Equation of state, phase transition, decomposition of β-HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) at high pressuresChoong-Shik Yoo and Hyunchae Cynn Citation: The Journal of Chemical Physics 111, 10229 (1999); doi: 10.1063/1.480341 View online: http://dx.doi.org/10.1063/1.480341 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/111/22?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Isothermal equations of state of beta octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine at high temperatures J. Appl. Phys. 97, 053513 (2005); 10.1063/1.1856227 On the nucleation mechanism of the β-δ phase transition in the energetic nitramine octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine J. Chem. Phys. 121, 5550 (2004); 10.1063/1.1782491 Isentropic compression loading of octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) and the pressure-induced phase transition at 27 GPa Appl. Phys. Lett. 85, 949 (2004); 10.1063/1.1771464 Temperature-dependent shear viscosity coefficient of octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX): Amolecular dynamics simulation study J. Chem. Phys. 112, 7203 (2000); 10.1063/1.481285 Monte Carlo calculations of the hydrostatic compression of hexahydro-1,3,5-trinitro-1,3,5-triazine and β-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine J. Appl. Phys. 83, 4142 (1998); 10.1063/1.367168

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Equation of state, phase transition, decomposition of b-HMX„octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine … at high pressures

Choong-Shik Yoo and Hyunchae CynnLawrence Livermore National Laboratory, Livermore, California 94551

~Received 5 February 1999; accepted 7 April 1999!

Pressure-volume relations and vibrational Raman spectra of unreacted HMX~octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine! have been obtained in both quasihydrostatic conditions to 45GPa and nonhydrostatic conditions to 10 GPa by using diamond-anvil cell, angle-resolvedsynchrotron x-ray diffraction, and micro-Raman spectroscopy. The results show that thehigh-pressure behavior of HMX strongly depends on the stress conditions. HMX is morecompressible in hydrostatic conditions~B0512.4 GPa andB8510.4! than in nonhydrostaticconditions~B0514.4 GPa,B8513.3!. This discrepancy in HMX compressibility can be explainedin terms of chemical reactions occurring in nonhydrostatic conditions. The static isotherm is in goodagreement with the shock Hugoniot, suggesting little temperature effect on the pressure–volumerelation. The hydrostatic data suggest thatb~monoclinic!-HMX undergoes two phase transitions:~i!a conformational transition at 12 GPa with no apparent abrupt volume change and~ii ! adiscontinuous one at 27 GPa with a 4% volume change. At 40 GPa, theb andc axes become nearlyidentical with the c/a ratio 1.62 andb5123°, approaching a nearly close-packed structure.© 1999 American Institute of Physics.@S0021-9606~99!51025-8#

I. INTRODUCTION

High-pressure thermodynamic and chemical propertiesof unreacted energetic molecules are fundamental to the de-scription of nonideal detonations, development of kineticmodels, and understanding the safety and sensitivity of highexplosives. These include the equation of state~EOS!, crys-tal structures, phase transitions, and thermal decompositionin a wide range of pressure and temperature. However, be-cause of high chemical reactivities of energetic molecules athigh pressures and temperatures, there exist very limited datafor unreacted systems. Futhermore, most of the existing dataare at relatively low pressures below 10 GPa.1

HMX ~octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine!is one of the most widely used energetic compounds and canbe made in four different crystal structures depending on therate of crystallization in solution, designated as thea, b, g,andd phases of HMX.2 The g phase was later found to be ahydrated form of HMX.3 The stabilities of these polymorphsare known to beb.a.g.d at ambient conditions.4 Al-though the stability field of these phases at high pressuresand temperatures are not very well known, theb phase isconsidered the most stable phase at high pressures at least to10 GPa.1,4,5 The b phase has a monoclinicP21 /c structurewith four molecules per unit cell at ambient conditions6 andtransforms to thed phase at 165–210 °C at ambientpressure.7 The d phase has a hexagonalP6122 structure andis considered to be stable at high pressures and high tempera-tures. Theb/d-phase transition is typically associated withthermal decomposition of HMX at high pressures above 0.2GPa, and the transition temperature strongly depends on theparticle size of theb phase.8

The isotherm of HMX has been measured up to 9 GPa atambient temperature in static compression.1 The Hugoniot of

HMX single crystals, on the other hand, has been measuredto 40 GPa.9 However, the data show a substantial softeningat high pressures above 30 GPa, which could be an indica-tion of a shock-induced chemical reaction or a phase transi-tion. Furthermore, comparing those previous shock9 andstatic1 results, it is interesting to note that the static isothermis stiffer than the shock Hugoniot. This result is rather un-usual. Because of high temperatures associated with shockcompressions, the Hugoniot of the normal solid should yielda higher pressure than the isotherm at a given volume. There-fore, it is clear that the pressure–volume–temperature~P–V–T! relation of HMX is not well understood even at verylow pressures.

