Stability of Crystals of II-VI and III-V Compounds in Terms of Three-Ion Interactions

By extending the theory developed in previous publications for the stability of rare-gas and alkali-halide crystals, it is shown that the stability of crystals of II-VI and III-V compounds whose ions are isoelectronic with rare-gas atoms is explained in terms of three-ion exchange interactions, without involving the concept of covalency. The analysis is based on a first- and second-order perturbation calculation, starting from complete ionicity in zeroth order of approximation. As in the case of rare-gas and alkali-halide crystals, Gaussian-type effective electron wave functions are used, taking into account the different size of anion and cation for each compound. It is shown that the theory accounts for all observed regularities on a quantitative basis. The occurrence of the sphalerite ($B3\mathrm{}$) and wurtzite ($B4\mathrm{}$) structures is explained; in addition, it is shown that the relative stability of these two structures is determined uniquely by three-ion interactions. By combining a Born-Mayer description for ionic solids with three-ion exchange interactions, general rules can be given which determine the relative stability of the four structures $B1\mathrm{}$ (sodium chloride), $B2\mathrm{}$ (cesium chloride), $B3\mathrm{}$ (sphalerite), and $B4\mathrm{}$ (wurtzite) observed with compounds of the type $\mathrm{RX}$.