From core to atmosphere, the oxidation states of elements in a planet shape its character. Oxygen fugacity (fO$_2$) is one parameter indicating these likely oxidation states. The ongoing search for atmospheres on rocky exoplanets benefits from understanding the plausible variety of their compositions, which depends strongly on their oxidation states -- and if derived from interior outgassing, on the fO$_2$ at the top of their silicate mantles. This fO$_2$ must vary across compositionally-diverse exoplanets, but for a given planet its value is unconstrained insofar as it depends on how iron (the dominant multivalent element) is partitioned between its 2+ and 3+ oxidation states. Here we focus on another factor influencing how oxidising a mantle is -- a factor modulating fO$_2$ even at fixed Fe$^{3+}$/Fe$^{2+}$ -- the planet's mineralogy. Only certain minerals (e.g., pyroxenes) incorporate Fe$^{3+}$. Having such minerals in smaller mantle proportions concentrates Fe$^{3+}$, increasing fO$_2$. Mineral proportions change within planets according to pressure, and between planets according to bulk composition. Constrained by observed host star refractory abundances, we calculate a minimum fO$_2$ variability across exoplanet mantles, of at least two orders of magnitude, due to mineralogy alone. This variability is enough to alter by a hundredfold the mixing ratio of SO$_2$ directly outgassed from these mantles. We further predict that planets orbiting high-Mg/Si stars are more likely to outgas detectable amounts of SO$_2$ and H$_2$O; and for low-Mg/Si stars, detectable CH$_4$, all else equal. Even absent predictions of Fe$^{3+}$ budgets, general insights can be obtained into how oxidising an exoplanet's mantle is.
Comment: 16 pages, 7 figures, accepted for publication in MNRAS