Lattice Dynamics

Abstract

In this chapter we are concerned with the thermal properties and lattice dynamics of a crystalline solid. Under thermal equilibrium conditions, the mass centers or the nuclei of the atoms in a solid are not at rest but instead they vibrate with respect to their mean equilibrium position. In fact, many thermal properties of a solid are determined by the amplitude and the phase factor of these 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 closed-shell electrons. These electrons are held together primarily by the van der Waal 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 is constituted 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 vibrations on metals or semiconductors is that they are the main scattering centers which would limit the carrier mobility in these materials. In fact, the interaction between the electrons and the lattice vibrations is usually responsible for the temperature dependence of the resistivity and carrier mobility in an undoped semiconductor. Furthermore, such interactions also play an important role in the thermoelectric effects of metals and semiconductors.