A PRIORI PREDICTION OF CRYSTAL STRUCTURE. I.D.Brown, Brockhouse Institute of Materials Research, McMaster University, Hamilton, Ontario, Canada L8S 4M1.

The structures of a number of inorganic solids can be predicted from a knowledge of only their chemical formula, by assuming that the solid will adopt the highest symmetry structure that is consistent with the chemical constraints. The atoms of the formula unit are used to find the highest symmetry bond graph (connectivity table) that gives the expected coordination numbers around each cation, and this graph is used to determine the highest possible point symmetries of the atoms. The space groups are then systematically searched to find those whose special positions match in number and symmetry the atoms in the formula unit. Further screening eliminates those space groups whose topology cannot accommodate the bond graph or whose geometry cannot accommodate the predicted bond lengths.

Bond graphs can be reliably constructed providing the atomic environments are regular and the total number of bonds is not too large. Special tables allow the high symmetry space groups to be rapidly screened for a match between the numbers and symmetries of the atoms and those of the special positions. The structure is determined if a successful candidate space group of cubic, tetragonal or trigonal symmetry exists, otherwise the structure has orthorhombic or lower symmetry and requires a different prediction technique. For some compounds it is only possible to generate a high symmetry structure by straining the bonds (e.g. perovskites). In these cases, the lowering of symmetry that relaxes the strains can often be predicted. The compounds NaCl, CsCl, ZnS, ZnO, CaF₂, TiO₂, SrTiO₃, MgSiO₃ and CaCrF₅ will be used to illustrate the method.