Theoretical constraints on the isotope effect for diffusion in minerals

Diffusive isotope effects are expected to be large for trace and minor cations that diffuse slowly relative to the major cations that occupy the same sites and diffuse by the same mechanism. Diffusive isotope effects are also expected to be large for elements that diffuse rapidly by a simple interstitial mechanism. In both of these cases, the correlation coefficient is similar to or equal to unity. Diffusive isotope effects are reduced when the diffusion process is correlated, as for (1) rapid diffusion of trace and minor cations by a vacancy mechanism, with a low migration barrier for the jump to a vacancy; (2) diffusion by an interstitialcy process, or a process involving interstitial-vacancy pairs; (3) diffusion in grain boundaries and dislocations, where both dimensional restrictions and non-uniformity of the structure enhance correlation. The correlation coefficient can be determined from independent experimental data on the jump frequencies involved in the diffusion process, and/or from theoretical calculations of the jump energies. Quantitative estimates of the isotope effect are made for several cations in periclase, olivine, magnetite and rutile.