New Measure of Distortion for Coordination Polyhedra

A new global measure of distortion for coordination polyhedra is proposed, based on a comparison of the ratios V_s(circumscribed sphere)/V_p(polyhedron) calculated, respectively, for the real and ideal polyhedra of the same number of coordinated atoms which have the same circumscribed sphere. This formula can be simplified to υ (%) = 100[V_i(ideal) − V_r(real)]/V_i, where V_i and V_r are the volumes of the above-defined polyhedra. The global distortion can be combined with other polyhedral characteristics, e.g. with the eccentricity of the central atom in the polyhedron or with the degree of sphericity of the coordination sphere [Balić Zõunić & Makovicky (1996). Acta Cryst. B52, 78–81].V_s/V_p ratios are given for a number of ideal polyhedra, including several types of trigonal coordination prisms, with the aim of facilitating the distortion calculations. The application examples included in the paper are: complex sulfides based on PbS and SnS archetypes, coordination polyhedra of large cations in feldspars, a phase transformation in a monoclinic amphibole and the subdivision of structures isopointal to ilmenite.