Anharmonic Contributions to Specific Heat

Abstract

At temperatures appreciably above the Debye temperature, anharmonic parts of the lattice potential of a crystal make a contribution to the specific heat at constant volume that is nearly linear with the temperature, but of uncertain sign. Calculations on bcc and fcc crystals with a single atom per unit cell, based on central Lennard-Jones forces, show that the net effect is one of specific heat decreasing as temperature increases. The complicated sums involved can be simplified by use of a matrix inverse to the harmonic dynamical matrix, or by neglecting the dependence of phonon frequency on polarization. The latter method is used here. Forces between nearest and next-nearest neighbors are considered, and phonon dispersion is included approximately.