ALGORITHM FOR CONSTRUCTION DATA BANKS OF THE CRYSTAL STRUCTURES WITH THE GIVEN CHEMICAL FORMULAS. V.R.Khachaturov, Computing Center RAS, Moscov R.V.Galiulin, Institute of Crystallography, Moscow

The Crystallochemical Shubnikov's law on coefficients ratio in chemical formulas according to multiplicity of thier Wyckoff positions in space group, creates the opportunity to enumerate all topologically different crystal structures for any set of chemical elements. The optimization of the-se types by packing with the account of ionic radii of their atoms, gives all metric realisations.

Each space group has special spectrum of multiplicity appropriate to it Wyckoff positions. For example, multiplicity spectrum of Wyckoff positions a,b,c,d,e,f,g,h,i,j,k,l,m,n in space group Pm3m is following: 1,1,3,3,6,6,8,12,12,12,24,24, 24,48. If the ratio of coefficients in crystallo-chemical formula is 1:1:3 (that takes place in perovskite) then atoms can take only five different sets of Wyckoff positions: a,b,c; a,b,d; g,g,k; g,g,l; g,g,m. To this cases correspond 3 topological different structures (positions c and d also positions l and m geometrically not distinguish). The last two types is not known. In case of chemical formula the number of different topological types for a given ratio infinitely, since it can be realise by the set of any Wyckoff position with free parameters. But use of Khacaturov's ray-method (Preprint of Computing Center Russian Ac.Sci., Moscow,1987, 26 p.) in the combination with the Vernadsky law on everywheresity of chemical elements permits to allocate the convex area in the space of chemical formulas with final number of integer points (polyhedron of chemical formulas), that has allowed work out this algorithm.