Possible splitting of energy levels of atoms or ions in octahedral crystals due to sets of equivalent neighbouring defects

Divalent ions when doped in alkali halide single crystals will go in alkali sites and form associate pairs with neighbouring cation vacancies or other impurity defects. As there will be sets of equivalent positions for such associated pairs, their energy levels will be degenerate. The reducible representations of these associated pairs involving first to sixth nearest neighbours have been reduced to the corresponding irreducible representations of the point group O _h , for cases having rock-salt structure as well as for cases having cesium chloride structure. It is pointed out that if there is a rapid hopping of the vacancies or the defects in the crystal one may expect because of the possible interactions in the system, a splitting of the energy levels of the pairs as indicated by the different irreducible representations. It is stated that this kind of splitting may be expected also in systems in which associated magnetic pairs are formed by two neighbouring spins.