ca0ff15b0fc21f42aabd09c66d5bba04.ppt

- Количество слайдов: 80

1 A Facility for Simulating the Dynamic Response of Materials Properties William A. Goddard, III Caltech ASCI Academic Strategic Alliances Program Site Visit October 8, 1998

2 Simulation Development Roadmap PROBLEM SOLVING ENVIRONMENT Molecular Processes Materials Science Constitutive Relations lism ralle d Pa Integ Micro. Mechanics SHOCK INDUCED COMRESSIBLE TURBULENCE AND MIXING n an Pa gra Reaction Pathways tion Equation of State Reaction Rates rall Binder and Grain Interactions Mesh Generation Solid Modeling Fracture and Fragmentation STAGE 3 ratio elis m Continuum Modeling and e. S INTERACTION OF STRONG SHOCK WAVES WITH SOLID MATERIALS Inte Le ng th an d. T im MP STAGE 2 DETONATION OF HIGH EXPLOSIVES ca les STAGE 1 Phase Transitions Solid Mechanics Fluid Mechanics Turbulence Modeling Compressible Mixing Shock-Contact Interaction Equation of State Computational Science

3 Goals of the proposed research • Provide 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.

4 Roadmap for Materials Properties

5 Materials Properties Milestones Relevant discipline Year 1 MP(core), SD Metal FFs MP(core), SD MP(core), HE, SD MP(core), SD, new MP(core), SD MP(core), HE MP(core), SD Year 2 Year 5 Eo. S database New functionals QM on metals for metals Expansion of QM capabilities for HE Ceramic FFs and Eo. S Parallel DFT-MD on Large Scale models Properties of QM based FFs brittle ceramics QMC in ab initio QM codes Metal-ceramic interface FF Parallelization of QMC codes MD simulations of MD simulations NEMD using DB: Transport HE with polymer with reactive FF properties Integration of atomistic simulation Cij at interfaces; heterogeneous and 2 D Eo. S models (Cij (T, P)) systems at high T and P NEMD, parallelization of NEMD Integration Viscosities of heavy metals MP(core), CT MP(core), HE Year 4 QM based FFs Properties from MD simulations MP(core), HE, CT MP(core), HE, SD, CT, new Year 3 Hypervelocity impact and planar shock wave simulations Reaction rates for HE’s from QM RR database Transport properties Property database

6 Simulation Development Roadmap MP HE • High Explosives Applications – Binder and Grain Interactions • Kel-F, Estane – Equation of State • HMX, TATB – Reaction Dynamics and Molecular Processes • Shocked HMX, TATB • Vibrational Analysis of Rapid Post-Shock Events • Shock Compression MD

7 Simulation Development Roadmap MP SD • Solid Dynamics Applications – Equations of State • Ta, Fe, Oxides, and Ceramics – Phase Transitions • Ta, Carbon, Ceramics – Constitutive Equations • Elastic properties of metals, alloys, and ceramics • Thermodynamic properties • Plasticity and behavior under large strain rates

8 Simulation Development Roadmap MP CT • Compressive Turbulence and Fluid Dynamics Applications Determine 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 rates • Mass transport in dense fluids (diffusion at high P & T) • Heat transport (thermal conductivity at high P & T) Shock propagation in fluids Negative pressure properties

9 Personnel — Materials Properties • Senior researchers – – – William 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 staff – – – – – Daniel 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 staff – Darryl Willick (MSC) – J. Kendall (MSC)

10 Organization - Materials Properties • External Collaborators – Carnegie Institute Washington – University of Tennessee • Materials Properties Meeting — Annual – – LANL, SNL, LLNL National Laboratories Utah and Illinois Alliance Centers November 10, 1997 January 28, 1999 (HE); January 29, 1999 (SD) • Interactions – – HE: Weekly Meetings, (daily email/phone) SD: Monthly Meetings MP: Monthly Meetings SI: Biweekly Meetings

11 External Meetings - Materials Properties • • • Energetic Materials GRC (Dasgupta, Sun) 11 th 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)