Because of high reactivities at high P–T conditions, it isdifficult to obtain EOS and structural information of unre-acted high explosives from shock-wave experiments. On theother hand, energetic molecules are made mostly of low-Zelements such as hydrogen, carbon, nitrogen, oxygen, whichlimit the structural studies using a conventional x-ray sourcewith a small amount of sample at high pressures. For thisreason, the previous studies were done in a relatively largesample using a Bridgman type apparatus below 10 GPa.1

Recent developments of diamond-anvil cell~DAC! technolo-gies coupled with an intense micron-beam synchrotron x rayand laser spectroscopy are now capable of probing detailedcrystal structural information from minute samples~less than1 mg! of low-Z materials at high pressures andtemperatures.10 Therefore, in this study we have investigatedb-HMX at high pressures and temperatures by using a DACcoupled with micro-Raman spectroscopy and angle-resolvedx-ray diffraction using an intense monochromatic synchro-tron beam and image-plate detectors. Our main results de-scribed in this article include:~i! isotherms of HMX obtained

JOURNAL OF CHEMICAL PHYSICS VOLUME 111, NUMBER 22 8 DECEMBER 1999

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in both hydrostatic and nonhydrostatic conditions;~ii ! chemi-cal reactions of HMX in nonhydrostatic conditions; and~iii !the evidence for the phase transitions of HMX in hydrostaticconditions at 12 and 27 GPa.

II. EXPERIMENTS

A new diamond-anvil cell was designed for the angle-resolved x-ray diffraction and optical studies, as shown inFig. 1. This cell was made of Vascamax-300 steel heattreated to RC-52 and consists of two parts: a piston and acylinder. The piston side of the cell has a large cone-shapeopening with an x-ray transparent Be seat supporting a dia-mond anvil for diffraction studies; whereas, the cylinder hasa WC seat with a slit supporting the other diamond anvil foroptical spectroscopy. This cell is capable of obtaining fullcircles of Debye–Scherrer diffraction rings up to 4Q580degrees on one side; yet, the numerical aperture of the otherside is 0.36 with a laser beam accessible up to 45 degreesnormal to the cell. By using 300-mm-flat diamond anvils, thiscell is capable of achieving 100 GPa.

Polycrystallineb-HMX ~a few micron-size grains! wasloaded in a 120-mm-sample chamber drilled on a rheniumgasket with or without an argon pressure medium. Theformer represents a quasihydrostatic experiment~hereafter,called ‘‘hydrostatic’’ for simplicity!, and the latter representsnonhydrostatic experiments. The pressure of the sample wasdetermined by the ruby luminescence technique. For high-temperature thermal decomposition studies, a large grain~30–50mm! of HMX single crystal was loaded with an ar-gon pressure medium, and the entire cell was heated exter-nally by using a heating tape wrapped around the cell. Tem-peratures were determined by using a thermocouple~K type!mounted between the gasket and diamond anvil.

X-ray diffraction patterns of the sample were angle re-solved on an image-plate~20340 cm2, Fuji!, using a focusedand monochromatic x-ray beam at 20 keV from Si~111!double crystals of the BL 10-2 at Stanford Synchrotron Ra-diation Laboratory. The x-ray beam was first selected to 500mm by 300 mm by two pairs of W slits and was furthercollimated by a small microcollimator~;30 mm, Rigaku!

