Crystallography Reports, Vol. 46, No. 1, 2001, pp. 1–3. Translated from Kristallografiya, Vol. 46, No. 1, 2001, pp. 7–9. Original Russian Text Copyright © 2001 by Budnikov, Pitirimov, Soldatov, Chuprunov. CRYSTALLOGRAPHIC SYMMETRY Information Patterns of Point Groups of Symmetry N. S. Budnikov, A. V. Pitirimov, E. A. Soldatov, and E. V. Chuprunov Nizhni Novgorod State University, Nizhni Novgorod, Russia e-mail:
[email protected] Received March 22, 1999 Abstract—An algorithm for calculating information entropy of regular point systems in crystallographic point groups has been described. The information patterns visualizing the information properties of the groups are described. © 2001 MAIK “Nauka/Interperiodica”. Traditionally, the structures of various materials are system of weighted points [2, 3]: described by geometric images with the aid of various (),, (),, polyhedra, spheres, sets of points, etc. Such a descrip- SfR=–∑ ij Zi Zj ln fRij Zi Zj .(2) tion makes the basis of the geometric method for repre- ij, senting the atomic structures of condensed media. Here, f(Rij, Zi, Zj) = fij is a nonnegative monotonic func- However, the geometric description is far from being tion of interpoint distances and point weights. The val- complete and can be used as a basis for studying the ues of this function can be interpreted as the probabili- relation between the structures of materials and their ties of certain (generally speaking, quite abstract) tran- physical properties only in some cases. In most sitions between the points i and j. The concrete form of instances, the geometric characteristics of atomic struc- this function depends on the physics of the problem to tures should be combined with the energy, entropy, and be solved.