Lattice Sum Evaluations of Ruby Spectral Parameters

This paper presents the results of an attempt to collate many of the known spectroscopic properties of ruby in the strong field coupling scheme within the framework of an ionic model. The Tanabe-Sugano theory extended to odd symmetry crystal fields is used in this analysis. The appropriate Madelung and higher order potentials are computed for both a point-ion and a point-dipolar lattice. The radius of convergence of these sums found with our procedure is much smaller than those reported by McClure and others. The lattice potentials derived from a particular model of the ${\mathrm{Cr}}^{3+}$ local environment give a reasonable fit to many of the measurable spectroscopic parameters. In addition to the conventional optical splittings, these include optical intensities, pressure and "electric field" effects. The interpretation of the ${\mathrm{Cr}}^{53}$ nuclear electric quadrupole moment is shown to be sensitive to the details of the ${\mathrm{Cr}}^{3+}$ environment. Some results are given for other ions and also for ${\mathrm{Al}}^{3+}$ in corundum.