-
A Facility for Simulating the Dynamic Response of
MaterialsMaterials PropertiesWilliam A. Goddard, IIICaltech
ASCI Academic Strategic Alliances ProgramSite VisitOctober 8,
19981
-
Simulation Development RoadmapPROBLEM SOLVING
ENVIRONMENTMeshGenerationSolidModelingFracture
andFragmentationMicroMechanicsConstitutiveRelationsPhase
TransitionsMaterialsScienceFluidMechanicsComputationalScienceSolidMechanicsMP2
-
Goals of the proposed researchProvide the Parameters Describing
the Materials Properties required for a Full Physics, Full
Chemistry 3-D Description of:Detonation of High Explosives (HE),
Solids Subjected to Severe Dynamic Loading (SD), Compressible
Turbulence and Mixing (CT).Develop the Technology Required to
Predict These Properties Solely from First Principles.Validate the
Accuracy of the Properties by Comparison to Experiments Under
Conditions Relevant to HE, SD and CT Applications.Implement the
Technology in the Most Efficient Manner for Massively Parallel
Computers.3
-
Roadmap for Materials Properties4
-
Materials Properties MilestonesMetal FFsQM on metalsExpansion of
QM capabilities for HEQMC in ab initio QM codesParallel DFTMD
simulations ofHE with polymerNew functionals for metalsQM based
FFsNEMD, parallelization of NEMDViscosities ofheavy metalsCeramic
FFsand EoSQM based FFsProperties from MD simulationsProperties of
brittle ceramicsIntegration of atomistic simulation and 2D EoS
models (Cij (T,P))DFT-MD on Large Scale models Year 1 Year 2Year 3
Year 4 Year 5 MD simulations with reactive FFReaction rates for HEs
from QMMP(core), SDMP(core), SDMP(core), SDMP(core), HE,
SDMP(core), SD,newMP(core), HE,CTMP(core), CTMP(core), HE,
SD,CT,newMP(core), HEMP(core), SDMP(core), HENEMD using reactive FF
Cij at interfaces; heterogeneous systems at high T and
PParallelization of QMC codesTransport propertiesEoS
databaseIntegrationProperty database RR databaseRelevant
disciplineHypervelocity impact and planar shock wave simulations
Metal-ceramic interface FF DB: Transport properties5
-
Simulation Development Roadmap MPHEHigh Explosives
ApplicationsBinder and Grain InteractionsKel-F, EstaneEquation of
StateHMX, TATBReaction Dynamics and Molecular ProcessesShocked HMX,
TATBVibrational Analysis of Rapid Post-Shock EventsShock
Compression MD6
-
Simulation Development Roadmap MPSDSolid Dynamics
ApplicationsEquations of StateTa, Fe, Oxides, and CeramicsPhase
TransitionsTa, Carbon, CeramicsConstitutive EquationsElastic
properties of metals, alloys, and ceramicsThermodynamic
propertiesPlasticity and behavior under large strain rates7
-
Simulation Development Roadmap MPCTCompressive Turbulence and
Fluid Dynamics ApplicationsDetermine material properties for fluids
Equation of state of Dense Fluids (P,V,T)Transport Properties of
Dense Fluids (at elevated T and P) Viscosity of dense fluids under
large shear ratesMass transport in dense fluids (diffusion at high
P & T)Heat transport (thermal conductivity at high P &
T)Shock propagation in fluidsNegative pressure properties
8
-
Personnel Materials PropertiesSenior researchersWilliam A.
Goddard (MSC)Ronald Cohen (CIW)Tahir Cagin (MSC)Siddharth Dasgupta
(MSC)Richard P. Muller (MSC)Graduate students (ASCI)Lu Sun
(Materials Sci.)Hao Li (Materials Sci.)Yue Qi (Materials
Sci.)Georgios Zamanakos (Physics)Ryan Martin (Materials
Sci.)Guofeng Wang (Materials Sci.)Postdoctoral staffDaniel Mainz
(non-ASCI)Gregg Caldwell (non-ASCI)Alejandro Strachan
(non-ASCI)John Che (non-ASCI)Ersan Demiralp (non-ASCI)Oguz Gulseren
(CIW)Hideki Ikeda (non-ASCI)Don Frasier (non-ASCI)Enrique Pifarre
(LANL, Feb 99)Professional support staffDarryl Willick (MSC)J.
Kendall (MSC)9
-
Organization - Materials PropertiesExternal
CollaboratorsCarnegie Institute WashingtonUniversity of
TennesseeMaterials Properties Meeting AnnualLANL, SNL, LLNL
National LaboratoriesUtah and Illinois Alliance CentersNovember 10,
1997January 28, 1999 (HE); January 29, 1999 (SD)InteractionsHE:
Weekly Meetings, (daily email/phone)SD: Monthly MeetingsMP: Monthly
MeetingsSI: Biweekly Meetings10
-
External Meetings - Materials PropertiesEnergetic Materials GRC
(Dasgupta, Sun)11th Detonation Symposium (Dasgupta)NATO ASI on QMC
(Cohen, Muller)2 Visits to SNL: PBC QM Quest (Muller)1 Visit to
LANL: QM ECP (Muller)Dislocations Workshop, LLNL (Cagin, Gulseren)1
Visit to LLNL: MP, HE, SD (Goddard)1 Visit to SNL: Multi-length
scale, Polymers (Goddard)1 Visit to LLNL: HE Aging (Goddard)MRS,
APS, ACS meeting presentations (~11)11
-
ASCI Materials Properties WorkshopNovember 10, 1997, Caltech
Laboratory PresentationsLLNLMailhiot, Ree, King,
FriedSNLHeffelfinger, MeliusLANLKressASAP Center
PresentationsCaltechGoddard, Tombrello, Cagin, Muller, Dasgupta,
Ortiz, Shepherd, MeironCIWCohenUtahVoth, Wight,
BoydIllinoisMartinez, Mitas12
-
Milestones, MP Software IntegrationMSC QM Software (Jaguar,
QM/MSC) Port to ASCI Machines Optimize parallelizationMSC MD
Software (MPSim) Port to ASCI Machines Optimize parallelizationMSC
Semi-empirical QM Software (MSC-INDO)Improve scaling for large
systemsIntegration of QM and MD Software use Caltech Integration
Platform13
-
Role of Computer Science (CSMP)ScaLAPACK workshop, January
1998Use of math libraries to parallelize codeSoftware IntegrationMP
integration framework integrates with Caltech ASCI frameworkNew
Algorithmic workShock dynamics for HE and SDImproved matrix
diagonalization work for QMVirtual Test facilityHE Database
Project14
-
Current Research in Methods for MPQuantum MechanicsPeriodic
SystemsHigh Accuracy for Large SystemsFast Results for Large
SystemsSolvation (Poisson-Boltzmann)Force FieldsPolarizable, Charge
TransferVariable Bond OrdersPhase TransitionsMixed Metal, Ceramic,
PolymerMesoScale DynamicsCoarse Grained FFDiffusionHybrid MD and
Meso DynamicsFrictionPhysics-based gridpoints for Finite Element
AnalysisMolecular DynamicsLarge Systems (CMM,
Parallel)Non-Equilibrium Viscosity, FrictionSolvation
(Poisson-Boltzmann)Hybrid QM/MDHierarchical NEIMOPlasticity, Twin
Formation, Crack InitiationInterfacial EnergiesHildebrand
SolubilitiesProcess SimulationVapor-Liquid EquilibriaReaction
Networks
15
-
Quantum Mechanics (HY=EY)Ab Initio (Exact
Hamiltonian)Pseudospectral Techniquesdealiasing, multigridImproved
scaling by factors of N to N2First Principles Solvation
Density Functional TheoryPeriodic Boundary ConditionsNew
FunctionalsTight Binding fit to accurate LAPWSemiempiricalTight
Binding or INDOFast Hamiltonian ConstructionMolecular Dynamics
Quantum Monte CarloMost accurate method (0.0004 eV for simple
reactions)Scales exponentially with sizeCombine with DFT (Only
simulate reacting electrons)16
-
QM Methodology (Jaguar)17Log (number basis
functions)JaguarGaussianCPU TimeCollaboration with Columbia U. and
Schrdinger Inc.
-
QM Parallelization (Jaguar)18Collaboration with Columbia U. and
Schrdinger Inc.
