Lattice constants and energies of ionic microcrystals

Abstract

The equilibrium nearest neighbour separation (“lattice constant”) and lattice energy of cubic crystals having the NaCl structure and containing N³ ions have been investigated theoretically as a function of N. Particular attention has been given to the effects of uncertainties in the inter-ionic potential parameters upon the reliability of conclusions drawn from such studies. In addition to “perfect” microcrystals (in which all ions are assumed to occupy their normal lattice positions), surface relaxation has been considered by minimizing the energy with respect to independent displacements of positive and negative surface, edge and corner ions. Results are presented for NaCl, KCl, MgO and CaO.

It is concluded that the lattice constants may be predicted more reliably than the energies and that they decrease with decreasing crystal size. It is demonstrated by extrapolation that the calculations of surface structure and energies of the halide microcrystals are consistent with data for the infinite plane surface,¹ but edge and corner effects produce surface structures for microcrystals differing significantly from those of the plane surface. The assumption of centro-symmetric pair potentials is inaccurate for ions in the polarized surface; for the halides the seriousness of this assumption is difficult to assess but in the oxides it leads to a complete breakdown of the model when the polarization energy is included.