Clustering in solid solutions

Abstract

For sometime it has been recognized that the usual approximation of a random distribution of two or more kinds of atoms among the equivalent lattice sites of a simple solid solution at equilibrium is often not correct though for many theoretical purposes With improvement of experimental techniques 1) and improved interpretation of data it became apparent that a deviation from randomness is a rule rather than an exception. Even in systems where long range order is not observed short range order has been frequently established 2). As long as all the atoms in a solid solution can be considered as having the same effective size and, if the binding can be represented as an interaction between nearest neighbors, then the usual theory of long and short range order as developed by B r a g g and W i 1l i a m s 3), B e t h e * ) and P e i e r l s ~ ) is in most instances quite sufficient. In that approximation the temperature and the interaction between neighbors determines the probability of the occurrence of a given concentration fluctuation or of a certain degree of order. These can be easily computed. The present paper, which is a part of a general s tudy of fluctuations in solid solutions, is concerned with the case of binary solid solutions which can be described in terms of interactions between nearest neighbors but in which the two kinds of atoms have different effective ionic radii. It is clear that the strains surrounding asolute atom or strains within and near a group of solute atoms will affect appreciably the energy of the configuration and thus the probability of its occurrence. M o t t and N a b a r r o 6) have shown that a flat disc-like shape of a precipitate produces less strain energy in the surrounding matrix, assumed to be continuous, than a spherical or needle-like precipitate. In this paper we shall deal with small clus-