Lattice Dynamics and Phase Transitions

Abstract

Vibrations of atoms about their equilibrium position is one of the fundamental properties of the crystal lattice. The set of phenomena associated with such vibrations and describing their laws is called lattice dynamics. Lattice dynamics lies at the basis of the theory of thermal properties of crystals and the present- day concepts of the electrical and magnetic properties of crystals, light scattering in them, etc. For instance, the anharmonicity of atomic vibrations in the crystal lattice determines the ratio between the heat capacity, compressibility, and the coefficient of linear thermal expansion (the Gruneisen ratio). The concept of the thermal motion of atoms and the vibration anharmonicity is the foundation of the modern theory of phase transitions in crystals (ferroelectric ones, in partic- ular, see [4.1]). Here we shall only state the principal conclusions of the theory of crystal lattice dynamics and consider, on their basis, the heat capacity, thermal conductivity, and thermal expansion of crystals.