# Simulations of the Kirkendall-Effect-Induced Deformation of Thermodynamically Ideal Binary Diffusion Couples with General Geometries

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## Abstract

The Kirkendall effect stems from the imbalance of atomic diffusion fluxes in a crystalline solid. Vacancy generation and annihilation, which compensate for the unbalanced fluxes, result in deformation that is experimentally observed as the motion of fiducial markers in a diffusion couple that can be approximated as a one-dimensional system. In multiple dimensions, such deformation occurs along both the directions parallel to and normal to the primary diffusion direction. In this article, we present a model that couples unbalanced interdiffusion and the resulting plastic deformation. One- and two-dimensional simulations are conducted with the analytically calculated diffusion coefficients of a thermodynamically ideal random alloy; the result shows that the ratio of the diffusion fluxes of the atomic species equals the ratio of atomic hop frequencies, which leads to the final volume ratio also given approximately by the hop frequency ratio if the initial volume ratio is equal. Moreover, the result also demonstrates that the conventional interdiffusion model fails to describe the Kirkendall void growth dynamics. For numerical implementation, we reformulate the diffusion equation to the smoothed boundary form and solve it within the deforming body governed by steady-state Navier-Stokes equation. This work demonstrates that the presented method can be a useful tool for studying Kirkendall-effect-induced deformation.

## Keywords

Diffusion Couple Kirkendall Void Kirkendall Effect Bottom Slab Equilibrium Mole Fraction## Notes

### Acknowledgments

H.C.Y. and K.T. thank for the support from NSF under Grant No. 0907030. K.T. acknowledges the support of NSF under Grant No. 0746424.

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