-
Quest: Sandia Software for PBC QM19MP/ASCI: Incorporate MSC GUI,
new ECP, Basis sets Port to other machines
-
CS/MP 1: Improved Matrix AccelerationQM ScalingN2 - N4
Hamiltonian ConstructionN3 DiagonalizationNeed both to scale as
N
Series of alkane chains, 276-552 basis functions, bandwidth ~80
basis functionsContour plot of Hamiltonian MatrixBand Diag: scales
good (N2.3) but overhead too highNormal Diag: scales poorly (N3.3)
but generally efficientBlock Diag: scales best (
-
Progress Molecular Dynamics (F=MA)Generalized Gibbs MD (Constant
T and P/S )Cell Multipole Methods (Octree, Fast Multipoles) Fast,
accurate NB evaluations for millions of atom systemsNEIMO Dynamics
Fast internal coordinate dynamicsHierarchical for coarse
grainingSolvation Poisson-Boltzmann solver (energy and
forces)Generalized BornOptimization for Highly Parallel
ComputersSGI Origin, HP ExemplarPorted to Intel quad-Pro21
-
MPSim with PB SolvationExplicit SolventAccurateTypically solvent
molecules account for 90% of computationpolymer motions limited by
diffusion rates in solventContinuum Solvent
(Poisson-Boltzmann)Solvent reduced to charges and forces on mesh
points around moleculeUse realistic solvent accessible
surfaceCalculate energies and forces (for dynamics)Dramatically
increases simulation timesProtocolUpdate PB Forces every N time
steps (Forces Expensive)Use mesh density sufficient for MD (coarser
than for QM).22
-
Integrate NEIMO in MPSimINTERNAL COORDINATE DYNAMICS:Problem: M
is full N by N (N is number of int. coord.)Inversion scales as N3,
too slow for every dynamics stepSolution: NEIMO = Newton Euler
Inverse Mass Operator Construct M-1 in terms of operators (scale as
N=1)(collaboration with JPL Space Robotics) Hierarchical NEIMO -
Treat segments as rigid clusters connected by flexible hinges,
Allows successively coarser descriptions for Large time and spatial
scales GoalsIncorporate NEIMO dynamics into MPSim (Forces use
CMM)Include Poisson-Boltzmann solvers ParallelizeTarget Systems: HE
grains in polymer binder.23
-
CS/MP 2: Lightweight Threads in MDParallelized MPSimEfficient on
KSR, Intel DeltaOther platforms less efficient Lightweight
ThreadsInexpensive intializationParallelization on commodity
microprocessorsSpeedup of 3.6 on 4 processors for a real
problemNext year, Expand to QMQM/MMHRV-1 Rhinovirus - 500,000
AtomsIntel QuadPentium, 2 GB RAM24Cagin, Li (MP), Thornley (CS)
-
Accomplishments, OverviewHigh ExplosivesMD Simulation of TATB,
HMX, and Kel-FSimulation of post-shock energy redistributionSolid
DynamicsMD Simulation of Metals and OxidesQM Simulation of HCP,
FCC, and BCC MetalsFF for BCC MetalsAlgorithmsShock MD
SimulatorPhase transitions in Oxides and MetalsBond-order-dependent
FF for Carbon25
-
Milestones, HETATB/HMX Molecular Structure
MD of inert and reactive explosives
Reaction Mechanism for TATB/HMX26
-
MD and Force Field Development for HMXLevel 0 - Generic Force
Field (Dreiding) - Can Do Any Combination Of Main Group
AtomsDensity of StatesPressure LoadingPhase transitionsLevel 1 -
Vibrationally accurate force field Develop for specific systems
DMN, HMX & RDXDFT (B3LYP) calculations on isolated
monomersQUEST calculations on condensed phase systemsFFOPT
parameterization of FF to fit QMVibrational Energy Transfer (VET):
Intra-, inter-molecular, phonon - phonon couplingsH-bond
interactions27
-
Crystallographic Forms of HMXStable @ 300K377 - 429 K429 K - to
melting pointr = 1.894r = 1.839r = 1.58r = 1.78Impact EnergyE =
0.75 kg/cm2Least sensitiveImpact EnergyE = 0.10 kg/cm2Most
sensitiveImpact EnergyE = 0.20 kg/cm2SensitiveImpact EnergyE = 0.20
kg/cm2Sensitive28
-
Correlation of Density of States (from MD) with Sensitivity (h50
measurement)TATB h50 = 3.2mg-HMX h50 = 0.14mb-HMX h50 = 0.33md-HMX
h50 = N/A most sensitivea-HMX h50 = N/A290200400600 cm-1Conclusion:
Impact sensitivity correlates with density of modes between 0-200
cm-1
-
Compare Vibrational Frequencies QM (DFT-B3LYP/6-31G**) with FF
(Dreiding) 300-200cm-1
Chart5
9.91-28.7
42.4660.63
7465.39
93.4667.34
103.674.44
116.1896.33
117.65103.28
124.41124.95
134.65128.87
214.63165.07
245.03170.13
285.46210.14
345.27213.68
384.03270.57
387.18299.81
401.28347.36
442.22349.12
442.74378.16
448.04403.44
472.41405.81
489.08431.07
517.6432.19
523.34598.91
535.39600.11
558.29630.22
560.11634.67
597.03652.42
601.62657.35
609.73732.21
628.5751.03
708.31753.29
733.72757.41
740.14757.75
782.64779.39
833.38843.95
877.46844.7
904.34881.96
908.96890.5
973.91945.28
974.34946.73
1003.96961.8
1019.97962.71
1124.791088.95
1168.411089.48
1204.191165.4
1206.331196.56
1245.071232.22
1253.441247.66
1294.171267.53
1313.331269.79
1447.771313.82
1449.131320.28
1478.311336.71
1485.081341.86
1577.91354.99
1585.421356.92
1652.721378.1
1676.71383
1692.361402.23
1694.881432.42
1701.131434.93
1710.371456.59
1730.121480.28
1731.721483.28
1740.831495.75
1741.851500.15
1760.641670.35
1762.741673.03
1812.631687.85
1817.411691.16
2960.83087.59
2961.563087.95
2964.643101.91
2964.733102.76
3021.013171.46
3021.383171.72
3027.63173.74
3028.063173.84
Dreiding
B3LYP/6-31G**
Mode Number
Frequency (cm-1)
Comparison of Frequencies for HMX beta form
laroux
Mode NumberDreidingHF/6-31G**B3LYP/6-31G**
19.9182.59-28.7017.56
242.46115.4760.6320.36
374.00118.8865.3997.12
493.46136.2467.3499.46
5103.6160.4074.44105.87
6116.18219.6096.33135.43
7117.65234.40103.28135.45
8124.41235.97124.95151.29
9134.65237.43128.87164.35
10214.63242.08165.07303.88
11245.03246.42170.13309.27
12285.46261.34210.14313.89
13345.27284.87213.68424.76
14384.03324.00270.57456.23
15387.18356.77299.81507.54
16401.28381.85347.36551.36
17442.22401.24349.12557.41
18442.74420.49378.16561.82
19448.04469.39403.44581.97
20472.41470.14405.81628.23
21489.08494.01431.07655.92
22517.60494.41432.19747.13
23523.34640.12598.91765.65
24535.39640.28600.11767.50
25558.29667.49630.22767.99
26560.11672.20634.67771.52
27597.03697.57652.42787.87
28601.62697.78657.35789.23
29609.73786.43732.21839.32
30628.50830.31751.03852.51
31708.31889.54753.29852.75
32733.72895.76757.41919.19
33740.14912.29757.75951.74
34782.64912.34779.39957.16
35833.38914.36843.951147.01
36877.46915.59844.701159.94
37904.34932.84881.961174.94
38908.96943.70890.501175.52
39973.911033.11945.281295.03
40974.341039.23946.731342.50
411003.961067.54961.801399.95
421019.971075.48962.711415.80
431124.791167.941088.951466.80
441168.411177.001089.481509.49
451204.191268.381165.401514.36
461206.331293.641196.561522.92
471245.071314.671232.221532.36
481253.441316.721247.661546.06
491294.171343.411267.531557.57
501313.331352.041269.791584.95
511447.771354.431313.821651.24
521449.131356.271320.281671.82
531478.311375.921336.711729.20
541485.081399.871341.861741.88
551577.901457.761354.991796.80
561585.421473.691356.921810.53
571652.721507.571378.101825.49
581676.701510.581383.001846.30
591692.361546.541402.231884.58
601694.881563.841432.421892.17
611701.131574.921434.931895.84
621710.371582.961456.591896.34
631730.121595.331480.281920.75
641731.721604.311483.281928.90
651740.831621.661495.751945.29
661741.851629.441500.151981.67
671760.641643.021670.352116.90
681762.741644.831673.032135.19
691812.631651.251687.852155.97
701817.411652.751691.162173.47
712960.803155.373087.592886.85
722961.563156.103087.952890.16
732964.643177.293101.912892.73
742964.733177.593102.762895.17
753021.013242.913171.462931.83
763021.383243.013171.722940.78
773027.603247.623173.742946.13
783028.063247.673173.842957.38
laroux
Dreiding
HF/6-31G**
B3LYP/6-31G**
Mode Number
Frequency (cm-1)
HMX Frequencies
Vib Freq Comp
Dreiding
B3LYP/6-31G**
Mode Number
Frequency (cm-1)
Comparison of Frequencies for HMX beta form
Vibrational Frequencies
DreidingHF/6-31G**B3LYP/6-31G**Expt.
9.9182.59-28.70
42.46also with 237.43115.4760.63
74.00118.8865.39
93.46136.2467.34
103.6160.4074.44
116.18219.6096.33
117.65234.40103.28
124.41235.97124.95
134.65237.43128.87
214.63242.08165.07
245.03246.42170.13
285.46261.34210.14
345.27284.87213.68
384.03324.00270.57
387.18356.77299.81
401.28381.85347.36
442.22401.24349.12
442.74420.49378.16
448.04469.39403.44
472.41470.14405.81
489.08494.01431.07
517.60494.41432.19
523.34640.12598.91
535.39640.28600.11
558.29667.49630.22
560.11672.20634.67
597.03697.57652.42
601.62697.78657.35
609.73786.43732.21
628.50830.31751.03
708.31889.54753.29
733.72895.76757.41
740.14912.29757.75
782.64912.34779.39
833.38914.36843.95
877.46915.59844.70
904.34932.84881.96
908.96943.70890.50
973.911033.11945.28
974.341039.23946.73
1003.961067.54961.80
1019.971075.48962.71
1124.791167.941088.95
1168.411177.001089.48
1204.191268.381165.40
1206.331293.641196.56
1245.071314.671232.22
1253.441316.721247.66
1294.171343.411267.53
1313.331352.041269.79
1447.771354.431313.82
1449.131356.271320.28
1478.311375.921336.71
1485.081399.871341.86
1577.901457.761354.99
1585.421473.691356.92
1652.721507.571378.10
1676.701510.581383.00
1692.361546.541402.23
1694.881563.841432.42
1701.131574.921434.93
1710.371582.961456.59
1730.121595.331480.28
1731.721604.311483.28
1740.831621.661495.75
1741.851629.441500.15
1760.64CH21643.021670.35
1762.741644.831673.03
1812.631651.251687.85
1817.41wag1652.751691.16
2960.80CH23155.373087.592978
2961.56symmetric3156.103087.95
2964.643177.293101.91
2964.73stretch3177.593102.762994
3021.01CH23242.913171.463027
3021.38anti3243.013171.72
3027.60symmetric3247.623173.74
3028.06stretch3247.673173.843038
Geometric Parameters
Partially updated data September 30, 1998
ValueExpt.Dreiding Exp-6CVFF?ExptDreiding Exp-6CVFF
Cell parameters
a6.546.6036.701615.1414.4485.611
b11.0511.09411.21723.8924.38313.29
c8.708.949.08925.915.8098.557
a90.090.0090.0090.090.090
b124.3125.55125.7190.090.0115.59
g90.090.0090.0090.090.090
Volume519.39532.799554.872138.72046.46575.414
