Correct enumeration of vibration frequencies in the Brillouin zone

Abstract

In order to calculate the vibration frequencies by Born's method the Brillouin zone is sub-divided into a number of points. The actual number of frequencies used by the workers for the calculation of Cv is, however, different from the number of points of the zone, resulting in a non-uniform distribution of points. It has been shown that this results in an incorrect value of the specific heat. As an example Hsieh's theoretical results have been used to recalculate the specific heat of silicon with a proper number of frequencies. The difference between these revised results and Hsieh's original calculations is found to be large.