The Bakerian lecture - The anomalous specific heats of crystals, with special reference to the contribution of molecular rotations

Abstract

The primary purpose of this lecture is to describe a tentative theory, which I have recently tried to improve, of the contribution that molecular rotations may make to the specific heats and in general to the equilibrium properties of crystals. The occasion of the Bakerian lecture, however, seems a fitting one for a general survey rather than for the detailed exposition of a particular theory, which at best is still far from a final state. I shall spend most of my time therefore in such a general survey of the theory of the specific heats of crystalline solids. Strictly speaking, the theory is not so much a theory of the specific heat as a theoretical construction of the free-energy function of the solid in terms of an assumed model for the atoms or molecules constituting its crystal lattice. From this free energy, the total energy content, specific heat, equation of state and other related equilibrium properties of the solid can of course be deduced by differentiation, and specific heats provide the most striking property easily submitted to comparison with experiment. When we set out to construct theoretical free-energy functions in this way, using the methods of statistical mechanics, the function that we actually construct is the partition function, the quantum mechanical generalization of Gibb’s phase integral ∫ e -E/ k T d Ω over the phase space of solid or other system. The free energy is merely - k T log (partition function). My first object is therefore to describe the present state of the theory of the partition functions of solids and their success or failure in describing the observed facts. This will lead us on naturally to the discussion of various types of anomaly in the specific heat curves not provided for by the simpler versions of the theory, and so to a description of attempts that have been made to explain them, among which the theory of molecular rotations in solids finds its natural place.