Changing the Parameters of Vacancy Formation and Self-Diffusion in a Crystal with Temperature and Pressure

Abstract

An analytical method for calculating the parameters of the electroneutral vacancies formation and self-diffusion of atoms in a single-component crystal is proposed. The method is based on the 4-parameters pairwise Mie--Lennard-Jones interatomic interaction potential. The method allows calculating all the activation processes parameters: Gibbs energy, enthalpy, entropy and volume for both the vacancy formation process and the self-diffusion process. The method is applicable at any pressure (P) and temperature (T). The temperature dependencies of the activation processes parameters for gold are calculated from T=10 K to 1330 K along two isobars P=0 and 24 GPa. It is shown that at low temperatures, due to quantum regularities, activation parameters strongly depend on temperature, and the entropy of activation processes in this region has a negative value. In the high temperature region, the probability of vacancy formation and the self-diffusion coefficient pass into classical Arrhenius dependencies with a weakly temperature-dependent enthalpy and with a positive value of the activation process entropy. Good agreements were obtained with the estimates of activation parameters for gold known from the literature. The values of activation parameters at T=0 K were discussed. Keywords: vacancy, self-diffusion, interatomic potential, gold, state equation, thermal expansion.