Schottky Energy Calculations for the Alkali Halides; Details and Results of Successive Approximations

Abstract

Results of theoretical determinations of the energy to form a Schottky defect, using a point-dipole model, are presented for alkali halides of the NaCl structure. The calculations were made under the following conditions: (1) Region I (in which the electrostatic and short-range interactions for each ion are treated in detail) contained 6, 18, 26, and 32 ions respectively. (2) Short-range parameters were determined from both the elastic and dielectric properties and the results compared. The "dielectric" parameters produced a better match between the dielectric properties of regions I and II (the dielectric continuum region) and showed better agreement with experimental values for the Schottky energy. (3) Derivations of detailed expressions and calculations were performed independently in two laboratories and cross-checked to eliminate errors.Region I displacements which are presented for the four cases indicate that an instability occurs in the 32-ion case for crystals in which the ions differ considerably in size. An analysis of this problem suggests that a modification of the Born repulsive energy expression is desirable when interaction between negative ions is appreciable.