The Systematics of Crystal Polymorphic Transformations (Generalized on the Basis of Buerger’s Criteria)

Abstract—An extended (3 × 3) classification of polymorphic transformations is proposed with the zeroth coordination sphere added to spheres I and II according to Buerger. Thus, the transformable coordination sphere is 0 for an atom or ion, 1 for a coordination polyhedron, and 2 for the nearest surroundings of a coordination polyhedron. The other classification parameter is determined by Buerger’s energetic transformation barrier. As well as reconstructive and deformation transformations, transformations of intermediate types occur, which are characterized by disordering of structural units (atoms, molecules, and other atomic complexes). The electron transitions within an atom, the variation of atomic spin, and magnetic ordering of atoms in a crystal structure are considered as examples of polymorphic transformations with the variations in the zeroth coordination sphere. The disordering transformations are illustrated by substitution–jumps of structural units and their free or hindered rotation. The concept of “polymorphism” for chemical elements is developed.