Deformation during interdiffusion

Abstract A general theory of stress and deformation during interdiffusion is presented which spans the gap between the Darken analysis of the Kirkendall effect and the recent treatment by Larche and Cahn of the interaction between stress and diffusion. Special consideration is given to the generation of internal stress and vacancy chemical potential, to the contribution of these potentials to the diffusion potentials, to the relaxation of these potentials via plastic deformation and vacancy creation/annihilation, and to convective transport due to deformation induced by diffusion. When the mobilities or the partial molal volumes of the components differ, the coupling of the relaxation equations for plastic strain and vacancy creation to the diffusion equations for the component densities can lead to a change in the rate-limiting step for interdiffusion as a function of the distance scale of the composition and stress profiles. The characteristic lengths at which these changes occur are determined by relations between the mobilities, the viscosity, and the rate constant for vacancy creation. When a relaxation process is rate-limiting, composition penetration profiles have an exponential (rather than error-function) form, and the integrated amount of material transported increases linearly with time (rather than as t 1 2 ).

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