Characteristic thermodynamic parameters of F^- Frenkel defect formation in β-PbF₂

Abstract

A systematic calculation is made of all the characteristic thermodynamic parameters associated with the formation of a fluoride-ion vacancy, interstitial and Frenkel defect in β-PbF₂. The relaxations and the changes in force constants accompanying the formation of a defect are estimated by performing a lattice statics calculation. Using the method of Haridasan, Govindarajan, Nerenberg and Jacobs, the entropy of formation at constant volume is calculated and found to increase with increasing temperature in the quasi-harmonic approximation. A harmonic model is found to give a constant value of the entropy at all temperatures. Using the available values of the internal energy change, it is estimated that, in the range 300–1075 K, the entropy of formation of an F^- Frenkel defect at constant pressure increases from 6•4k_B to 8•2k_B, the Helmholtz free energy to form the defect at constant volume decreases smoothly, the enthalpy of formation at constant pressure increases from 1•317 to 1•42eV and the volume change accompanying the formation of a Frenkel defect increases to a value of 0•44 times the molar volume near melting point.