9780195119657

Statistical Mechanics of Solids

by
  • ISBN13:

    9780195119657

  • ISBN10:

    0195119657

  • Format: Hardcover
  • Copyright: 2000-09-21
  • Publisher: Oxford University Press

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Summary

This monograph, suitable for use as an advanced text, presents the statistical mechanics of solids from the perspective of the material properties of the solid state. The statistical mechanics are developed as a tool for understanding properties and each chapter includes useful exercises to illustrate the topics covered. Topics discussed include the theory of the harmonic crystal, the theory of free electrons in metal and semiconductors, electron transport, alloy ordering, surfaces and polymers.

Table of Contents

The Basics of Thermodynamics
1(33)
The existence of equilibrium and state functions
1(1)
Empirical temperature scales
2(1)
The ideal gas temperature
2(1)
The mechanical equivalent of heat
3(1)
Walls and the zeroth law of thermodynamics
4(1)
Spontaneous, reversible, and irreversible processes
5(1)
Work and the dependence of work on the path
6(2)
The first law of thermodynamics
8(1)
Heat capacity, energy, and enthalpy
9(1)
The second law of thermodynamics and entropy
10(4)
Free energies and equilibrium conditions
14(2)
Thermodynamic potentials and Legendre transformations
16(4)
Chemical potentials
20(1)
Conditions of phase equilibria and stability
21(3)
Euler's theorem and the Gibbs-Duhem equation
24(2)
Reciprocity relations of Maxwell
26(1)
Useful differential relations
27(1)
Equations of state and heat capacity relations
28(3)
Magnetic systems
31(3)
Exercises
32(2)
Principles of Statistical Mechanics
34(35)
Definitions for statistical mechanics
34(1)
Thermodynamic state
35(1)
Comparison of microscopic and macroscopic state
36(1)
The relation between microscopic and macroscopic state
37(1)
System and environment
38(1)
Quantum states of macroscopic systems
39(1)
Time averages
40(1)
Ensembles
41(1)
The canonical ensemble
42(2)
The canonical most probable distribution
44(3)
Summary of definitions of probabilities
47(1)
The canonical ensemble and thermodynamics
48(6)
Statistical entropy and the second law of thermodynamics
54(2)
The semicalassical approximation
56(4)
The grand canonical ensemble
60(3)
The pressure ensemble
63(1)
Fluctuations
64(5)
Exercises
67(2)
Particle Statistics
69(23)
Entropy and number of complexions
69(2)
Particle distribution functions
71(3)
Particle statistics and thermodynamics
74(2)
The ideal gas
76(5)
Particle statistics from the grand canonical ensemble
81(3)
Representations of the density of states
84(2)
Maxwell's velocity distribution
86(1)
Two-dimensional ideal gas
87(1)
Independent particles and subsystems
88(4)
Exercises
90(2)
The Harmonic Crystal
92(32)
The harmonic model
92(1)
The monatomic linear chain and normal mode analysis
93(8)
Partition function and free energy of the harmonic crystal
101(3)
General heat capacity equations
104(2)
The Einstein model
106(1)
Superposition of Einstein oscillators
107(1)
The Debye model
108(4)
Debye energy and heat capacity
112(3)
Relation between Einstein and Debye characteristic temperatures
115(1)
Comparison of Debye theory with experiment
116(3)
The phonon gas
119(5)
Exercises
121(3)
Anharmonic Properties and the Equation of State
124(19)
The crystal potential energy
124(5)
Anharmonic properties and the Gruneisen assumption
129(5)
Heat capacity at constant pressure
134(1)
Debye theory and the Gruneisen assumption
134(2)
Vibrational anharmonicity
136(1)
Theory of the Gruneisen parameter
137(6)
Exercises
141(2)
Free Electron Theory in Metals and Semiconductors
143(34)
Free electrons in metals
143(1)
Statistics for the electron gas
144(1)
The distribution of free electrons
145(3)
Thermodynamic properties of the free electron gas
148(4)
Electronic heat capacity in metals
152(1)
Equation of state of the free electron gas
153(2)
Thomas--Fermi theory
155(4)
Review of results of band theory
159(3)
Impurity levels in semiconductors
162(1)
Electron distribution in intrinsic semiconductors
163(4)
Electron statistics in extrinsic semiconductors
167(4)
Mass action laws for extrinsic semiconductors
171(2)
Relation between Fermi level and impurity concentration
173(4)
Exercises
175(2)
Statistical-Kinetic Theory of Electron Transport
177(25)
