Statistical Mechanics of Elasticity Book

Part 1. Classical Theory
  Chapter 1. Thermoelasticity from the Continuum Viewpoint
    1.1 Introduction
    1.2 Kinematics of Continua
    1.3 Mechanics
    1.4 Thermodynamics
    1.5 Various Thermodynamic Potentials
    1.6 Thermoelastic Stress--Strain Relations
    1.7 Thermoelastic Relations for Small Changes from Reference State
    1.8 Related thermodynamic Functions
    1.9 Elastic Constants in Terms of Displacement Gradients
    1.10 Isotropic Solids
    Appendix Notation of Thurston (1964)
  Chapter 2. Concepts of Classical Statistical Mechanics
    2.1 Introduction
    2.2 Hamiltonian Mechanics
    2.3 Use of Statistics in Statistical Mechanics
    2.4 Phase Functions and Time Averages
    2.5 Phase Space Dynamics of Isolated Systems
    2.6 Systems in Weak Interaction
    2.7 Canonical Distribution
    2.8 Time Averages versus Ensemble Averages
  Chapter 3. Corresponding Concepts in Thermodynamics and Statistical Mechanics
    3.1 Introduction
    3.2 Empirical Temperature
    3.3 Quasi-Static Process
    3.4 Phase Functions for Generalized Forces
    3.5 First Law of Thermodynamics
    3.6 Second Law of Thermodynamics
    3.7 Use of Mechanical Variables as Controllable Parameters
    3.8 Fluctuations
    3.9 Partition Function Relations
    3.10 Continuum Formulations of Nonuniform Processes
    3.11 Equipartition Theorem
    3.12 Entropy from the Information Theory Viewpoint
  Chapter 4. Crystal Elasticity
    4.1 Introduction
    4.2 Bravais Lattices
    4.3 The Atomistic Concept of Stress in a Perfect Crystal
    4.4 Harmonic and Quasi-Harmonic Approximations
    4.5 Thermoelastic Stress-Strain Relations Based on the Harmonic Approximation
    4.6 Cauchy Relations
    4.7 Stress Ensemble
    4.8 Linear Chain with Nearest Neighbor Interactions
    4.9 Lattice Dynamics and Crystal Elasticity
  Chapter 5. Rubber Elasticity, I
    5.1 Introduction
    5.2 Relative Roles of Internal Energy and Entropy
    5.3 Atomic Structure of Long-Chain Molecules and Networks
    5.4 One-Dimensional Polymer Model
    5.5 Three-Dimensional Polymer Models
    5.6 Network Theory of Rubber Elasticity
  Chapter 6. Rubber Elasticity, II
    6.1 Introduction
    6.2 Curvilinear Coordinates
    6.3 Geometric Constraints
    6.4 An Example
    6.5 Curvilinear Coordinates for Stressed Polymer Chains
    6.6 Rigid and Flexible Polymer Models
    6.7 Use of S = k log p for Stretched Polymers
    6.8 Strain Ensemble for Short Freely Jointed Chains
    6.9 Stress Ensemble for Chain Molecules
    6.10 Statistical Mechanics of Phantom Networks Addendum. Atomic View of Stress in Polymer Systems
  Chapter 7. Rate Theory in Solids
    7.1 Introduction
    7.2 Impurity Atom Diffusion
    7.3 A Simple One-Dimensional Rate Theory
    7.4 Exact Normalization
    7.5 Many Degrees of Freedom
    7.6 Transition-State Assumption
    7.7 Brownian Motion
    7.8 Kramers Rate Formula Part 2. Quantum Theory
  Chapter 8. Basic Concepts of Quantum Mechanics
    8.1 Introduction
    8.2 Structure of Classical Mechanics
    8.3 Structure of Quantum Mechanics
    8.4 Consequences of the Fourier Transform Relation between psi subscript x (x) and psi subscript p (p)
    8.5 Extension to Three-Dimensional Motion and to N Particles
    8.6 Hydrodynamic Analogy to Quantum Mechanics
    8.7 Initial-Value Problems
    8.8 Aspects of the Measurement Process
    8.9 Some Examples of Stationary States
    8.10 Tensor Product of Two Spaces
    8.11 Electron Spin
    8.12 Identical Particles and the Pauli Principle
  Chapter 9. Interatomic Interactions
    9.1 Introduction
    9.2 Hydrogen Molecule
    9.3 Adiabatic Approximation
    9.4 Hellmann-Feynman Theorem
    9.5 Harmonic Elastic Moduli Based on Hellmann--Feynman Theorem
    9.6 Categories of Interatomic Force Laws
  Chapter 10. Quantum Statistical Effects
    10.1 Introduction
    10.2 Quantum Statistical Mechanics
    10.3 Quantum Statistical Effects in Crystals
    10.4 Quantum Statistics for Polymer Models
    10.5 Gaussian Wave Packet Dynamics
    10.6 Canonical Ensemble in Terms of Coherent States
    10.7 Quantum Effects on Rate Processes
  References; Index