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Dynamical Theory of Crystal Lattices

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At the time of the original publication of Dynamical theory of crystal lattices it represented the final account of the subject; in many ways it still does. The book is divided into four sections. The first of these is very general in nature and deals with the general statistical mechanics of ideal lattices, leading to the electric polarizability and to the scattering of light. The second part deals with the properties of long lattice waves; the third with thermal properties and the fourth with optical properties.
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Peking University
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Table of Contents

I Atomic Forces
1 Theoretical Considerations 1
2 Ionic Radii 15
3 Houristic Expressions for Lattice Energies 19
II Lattice Vibrations
4 Simple Approximate Treatment of Thermodynamical Behaviour 38
5 Vibrations of a Diatomic Chain 55
6 Frequency Spectrum of Lattice Vibrations and Specific Heats 61
7 Long Lattice Vibrations in the Optical Branches 82
8 Infra-red Dispersion and the Retardation Effect on Lattice Vibrations 89
9 Atomic Theory of Long Optical Vibrations and Infra-red Dispersion 100
10 Experimental Aspect of Infra-red Dispersion by Ionic Crystals 116
III Elasticity and Stability
11 Homogeneous Deformation and the Elastic Constants 129
12 Mechanical Stability of Simple Lattices 140
13 Relative Stability and Polymorphism 154
IV Quantum Mechanical Foundation
14 Quantum Mechanics of Molecular Systems 166
15 Normal Coordinates 173
16 Statistical Mechanics of Systems of Oscillators 178
17 Statistical Mechanics of a Molecular System under External Forces 181
18 Static Polarizability and Polarizability in Variable Fields 189
19 The Rayleigh and Raman Scattering of Light 199
20 Placzok's Approximation 204
21 Expansion of the Optical Parameters and the Classification of Optical Effects 208
V The Method of Long Waves
22 The Geometry of Perfect Lattices 213
23 The Infinite Lattice Model and General Invariance Relations 217
24 Lattice Waves 223
25 Failure of the Method of Homogeneous Deformation and the Method of Long Waves 225
26 Long Acoustic Vibrations 229
27 The Elastic Constants for Non-ionic Crystals 236
28 Equilibrium Conditions (vanishing stresses) and Further Invariance Relations 240
29 Central Forces 245
30 Coulomb Field in a Dipole Lattice - Ewald's Method and Separation of the Macroscopic Field 248
31 Acoustic Vibrations in Ionic Lattices (rigid ion model) 255
32 The Elastic and Piezoelectric Constants and the Dielectric Tensor 262
33 Phenomenological Discussion of the Dispersion Formula for Complex Lattices 265
34 Long Optical Vibrations in Ionic Lattices (rigid ion model) 270
35 Polarizable Ions 272
VI The Free Energy
36 The Specification of Finite Strains 278
37 Phenomenological Discussion of the Free Energy of a Lattice 282
38 Normal Coordinates of a Lattice 293
39 Normalization of Physical Parameters, Selection Rules and Expansion Methods 302
40 The Normalized Hamiltonian 306
41 The Free Energy 312
42 The Static (Non-vibrating) Lattice 319
43 The T[superscript 4]-law 322
VII The Optical Effects
44 The Microscopic Theory of Dispersion 328
45 The Local Treatment of Optical Effects 339
46 The Effect of the Anharmonic Potential on Dispersion 341
47 The Dispersion Formula with Damping 355
48 The Effect of the Second-order Electric Moment 363
49 The First and Second-order Raman Effects 367
50 The Brillouin Components of the Thermal Scattering of Light 373
App. I Some Common Lattice Structures (p. 1) 382
App. II Madelung's Energy (p. 3) 385
App. III Evaluation of Simple Lattice Sums (p. 23) 388
App. IV The Approximation to the Vibrational Spectrum with the help of the Cyclic Boundary Condition (p. 45) 391
App. V Energy Density in Ionic Crystals (p. 83) 396
App. VI The Inner Field in Uniformly Polarized Crystals with Tetrahedral Symmetry (the Lorentz Field) (p. 104) 398
App. VII The Adiabatio Approximation (p. 170) 402
App. VIII Elimination of the Electronic Motion (p. 172) 406
App. IX Double Refraction and Optical Rotation (p. 333) 408
App. X Recent Publications 411
Index 415
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