Monte Carlo simulation of atom diffusion via vacancies in nanofilms with a model simple cubic lattice system

Monte Carlo simulation was employed to investigate correlation factors of atoms (f(A)) diffusing via vacancies in nanofilms possessing a simple cubic lattice that was selected as a model system. The correlation factors change significantly with varying the film thickness, as well as jump frequency ratios. When the film thickness is sufficiently large, f(A) approaches 0.6531, a limiting value for the 3D bulk lattice. As the film thickness is considerably small, f(A) converges to 0.4669, a limiting value for the 2D square lattice. A minimum of the factors, corresponding to 2/3 x f(A)(3D-SC) (= 0.4354), occurred in a specific nanofilm regime ranging from about 100 to 500 atomic layers, which was mainly due to confinement of atoms movement to nanofilms. Correlation factors of vacancy diffusion (f(v)) were also investigated and exhibited similar trend of the relations between the factors and the film thickness in a certain nanofilm regime. The relation between the correlation factors and the film thickness is analyzed and discussed.