approximately 30 mm away from the sample. Consideringthe divergence of the beam, 2.3 mrad, it provided a gasketfree diffraction pattern from the sample greater than 90mmin diameter. Exposed imaging plates were read by a scanner~BAS-2500, Fuji! at 100 mm resolution, and concentricDebye–Scherrer diffraction rings were then integrated intoan intensity versus 2Q by using a modified NIH image pro-cessing program. The image plate was placed approximately15 cm from the sample, which recorded the angle-resolveddiffraction up to 2Q535 degrees using a diamond-anvil cell.The distance from the sample to the image plate was cali-brated either by taking two images at two locations separatedby a known distance~typically 15 cm! or by using an internalx-ray standard. Additional information can be foundelsewhere.10

High-pressure Raman spectra of the samples were takenusing an Ar1 ion laser tuned at 514.5 nm to excite thesample and a triple monochromator coupled with a liquid-N2

cooled CCD detector. The scattered radiation from thesample was collected using a microscope with a 403 objec-tive ~UT-40, Leitz!, which allowed visual observation and

FIG. 2. Typical image-plate record of an x-ray diffraction pattern obtainedfrom b-HMX at 0.2 GPa, after removing a structureless background. Thisrecord was obtained for a 30 min exposure at a distance approximately 15cm from the sample by using 30-mm-synchrotron x-ray beam at 20 000 keV.

FIG. 3. The calculated and measured angle-resolved x-ray diffraction pat-terns ofb-HMX at 0.2 GPa. The measured one was obtained by integrationof the image-plate record in Fig 1. The calculation was based on a mono-clinic unit cell structure. The detailed results are shown in Table I.

FIG. 1. A cross sectional view of the diamond-anvil cell for angle-resolvedx-ray diffraction and optical spectroscopy.

10230 J. Chem. Phys., Vol. 111, No. 22, 8 December 1999 C. S. Yoo and H. Cynn

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micro-Raman spectroscopy. The incident beam was focusedto approximately 5mm in diameter and the scattered lightfrom this area was then transposed to the entrance slit with;100mm opening of the spectrometer. Considering the 403magnification, the collected Raman spectrum representsabout 2–3mm at the sample, enabling the spatially resolvedinvestigation of mixed phases.

III. ISOTHERMS OF UNREACTED HMX

Figure 2 shows a typical image-plate record ofb-HMXat 0.2 GPa after removing the structureless background. Con-centric rings in the figure represent Debye–Scherrer diffrac-tions from various hkl lattice planes of monoclinicb-HMXbetween 2Q50 and 30 degrees. The angle resolved x-raydiffraction is then obtained by integrating these concentricDebye–Scherrer rings as shown in Fig. 2. The calculatedx-ray diffraction ofb-HMX is also plotted together in Fig. 3

for comparison, and the results are summarized in Table I.More than twenty peaks can be easily assigned for theP21 /c monoclinic structure ofb-HMX, and the agreementbetween the measured and calculated diffraction patterns isvery good. Refined cell parameters ofb-HMX at 0.2 GPa area56.495(60.014) Å, b510.952(60.010) Å, c58.693(60.024) Å, b5124.53°~60.20! with r51.931 g/cm3. Thisstructure is consistent with that ofb-HMX: a056.54 Å, b0

511.05 Å, c058.70 Å, b5124.30°,r51.893 g/cm3 at am-bient conditions.6 Many, but not all, of these diffractionpeaks have been used to determine crystal structures ofHMX to 45 GPa in hydrostatic conditions~Table II! and to10 GPa in nonhydrostatic conditions~Table III!. Typically,about ten diffraction lines were used for the data below 30GPa, but only six lines at higher pressures.

The pressure–volume relation ofb-HMX is representedin Fig. 4, showing characteristically different behaviors ofHMX depending on hydrostaticity of the sample. The dataobtained in hydrostatic~solid circles! and nonhydrostatic~open circles! conditions in this study are plotted togetherwith those1 previously obtained to 9 GPa~open diamonds!.The isotherms have been fitted to the third-order Birch Mur-naghan~BM! equation-of-state;11

P~GPa!5 32B0@h27/32h25/3#@123~12B8/4!~h22/321!#,

whereh5V/V0 and B0 and B8 are, respectively, the bulkmodulus and its pressure derivative. The best fits were ob-tained with

B0512.4 GPa, B8510.4,

below 27 GPa in hydrostatic,

B0514.4 GPa, B8513.3,

below 10 GPa in nonhydrostatic.

