Dependencies of the parameters of vacancy formation and self-diffusion in a single-component crystal on temperature and pressure

Abstract

An analytical method for calculating the parameters of electroneutral vacancy formation and self-diffusion of atoms in a single-component crystal is proposed. The method is based on the four-parameter pairwise Mie–Lennard-Jones interatomic interaction potential. The method allows calculation of all activation process parameters, that is, 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 dependences of the activation process parameters for gold have been calculated from T = 10 K–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 dependences, with a weakly temperature-dependent enthalpy and a positive value of the activation process entropy. Good agreement has been obtained with estimated activation parameters for gold in the literature. It is shown that at T = 0 K the activation process parameters reach their minima: the Gibbs energy, enthalpy, and volume of the activation process all become zero, and the minimum of the activation process entropy lies in the negative region. The connection of the proposed calculation method with the Varotsos cBΩ model is discussed.