The measurement of solute-vacancy interaction energies

Abstract

The extent to which solute atoms and vacancies interact is an important factor in determining the kinetics of diffusion processes in alloys and has attracted considerable interest from both a practical and a theoretical point of view over the last decade. Many attempts have been made to establish the values of the binding energy between vacancies and specific solutes in various solvents but the results have frequently been contradictory and relatively few published values are regarded as reliable. In this paper the various methods of experimentally determining the binding energy will be reviewed. The binding energy, Et“, between a single solute atom and a single vacancy is defined as the difference between the energy of formation of a vacancy in a site having only solvent atoms as nearest ,neighbours (assumed equal to that in the pure solvent, EF) and that in a site which has one solute atom in the first co-ordination shell. Strictly this defines a “first nearest neighbour binding energy” but it is generally assumed that interactions at greater distances are negligible and no attempt has been made either to calculate or measure any long range interaction. Binding will also occur between higher order groups of atoms and/or vacancies leading to other terms of the type Ek_ jv but we shall be mainly concerned with single vacancy-single solute interaction which is expected to predominate in dilute alloys; we shall thus use the symbol EB. When EB is positive it is energetically favourable for vacancies to form next to solute atoms, a tendency which is opposed by entropy considerations. The total defect concentration in an alloy is greater than in the pure solvent by an amount which depends upon EB and T, and the defects are partitioned between associated and unassociated sites. The proportion of associated vacancies increases as E0 increases and as temperature decreases. The experimental methods of measuring EB may be classified into two groups (a) those in which EB is derived from measurements of the vacancy concentration in alloys of known composition and (b) those which attempt to deduce EB from the measured effects of known concentrations of solute on vacancy mobility. The former is thus essentially a thermodynamic approach and the latter a kinetic one.