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Ⅰ．Introduction 1

Ⅱ．Elements of the Theory of Lattice Dynamics 5

1．Equations of Motion of a Vibrating Lattice 5

2．The Cyclic Boundary Condition and Ledermann＇s Theorem 21

3．Normal Coordinates of a Lattice 29

4．Historical Survey 38

Ⅲ．Theory of the Vibrational Frequency Spectra of Solids 45

1．Introduction 45

2．Expressions for Frequency Spectra 53

3．Singularities in Frequency Spectra 65

4．Topological Basis for Singularities in Frequency Spectra 76

5．Approximate Spectrum Calculations 84

6．Vibrational Frequency Spectra of Lattices with Long-Range Interactions Between Ions 103

Ⅳ．Calculations of Thermodynamic Functions without the Use of the Frequency Spectrum 117

1．Thirring＇s Expansion and Its Analytic Continuation 117

2．Houston＇s Method 121

Ⅴ．The Effect of Defects and Disorder on Lattice Vibrations 129

1．Introduction 129

2．Rayleigh＇s Theorems 132

3．Mathematical Preliminaries 136

4．Lattice Models to be Studied 150

5．Effects of Defects on The Vibrations of Monatomic Lattices 159

6．Effects of Defects on the Vibrations of Diatomic Lattices 179

7．Disorder in Two-Component Lattices 188

Ⅵ．The Effects of Surfaces on the Vibrations of Crystal Lattices 213

1．Size Effect in the Low Temperature Specific Heat of Small Particles 213

2．Surface Vibration Modes in a Semi-Infinite Continuum 218

3．Surface Vibration Modes in Discrete Lattices 219

4．Interactions of Defects with Boundary Surfaces 227

Ⅶ．Scattering of X-Rays and Cold Neutrons by Lattice Vibrations 231

1．Introduction 231

2．Localization of an Atom about Its Equilibrium Position 236

3．Theory of the Scattering of X-Rays by Thermal Lattice Vibrations 242

4．Experimental Determination of Frequency Spectra by X-Ray Methods 252

5．The Determination of Lattice Vibrational Spectra by Slow Neutron Scattering Experiments 258

6．Experimental Determination of Frequency Spectra by Neutron Diffraction Methods 264

7．Time-Relaxed Position and Momentum Correlation Functions 273

8．Time-Relaxed Momentum Correlation Functions and Irrever-sibility 281

REFERENCES 289

AUTHOR INDEX 299

SUBJECT INDEX 305