12 ASCI Materials Properties Workshop • November 10, 1997, Caltech Laboratory Presentations • LLNL – Mailhiot, Ree, King, Fried • SNL – Heffelfinger, Melius • LANL – Kress ASAP Center Presentations • Caltech – Goddard, Tombrello, Cagin, Muller, Dasgupta, Ortiz, Shepherd, Meiron • CIW – Cohen • Utah – Voth, Wight, Boyd • Illinois – Martinez, Mitas

13 Milestones, MP Software Integration • MSC QM Software (Jaguar, QM/MSC) Port to ASCI Machines Optimize parallelization • MSC MD Software (MPSim) Port to ASCI Machines Optimize parallelization • MSC Semi-empirical QM Software (MSC-INDO) Improve scaling for large systems • Integration of QM and MD Software use Caltech Integration Platform

14 Role of Computer Science (CS MP) • Sca. LAPACK workshop, January 1998 – Use of math libraries to parallelize code • Software Integration – MP integration framework integrates with Caltech ASCI framework • New Algorithmic work – Shock dynamics for HE and SD – Improved matrix diagonalization work for QM • Virtual Test facility – HE Database Project

15 Current Research in Methods for MP • Quantum Mechanics – – Periodic Systems High Accuracy for Large Systems Fast Results for Large Systems Solvation (Poisson-Boltzmann) • Force Fields – – Polarizable, Charge Transfer Variable Bond Orders Phase Transitions Mixed Metal, Ceramic, Polymer • Meso. Scale Dynamics – – – Coarse Grained FF Diffusion Hybrid MD and Meso Dynamics Friction Physics-based gridpoints for Finite Element Analysis • Molecular Dynamics – Large Systems (CMM, Parallel) – Non-Equilibrium Viscosity, Friction – Solvation (Poisson-Boltzmann) – Hybrid QM/MD – Hierarchical NEIMO – Plasticity, Twin Formation, Crack Initiation – Interfacial Energies – Hildebrand Solubilities • Process Simulation – Vapor-Liquid Equilibria – Reaction Networks

16 Quantum Mechanics (HY=EY) • Ab Initio (Exact Hamiltonian) – Pseudospectral Techniques dealiasing, multigrid – Improved scaling by factors of N to N 2 – First Principles Solvation • Density Functional Theory – Periodic Boundary Conditions – New Functionals – Tight Binding fit to accurate LAPW • Semiempirical – Tight Binding or INDO – Fast Hamiltonian Construction – Molecular Dynamics • Quantum Monte Carlo – Most accurate method (0. 0004 e. V for simple reactions) – Scales exponentially with size – Combine with DFT (Only simulate reacting electrons)

17 QM Methodology (Jaguar) • CURRENT STATUS: • Single processor speed 9 times faster than best alternate methodology • Scales a factor of N 2 better than best alternate methodology CPU Time • Psuedospectral Technology (with Columbia U. ) Multigrids Dealiasing functions • Replace N 4 4 -center Integrals with N 3 potentials • Use Potentials to Form Euler-Lagrange Operator: Gaussian Jaguar Log (number basis functions) Collaboration with Columbia U. and Schrödinger Inc.

18 QM Parallelization (Jaguar) Collaboration with Columbia U. and Schrödinger Inc.

19 Quest: Sandia Software for PBC QM MP/ASCI: Incorporate MSC GUI, new ECP, Basis sets Port to other machines

20 CS/MP 1: Improved Matrix Acceleration Series of alkane chains, 276 -552 basis functions, bandwidth ~80 basis functions Muller (MSC) - Ward (UTenn) • QM Scaling – N 2 - N 4 Hamiltonian Construction – N 3 Diagonalization – Need both to scale as N Contour plot of Hamiltonian Matrix Band Diag: scales good (N 2. 3) but overhead too high Normal Diag: scales poorly (N 3. 3) but generally efficient Block Diag: scales best (

