On the Vibrational Spectra of Crystals

In order to check the accuracy of distributions of characteristic vibration frequencies in crystals as calculated by approximate methods proposed by various workers, the frequency distribution is calculated rigorously for a lattice for which this is possible, viz., a two-dimensional square lattice with vibrations perpendicular to the lattice plane. The calculation is then repeated by the use of the various approximate methods, and comparisons are drawn. The effect of using any of the approximate distributions in place of the exact one in the calculation of thermodynamic functions is illustrated by a calculation of the specific heat of this same crystal. Finally, an extension to three dimensions is discussed.