The free energy for diffusion in crystalline silicon was calculated by combining a thermodynamic integration method with ab initio molecular dynamics simulations. The entropy of diffusion was found to be negative, and its magnitude increased with increasing atomic size of the diffusing species.

Free Energy and Entropy of Diffusion by ab initio Molecular Dynamics: Alkali Ions in Silicon. Milman, V., Payne, M.C., Heine, V., Needs, R.J., Lin, J.S., Lee, M.H.: Physical Review Letters, 1993, 70[19], 2928-31