Influence of Short-Range Three-Ion Interactions on Polymorphism and Elastic Constants of Simple Solids. I. Alkali Halide Crystals

A theoretical analysis is made of crystal stability and of low-temperature deviations from the Cauchy relations between elastic constants of ionic crystals with $\mathrm{AX}$ composition and with cubic or hexagonal structure. The Born-Mayer model is used as a basis, extended to take into account short-range three-ion interactions of exchange type. These interactions are evaluated in first and second orders of perturbation theory, adopting a Gaussian effective-electron approximation. In the stability analysis, four different crystal structures ($B1\mathrm{}$, $B2\mathrm{}$, $B3\mathrm{}$, and $B4\mathrm{}$,) are compared for each compound. In this paper, the results are reported for alkali halide crystals. Good agreement with experimental results is found. A following paper will deal with solid ionic compounds whose cations possess a complete outer $d$ shell of electrons.