Contributions to the theory of the specific heat of crystals II—On the vibrational spectrum of cubical lattices and its application to the specific heat of crystals

Abstract

1—An investigation of the features of the vibrational spectrum of a cubical crystal has been made by means of a geometrical method described below; the two-dimensional case has been treated in detail, the three-dimensional case in outline. The main result has been the discovery of a number of maxima of the density of the vibrations. The significance of the results is discussed especially in relation to the Debye Theory of specific heats. 2—One-Dimensional Theory The density of the vibrations for a linear lattice containing two types of particles has been worked out in Part I. The density curves are shown in fig. 1, the mass difference causing the appearance of two additional maxima; it is as well to emphasize here that it is really the number of vibrations in the immediate neighbourhood of the maximum—what one might term the "weight" of the maximum—which is important, rather than the fact that the density becomes infinite. For instance, one obtains the first two maxima for very small mass differences, where one can hardly expect a perceptible difference in any physical property as compared with the case of equal masses.