On the Effect of Nonequilibrium Vacancies on the Kinetics of Kirkendall Diffusion

Abstract

Vacancy diffusion models which predict parabolic diffusion-penetration kinetics implicitly assume that vacancy equilibrium is maintained everywhere. However, a nonequilibrium vacancy distribution is generally established by the pumping action of the chemical gradient in the Kirkendall effect. A more general diffusion model is, therefore, developed in which vacancies are not necessarily maintained in equilibrium. The behavior of the model is then investigated and nonparabolic kinetics are found. However, the kinetics approach those of the equilibrium model as either the vacancy lifetime approaches zero or as the diffusion time becomes very long. The applicability of the equilibrium model, therefore, depends upon the particular system and diffusion time. The results are compared with experiment, and it is concluded that nonparabolic effects are probably of little importance in usual face-centered-cubic metallic systems by the time diffusion measurements are made by conventional sectioning methods, i.e., when Dt>∼10−5 cm2.