An analytic expression approximating the Debye heat capacity function

Abstract

It is important to have analytic expressions for critical functions in the equations of state of materials. The Debye model has been very successful in approximating the thermal energy properties of a variety of solids, but is nonanalytic. Existing approximations suffer from various shortcomings, the most common being lack of applicability over some temperature range. A new analytic and integrable functional form that closely approximates the Debye model for the heat capacity is presented. This form, based on the mean of two Einstein heat capacity functions with a low temperature correction, exhibits deviations from the Debye model smaller than typical experimental scatter in heat capacity data.