21 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 systems • NEIMO Dynamics – Fast internal coordinate dynamics – Hierarchical for coarse graining • Solvation – Poisson-Boltzmann solver (energy and forces) – Generalized Born • Optimization for Highly Parallel Computers – SGI Origin, HP Exemplar – Ported to Intel quad-Pro

22 MPSim with PB Solvation • Explicit Solvent – Accurate – Typically solvent molecules account for 90% of computation – polymer motions limited by diffusion rates in solvent • Continuum Solvent (Poisson-Boltzmann) – – Solvent reduced to charges and forces on mesh points around molecule Use realistic solvent accessible surface Calculate energies and forces (for dynamics) Dramatically increases simulation times • Protocol – Update PB Forces every N time steps (Forces Expensive) – Use mesh density sufficient for MD (coarser than for QM).

23 Integrate NEIMO in MPSim INTERNAL COORDINATE DYNAMICS: Problem: M is full N by N (N is number of int. coord. ) Inversion scales as N 3, too slow for every dynamics step Solution: 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 • Goals – Incorporate NEIMO dynamics into MPSim (Forces use CMM) – Include Poisson-Boltzmann solvers – Parallelize • Target Systems: HE grains in polymer binder.

24 CS/MP 2: Lightweight Threads in MD Cagin, Li (MP), Thornley (CS) • Parallelized MPSim – Efficient on KSR, Intel Delta – Other platforms less efficient • Lightweight Threads – Inexpensive intialization – Parallelization on commodity microprocessors – Speedup of 3. 6 on 4 processors for a real problem • Next year, Expand to – QM/MM HRV-1 Rhinovirus - 500, 000 Atoms Intel Quad. Pentium, 2 GB RAM

25 Accomplishments, Overview • High Explosives – MD Simulation of TATB, HMX, and Kel-F – Simulation of post-shock energy redistribution • Solid Dynamics – MD Simulation of Metals and Oxides – QM Simulation of HCP, FCC, and BCC Metals – FF for BCC Metals • Algorithms – Shock MD Simulator – Phase transitions in Oxides and Metals – Bond-order-dependent FF for Carbon

26 Milestones, HE • TATB/HMX Molecular Structure • MD of inert and reactive explosives • Reaction Mechanism for TATB/HMX

27 MD and Force Field Development for HMX • Level 0 - Generic Force Field (Dreiding) - Can Do Any Combination Of Main Group Atoms – Density of States – Pressure Loading – Phase transitions • Level 1 - Vibrationally accurate force field Develop for specific systems DMN, HMX & RDX – – DFT (B 3 LYP) calculations on isolated monomers QUEST calculations on condensed phase systems FFOPT parameterization of FF to fit QM Vibrational Energy Transfer (VET): Intra-, inter-molecular, phonon - phonon couplings – H-bond interactions

28 Crystallographic Forms of HMX Impact Energy E = 0. 20 kg/cm 2 E = 0. 10 kg/cm 2 Sensitive Most sensitive r = 1. 58 r = 1. 78 r = 1. 894 429 K - to melting point r = 1. 839 Impact Energy E = 0. 75 kg/cm 2 Impact Energy Least sensitive E = 0. 20 kg/cm 2 Sensitive Stable @ 300 K 377 - 429 K

29 Correlation of Density of States (from MD) with Sensitivity (h 50 measurement) b-HMX h 50 = 0. 33 m TATB h 50 = 3. 2 m a-HMX h 50 = N/A g-HMX h 50 = 0. 14 m 0 200 400 d-HMX h 50 = N/A most sensitive Conclusion: Impact sensitivity correlates with density of modes between 0 -200 cm-1 600 cm-1

30 Compare Vibrational Frequencies QM (DFT-B 3 LYP/6 -31 G**) with FF (Dreiding) 0 -200 cm-1

31 Pressure Dependence of Crystallographic Cell Parameters for b-HMX (Theory using Dreiding, open symbols) with Experiments from Cady & Ollinger (filled symbols) B C A

