On the stability of different cubic lattices for the ionic compounds of AC‐type

The stability of cubic CsCl, NaCl, and ZnS type lattices at zero pressure is considered. Assuming completely ionic bonding and Huggins‐Mayer repulsion potential, the lowest‐energy criterion and the mechanical stability conditions are combined into a new stability criterion. The combined criterion is presented in a form of a diagram which is divided into the stability regions for the three cubic lattices, in terms of two parameters: the range of repulsive forces and the difference between ionic radii. Data on all alkali halides and eight compounds of zinc and cadmium are compared with theory. In 25 cases, out of 28 considered, the combined stability criterion correctly predicts the stable lattice. In the three cases where the theory fails the measured elastic constants disagree with the Cauchy relations to such an extent that the central force model is, presumably, inadequate. In addition, diagrams are presented in which the elastic constants of all three cubic structures are plotted as functions of the range of the repulsive forces and the difference in ionic sizes.