This result is illustrated as the solid lines in Fig. 4. The fitsare generally good at low pressures below 10 GPa for thenonhydrostatic data and below 27 GPa for the hydrostaticdata. Clearly, the nonhydrostatic data above 10 GPa are quiteunusual, showing large scattering of the data. This could bean indication for chemical reactions occurring at these pres-sures. In fact, our Raman studies which will be discussed inSec. IV support the idea that chemical reaction occurs innonhydrostatic conditions even below 10 GPa. The hydro-static data also show a departure from the fit above 27 GPawith an abrupt change in volume, which is likely due to aphase transition. Having a phase transition at 27 GPa, the

TABLE I. Refined cell parameters of HMX-II at 0.2 GPa, resulting ina56.495(60.014) Å, b510.952(60.010) Å, c58.693(60.024) Å,b5124.53°~60.20!, r51.931 g/cm3.

hkl dcal~Å) I cal dobs~Å) l obs Dd(Å)

011 5.9943 18 5.9926 34 0.0017020 5.4761 9 5.4802 18 20.0041

2111 5.4899 9100 5.3510 ,1110 4.8078 9 4.8042 15 0.0036021 4.3502 ,1

2102 4.3134 64 4.3143 66 20.00092121 4.1455 ,12112 4.0134 9 4.0153 6 20.0019

120 3.8272 45 3.8336 51 20.0064002 3.5811 ,1 3.5637 2 0.0174012 3.4038 9

2122 3.3885 18 3.3864 32 0.0021111 3.2910 9031 3.2526 27 3.2649 21 20.0124

2202 3.1723 9 3.1819 7 20.0096022 2.9971 36 3.0016 39 20.0045121 2.9193 9

2132 2.7866 100 2.7904 100 20.0038200 2.6755 ,1 2.6775 4 20.0020

2123 2.5401 ,1 2.5326 3 0.00752141 2.5139 9 2.5326 3 20.0186

131 2.5076 ,1 2.5060 2 0.0016220 2.4039 9 2.4026 20 0.0013

2133 2.2549 9 2.2594 4 20.0045042 2.1751 18 2.1791 8 20.0040214 2.1161 ,1 2.1138 2 0.0023

TABLE II. The pressure dependence of HMX crystal structure in nonhydrostatic conditions.

P ~GPa! a ~Å! b ~Å! c ~Å! b ~deg! V (cm3/g) V/V0

0.00 6.540 11.050 8.700 124.30 0.5284 1.00000.70 6.510 10.985 8.698 124.66 0.5205 0.98501.70 6.431 10.773 8.612 124.78 0.4987 0.94372.93 6.318 10.538 8.540 124.82 0.4749 0.89873.94 6.275 10.431 8.493 124.82 0.4643 0.87876.12 6.230 10.240 8.418 125.13 0.4468 0.84567.64 6.203 10.080 8.408 125.15 0.4373 0.8276

10.50 6.119 9.818 8.412 125.26 0.4198 0.7945

10231J. Chem. Phys., Vol. 111, No. 22, 8 December 1999 b-HMX at high pressures

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hydrostatic data can be described in terms of two smoothcurves which result in a 4% volume change at the transitionpressure. The existence of a phase transition at 27 GPa isalso supported by our Raman results which will be discussedin Sec. VI.

It is clear from Fig. 4 that the previous data1 show agood agreement with our hydrostatic data to about 4 GPa.However, above this pressure the previous data rapidlystiffen and approach our nonhydrostatic data. This is prob-ably due to the fact that the previous experiments were donein a methanol–ethanol pressure medium by using a WC-Bridgman anvil technique.1 The methanol–ethanol mixtureis still close to a nonhydrostatic condition with respect to thehydrostatic conditions provided by using an argon pressuremedium. For example, the bulk modulus~or, stiffness! of Aris about 1.4 GPa, substantially smaller than that of methanol,ethanol, or any other covalently bonded hydrocarbon rangingfrom 10 to 20 GPa.12 In fact, the stiffness of most HEs is also

within a similar range, 10–20 GPa. Consequently, the shearstrength of Ar is also expected to be smaller, providing abetter hydrostatic condition.

