failure response of coals under appropriate loading which simulate the field conditions. However, traditionally, material properties are evaluated from either uniaxial or cylindrical triaxial tests under an idealized two-dimensional loading (confining pressure and axial load) that does not reflect the true loading conditions existing in the field. Also, coal being a highly anisotropic matenal presents additional difficulties to the designer because its response not only varies with location but also with respect to direction or onentation even in the same mining area. Under such a situation, an analysis algorithm, which uses appropriate constitutive relationships and finite element method to discretize the overlying and underlying strata as well as the mined zones, can provide a tool to evaluate the ground control problems related to underground mining [1]. Application of an elastic-plastic constitutive model to analyze a boundary value problem requires input of realistic values of the associated material constants. Thus, 3-D testing and anisotropic modeling of coal are essential to evaluate realistically the material properties that accurately describe the coal behavior in the field. With this in mind. a hligh Capacity Cubical Device (HCCD) (30,0(00 psig) was designed and fabricated at the University of Oklahoma The device has been successfully calibrated and used by Mishra [21 to study the behavior of plain and fiber-reinforced concrete. A combined experimental and analytical study was undertaken to investigate the deformation behavior of coal specimens under simulated 3-D loading by using the IICCD. The experimental data was used to develop the constitutive model. In this paper, the testing of the cubical coal specimens. determination of associated model parametcrs. and the formulation of the elasto-plastir constitutive. 1r- ,-:lr.a.t describes the strers-stramn and volumetric response of the coal, itiuAuul,-L unloading and retoading sequence, are presented. DESCRIPTION OF EQUIPMENT AND PREPARATION OF CUBICAL SPECIMENS A cubical device is an apparatus that provides independent control for the application of load and measurement of deformation along three mutually perpendicular directions at the same Mat, Res, Soc. Symp. Proc Vol 296 , 1993 Materials Research Society
K 350
time. The name cubical device stems from the fact that this apparatus has a cubical space frame, with a central cubical cavity to accommodate the specimen as well as to act as a reaction frame for the loading. The HCCD has five major components: (1) cubical space frame and six side walls; (2) deformation measuring system; (3) hydraulic pressure system; (4) digital data acquisition system; and (5) central monitoring unit. The test set-up and their inter-connections for HCCD are described in detail by Mishra [2]. The device (I-ICCD) used in this study for 3-D testing requires cubical specimens that are slightly less than 4 in. (approximately 3.94 in.) in size. The coal chunks were first broken into smaller pieces, approximately 7 in. in dimension, using a hand saw and a ruler. These smaller pieces were then used to prepare the desired cubical specimens using a high quality circular saw of 18 in. diameter with clamps to tightly hold the coal sample in place while cutting. The surfaces of coal were rough after cutting. To prevent uneven stress distribution, the irregularities were filled by applying a thin coat of a resin based body filler compound containing polyester styrene monomer, commercially called 'Bondo'. Then, the surfaces were smoothed by using a sanding machine. These steps not only ascertained uniform distribution of load on the specimen surface, but also helped to prevent moisture from escaping between the time the specimens were prepared and the actual tests were conducted. Before coating the specimen with Bondo, sketches showing the bedding planes, cleat cracks and crack orientations on the specimen surfaces were drawn for all six faces. Those sketches were essential for identification of bedding planes. DESCRIIrION OF THE DEVELOPED CONSITrUTIVE MODEL The most important feature of the constitutive model developed is that it accounts for inherent anisotropy, which is an important property of materials such as coal. Because the nature of deposition and presence of cracks and bedding planes, coals exhibit a high degree of anisotropy. Another attractive feature of the model is that it accounts for anisotropy even in the elastic range. Also, the model is capable of predicting volumetric response in the compressive as well as in the dilative regions. Loading Surface The equation of the loading surface is proposed in the form F=1•-[•CEjA-
J-
K
1g(8,J)
=
(1)
where cx, n and K are failure parameters and P3 is a hardening function. Also, 1, J1and K are non-dimensional quantities given by : r = r/ Pa, Ji = J1 /Pa , and K = K / Pa, where Pa is the atmospheric pressure and K is the cohesive strengtI,. In the~e relationships, the stress invariants J1, J2) and J3D are given by J 1 = 0 1 1 =Gl 1 +0
2 2 + 0 33
; J2D='SiJS'; J3D=j-SijSJkSk
(2)
in which r= 2J2D, and 0=
cos1 13V3 J31)/2Q21)2]
(3)
The variable J1A in Eq. (1) is given by JIA=I4iI O11 +a22022+a33'Y33)
(4)
where the coefficients a31 , a22 and a33 are anisotropic coefficients and are positive quantities that can be determined from the stress-strain response under the hydrostatic compression loading.
351
Following the work of Faruque and Chang [3] the function g (0, J1 ), which accounts for the shape of the yield surface and the failure surface, is defined as follows:
g(,I)I o (~os -(A cos 3
-0)
(5)
where A =exp (-yJ)
(6)
The variable Y is another material constant that accounts for the variation of the shape of the yield surface on the octahedral plane. Anisotropic Elastic Behavior Since coals are usually found in nature as a layered material it may be reasonable to treat such materials as transversely isotropic. The linear elastic stress-strain relations for a transversely isotropic material in the elastic range can be written in a matrix form in terms of five elastic constants, as follows: V'
V'
E'
E'
E'
v'E
)
.
