NEW MEASURES OF SIMILARITY FOR CRYSTAL STRUCTURES. E. Makovicky, Geological Institute, University of Copenhagen

T.Balic-Zunic, HALDOR TOPSOE A/S, Lyngby, Denmark

Modular description of complex crystal structures requires (a) definition of categories that are more general than those of isotypes, homeotypes, polytypes and homologues (polysomes), (b) definition of a measure of similarity of the (more or less distorted) derivative slabs/blocks to their archetype/aristotype.

Proposed classification categories higher than homologous series are the series of plesiotypes in which iso-/homeotypic or homologous structure portions combine with structural elements that differ from one member to another (they are called series of merotypes if these new elements are distinct types of interlayers).

Distortion of crystal structures can be quantified using the CN- dependent concept of "centroid" of the coordination polyhedron and the derived measures of cation excentricity and polyhedron sphericity (Balic-Zunic & Makovicky 1996). In addition, we shall define a parameter-free measure of distortion of the coordination polyhedron away from its ideal shape.This measure involves calculation of the ratio of the volume of (least-squares) circumscribed sphere to the volume of the coordination polyhedron under study and the comparison of this ratio to a similar ratio for the ideal polyhedron. This measure works unambiguously for tetrahedra, octahedra and all other cases for which the number of polyhedral faces is constant. Distortion measures for the studied structure (fragment) are then compared those observed for the archetype/aristotype. Balic-Zunic, T. & Makovicky, E. (1996): Acta Cryst. B52, 78-81.