Preferential formation of 13C–18O bonds in carbonate minerals, estimated using first-principles lattice dynamics

Equilibrium constants for internal isotopic exchange reactions of the type:Ca12C18O16O2+Ca13C16O3↔Ca13C18O16O2+Ca12C16O3Ca12C18O16O2+Ca13C16O3↔Ca13C18O16O2+Ca12C16O3for individual CO32− groups in the carbonate minerals calcite (CaCO3), aragonite (CaCO3), dolomite (CaMg(CO3)2), magnesite (MgCO3), witherite (BaCO3), and nahcolite (NaHCO3) are calculated using first-principles lattice dynamics. Calculations rely on density functional perturbation theory (DFPT) with norm-conserving planewave pseudopotentials to determine the vibrational frequencies of isotopically substituted crystals. Our results predict an ∼0.4‰ excess of 13C18O16O22− groups in all studied carbonate minerals at room-temperature equilibrium, relative to what would be expected in a stochastic mixture of carbonate isotopologues with the same bulk 13C/12C, 18O/16O, and 17O/16O ratios. The amount of excess 13C18O16O22− decreases with increasing temperature of equilibration, from 0.5‰ at 0 °C to <0.1‰ at 300 °C, suggesting that measurements of multiply substituted isotopologues of carbonate could be used to infer temperatures of ancient carbonate mineral precipitation and alteration events, even where the δ18O of coexisting fluids is uncertain. The predicted temperature sensitivity of the equilibrium constant is ∼0.003‰/°C at 25 °C. Estimated equilibrium constants for the formation of 13C18O16O22− are remarkably uniform for the variety of minerals studied, suggesting that temperature calibrations will also be applicable to carbonate minerals not studied here without greatly compromising accuracy. A related equilibrium constant for the reaction:Ca12C18O16O2+Ca12C17O16O2↔Ca12C18O17O16O+Ca12C16O3Ca12C18O16O2+Ca12C17O16O2↔Ca12C18O17O16O+Ca12C16O3in calcite indicates formation of 0.1‰ excess 12C18O17O16O2− at 25 °C. In a conventional phosphoric acid reaction of carbonate to form CO2 for mass-spectrometric analysis, molecules derived from 13C18O16O22− dominate (∼96%) the mass 47 signal, and 12C18O17O16O2− contributes most of the remainder (3%). This suggests that carbonate internal equilibration temperatures can be recovered from acid-generated CO2 if abundances of isotopologues with mass 44–47 can be measured to sufficient precision. We have also calculated 18O/16O and 13C/12C reduced partition function ratios for carbonate minerals, and find them to be in good agreement with experiments and empirical calibrations. Carbon and oxygen isotope fractionation factors in hypothetical 40Mg—magnesite and 40Ba—witherite indicate that M2+-cation mass does not contribute significantly to equilibrium isotopic fractionations between carbonate minerals.