Free electrons in external fields and temperature gradients
177(3)
The statistical-kinetic method
180(1)
The Boltzmann transport equation
181(4)
Formal flux equations
185(1)
The electrical conductivity of metals
186(2)
Thermal conductivity and the Wiedemann-Franz law
188(4)
The isothermal Hall effect
192(4)
Electrical conductivity in semiconductors
196(6)
Exercises
201(1)
Order-Disorder Alloys
202(32)
Order-disorder structures
202(1)
The order-disorder transition
203(1)
Description of the degree of order
204(5)
The Order-disorder partition function
209(4)
The Kirkwood method
213(4)
The Bragg--Williams approximation
217(5)
The second moment approximation
222(3)
The quasi-chemical approximation
225(5)
Comparison with experiment
230(4)
Exercises
232(2)
Magnetic Order
234(24)
Magnetic response
234(2)
Paramagnetism of independent moments
236(4)
Paramagnetism of free electrons
240(2)
Ferromagnetism: mean field theory
242(3)
The Ising model for ferromagnetism
245(3)
Antiferromagnetism: mean field theory
248(3)
Spin waves
251(7)
Exercises
256(2)
Phase Equilibria
258(30)
Phase equilibria in one-component systems
258(4)
The van der Waals model
262(8)
Sublimation
270(2)
The liquid state
272(4)
Communal entropy
276(1)
Vibrations and melting
277(4)
Melting
281(1)
Regular solution theory of binary alloys
282(6)
Exercises
286(2)
Critical Exponents and the Renormalization Group
288(30)
Equivalent models
288(1)
Critical points
289(3)
Landau theory and the Kirkwood expansion
292(3)
Fluctuations and correlation length
295(3)
The monatomic Ising chain
298(4)
Renormalization of the one-dimensional Ising model
302(3)
The Kadanoff construction
305(6)
The renormalization group
311(2)
Scaling and the renormalization group
313(3)
Numbers
316(2)
Exercises
317(1)
Surfaces and Interfaces
318(31)
Basic concepts
318(4)
Thermodynamics of interfaces
322(3)
Thermodynamics of adsorption on solid surfaces
325(3)
Adhesion and cohesion
328(5)
Critical point and critical exponent for surface tension
333(2)
Monolayer adsorption: Langmuir isotherm
335(4)
Monolayer adsorption: mobile layer
339(1)
Multilayer adsorption: BET isotherm
340(5)
Segregation of impurities at interfaces
345(4)
Exercises
346(3)
The Theory of Random Flight
349(26)
Introduction
349(1)
The mean square total displacement
350(4)
Random flight on a lattice
354(7)
Reflecting and absorbing barriers
361(2)
The Markoff method
363(4)
The general solution
367(3)
Self-similarity
370(1)
The diffusion equation from random flights
371(4)
Exercises
373(2)
Linear Polymer Chains
375(28)
Polymer chains and random flight
375(1)
Persistence length
376(3)
Chain length fluctuations
379(2)
Density in a polymer chain
381(1)
Partition function of a polymer chain
381(2)
Excluded volume
383(2)
The force ensemble and chain elasticity
385(4)
Elastomers
389(6)
The Flory correction
395(1)
Solutions and gels
395(8)
Exercises
401(2)
Vacancies and Interstitials in Monatomic Crystals
403(28)
Choice of ensemble
403(1)
The vacancy concentration
404(3)
The crystal free energy
407(3)
Vacancies and thermodynamic functions
410(3)
The vacancy formation functions
413(5)
Vacancies, divacancies, and interstitials
418(4)
Some numerical results
422(9)
Exercises
429(2)
Point Defects in Dilute Alloys
431(19)
General comments
431(2)
The statistical count for substitutional defects
433(2)
Defect concentration formulas for substitutional defects
435(5)
Internal equilibria for substitutional defects
440(1)
Quenched-in resistivity of dilute binary alloys
441(2)
Some general theory
443(3)
Thermodynamics of the dilute alloy
446(4)
Exercises
448(2)
Diffusion in Simple Crystals
450(19)
The empirical laws of diffusion
450(2)
Transition probabilities and Fick's laws
452(3)
Atomic jumps and the diffusion coefficient
455(2)
The jump frequency in one dimension
457(3)
Many-body theory of the jump frequency
460(6)
The diffusion coefficient
466(3)
Exercises
467(2)
Appendix 1 Combinatorial Problems in Statistical Mechanics 469(4)
Appendix 2 The Method of Undetermined Multipliers 473(4)
Appendix 3 Stirling's Approximation 477(2)
Appendix 4 Sums and Integrals 479(5)
Appendix 5 Fermi Integrals 484(4)
Appendix 6 Kirkwood's Second Moment 488(4)
Appendix 7 The Generalized Lattice Gas 492(3)
Appendix 8 Dyadics and Crystal Symmetry 495(10)
Additional Readings 505(4)
Index 509

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