Relations and models on diffusivity

The compensation law is a very rough empirical correlation between the activation energy and the pre-exponential factor of diffusion. Winchell (1969) showed that the logarithm of the pre-exponential factor (A) is roughly linear to the activation energy ( )  

Therefore, the compensation law is equivalent to the statement that in a In D versus 1/T plot, all lines for various species intersect at one common point. 

In addition to applications to diffusion in the same phase, the compensation law has also been applied to the diffusion of a given species in many phases (Bejina and Jaoul, 1997). This is equivalent to the assumption that at some critical temperature, the diffusion coefficients of the species in all phases would be the same. The relation again is expected to be very approximate. 

Not many practical uses have been found for the compensation law because it is not accurate enough. One potential use of the compensation law is that if one knows the diffusivity at one single temperature, then both the pre-exponential factor A and the activation energy E may be estimated. That is, the temperature dependence of the diffusivity may be inferred. In practice, however, because the compensation law itself is not accurate, the uncertainty of the approach is very large (intolerable in geologic applications). Hence, the approach is not recommended. 

Diffusion is due to random motion of particles. Conduction is due to motion of ions under an electric field. Ionic diffusivity and conductivity are hence related. Under an electric field, the velocity of an ion is proportional to the electric 

---