E'
E
1
S
0 0
'
00
E E
evE' Yz~x 8xv00_ 0
0
0 0 0 0
0 0)_0 •,0 0 00
0
0
0
0
Tzx xy
C
(7)
The physical meaning of E, E ', V.v' G and G can be found elsewhere [4j. and it may noted that the constant G is not independent and can oe aetermined from G = E 12 ( I+ ', ). The material constants E, E '. v and v' can be determined from a combination of unloadingreloading curves for different loading paths tnamely. SS, TE, TC), at the same level of confining pressure. To determine the shear modulus G' . one needs to have a uniform shear stress state in the cubical specimen on the pnncipal axis of the material. Because this is verdifficult to achieve experimentally, Atkinson [5j proposed a procedure in which specimens are prepared by cutting them at an angle of 45- to the bedding Wlane. Although the procedure appears to be straightforward to prepare a specimen at the 45, angle with the beddinT plane, in reality it is not an easv task. Sometimes bLldwng planes are not clearly visible in coal specimens. Also, cutting coal specimens exacuy at 45' angle may be a difficult task. Thus, : direct evaluation of G' from experimental data
i;
irequentlv avoided.
In tlis regard, an
assumption introduced by Leknitskfi [61 was used to relate G' to E, E ' and V as follows C'= IEE'
/I1E((+
2 ')+
E',.
DETERMINATION OF THE MATERIAL CONSTANTS The constitutive model outlined in the previous section requires determination of the following fourteen material constants,: (1) tour elastic constants ( E. F '. v and v'). (2) two
352
anisotropic constants associated with the plastic behavior (a22 and a33); (3) four constants associated with the transition and the yield surface (a, n, k and 1) ; and (4) four constants associated with hardening (01 , N , 1l1 and 112). These material parameters were determined by
conducting tests along various stress paths (namely, Hydrostatic Compression (HC),
Conventional Triaxial Compression (CTC), Simple Shear (SS), Triaxial Extension (TE), and Triaxial Compression (TC) [4] ) under various confining pressures. It is important that the constitutive law be valid for all the major stress paths that the material (coal) can experience. So the experimental program was designed in such way that the test results can be used directly to determine these material constants or parameters. The different stress paths and values of confining pressures used in the test program are presented in Table 1. The anisotropic constants (a22 and a33) and the hardening parameters (01, , 111 and 112) were determined from the HC tests. Also, the unloading-reloadk.g cycles at the same level of confining pressures for different stress paths were utilized to evaluate the elastic constants (E, E ', v and v'). The failure stresses (as given in last column of Table 1) for various shear tests were used to compute the yield and/or failure parameters (cc, n , k and I ). The parameters used in this study are presented in Table 2. MODEL PREDICTIONS VERSUS EXPERIMENTAL OBSERVATIONS Although an anisotropic constitutive model may be more appropriate for coals because such materials exhibit some degree of inherent anisotropy, it is desirable to investigate the degree of anisotropy involved in such materials. If the degree of anisotropy is not very significant, then the material can be modeled as isotropic for simplicity. With this objective in mind, an attempt was made to compare the transversely isotropic and isotropic idealizations for the LeFlore coal for TC, TE and SS tests at confining pressures of 1,600, 3,200 and 5,600 psi. The parameters used for isotropic idealization are also presented in Table 2. It can be observed that for isotropic behavior E = E', v = V, and a22 = a33 = I. The comparison between the predicted stress-strain response for both idealizations, transversely isotropic and isotropic, with the experimental data for TC tests at 5,600 psi confining pressure is shown in Fig. 1. An unloading and reloading cycle was conducted in the deviatoric portion of the test. In this case, the unloading-reloading sequence was performed prior to the specimen failure and after the specimen showed a significant amount of non-linearity. The model predictions and the experimental data are found to be in very good agreement for the entire loading history including unloading and reloading. Particularly, for the transversely isotropic idealization the predicted ultimate stress is only slightly different (less than 8%) from the experimental data. Also, it is observed that both the models were able to predict the loading and unloading behaviors quite accurately. A comparison of the volumetric strain response is presented in Fig. 2. In this figure, the volumetric strain is plotted against the major principal strain (ez for this case). Evidently, the change in the volumetric response from compression to dilation is predicted well by the model. The discontinuity in the experimental data induced by the unloading-reloading operation, as shown in Fig. 2, is possibly caused by the internal cracks; also, it might be partly attributed to the experimental enors. It may be noted that in the experiment, volumetric strains are obtained by idding the normal components of the deviatoric strains along the x, y and z axes. Similar comparisons with the observed volumetric behavior of SS test at confining pressure of 5,600 psi are compared with the model predictions in Fig. 3. It is observed that the model predicted by the transversely isotropic idealization are in better agreement with the experimental values than those predicted by the isotropic idealization. A comparison of the predicted stress-strain response with experimental data for SS and TE te-,s conducted at a confining pressure of 3,200 and 1,600 psi is presented in Figs. 4 and 5. 'imilar observations, as for the TC stress path test, can be made here. For all the coe•s tested, it can be seen that the slopes of loading and unloading parts of the stress-strain response are predicted quite accurately, indicating that the representation of the elastic constant (E, E' and G') as a linear function of the initial confining pressure is a good approximation for the range of confining pressure considered.
