Carbon isotope fractionation between CO2 and carbon in silicate melts at high temperature

The isotopic fractionation of carbon between CO2 gas and silicate melts is a crucial parameter to understand the carbon cycle at the planetary scale that requires accurate quantification. In this study, we conducted experiments to determine the carbon isotope fractionation between CO(2 )gas and carbon dissolved in silicate melt at 350 - 420 MPa and 1160 - 1225 degrees C, across a range of melt compositions. A linear relationship emerges between the fractionation coefficient and the degree of polymerization of the melt (NBO/T; non-bridging oxygens per tetrahedral cation) with the fractionation coefficient increasing for depolymerized melts (e.g., basalt) and decreasing for polymerized melts (e.g., rhyolite): 1000ln alpha(gas_melt)= 3.251 x NBO/T +0.026(R-2 = 0.74) or 1000ln alpha(gas_melt)= _ 0.087 x (SiO2 +Al2O3)wt% + 7.968(R2 = 0.74). These equations enable the calculation of carbon fractionation coefficients in silicate melts, providing a mean to interpret delta 13C-value measurements in natural volcanic gases and melts through forward and backward modelling of degassing paths from mantle to surface. We hypothesize that the ratio of CO32-/CO(2 )dissolved in the melt is the key parameter behind this relationship. Carbon dissolved as CO2 molecular transfers to the gas phase with a fractionation coefficient of 0 %o whilst carbon dissolved as CO32- transfers with a fractionation coefficient of 2.9 %o. The relationship is calibrated from NBO/T=0 to 0.88, covering most major melt compositions. However, at NBO/T>0.88, as the CO32-/CO2 ratio reaches its maximum in silicate melt, correspondingly the fractionation coefficient reaches its maximum of 2.9 %o, both are expected to stabilize and remain constant. Carbon isotopic fractionation might hence offer a window into carbon speciation in natural melts.