Chapter 7 demonstrates the application of statistical thermodynamics theory to crystalline solids. Because of its relevance to electron transport in metallic crystalline solids, the electron gas theory for metals is also described in this chapter. This chapter provides only an introduction to the microscale thermophysics of solids. Readers interested in more comprehensive treatments of solid state thermophysics should consult the references cited at the end of this chapter.

Monatomic Crystals

Our objective here is to use statistical thermodynamics tools to evaluate thermodynamic properties of solid crystals. Our first goal is to derive a relation for the partition function Q. In doing so, we will specifically consider the structure of a monatomic crystal. One approach is to model the crystal as a system of regularly spaced masses and springs as indicated schematically in Figure 7.1. The springs represent the interatomic forces that each atom experiences. The mean locations of the masses are at regularly spaced lattice points.

Actually, each atom sits in a potential well whose minimum is at a lattice point. The potential well for each atom is usually very steep. Each atom vibrates about its equilibrium position with a small amplitude, which suggests that we can work with a Taylor series representation of the potential valid near the equilibrium point.

Rather than working with the potential for a single atom, we will consider the potential for the crystal as a whole, which we will designate as Φ.