353
CONC~LUSIONS 1. Elastic moduli of the LeFlore coal are pressure dependent. For the range of confining pressure (ao) considered, the elastic moduli are linear functions of ao. 2. The elasto-plastic transversely isotropic constitutive model is found to satisfactorily represent the stress-strain and the volumetric-axial strain behavior of LeFlore coal under various stress paths and confining pressures. 3. The slopes of unloading-reloading stress-strain response are predicted quite accurately, indicating that the representation of the elastic constants as a linear function of the initial confining pressure is a good approximation. 4. The predictions of stress-strain and volumetric responses using the transversely isotropic model are in better agreement with the experimental data than those predicted by the isotropic model. ACKNOWLEDGEMENTS The financial support for this study was provided by the Oklahoma Mining and Mineral Resources Research Institute (OMMRRI), Also, technical assistance by Dr. Y.M. Najjar is gratefully acknowledged. REFERENCES 1 2 3 4 5 6
Z.T.Bieniawski, 'Analytical Modeling as a Geomechanics Aid for Mine Design Application in the USA,' International Bureau of Rock Mechanics, 7th Plenary Scientific Session, Katowics, 24-26 June, 1981, pp. 7-22. (1981). D. K. Mishra, 'A High Capacity Cubical Device : Development and Performance Evaluation,' M.S. Thesis, School of Civil Engineering and Environmental Science Univ. of Oklahoma, Norman, Ok. (1991). M.O. Faruque and C.J. Chang, 'New Cap Type Model for Failure and Yielding of Pressure Sensitiere Materials', J. Eng. Mech. Div., ASCE, Vol. 112, pp. 1041-1053. (1986). W.F. Chen and A.F Saleeb, Constitutive Equation for Engineering Materials, Vol. 1, Elasticity and Modeling, John Wiley and Sons, New York. (1982). R.H. Atkinson, 'Constitutive Relations of An Illinois Coal (Hlerrin #6 Seam)', Report, Univ. of Colorado, Boulder, 94p. (1974). S.G. Lekhritskii, Theory of Elasticity of an Anisotropic Body, Mir Publishers, Moscow. pp. 60. (1981).
6000
to
LU
------
.5:
•o-
Trans Observation
400--0
/
0
0fservation Ob
G*---
?2.5
0
25
5,0
CopesonTss0T)a0o-pesi ,0 STRAN (%)
Fig.l Comparison of Observed and Predicted Stress-Strain Response for Triaxial Compression Tests (TC) at OoD= 5,600 psi
0
opeso
1
2
etoa •
3
,0
STRAN' (%)
4
s
Fig.2 Comparison of Observed and Predicted Volumetric Response for Triaxial Compression Tests at 0c, = 5,600 psi
5
354
Table 1 : Test Program and the Effect of Confining Pressures and Stress paths on
.5
Spece. Stress Confining Path Pressure No. (psi) 800 TC 30 TC 1,200 18 1,600 TC 16 3,200 TC 19
17 20 4 6 24 8 33 5 14 1 23 32 13 21 25 26
2
TC TC TE TE TE TE
TE
SS SS SS SS SS CIC CTC CTC CTC HC
Failure L'trength (r) (psi) 1837 2572 3307 6001
3,200
6001
5,600
8328
1,600
1837
1,600 3,200 3,200 5,600 1,200 1,600 3,200 3,600 5600 800 800 1,200 1,200
3555 3674 5634 5756 1556 2121 4101 4384 6293 6042 5716 6369 6532
ISO Trans. Tvan Iso.
0 %--
e
Failure Shear Strength (r)
;-
0
-
o
45 o
STRANI
14,500
.000
0
--I S
i 0a 0-
-0 0
Io Tran.
c. C Observation 10
5
0
5
0
curve to asymptotes.
STRAH (¶4)
Used in This Table 2: Material Constants Study for Transversely Isotropic and Isotropic idealizations
Fig.4 Comparison of Observed and Predicted Stress-Strain Response for Triaxial Extension Tests (TE) at m 3,200 psi
Trans. Isotropic a* b* 0.38 0.22
Isotropic c* c* 0.31 0.31
a
1.29 80.0
1 80.0
' k (psi) n
45.0 300.0 1.12
45.0 300.0
600
1.12
400
Pi
1.685
1.685
Th
55000.0
55000.0
0.91
0.91
0.21
0.21
a* = 190,000+93.2 * confining pressure b* = 230,000+95.4 * confining pressure c* = 220,000+100 * confining pressure
(%)
1500
obtained by extrapolating the stress-strain
112
20
Fig.3 Comparison of Observed and Predicted Volumetric Response for Simple Shear Test (SS) at (o7= 5,600 psi
r='2JT2D. Also, the failure stresses pertaining to experimental data were
a22, a33
1.5
10
.5
The failure shear strength (r) is defined as
E E' v v
v
lOOO 0 .
