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: (CaCOO2)-C-12-O-18-O-16 + (CaCO3)-C-13-O-16 <-> (CaOOO2)-O-13-O-18-O-16 + (CaCO3)-C-12-O-16 for 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 nor m-conserving planewave pseudopotentials to determine the vibrational frequencies of isotopically substituted crystals. Our results predict an similar to 0.4%. excess of (COO22-)-C-13-O-18-O-16 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 C-13/C-12, O-18/O-16, and O-17/O-16 ratios. The amount of excess (COO22-)-C-13-O-18-O-16 decreases with increasing temperature of equilibration, from 0.5 parts per thousand at 0 degrees C to < 0.1 parts per thousand at 300 degrees 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 6180 of coexisting fluids is uncertain. The predicted temperature sensitivity of the equilibrium constant is similar to 0.003 parts per thousand/degrees C at 25 degrees C. Estimated equilibrium constants for the formation of (COO22-)-C-13-O-18-O-16 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: (CaCOO2)-C-12-O-18-O-16 + (CaCOO2)-C-12-O-17-O-16 <-> (CaCOOO)-C-12-O-18-O-17-O-16 + (CaCO3)-C-12-O-16 in calcite indicates formation of 0.1 parts per thousand excess (COOO2-)-C-12-O-18-O-17-O-16 at 25 degrees C. In a conventional phosphoric acid reaction of carbonate to form CO2 for mass-spectrometric analysis, molecules derived from (COO22-)-C-13-O-18-O-16 dominate (similar to 96%) the mass 47 signal, and (COOO2-)-C-12-O-18-O-17-O-16 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 O-18/O-16 and C-13/C-12 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 Mg-40-magnesite and Ba-40-witherite indicate that M2+-cation mass does not contribute significantly to equilibrium isotopic fractionations between carbonate minerals. (c) 2006 Elsevier Inc. All rights reserved.