Statistical Mechanics of Elasticity,9780486422602

Statistical Mechanics of Elasticity

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Edition: 2nd
ISBN13: 9780486422602
ISBN10: 0486422607
Format: Paperback
Pub. Date: 2017-05-17
Publisher(s): Dover Publications
List Price: $26.70

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Summary

This advanced, self-contained treatment illustrates the general principles of statistical mechanics, focusing on their application to the elastic behavior of solids. Part 1 is based solely on classical mechanics, with a summary of thermoelasticity from the continuum viewpoint, followed by a study of the thermoelastic behavior of both crystalline and polymeric solids. Part 2 is based on quantum mechanics, discussing their role in interatomic force laws and their effects on the low-temperature mechanical behavior of solids and on the rates of thermally activated processes. A practical alternative to the usual course in statistical mechanics, this volume will prove valuable to students of physics and chemistry as well as to polymer physicists. 1983 edition. 96 figures.

Author Biography

Jerome H. Weiner is Professor Emeritus of Engineering and Physics at Brown University. His other Dover book, co-written with Bruno A. Boley, is Theory of Thermal Stresses.

Table of Contents

PART ONE CLASSICAL THEORY
Thermoelasticity from the Continuum Viewpoint
3(46)
Introduction
3(1)
Kinematics of Continua
4(5)
Mechanics
9(6)
Thermodynamics
15(9)
Various Thermodynamic Potentials
24(3)
Thermoelastic Stress-Strain Relations
27(3)
Thermoelastic Relations for Small Changes from Reference State
30(4)
Related Thermodynamic Functions
34(4)
Elastic Constants in Terms of Displacement Gradients
38(4)
Isotropic Solids
42(7)
Appendix: Notation of Thurston (1964)
47(2)
Concepts of Classical Statistical Mechanics
49(36)
Introduction
49(1)
Hamiltonian Mechanics
50(4)
Use of Statistics in Statistical Mechanics
54(2)
Phase Functions and Time Averages
56(5)
Phase Space Dynamics of Isolated Systems
61(11)
Systems in Weak Interaction
72(4)
Canonical Distribution
76(4)
Time Averages versus Ensemble Averages
80(5)
Corresponding Concepts in Thermodynamics and Statistical Mechanics
85(42)
Introduction
85(2)
Empirical Temperature
87(1)
Quasi-Static Process
88(1)
Phase Functions for Generalized Forces
89(1)
First Law of Thermodynamics
90(3)
Second Law of Thermodynamics
93(3)
Use of Mechanical Variables as Controllable Parameters
96(8)
Fluctuations
104(11)
Partition Function Relations
115(1)
Continuum Formulations of Nonuniform Processes
116(2)
Equipartition Theorem
118(2)
Entropy from the Information Theory Viewpoint
120(7)
Crystal Elasticity
127(58)
Introduction
127(2)
Bravais Lattices
129(2)
The Atomistic Concept of Stress in a Perfect Crystal
131(9)
Harmonic and Quasi-Harmonic Approximations
140(3)
Thermoelastic Stress--Strain Relations Based on the Harmonic Approximation
143(7)
Cauchy Relations
150(6)
Stress Ensemble
156(4)
Linear Chain with Nearest Neighbor Interactions
160(14)
Lattice Dynamics and Crystal Elasticity
174(11)
Rubber Elasticity, I
185(26)
Introduction
185(1)
Relative Roles of Internal Energy and Entropy
186(2)
Atomic Structure of Long-Chain Molecules and Networks
188(5)
One-Dimensional Polymer Model
193(5)
Three-Dimensional Polymer Models
198(7)
Network Theory of Rubber Elasticity
205(6)
Rubber Elasticity, II
211(46)
Introduction
211(1)
Curvilinear Coordinates
212(5)
Geometric Constraints
217(4)
An Example
221(2)
Curvilinear Coordinates for Stressed Polymer Chains
223(5)
Rigid and Flexible Polymer Models
228(6)
Use of S = k log p for Stretched Polymers
234(3)
Strain Ensemble for Short Freely Jointed Chains
237(7)
Stress Ensemble for Chain Molecules
244(3)
Statistical Mechanics of Phantom Networks
247(10)
Addendum Atomic View of Stress in Polymer Systems
1
Rate Theory in Solids
257(40)
Introduction
257(1)
Impurity Atom Diffusion
258(3)
A Simple One-Dimensional Rate Theory
261(4)
Exact Normalization
265(2)
Many Degrees of Freedom
267(8)
Transition-State Assumption
275(1)
Brownian Motion
276(11)
Kramers Rate Formula
287(10)
PART TWO QUANTUM THEORY
Basic Concepts of Quantum Mechanics
297(50)
Introduction
297(1)
Structure of Classical Mechanics
298(1)
Structure of Quantum Mechanics
299(4)
Consequences of the Fourier Transform Relation between ψx(x) and ψp(p)
303(9)
Extension to Three-Dimensional Motion and to N Particles
312(3)
Hydrodynamic Analogy to Quantum Mechanics
315(3)
Initial-Value Problems
318(2)
Aspects of the Measurement Process
320(2)
Some Examples of Stationary States
322(12)
Tensor Product of Two Spaces
334(2)
Electron Spin
336(4)
Identical Particles and the Pauli Principle
340(7)
Interatomic Interactions
347(25)
Introduction
347(1)
Hydrogen Molecule
348(5)
Adiabatic Approximation
353(4)
Hellmann--Feynman Theorem
357(3)
Harmonic Elastic Moduli Based on Hellmann-Feynman Theorem
360(5)
Categories of Interatomic Force Laws
365(7)
Quantum Statistical Effects
372(49)
Introduction
372(1)
Quantum Statistical Mechanics
372(14)
Quantum Statistical Effects in Crystals
386(17)
Quantum Statistics for Polymer Models
403(3)
Gaussian Wave Packet Dynamics
406(6)
Canonical Ensemble in Terms of Coherent States
412(4)
Quantum Effects on Rate Processes
416(5)
References 421(10)
Index 431

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