V
800 60
' !e 200 .zing DMNA seeded in argon. DMNI A was studied since it is a simple analogue ol cyclic nitramines such A This spectra'u is characteristic of all the compounds studied It reveals a prominent ' tDX. peak whose arrival time to the detector is measured as 23.2 l1ScC. This time corresponds to a mass-to-charge ratio (m/z) of 3U and is attributed to the NO' ion. Similar results were obtained when using air or nitrogen as the carrier gas. No such peak was observed. however. when the laser was tuned to an off-resonance transition. The observed peak is void of any interference and is c!carly a result of a REMPI process.
376
120-
250
80-
200
,
,
,
7/
05
C Z
0
_
150/
_z i/~
phonons faster than the bulktibraiions. producing,a
temporary tempcrature onerhoot :ind a transicnt hol vibrational quasitemperature is complete spot reached has system the by 30 ps, and the thermal equilibrium temperature, T 1, by approximately 70 ps A smaller compression ratio (stronger shock) results in a higher initial phonon quasitemperature and a hiýher final vibrational temperaturc I lowever. independent of the strength of the shock, most of the rise of the ibiatiof!l quasiten-pe',c. occurs in 30 ps. and thermal equilibrium is reached in approximatie tei ce this timnc lhe details of the time dependencies calculated here depend on the naphthalene parameters used in the calculations Howecr. for molecular solids as large or larger than naphthalene, such
382
as HMX, the results should not vary by more than a factor of two from those presented in Figures 1.5a In a DPD the vibrations are pumped by the phonons faster than the bulk vibrations, so the DPD vibrational quasitemperature, 0 d, will overshoot the bulk vibrational quasitemperature 0 vib The rapid phonon equilibration will maintain the DPD phonon quasitemperature at the bulk value although Gd exceeds 0 vib. Two factors determine the peak DPD vibrational quasitemperature' the shock compression ratio V1/Vo, and the defect enh2ncement factor ý,. ý, is the ratio of the DPD anharmonic coupling to the bulk anharmonic coupling of phonons to the doorway modes. A typical calculation of the three quasitemperatures is shown in Figure I for VI/V 0 = 0.8 (p = 4.7 GPa), and ý = 2.0. Gd rises faster and peaks at a much higher temperature than 0vib Therefore, a transient hot spot is created in the DPD due to enhanced anharmonic coupling Because DPD vibrations equilibrate with the phonor.s so rapidly, hot spots are formed right behind the shock front, typically within Distance Behind Shock Front (nm) 50 nm of the front Phonons and bulk 8 402o vibrations equilibrate in about 70 ps, (a) o while the hot spot, which heats up and 2.6 cools down, equilibrates with the bulk in 2.0 '5 Z about 120 ps. If the hot spot reacts, it 1.6 9 will generate additional heat and will not cool down as shown in Figure 1. Just after the shock front passes, the molecules in the DPD absorb phonons faster than the bulk
If the Xd is small,
which is the ct.se being considered here, it does not deplete the phonon bath, and therefore has little effect on the uppumping of the bulk material But if Xd is large, as when the DPD is present in a small isolated grain of material, there will not be enough excited phonons in the grain to produce the large temperature overshoot needed for ignition This suggests a size effect in hot spot initiated ';hock chemistry 5 The prediction, that small grams should be less reactive than large grains, has been observed in some expenments 23,24 It is important to distinguish the size effect on reactivity predicted by our model from the size effect observed in Jetonation studies detonation properties are not a simple function of grain size since grain size changes the
-1
-10-
1.0
E; 0 10 10 40 0 (b)
o0.
. 40.
I 12030 160 4
~20 8 .
80
20 120
.
.
.
.
.