s1.8941.8461.7731.8391.9221.709
Molecular geometry
N-N1.354(l)/1.373(s)1.318(s)/1.319(l)1.207(l)/1.297(s)1.353(s)/1.366(l)1.320(s)/1.323(l)
N-C1.437/1.448/1.455/1.4721.453/1.455/1.456/1.4571.474/1.466/1.623/1.6581.444/1.448/1.451/1.4711.454/1.460
N-O1.205/1.209/1.221/1.2331.200/1.201/1.2021.045/1.063/1.149/1.1621.214/1.223/1.236/1.2371.200/1.201
O-N-O125.9/126.7113.5/114.4124.8/124.9113.1/113.3
O-N-N115.9/116.2/117.4/117.9122.2/122.6/123.4/123.9116.4/117.2/118.0/118.8123.2/123.5/123.7
N-N-C115.1/117.4/118.2118.7/120.2/120.4/120.5115.9/119.2/119.3/119.6119.3/119.6/119.8/121.1
C-N-C122.4(l)/123.8(s)119.4(s)/120.8(l)119.6/123.7119.6/120.4
N-C-N110.1/113.5111.7(s)/115.1(l)110.5/113.1112.6/116.1
NO2(inv)0.4/0.70.1/0.20.8/1.90.5/1.7
N-NO2(inv)8.0(s)/20.3(l)1.13.4(s)/12.2(l)1.8(s)/4.1(l)
N-C-N-C18.1/43.3/101.7/117.10.8/67.5/83.3/117.964.7/68.2/100.7/105.033.8/64.5/77.8/119.8
C-N-N-O0.9/1.3/10.7/21.72.6/3.1/3.6/4.61.4/3.2/5.3/9.70.6/2.2/7.0/9.6
Short contact
CH:::O-N-O2.192/2.3372.367/2.3892.22/2.45/2.482.117/2.2292.396/2.350
Crystal# of molecules28
Total Eunits kcal/mol-190.727-95.3635-636.684-79.5855
Bondunits kcal/mol15.10897.5544566.2628.28275
Angleunits kcal/mol14.98637.4931572.45399.0567375
Torsionunits kcal/mol12.08616.0430547.88255.9853125
Inversionunits kcal/mol0.0610.03052.22980.278725
vdWunits kcal/mol31.417315.70865126.98115.872625
Electrostaticunits
kcal/mol-264.387-132.1935-952.493-7.5010670888
Differenceunits kcal/mol-15.778
DFT/6-31G**unit Hartree-1196.557378160650-1196.553819922900
Differenceunit kcal/mol-2.2185950404
Singleunit kcal/mol39.395641.51
Differenceunit kcal/mol-2.1144
Bulk Modulus15.14
Young's Modulus26.08
333.31
48.57
Expt.DFT/6-31G**Expt.DFT/6-31G**
N-N1.354(l)/1.373(s)1.392(l)/1.401(s)1.353(s)/1.366(l)1.406(s)/1.417(l)
N-C1.437/1.448/1.455/1.4721.442/1.451/1.461/1.4781.444/1.448/1.451/1.4711.450/1.458
N-O1.205/1.209/1.221/1.2331.224/1.226/1.2311.214/1.223/1.236/1.2371.223/1.224
O-N-O125.9/126.7126.8/127.4124.8/124.9126.4/127.5
O-N-N115.9/116.2/117.4/117.9115.1/115.8/116.7/118.0116.4/117.2/118.0/118.8116.2/116.8
N-N-C115.1/117.4/118.2114.5/117.9/118.1/118.2115.9/119.2/119.3/119.6117.4/117.5/117.6
C-N-C122.4(l)/123.8(s)123.4/123.7119.6/123.7120.9/124.6
N-C-N110.1/113.5111.3/114.2110.5/113.1114.2
NO2(inv)0.4/0.71.3/2.10.8/1.90.1/0.6
N-NO2(inv)8.0(s)/20.3(l)7.5/18.63.4(s)/12.2(l)5.0/20.6
N-C-N-C18.1/43.3/101.7/117.119.4/43.1/99.3/113.564.7/68.2/100.7/105.072.2/72.3/93.4/93.6
C-N-N-O0.9/1.3/10.7/21.72.8/4.7/7.2/18.21.4/3.2/5.3/9.73.1/11.6/11.8
Experiment Yellow
DFT/6-31G** Red
Pressure (Gpa)ABC
0.006.5411.038.71
1.616.3910.668.57
2.476.3510.58.54
3.246.3010.418.51
4.036.3010.298.51
4.826.2610.198.51
5.426.2410.168.48
6.316.2210.088.51
6.746.2210.018.51
7.476.219.988.49
Press. (Gpa)beta
0.00124.4
1.61125.0
2.47125.2
3.24125.4
4.03125.4
4.82125.5
5.42125.4
6.31125.3
6.74125.3
7.47125.7
Pressure (Gpa)ABCbeta
0.006.4612.597.81121.00
16.44412.6967.704122.672
26.35212.1737.781121.527
36.32812.1837.764123.132
46.30312.0567.805123.909
56.2711.6467.965123.869
66.24711.5637.945124.023
76.15711.6767.782122.953
86.16611.5157.809123.587
96.23910.1178.774125.324
106.18710.7498.262125.074
(CH3)2-N-NO2Expt.B3LYP/6-31G**
N-N1.3321.377
N-O1.2281.234
N-C1.439/1.4531.451
C-H0.957/0.960/0.907/0.9921.086/1.096
O-N-O124.2125.1
O-N-N117.9117.4
N-N-C117.7/118.1119.8
C-N-C124.2120.4
H:::O2.18
Geometric Parameters
6.5411.038.71
6.3910.668.57
6.3510.58.54
6.310.418.51
6.310.298.51
6.2610.198.51
6.2410.168.48
6.2210.088.51
6.2210.018.51
6.219.988.49
A
B
C
Pressure (GPa)
Cell Parameters
Linear Compression of beta HMC
124.4
125
125.2
125.4
125.4
125.5
125.4
125.3
125.3
125.7
beta
Pressure (GPa)
Angle (degrees)
Angle Variation
6.4612.597.81
6.44412.6967.704
6.35212.1737.781
6.32812.1837.764
6.30312.0567.805
6.2711.6467.965
6.24711.5637.945
6.15711.6767.782
6.16611.5157.809
6.23910.1178.774
6.18710.7498.262
A
B
C
Pressure (GPa)
Cell Params (A)
Cell Parameter vs Pressure
MBD08EAF3A7.unknown
MBD08EB30F9.unknown
-
Pressure Dependence of Crystallographic Cell Parameters for
b-HMX (Theory using Dreiding, open symbols) with Experiments from
Cady & Ollinger (filled symbols)BCA31
Chart3
6.546.60311.0311.0948.718.94
16.495110.80818.875
6.391.6110.661.618.571.61
26.428210.61828.816
6.352.4710.52.478.542.47
36.38310.47238.765
6.33.2410.413.248.513.24
6.36.34210.2910.3528.518.721
6.264.8210.194.828.514.82
56.31510.25258.681
6.245.4210.165.428.485.42
66.284610.16468.645
6.226.3110.086.318.516.31
6.226.7410.016.748.516.74
76.261710.08678.611
6.217.479.987.477.477.47
86.24810.0178.498.58
96.22299.95398.551
106.205109.895108.524
A(expt)
A(exp-6)
B (expt)
B(exp-6)
C(expt)
C(exp-6)
Pressure (GPa)
Cell Length (A)
Cell Length vs Pressure Dreiding Exp-6
laroux
PressureabcbetaVolume
112.83924.90615.793121.8488
212.71524.37415.838122.494138
312.62924.02815.844122.8459
412.5629823.8494215.78751123.0189
512.49623.51415.809123.283881
1012.43621.01316.944125.333610
Pressure (Gpa)A (expt)A (MD)B (expt)B (MD)C( expt)C (MD)beta
(expt)beta (MD)PressureA(expt)A(exp-6)A(LJ9-6)B
(expt)B(exp-6)B(LJ9-6)C(expt)C(exp-6)C(LJ9-6)beta
(expt)beta(exp-6)beta(LJ9-6)
0.006.5411.038.71124.40.006.546.6036.5311.0311.09410.7888.718.948.868124.4125.55125.56
1.006.419512.4537.8965121.84881.006.4956.43110.80810.5298.8758.812125.92125.86
1.616.3910.668.57125.01.616.3910.668.57125.0
26.357512.1877.919122.4926.4286.36910.61810.3518.8168.761126.05126
2.476.3510.58.54125.22.476.3510.58.54125.2
36.314512.0147.922122.845936.386.32310.47210.2158.7658.716126.14126.1
3.246.3010.418.51125.43.246.3010.418.51125.4
4.036.306.2814910.2911.924718.517.893755125.4123.018946.306.3426.28710.2910.35210.1048.518.7218.676125.4126.21126.18
4.826.2610.198.51125.54.826.2610.198.51125.5
56.24811.7577.9045123.2856.316.25810.25210.0098.6818.639126.28126.26
5.426.2410.168.48125.45.426.2410.168.48125.4
6.316.2210.088.51125.366.2846.23410.1649.9288.6458.606126.35126.33
6.746.2210.018.51125.36.316.2210.088.51125.3
7.476.219.988.49125.76.746.2210.018.51125.3
106.21810.50658.472125.3376.2616.21210.0869.8568.6118.574126.42126.41
7.476.219.98125.7
86.246.19310.0179.7928.498.588.545126.48126.48
96.2226.1779.9539.7348.5518.518126.55126.55
106.2056.1619.8959.6818.5248.492126.61126.62
HMX-beta Dreiding - Unit cell 0K
PressureVolumeDensityVol MCXX532.7990
0544.7851.80543532.799504.5261
0.5532.2061.8481486.4892
1522.1361.88374504.526472.9163
1.5513.7531.91448461.9374
2506.5941.94154486.489452.6885
2.5500.3421.96579444.6576
3494.7971.98783472.916437.5487
3.5489.8172.00804431.1698
4485.2772.02682461.937425.3699
4.5481.122.04433420.05710
5477.2622.06086452.688415.15611
5.5473.6672.0765410.60112
6470.2952.09139444.657406.35213
6.5467.1142.10563402.35514
7464.0912.11935437.548398.59915
7.5457.3382.15064395.04716
8454.6152.16352431.169391.68117
8.5452.0292.1759388.4818
9449.5632.18783425.369385.43119
9.5447.2082.19936382.52120
10444.9542.2105420.057379.73421
10.5442.7892.2213377.06122
11440.7082.23179415.156374.49623
11.5438.7042.24199372.02824
12436.7692.25192410.601369.64925
12.5434.92.2616367.35426
13433.0932.27103406.352365.13927
13.5431.3432.28025362.99628
14429.6452.28926402.355360.92329
14.5427.9972.29808358.91330
15426.3932.30672398.599356.96331
15.5424.8372.31517355.06932
16423.3212.32346395.047353.2333
16.5421.8452.33159351.4434
17420.4062.33957391.681349.69935
17.5419.0022.34741348.00436
18417.6312.35511388.48346.35237
18.5416.2932.36268344.7438
19414.9852.37013385.431343.16839
19.5413.7072.37746341.63340
20412.4562.38467382.521340.13441
20.5411.2322.39177338.66842
21410.0332.39876379.734337.23643
22407.7082.41244377.061335.83444
23405.4732.42573374.496334.46245
24403.3232.43867372.028333.11846
25401.2492.45127369.649331.80147
26399.2482.46355367.354330.5148
27397.3142.47555365.139329.24549
28395.4432.48726362.996328.00450
29393.6312.49871360.923326.78651
30391.8742.50991358.913325.59152
31390.1692.52088356.963324.41853
32388.5132.53162355.069323.26554
33386.9042.54216353.23322.13355
34385.3382.55248351.44321.0256
35383.8142.56262349.699319.92657
36382.332.57256348.004318.85258
37380.8832.58234346.352317.79459
38379.4722.59194344.74316.75460
39378.0952.60138343.168315.7361
40376.752.61067341.633314.72262
45370.4652.65496334.462313.7363
50364.8032.69617328.004312.75264
55359.6522.73478322.133311.78965
60354.932.77117316.754310.8466
65350.5692.80564311.789309.90667
70346.5162.83845307.182308.98568
75342.7322.86979302.884308.07769
80339.1812.89983298.858307.18270
85335.8372.92871295.074306.29971
90332.6762.95654291.503305.42872
95329.682.98341288.123304.56973
100326.833.00942284.915303.72174
110321.5183.05915302.88475
120316.6493.10618302.05976
130312.1543.15091301.24377
140307.9793.19362300.43878
150304.0823.23456299.64379
175295.4463.33035298.85880
200287.7213.41848298.08381
225280.9773.50053297.31782
250274.9223.57763296.5683
275269.4263.6506295.81384
300264.3923.72012295.07485
294.34386
293.62287
292.90888
292.20189
291.50390
290.81291
290.12992
289.45293
288.78494
288.12395
287.46896
286.8297
286.17898
285.54499
284.915100
HMX-beta Dreiding - Unit cell 0KP1 symmetry
PressureVolumeDensity
0544.8031.80537
10444.9552.2105
20412.4582.38466
30391.8752.50992
40376.7512.61067
50364.8032.69618
60354.932.77117
70346.5162.83846
80339.1812.89984
90332.6762.96655
100326.833.00944
110321.5173.05916
120316.6493.10619
130312.1543.15092
140307.9793.19363
150304.0813.23457
175295.3353.33036
200287.7213.41849
225280.9773.50054
250274.9223.57764
275269.4273.65061
300264.3913.72014
Volume
Pressurealphadeltagamma
02156.6841793.6371163.69
101798.7181364.080965.189
201675.3981260.751887.488
301594.3971195.664835.488
401533.6321148.286801.313
501483.7401109.074772.52
601441.8711077.457749.532
701404.8321049.640729.841
