Quantification of the deviations from closest sphere packings

In order to quantify the deviation of the anion arrangement in a crystal structure from a closest sphere packing two parameters are introduced: Δd_rel is the relative difference between the longest and the shortest distance to neighbouring atoms within a distorted closest-packed arrangement and s is the standard deviation of the normalized distances to all neighbouring atoms. The applicability of these parameters is compared with that of the distortion parameter U_cp introduced by Thompson & Downs (2001). Deviations from ideal sphere packings in pyroxenes, staurolite, kyanite, and olivine- and spinel-type structures are considered.