Z -5 0 -15 0 (C)
00
10 40
40
30 160
200
z -5 o -o0 -15
0
10
20
30
40
Time (ps) Figure 2 Computcd time dcpendent chemical rcaction protabilitics for defect perturbed domains and bulk material for shock compression values of (a) 0.85, (b) 0.80. and (c)0 75 lit each panel, solid lines refcr to anharnonic enhancements r of 2.6. gi0. and 1 6. from lop to bottom The bulk reaction probabililt (. I). given by the dashed curves. remains small until the compression VI/V0 g 0 70
reac~iot. rrobability as well as the porosity, which has a significant effect on the likelihool' of detonation 24 Using pressure dependent reaction rates for HMX. for a given set of vibrational quasitemperature profiles, as in Figure 1, the reaction probability N(p,t) can be calculated
383
5a for bulk molecules or DPD molecules, using Ovib(t) or ed(t), respectively. Figure 2 shows results for the bulk material (, = 1) and for DPDs with anharmonic enhancement (, > 1) The different panels are for various compression ratios. It is evident from Figure 2 that a small increase of , above unity enhances the defect reaction probability by many orders of magnitude relative to the bulk. For example, at VINo = 0.80 (Figure 2a) and ý = 2, the probability of a reaction in the DPD exceeds that in the bulk by about 108. For VINV 0 = 0.85 (Figure 2b) at 40 ps, the bulk reaction probability is -10-9 while for
,
= 2, the DPD reaction
probability is -10-1. The reaction probability for the bulk begins to approach unity for VI/Vo = 0.75, so that a shock of about 10 GPa should be sufficient to reproducibly initiate ideal, defect-free, crystalline HMX At high compressions, the enhancement of DPD reactivity ir unimportant since both the bulk and the DPD react completely. The DPD reaches a reaction probab;litv of unity faster znan the bulk and closer to the shock front, but since the bulk also obt, .' reaction probability, the few tens of ps difference in time will be insignificant The net result is that the anharmonic enhancement of DPD reactivity takes on the greatest significance for relatively weak shocks Acknowledgments This research was supported by the US Army Research Office grant DAALO-90-G0030 to D. D. D., and by the Office of Naval Research, Physics Division grant N00014-89-J1119 to M. D. F. We gratefully acknowledge many discussions with Prof. Y. Gupta of Washington State University who showed us how to calculate the final temaperature after irreversible compression, and several helpful conversations with Dr Craig Tarver of Lawrence Liverm-ore National Laboratory and Dr Caryle Storm of Los Alamos National Laboratory
References (1)
Coffey, C S , Toton, E T. J. Chem. Phys. !982, 76, 949
(2) (3) (4) (5)
Trevino, S F , Tsai, D H J. Ceiem. Phys. 1984, 81, 348 Zerilli, F J . Toton. E T Phvs. Rev. B 1984, 29, 5891 Walker, F. E J. AppL Phys. 1988, 63, 5548 a Andrei T'ornakoff, M D Fayer, and D D Dlott, J Phys Chem accepted 1993 b Dlott, D D , Fayer, M D .1.Chem. Phyvs. 1990, 92, 3798 Wei, T G , Wyatt, R E '. Phys. Condens.Matter 1990, 2, 9787 Tarver, C M Combustionand Flame 1982, 46, 157 Bardo, R D Int. J. Quantum Chem. S 1986, 20, 455 Eyring, H , Powell, R E, Duffrey, G H , Darlin, R B (Y'hen,. Rev. 1949. 45, 69 Eyring. H Science 1978, 199, 740 Chen, S , Lee, I -Y S , Tolbert, W A , Wen, X, Dlott. D I) .1 P'hi-. ('hem 1992 in press Dlott, D D In Shock ('omlpression in CondensedMatter 1991. S C Schmidt. R, I) Wen, X , Tolb, t. W A. Dlott, D D Chem. Phivs. Lett 1992. 192. 315 Mader, C L NumericalModehng of Detonations, University of California Press Berkeley, CA, 1979 Johnson, J N. Tang. P K Forcst C A a. Ai), : '-,v., 1985. 57, 4323 Johnson, J N Proc. Roy. Soc. London A 1987, 413. 329 Johnson, J N In Shock Waves in Condensed Matter, 1988, S C Schmidt and N C Holmes, Ed, NorthHolland Amsterdam, 1988, p 527 Karo, A. M., Hardy, J Rý .1.t/, (Paris)C
(6) (7) (8) (9) (10)
(11) (12) (13) (14)
I. 384
(15) (16) (17)
(18) (19) (20) (21)
(22) (23) (24)
1987, 9, 235. Bowden, F P ; Yoffe, A. D. FastReactions in Solids, Academic Press. New York, 1958. Campbell, A W.; Davis, W C ; Travis, J R Phys. Fluids 1961, 4, 498 Mader, C . L. Phys. Fluids 1963, 6, 375 Armstrong, R. W.; Coffey, C. S.; Elban, W. L. ActaMetall. 1982, 30, 2111. Armstrong, R. W.; Elban, W. L. 'Microstructural origins of hot spots in RDX crystals,' Chemical Propulsion Information Agency Publication #475, 1987. Elban, W. L.; Hoffsommer, J. C.; Armstrong, R. W. J. Mat. Sci. 1984, 19, 552. McGuire, R. R Working Group Meeting on the Sensitivity ofExplosives, Center for Technology and Research, New Mexico Insitute of Technology, 1987; p 624 Wilson, W. L.; Wackerle' G.; Fayer, M. D. J. Chem. Phys. 1987, 87, 2498. Tsai, D. H J. Chem. Phys. 1991, 95, 7497. Tang, P. K.; Johnson, J N.; Forest, C. A. In Proceedings'rthe Eighth International Symposium on DetonationProcesses,Office of Naval Research. Silver Spring, MD, 1985; p 52. Kassoy, D. R., Kapila, A., Stewart, D S Combust. Sci. Tech. 1989, 63, 33. Taylor, B. C.; Ervin, L. W. In Proceedingsof the Seventh InternationalSymposium on DetonationProcesses,Office of Naval Research: Silver Spring, MD, 1982; p 3. Neilsop, A. T. In Working GroupMeeting ono the Sensiiivuy of Explosives, Center for Technology and Research, New Mexico Insitute of Technology, 1987; p 56.
