A theoretical model of isotopic fractionation by thermal diffusion and its implementation on silicate melts

Abstract:

Huang et al (2010) found that Fe, Ca and Mg isotope fractionations of high-temperature silicate melts are only associated with the temperature gradients in thermal diffusion processes and are independent of compositions and mean temperatures ^[1]. Richter et al (2010) doubted that the existing data are sufficient to obtain such conclusion ^[2]. A few theoretical models have been proposed for explaining isotopic fractionations in these processes under high temperatures ^{[3, 4]}. However, molecular-level mechanisms and theoretical treatments of these processes are still under debating.

Here we provide a unified theory based on the local thermodynamic equilibrium treatment (LTE) of statistical mechanics for evaluating thermal isotopic fractionations under a wide range of temperatures. Under high temperatures, our theory however can be reasonably approximated to this equation:

where A and B are constants which are related to specific isotope systems and chemical compositions of silicate melts. If the thermal gradient is not very large and the mean temperature is high, the second part of the above equation can be safely neglected and obtain an extremely simple equation which is linearly depended on temperatures, agreeing with what Huang et al (2010) concluded. Based on this terse equation, we can not only easily provide isotope fractionation data for almost all kinds of isotope systems, but also can provide the mechanisms of isotope fractionation in thermal diffusion processes.

[1] Huang et al (2010) Nature 464, 396-400.

[2] Richter et al (2010) Nature 472, E1-E1.

[3] Dominguez et al (2011) Nature 473, 70-73.