Vibrational entropy of formation of Frenkel defects in alkaline earth fluorides

Abstract

The formation entropy of Frenkel defects in alkaline earth fluorides is calculated at high temperatures using the Green's function techniques. Two different methods, which we call the determinant method and the integration method, are employed for the purpose. Unlike the previous theoretical work on the determinant method, that used Green's functions scaled from their 0 K values in high temperature calculations, we computed both Green's functions and change in force constants exactly at the desired temperature. The effect of scaling is found to overestimate the entropy. The exact calculations yield small values of entropy (0.58 k B for CaF 2, 0.9 k B for SrF 2 and 3.0 k B for BaF 2) which are in fair agreement with the experimental data derived from conductivity studies. The large values of entropy obtained from specific heat data analysis seems to be due to the use of an inadequate defect model.