Abstract. Oxygen fugacity (fO2) is a fundamental variable affecting phase equilibrium in magmas, and in externally heated pressure vessel experiments it is typically controlled by using redox buffer assemblages. However, these do not allow fine enough resolution; for example, most arc magmas fall between the fO2 imposed by the neighboring Ni–NiO and Re–ReO2 buffers and so does the transition of S2− to S6+ in magmas. Here we propose a new method to quantitatively impose fO2 in hydrous high-P–T experiments in molybdenum hafnium carbide (MHC) pressure vessels by admixing small amounts of hydrogen into the Ar pressure medium. The thermodynamic calculation procedure used to determine the initial amount of hydrogen to be loaded to constrain desired fO2 values was verified by CoPd alloy redox sensor experiments to be accurate within ±0.3 log units for the pressure (P) – temperature (T) range of 940–2060 bar and 800–1100 ∘C. As hydrogen can be slowly lost from the pressure medium due to diffusion through the vessel walls at high T, we also determined the hydrogen permeability of the MHC alloy as a function of T. The such-obtained hydrogen permeability equation for the MHC alloy can be used to determine the rate of fO2 increase for any MHC pressure vessel configuration. As the rate of fO2 increase is slow (e.g., 0.36 log units per day in our setup at T= 1000 ∘C), we propose that H2 addition to the Ar pressure medium is an effective way to accurately impose fO2 in many types of experiments conducted in MHC vessels allowing experimentation up to T= 1200 ∘C and P= 300 MPa.

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Oxygen fugacity (fO 2 ) is typically controlled in high P-T experiments by using solid state redox buffer assemblages. However, these are restricted to impose discrete fO 2 values often with significant gaps between neighbouring assemblages. Semi-permeable hydrogen membranes (Shaw 1963) are often used in internally heated pressure vessels for more flexible fO 2 control in hydrous experiments; however, their implementation in more widely available externally-heated pressure vessels have not yet gained space. We propose a prototype Molybdenum-Hafnium Carbide (MHC) pressure vessel apparatus that simultaneously allows rapid quenching and flexible, precise, and accurate redox control via a custom-designed hydrogen membrane. Test runs with two membranes at a time, one imposing and another one monitoring fH 2 , demonstrated that 95% of the imposed hydrogen pressure was attained inside the pressure vessel within 2 hours at 800 -1000⁰C, after which a steady state equilibrium was established. Furthermore, This is the peer-reviewed, final accepted version for American Mineralogist, published by the Mineralogical Society of America.The published version is subject to change. Cite as Authors (Year) Title. American Mineralogist, in press.

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