The free energy for diffusion in crystalline Si was calculated by combining a thermodynamic integration method with  ab initio  molecular dynamics simulations. The diffusion entropy was found to be negative.

V.Milman, M.C.Payne, V.Heine, R.J.Needs, J.S.Lin, M.H.Lee: Physical Review Letters, 1993, 70[19], 2928-31