| Summary: | 博士 === 國立中興大學 === 材料科學與工程學系所 === 97 === Monte Carlo (MC) simulation was used to investigate correlation factors of atoms (fA) diffusing via vacancies in the films possessing simple cubic (SC), body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal close packed (HCP) lattices. This topic has never been investigated before. The MC codes were firstly verified by calculating of the correlation factors fA for various types of lattices as fully periodic boundary conditions were employed. The obtained fA-values were consistent with those available in the literatures.
The aim of this work is to investigate the correlation factors of atom diffusion via vacancies in the film system, especially in the nanofilm regime, where the atom movement was constrained. A simple cubic lattice was selected as a model system for performing detail studies of the MC simulation. The film thickness (MZ) of the films was a prime input parameter in this study. Number of jumps per atom (NJPA) was varied to investigate the convergence of fA. Influences of jump frequency ratios of the atom-vacancy exchange on the film surface and in the interior of the films (Γs/Γi) on the correlation factors were also explored. Periodic boundary conditions were imposed in the directions (x and y) parallel the film surface while the reflective type boundary condition was applied in the film thickness (z-direction) to restrict atom-vacancy exchanges within the films. The correlation factors of atom diffusion of the films with BCC, FCC, and HCP lattices were also explored. Initially, the jump frequency ratio was set to be identical (Γs/Γi =1). The correlation factors show strong dependence of the film thickness, as well as jump frequency ratios in all investigated lattices. When the film thickness is sufficiently large, fA approaches reasonably to the values of the corresponding 3D bulk lattices. As the film thickness is considerably small, fA reaches to the values of the 2D lattices, as expected. The values of fA converge to 2/3 of 3D bulk lattices in the nanofilm regime at sufficiently large NJPA. Minimum plateau of the factors can be observed in the nanofilm regime for the SC and HCP lattices while cannot be found for BCC and FCC lattices. The minimum plateau is due to the confinement of atom diffusion in the nanofilms. The occurrence of the minimum is associated with the faction of the coordination number over the film surface. As Γs/Γi is sufficiently large all the values of fA converge to the limiting value of 2D lattices irrespective of NJPA in nanofilm regime,.
In addition to fA, correlation factors of vacancy diffusion (fv) in such films with SC and FCC structures were also investigated. The factors fv also show strong dependence of the film thickness MZ. The fv vs. MZ curves also exhibit a minimum plateau in the nanofilm regime. The components of fAx, fAy, and fAz, the corresponding fA in x, y, and z directions, were further analyzed to interpret the correlation effect in the films. The relation of the correlation factors fA and fv with the film thickness MZ in the nanofilm regime were further explored and discussed.
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