Simultaneous Calculation of Chemical and Isotope Equilibria Using the GEOCHEQ_Isotope Software: Iron Isotopes

The GEOCHEQ_Isotope software package, previously developed to calculate chemical and isotopic equilibria of carbon and oxygen in hydrothermal and hydrogeochemical systems by minimizing Gibbs energy, was extended to the simultaneous calculation of isotopic effects of carbon, oxygen, and iron (the main objective of the study). As for carbon and oxygen, the β-factor formalism was used to develop algorithms and a database for the calculation of iron isotopic effects. According to the developed algorithm, the Gibbs energy G*(P, T) of formation of a rare isotopologue was calculated through the Gibbs energy of formation of the main isotopologue taking into account the value of the ⁵⁶Fe/⁵⁴Fe β-factor of this substance and the mass ratio of ⁵⁴Fe and ⁵⁶Fe isotopes. The approximation of ideal isotope mixture was used. The temperature dependence of the β-factor is unified in the form of a third-order polynomial by inverse even degrees of absolute temperature. Based on a critical analysis of currently available data on equilibrium isotopic factors obtained by different methods (elastic and inelastic γ-resonance scattering, isotope exchange experiments, and ab-initio calculations), the main result was obtained: for the first time, internally consistent database on iron β-factors of minerals and water complexes was developed. To develop the database, minerals and aqueous complexes for which the estimates of the equilibrium fractionation factors of iron isotopes obtained by different methods exist and consistent within the error of the methods have been identified: metallic iron (α-Fe), hematite, magnetite, siderite, pyrite, and the aqueous complexes \({\text{Fe(III)(}}{{{\text{H}}}_{{\text{2}}}}{\text{O)}}_{6}^{{3 + }}\) and \({\text{Fe(III)(}}{{{\text{H}}}_{{\text{2}}}}{\text{O)}}_{6}^{{2 + }}\) . The values of the iron β-factors for these minerals and aqueous complexes, accepted as reference ones, formed the “mainstay” of the developed database. Considering that the equilibrium isotopic shifts of iron between minerals and water complexes are estimated much more accurately within the framework of one method rather than the corresponding β-factors, the database was made consistent by linking the ln β values for minerals and water complexes to the reference ln β values. The application of the GEOCHEQ_Isotope software package to the closed carbonaceous hydrothermal system H₂O–CO₂–Fe₂O₃–FeO–CaO (T = 200°C, P = 16–50 bar) has shown the possibility of its use for the calculation of changes in mineral composition and isotopic effects on oxygen, carbon, and iron.