The entropy of a point defect in an ionic crystal

Abstract

Two methods have been developed for the calculation of the vibrational entropy change associated with some designated defect processes (formation, association or migration) in an ionic crystal. One of these uses periodic boundary conditions and a very large unit cell called a ‘supercell’. The other approach is based on the Mott–Littleton strategy of dividing the crystal into an inner region containing usually ca. 100–250 ions and an outer region which comprises the remainder of the crystal. The vibrational entropy change is then approximated by calculating the vibrational frequencies for the inner region only in the initial and final defect states. In a variation of this crystallite method a transformation is made to the Green matrix representation. This has some practical advantage as well as that of greater elegance, but it is somewhat inconvenient to apply in practice. Conceptual and practical problems associated with each method are discussed and particular attention is given to the numerical consistency of the different approaches.