Molecular dynamical calculations of energy transport in crystalline solids

Abstract Thermal conductivity (diffusivity), heat pulse propagation, and shock wave propagation in one-, two, and three-dimensional lattices have been studied by the method of molecular dynamics, a method well suited to non-equilibrium and strongly anharmonic problems. In this review, particular attention has been paid to the approach to thermal equilibrium after a disturbance. In one dimension, it is shown that energy sharing between modes of vibration is difficult, therefore it is doubtful that the soliton concept is a useful one in non-linear problems where thermal relaxation is involved. In two and three dimensions, energy sharing occurs readily. Under appropriate conditions heat flow occurs by diffusion and a temperature gradient is set up. The computed value of lattice thermal conductivity is in agreement with experiment. In pulsed heating, the coupling between the thermal and elastic disturbances generates a composite second sound wave which leads to a simple explanation of the temperature dependent second sound velocity observed experimentally. In shock compression, the thermal relaxation behind the shock front causes the shock profile to be non-steady overall, in contradiction to the steady profile assumed in the usual Hugoniot relations for a continuum. The PVT relationship deduced from shock wave data are affected to a significant extent at high compressions.

[1]  J. Tasi.  Perturbation solution for shock waves in a dissipative lattice , 1973 .

[2]  T. Schneider,et al.  Solitonlike Properties of Heat Pulses , 1977 .

[3]  G. Dienes,et al.  A model for shock waves in solids and evidence for a thermal catastrophe , 1975 .

[4]  William G. Hoover,et al.  Microscopic fracture studies in the two-dimensional triangular lattice , 1976 .

[5]  E. A. Jackson.  Nonlinear Coupled Oscillators. I. Perturbation Theory; Ergodic Problem , 1963 .

[6]  G. Dienes,et al.  Molecular Dynamic Simulations of Shock Waves in a Three‐Dimensional Solid , 1972 .

[7]  Robert A. Guyer,et al.  SECOND SOUND IN SOLID HELIUM , 1966 .

[8]  L. Verlet.  Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules , 1967 .

[9]  R. Cotterill,et al.  Molecular dynamics studies of melting: II. Dislocation density and thermodynamic functions , 1974 .

[10]  P. Ortoleva,et al.  Computer molecular dynamics studies of a chemical instability , 1976 .

[11]  B. Alder,et al.  Studies in Molecular Dynamics. II. Behavior of a Small Number of Elastic Spheres , 1960 .

[12]  E. A. Jackson,et al.  Thermal conductivity of one-dimensional lattices , 1968 .

[13]  H. Nakazawa.  On the Lattice Thermal Conduction , 1970 .

[14]  B. Alder,et al.  Studies in Molecular Dynamics. I. General Method , 1959 .

[15]  L. Sham.  Equilibrium Approach to Second Sound in Solids , 1967 .

[16]  R. Cotterill,et al.  Molecular dynamics studies of melting : I. dislocation density and the pair distribution function , 1973 .

[17]  P. A. Urtiew,et al.  Thermal relaxation at interfaces following shock compression , 1974 .

[18]  S. Block,et al.  The diamond cell stimulates high-pressure research , 1976 .

[19]  W. Streett,et al.  Computer Simulation of Metastable Fluid States in the Lennard-Jones System , 1976, Journal of research of the National Bureau of Standards. Section A, Physics and chemistry.

[20]  B. Alder,et al.  Velocity Autocorrelations for Hard Spheres , 1967 .

[21]  K. Ishii,et al.  Localization of Normal Modes and Energy Transport in the Disordered Harmonic Chain , 1970 .

[22]  P. A. Urtiew,et al.  Temperature deposition caused by shock interactions with material interfaces , 1974 .

[23]  R. Guyer,et al.  Solution of the Linearized Phonon Boltzmann Equation , 1966 .

[24]  Stanley Block,et al.  Ultrahigh pressure diamond‐anvil cell and several semiconductor phase transition pressures in relation to the fixed point pressure scale , 1975 .

[25]  D. H. Tsai,et al.  Molecular-dynamical study of second sound in a solid excited by a strong heat pulse , 1976 .

[26]  J. Tasi.  Perturbation solution for growth of nonlinear shock waves in a lattice , 1972 .

[27]  Joseph Ford,et al.  COMPUTER STUDIES OF ENERGY SHARING AND ERGODICITY FOR NONLINEAR OSCILLATOR SYSTEMS , 1963 .

[28]  J. Barker,et al.  What is "liquid"? Understanding the states of matter , 1976 .

[29]  J. H. Weiner,et al.  Crack and dislocation propagation in an idealized crystal model , 1975 .

[30]  J. M. Dickey,et al.  Computer Simulation of the Lattice Dynamics of Solids , 1969 .

