Reactive diffusion and stresses in spherical geometry

We present an analytical model to calculate development of stress and plastic relaxation during reactive diffusion in core shell nanostructures. The complex model can be considered as a Stephenson’s model [Acta Metal 1988;36:2663] on spherical geometry. Using our derivation, however, even the original equations for the planar case may be deduced in an easier way than in the original work by Stephenson. We apply the model to the reaction in spherical triple layers A/B/A and B/A/B, for which Schmitz et al. [Acta Mater 2009;57:2673] observed by atom probe tomography that growth rate depends on the stacking order. Comparison with experimental data proves that significant deviations from vacancy equilibrium appear which control the stability and reaction rate of the nanometric diffusion couples.