Statistical physics of crystals and liquids : a guide to highly accurate equations of state / Duane C. Wallace.

Format:

Book

Author/Creator:

Wallace, Duane C.

Language:

English

Subjects (All):

Equations of state.

Crystals.

Liquids.

Statistical physics.

Physical Description:

xv, 312 pages : illustrations ; 23 cm

Place of Publication:

River Edge, N.J. : World Scientific, [2002]

Summary:

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?

Contents:

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.

Notes:

Includes bibliographical references (pages 297-302) and index.

ISBN:

9812381120

9812381139

OCLC:

51963289