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–. Our results show that the incorporation of SO42– 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– incorporated into the apatite structure. Co-incorporation of SO42– and SO32– is energetically favored when the lone pair electrons of SO32– 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+/∑S 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.