Attractive or repulsive interactions in different structure types

Abstract

Abstract Homogeneous structures of elements A have identical self-coordination numbers of different shells like 4 12 12 of diamond or 8 6 12 of the bcc tungsten lattice (aristotype). AxBy compounds of these aristotypes are characterized by the numbers T1 T2 T3; y/x like 0 12 0; 1 or 0 6 12; 1 for ZnS or CsCl. The T1, T2, T3 values of all possible structures are at different locations of a three-dimensional polyhedron (structure map). Minimum or maximum T2 values can be correlated with attractive or repulsive A–A interactions. Homogeneous structures at y=x or homologous structures at y>x with identical T1, T2, T3 values of all A and all B are at corners of the T1, T2, T3 polyhedron. The potential of A+ and B− atoms is similar to the distribution of A=oil and B=water in ordered surfactants. Usually, the shape of the potential of A+ atoms depends on T1 values: tubes at T1=2, layers or a network of tubes at increased T1 values and isolated micelles at decreased values. Homogeneous or homologous structures with T1≥2 nearest neighbors like NaTl or CeCd2 are candidates for vacancy diffusion mechanisms. A fast interstitial mechanism can be achieved in blocked structures with vacant positions □ like Ca□F2 or CaTiO3□3. Homologous structures with y/x=2, 4 or 6 containing 3, 5 or 7 equivalent positions are candidates for spin glasses or relaxor ferroelectrics.