4 pressure , pH , and composition-dependent model for ionic substitution in minerals 5

14 The mineral apatite, Ca10(PO4)6(F,OH,Cl)2, incorporates sulfur (S) during crystallization 15 from S-bearing hydrothermal fluids and silicate melts. Our previous studies of natural and 16 experimental apatite demonstrate that the oxidation state of S in apatite varies systematically as a 17 function of oxygen fugacity (fO2). The S oxidation states –1 and –2 were quantitatively 18 identified in apatite crystallized from reduced, S-bearing hydrothermal fluids and silicate melts 19 by using sulfur K-edge X-ray absorption near-edge structure spectroscopy (S-XANES) where 20 2 S/ΣS in apatite increases from ~0 at FMQ−1 to ~1 at FMQ+2, where FMQ refers to the 21 fayalite-magnetite-quartz fO2 buffer. In this study, we employ quantum-mechanical calculations 22 to investigate the atomistic structure and energetics of S(-I) and S(–II) incorporated into apatite 23 and elucidate incorporation mechanisms. 24 One S(–I) species (disulfide, S2) and two S(–II) species (bisulfide, HS, and sulfide, S) 25 are investigated as possible forms of reduced S species in apatite. In configuration models for the 26 simulation, these reduced S species are positioned along the c-axis channel, originally occupied 27 by the column anions F, Cl, and OH in the endmember apatites. In the lowest-energy 28 configurations of S-incorporated apatite, disulfide prefers to be positioned halfway between the 29 mirror planes at z = 1/4 and 3/4. In contrast, the energy-optimized bisulfide is located slightly 30 away from the mirror planes by ~0.04 fractional units in the c direction. The energetic stability of 31 these reduced S species as a function of position along the c-axis can be explained by the 32 geometric and electrostatic constraints of the Ca and O planes that constitute the c-axis channel. 33 The thermodynamics of incorporation of disulfide and bisulfide into apatite are evaluated by 34 using solid-state reaction equations where the apatite host and a solid S-bearing source phase 35 (pyrite and Na2S2(s) for disulfide; troilite and Na2S(s) for sulfide) are the reactants, and the S36 incorporated apatite and an anion sink phase are the products. The Gibbs free energy (G) is 37 lower for incorporation with Na-bearing phases than with Fe-bearing phases, which is attributed 38 to the higher energetic stability of the iron sulfide minerals as a source phase for S than the 39 sodium sulfide phases. The thermodynamics of incorporation of reduced S are also evaluated by 40 using reaction equations involving dissolved disulfide and sulfide species (HnS2(aq) and HnS 41 n) (aq); n = 0, 1, and 2) as a source phase. The G of S-incorporation increases for fluorapatite and 42 3 chlorapatite and decreases for hydroxylapatite as these species are protonated (i.e., as n changes 43 from 0 to 2). These thermodynamic results demonstrate that the presence of reduced S in apatite 44 is primarily controlled by the chemistry of magmatic and hydrothermal systems where apatite 45 forms (e.g., abundance of Fe; solution pH). Ultimately, our methodology developed for 46 evaluating the thermodynamics of S incorporation in apatite as a function of temperature, pH, 47 and composition is highly applicable to predicting the trace and volatile element incorporation in 48 minerals in a variety of geological systems. In addition to solid-solid and solid-liquid equilibria 49 treated here at different temperatures and pH, the methodology can be easily extended also to 50 different pressure conditions by just performing the quantum-mechanical calculations at elevated 51 pressures. 52