A note on the spectrum of the frequencies of a polar crystal lattice

The following considerations deal with those vibrations of a polar crystal lattice in which the ions are moving as a whole. The frequencies of these vibrations extend from the slow macroscopic elastic waves to the infra-red region, and can be calculated by the methods of classical mechanics. (Higher frequencies occurring in optical phenomena are connected with excitations of electrons. They are not considered here.) The oldest problem, which depends on a knowledge of the lattice frequency spectrum, is that of the calculation of specific heat; other such problems are those of the calculation of thermal expansion and other thermodynamical properties of crystals. Very rough approximations (Debye’s method) are generally used, and give quite reasonable results. But a close comparison of theoretical results with experimental observations shows that the method is not completely satisfactory (e. g. , Debye’s characteristic temperature, Θ, is not constant). The most important vibration in a binary polar lattice is that in which the vibrations of the two kinds of ions are in opposite phase—it gives rise to the infra-red absorption known as residual rays (reststrahlen). Recently the existence of secondary absorption maxima in the infra-red region has been discovered: their explanation depends on a knowledge of thewhole frequency spectrum of the lattice.