Structure maps for crystal engineering

Abstract

The ordering of A and B atoms of compounds A_xB_y on the different positions of a lattice is analyzed by the numbers T₁ T₂ T₃; r of nearest, next-nearest and third neighbors of the same kind and the ratio r=y/x. The T₁, T₂ or T₁, T₂, T₃ structure maps containing all possible structures select the structures with maximum attractive or repulsive interactions which are stabilized by enthalpy. These structures at the borders of the structure maps are assembled from different structural units with different physical properties. The square net, body-centered cubic and diamond lattices containing surface structures, ordered alloys or semiconducting adamantanes are closely related. A periodic variation of crystal structures and interactions is suggested for the low-temperature modifications of the elements.