The general treatment of the Gibbs–Thomson effect for a hollow nanosphere is presented. It allows for a vacancy composition profile across the nanoshell to be defined by a continuously decreasing function as well as by a continuous function with a minimum. The range for the controlling parameter of the vacancy motion within a binary alloy nanoshell is determined in terms of the phenomenological coefficients as well as the (measurable) tracer diffusion coefficients (D*A,D*B) of the atomic components. On the basis of a theoretical description and kinetic Monte Carlo simulations, it is demonstrated that for a hollow random binary alloy nanosphere with an equi-atomic (initially homogeneous) composition and neglecting the radial dependence of vacancy formation free energy, the controlling parameter of the shrinking rate in the limiting case D*A ≫ D*B can be estimated with reasonable accuracy as the geometric mean of the tracer diffusion coefficients of the atomic components.
Philosophical Magazine Vol. 88, Issue 10, p. 1525-1541