Effect of Diffusion Induced Driving Forces on Interdiffusion - Stress Development/Relaxation and Kinetics of Diffusion Processes
General description of the interplay between the Kirkendall shift (as a special way of relaxation) and diffusion induced driving forces in diffusion intermixing of binary systems is given. It is shown that, if the Kirkendall shift is negligible, a steady state Nernts-Planck regime is established with diffusion coefficient close to the slower diffusivity, independently of the type of the diffusion induced field and also independently whether this is a single field or a combination of different fields (e.g. stress field and extra chemical potential of non-equilibrium vacancies). Deviations from parabolic kinetics are expected only before or after this steady state stage. Using the results of our previous paper, on development and relaxation of diffusion induced stresses, it is illustrated that the setting of time of the Nernst-Planck regime is very short: intermixing on the scale of few tenths of nanometer is enough to reach it. It is also illustrated that this stage is realized even in the case of asymmetric interdiffusion (in one side of the diffusion zone the diffusion is orders of magnitude higher than in the other), when the stress distribution has a more complex form (having a sharp peak at the interface). Surprisingly the steady state is longer than it would be expected from the relaxation time of Newtonian flow: This is so because the composition profile is not static but changes fast in the timescale of the stress relaxation, and thus the stress re-develops continuously.
B.S. Bokstein, A.O. Rodin and B.B. Straumal
D. L. Beke et al., "Effect of Diffusion Induced Driving Forces on Interdiffusion - Stress Development/Relaxation and Kinetics of Diffusion Processes", Defect and Diffusion Forum, Vols. 309-310, pp. 113-120, 2011