Attractive or repulsive interactions in different structure types

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). A(x)B(y) compounds of these aristotypes are characterized by the numbers T, T-2 T-3; y/x like 0 12 0; 1 or 0 6 12; 1 for ZnS or CsCl. The T-1, T-2, T-3 values of all possible structures are at different locations of a three-dimensional polyhedron (structure map). Minimum or maximum T-2 values can be correlated with attractive or repulsive A-A interactions. Homogeneous structures at y = x or homologous structures at y > x with identical T-1, T-2, T-3 values of all A and all B are at corners of the T-1, T-2, T-3 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 T-1 values: tubes at T-1 = 2, layers or a network of tubes at increased T-1 values and isolated micelles at decreased values. Homogeneous or homologous structures with T-1 greater than or equal to 2 nearest neighbors like NaT1 or CeCd2 are candidates for vacancy diffusion mechanisms. A fast interstitial mechanism can be achieved in blocked structures with vacant positions square like CasquareF(2) or CaTiO(3)square(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. (C) 2003 Elsevier Ltd. All rights reserved