Phonons: Theory and Experiments I

1 Introduction.- 1.1 The Static Lattice Model and Its Limitations.- 1.2 Early History of Lattice Dynamics.- 1.3 The Adiabatic and Harmonic Approximations.- 1.4 Organization of the Book.- 1.5 Problems.- 2. Dynamics of the Linear Diatomic Chain.- 2.1 Classical Mechanics.- 2.2 Quantum Mechanics.- 2.3 Problems.- 3. Dynamics of Three-Dimensional Crystals.- 3.1 Equations of Motion and Atomic Force Constants.- 3.2 Dynamical Matrix and Eigenvectors.- 3.3 Periodic Boundary Conditions, Reciprocal Lattices and Brillouin Zones.- 3.4 Normal Coordinates, Phonons.- 3.5 Density of States and Specific Heat.- 3.6 Connection of Lattice Dynamics with the Theory of Elasticity.- 3.7 An Illustration: Phonon Dispersion of Monoatomic Crystals with fcc Structure.- 3.8 Problems.- 4. Interatomic Forces and Phonon Dispersion Curves.- 4.1 Lattice Dynamics of the Solid Inert Gases.- 4.2 The Rigid-Ion Model for Ionic Crystals.- 4.3 The Shell Model.- 4.4 The Adiabatic Bond Charge Model.- 4.5 The Valence Force Model.- 4.6 Internal and External Vibrations in Molecular Crystals.- 4.7 Phonons in Metals.- 4.8 Problems.- 5. Anharmonicity.- 5.1 The Anharmonic Diatomic Molecule.- 5.2 The Anharmonic Linear Chain.- 5.3 The Anharmonic Three-Dimensional Crystal.- 5.4 The Self-Consistent Harmonic Approximation (SCHA).- 5.5 Response Function and Perturbation Theory of Phonon-Phonon Interactions.- 5.6 Problems.- A Periodicity of Eigenfrequencies and Atomic Displacements in Reciprocal Space.- B An Important Lattice Sum.- C Hamiltonian for the Diatomic Chain in Terms of Normal Coordinates.- D Commutator Relations for Normal Coordinates.- E The Occupation Number Representation.- F Restriction on Atomic Force Constants Which Follow from the Space Group Symmetry of the Crystal.- G Dynamical Matrix.- J Force Constants forCentral Forces.- K Evaluation of the Coulomb Matrix Using Ewald's Method.- L The Valence Force Model.- M The Saddle-Point Method.- N The Free Energy in the Harmonic or Quasiharmonic Approximation.- O The Self-Consistent Harmonic Approximation (SCHA).- P Expansion Coefficients of Anharmonic Terms.- Q Constants and Units.- General References.- References.