Entropy of formation of a Frenkel defect in CaF2: A Green-function calculation

The results on the dynamics associated with an anion interstitial and with a vacancy at an anion site, discussed in our earlier work, are employed in this paper to compute the entropy of formation of a Frenkel defect in Ca${\mathrm{F}}_2$. The interstitial and the vacancy are assumed to be far apart and hence each case is discussed separately. The symmetry coordinates of the $F_{1u}$ representation for the interstitial and of the $F_2$ representation for the vacancy are chosen so as to decouple the degrees of freedom of this defect from the defect space. Then both the methods of Govindarajan et al. and of Mahanty and Sachdev are applied to these two defect systems to calculate the entropy of formation of an isolated interstitital and of an isolated vacancy. The entropy of formation of anion Frenkel defect in Ca${\mathrm{F}}_2$ computed from both methods agrees well with recent experimental results.