INORGANIC STRUCTURAL CHEMISTRY WITH CRYSTALLOGRAPHIC DATABASES. G.Bergerhoff and M.Berndt, University of Bonn, Germany

Application of a clearcut definition for the concept of isotypism to the crystallographic databases allows to find new and old relations between inorganic crystal structures. First of all data have to be standardized in order to get a uniform description of crystal structures. We started to apply STRUCTURE TIDY, the procedure of L.M.Gelato and E.Parth (J.appl.Cryst. 20 (1987) 139-143), to the ICSD (Inorganic Crystal Structure Database). But there are limits of this method if cell dimensions or coordinates are near specific values. In a second step, therefore, all structures within an isopointal group are compared with each other. The structural difference between structure (1) and structure (2) is now the degree [[Delta]] of isotypism, which is zero for complete coincidence (m = multiplicity).

[[Delta]]= (((2^1/2 * [[Delta]](c))+1) * [[Delta]](d)) - 1

where is [[Delta]](c) = ([[Sigma]] (m * ((x₁-x₂)² + (y₁-y₂)² + (z₁-z₂)²)^1/2)) / [[Sigma]] m

[[Delta]](d) = a₁² * b₂ * c₂ / a₂² * b₁ * c₁ where a₁> a₂, b_2^, > b₁, c₂ > c₁

[[Delta]](c) is the weighted mean difference of the coordinates of both structures, [[Delta]](d) combines the relation between the cell dimensions of both structures. [[Delta]] is calculated and reduced to the minimum value by selecting the best fitting set of equivalent coordinates and cell choice. The comparison by means of the [[Delta]] value can also be expanded beyond the limits of an isopointal group. In course of the indexing process of the database the minimal [[Delta]] value is stored as a retrieval parameter in the revised version SICS (Standardized Inorganic Crystal Structures) of the ICSD. The user now can choose any structure and ask for isotypes within a preselected [[Delta]] range. For the effectivity of this way of retrieval several examples are given. This algebraic procedure has the advantage not to be dependent on theories of bonding and connections. For a real impression of the structures compared we use DIAMOND, a graphics system easily used in connection with the databases. Further information you may find in WWW: http://www.rhrz.uni-bonn.de/~unc442/diamond.html