On the equilibrium distribution of the impurity atoms in real crystals

Abstract

This work discusses the equilibrium distribution of impurity atoms among different sinks and the matrix of a real crystal. A simple formula, interpolating the McLean formula is obtained. Impurity segregation in crystals, containing two types of sinks (e.g. grain boundaries and dislocations) is investigated. Impurity concentration on a weakly- binding sink (grain boundary) as a function of the temperature, T, may be represented by a curve, the shape of which depends on the ratio of the average impurity concentration and the relative volume of a strongly-binding sink (dislocation) and on the ratio of the binding energies of an impurity atom on different sinks. There are four possible shapes of the curve. Three of them are not monotonic and show a maximum at T=Tmax. One of these three also exhibits a minimum at T=Tmin < Tmax. This may be used to diminish the content of a “harmful” impurity on the grain boundaries.