A perturbative expression for the self diffusion coefficient was derived by assuming that the particles were executing anharmonic vibrations around the sites with local potential minima and jump to neighbouring sites after a certain waiting time. The derived expression was a natural extension of the expression obtained by Zwanzig that assumed harmonic oscillations. The relationship between the low-frequency oscillation and the deviation from the harmonic behaviour was also shown. It was shown that the self-diffusion coefficient increased with the magnitude of the anharmonicity. In other words, an increase in anharmonicity resulted in a decrease in the activation energy. This finding could have implications in diverse topics related to atomic transport, such as cases where the interatomic potential was soft or in cases where the material was disordered. In particular, it was noted that the model captured the essence of ion transport in superionic conductors. For instance, the derived expression showed clearly that the low frequency oscillation was related to the deviations from the harmonic behaviour. Low-frequency oscillation was one of the phenomena observed in many superionic conductors.

The Effect of the Anharmonicity in a Perturbation Estimate of the Self-Diffusion Coefficient. T.Indoh, M.Aniya: Physics Research International, 2011, 645264