Polymorphism of Elementary Substances and the Principle of Uniformity

Crystallography Reports Vol. 39. No. 3. 1994. pp. 402 - 408 Translated from Kristallografya, Vol. 39, No. 3. 1994. pp. 457-463 . Original Russian Text Copyright Ó 1994 by Blatov, Pol'kin, Serezhkin.

Polymorphism of Elementary Substances and the Principle of Uniformity

V.A.BIatov,V.A.Pol'kin, and V.N.Serezhkin

Samara State University, Samara, Russia

Received June 28, 1993; in final form, November 10, 1993

Abstract - The problem of quantitatively estimating the uniformity of crystalline structures is discussed. The root-mean-square error (G₃ of the quantizer corresponding to the lattice of gravity centers of a crystal's structural units was put forward as a criterion for the uniformity. The mentioned characteristic is shown to consider specific features of the lattice uniformity in a more detailed way than the known criteria. Analyzing structures of elementary systems shows that the uniformity changes under thermal phase transitions and depends on the position of an element in the Periodic Table. The value of G₃ was suggested to serve as a semiquantitative estimation of the ratio of contributions from directed and undirected interactions into the total crystal energy.