A new ab initio modeling scheme for the ion self-diffusion coefficient applied to the ε-Cu₃Sn phase of the Cu–Sn alloy

Abstract

We present a new modeling scheme for ion self-diffusion coefficient, which broadens the applicable scope of ab initio approach. The essential concepts of the scheme are 'domain division' and 'coarse graining' of the diffusion network based on the barrier energies predicted by the ab initio calculation. The scheme was applied to evaluate Cu ion self-diffusion coefficient in ε-Cu 3 Sn phase of Cu-Sn alloy, which is a typical system having long-range periodicity. The model constructed with the scheme successfully reproduces the experimental values in a wide temperature range.

Quantum annealing approach to Ionic Diffusion in Solid

“…Further consideration is required to take into account the fact that a pulling-back process itself is also subject to a pulling-back. Such multiple processes are finally convoluted into a form [20] as,…”

“…The macroscopic observable for the phenomena is the diffusion coefficients D. Though many ab initio electronic structure analyzes have been made on the phenomena, the direct knowledge obtained is just the microscopic 'easier paths' for the ion to be hopped to. The difficulty to connect the microscopic pictures to the macroscopic quantity is the counting of possiblem multiple scatterings of the coalescence between an ion and a vacancy [20]. The process is represented by the quantity f which is called as correlation factor [15,20].…”

“…The difficulty to connect the microscopic pictures to the macroscopic quantity is the counting of possiblem multiple scatterings of the coalescence between an ion and a vacancy [20]. The process is represented by the quantity f which is called as correlation factor [15,20]. The evaluation of f is then identified as a key stone to connect the microscopic process analysis and the evaluation of the practically useful macroscopic quantity [20].…”

“…The process is represented by the quantity f which is called as correlation factor [15,20]. The evaluation of f is then identified as a key stone to connect the microscopic process analysis and the evaluation of the practically useful macroscopic quantity [20]. For the evaluation, we have to identify the optimum routing for a vacancy to hop around on the lattice sites for a given set of anisotropic easiness for the possible hopping.…”

Application of canonical augmentation to the atomic substitution problem

“…If we consider vacancy-type defects as a form of substitution (by a vacancy), this covers another industrially important problem: understanding how defects affect materials properties. 2,3 This problem arises during the evaluation of sample qualities, damages, and degradation. Ab initio calculations based on density functional theory (DFT) are the most promising framework for such an assessment; they utilize the microscopic structure models of the substitutions.…”