Diffusion and Melting
The paper reviews the correlation between the processes of diffusion and melting. It is shown that the entropy of fusion and the melting temperature have a governing influence on the self-diffusion rates in solids. The relationship between self-diffusion coefficient (D) in solids and the melting parameters can be expressed as follows: D = fa2ν exp (κSm / R) exp (– κSmTm / RT) , where f is the correlation factor, a the lattice parameter, ν the vibration frequency, Sm the entropy of fusion, Tm the melting temperature in degree K, κ a constant and R, T have their usual meaning. The above equation has been derived on the basis that the free energy of activation for diffusion is directly proportional to the free energy of liquid phase. The well known relationships of the activation energy for self-diffusion with the melting point and enthalpy of fusion can be derived on the basis of this assumption. The constant κ is a group constant for any class or group of solids having identical physical and chemical properties. The validity of the above equation is demonstrated by the fact that when the self-diffusion coefficients are plotted as a function of homologous temperature, they scale inversely with the magnitude of the entropy of fusion. The hierarchy of self-diffusion rates within any group of solids is governed by the magnitude of the entropy of fusion and the melting temperature. The paper also discusses some interesting fall out of the close relationship between the diffusion and the melting parameters concerning (a) the diffusion in elemental anisotropic lattices, (b) anomalous diffusion behavior in bcc transition metals, lanthanides and actinides and (c) congruently melting compounds.
G. B. Kale, M. Sundararaman, G. K. Dey and G. P. Tiwari
G.P. Tiwari and R.S. Mehrotra, "Diffusion and Melting", Defect and Diffusion Forum, Vol. 279, pp. 23-37, 2008