32 Elastic Constants and Bulk Modulus of b-HMX Experimental Data (Joe Zaug, LANL), Theory (Dreiding)

33 HMX Cold Compression Curves for the 4 crystal morphologies • a form is the least compressible followed closely by the g form a g d b • d form is the most compressible • stable b form is intermediate in compressibility

34 Isothermal P-V curves for b-HMX • Procedure • Minimize at 0 K • Increase T by 300 K increments • 20 ps MD at each T • Results • Evidence of melting or phase transition above 600 K Melting behavior? • Compressibility similar for P > 25 GPa

35 Calculation of Shock Adiabat intersection with P-V isotherms 0 K 600 K Tang’s Adiabat • PV Isotherm from Simulations Allows the T for the Adiabat to be calculated from intersection points

36 b-HMX Cv from Phonon Dispersion Curves of Crystal 27 K points 343 K points 125 K points • 125 K points in Brillouin zone adequate • 90% of asymptotic high T limit reached at 1400 K

37 Convergence of Gruneissen Parameter from 50 ps (0. 5 fs step) MD of 4 x 3 x 2 supercell of b-HMX • Gruneissen parameter converged by 40 ps of MD

38 TATB (1, 3, 5 -triamino-2, 4, 6 -trinitrobenzene) Overview • planar structure, compact packing and high density • Experimental density at STP is 1. 9374 g/cc. • TATB crystal has low symmetry: triclinic (P-1). a (A) Expt. 300 K b (A) c (A) density (g/cc) 9. 01 9. 028 6. 812 1. 9374 Dreiding Exp 6 8. 986 8. 976 6. 883 1. 8852 error 0. 27% 0. 58% 1. 04% 2. 69%

39 TATB Isothermal Equation of State Expt. MD 300 K MD Dreiding FF Expt. (Cady)

40 TATB Isothermal EOS, Dreiding Force Field

41 TATB Future Work • • • Shock Hugoniot from isotherms Gruneissen Parameter Further Force Field Improvement Surfaces, Defects Interaction with Kel-F MD Fast Loading with surfaces & Kel-F

42 Kel-F 800 Overview • • • Kel-F 800 is a random copolymer of chlorotrifluoroethylene and vinylidene fluoride monomer units in a 3: 1 ratio. The presence of the vinylidene fluoride disrupts the crystallinity of the chlorotrifluroethylene to form an essentially amorphous polymer Although amorphous, the polymer is very dense due to the presence of the Cl and F atoms It is used in composites and as a binder for many plasticbonded explosive systems First atomistic/molecular study of Kel-F 800 system.

43 Kel-F 800 Atomistic Simulations Strategy for building amorphous polymers • Assume infinite solid with periodic supercell • Choose a molecular weight and a number of chains per unit cell • Use torsional potential and nonbond interactions to evaluate energy of growing system • Build each chain simultaneously monomer by monomer using Monte Carlo sampling. • anneal structure with MD at various Temperatures and Pressures (or volumes) • Standard techniques lead to density too low • The MSC Cohesive Energy Density Module uses a strategy that leads to excellent density and cohesive energy

44 Kel-F 800 Atomistic Simulations 20 Angstroms 24 monomers - 2 chains 50 Angstroms 24 monomers - 16 chains

45 Kel-F 800 • • • Due to the lack of experimental data for the pure Kel-F 800 polymer system, poly(chlorotrifluorethlene-co-vinylidene fluoride) Some validation work was done by calculating Cohesive Energy Densities and Solubility parameters using a MSC “in-house” developed code. Initial studies and choice of force field were conducted on pure PCTFE, poly(chlorotrifluoroethylene) for which some experimental data is known. Dreiding-EXP 6 force field is consistent with experiment 75 Cohesive Energy Density PCTFE 70 Upper limit of Experiment 65 60 Experimental Range 55 50 45 lower limit of Experiment Dreiding-EXP 6 40 2 5 16 No of "Polymer" chains in cell Cohesive Energy Density |CED| (cal/cm^3) Validation |CED| (cal/cm^3) COMPASS Kel-F 800 100 80 Dreiding-EXP 6 60 40 COMPASS 20 0 2 5 16 No of "Polymer"chains in cell

