Interaction between the Kirkendall effect and the inverse Kirkendall effect in nanoscale particles

A simple kinetic model of the interaction between the Kirkendall effect and the inverse Kirkendall effect in hollow nano-shell formation by solid-state reaction is presented. The difference in vacancy concentrations at the inter-phase boundaries (and corresponding vacancy gradients) is taken into account as well as the curvature effect on the driving force of the reaction. A criterion for nano-shell formation is proposed.