Calculation Features from First Principles of the Diffusion Activation Energy for the Systems Ag–Mo and Mo–Ag

Abstract

Background. We investigated diffusion coefficient parameters for a vacancy diffusion mechanism in the presence of two point defects (vacancies and impurity atoms), taking into account the temperature factor, and conducted by means of computer simulations based on density functional theory (DFT). Objective. Development of theoretical concepts of the mechanisms of diffusion at the atomic and subatomic levels, including the temperature dependence of the vacancy formation energy, the migration energy, and the diffusion activation energy in the metallic systems Ag – Mo and Mo – Ag. Methods. The calculations were performed in VASP, using the full-potential projector augmented wave (PAW) method, and a PBE-sol generalized gradient approximation . Optimization of the structure geometry was carried out by relaxation of the ions' positions in a super cell made by 64 atoms. A specific feature of the calculations was the application of experimental values for the lattice parameters of the core element matrix at relevant temperatures. Results. The peculiarities of calculating the vacancy formation energy, the migration energy, and the diffusion activation energy from first principles are presented. It is shown that thermal excitation has a significant impact on the vacancy formation energy, the migration energy, and the diffusion activation energy at high temperatures. Also, the possibility of a compensation effect has been found, namely, the simultaneous changing of the various free energy contributions to the energy of vacancy formation in metallic systems Ag – Mo and Mo – Ag. Evaluation of the contributions of free vibration energy, electronic thermal excitation energy, and energy of pair interactions depending on temperature helps to clarify the picture of the effect of material’s thermal expansion. Conclusions. The estimated vacancy formation energy, the migration energy, and the diffusion activation energy are in good agreement with previously reported theoretical and experimental data. The presence of the mutual compensation of different contributions to the vacancy formation energy in the metallic complex systems has been confirmed. Confirming the existence and the characteristics of a compensation effect for the system Mo – Ag requires more research.