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

Abstract

Equilibrium constants for internal isotopic exchange reactions of the type: Ca^(12)C^(18)O^(16)O_2+Ca^(13)C^(16)O_3 ↔ Ca^(13)C^(18)O^(16)O_2+Ca^(12)C^(16)O_3 for individual CO_3^(2−) groups in the carbonate minerals calcite (CaCO_3), aragonite (CaCO_3), dolomite (CaMg(CO_3)_2), magnesite (MgCO_3), witherite (BaCO_3), and nahcolite (NaHCO_3) 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 ^(13)C^(18)O^(16)O_2^(2-) 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 ^(13)C/^(12)C, ^(18)O/^(16)O, and ^(17)O/^(16)O ratios. The amount of excess ^(13)C^(18)O^(16)O^(2-)_2 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 δ^(18)O 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 ^(13)C^(18)O^(16)O^(2-)_2 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: Ca^(12)C^(18)O^(16)O_2+Ca^(12)C^(17)O^(16)O_2 ↔ Ca^(12)C^(18)O^(17)O^(16)O+Ca^(12)C^(16)O_3 in calcite indicates formation of 0.1‰ excess ^(12)C^(18)O^(17)O^(16^O^(2−) at 25 °C. In a conventional phosphoric acid reaction of carbonate to form CO_2 for mass-spectrometric analysis, molecules derived from ^(13)C^(18)O^(16)O_2^(2-) dominate (∼96%) the mass 47 signal, and ^(12)C^(18)O^(17)O^(16)O^(2−) contributes most of the remainder (3%). This suggests that carbonate internal equilibration temperatures can be recovered from acid-generated CO_2 if abundances of isotopologues with mass 44–47 can be measured to sufficient precision. We have also calculated ^(18)O/^(16)O and ^(13)C/^(12)C 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 ^(40)Mg—magnesite and ^(40)Ba—witherite indicate that M^(2+)-cation mass does not contribute significantly to equilibrium isotopic fractionations between carbonate minerals.

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