46 Kel-F 800 Future work • • Determine how properties depend on number of chains • find compromise between accuracy and speed. Calculate GRUNEISSEN parameters and other physical properties • as a function of temperature and pressure • from longer Molecular Dynamics runs Repeat for Estane binder Use binder with finite crystals of HE, apply shear loading

47 Large scale MD simulations of HE • High explosives: HMX, TATB grains in a polymeric binder (kel. F, estane) • Model HE System – periodic in all 3 directions • x- and y-direction extent (10 nm) • z-direction extent (1 -10 mm) • Allow axial compressive loading using new steady state algorithms (Cagin, Goddard) grains polymer 1 -10 mm polymer 10 nm

Milestones, Solid Dynamics • Equation of State for Metals and Alloys – Many body FF for fcc metals – Many body FF for bcc metals • • • Force fields for oxides and ceramics Phase transformations in metals and ceramics Equation of state for metals and ceramics Mechanical and thermodynamic properties of metals Energetics for Dislocation Models (from QM and MD) 48

Accomplishments, QM Metals 49 • Simulation of BCC Metals (Cohen) – EOS of Ta – LAPW LDA, GGA, Spin-Orbit Curves – Mixed Basis Code, scales very well on ASCI machines • Simulation of HCP metals (Cohen) – Results for Co (magnetic) and Re (non-magnetic) are in good agreement with experiment. – Theory consistent with behavior of other metals except Fe. – Problem with Fe: theory not agree with recent experiments on Fe

50 DFT Simulation of Ta EOS • Local Density Approximation – Available in all codes • Quest, Mixed Basis, LAPW – Underestimates EOS curves Exper • Generalized Gradient Approximation – Now Available in fast codes – Greatly improves EOS LDA • Spin Orbit Coupling – Important for Ta EOS – Can Effective Core Potential Simulate These Effect? Exper • Find FF to fit QM GGA

Elastic Constants of BCC Ta 51

52 Equations of State and Elasticity of HCP Metals • Recent diamond anvil experiments (Singh et al. , 1998; Mao et al. , 1998) using a novel technique give elastic constants for hcp fe quite different than theory (Stixrude and Cohen, Science, 1995; Soderlind et al. , 1996). • Is there a problem with theory or experiment? • How accurately can we predict elastic behavior of metals?

EOS for HCP Fe, Co and Re (Cohen) Wrong Shape Excellent Agreement 53 Correct Shape Fe: lines: LAPW GGA, solid: non-magnetic, dashed: afm. II, points: exp. (Jephcoat et al. , 1986, M Co: ferromagnetic, GGA solid, LDA dashed, points: exp: (Fujihisa and Takemura, 1996) Re: non-magnetic solid: GGA, dashed: LDA, points: exp. (Jeanloz et al. , 1991; Marsh, 1980)

Elastic Constants of HCP Co (Cohen) 54 DFT Exper Tight Binding V(au) Solid: LAPW GGA, dashed: LDA, points: exp.

Elastic Constants for HCP Fe (Cohen) V(au) Solid: LAPW GGA, dashed, tight-binding model 55

Acoustic Velocities for HCP Fe Inner core Solid: LAPW GGA, symbols: exp. 56

MP: Force Fields for material properties • Many body force fields for metals and alloys – fcc transition metals ( Al, Ni, Cu, Ag, Au, Pt, Rh, Pb) – bcc transition metals ( Ta, Fe, W, V, Cr, Mo). • MS-Q Force fields for oxides, ceramics and minerals – eg. Si. O 2, Al 2 O 3, Zr. O 2, Mg. O, Ca. O, B 2 O 3 , Na 2 O, Ti. O 2. • Reactive bond order dependent force fields – Generalized Bond Order Dependent Force Fields for hydrocarbons • Inclusion of long range interactions (Coulomb and dispersion) • Accurate valence for organic HE – Vibrationally accurate FF for H. E. from ab initio calculations 57

