The mineral apatite, Ca10(PO4)6(F,OH,Cl)2, incorporates sulfur (S) during crystallization from S-bearing hydrothermal fluids and silicate melts. Our previous studies of natural and experimental apatite demonstrate that the oxidation state of S in apatite varies systematically as a function of oxygen fugacity (fO2). The S oxidation states –1 and –2 were quantitatively identified in apatite crystallized from reduced, S-bearing hydrothermal fluids and silicate melts by using sulfur K-edge X-ray absorption near-edge structure spectroscopy (S-XANES) where S 6+/ΣS in apatite increases from ~0 at FMQ-1 to ~1 at FMQ+2, where FMQ refers to the fayalite-magnetite-quartz fO2 buffer. In this study, we employ quantum-mechanical calculations to investigate the atomistic structure and energetics of S(-I) and S(-II) incorporated into apatite and elucidate incorporation mechanisms.

One S(-I) species (disulfide, S22) and two S(-II) species (bisulfide, HS, and sulfide, S2−) are investigated as possible forms of reduced S species in apatite. In configuration models for the simulation, these reduced S species are positioned along the c-axis channel, originally occupied by the column anions F, Cl, and OH in the end-member apatites. In the lowest-energy configurations of S-incorporated apatite, disulfide prefers to be positioned halfway between the mirror planes at z = 1/4 and 3/4. In contrast, the energy-optimized bisulfide is located slightly away from the mirror planes by ~0.04 fractional units in the c direction. The energetic stability of these reduced S species as a function of position along the c-axis can be explained by the geometric and electrostatic constraints of the Ca and O planes that constitute the c-axis channel.

The thermodynamics of incorporation of disulfide and bisulfide into apatite is evaluated by using solid-state reaction equations where the apatite host and a solid S-bearing source phase (pyrite and Na2S2(s) for disulfide; troilite and Na2S(s) for sulfide) are the reactants, and the S-incorporated apatite and an anion sink phase are the products. The Gibbs free energy (ΔG) is lower for incorporation with Na-bearing phases than with Fe-bearing phases, which is attributed to the higher energetic stability of the iron sulfide minerals as a source phase for S than the sodium sulfide phases. The thermodynamics of incorporation of reduced S is also evaluated by using reaction equations involving dissolved disulfide and sulfide species [HnS(aq)(2n) and HnS(aq)(2n); n = 0, 1, and 2] as a source phase. The ΔG of S-incorporation increases for fluorapatite and chlorapatite, and decreases for hydroxylapatite, as these species are protonated (i.e., as n changes from 0 to 2). These thermodynamic results demonstrate that the presence of reduced S in apatite is primarily controlled by the chemistry of magmatic and hydrothermal systems where apatite forms (e.g., an abundance of Fe; solution pH). Ultimately, our methodology developed for evaluating the thermodynamics of S incorporation in apatite as a function of temperature, pH, and composition is highly applicable to predicting the trace and volatile element incorporation in minerals in a variety of geological systems. In addition to solid-solid and solid-liquid equilibria treated here at different temperatures and pH, the methodology can be easily extended to different pressure conditions by just performing the quantum-mechanical calculations at elevated pressures.

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