Kinetic and equilibrium Ca isotope effects in high-T rocks and minerals

Calcium isotope data (δ⁴⁴Ca, μ^42/44Ca, and μ^48/44Ca)are reported for high-temperature metamorphic rocks and minerals, and compared with density-functional theory (DFT)estimates of equilibrium Ca isotope fractionation factors for plagioclase, garnet, clinopyroxene, orthopyroxene, olivine, and apatite. The data and calculations are used to evaluate equilibrium and kinetic fractionation effects that apply to high-temperature metamorphism, where extended residence at high temperature should promote equilibration, but where centimeter-to-meter scale Ca transport could produce diffusive kinetic effects. At upper-granulite facies conditions (T ≥ ∼900 °C), DFT-predicted equilibrium fractionations between minerals are ≤0.8‰, decreasing to ca. 0.6‰ at 1100 °C. We find much larger δ⁴⁴Ca variations in both whole-rock samples (range of ∼4‰)and individual minerals (range of ∼8‰), and large variations in the Ca isotope fractionation between mineral pairs (e.g. Δ⁴⁴Ca_grt-plag from −1.5 to +1.5‰). Deviations from equilibrium tend to be larger in concert with indications of higher temperature, such as increasing whole-rock Mg#, plagioclase anorthite content, orthopyroxene Ca/Mg, and garnet Mg#. These large variations are inferred to be due to intragranular or grain-boundary diffusion during metamorphism, as this is the only mechanism that can produce such large isotopic variations. We can confirm the kinetic origin of the variations using measurements of μ^48/44Ca by MC-ICP-MS to distinguish kinetic from equilibrium fractionation processes using a triple-isotope approach. A new variable (Δ⁴⁸Ca^′)quantifies deviations from the Ca-isotope equilibrium slope on a plot of ⁴⁸Ca/⁴⁴Ca vs. ⁴²Ca/⁴⁴Ca. Available geochronological constraints and numerical modeling indicate that observed kinetic isotope fractionations between adjacent high and low Ca rock layers require effective Ca diffusivities of 10⁻¹⁰ to 10⁻⁷ m²/yr, and a ratio of Ca isotope diffusivities of D₄₄/D₄₀ ≈ 0.99. The diffusivities are consistent with Ca transport by volume- and grain-boundary diffusion. The apparent contrast in isotopic diffusivities is large and more consistent with silicate liquids than aqueous fluids. This study confirms that kinetic Ca isotope effects are abundant in nature and can overwrite small equilibrium effects, even at high temperatures and even when other techniques (such as Fe-Mg exchange and Ca-in-Opx thermometry)suggest the establishment of chemical equilibrium. Our results imply that kinetic fractionation effects may complicate the use of δ⁴⁴Ca measurements for geothermometry or as a tracer of carbonate recycling into the mantle.