Many body potentials for Metals and Alloys (bcc metals) • Many body potential for bcc metals • Repulsive core potential • N-body density term • Functional form of N-body term 58

Morse Stretch Variable Charge (MS-Q) FF for oxides and ceramics 59 New Approach allow Charges to vary with time as structure changes • Predict charges using QEq: (Rappe and Goddard, 1991) – – c. A = 0. 5*(IP+EA) Electronegativity J JAA = (IP - EA) Hardness R A 0 Size of charge distribution on A. JAB Shielded Coulomb Potential All parameters determined from atomic data (not adjustable) AA • Describe Pauli Repulsion and other terms using 2 -body Morse-Stretch (Demiralp, Cagin and Goddard, 1997) RA 0 + RB 0 – 3 parameters per atom pair, chosen to reproduce structure, energy and elastic properties of condensed phases – Universal: same O-O for all oxides, same Si-O for all silicas

MP: FF Development Future Plan 60 • First principles based force fields for Ta and Fe – QM-DFT Eo. S, – Defect energies, (eg. vacancy formation, surface energies) – Energy difference between fcc-bcc-hcp phases. • First principles based reactive force fields for oxides and ceramics – Detailed and more accurate parameterization of QEq parameters, – QM calculations on possible polymorphs, – QM calculations for Eo. S. • Bond order dependent/Reactive Force Fields for C-N-O-H for HEDM

Properties of bcc metals from new FF (Fe and Ta) exp MSC Finnis-Sinclair Johnson-Oh exp MSC 61

Physical properties of a-iron 62 Phonon Frequencies MSC-FF Experiment n. NL 9. 70 9. 26 n. NT 1 2. 66 4. 53 THz n. NT 2 6. 46 6. 45 n. H 9. 45 8. 56 Defect Properties Vacancy formation Evf (e. V) MSC-FF Experiment 1. 88 1. 69 -189 g (100) 2420 2417 Surface energies g(110) g(111) m. J/m 2 2304 2417 2616 2417

Deformation processes in metals and alloys as a function of strain rate (uniaxial) 63 Constant strain rate (infinite length bar) 2 nm 0. 5% /ps 1% /ps 2% /ps 5% /ps

Plasticity: Deformation and flow as a function of strain rate Yield point Twin formation Work hardening Elastic region Plastic flow Viscosity ~60 -70 c. P (m. Pa. s) s = 3 -3. 5 GPa (de / dt) = 50 GHz h = s / (de / dt) 64

65 Strain rate induced amorphization in metals and alloys Elastic constants vs strain T = 300 K Strain rate = 5%/ps

Pressure induced phase transformations in silica Pressure vs density 66 Temperature dependence of transition pressure

67 Structure of vitreous silica from MD with MS-Q FF THEORY EXPERIMENT • Start from crystal • Heat to 4000 K (to obtain melt) • Equilibrate at 4000 K • Cool slowly and allow density relax Pair distribution function

Force Fields from ab initio QM (DFT-GGA): Mg. O Force field is derived from the Eo. S calculated using QM No empirical data is used. We used new FF to study the phase diagram of Mg. O 68

Phase Diagram of Mg. O from q. MS-Q FF 69 • QM-DFT derived FF is used – q. MS-Q Force Fields, 1998. • Solid-Liquid phase boundary is calculated from MD simulations performed in solid and liquid phases and Clapeiron equation • Phase transition kinetics and details of the B 1 -B 2 transition explored in detail by QM-DFT and MD Mg. O Phase coexistence using q. MS-Q FF B 2 B 1 Strachan, Cagin, Demiralp, Goddard, 1998. Liquid

Determination of kinetics of B 1 -B 2 Transition Path • Both DFT-GGA and classical FF methods are employed to calculate the enthalpy along transition path from B 1 to B 2 • Calculated barriers, DH, are – 6. 9 kcal/mol from QM – 4. 6 kcal/mol from MD • The path is defined as the change in angle a = 90 to 109 – l = 0, a = 90 – l = 1, a = 109 70