801372.7121026.347711.544
901343.8591005.530696.376
1001318.511987.145682.706
1101295.164970.217670.34
1201274.049956.766665.167
1301254.830940.519648.616
1401236.969927.173638.775
1501220.607914.647626.62
1751183.940886.275608.839
2001152.466861.282589.181
2251124.330832.197571.854
2501099.444819.922557.552
2751076.734802.667544.772
3001055.345780.373532.787
Pressurealphadeltagammabeta
01.000001.000001.000001.00000
100.834020.760510.829420.81673
200.776840.702900.762650.75708
300.739280.666610.717960.71930
400.711110.640200.688600.69154
500.687970.618340.663850.66961
600.668560.600710.644100.65148
700.651390.585200.627180.63604
800.636490.572220.611450.62258
900.623110.560610.598420.61064
1000.611360.550360.586670.59990
1100.600530.540920.576050.59015
1200.590740.533420.571600.58122
1300.581830.524360.557380.57297
1400.573550.516920.548920.56530
1500.565960.509940.538480.55815
1750.548960.494120.523200.54210
2000.534370.480190.506300.52812
2250.521320.463970.491410.51574
2500.509780.457130.479120.50463
2750.499250.447510.468140.49454
3000.489340.435080.457840.48530
Pressure0K300K600K900K1200K1500K1800K0K
02179.2122253.522353.532489.322894.913067.673534.02544.803
2501635.41652.611670.51700.331720.481740.88
501459.2121483.421497.61513.651533.011548.831559.65364.803
7501395.671409.921423.441429.911442.651456.62
1001307.321334.331345.861352.741363.921375.221384.23326.83
12501288.491295.921305.161311.371312.51332.27
1501216.3241252.871260.51267.371270.851284.281285.65304.081
1751181.341196.441224.821232.471239.421244.391249.41295.335
2001150.8841156.81202.761200.471209.691218.541215.31287.721
2251123.9081126.21171.221174.431178.281184.651198.91280.977
2501099.6881099.471137.581147.961144.361155.21167.59274.922
2751077.7081075.871119.761126.061127.81131.61141.97269.427
3001057.5641055.511094.081079.711115.431117.791120.41264.391
Pressure0K300K600K900K1200K1500K1800K
01111111
2500.72570911290.70218352860.67106679740.5873515930.56084259390.4926061539
500.66960534360.65826795410.63632076070.60805762220.52955359580.50488807470.4413246105
7500.61932887220.59906608370.571818810.49393936250.4702754860.4121708423
1000.59990491980.59210923360.57184739520.54341747950.47114418060.4482946340.3916870872
12500.57176772340.55062820530.52430382590.45299163010.42784914940.3769842842
1500.55814854180.55596134050.53557847150.50912297330.43899464920.41864998520.3637925082
1750.54209503250.53092051550.52041826530.49510308040.42813766230.40564663080.3535378974
2000.52811933850.51333025670.5110451110.48224816420.4178679130.397220040.3438888292
2250.51574055210.49975149990.49764396460.47178747610.40701783480.38617256750.3392482216
2500.5046264430.48789005640.48335054150.46115405010.39530071750.37657244750.3303857929
2750.49454022830.47741755120.47577893630.45235646680.38958033240.36887931230.3231362584
3000.485296520.46838279670.46486766690.43373692410.38530731530.36437752430.3170355572
Cold Compression HMX beta
PressureDreidingCVFFCVFF
011575.415
2500.7324035696421.436
500.66960534360.6407236516368.682
7500.6109851151351.57
1000.59990491980.5687877445327.289
12500.5526845842318.023
1500.55814854180.5263592364302.875
1750.54209503250.5152316154296.472
2000.52811933850.4950861552284.88
laroux
A (expt)
A (MD)
B (expt)
B (MD)
C( expt)
C (MD)
Pressure (GPa)
Cell Length (A)
Cell Length vs Pressure
Sheet1
beta (expt)
beta (MD)
Pressure (GPa)
beta (degrees)
Cell Angle vs Pressure
Sheet2
0K Cold Compression
Vol MCXX
Volume (unit cell A**3)
Pressure (GPa)
HMX-beta Dreiding EOS
Sheet3
OK
Volume (unit cell A**3)
Pressure (GPa)
P1 symmetry HMX-beta
alpha
Volume (A**3)
Pressure (GPa)
EOS HMX-alpha Dreiding II
delta
Volume (A**3)
Pressure (GPa)
EOS HMX-delta Dreiding II
gamma
Volume (A**3)
Pressure (GPa)
EOS HMX-gamma Dreiding II
alpha
delta
gamma
beta
V/V_o
Pressure (GPa)
Cold Compression Curve for HMX
0K
300K
600K
900K
1200K
1500K
1800K
Volume (A**3)
Pressure (GPa)
EOS
0K
300K
600K
900K
1200K
1500K
1800K
V/V_o
Pressure (Gpa)
EOS HMX-beta
Dreiding
CVFF
V/V_0
Pressure (GPa)
HMX-beta EOS
A(expt)
A(exp-6)
B (expt)
B(exp-6)
C(expt)
C(exp-6)
Pressure (GPa)
Cell Length (A)
Cell Length vs Pressure Dreiding Exp-6
beta (expt)
beta(exp-6)
beta(LJ9-6)
Pressure (GPa)
Angle
Cell angle beta vs pressure Dreiding Exp-6
-
Elastic Constants and Bulk Modulus of b-HMX Experimental Data
(Joe Zaug, LANL), Theory (Dreiding)32
Chart1
20.824.9
44.5
137.3
0.6-0.1
26.921.4
6.617.5
-1.50.05
17.624.4
0.1-0.9
2.913.4
3-2.6
6.65.7
3.85.6
12.513.7
Experiment
Exp-6
Constants
GPa
HMX beta Elastic Constants & Bulk Modulus
laroux
HMX Dreiding II Exponential-6Energy
PressurebetaalphagammadeltabetaalphagammadeltaPressurebetaalphagammadelta
01111532.7992046.461071.921681.680374.955-795.22-439.285-512.683
10.94693496050.95363701220.95842040450.946244232504.5261951.581027.351591.281376.805-789.009-436.37-506.649
20.91308166870.92337011230.92866631840.9074437467486.4891889.64995.4561526.032380.634-775.887-429.71-492.749
30.8876067710.90043782920.90581853120.873138766472.9161842.71970.9651468.343385.48-759.15-421.118-471.939
40.86700050110.8816883790.88564445110.8290102754461.9371804.34949.341394.134390.985-740.002-410.412-434.99
50.84964123430.86540660460.86858067770.8089945769452.6881771.02931.0491360.475396.974-718.555-398.681-413.343
60.83456800780.85159250610.85369710430.7928321678444.6571742.75915.0951333.296403.324-696.22-386.17-391.925
70.82122526510.83900002930.84048436450.7789769754437.5481716.98900.9321309.997409.968-672.206-373.051-370.189
80.8092526450.82783440670.82837245320.7671792493431.1691694.13887.9491290.158416.857-647.598-359.171-348.812
90.79836673870.81755323830.81756940820.7563151135425.3691673.09876.3691271.889423.943-621.912-345.122-326.564
100.788396750.80810277260.80770766480.746551068420.0571653.75865.7981255.4610431.203-595.503-330.788-304.19
110.77919815920.79960517190.79859037990.7374530232415.1561636.36856.0251240.1611438.611-569.272-316.111-281.159
120.77064896890.79119552790.79012706170.7291458541410.6011619.15846.9531226.1912446.149-540.853-301.202-258.112
130.76267410410.78354328940.78221602360.7214571143406.3521603.49838.4731213.2613453.802-512.716-286.043-234.897
140.75517221320.7763943590.7747434510.714131107402.3551588.86830.4631200.9414461.553-484.328-270.574-211.014
150.74812265040.76967055310.76780916490.7073700109398.5991575.10823.031189.5715469.395-455.624-255.154-187.304
160.74145597120.7631470930.76107638630.7012154512395.0471561.75815.8131179.2216477.317-425.869-239.145-164.239
170.73513839180.75710250870.7547951340.6949419628391.6811549.38809.081168.6717485.312-396.516-223.236-139.224
180.72913049760.75124849740.74881241140.6893998858388.481537.40802.6671159.3518493.371-366.397-207.164-115.771
190.72340788930.74581961040.74305918350.6838399696385.4311526.29796.5115019501.489-336.864-190.813-90.894
200.71794616730.74025390190.73758302860.6787022501382.5211514.90790.631141.3620509.663-304.96-174.416-66.6792
210.71271530160.73507422570.73227386370.6737786024379.7341504.30784.9391133.0821517.886-273.7-157.715-42.3059
220.70769840030.73029035510.72727349060.6690690262377.0611494.51779.5791125.1622526.154-243.431-141.201-17.8585
230.70288420210.72552114380.7223365550.6644486466374.4961484.75774.2871117.3923534.465-211.895-124.1357.24654
240.69825206130.72089852720.71766736320.6600601779372.0281475.29769.2821110.0124542.814-179.942-107.26932.1537
250.69378696280.71627591060.71314370480.6559155131369.6491465.83764.4331103.0425551.201-146.631-90.234356.6769
260.68947952230.71194648320.70879356670.6514081157367.3541456.97759.771095.4626559.621-114.108-73.175684.4305
270.68532223220.70785160720.70454045080.647471576365.1391448.59755.2111088.8427568.071-82.1752-55.8499109.714
280.68130007750.70374695820.70041141130.6436063936362.9961440.19750.7851082.3428576.553-48.8941-38.3858135.447
290.67740930440.69998924970.69650440330.6398958185360.9231432.50746.5971076.129585.06-17.3255-21.2675161.048
300.67363677480.69611915210.69257780430.6362863327358.9131424.58742.3881070.0330593.59616.2813-3.46629186.831
310.66997685810.69249826530.68882752440.632813615356.9631417.17738.3681064.1931602.15448.797714.1146212.459
320.66642204660.68882851360.68513601760.6293825222355.0691409.66734.4111058.4232610.73782.842131.9894238.656
330.66297046350.68535422140.68148742440.626094144353.231402.55730.51052.8933619.342116.07850.2202264.542
340.65961084760.68223664280.67798716320.6229009086351.441396.17726.7481047.5234627.966146.82468.2592290.458
350.65634319880.67853757220.67453821180.6197968698349.6991388.60723.0511042.335636.61184.34486.5494316.39
360.65316188660.67559590710.66926076570.6167463489348.0041382.58717.3941037.1736645.272215.04115.339342.577
370.65006128010.67231707440.66633610720.6137909709346.3521375.87714.2591032.237653.952250.265131.799368.706
380.64703574890.66923858760.66302615870.6108891109344.741369.57710.7111027.3238662.649284.18150.908395.092
390.6440852930.66626760360.65981789690.6080645545343.1681363.49707.2721022.5739671.361317.799169.939421.412
400.64120428150.66320866280.65516456450.6053173017341.6331357.23702.2841017.9540680.087353.291196.988447.687
410.63839083780.66029143010.65244234640.6026354598340.1341351.26699.3661013.4441688.828388.03213.978473.962
420.63563933120.65746704060.6495661990.59998335338.6681345.48696.2831008.9842697.582422.549232.357500.613
430.63295163840.65469151610.64679733560.5974204367337.2361339.80693.3151004.6743706.349457.23250.482526.952
440.63032025210.6519111050.64407511750.5949050949335.8341334.11690.3971000.4444715.129492.768268.72553.477
450.62774517220.64936035890.64142473320.592443271334.4621328.89687.556996.345723.919526.081286.88579.994
460.62522264490.64657506130.63882099410.5900272347333.1181323.19684.765992.23746732.721563.339305.123606.605
