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Quantifying the oxygen fugacity (fo2) of high temperature lithospheric fluids, including hydrothermal systems, presents a challenge because these fluids are difficult to capture and measure in the same manner as quenched glasses of silicate melts. The chemical properties of fluids can however be inferred through mineral proxies that interacted with the fluids through precipitation or recrystallization. Here, we present hydrothermal experiments to quantify the partition coefficients of rare earth elements (REEs) – including redox-sensitive Ce and Eu – between zircon and fluid. Experiments were conducted in a piston cylinder device at temperatures that range from 1200 to 800 ◦C under fo2-buffered conditions in a SiO2-ZrO2-NaCl-REE-oxide system, and similar experiments were performed in the absence of NaCl (31 total experiments). The fo2 was buffered to values that range from approximately 3 log units below to 7 log units above the fayalite magnetite quartz equilibrium. Zircon REE concentrations were quantified using laser ablation inductively coupled plasma mass spectrometry whereas the quenched fluids were extracted and measured by solution-based inductively coupled plasma mass spectrometry. Zircon Ce anomalies, quantified relative to La and Pr, exhibit sensitivity to oxygen fugacity and temperature and our preferred calibration is: log [􀀀 Ce Ce* ) D 􀀀 1 ] = (0.237 ± 0.040)× log(fo2) + 9437±640 T(K) 􀀀 5.02 ± 0.38 where the Ce anomalies are calculated from the partition coefficients for La, Ce, and Pr. Zircon Eu anomalies are also a function of oxygen fugacity though they exhibit no systematic dependence on T. Our preferred calibration is described by: 􀀀 Eu Eu* ) D = 1 1+100.30±0.04􀀀 [0.27±0.03]×ΔFMQ We performed additional calculations, in which lattice strain parabolas were fit to all non-redox sensitive rare earth elements that were added to the starting composition (i.e., La, Pr, Sm, Gd, Dy, Ho, Tm, Lu) as an alternate means to calculate anomalies. This method yields broadly similar results, though we prefer the La-Pr calibrations due to the non-systematic REE patterns frequently encountered with hydrothermal zircons; e.g., LREE zircon enrichment relative to other REEs. These experiments are applied to quantify the fo2 of fluids during mineralization of critical element-bearing systems, and separately to calculate the oxygen fugacity values of fluids formed during plate boundary processes. 

Abstract Partition coefficients for rare earth elements (REEs) between apatite and basaltic melt were determined as a function of oxygen fugacity (fO2; iron-wüstite to hematite-magnetite buffers) at 1 bar and between 1110 and 1175 °C. Apatite-melt partitioning data for REE3+ (La, Sm, Gd, Lu) show near constant values at all experimental conditions, while bulk Eu becomes more incompatible (with an increasing negative anomaly) with decreasing fO2. Experiments define three apatite calibrations that can theoretically be used as redox sensors. The first, a XANES calibration that directly measures Eu valence in apatite, requires saturation at similar temperature-composition conditions to experiments and is defined by: ( E u 3 + ∑ E u ) Apatite  = 1 1 + 10 - 0.10 ± 0.01 × l o g ⁡ ( f o 2 ) - 1.63 ± 0.16 . The second technique involves analysis of Sm, Eu, and Gd in both apatite and coexisting basaltic melt (glass), and is defined by: ( Eu E u * ) D Sm × Gd = 1 1 + 10 - 0.15 ± 0.03 × l o g ⁡ ( f o 2 ) - 2.46 ± 0.41 . The third technique is based on the lattice strain model and also requires analysis of REE in both apatite and basalt. This calibration is defined by ( Eu E u * ) D lattice strain = 1 1 + 10 - 0.20 ± 0.03 × l o g ⁡ ( f o 2 ) - 3.03 ± 0.42 . The Eu valence-state partitioning techniques based on (Sm×Gd) and lattice strain are virtually indistinguishable, such that either methodology is valid. Application of any of these calibrations is best carried out in systems where both apatite and coexisting glass are present and in direct contact with one another. In holocrystalline rocks, whole rock analyses can be used as a guide to melt composition, but considerations and corrections must be made to either the lattice strain or Sm×Gd techniques to ensure that the effect of plagioclase crystallization either prior to or during apatite growth can be removed. Similarly, if the melt source has an inherited either a positive or negative Eu anomaly, appropriate corrections must also be made to lattice strain or Sm×Gd techniques that are based on whole rock analyses. This being the case, if apatite is primary and saturates from the parent melt early during the crystallization sequence, these corrections may be minimal. The partition coefficients for the REE between apatite and melt range from a maximum DEu3+ = 1.67 ± 0.25 (as determined by lattice strain) to DLu3+ = 0.69 ± 0.10. The REE partition coefficient pattern, as observed in the Onuma diagram, is in a fortuitous situation where the most compatible REE (Eu3+) is also the polyvalent element used to monitor fO2. These experiments provide a quantitative means of assessing Eu anomalies in apatite and how they be used to constrain the oxygen fugacity of silicate melts.