Lattice Dynamics

Abstract

This chapter presents the thermal properties and lattice dynamics of solids. In thermal equilibrium, the mass centers or the nuclei of the atoms in a solid are not at rest, but instead they vibrate with respect to their equilibrium positions. In fact, many thermal properties of solids are determined by the amplitude and phase factor of the atomic vibrations. For example, the specific heat of an insulator is due entirely to its lattice vibrations. Solid argon, which is perhaps the simplest solid of all, consists of a regular array of neutral atoms with tightly bound closedshell electrons. These electrons are held together primarily by the van der Waals force, and hence interact only with their nearest-neighbor atoms. The physical properties of such a solid are due entirely to the thermal vibrations of its atoms with respect to their equilibrium positions. Therefore, the specific heat for such a solid results entirely from its lattice vibrations. On the other hand, the specific heat for metals is dominated by the lattice-specific heat at high temperatures, and by the electronic specific heat at very low temperatures. The most important effect of the lattice vibration on metals or intrinsic semiconductors is that it is the main scattering source that limits the carrier mobility in these materials. In fact, the interaction between the electrons and lattice vibrations is usually responsible for the temperature dependence of the resistivity and carrier mobility in metals or lightly doped semiconductors. Furthermore, such interactions may also play an important role in the thermoelectric effects of metals and semiconductors.