Ab initio calculations of the isotopic effects of sulfate and Mg impurities in carbonate minerals

Impurities in CaCO₃ minerals, present as ion substitutions (e.g., Mg²⁺ for Ca²⁺, SO₄^2- for CO₃^2-), are common and known to affect the fractionation of isotopes between the mineral and its parent fluid (e.g., the carbonate–water O isotope fractionation, the CAS–SO₄^2- S isotope fractionation). The difficulty in achieving isotopic equilibrium during experimental precipitation of carbonate minerals motivates the calculation of such effects by ab initio DFT methods. However, even a single substitution in a model lattice composed of as many atoms as computationally possible results in impurity concentrations that are much higher than those typical of most natural and experimental samples. For example, calculations of the CAS–SO₄^2- S isotope fractionation were performed at CAS concentrations of 59,000 and 30,000 ppm in calcite and aragonite, respectively, ∼threefold higher than the highest natural concentrations. The calculations yielded a CAS–SO₄^2- S isotope fractionation of 3.6 and 4.5‰ in calcite and aragonite (at 25°C), respectively, at odds with experimental values of ∼1‰ at the highest CAS concentrations in both calcite and aragonite. It is unknown whether the disagreement arises from the much higher CAS concentration in the calculations than in the experiments.

To overcome these computational limitations, we developed an approach in which the fractionation in the computationally largest possible “doped” model lattice is combined with the fractionation in a “pure” lattice. Using this approach, we determined the dependence of mineral–solution isotopic fractionation on the concentration of SO₄^2- and Mg²⁺ impurities in CaCO₃. The doped and pure lattices were modeled using ab initio methods implemented in the PWscf code of the Quantum ESPRESSO package, using periodic boundary conditions and the PBE exchange-correlation functional. Trigonal calcite and orthorhombic aragonite unit cells were used to form supercells of various dimensions containing 10 to 540 atoms. The ionic cores were described by ultrasoft pseudopotential and the Brillouin zone sampling was restricted to a single k-point for large supercells. Doped supercells contained a single SO₄^2- or Mg²⁺, and pure cells contained none. We calculated the defect formation energies and observed that the spurious effect from the impurities in imaginary supercells is minimized for a supercell size of ∼40 atoms or more. Phonon frequencies were calculated for various isotopic combinations using the PHonon code, and the frequencies were used to calculate the isotopic fractionation using the reduced partition function theory. The dependence of the bulk mineral–solution isotopic fractionation on the impurity concentration was then calculated as a weighted average of a single doped supercell and an arbitrary number of pure supercells. We will present the impurity dependence of the mineral–solution fractionation of O, C, Ca, Mg, and S isotopes and the carbonate clumped isotope composition of the CaCO₃, and compare to observations, where available. We suggest that a similar approach can be used to study the effect of any impurity, at an arbitrary concentration, on any isotopic system, in any mineral.