Vacancy-wind effect in diffusion and deviations from thermodynamic equilibrium conditions

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Abstract
The vacancy-flow (or "wind") term which appears in kinetic treatments of the diffusion equations is discussed in terms of the vacancy concentrations which appear when a vacancy flow is distorted by an impurity. It is pointed out that this term arises from local distortions in the vacancy-concentration profile and not from any overall deviation of the material from equilibrium vacancy concentrations. Thus, the theory of Kirkaldy and Lane, which considers only net deviations from equilibrium averaged over an entire plane, does not include the vacancy-wind term. Several physical analogies help to describe the basic process. The vacancy-wind term can be large and introduces cross terms in the general thermodynamic equations.The vacancy-wind effect arises from motion of atoms other than the particular diffusing atom. For an accurate kinetic analysis, motion of the diffusing atom itself also must be considered. This motion produces a "mobile-impurity" effect and introduces an additional distortion in the local vacancy distribution. Equations including this effect are discussed. The close relationship between mobile-impurity effects and the correlation factor is shown. For self-diffusion, mobile-impurity and vacancy-wind effects exactly cancel in their influence on vacancy distributions.

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