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: Delta d (sub rel) is the relative difference between the longest and shortest distance to neighbouring atoms within a distorted closest-packing 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 (sub cp) introduced by (sub ) Thompson & Downs (2001). Deviations from ideal sphere packing in pyroxenes, staurolite, kyanite and olivine- and spinel-type structures are considered.