Solid Matter at Low Temperatures

Abstract

The purpose of this chapter is to summarize the basic properties of solid materials at low temperatures [3.1-3.8] that are relevant for the design and construction of low-temperature apparatus and for performing experiments with such apparatus. These properties are, in particular, specific heat, thermal expansion, thermal conductivity and magnetic susceptibility. The latter property will also be discussed in later chapters in connection with magnetic cooling and thermometry. Quite generally one can say that the properties of materials can be better understood when the temperature is reduced further (except for some exotic cases like solid 3 He), because as the temperature is lowered the properties of materials become more and more "ideal" or "simpler"; they approach their theoretical models more closely. At low temperatures the number of excitations decreases and the vibrations of the atoms can be described in the harmonic approximation, which means that the potential V * as a function of distance r − r 0 from the equilibrium position r 0 of the atom can be written as V * (r − r 0) ∝ (r − r 0) 2. (3.1) In this approximation there is no thermal expansion because thermal expansion results from the anharmonic parts of the potential, for which we would have to introduce higher-order terms in the above equation. As a result, the thermal expansion coefficient becomes smaller and smaller, as we approach lower and lower temperatures (Sect. 3.2). A further advantage of low temperatures for the description of the properties of materials is the fact that various "parts" of a material can be treated independently. For example, in many cases one can consider the nuclear spin system (which is of great importance at ultralow temperatures) independently of the electrons and the lattice vibrations (Chap. 10). Of course, this is not true for all the "parts" of a material. For example, the temperature dependence of the electrical resistivity of a metal just results from the interaction of conduction electrons with the lattice. The fact that the specific heat and the thermal conductivity due to F. Pobell, Matter and Methods at Low Temperatures