Stability of Crystals of Rare-Gas Atoms and Alkali Halides in Terms of Three-Body Interactions. I. Rare-Gas Crystals

Abstract

Several attempts have been undertaken in the literature to explain the observed stability of the face-centered-cubic (fcc) configuration for rare-gas crystals (except helium), which structure, according to calculations based on pair potentials, should be somewhat less stable than that of hexagonal closest packing (hcp). These attempts have failed or the results been found to be inconclusive. It is shown here how the fcc stability can be explained in terms of three-body exchange interactions between nearest neighbors in the crystals. On the basis of detailed results for neon atoms, the stability analysis may be based on an effective-electron model with Gaussian distribution of charge. No multipole expansions are invoked. The three-body interactions in first and second orders of perturbation theory follow simple symmetry principles, and their combined effect stabilizes the fcc over the hcp structure by a difference of up to four percent of the cohesive energy for the heavier atoms. Finally crystal stability is considered in its relation to total cohesive energy, and energy of vacancy formation, for the close-packed structures.