Statistical Physics Of Crystals And Liquids: A Guide To Highly Accurate Equations Of State

by Duane C Wallace

Overview

This important book presents a unified formulation from first principles of the Hamiltonian and statistical mechanics of metallic and insulating crystals, amorphous solids, and liquids. Extensive comparison of theory and experiment provides an accurate understanding of the statistical properties of phonons, electrons, and phonon-phonon and electron-phonon interactions in elemental crystals and liquids. Questions are posed along the following lines: What is the “best” theory for a given property? How accurate is a good theory? What information is gained by a comparison of theory and experiment? How accurate is a good experiment?

Product Details

ISBN-13:	9789812381132
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	01/14/2003
Pages:	328
Product dimensions:	6.00(w) x 8.90(h) x 0.70(d)

Table of Contents

	Preface	v
Chapter 1	Condensed Matter Hamiltonian	1
1	Nature of Condensed Matter	1
	Structure of the Theory	1
	Metals	3
	Van der Waals Forces	5
	Covalent Bonding and Other Types	7
	Condensed Matter Regime	8
2	Density Functional Theory	10
	Many-Electron Problem	10
	Many-Electron Groundstate	13
	Kohn-Sham Formulation	14
	Current Applications of Density Functional Theory	18
3	Electronic Excited States in Metals	19
	What Kind of Theory is Needed	19
	One-Electron Approximation: The Groundstate	20
	One-Electron Approximation: Excited States	22
	Calibration from Density Functional Theory	24
4	Total Hamiltonian	25
	Nuclear Motion Hamiltonian	25
	Electrons at the Reference Structure	27
	Notes on the Resolution of the Total Hamiltonian	29
5	Nearly-Free-Electron Metals	31
	Pseudopotential Perturbation Theory	31
	Groundstate Electron Density	33
	Screening and Exchange-Correlation Potentials	35
	Electron-Ion Interaction	37
	Electronic Groundstate Energy	39
	Adiabatic Potential	42
	Electronic Excited States	43
	Calibration of Pseudopotential Models	44
Chapter 2	Statistical Mechanics	49
6	Averaging Techniques	49
	Fluctuating Equilibrium State	49
	Laboratory Systems and Theoretical Systems	51
	Time Averages for a Molecular Dynamics System	53
	Phase Space Averages for a Single System	55
	Internal Consistency	58
7	Quantum Statistical Mechanics	60
	Canonical Distribution	60
	Thermodynamics	62
	Fluctuations	64
	Trace Formulation and Particle Exchange Symmetry	66
	Quantum Particle Statistics	67
	Excitation of Reference Structure Electrons	69
	Perturbation Expansion of the Free Energy	72
8	Thermoelasticity	74
	Thermoelastic State Functions	74
	Stresses and Elastic Constants	76
	Stress-Strain Relations	78
	Wave Propagation	80
	Thermoelasticity Extension Notes	82
9	Classical Statistics: Derivation	84
	Partition Function for Quantum Nuclear Motion	84
	Expansion in Quantum Corrections	86
	Nuclear Motion Free Energy	88
	Electronic Excitation plus Nuclear Motion	91
	Notes on Classical Statistical Mechanics	93
10	Classical Statistics: Applications	94
	Canonical Distribution	94
	Stresses and Elastic Constants	96
	Stress Fluctuations	99
	Relation Between Different Distributions	102
	Three Canonical Distributions	105
11	Interpretation of Statistical Mechanics	108
	Summary of the Formulation	108
	Meaning of Entropy	109
	Interpretation of Molecular Dynamics Calculations	110
Chapter 3	Lattice Dynamics	115
12	Lattice Statics	115
	Displacement Expansion of the Potential	115
	Surface Effects and Equilibrium Conditions	116
	Invariance and Stability	119
	Stresses and Elastic Constants	121
	Wave Propagation	124
13	Quasiharmonic Phonons	125
	Historical Note	125
	Lattice Vibration Problem	127
	Transformation to Phonons	129
	Properties of Phonons	132
14	Theory and Experiment	134
	Long Wavelength Acoustic Waves	134
	Nearly-Free-Electron Metals	137
	Note on Volume Dependent Potentials	139
	Theory and Experiment for Elastic Constants	141
	Theory and Experiment for Phonons	143
15	Experimental Phonon Data	145
	Phonon Dispersion Curves	145
	Phonon Frequency Distribution	147
	Phonon Moments	149
Chapter 4	Statistical Mechanics of Crystals	155
16	Quantum Nuclear Motion	155
	Interacting Phonon Description	155
	Nuclear Motion Free Energy	157
	Theory and Experiment at Zero Temperature	159
	Theory and Experiment in the Low Temperature Regime	162
	Thermodynamic Functions in the Dispersion Regime	165
17	Classical Nuclear Motion	167
	Quantum Free Energy at High Temperatures	167
	Failure of Anharmonic Perturbation Theory	169
	Classical Nuclear Motion from Computer Simulations	172
18	Electronic Excitations	175
	Reference Structure Electrons	175
	Interacting Electron-Phonon Description	179
	Interaction Free Energy	182
	Nearly-Free-Electron Metals	184
	Properties of the Interaction Free Energy	186
	Theory and Experiment for Electron-Phonon Interactions	188
19	Learning From Thermodynamic Data	190
	Thermal Expansion	190
	Thermodynamic Gruneisen Parameter	193
	Regimes of Quantum and Classical Nuclear Motion	195
	Volume Effects and Temperature Effects	198
	Anharmonic Entropy at High Temperatures	200
	Special Entropy Analyses	202
20	Crystal Equation of State	207
	Form and Range of Validity	207
	Calibration of the Static Lattice Potential	209
	Calibration of the Thermal Part	212
	Planar Shocks in Solids	214
Chapter 5	Liquid Dynamics and Statistical Mechanics	219
21	Configurational Correlations in a Monatomic Liquid	219
	Multiparticle Correlation Functions	219
	Correlation Entropy	224
	Pair Correlation Entropy	226
	Higher-Order Correlation Entropy	228
22	Melting of Elements	230
	Experimental Entropy of Fusion	230
	Normal and Anomalous Melting	233
	Historical Note on Melting Rules	234
	Normal Melting Rule	236
	Anomalous Melting Process	239
23	Liquid Dynamics Theory	242
	Interpretation of Specific Heat Data	242
	Random, Symmetric, and Crystalline Valleys	244
	Ion Motion Hamiltonian	246
	Liquid Free Energy	249
	Theory and Experiment for the Entropy	252
	Nature of the Transit Process	253
24	Verification From Computer Simulations	256
	Molecular Dynamics Equilibrium States	256
	Properties of the Random Valleys	259
	Crystal and Symmetric Valleys	261
	Observation of Single Transits	265
25	Liquid Equation of State	267
	Ions and Electrons at High Temperatures	267
	Classical Nuclear Motion from Computer Simulations	269
	Role of Liquid Dynamics Theory	271
Chapter 6	Phase Transitions and Nonequilibrium Processes	275
26	Theoretical Analysis of Phase Transitions	275
	Phase Boundary and Two-Phase Region	275
	Relations Across the Transition	277
	Note on Thermodynamic Stability	279
	Theory and Experiment for Crystal-Crystal Transitions	280
	Soft Phonons	282
	Compression Dependence of the Melting of Elements	285
27	Nonequilibrium Processes	288
	Information Content of the Partition Function	288
	Extension to Metastable States	289
	Application to Supercooled Liquids	290
	Glass Transition	292
	Bibliography	297
	Index	303