Pressure-induced changes of the lattice parameters arerepresented in Figs. 5~a!–5~c!, showing the anisotropic com-pression ofb-HMX. The b axis is the most compressible;whereas, thec axis essentially remains unchanged with pres-sure@Fig. 5~a!#. As a result, theb axis approaches nearly thesame value as thec axis above 40 GPa. The angleb remainsnearly unchanged at 125° to about 25 GPa and then slightlydecreases to 123° above this pressure as shown in Fig. 5~b!.At 40 GPa, thec(orb)/a ratio of b-HMX in Fig. 5~c! be-comes 1.62, approaching a nearly close-packed structure.

IV. CHEMICAL REACTIONS IN NONHYDROSTATICCONDITIONS

Note in Fig. 4 that at a given volume the hydrostaticpressure is lower than the nonhydrostatic one. This is quiteunusual for a shear-induced stress change, because the devia-toric stress in nonhydrostatic conditions should soften thecompression curve. Therefore, the difference between thehydrostatic and nonhydrostatic results in Fig. 4 cannot beexplained in terms of a shear-induced compression change.The unusual compression behavior of HMX is likely due tochemical reaction occurring in nonhydrostatic conditions. Infact, our Raman results of HMX support this conjecture.

Figure 6 shows Raman spectra of HMX obtained in~a!hydrostatic and~b! nonhydrostatic conditions, showing asimilar stress dependent behavior ofb-HMX. The vibra-tional features at 6 GPa in Fig. 6~a! consist of phonon bandsbelow 400 cm21, torsional bands between 400 and 600cm21, ring-NO2 deformations between 600 and 800 cm21

and ring stretching modes between 800 and 1100 cm21.13 Allof these bands harden~shift toward higher vibrational fre-quencies! with increasing pressure. The intensity of phononsrapidly diminishes with increasing pressure; whereas, the vi-brons remain relatively strong at all pressures. These changesin vibration bands occur reversibly with the reversal of pres-

FIG. 4. The pressure-volume relations of HMX in hydrostatic and nonhy-drostatic condition, showing that the HMX isotherm strongly depends on thestress condition of the sample. The isotherm previously obtained in WCBridgman-anvil x-ray experiments~Ref. 1! are also plotted for comparison.The detailed results are also summarized in Table II for nonhydrostatic dataand Table III for hydrostatic ones.

TABLE III. The pressure dependence of HMX crystal structure in hydrostatic conditions.

P ~GPa! a ~Å! b ~Å! c ~Å! b ~deg! V (cm3/g) V/V0

0.00 6.540 11.050 8.700 124.30 0.5284 1.00000.20 6.501 11.072 8.702 124.10 0.5276 0.99852.50 6.369 10.465 8.568 125.29 0.4742 0.89744.10 6.274 10.268 8.465 125.44 0.4520 0.85544.60 6.251 10.222 8.470 125.31 0.4493 0.85035.70 6.192 10.150 8.446 124.86 0.4432 0.83867.00 6.177 9.826 8.465 125.29 0.4266 0.80737.10 6.173 10.010 8.380 125.36 0.4297 0.8131

10.60 5.997 9.654 8.334 124.36 0.4052 0.766814.10 6.188 9.503 8.235 127.29 0.3919 0.741715.80 6.092 9.303 8.252 125.52 0.3873 0.732922.90 5.793 8.957 8.381 125.11 0.3619 0.684924.90 5.702 9.212 8.168 124.44 0.3602 0.681626.00 5.677 9.188 8.152 124.49 0.3566 0.674829.30 5.468 9.010 8.153 125.00 0.3348 0.633532.10 5.208 8.960 8.299 124.63 0.3242 0.613536.90 5.205 8.429 8.639 123.93 0.3199 0.605442.60 5.116 8.374 8.584 123.44 0.3122 0.5908

10232 J. Chem. Phys., Vol. 111, No. 22, 8 December 1999 C. S. Yoo and H. Cynn

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sure as shown in the 6 GPa spectrum at the top of Fig. 6~a!,indicating that no chemical change occurs in hydrostatic con-ditions.

