Comment on the paper ‘‘Theta series and magic numbers for diamond and certain ionic crystal structures’’ [J. Math. Phys. 2 8, 1653 (1987)]

Abstract

Sloane’s work [J. Math. Phys. 28, 1653 (1987)] is supplemented by published theorems that have been applied to the NaCl, CsCl, ZnS, and CaF2 structures to give formulas for the radii of all occupied shells (i.e., all radii for which Sn=0 are identified) and to give the species of atoms in each shell. In this paper the sort of information these theorems can provide is briefly reviewed and some predictions based on them are checked with the tabulated results of Sloane and others.