470.62275079350.64400965570.63627136350.587688502331.8011317.94682.032988.30447741.535598.375323.381632.923
480.62032774090.64137583930.63376744530.5853622568330.511312.55679.348984.39248750.358635.158341.696659.677
490.61795348710.6388641850.63127565490.5830990438329.2451307.41676.677980.58649759.191670.983360.31686.249
500.61562427860.63642094150.62906093740.5808732934328.0041302.41674.303976.84350768.033706.593377.193712.922
510.61333823820.63408520080.62657754310.5786951144326.7861297.63671.641973.1851776.884741.253396.494739.554
520.61109536620.63161752490.6242499440.5765609391325.5911292.58669.146969.59152785.742778.624414.967766.163
530.60889378550.6291693950.62197272180.5744600637324.4181287.57666.705966.05853794.608816.474433.389792.875
540.60672974240.62688251910.61975893720.5724121117323.2651282.89664.332962.61454803.482852.419451.629819.397
550.60460511370.62459075670.61753768940.5703897293322.1331278.20661.951959.21355812.363889.204470.276846.08
560.60251614590.62235763220.61538827520.5684048095321.021273.63659.647955.87556821.252925.708488.654872.75
570.60046283870.62002677790.61326778120.5664603254319.9261268.86657.374952.60557830.148964.478507.111899.361
580.59844706920.61801354530.6111976640.564549736318.8521264.74655.155949.39258839.046998.575525.453925.954
590.59646132970.61579996680.60914620490.5626694734317.7941260.21652.956946.2359847.9541036.65543.937952.59
600.59450937410.6136743450.60714045820.5608195376316.7541255.86650.806943.11960856.8631073.87562.332979.232
610.59258744860.61157804210.60515803420.5590023072315.731251.57648.681940.06361865.7811111.19580.8031005.84
620.59069555310.60974560950.60321106050.5572058893314.7221247.82646.594937.04262874.7051144.4599.2521032.59
630.58883368780.60747339310.60120717960.5554451501313.731243.17644.446934.08163883.6331186.18618.5471059.22
640.58699809870.60556277670.59937961790.5537111698312.7521239.26642.487931.16564892.5671221.92636.4441085.88
650.58519066290.60379386840.59752033730.5520057324311.7891235.64640.494928.29765901.5051255.47654.9141112.51
660.58340950340.60155585740.59564146580.5503240807310.841231.06638.48925.46966910.4481298.61673.8831139.18
670.58165649710.59974785730.5938932010.5486721612309.9061227.36636.606922.69167919.3921333.97691.7931165.77
680.57992789030.59788121930.59208616310.5470434328308.9851223.54634.669919.95268928.3411371.12710.5891192.37
690.57822368290.59624913260.59027632660.5454355169308.0771220.20632.729917.24869937.2981403.97729.6981219.03
700.57654387490.59418214870.58858590190.5438537653307.1821215.97630.917914.58870946.251446.29747.8061245.64
710.57488658950.59268688370.58690573920.5422934209306.2991212.91629.116911.96471955.211477.31766.0731272.27
720.57325182670.59075183490.58520598550.5407532943305.4281208.95627.294909.37472964.1731518784.8021298.93
730.57163958640.58908065640.58355474290.5392405214304.5691205.53625.524906.8373973.1391553.69803.2471325.48
740.57004799180.58746322920.58191469510.537746777303.7211202.22623.766904.31874982.1071588.64821.8211352.05
750.56847704290.58558681820.58028864090.5362702773302.8841198.38622.023901.83575991.0781629.84840.4921378.68
760.56692861660.58409155320.57870176880.5348139955302.0591195.32620.322899.386761000.051663.08858.9461405.29
770.56539708220.58238128280.57712795730.5333743637301.2431191.82618.635896.965771009.031701.56877.4971431.95
780.56388619350.580827380.57556440780.5319650588300.4381188.64616.959894.595781018.011736.99896.181458.38
790.56239407360.57921972580.57397940140.5305646734299.6431185.35615.26892.24791026.991774.13915.3591485
800.56092072240.5776365040.57246343010.5291833167298.8581182.11613.635889.917801035.971811.16933.9351511.57
810.55946614010.57613635250.57096704980.5278192046298.0831179.04612.031887.623811044.961846.72952.5041538.15
820.55802844980.57452381190.56957049030.5264735265297.3171175.74610.534885.36821053.941885.38970.0371564.71
830.55660765130.57302366040.56809276810.5251427144296.561172.67608.95883.122831062.931921.91988.8171591.28
840.55520562160.5716652170.56667661770.523829147295.8131169.89607.432880.913841071.921955.231007.041617.83
850.5538186070.57024813580.56522594970.5225310404295.0741166.99605.877878.73851080.911990.551025.921644.38
860.55244660740.56881150870.56383032320.5212477998294.3431164.05604.381876.572861089.92026.671044.31670.93
870.55109337670.56735533560.56243189790.51998002293.6221161.07602.882874.44871098.892063.641062.931697.48
880.54975328410.56593825440.56104466750.5187271062292.9081158.17601.395872.333881107.882100.111081.631724.02
890.54842632960.56457492450.5596882230.5174878693292.2011155.38599.941870.249891116.882135.621100.121750.56
900.54711626710.56319693520.55832897980.5162634984291.5031152.56598.484868.19901125.872171.911118.871777.08
910.54581934280.56185803780.55698559590.5150522097290.8121149.82597.044866.153911134.872207.611137.61803.62
920.54453743340.56049959440.55567393090.5138540031290.1291147.04595.638864.138921143.872244.21156.081830.15
930.54326678540.55916558350.55432308380.5126694734289.4521144.31594.19862.146931152.872280.531175.341856.66
940.54201302930.55778270770.5530683260.5114974311288.7841141.48592.845860.175941161.872318.561193.421883.19
950.54077241140.55660017790.55177998360.5103384711288.1231139.06591.464858.226951170.872351.531212.181909.71
960.53954305470.55533946420.55052709160.5091908092287.4681136.48590.121856.296961179.872386.921230.621936.23
970.53832683620.55407386410.54927140090.5080556348286.821133.89588.775854.387971188.872422.881249.271962.73
980.5371218790.55281315050.54802317340.5069323534286.1781131.31587.437852.498981197.872459.021268.011989.24
990.53593193680.55137652340.54679733560.5058203701285.5441128.37586.123850.628991206.872500.661286.632015.75
1000.5347513790.55038456650.5455798940.5047196851284.9151126.34584.818848.7771001215.872529.751305.32042.25
Pressure0K300K600K900K1200K0K300K600K900K1200K
011111532.799571.65598.52825.09994.71
50.84964123430.80918394120.78749248150.58289398730.4968181681452.688462.57471.33480.94494.19
100.788396750.74647074260.72597406940.53477802420.4479597068420.057426.72434.51441.24445.59
150.74812265040.70866789120.68360288710.50535093140.4198912246398.599405.11409.15416.96417.67
200.71794616730.67975159630.65498228960.47783878120.4035648581382.521388.58392.02394.26401.43
250.69378696280.65634566610.63423110340.46346459170.3878416825369.649375.2379.6382.4385.79
300.67363677480.63897489720.61369711960.45115078360.3766223321358.913365.27367.31372.24374.63
350.65634319880.62186652670.5981086680.43850973830.3645886741349.699355.49357.98361.81362.66
400.64120428150.60874661070.58337231840.42757759760.357209639341.633347.99349.16352.79355.32
450.62774517220.596361410.57269598340.41551830710.3477495954334.462340.91342.77342.84345.91
500.61562427860.58471092450.5602820290.4095795610.3402599753328.004334.25335.34337.94338.46
550.60460511370.57465232220.55164405530.40073204140.3342783324322.133328.5330.17330.64332.51
600.59450937410.56487361150.54193677740.3936176660.3283067427316.754322.91324.36324.77326.57
650.58519066290.55539228550.53281427520.38850307240.3240240874311.789317.49318.9320.55322.31
700.57654387490.54689057990.52499498760.38286732360.3176101577307.182312.63314.22315.9315.93
750.56847704290.53952593370.51841208310.37724369460.3132370239302.884308.42310.28311.26311.58
800.56092072240.53286101640.51366704540.37338956960.3099596867298.858304.61307.44308.08308.32
850.5538186070.52402693960.50377598080.36854161360.3068633069295.074299.56301.52304.08305.24
900.54711626710.52252252250.50035086550.36319674220.3017160781291.503298.7299.47299.67300.12
950.54077241140.51267383890.49562253560.35889418120.299494325288.123293.07296.64296.12297.91
1000.5347513790.50819557420.48810398980.35577936950.2954730524284.915290.51292.14293.55293.91
Tang's Data
Pressure(Gpa)V/V_0
0.0001.000
0.1030.990
0.2320.980
0.3730.970
0.5270.960
0.6980.950
0.8850.940
1.0900.930
1.3200.920
1.5700.910
1.8500.900
2.1700.890
2.5100.880
2.9000.870
3.3400.860
3.8200.850
4.3700.840
5.0000.830
5.7000.820
6.5000.810
7.4200.800
8.4800.790
9.6900.780
11.1000.770
12.8000.760
14.7000.750
17.0000.740
19.7000.730
23.1000.720
27.1000.710
32.1000.700
38.3000.690
46.2000.680
56.4000.670
69.8000.660
88.0000.65
Energy
Pressure300K600K900K1200K
0426.93475.80532.01580.11
5454.55505.03551.30609.08
10485.14544.34593.55633.22
15530.41572.86642.94679.46
20573.36633.83670.56719.88
25621.28679.94734.34779.74
30673.98723.23767.68833.99
35712.93764.03828.85845.89
40781.73811.28874.00912.43
45826.86876.33909.52987.17
50876.92909.63974.02993.94
55921.92972.751004.821047.92
60980.231024.881043.781095.60
651021.931060.151090.311142.65
701091.111145.891166.651203.31
751105.641195.401210.431265.76
801191.171233.371251.921295.94
851303.121254.651315.751378.50
901300.641331.421353.511362.28
951335.721394.691393.521508.14
1001395.701405.051466.531546.68
Elastic ConstantsExperimentExp-6
C1120.824.9
C1244.5
C13137.3
C150.6-0.1
C2226.921.4
C236.617.5
C25-1.50.05
C3317.624.4
C350.1-0.9
C442.913.4
C463-2.6
C556.65.7
C663.85.6
K12.513.7
laroux
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
beta
alpha
gamma
delta
V/V_0
Pressure (GPa)
HMX EOS Dreiding Exp-6
Sheet1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
beta
Energy (kcal/mol)
Pressure (GPa)
EOS beta Pressure vs. Internal Energy Dreiding Exp-6
Sheet2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
alpha
Energy (kcal/mol)
Pressure (GPa)
HMX alpha Pressure vs Internal Energy Exp-6
Sheet3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
gamma
Energy (kcal/mol)
Pressure (GPa)
HMX gamma Pressure vs. Internal Energy Exp-6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
delta
Energy (kcal/mol)
