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

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 S 6+ , S 4+ , and S 2− into the apatite end-members fluor-, chlor-, and hydroxylapatite, [Ca 10 (PO 4 ) 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 S 6+ and troilite for S 2− ) 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 La 3+ + PO 4 3− ↔ Ca 2+ + SO 4 2− . Our results show that the incorporation of SO 4 2− into La- and Na-bearing apatite, Ca 8 NaLa(PO 4 ) 6 (F,Cl,OH) 2 , is energetically favored over the incorporation into La- and Si-bearing apatite, Ca 9 La(PO 4 ) 5 (SiO 4 )(F,Cl,OH) 2 (the difference in incorporation energy, Δ E rxn , is 10.7 kJ/mol). This thermodynamic gain is partially attributed to the electrostatic contribution of Na + , and the energetic contribution of La 3+ to the stability of SO 4 2− incorporated into the apatite structure. Co-incorporation of SO 4 2− and SO 3 2− is energetically favored when the lone pair electrons of SO 3 2− face toward the anion column site, compared to facing away from it. Full or partial incorporation of S 2− is favored on the column anion site in the form of [Ca 10 (PO 4 ) 6 S] and [Ca 20 (PO 4 ) 12 SX 2 )], where X = F, Cl, or OH. Upon full incorporation (i.e., replacing all column ions by sulfide ions), S 2− 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 S 2− demonstrate that in an energy-optimized structure, S 2− is displaced from the mirror plane at z = ¼ or ¾, by 1.0 to 1.6 A, depending on the surrounding species (F − , Cl − , or OH − ); however, the probability for S 2− 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 (S 6+ , S 4+ , S 2− ) 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 S 6+ , S 4+ , and S 2− incorporation into apatite, where the ratio of S 6+ /∑S in apatite is controlled by oxygen fugacity ( f O 2 ). 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.