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Abstract 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)(2−n) and HnS(aq)(2−n); 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. 

Abstract Many intermediate to felsic intrusive and extrusive rocks contain mafic magmatic enclaves that are evidence for magma recharge and mixing. Whether enclaves represent records of prolonged mixing  or syn‐eruptive recharge depends on their preservation potential in their intermediate to felsic host magmas. We present a model for enclave consumption where an initial stage of diffusive equilibration loosens the crystal framework in the enclave followed by advective erosion and disaggregation of the loose crystal layer. Using experimental data to constrain the propagation rate of the loosening front leads to enclave “erosion” rates of 10⁻⁵–10⁻⁸ cm/s for subvolcanic magma systems. These rates suggest that under some circumstances, enclave records are restricted to syn‐eruptive processes, while in most cases, enclave populations represent the recharge history over centuries to millennia. On these timescales, mafic magmatic enclaves may be unique recorders that can be compared to societal and written records of volcano activity.