An empirical model for the calculation of spinel-melt equilibria in mafic igneous systems at atmospheric pressure: 1. Chromian spinels

Abstract

 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 f _O2< −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:

K ^Sp _i =A/T(K)+B log f _O2+C ln (Fe³⁺/Fe²⁺)_L+D ln R _L +E,

where K ^Sp _i is an equilibrium constant and R _L 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 , K _FeCr2O4, and Ti _Sp /Ti _L . These expressions have been combined into a single program called SPINMELT, which calculates chromite crystallization temperature and composition at a given f _O2 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.