Theoretical constraints on the isotope effect for diffusion in minerals

Abstract

Isotopes of the same element generally diffuse at slightly different rates within a mineral, due to the difference in their masses. The magnitude of the mass dependence of the diffusion coefficient depends on the product of the correlation coefficient f (representing the degree to which the diffusion process deviates from a random walk) and the coupling coefficient K (representing the degree to which the motion of an atom during a single jump is coupled to that of other nearby atoms). Whereas K has been found to vary over a relatively narrow range, f can vary over a wide range from ∼0 to 1.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.