385
Author Index Ammon, H.L., 227 Armstrong, R.W.. 93, 227 Baird, James K., 355 Baker, P.J., 107 Bardo, Richard D., 167 Beard, B.C., 93, 189, 257 Behrens, Jr., Richard, 13 Block, S., 199 Boris, Jay P., 161 Botcher, Tod R., 47 Brenner, D.W., 123, 183 Brill, Thomas B., 269 Bulusu, Suryanarayana, 13, 287 Cady, Howard H., 243 Chen, Dar-Hao, 349 Chen, Jenn-Shing, 355 Coffey, C.S., 63 Covino, J., 173 De Lozanne, Alex. 221 Dick, Jerry J., 75 Dlott, Dana D.. 379 Du, Z.Y., 227 Egghart, Heinrich, 305 Ehrlich, Michael J.. 305 Elban, W.L.. 93, 227 Elert, M.L., 123 Fayer, M.D., 379 Finnegan, S.A., 173 Fried. Laurence E.. 35 Friedman. Jacob. 305 Gallagher, Hugh G.. 215 Gao, Guang, 149 Gilardi, Richard, 233. 237 Glancy, B.C., 93 Guirguis, Raafat H.. '99 Heimdahl, O.E.R., 173 Herley, Patrick J.. 87 Hsieh. Wen H.. 331 Isom. K.B.. 293 Jayakody, J.R.P.. 287 Jones. Hermenzo D.. 311 Jones. William. 87 Kebah;in. P.L.. 357 Ka.,J.J.. 361
Kukreti, Anant R.. 349 Kunz, A. Barry, 149 Kuo, Kenneth K... 331 Lanzerotti, M. Yvonne D.. 81 Lee, Kien-yin. 237
Lemire, G.W., 373 LUrdfors, A.J., 173 Litzinger, Thomas A., 331 Marino, R.A., 287 Mellor, A.M., 107, 293 Miller, Philip J., 199, 299 Mintmire, J.W., 123 Moore, J.J., 319 Nelson, Keith A., 129 Oran, Elaine S.. 161 Pace, M.D., 53 Pandey, Ravindra, 149 Pederson, L.R.. 361 Phillips, Lee. 155. 161 Piermarini. G.J.. 199 Pinto, James J., 41. 81 Prieve, Dennis, 141 Pringle, J.K.. 173 Rabitz, Herschel. 281 Ritchie, James P.. 99 Robertson, D.H., 123. 183 Ruggiero, Anthony J.. 35 Russell. T.P., 199 Sandusky. H.W.. 93 Sausa. R.C.. 373 Sharma, J.. 189. 257 Sherwood. John N.. 215 Simeonsson, J.B.. 373 Sinkovits. Robert S.. 161 Stine. James R., 3 Storm, Carlyle B.. 25 Tokmakoff. Andrei. 379 Travis. James R., 25 Tsai, D.H.. 113 Vilallonga. Eduardo. 281 Wagner. James W . 305 Wang. Weining. 12'9 Wefers. Marc 123., N , 183 '1?9 White, C.T.. Wiegand. D.A.. 293 Wight, Charles A , 47 Wolfe, Allan. 81 Wormhoudt. J.. 367 Yoo, Minsun. 221 Yoon, Seokwon. 221 Zaman. Musharraf M._. 349 Zener. Clarence. 141 Zerilli, Frank J., 311 Zhang, X.J.. 227
387
Subject Index acoustic modes, 167 adhesion at propellant-liner interface, 257 ADN - see ammonium dinitramide AIIAP, 299 Al0 319 alpha-NTO, 237 amalgamated vibrations calculated, 35 AMBER, computer program, 99 aminonitrofurazans, 25 ammonium dichromate, 361 dinitramide (ADN), 53, 199, 269 nitrate (AN), 269, 361 perchlorate (AP), 53, 93, 221, 257, 269,. 361 picrate, 25 amorphous film. 47 anharmonic coupling, 379 anisotropy, 349 of plasticity, 99
computer codes, AMBER, 99 DYNA2D, 299 EPIC. 311 MOPAC/PM#, 35 generation of multiple excitation pulses, 129 computing, parallel, 155 conical face defects, 243 Connection Machine, 155 constituent volumes, 3 constitutive model. 349 cook-off mechanism. 331 correlation time, 287 critical temperature rise. 107 crystal, 75 structure, 233. 237 crystalline solid. 113 crystallization. 215 cubanes, energetic. 233
AP - see ammonium perchlorate
Arrhenius function, 269 rate, 25 atom-atom closest contact, 99 interactions. 75 atomic composition, 3 force microscopy (AFNI), 221 atomization of metal prodt,'ets, 87 Auger electron spectroscopy (AES). 257 benzotrifuroxan. 25 beta-NTO, 237 binding energy, 41 BN boron nitride. 167 buckled lattice. 113 ceramic(s) oxides, 361 synthesis, 361 chemical analyses. 93 equilibrium calculations. 311
reaction dynamics, 129 chemically reactive solids. 129 CH 3NO, 373 C-J (Chapman-Jouget) pressure, 25. 299 velocity, 25. 299 CO, laser, 47 coaf, 349 combustion, 269 synthesis. 319. 361 composition B(59%RDX/40%TNT.1%wax). 81 tetrahedron. 25
DATUI. 189 debris bubble impact, 173 decomposition, 13. 355 of solids, 281 process. 367 thermal, 47 times. 41 defect-perturbed domain, 379 defects. 155. 161 impurities. 113 propagation of. 113 density. 25. 299 prediction. 3 detection. 373 detonation. 123. 155 front. 183 velocity. 25. 305 diagnostic technique. 367 1.3-diamino-2,4.6-trinitobenzene, 25 diamond anvil high pressure cell (DAC). 199 differential scanning calorimetry (DSC). 41 diffusion coefficient. 355 DINGU (I.4-dinitroglycolurilci. 41
