Theoretical Calculation of Activation Free Energy for Self-Diffusion in Prototype Crystal

Abstract

We investigate temperature dependency of the activation free energy for the atomic diffusion in the fcc Lennrad-Jones system within the transition states theory based on the quasi-harmonic approximation. The activation free energy consists of the static activation energy and the vibrational free energy difference between the saddle point and the equilibrium state, and it is shown that both of them strongly depend on the system volume and the temperature. The temperature dependencies of both quantities exhibit opposite tendencies, i.e., the static activation energy decreases, while the free energy difference increases with increasing temperature. As a result, the activation free energy shows a weak temperature dependency. We discuss the effects of anharmonicity on the activation free energy by comparing the activation free energy obtained by the quasi-harmonic and harmonic approximations.