Pressure (GPa)
HMX delta Pressure vs. Internal Energy Exp-6
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
0K
300K
600K
900K
1200K
Volume (A**3)
Pressure (GPa)
EOS HMX beta Dreidxing Exp-6 Temp
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0K
300K
600K
Tang's Adiabat
V/V_0
Pressure (GPa)
HMX beta EOS Dreiding Exp-6
300K
600K
900K
1200K
Pressure (GPa)
Internal Energy (kcal/mol)
HMX beta Dreiding Exp-6 EOS Internal Energy vs Pressure
Experiment
Exp-6
Constants
GPa
HMX beta Elastic Constants & Bulk Modulus
-
HMX Cold Compression Curves for the 4 crystal morphologies a
form is the least compressible followed closely by the g form d
form is the most compressible stable b form is intermediate in
compressibilityadb33g
Chart1
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99999999
100100100100
beta
alpha
gamma
delta
V/V_0
Pressure (GPa)
HMX EOS Dreiding Exp-6
laroux
HMX Dreiding II Exponential-6Energy
PressurebetaalphagammadeltabetaalphagammadeltaPressurebetaalphagammadelta
01111532.7992046.461071.921681.680374.955-795.22-439.285-512.683
10.94693496050.95363701220.95842040450.946244232504.5261951.581027.351591.281376.805-789.009-436.37-506.649
20.91308166870.92337011230.92866631840.9074437467486.4891889.64995.4561526.032380.634-775.887-429.71-492.749
30.8876067710.90043782920.90581853120.873138766472.9161842.71970.9651468.343385.48-759.15-421.118-471.939
40.86700050110.8816883790.88564445110.8290102754461.9371804.34949.341394.134390.985-740.002-410.412-434.99
50.84964123430.86540660460.86858067770.8089945769452.6881771.02931.0491360.475396.974-718.555-398.681-413.343
60.83456800780.85159250610.85369710430.7928321678444.6571742.75915.0951333.296403.324-696.22-386.17-391.925
70.82122526510.83900002930.84048436450.7789769754437.5481716.98900.9321309.997409.968-672.206-373.051-370.189
80.8092526450.82783440670.82837245320.7671792493431.1691694.13887.9491290.158416.857-647.598-359.171-348.812
90.79836673870.81755323830.81756940820.7563151135425.3691673.09876.3691271.889423.943-621.912-345.122-326.564
100.788396750.80810277260.80770766480.746551068420.0571653.75865.7981255.4610431.203-595.503-330.788-304.19
110.77919815920.79960517190.79859037990.7374530232415.1561636.36856.0251240.1611438.611-569.272-316.111-281.159
120.77064896890.79119552790.79012706170.7291458541410.6011619.15846.9531226.1912446.149-540.853-301.202-258.112
130.76267410410.78354328940.78221602360.7214571143406.3521603.49838.4731213.2613453.802-512.716-286.043-234.897
140.75517221320.7763943590.7747434510.714131107402.3551588.86830.4631200.9414461.553-484.328-270.574-211.014
150.74812265040.76967055310.76780916490.7073700109398.5991575.10823.031189.5715469.395-455.624-255.154-187.304
160.74145597120.7631470930.76107638630.7012154512395.0471561.75815.8131179.2216477.317-425.869-239.145-164.239
170.73513839180.75710250870.7547951340.6949419628391.6811549.38809.081168.6717485.312-396.516-223.236-139.224
180.72913049760.75124849740.74881241140.6893998858388.481537.40802.6671159.3518493.371-366.397-207.164-115.771
190.72340788930.74581961040.74305918350.6838399696385.4311526.29796.5115019501.489-336.864-190.813-90.894
200.71794616730.74025390190.73758302860.6787022501382.5211514.90790.631141.3620509.663-304.96-174.416-66.6792
210.71271530160.73507422570.73227386370.6737786024379.7341504.30784.9391133.0821517.886-273.7-157.715-42.3059
220.70769840030.73029035510.72727349060.6690690262377.0611494.51779.5791125.1622526.154-243.431-141.201-17.8585
230.70288420210.72552114380.7223365550.6644486466374.4961484.75774.2871117.3923534.465-211.895-124.1357.24654
240.69825206130.72089852720.71766736320.6600601779372.0281475.29769.2821110.0124542.814-179.942-107.26932.1537
250.69378696280.71627591060.71314370480.6559155131369.6491465.83764.4331103.0425551.201-146.631-90.234356.6769
260.68947952230.71194648320.70879356670.6514081157367.3541456.97759.771095.4626559.621-114.108-73.175684.4305
270.68532223220.70785160720.70454045080.647471576365.1391448.59755.2111088.8427568.071-82.1752-55.8499109.714
280.68130007750.70374695820.70041141130.6436063936362.9961440.19750.7851082.3428576.553-48.8941-38.3858135.447
290.67740930440.69998924970.69650440330.6398958185360.9231432.50746.5971076.129585.06-17.3255-21.2675161.048
300.67363677480.69611915210.69257780430.6362863327358.9131424.58742.3881070.0330593.59616.2813-3.46629186.831
310.66997685810.69249826530.68882752440.632813615356.9631417.17738.3681064.1931602.15448.797714.1146212.459
320.66642204660.68882851360.68513601760.6293825222355.0691409.66734.4111058.4232610.73782.842131.9894238.656
330.66297046350.68535422140.68148742440.626094144353.231402.55730.51052.8933619.342116.07850.2202264.542
340.65961084760.68223664280.67798716320.6229009086351.441396.17726.7481047.5234627.966146.82468.2592290.458
350.65634319880.67853757220.67453821180.6197968698349.6991388.60723.0511042.335636.61184.34486.5494316.39
360.65316188660.67559590710.66926076570.6167463489348.0041382.58717.3941037.1736645.272215.04115.339342.577
370.65006128010.67231707440.66633610720.6137909709346.3521375.87714.2591032.237653.952250.265131.799368.706
380.64703574890.66923858760.66302615870.6108891109344.741369.57710.7111027.3238662.649284.18150.908395.092
390.6440852930.66626760360.65981789690.6080645545343.1681363.49707.2721022.5739671.361317.799169.939421.412
400.64120428150.66320866280.65516456450.6053173017341.6331357.23702.2841017.9540680.087353.291196.988447.687
410.63839083780.66029143010.65244234640.6026354598340.1341351.26699.3661013.4441688.828388.03213.978473.962
420.63563933120.65746704060.6495661990.59998335338.6681345.48696.2831008.9842697.582422.549232.357500.613
430.63295163840.65469151610.64679733560.5974204367337.2361339.80693.3151004.6743706.349457.23250.482526.952
440.63032025210.6519111050.64407511750.5949050949335.8341334.11690.3971000.4444715.129492.768268.72553.477
450.62774517220.64936035890.64142473320.592443271334.4621328.89687.556996.345723.919526.081286.88579.994
460.62522264490.64657506130.63882099410.5900272347333.1181323.19684.765992.23746732.721563.339305.123606.605
470.62275079350.64400965570.63627136350.587688502331.8011317.94682.032988.30447741.535598.375323.381632.923
480.62032774090.64137583930.63376744530.5853622568330.511312.55679.348984.39248750.358635.158341.696659.677
490.61795348710.6388641850.63127565490.5830990438329.2451307.41676.677980.58649759.191670.983360.31686.249
500.61562427860.63642094150.62906093740.5808732934328.0041302.41674.303976.84350768.033706.593377.193712.922
510.61333823820.63408520080.62657754310.5786951144326.7861297.63671.641973.1851776.884741.253396.494739.554
520.61109536620.63161752490.6242499440.5765609391325.5911292.58669.146969.59152785.742778.624414.967766.163
530.60889378550.6291693950.62197272180.5744600637324.4181287.57666.705966.05853794.608816.474433.389792.875
540.60672974240.62688251910.61975893720.5724121117323.2651282.89664.332962.61454803.482852.419451.629819.397
550.60460511370.62459075670.61753768940.5703897293322.1331278.20661.951959.21355812.363889.204470.276846.08
560.60251614590.62235763220.61538827520.5684048095321.021273.63659.647955.87556821.252925.708488.654872.75
570.60046283870.62002677790.61326778120.5664603254319.9261268.86657.374952.60557830.148964.478507.111899.361
580.59844706920.61801354530.6111976640.564549736318.8521264.74655.155949.39258839.046998.575525.453925.954
590.59646132970.61579996680.60914620490.5626694734317.7941260.21652.956946.2359847.9541036.65543.937952.59
600.59450937410.6136743450.60714045820.5608195376316.7541255.86650.806943.11960856.8631073.87562.332979.232
610.59258744860.61157804210.60515803420.5590023072315.731251.57648.681940.06361865.7811111.19580.8031005.84
620.59069555310.60974560950.60321106050.5572058893314.7221247.82646.594937.04262874.7051144.4599.2521032.59
630.58883368780.60747339310.60120717960.5554451501313.731243.17644.446934.08163883.6331186.18618.5471059.22
640.58699809870.60556277670.59937961790.5537111698312.7521239.26642.487931.16564892.5671221.92636.4441085.88
650.58519066290.60379386840.59752033730.5520057324311.7891235.64640.494928.29765901.5051255.47654.9141112.51
660.58340950340.60155585740.59564146580.5503240807310.841231.06638.48925.46966910.4481298.61673.8831139.18
670.58165649710.59974785730.5938932010.5486721612309.9061227.36636.606922.69167919.3921333.97691.7931165.77
680.57992789030.59788121930.59208616310.5470434328308.9851223.54634.669919.95268928.3411371.12710.5891192.37
690.57822368290.59624913260.59027632660.5454355169308.0771220.20632.729917.24869937.2981403.97729.6981219.03
700.57654387490.59418214870.58858590190.5438537653307.1821215.97630.917914.58870946.251446.29747.8061245.64
710.57488658950.59268688370.58690573920.5422934209306.2991212.91629.116911.96471955.211477.31766.0731272.27
720.57325182670.59075183490.58520598550.5407532943305.4281208.95627.294909.37472964.1731518784.8021298.93
730.57163958640.58908065640.58355474290.5392405214304.5691205.53625.524906.8373973.1391553.69803.2471325.48
740.57004799180.58746322920.58191469510.537746777303.7211202.22623.766904.31874982.1071588.64821.8211352.05
750.56847704290.58558681820.58028864090.5362702773302.8841198.38622.023901.83575991.0781629.84840.4921378.68
760.56692861660.58409155320.57870176880.5348139955302.0591195.32620.322899.386761000.051663.08858.9461405.29
770.56539708220.58238128280.57712795730.5333743637301.2431191.82618.635896.965771009.031701.56877.4971431.95
780.56388619350.580827380.57556440780.5319650588300.4381188.64616.959894.595781018.011736.99896.181458.38
790.56239407360.57921972580.57397940140.5305646734299.6431185.35615.26892.24791026.991774.13915.3591485
800.56092072240.5776365040.57246343010.5291833167298.8581182.11613.635889.917801035.971811.16933.9351511.57