discreet-continuum theory. 281 dislocations. 93, 215. 227 energy. 63 motion. 63 dispersed solid particles. 305 DMD (1.4-dimethyl-2.5-dinitroglvcolurile). 41 DMNA. 373 DNNC (l.3.3.5-!.--.rtrohexahydropv.-, ine). 269 uoorway modes. 379 drop test. 25 droplet impact. 141 DYNA2N). computer program. 299 dynamic deformation. 173
388
EDXD spectra, 199 elastic constants, 349
electron(-) beam, 87 induced decomposition, 87 paramagnetic resonance (EPR), 53 spin concentration, 53 relaxation, 53 electronic excitations, 189 structure, 149 electrostatic discharge (ESD), 293 embedded cluster simulation, 149 energetic layered materials. 167 materials. 25. 81, 129, 173. 257, 269. 273. 361 energy dispersive x-ray diffraction (EDXD). 199 localization, 63 transfer. 281 rates. 35 enthalpy change, 319 EPIC, computcr program. 311 EPR spectra, 53 equation of state, 299. 311 equilibrium, 113 explosion, droplet. 141 explosive(s). 13. 233 crystals. 63. 243 femtosecond spectroscopy, 129 Fick's first law, 355 second law. 355 fizz zone. 269. 331 foam layer. 331 zone. 269 fracture. 293 mechanics. 227 surface topography. 81 fragment impact modelling. 173 FTIR spectra, 199 spectroscopy. 47. 269 furoxans. 25 GAP. 269 gas. 355 evolution rate. 355 products. 269 graphite intercalation. 167 growing crystals. 243 Hamiltonian. 35 hardness. 227 testing. 93 HCI gas. 319 heat of formation, 3. 25 hexanitrohenzene. 25 hexanit- in 'enyl. 25 hexanit! it. ..cnyldiamine. 25
high(-) acceleration, 81
explosives, 25 pressure deformation, 349 resolution transmission electron microscope (HRTEM), 87 speed photography, 93 HMX. 13, 25, 35, 41, 53, 81. 227. 243, 269, 379 HNIW (hexanitro-hexaazisowurtzitane), 41, 53, 199 holography, time resolved, 305 homogeneous initiation, 183 hot fragment conductive ignitior.. 331 spots, 107, 155, 227 anelastic/plastic compression. 113 elastic compression, 113 formation. 293, 379 heating. 113 quenching, 293 HTPB(hydroxyl-terminated polybutadiene)/AP. 107. 173, 293 ignition. 107 and combustion behavior of solid propellants, 331 temperature. 293 threshold. 63 impact initiation. 293 sensitivity, 25. 35. 107. 173 impurities. 113 impurity defects, 113 infrared fiber optics. 367 laser pyrolysis. 47 initiation. 63. 107. 155. 183 insensitive high explosive. 237 materials, 167 insulator. 221 intercalated materials. 167 intermediate products, 13 IR transmission spectra. 367 isentropes. NM/PMMA/AI. 311 Jones-Wilkins-Lee (JWL)., 299
modified. 299
Kamlet (oxygen balance). 25 kinetic energy distribution. 113 laser-based. 373 lattices. 161 lead azide. 305 styphnate, 35 liquid(-) phase decomposition. 13 state perturbation theory. 311 local melting. 113
389
M39(RDX75 %,binder25 %), 367 magic angle spinning, 287 mass spectrometry, 13 transport, cumulative, 355 Maxwellian distribution, 113 MD, molecular dynamics, 183 mechanical behavior, 81 twins, 243 mechanisms of heating, 113 metal azides, 87 nitrates, 361 oxides, 361 particles, 87 metallized explosives, 311 microindentation, 93 microstructure, 93 Moby-Dick test, 299 model energetic molecular solid, 183 molecular(-) bond reorganization, 123 bulk dynamics, 281 dynamics (MD), 113, 123, 155, 161, 183 level theory, 167 structure, 3, 41 3-D molecular dynamics, 155 monotonic Lagrangian grid, 161 MOPACIPM#. computer program. 35 Morse potential, 113 mullite, 361 multi-crystalline explosives, 63 multiphonon up pumping, 189. 379 multiple fragmentation theory. 281 probe femtosecond spectroscopy, 129 munitions hazards assessments. 173 naphthalene. 379 NC(13%N), 269 nitramine-based solid propellants (RDX). 47. 331 nitramines, 13 nitrocellulose. 287 nitroguanidine, 3 nitromethane. 75. 155 nitromethane/PMMA/AI. 311 nitroso compounds. 227 nitroxide free-radica!, 53 NMR chemical shift anisotropy. 287 magic angle spinning (MAS). 287 N-N bond distance. 41 NO, 373 NO, 53, 373 N204, 4-v non-ideal explosive, 299 non-wetting surface, 141 NTO(5-Nitro-2.4-dihydro-3H-1,2.4triazol-3-one). 237 identification, 237