The spectral changes in nonhydrostatic conditions in Fig.6~b! are markedly different from those in hydrostatic condi-tions. The width of the bands are substantially broader innonhydrostatic conditions, particularly of the phonons, dueto inhomogeneous pressure broadening. There is a broadstructureless background which increases the intensity as thepressure increases and obscures the vibrational featuresabove 25 GPa. The strong increase in background is gener-

ally observed at all nonhydrostatic pressures and is likely dueto laser-induced fluorescence. Furthermore, these spectralchanges occur irreversibly in a nonhydrostatic condition. Thespectrum quenched from 40 to 6 GPa in Fig. 6~b! still exhib-its a strong fluorescence without any indication of thephonons. Therefore, we attribute these irreversible spectralchanges to the chemical reactions of HMX in nonhydrostaticconditions which even occur at 6 GPa.

Similar laser-induced fluorescence and irreversiblechanges can be observed even in hydrostatic conditionswhen HMX undergoes thermal decomposition at high tem-peratures. Figure 7 shows the changes in Raman spectra ofsingle crystal HMX in an argon pressure medium at severaltemperatures at 32 GPa. Clearly, the fluorescence of HMX isobserved above 120°, similar to that observed from nonhy-drostatically compressed HMX in Fig. 6~b!. This strong fluo-rescence again obscures all the vibrational details above230 °C, clear evidence for thermal decomposition. Above230 °C, the thermal decomposition of HMX is apparent evenin a visual observation: transparent HMX gradually developsyellowish color up to 320 °C at which point it rapidly tumsdark brown. It is entirely possible that the enhancement ofthermal decomposition at 320 °C is due to a phase transitionfrom theb phase to a high-temperature polymorphd-HMX.

FIG. 5. Unit cell parameters of HMX plotted as a function of pressure:~a!a, b, c, ~b! b, and~c! a/c andb/c. Note that theb andc axes are essentiallyidentical above 33 GPa and thec/a ratio becomes about 1.62, suggestingthat HMX becomes a close-packed structure at these pressures.

FIG. 6. Raman spectra of HMX at several pressures of~a! hydrostatic~top!and~b! nonhydrostatic~bottom! conditions. Note that the spectral change ofHMX in an argon pressure medium occurs reversibly to 45 GPa, whereas itoccurs irreversibly in the absence of a pressure medium. The irreversiblespectral changes of HMX are due to chemical reactions occurring in non-hydrostatic conditions.

10233J. Chem. Phys., Vol. 111, No. 22, 8 December 1999 b-HMX at high pressures

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Recall that theb→d phase transition of HMX at high tem-perature and high pressure is typically associated with ther-mal decomposition.8 Clearly, the results of both Raman andvisual observations at high temperatures support the conclu-sion that the laser-induced fluorescence in Fig. 6 is due tochemical decomposition of HMX.

V. PHASE TRANSITIONS

Pressure-induced changes in Raman spectra of HMX inhydrostatic conditions indicate thatb-HMX transforms toe-HMX at 12 GPa and, subsequently, tof HMX at 27 GPa.The latter transition was also evident in our x-ray data men-tioned in Sec. III. Figure 8 shows the pressure-inducedchanges in~a! the phonon modes,~b! NO2-ring deforma-tional modes, and~c! ring-stretching modes. The most char-acteristic spectral changes to the phase transitions occur inthe NO2-ring deformation modes~b!, showing the modesplitting with increasing pressure. The splitting initially oc-curs only in theg(NO2) mode at 760 cm21 at 12 GPa, form-ing a triplet. However, at higher pressures between 21 and 31GPa bothg(NO2) and ring-g(NO2) torsional modes splitinto many multiplets. Furthermore, the frequency differencesin these multiplets continuously decrease with increasingpressure, forming one broad envelope for these modes be-tween 700 and 800 cm21 above 35 GPa. The phase transitionof HMX at 12 GPa has been predicted previously.14 On theother hand, the spectral changes between 21 and 35 GPa areprobably associated with the phase transition at 27 GPa men-tioned above.

Note that the changes in Raman spectra associated withthe phase transitions mostly occur in the delocalized ringvibration region, particularly in the vicinity of ring-NO2 tor-sional vibrations at 550–800 cm21. The changes in the othermodes such as ring stretching modes at 800–1000 cm21 andNO2 and N–N stretching modes at 1000–1200 cm21 are notcharacteristic to the phase transition at 12 GPa in particular.This indicates that the transition is likely conformational,which probably occurs martensitically rather than recon-structively. For this reason, we assume that HMX remains ina monoclinic structure. This conclusion is also consistentwith the x-ray data, showing nearly no volume change asso-

ciated with this transition at 12 GPa. A similar conforma-tional phase transition has also been observed in other cyclicmethylenenitramines. For example, a cyclic trimer RDX-I~an orthorhombic structure with a Pbca space group15! trans-forms to RDX-II at 4 GPa with a small volume change about1%.1 The vibrational16 and x ray1,17 studies suggested thatthe structure of RDX-II is still an orthorhombic structurewith probably different site symmetries from RDX-I.

