Statistics of Crystallographic Sites of Central Monatomic Entities

Abstract

Nonrigid properties of monatomic entities manifest themselves in the whole geometry of their environs. Until now we studied the statistics of these geometries using radial distributions of interatomic vectors. The classification of surroundings of a certain central monatomic entity M^Z+ can be based also on their symmetry. It has group — theoretical properties and it can be described by means of non — crystallographic symmetry point groups, of which there are infinitely many. There is, however, a finite amount of crystallographic point groups, viz. 2 one-dimensional, 10 two-dimensional and 32 three-dimensional point groups. The latest of them also describe the site symmetry of monatomic entity in the crystal structure and thus also the symmetry of its surroundings. Surroundings of monatomic entity means here, however, not only the near surroundings usually consisting of coordinating ligands, but the complete surroundings containing all other non coordinating entities of the structure. The symmetry of an ideal crystal structure — of discontinuum, is described by one of 230 space groups. The site symmetry of each monatomic entity of the structure thus has a certain connection with the relative positions of entities which may be classified based on the conception of lattice complexes.