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

When a homogeneous system is placed under a temperature gradient for a sufficient time, both its chemical and isotopic compositions will differentiate between the hot and the cold ends. Molecular-level knowledge of this process is of critical importance to understanding concentration and isotopic distributions in many geologic systems. Recently, different theoretical models have been proposed to explain isotopic fractionations observed in laboratory experiments under high temperatures, but there is still a lot of debating. Here we provide a unified theory based on local thermodynamic equilibrium approach to evaluating thermal isotope fractionations under a wide range of temperatures. For high temperature silicate melts, our theory offers a simple equation for calculating isotopic fractionations of all isotope systems: ΔXM = −(3/2)ln(m∗/m)ln(T/T0). The results from this equation agree with observed data for the most of network modifiers and resolve existing discrepancies among different interpretations. It can also explain O and Si isotope results if consider their diffusing species not as a single ion but a larger unit (e.g., [SiO3] or [SiO4]). The simplicity of the equation support a classical mechanical collision model for high-temperature diffusing particles in silica melts.