FREE-ENERGY OF FORMATION OF DEFECTS IN POLAR SOLIDS

A more exact method than hitherto available, based on lattice statics and quasi-harmonic lattice dynamics, is presented for the direct minim isation of the free energies of periodic solids with very large unit c ells. This is achieved via the calculation of analytic derivatives of the vibrational frequencies with respect to all external and internal variables. The method, together with large defective supercells, is us ed to calculate the free energies of defects in MgO as a function of t emperature. A major advantage of the supercell approach is that consta nt-volume and constant-pressure quantities are calculated independentl y. This allows a critical appraisal of the common approximations used for many years: (i) to convert constant-volume defect parameters to co nstant-pressure and (ii) to justify the use of static calculations at constant volume in the interpretation of experimental data obtained at constant pressure and at high temperatures. Defect enthalpies show on ly a small variation with temperature and differ by ca. 2% from the in ternal energy change in the static limit. An assessment is also made o f the commonly used ZSISA approximation, in which the free energy at e ach temperature is minimised with respect to external strains only, si multaneously determining the internal strains by minimising the static lattice energy.