810.55946614010.57613635250.57096704980.5278192046298.0831179.04612.031887.623811044.961846.72952.5041538.15
820.55802844980.57452381190.56957049030.5264735265297.3171175.74610.534885.36821053.941885.38970.0371564.71
830.55660765130.57302366040.56809276810.5251427144296.561172.67608.95883.122831062.931921.91988.8171591.28
840.55520562160.5716652170.56667661770.523829147295.8131169.89607.432880.913841071.921955.231007.041617.83
850.5538186070.57024813580.56522594970.5225310404295.0741166.99605.877878.73851080.911990.551025.921644.38
860.55244660740.56881150870.56383032320.5212477998294.3431164.05604.381876.572861089.92026.671044.31670.93
870.55109337670.56735533560.56243189790.51998002293.6221161.07602.882874.44871098.892063.641062.931697.48
880.54975328410.56593825440.56104466750.5187271062292.9081158.17601.395872.333881107.882100.111081.631724.02
890.54842632960.56457492450.5596882230.5174878693292.2011155.38599.941870.249891116.882135.621100.121750.56
900.54711626710.56319693520.55832897980.5162634984291.5031152.56598.484868.19901125.872171.911118.871777.08
910.54581934280.56185803780.55698559590.5150522097290.8121149.82597.044866.153911134.872207.611137.61803.62
920.54453743340.56049959440.55567393090.5138540031290.1291147.04595.638864.138921143.872244.21156.081830.15
930.54326678540.55916558350.55432308380.5126694734289.4521144.31594.19862.146931152.872280.531175.341856.66
940.54201302930.55778270770.5530683260.5114974311288.7841141.48592.845860.175941161.872318.561193.421883.19
950.54077241140.55660017790.55177998360.5103384711288.1231139.06591.464858.226951170.872351.531212.181909.71
960.53954305470.55533946420.55052709160.5091908092287.4681136.48590.121856.296961179.872386.921230.621936.23
970.53832683620.55407386410.54927140090.5080556348286.821133.89588.775854.387971188.872422.881249.271962.73
980.5371218790.55281315050.54802317340.5069323534286.1781131.31587.437852.498981197.872459.021268.011989.24
990.53593193680.55137652340.54679733560.5058203701285.5441128.37586.123850.628991206.872500.661286.632015.75
1000.5347513790.55038456650.5455798940.5047196851284.9151126.34584.818848.7771001215.872529.751305.32042.25
Pressure0K300K600K900K1200K0K300K600K900K1200K
011111532.799571.65598.52825.09994.71
50.84964123430.80918394120.78749248150.58289398730.4968181681452.688462.57471.33480.94494.19
100.788396750.74647074260.72597406940.53477802420.4479597068420.057426.72434.51441.24445.59
150.74812265040.70866789120.68360288710.50535093140.4198912246398.599405.11409.15416.96417.67
200.71794616730.67975159630.65498228960.47783878120.4035648581382.521388.58392.02394.26401.43
250.69378696280.65634566610.63423110340.46346459170.3878416825369.649375.2379.6382.4385.79
300.67363677480.63897489720.61369711960.45115078360.3766223321358.913365.27367.31372.24374.63
350.65634319880.62186652670.5981086680.43850973830.3645886741349.699355.49357.98361.81362.66
400.64120428150.60874661070.58337231840.42757759760.357209639341.633347.99349.16352.79355.32
450.62774517220.596361410.57269598340.41551830710.3477495954334.462340.91342.77342.84345.91
500.61562427860.58471092450.5602820290.4095795610.3402599753328.004334.25335.34337.94338.46
550.60460511370.57465232220.55164405530.40073204140.3342783324322.133328.5330.17330.64332.51
600.59450937410.56487361150.54193677740.3936176660.3283067427316.754322.91324.36324.77326.57
650.58519066290.55539228550.53281427520.38850307240.3240240874311.789317.49318.9320.55322.31
700.57654387490.54689057990.52499498760.38286732360.3176101577307.182312.63314.22315.9315.93
750.56847704290.53952593370.51841208310.37724369460.3132370239302.884308.42310.28311.26311.58
800.56092072240.53286101640.51366704540.37338956960.3099596867298.858304.61307.44308.08308.32
850.5538186070.52402693960.50377598080.36854161360.3068633069295.074299.56301.52304.08305.24
900.54711626710.52252252250.50035086550.36319674220.3017160781291.503298.7299.47299.67300.12
950.54077241140.51267383890.49562253560.35889418120.299494325288.123293.07296.64296.12297.91
1000.5347513790.50819557420.48810398980.35577936950.2954730524284.915290.51292.14293.55293.91
Tang's Data
Pressure(Gpa)V/V_0
0.0001.000
0.1030.990
0.2320.980
0.3730.970
0.5270.960
0.6980.950
0.8850.940
1.0900.930
1.3200.920
1.5700.910
1.8500.900
2.1700.890
2.5100.880
2.9000.870
3.3400.860
3.8200.850
4.3700.840
5.0000.830
5.7000.820
6.5000.810
7.4200.800
8.4800.790
9.6900.780
11.1000.770
12.8000.760
14.7000.750
17.0000.740
19.7000.730
23.1000.720
27.1000.710
32.1000.700
38.3000.690
46.2000.680
56.4000.670
69.8000.660
88.0000.65
Energy
Pressure300K600K900K1200K
0426.93475.80532.01580.11
5454.55505.03551.30609.08
10485.14544.34593.55633.22
15530.41572.86642.94679.46
20573.36633.83670.56719.88
25621.28679.94734.34779.74
30673.98723.23767.68833.99
35712.93764.03828.85845.89
40781.73811.28874.00912.43
45826.86876.33909.52987.17
50876.92909.63974.02993.94
55921.92972.751004.821047.92
60980.231024.881043.781095.60
651021.931060.151090.311142.65
701091.111145.891166.651203.31
751105.641195.401210.431265.76
801191.171233.371251.921295.94
851303.121254.651315.751378.50
901300.641331.421353.511362.28
951335.721394.691393.521508.14
1001395.701405.051466.531546.68
Elastic ConstantsExperimentExp-6
C1120.824.9
C1244.5
C13137.3
C150.6-0.1
C2226.921.4
C236.617.5
C25-1.50.05
C3317.624.4
C350.1-0.9
C442.913.4
C463-2.6
C556.65.7
C663.85.6
K12.513.7
laroux
beta
alpha
gamma
delta
V/V_0
Pressure (GPa)
HMX EOS Dreiding Exp-6
Sheet1
beta
Energy (kcal/mol)
Pressure (GPa)
EOS beta Pressure vs. Internal Energy Dreiding Exp-6
Sheet2
alpha
Energy (kcal/mol)
Pressure (GPa)
HMX alpha Pressure vs Internal Energy Exp-6
Sheet3
gamma
Energy (kcal/mol)
Pressure (GPa)
HMX gamma Pressure vs. Internal Energy Exp-6
delta
Energy (kcal/mol)
Pressure (GPa)
HMX delta Pressure vs. Internal Energy Exp-6
0K
300K
600K
900K
1200K
Volume (A**3)
Pressure (GPa)
EOS HMX beta Dreidxing Exp-6 Temp
0K
300K
600K
Tang's Adiabat
V/V_0
Pressure (GPa)
HMX beta EOS Dreiding Exp-6
300K
600K
900K
1200K
Pressure (GPa)
Internal Energy (kcal/mol)
HMX beta Dreiding Exp-6 EOS Internal Energy vs Pressure
Experiment
Exp-6
Constants
GPa
HMX beta Elastic Constants & Bulk Modulus
-
Isothermal P-V curves for b-HMX Procedure Minimize at 0K
Increase T by 300K increments 20ps MD at each T Results Evidence of
melting or phase transition above 600K Compressibility similar for
P > 25GPa
34Melting behavior?
Chart1
00000
55555
1010101010
1515151515
2020202020
2525252525
3030303030
3535353535
4040404040
4545454545
5050505050
5555555555
6060606060
6565656565
7070707070
7575757575
8080808080
8585858585
9090909090
9595959595
100100100100100
0K
300K
600K
900K
1200K
Volume (A**3)
Pressure (GPa)
EOS HMX beta Dreidxing Exp-6 Temp
laroux
HMX Dreiding II Exponential-6Energy (Kcal/mol/unit cell)Energy
(J/Kg)
PressurebetaalphagammadeltabetaalphagammadeltaPressurebetaalphagammadeltabetaalphagammadelta
01111532.7992046.461071.921681.680374.955-795.22-439.285-512.6832.65E+06-1.41E+06-1.55E+06-1.21E+06Kcal-2-joule4186.8Mass
of unit cellAvogadro # *unit cell mass * a.u.-2-Kg1.00E-03
10.94693496050.95363701220.95842040450.946244232504.5261951.581027.351591.281376.805-789.009-436.37-506.6492.66E+06-1.39E+06-1.54E+06-1.19E+06
20.91308166870.92337011230.92866631840.9074437467486.4891889.64995.4561526.032380.634-775.887-429.71-492.7492.69E+06-1.37E+06-1.52E+06-1.16E+06
30.8876067710.90043782920.90581853120.873138766472.9161842.71970.9651468.343385.48-759.15-421.118-471.9392.73E+06-1.34E+06-1.49E+06-1.11E+06
40.86700050110.8816883790.88564445110.8290102754461.9371804.34949.341394.134390.985-740.002-410.412-434.992.76E+06-1.31E+06-1.45E+06-1.03E+06
50.84964123430.86540660460.86858067770.8089945769452.6881771.02931.0491360.475396.974-718.555-398.681-413.3432.81E+06-1.27E+06-1.41E+06-9.74E+05
60.83456800780.85159250610.85369710430.7928321678444.6571742.75915.0951333.296403.324-696.22-386.17-391.9252.85E+06-1.23E+06-1.37E+06-9.24E+05
70.82122526510.83900002930.84048436450.7789769754437.5481716.98900.9321309.997409.968-672.206-373.051-370.1892.90E+06-1.19E+06-1.32E+06-8.72E+05
80.8092526450.82783440670.82837245320.7671792493431.1691694.13887.9491290.158416.857-647.598-359.171-348.8122.95E+06-1.14E+06-1.27E+06-8.22E+05
90.79836673870.81755323830.81756940820.7563151135425.3691673.09876.3691271.889423.943-621.912-345.122-326.5643.00E+06-1.10E+06-1.22E+06-7.70E+05
100.788396750.80810277260.80770766480.746551068420.0571653.75865.7981255.4610431.203-595.503-330.788-304.193.05E+06-1.05E+06-1.17E+06-7.17E+05
110.77919815920.79960517190.79859037990.7374530232415.1561636.36856.0251240.1611438.611-569.272-316.111-281.1593.10E+06-1.01E+06-1.12E+06-6.63E+05
120.77064896890.79119552790.79012706170.7291458541410.6011619.15846.9531226.1912446.149-540.853-301.202-258.1123.15E+06-9.56E+05-1.06E+06-6.08E+05
130.76267410410.78354328940.78221602360.7214571143406.3521603.49838.4731213.2613453.802-512.716-286.043-234.8973.21E+06-9.06E+05-1.01E+06-5.54E+05
140.75517221320.7763943590.7747434510.714131107402.3551588.86830.4631200.9414461.553-484.328-270.574-211.0143.26E+06-8.56E+05-9.57E+05-4.97E+05
150.74812265040.76967055310.76780916490.7073700109398.5991575.10823.031189.5715469.395-455.624-255.154-187.3043.32E+06-8.05E+05-9.02E+05-4.41E+05
160.74145597120.7631470930.76107638630.7012154512395.0471561.75815.8131179.2216477.317-425.869-239.145-164.2393.37E+06-7.53E+05-8.46E+05-3.87E+05
170.73513839180.75710250870.7547951340.6949419628391.6811549.38809.081168.6717485.312-396.516-223.236-139.2243.43E+06-7.01E+05-7.89E+05-3.28E+05
180.72913049760.75124849740.74881241140.6893998858388.481537.40802.6671159.3518493.371-366.397-207.164-115.7713.49E+06-6.48E+05-7.32E+05-2.73E+05
