The isotope effect for Mg-Fe interdiffusion in olivine and its dependence on crystal orientation, composition and temperature

Abstract

Isotopic fractionation associated with diffusion in crystals is the most reliable means of understanding the origin of mineral zoning in igneous and metamorphic rocks. We have experimentally determined the relative diffusivities of iron isotopes in olivine as a function of crystallographic orientation, composition, and temperature. For two isotopes i and j of an element, the isotope effect for diffusion is parameterized as D<inf>i</inf>/D<inf>j</inf> = (m<inf>j</inf>/m<inf>i</inf>)^β, where β is a dimensionless parameter, and D and m stand for diffusivity and mass, respectively. A series of single crystal diffusion couple experiments were conducted at an oxygen fugacity of QFM – 1.5 at temperatures of 1200, 1300, and 1400 °C. For the Fo<inf>83.4</inf>-Fo<inf>88.8</inf> composition pair, β<inf>Fe</inf> is isotropic and a value of 0.16 ± 0.09 can be used to describe diffusion along all major crystallographic axes in olivine. Based on our experiments and previously reported coupled Mg-Fe isotopic data, we also estimate β<inf>Mg</inf> = 0.09 ± 0.05 for this range of olivine composition. For the Fo<inf>88.8</inf>-Fo<inf>100</inf> composition pair, β<inf>Fe</inf> becomes anisotropic with β<inf>Fe [100]</inf> = 0.11 ± 0.03, β<inf>Fe [010]</inf> = 0.14 ± 0.03 (both within error of the value measured for the Fo<inf>83.4</inf>-Fo<inf>88.8</inf> pair), and β<inf>Fe [001]</inf> = 0.03 ± 0.03. For Fo# between 83.4 and 100, β<inf>Fe [100]</inf> and β<inf>Fe [010]</inf> are thus independent of composition. The reason why β<inf>Fe [001]</inf> transitions from ∼0.16 to ∼0.03 close to the Mg-endmember is unclear. Over the temperature range studied, a dependence of β<inf>Fe</inf> on temperature was not resolved. General analytical expressions are introduced to calculate isotopic fractionation as a function of distance, time, β and the concentration contrast between the diffusing media for spherical, cylindrical, and planar geometries.