In this chapter, we consider what happens when the lattice is no longer in equilibrium. In Chapter 8 we considered the motion of electrons in a crystal assuming that the ions were at rest for all times about their equilibrium positions. The presence of the ionic potential on the electrons results in energy-band formation: allowed ranges of energies for the electrons. However, this is not a physically realistic situation, since at nonzero lattice temperatures, the ions undergo some oscillation about their equilibrium positions. This additional motion, called lattice vibration, has important consequences on the behavior of the electrons. In Section 9.1 we consider lattice vibrations and the quanta of lattice vibrations, phonons. In the subsequent sections, we then examine how phonons influence the electronic properties of a crystal.

Lattice Vibrations and Phonons

From the discussion in Chapter 7, we found that the equilibrium configuration of the ions results in the minimum potential energy of the crystal. As the ions become more compressed, a repulsive force due to the nuclear-nuclear interaction acts to restore the system back to equilibrium. Similarly, as the lattice is stretched, the attractive force from the molecular bonds formed between adjacent ions acts again to restore equilibrium. Hence a lattice can be thought of as a collection of mass centers situated at definite positions and held together by the action of an elastic restoring force. The system has a definite minimum potential energy.