190.72340788930.74581961040.74305918350.6838399696385.4311526.29796.5115019501.489-336.864-190.813-90.8943.55E+06-5.95E+05-6.75E+05-2.14E+05
200.71794616730.74025390190.73758302860.6787022501382.5211514.90790.631141.3620509.663-304.96-174.416-66.67923.60E+06-5.39E+05-6.17E+05-1.57E+05
210.71271530160.73507422570.73227386370.6737786024379.7341504.30784.9391133.0821517.886-273.7-157.715-42.30593.66E+06-4.84E+05-5.58E+05-9.97E+04
220.70769840030.73029035510.72727349060.6690690262377.0611494.51779.5791125.1622526.154-243.431-141.201-17.85853.72E+06-4.30E+05-4.99E+05-4.21E+04
230.70288420210.72552114380.7223365550.6644486466374.4961484.75774.2871117.3923534.465-211.895-124.1357.246543.78E+06-3.75E+05-4.39E+051.71E+04
240.69825206130.72089852720.71766736320.6600601779372.0281475.29769.2821110.0124542.814-179.942-107.26932.15373.84E+06-3.18E+05-3.79E+057.58E+04
250.69378696280.71627591060.71314370480.6559155131369.6491465.83764.4331103.0425551.201-146.631-90.234356.67693.90E+06-2.59E+05-3.19E+051.34E+05
260.68947952230.71194648320.70879356670.6514081157367.3541456.97759.771095.4626559.621-114.108-73.175684.43053.96E+06-2.02E+05-2.59E+051.99E+05
270.68532223220.70785160720.70454045080.647471576365.1391448.59755.2111088.8427568.071-82.1752-55.8499109.7144.02E+06-1.45E+05-1.97E+052.59E+05
280.68130007750.70374695820.70041141130.6436063936362.9961440.19750.7851082.3428576.553-48.8941-38.3858135.4474.08E+06-8.64E+04-1.36E+053.19E+05
290.67740930440.69998924970.69650440330.6398958185360.9231432.50746.5971076.129585.06-17.3255-21.2675161.0484.14E+06-3.06E+04-7.52E+043.80E+05
300.67363677480.69611915210.69257780430.6362863327358.9131424.58742.3881070.0330593.59616.2813-3.46629186.8314.20E+062.88E+04-1.23E+044.40E+05
310.66997685810.69249826530.68882752440.632813615356.9631417.17738.3681064.1931602.15448.797714.1146212.4594.26E+068.62E+044.99E+045.01E+05
320.66642204660.68882851360.68513601760.6293825222355.0691409.66734.4111058.4232610.73782.842131.9894238.6564.32E+061.46E+051.13E+055.62E+05
330.66297046350.68535422140.68148742440.626094144353.231402.55730.51052.8933619.342116.07850.2202264.5424.38E+062.05E+051.78E+056.23E+05
340.65961084760.68223664280.67798716320.6229009086351.441396.17726.7481047.5234627.966146.82468.2592290.4584.44E+062.60E+052.41E+056.84E+05
350.65634319880.67853757220.67453821180.6197968698349.6991388.60723.0511042.335636.61184.34486.5494316.394.50E+063.26E+053.06E+057.46E+05
360.65316188660.67559590710.66926076570.6167463489348.0041382.58717.3941037.1736645.272215.04115.339342.5774.56E+063.80E+054.08E+058.07E+05
370.65006128010.67231707440.66633610720.6137909709346.3521375.87714.2591032.237653.952250.265131.799368.7064.62E+064.42E+054.66E+058.69E+05
380.64703574890.66923858760.66302615870.6108891109344.741369.57710.7111027.3238662.649284.18150.908395.0924.68E+065.02E+055.34E+059.31E+05
390.6440852930.66626760360.65981789690.6080645545343.1681363.49707.2721022.5739671.361317.799169.939421.4124.75E+065.62E+056.01E+059.93E+05
400.64120428150.66320866280.65516456450.6053173017341.6331357.23702.2841017.9540680.087353.291196.988447.6874.81E+066.24E+056.96E+051.06E+06
410.63839083780.66029143010.65244234640.6026354598340.1341351.26699.3661013.4441688.828388.03213.978473.9624.87E+066.86E+057.57E+051.12E+06
420.63563933120.65746704060.6495661990.59998335338.6681345.48696.2831008.9842697.582422.549232.357500.6134.93E+067.47E+058.22E+051.18E+06
430.63295163840.65469151610.64679733560.5974204367337.2361339.80693.3151004.6743706.349457.23250.482526.9524.99E+068.08E+058.86E+051.24E+06
440.63032025210.6519111050.64407511750.5949050949335.8341334.11690.3971000.4444715.129492.768268.72553.4775.06E+068.71E+059.50E+051.30E+06
450.62774517220.64936035890.64142473320.592443271334.4621328.89687.556996.345723.919526.081286.88579.9945.12E+069.30E+051.01E+061.37E+06
460.62522264490.64657506130.63882099410.5900272347333.1181323.19684.765992.23746732.721563.339305.123606.6055.18E+069.96E+051.08E+061.43E+06
470.62275079350.64400965570.63627136350.587688502331.8011317.94682.032988.30447741.535598.375323.381632.9235.24E+061.06E+061.14E+061.49E+06
480.62032774090.64137583930.63376744530.5853622568330.511312.55679.348984.39248750.358635.158341.696659.6775.30E+061.12E+061.21E+061.55E+06
490.61795348710.6388641850.63127565490.5830990438329.2451307.41676.677980.58649759.191670.983360.31686.2495.37E+061.19E+061.27E+061.62E+06
500.61562427860.63642094150.62906093740.5808732934328.0041302.41674.303976.84350768.033706.593377.193712.9225.43E+061.25E+061.33E+061.68E+06
510.61333823820.63408520080.62657754310.5786951144326.7861297.63671.641973.1851776.884741.253396.494739.5545.49E+061.31E+061.40E+061.74E+06
520.61109536620.63161752490.6242499440.5765609391325.5911292.58669.146969.59152785.742778.624414.967766.1635.56E+061.38E+061.47E+061.81E+06
530.60889378550.6291693950.62197272180.5744600637324.4181287.57666.705966.05853794.608816.474433.389792.8755.62E+061.44E+061.53E+061.87E+06
540.60672974240.62688251910.61975893720.5724121117323.2651282.89664.332962.61454803.482852.419451.629819.3975.68E+061.51E+061.60E+061.93E+06
550.60460511370.62459075670.61753768940.5703897293322.1331278.20661.951959.21355812.363889.204470.276846.085.74E+061.57E+061.66E+061.99E+06
560.60251614590.62235763220.61538827520.5684048095321.021273.63659.647955.87556821.252925.708488.654872.755.81E+061.64E+061.73E+062.06E+06
570.60046283870.62002677790.61326778120.5664603254319.9261268.86657.374952.60557830.148964.478507.111899.3615.87E+061.70E+061.79E+062.12E+06
580.59844706920.61801354530.6111976640.564549736318.8521264.74655.155949.39258839.046998.575525.453925.9545.93E+061.76E+061.86E+062.18E+06
590.59646132970.61579996680.60914620490.5626694734317.7941260.21652.956946.2359847.9541036.65543.937952.595.99E+061.83E+061.92E+062.24E+06
600.59450937410.6136743450.60714045820.5608195376316.7541255.86650.806943.11960856.8631073.87562.332979.2326.06E+061.90E+061.99E+062.31E+06
610.59258744860.61157804210.60515803420.5590023072315.731251.57648.681940.06361865.7811111.19580.8031005.846.12E+061.96E+062.05E+062.37E+06
620.59069555310.60974560950.60321106050.5572058893314.7221247.82646.594937.04262874.7051144.4599.2521032.596.18E+062.02E+062.12E+062.43E+06
630.58883368780.60747339310.60120717960.5554451501313.731243.17644.446934.08163883.6331186.18618.5471059.226.25E+062.10E+062.19E+062.50E+06
640.58699809870.60556277670.59937961790.5537111698312.7521239.26642.487931.16564892.5671221.92636.4441085.886.31E+062.16E+062.25E+062.56E+06
650.58519066290.60379386840.59752033730.5520057324311.7891235.64640.494928.29765901.5051255.47654.9141112.516.37E+062.22E+062.32E+062.62E+06
660.58340950340.60155585740.59564146580.5503240807310.841231.06638.48925.46966910.4481298.61673.8831139.186.44E+062.30E+062.38E+062.68E+06
670.58165649710.59974785730.5938932010.5486721612309.9061227.36636.606922.69167919.3921333.97691.7931165.776.50E+062.36E+062.45E+062.75E+06
680.57992789030.59788121930.59208616310.5470434328308.9851223.54634.669919.95268928.3411371.12710.5891192.376.56E+062.42E+062.51E+062.81E+06
690.57822368290.59624913260.59027632660.5454355169308.0771220.20632.729917.24869937.2981403.97729.6981219.036.63E+062.48E+062.58E+062.87E+06
700.57654387490.59418214870.58858590190.5438537653307.1821215.97630.917914.58870946.251446.29747.8061245.646.69E+062.56E+062.64E+062.94E+06
710.57488658950.59268688370.58690573920.5422934209306.2991212.91629.116911.96471955.211477.31766.0731272.276.75E+062.61E+062.71E+063.00E+06
720.57325182670.59075183490.58520598550.5407532943305.4281208.95627.294909.37472964.1731518784.8021298.936.82E+062.68E+062.77E+063.06E+06
730.57163958640.58908065640.58355474290.5392405214304.5691205.53625.524906.8373973.1391553.69803.2471325.486.88E+062.75E+062.84E+063.12E+06
740.57004799180.58746322920.58191469510.537746777303.7211202.22623.766904.31874982.1071588.64821.8211352.056.94E+062.81E+062.91E+063.19E+06
750.56847704290.58558681820.58028864090.5362702773302.8841198.38622.023901.83575991.0781629.84840.4921378.687.01E+062.88E+062.97E+063.25E+06
760.56692861660.58409155320.57870176880.5348139955302.0591195.32620.322899.386761000.051663.08858.9461405.297.07E+062.94E+063.04E+063.31E+06
770.56539708220.58238128280.57712795730.5333743637301.2431191.82618.635896.965771009.031701.56877.4971431.957.13E+063.01E+063.10E+063.37E+06
780.56388619350.580827380.57556440780.5319650588300.4381188.64616.959894.595781018.011736.99896.181458.387.20E+063.07E+063.17E+063.44E+06
790.56239407360.57921972580.57397940140.5305646734299.6431185.35615.26892.24791026.991774.13915.35914857.26E+063.14E+063.24E+063.50E+06
800.56092072240.5776365040.57246343010.5291833167298.8581182.11613.635889.917801035.971811.16933.9351511.577.32E+063.20E+063.30E+063.56E+06
810.55946614010.57613635250.57096704980.5278192046298.0831179.04612.031887.623811044.961846.72952.5041538.157.39E+063.26E+063.37E+063.62E+06
820.55802844980.57452381190.56957049030.5264735265297.3171175.74610.534885.36821053.941885.38970.0371564.717.45E+063.33E+063.43E+063.69E+06
830.55660765130.57302366040.56809276810.5251427144296.561172.67608.95883.122831062.931921.91988.8171591.287.51E+063.40E+063.50E+063.75E+06
840.55520562160.5716652170.56667661770.523829147295.8131169.89607.432880.913841071.921955.231007.041617.837.58E+063.46E+063.56E+063.81E+06
850.5538186070.57024813580.56522594970.5225310404295.0741166.99605.877878.73851080.911990.551025.921644.387.64E+063.52E+063.63E+063.88E+06
860.55244660740.56881150870.56383032320.5212477998294.3431164.05604.381876.572861089.92026.671044.31670.937.71E+063.58E+063.69E+063.94E+06
870.55109337670.56735533560.56243189790.51998002293.6221161.07602.882874.44871098.892063.641062.931697.487.77E+063.65E+063.76E+064.00E+06