It is interesting to recall that a large scattering of thex-ray data in nonhydrostatic conditions~Fig. 4! occurs above

FIG. 7. Raman spectra of HMX at several high temperatures at hydrostatic32 GPa, showing laser-induced fluorescence due to thermal decomposition.

FIG. 8. Raman spectra of HMX at hydrostatic high pressures in the regionsof ~a! phonons,~b! NO2-ring deformations, and~c! ring stretchings. Thesplittings of vibrational modes in~b! suggest that HMX undergoes twophase transitions: one at 12 GPa and the other between 21 and 35 GPa. Thex-ray data suggest that the latter transition occurs at 27 GPa~see Fig. 3!.

10234 J. Chem. Phys., Vol. 111, No. 22, 8 December 1999 C. S. Yoo and H. Cynn

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12 GPa. This might indicate an enhancement of HMX de-composition due to the phase transition at 12 GPa, which issimilar to the enhancement seen at high temperatures as aresult of theb→g phase transition.

VI. COMPARISON WITH SHOCK-WAVE RESULTS

Our x ray and Raman results explain the unusual stiff-ness of the previous isotherm1 with respect to the shockHugoniot. Figure 9 compares our isotherms obtained in hy-drostatic ~solid circles! and nonhydrostatic~open circles!conditions with the shock Hugoniot~open squares! of HMXsingle crystals. As mentioned above, the difference betweentwo isotherms is due to exothermic reaction of HMX undernonhydrostatic compressions. The hydrostatic isotherm onthe other hand agrees very well with the shock Hugoniot, atleast to 27 GPa. This result implies that the pressure-volumerelation of HMX depends little on temperature and the Gru¨n-eiseng should be close to zero. The data above 27 GPa showa small difference between the shock and static data, whichprobably represents kinetic effects of the phase transitionand/or chemical reaction associated with shock compression.

It should be emphasized that, despite the fact that shockcompression is nonhydrostatic compression, the Hugoniot israther consistent with the hydrostatic isotherm than the non-hydrostatic one. This indicates the kinetic effect of the reac-tion under shock compression; that is, the shock loadingtypically occurs within a few 100 ns, not long enough toinduce the chemical reaction in HMX single crystals or theextent of reaction is too small to be observed. Similar kineticeffects have been observed in many other systems includingCS2 and H2.18,19

In conclusion, we presented a direct evidence that non-hydrostatic compression of HMX induces chemical reactionsin HMX at ambient temperature. This reaction is probablyrelated to an increase in shear with increasing pressure.Chemical reactions in nonhydrostatic conditions havebeen observed previously in nitromethane20 and 1,4-dinitrocubane,21 all of which can be considered as a shear-induced chemical reaction. Our hydrostatic data, on the otherhand, indicate no apparent chemical reactions and suggestthe phase transitions toe-HMX at 12 GPa and tof-HMX at27 GPa. We also conjectured a small value for the Gru¨neisenparameterg of HMX based on a good agreement betweenour hydrostatic isotherm and the shock Hugoniot.

ACKNOWLEDGMENTS

X-ray diffraction studies were done on the beamline10-2 at the SSRL. We thank P. Pagoria for providing HMXsamples and K. Visbeck for experimental assistance. Discus-sions with B. Baer, F. Ree, L. Fried, and M. Howard werevaluable for this study. This work was done in support of aJoint DoD/DOE Munitions Technology Development Pro-gram and has been done under the auspices of the US De-partment of Energy by the Lawrence Livermore NationalLaboratory under Contract No. W-7405-ENG-48.

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FIG. 9. The isotherms of HMX in comparison with the Hugoniot of shock-compressed HMX single crystals, showing the hydrostatic isotherm is nearlyconsistent with the Hugoniot.

10235J. Chem. Phys., Vol. 111, No. 22, 8 December 1999 b-HMX at high pressures

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