Extended Bond Order Dependent - FF 71 • Brenner Bond Order Dependent Force Fields Bij depends on local bonding environment VR, VA: short range repulsive and attractive terms Does not describe nonbond interactions (coulomb and dispersion) Cannot describe molecular crystals(HMX, TATB) and graphite

Extended Bond Order Dependent - FF 72 Includes nonbond interactions (coulomb and dispersion) in a systematic manner, describes molecular crystals (HMX, TATB), graphite, reactions, phase transitions

73 GEEBOD-FF for Carbon: Diamond to Graphite at high T&P 1 ps 10 ps 25 ps Che, Cagin, Goddard, 1998. 35 ps

Diamond to Graphite phase transition New extended bond order dependent potentials allow PT to graphite 74

MP: Solid Dynamics Future Plan 75 • High T and P studies on bcc metals – Equation of State of Ta at elevated temperature – Elastic constants of Ta and Fe at elevated temperature and pressures – Plasticity of Ta and Fe subjected to large loads (compressive, tensile, shear) – Strain rate (compression, tension) dependent mechanical behavior Ta, Fe • Hypervelocity impact and shock wave simulations on Fe and Ta – Ta, Fe, Al, flyer plate vs target – Shock wave simulations on Fe • Calculation of defect energetics in metals – Point defects – Surface free energy – Dislocation core energy from large scale atomistic calculations

Atomic Level Simulation of Shock Waves 76 1. Use atomistic FF to calculate the dynamics 2. Derive mesoscopic description A) B) Elastic Body Material Up -Up Simulated Material L(t) = Lo - 2 t Up Piston

Nonequilibrium molecular dynamics (NEMD) • Predict flow properties (viscosity as a function strain rate) y • Using the constitutive relation x – stress = viscosity * strain rate • Build strain terms into atomistic equations of motion (Eo. M) – Eo. M for planar Coueutte Flow • Thermostat to eliminate heat – Eg. Gaussian thermostat: 77 . Qa = Pa/ma - g ya/nx. Pa = Fa - g Pay nx - a Pa

Shear viscosity of Cu: Au alloy from NEMD 78 Non equilibrium molecular dynamics simulations on Cu: Au alloy viscosity at 0, 25%, 50%, 75% and 100% concentrations at T = 1500 K, 1750 K, 2000 K at shear rates 2, 1, 0. 5, 0. 25 (1/ps) viscosity 4 1500 K 1750 K 2000 K 3 1500 K 1750 K 2000 K Experiment 2 0. 5 1. 0 Square root of strain rate 1. 5 0. 20. 40. 60. Au% Qi, Cagin, Goddard, 1998. 80. 100.

79 GEEBOD-FF for Carbon: Thermal conductivity from NEMD Che, Cagin, Goddard, 1998.

MP: publications and submitted manuscripts • • • 80 “Pressure induced phase transformations in silica, ” Cagin et. al, MRS Symp. Series Vol 492, 287 -292 (1998). “Q-SC many body potentials for fcc metals, ” Kimura et. al. , Phys. Rev. B 1, submitted. “The MS-Q FF for ceramics, ” Demiralp et al. , Phys. Rev. Lett. , submitted. “Shear viscosity of liquid metal alloy Au: Cu, ” Qi et. al. , Phys. Rev. E, submitted. “Strain rate induced amorphization in metallic nanowires, ” Ikeda et. al. , Phys. Rev. Lett. , submitted. “Generalized empirical bond order force fields, ” Che et. al. , J. Phys. Chem. , submitted. “MD simulations of vitreous silica, ” Huff et al. , J. Non Cryst. Solids, submitted. “Case studies on glass formation and crystallization in alloys, ” Qi et. al. , Phys. Rev. B 1, submitted. “Theoretical assessment of phases of Mg. O from DFT and MD, ” Strachan et. al. , Phys. Rev B 1, submitted.