Kirkendall effect analysis

We use the term Kirkendall effect to include both Kirkendall shift and Kirkendall voiding (or Frenkel voiding). We present a detailed analysis of the interaction of the Kirkendall effect and the inverse Kirkendall effect in nanoscale... 

In diffusional processes, such as the classic Kirkendall effect of interdiffusion in a bulk diffusion couple of A and B, the atomic flux of A is not equal to the opposite flux of B. If we assume that A diffuses into B faster than B diffuses into A, we might expect that there will be a compressive stress in B, since there are more A atoms diffusing into it than B atoms diffusing out of it. However, in Darken s analysis of interdiffusion, there is no stress generated in either A or B. But Darken has made a key assumption that vacancy concentration is in equilibrium everywhere in the sample. To achieve vacancy equilibrium, we must assume that lattice sites can be created and/or annihilated in both A and B, as needed. Hence, provided that the lattice sites in B can be added to accommodate the incoming A atoms, there is no stress. The addition of a large number of lattice sites implies an increase in lattice planes if we assume that the mechanism of vacancy creation and/or annihilation is by dislocation climb mechanism. It further implies that lattice planes can migrate. 

L. Hdglund, and J. Agren, J., Analysis of the Kirkendall effect, marker migration and pore foimation,... 

Simplified Analysis of the Competition Between Kirkendall-Driven and Curvature-Driven Effects... 

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