An ab-initio study of the energetics and geometry of sulfide, sulfite, and sulfate incorporation into apatite: The thermodynamic basis for using this system as an oxybarometer

Abstract Despite many studies reporting the presence of S-bearing apatite in igneous and hydrothermal systems, the oxidation states and incorporation mechanisms of S in the apatite structure remain poorly understood. In this study, we use ab initio calculations to investigate the energetics and geometry of incorporation of S with its oxidation states S6+, S4+, and S2− into the apatite end-members fluor-, chlor-, and hydroxylapatite, [Ca10(PO4)6(F, Cl, OH)2]. The relative stability of different oxidation states of S in apatite is evaluated by using balanced reaction equations where the apatite host and a solid S-bearing source phase (e.g., gypsum for S6+ and troilite for S2−) are the reactants, and the S-incorporated apatite and an anion sink phase are the products. Here, the reaction energy of the balanced equation indicates the stability of the modeled S-incorporated apatite relative to the host apatite, the source, and sink phases. For the incorporation of S into apatite, coupled substitutions are necessary to compensate for charge imbalance. One possible coupled substitution mechanism involves the replacement of La3++PO43−↔Ca2++SO42−. $\begin{array}{} \text{La}^{3+} + \text{PO}_4^{3-} \leftrightarrow \text{Ca}^{2+} + \text{SO}_4^{2-}. \end{array} $ Our results show that the incorporation of SO42− $\begin{array}{} \text{SO}_4^{2-} \end{array} $ into La- and Na-bearing apatite, Ca8NaLa(PO4)6(F, Cl, OH)2, is energetically favored over the incorporation into La- and Si-bearing apatite, Ca9La(PO4)5(SiO4)(F, Cl, OH)2 (the difference in incorporation energy, ΔErxn, is 10.7 kJ/mol). This thermodynamic gain is partially attributed to the electrostatic contribution of Na+, and the energetic contribution of La3+ to the stability of SO42− $\begin{array}{} \text{SO}_4^{2-} \end{array} $ incorporated into the apatite structure. Co-incorporation of SO42− $\begin{array}{} \text{SO}_4^{2-} \end{array} $ and SO32− $\begin{array}{} \text{SO}_3^{2-} \end{array} $ is energetically favored when the lone pair electrons of SO32− $\begin{array}{} \text{SO}_3^{2-} \end{array} $ face toward the anion column site, compared to facing away from it. Full or partial incorporation of S2− is favored on the column anion site in the form of [Ca10(PO4)6S] and [Ca20(PO4)12SX2)], where X = F, Cl, or OH. Upon full incorporation (i.e., replacing all column ions by sulfide ions), S2− is positioned in the anion column at z = 0.5 (halfway between the mirror planes at z = ¼ and z = ¾) in the energy-optimized structure. The calculated energies for partial incorporation of S2− demonstrate that in an energy-optimized structure, S2− is displaced from the mirror plane at z = ¼ or ¾, by 1.0 to 1.6 Å, depending on the surrounding species (F−, Cl−, or OH−); however, the probability for S2− to be incorporated into the apatite structure is highest for chlorapatite end-members. Our results describe energetically feasible incorporation mechanisms for all three oxidations states of S (S6+, S4+, S2−) in apatite, along with structural distortion and concurring electronic structure changes. These observations are consistent with recently published experimental results (Konecke et al. 2017) that demonstrate S6+, S4+, and S2− incorporation into apatite, where the ratio of S6+/ΣS in apatite is controlled by oxygen fugacity (fO2). The new computational results coupled with published experimental data provide the basis for using S in apatite as a geochemical proxy to trace variations in oxygen fugacity of magmatic and magmatic-hydrothermal systems.