An empirical model for the calculation of spinel-melt equilibria in mafic igneous systems at atmospheric pressure: 1. Chromian spinels
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In order to develop a model for simulating naturally occurring chromian spinel compositions, we have processed published experimental data on chromian spinel-melt equilibrium. Out of 259 co-existing spinel-melt experiments reported in the literature, we have selected 118 compositions on the basis of run time, melt composition and experimental technique. These data cover a range of temperatures 1150–1500° C, oxygen fugacities of −13<log fO2< −0.7, and bulk compositions ranging from basalt and norite, to komatiite. Six major spinel components with Cr3+, Al3+, Ti4+, Mg2+, Fe3+ and Fe2+-bearing end-members were considered for the purpose of describing chromite saturation as a function of melt composition, temperature and oxygen fugacity at 1 atmosphere pressure (0.101 MPa). The empirically calibrated mineral-melt expression based on multiple linear regressions is:
KSpi=A/T(K)+B log fO2+C ln (Fe3+/Fe2+)L+D ln RL+E,
where KSpi is an equilibrium constant and RL is a melt structure-chemical parameter (MSCP). Twenty-eight forms of equilibrium constants were considered, including single distribution coefficients, exchange equilibrium constants, formation constants for AB2O4 components, as well as simple “spinel cation ratios”. For each form of the equilibrium constants, a set of 16 combinations of the MSCPs have been investigated. The MSCP is present in the form of composite ratios [e.g., Si/O, NBO/T,(Al+Si)/Si, or (Na+K)/Al] or as simple cation ratios (e.g., Mg/Fe2+). For the calculation of Fe3+ and Fe2+ species in silicate melts, we used existing equations, whereas the Fe3+/Fe2+ ratio of spinels was calculated from the spinel stoichiometry. The regression parameters that best repoduce the experimental data were for the following constants: (Fe3+/Fe2+)Sp, (Mg/Fe2+)Sp/(Mg/Fe2+)L, (Cr/Al)Sp/ (Cr/Al)L, KFeCr2O4, and TiSp/TiL. These expressions have been combined into a single program called SPINMELT, which calculates chromite crystallization temperature and composition at a given fO2 with an average accuracy of ∼10° C and 1–2 mol%. An example of the use of SPINMELT is presented for a magma parental to the Bushveld Complex.
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