Size-dependent concentrations of thermal vacancies in solid films.

Solid films are considered as typical model systems to study size effects on thermal vacancy concentration in nanomaterials. By combining the generalized Young-Laplace equation with the chemical potential of vacancies, a strict size-dependent thermodynamic model of vacancies, which includes the surface intrinsic elastic parameters of the eigenstress, Young's modulus and the geometric size of the solid films, was established. The vacancy concentration changes in the film with respect to the bulk value, depending on the geometric size and surface stress sign of the solid films. Atomistic simulations of Au and Pt films verified the developed thermodynamic model. These results provide physical insights into the size-dependent thermal vacancy concentration in nanomaterials.