Low-Temperature Specific Heat

Abstract

Numerous discussions of lattice specific heat are available in the literature; for descriptive introductory summaries, the reader is directed to standard texts, such as that of Kittel [Kit68], and a cryogenic monograph in this series by Gopal [Gop66]. In developing the Debye equations, it is usual to begin by calculating the thermal energy associated with the vibrations of N atoms of a solid. The resulting quantity is conveniently referred to as the “heat capacity” of the assembly. The Debye calculation takes place implicitly at constant volume, and leads accordingly to the constant-volume heat capacity, C _v , which is, therefore, associated with some fixed volume, V, of material. If the solid is heated at constant pressure it generally expands, and in so doing absorbs some extra energy. The difference between the associated constant-pressure heat capacity, C _p , and C _v at some temperature T, is C _p — C _v = TVβ ²_v K, where β _v is the volume expansion coefficient and K is the bulk modulus. Unless lattice expansion and its consequences are of special interest, as in Chapter 9, the difference C _p – C _v may be neglected, particularly below room temperature [Kit68, p. 165], and the bare symbol, C, may be assigned to the general heat capacity. In what follows that symbol will also be assigned to the molar heat capacity or the molar specific heat, while the superscripts v and g will designate specific heats per unit volume (cm³) and per gram, respectively. A subscript g may be employed to indicate lattice¹ specific heat if a distinction between it and the electronic specific heat component of metals (see below) is to be made.