octaazacubane, 25 Octol(70%HMX/30%TNT), 81 optic modes, 167 optical absorption. 189 polarizing light microscopy, 199 outgassing rate, 355 oxygen balance, 25 parallel computing, 155 Pb styphnate, 35 pentanitroaniline, 25 pentolite(50%RDX,50%TNT). 299 PETN(pentaerythritol tetranitrate), 3, 75, 99, 167, 243, 299 phase transition. 123 phonons, 35 photofragment, 373 picramide. 25, 189 picric acid. 25 plastic deformation rate. 63 flow, 293 strain rate. 63 PNA p-nitroaniline. 199 polarized light strain, 199, 243 polycrystalline film, 47 polycyclic compounds. 233 polymer, 287 polymorphs. 237 potential energy. 227 potentials modified Tersoff. 123 Morse. 113 power spectral statistical techniques. 81 pressure dependence of acoustic, optic modes. 167 prompt detonation. 173 propellants. 13. 25. 107. 233 activation energy. 331 combustion. 269 radiative properties. 331 thermal conductivity. 331 pulse shaping. 129 pyrolysis, 13 by infrared laser. 47 quantum dynamics. 281 reaction of Al in explosive mixture. 311 radiation damage. 257 rapid compression. 113 rarefaction shocks. 123 RDX cyclotrimethylenetrinitramine. 93 RDX (1.3.5-trmnitrohexahvdro-l.3.5-triazine). 3. 13. 41. 47. 53. 93. 199. 227. 243. 257. 269. 367. 373 crystal. 149 reaction chamber. 319 driven shock simulation. 123 front. 305 interface. 319 onset. 63 pathway. 13
390
relaxation, 113 resonance-enhanced multiphoton ionization, 373 rigid slip, 99 Saint Roberts burning rate, 331 scanning electron microscope (SEM), 237, 243, 257 secondary ion mass spectrometry (SIMS), 257 neutral mass spectrometry (SNMS), 257 sensitivity, 25, 161, 189, 257 control, 25 impact, 173 of energetic materials, 331 test, 25 shake-up transitions, 189 shear, 75 banding, 107 bands. 113 shock(s), 155, 173 compression, 113 front, 305 propagation, 305 initiated molecular reactions. 379 initiation, 25 loading, 93 high amplitude. 63 radius, 305 reactivity, 93 response, 173 sensitivity, 75 with defects, 161 simulation, 123, 183 embedded cluster. 149 simultaneous thermogravimetric modulated beam mass spectroscopy, 13 single bond rotations. 99 slip. 99. 227 planes. 113 systems, 113 SOLGASMIXPV computer program. 319 solid propellants. 355 combustion. 367 properties. 331 spatial power spectra (fracture surface profiles). 81 split shock waves. 123 stability. 41 relative. 13 stacking fault. 215 stereographic projection. 227 steric hindrance. 75 strain. 349 energy. 113 strand burning. 367 stress, 349 reduction. 99 structure, electronic. 149 supercritical shear. 75 surface analysis by laser ionization (SALI). 257 burning heat release. 331 chemistry. 269
mass spectrometry, 257 modification, 221 synchrotron x-radiation, 215 TATB - see triamino-trinitrobenzene TEM, 361 temperature-pressure phase diagrams, 199 3-D testing, 349 1,2.4.5-tetranitrobenzene. 25 tetryl, 3 thermal decomposition, 13. 47. 26? excitation, 293 gradient analysis (TGA), 41 thermochemical and mechanical properties, 331 thin films, 47 TiB 2. 319 time(-) dependent energy release, 311 by Al reaction. 311 equation of state. 299 lag method, 355 resolved holography, 305 to-ignition. 167 TNB - see trinitrobenzene TNT - see trinitrotoluene transversely isotropic. 349 triamino-trinitrobenzene (TATB). 25, 35, 167. 189. 243. 257 1.3.5-triamino-2.4.6-trinitrobenzent.. 25 triaxial compression. 349 trinitrobenzene (TNB). 25. 189 trinitrotoluene (TNT). 3. 25. 81. 215. 373 twinning. 215. 227 two particle interaction. 305 TZX (diaminotetrazinedianoxide). 25 ultracentrifuge. 81 ultra-high vacuum. 221 underwater explosives. 299 unit cells. 227 unixial strain. 75 urea. 361 uv dissociation. 373 photolysis. 53 vacancies. 113 vapor deposition. 47 vibron frequencies. 35 Vickers hardness. 93 video imaging burn front. 319 weapon design. 173 wedge test. 173 win.m no;,: defects in TATB. 243 XPS - see photoelectron spectroscopy x-ray photoelectron spectroscopy. 189 diffraction (XRD). 361 irradiation. 41 photoelectron spectroscopy (XPS). 41. 93. 257

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