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E-grāmata: Topics in the Theory of Solid Materials [Taylor & Francis e-book]

(University of Manitoba, Winnipeg, Canada)
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Topics in the Theory of Solid Materials provides a clear and rigorous introduction to a wide selection of topics in solid materials, overlapping traditional courses in both condensed matter physics and materials science and engineering. It introduces both the continuum properties of matter, traditionally the realm of materials science courses, and the quantum mechanical properties that are usually more emphasized in solid state physics courses, and integrates them in a manner that will be of use to students of either subject. The book spans a range of basic and more advanced topics, including stress and strain, wave propagation, thermal properties, surface waves, polarons, phonons, point defects, magnetism, and charge density waves.

Topics in the Theory of Solid Materials is eminently suitable for graduates and final-year undergraduates in physics, materials science, and engineering, as well as more advanced researchers in academia and industry studying solid materials.
Preface xiii
Strain and stress in continuous media
1(21)
Introduction
1(1)
Deformation: strain and rotation
2(5)
The strain tensor
4(2)
The rotation tensor
6(1)
Forces and stress
7(3)
Linear elasticity
10(10)
Hooke's law
12(1)
Isotropic media
13(3)
Elastic moduli
16(2)
Stability conditions
18(2)
Equilibrium
20(2)
Wave propagation in continuous media
22(12)
Introduction
22(1)
Vector fields
22(2)
Equation of motion
24(3)
Wave propagation
27(7)
Shear and rotational waves
27(1)
Dilatational or irrotational waves
28(2)
General discussion
30(1)
Appendix to
Chapter 2
31(3)
Thermal properties of continuous media
34(14)
Introduction
34(1)
Classical thermodynamics
34(4)
The Maxwell relations
34(1)
Elastic constants, bulk moduli and specific heats
35(3)
Thermal conduction and wave motion
38(3)
Wave attenuation by thermal conduction
41(7)
Surface waves
48(9)
Introduction
48(1)
Rayleigh waves
49(1)
Boundary conditions
50(1)
Dispersion relation
51(3)
Character of the wave motion
54(3)
Dislocations
57(16)
Introduction
57(1)
Description of dislocations
57(5)
Deformation fields of dislocations
62(7)
Screw dislocation
63(2)
Edge dislocation
65(4)
Uniform dislocation motion
69(2)
Further study of dislocations
71(2)
Classical theory of the polaron
73(17)
Introduction
73(1)
Equations of motion
74(4)
The constant-velocity polaron
78(8)
Polaron in a magnetic field: quantization
86(4)
Atomistic quantum theory of solids
90(19)
Introduction
90(1)
The hamiltonian of a solid
90(1)
Nuclear dynamics: the adiabatic approximation
91(2)
The harmonic approximation
93(1)
Phonons
94(9)
Periodic boundary conditions for bulk properties
94(3)
The dynamical matrix of the crystal
97(3)
The normal modes of crystal vibration
100(2)
Electrons and phonons: total energy
102(1)
Statistical thermodynamics of a solid
103(5)
Partition function of the crystal
104(1)
Equation of state of the crystal
105(2)
Thermodynamic internal energy of the crystal; phonons as bosons
107(1)
Summary
108(1)
Phonons
109(17)
Introduction
109(1)
Monatomic linear chain
110(6)
Diatomic linear chain
116(5)
Localized mode of a point defect
121(5)
Classical atomistic modelling of crystals
126(14)
Introduction
126(1)
The shell model for insulating crystals
126(3)
Cohesive energy of a crystal
129(2)
Elastic constants
131(4)
Dielectric and piezoelectric constants
135(5)
Classical atomic diffusion in solids
140(23)
Introduction
140(1)
The diffusion equation
141(6)
Derivation
141(3)
Planar source problem
144(3)
Diffusion as a random walk
147(4)
Equilibrium concentration of point defects
151(3)
Temperature dependence of diffusion: the Vineyard relation
154(9)
Appendix to
Chapter 10: Stirling's formula
161(2)
Point defects in crystals
163(33)
Introduction
163(5)
Crystals and defects
163(2)
Modelling of point defects in ionic crystals
165(3)
Classical diffusion
168(5)
Copper and silver diffusion in alkali halides
168(3)
Dissociation of the oxygen-vacancy defect complex in BaF2
171(2)
Defect complex stability
173(3)
Impurity charge-state stability
176(1)
Nickel in MgO
176(1)
Oxygen in BaF2
177(1)
Optical excitation
177(4)
Frenkel exciton and impurity absorption in MgO
178(1)
Cu+ in NaF
179(1)
O- in BaF2
179(2)
Spin densities
181(2)
F center in NaF
181(1)
F+2 center in NaF
182(1)
(F+2)* center in NaF
182(1)
Local band-edge modification
183(2)
Valence band edge in NiO: Li
183(1)
Conduction band edge in BaF2: O-
184(1)
Electronic localization
185(2)
Quantum diffusion
187(2)
Effective force constants for local modes
189(1)
Summary
190(6)
Appendix to
Chapter 11: the ICECAP method
193(3)
Theoretical foundations of molecular cluster computations
196(54)
Introduction
196(1)
Hartree--Fock approximation
197(11)
The approximation
197(4)
Normalization
201(1)
Total energy
202(2)
Charge density and exchange charge
204(3)
The single-particle density functional
207(1)
The Fock equation
208(10)
The variational derivation
208(6)
Total energy algorithm
214(1)
Solution of the Fock equation
214(4)
Localizing potentials
218(3)
Embedding in a crystal
221(8)
Introduction
221(2)
Approximate partitioning with a localizing potential
223(4)
Summary
227(2)
Correlation
229(9)
One-, two- and N-particle density functionals
238(12)
Introduction
238(1)
Density functional of Hohenberg and Kohn
239(2)
Reduced density matrices
241(4)
The many-fermion system
245(3)
The density functional and the two-particle density operator
248(2)
Paramagnetism and diamagnetism in the electron gas
250(48)
Introduction
250(1)
Paramagnetism of the electron gas
251(18)
The total energy
251(3)
The magnetic susceptibility
254(3)
Solution at low temperature
257(9)
Solution at high temperature
266(3)
Diamagnetism of the electron gas
269(29)
Introduction
269(1)
The Landau levels
270(3)
The Fermi distribution
273(8)
Energy considerations
281(2)
Magnetization: the de Haas--van Alphen effect
283(8)
Diamagnetism at T = 0
291(3)
Appendix to
Chapter 13
294(4)
Charge density waves in solids
298(36)
Introduction
298(1)
Effective electron--electron interaction
299(4)
The Hartree equation: uniform and periodic cases
303(10)
The Hartree approximation
303(3)
The uniform solution
306(3)
The periodic solution
309(4)
Charge density waves: the Mathieu equation
313(18)
The Mathieu equation
313(3)
Solution away from the band gap
316(2)
Solution near the band gap
318(4)
The self-consistency condition
322(6)
The total energy
328(3)
Discussion
331(3)
References 334(5)
Exercises 339(7)
Answers 346(7)
Author index 353(4)
Subject index 357