The diffusion of supersaturated concentrations of vacancies in dilute f.c.c. alloys

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Abstract
In this paper the influence of substitutional solutes on the diffusion of non-equilibrium concentrations of vacancies in f.c.c. metals is considered for the case that isolated vacancies, isolated impurities and vacancy–impurity pairs are involved. The pairs are treated by approximate methods in which vacancies and solute atoms at greater separation than the nearest-neighbour distance are considered to be non-interacting. Detailed formulae are presented for the vacancy diffusion constant D eff taking into account (1) correlation between successive jumps of the bound vacancy and (2) the influence of gradients in the concentration of solute on the total flux of vacancies. For very dilute alloys (≤ 3 × 10−1 at. %) the correction on D eff due to the migration of the pairs can be adequately described by the ratio of the diffusion constants for the solute and for the solvent appropriate to equilibrium concentrations of vacancies, and can thus be obtained from tracer diffusion data. D eff is a composite quantity; the corresponding effective energy of motion depends on temperature and concentration of impurities. Theory shows that solutes which diffuse slower than the solvent do not affect the vacancy diffusion constant; faster moving solutes generally enhance the diffusion rate. Retardations are only to be expected under special experimental conditions. Also the proper pre-exponential factors are calculated; they can differ many orders of magnitude from the factors to be used in the case of pure solvent.