Modeling of formation of binary-phase hollow nanospheres from metallic solid nanospheres

Spontaneous formation of binary-phase hollow nanospheres by reaction of a metallic nanosphere with a non-metallic component in the surrounding atmosphere is observed for many systems. The kinetic model describing this phenomenon is derived by application of the thermodynamic extremal principle. The necessary condition of formation of the binary-phase hollow nanospheres is that the diffusion coefficient of the metallic component in the binary phase is higher than that of the non-metallic component (Kirkendall effect occurs in the correct direction). The model predictions of the time to formation of the binary-phase hollow nanospheres agree with the experimental observations.