[31]  Norman J. Zabusky,et al.  Solitons and energy transport in nonlinear lattices , 1973 .

[32]  Aneesur Rahman,et al.  Correlations in the Motion of Atoms in Liquid Argon , 1964 .

[33]  D. J. Channin,et al.  Heat Pulses in NaF: Onset of Second Sound , 1970 .

[34]  L. Verlet,et al.  Perturbation Theory and Equation of State for Fluids , 1969 .

[35]  Jerome K. Percus,et al.  Ensemble Dependence of Fluctuations with Application to Machine Computations , 1967 .

[36]  William G. Hoover,et al.  Dense-fluid shear viscosity via nonequilibrium molecular dynamics , 1975 .

[37]  L. Brillouin,et al.  Wave Propagation in Periodic Structures , 1946 .

[38]  J. Tasi,et al.  Shock waves in diatomic chains—II. nonlinear analysis , 1976 .

[39]  J. E. Sinclair.  The influence of the interatomic force law and of kinks on the propagation of brittle cracks , 1975 .

[40]  W. Visscher,et al.  Lattice Thermal Conductivity in Disordered Harmonic and Anharmonic Crystal Models , 1967 .

[41]  L. Collatz.  The numerical treatment of differential equations , 1961 .

[42]  L. Verlet.  Computer "Experiments" on Classical Fluids. II. Equilibrium Correlation Functions , 1968 .

[43]  J. Wilks,et al.  III. Second sound and the thermo-mechanical effect at very low temperatures , 1952 .

[44]  S. Kormer.  Reviews of Topical Problems: Optical Study of the Characteristics of Shock-Compressed Condensed Dielectrics , 1968 .

[45]  J. Schiffgens,et al.  Computer simulations of vacancy and interstitial interactions with the (a/2) 〈110〉 edge dislocation in copper , 1974 .

[46]  D. J. Pastine.  An Equation of State for Face‐Centered‐Cubic Metals , 1964 .

[47]  N. Zabusky,et al.  Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States , 1965 .

[48]  S. P. Marsh,et al.  Equation of State for Nineteen Metallic Elements from Shock‐Wave Measurements to Two Megabars , 1960 .

[49]  J. Barker,et al.  Theories of Liquids , 1972 .

[50]  G. Vineyard,et al.  THE DYNAMICS OF RADIATION DAMAGE , 1960 .

[51]  W. Visscher.  Localization of Normal Modes and Energy Transport in the Disordered Harmonic Chain , 1971 .

[52]  Norman J. Zabusky,et al.  Solitons and Bound States of the Time-Independent Schrödinger Equation , 1968 .

[53]  T. Schneider,et al.  Molecular-dynamics study of a three-dimensional one-component model for distortive phase transitions , 1978 .

[54]  P. J. Schneider,et al.  Conduction heat transfer , 1974 .

[55]  E. A. Jackson.  Nonlinear Coupled Oscillators. II. Comparison of Theory with Computer Solutions , 1963 .

[56]  R. Peierls,et al.  Quantum theory of solids , 1956 .

[57]  W. Visscher,et al.  Dynamics of Distorted Harmonic Lattices. II. The Normal Modes of Isotopically Disordered Binary Lattices , 1967 .

[58]  J. Tasi.  Reflection of nonlinear shock waves in a lattice , 1976 .

[59]  I. R. Mcdonald,et al.  On the calculation by molecular dynamics of the shear viscosity of a simple fluid , 1973 .

[60]  E. Prohofsky,et al.  Second-Sound Propagation in Dielectric Solids , 1964 .

[61]  Joseph Ford,et al.  Equipartition of Energy for Nonlinear Systems , 1961 .

[62]  D. H. Tsai,et al.  Shock wave propagation in cubic lattices , 1966 .

[63]  E. Lloyd.  Accurate Characterization of the High-Pressure Environment , 1971 .

[64]  Paul C. Martin,et al.  Unified Approach to Interacting Phonon Problems , 1966 .

[65]  W. Visscher,et al.  Dynamics of Disordered Harmonic Lattices. I. Normal-Mode Frequency Spectra for Randomly Disordered Isotopic Binary Lattices , 1967 .

[66]  I. Torrens.  Computer simulation in radiation damage studies , 1973 .

[67]  L. Girifalco,et al.  Application of the Morse Potential Function to Cubic Metals , 1959 .

[68]  L. Graham,et al.  Edge dislocation core structure and the peierls barrier in body‐centered cubic iron , 1966 .

[69]  L. Sham.  Temperature Propagation in Anharmonic Solids , 1967 .

[70]  R. Cotterill,et al.  Molecular dynamics studies of melting: III. Spontaneous dislocation generation and the dynamics of melting , 1974 .

[71]  G. E. Duvall,et al.  Finite amplitude longitudinal waves in lattices , 1969 .