Ti 3+ – and Ti 4+ – rich fassaites at the birth of the solar system: Thermodynamics and applications

Abstract

A thermodynamic model is developed for pyroxenes in the chemical (mineralogical) system CaMgSi2O6 (diopside, Di, 1) – CaTiAlSiO6 (grossmanite, Gr, 2) –CaMg1/2 Ti1/2AlSiO6 (alumino – buffonite, AlBf, 3) – CaAl2SiO6 (Calcium Aluminum Tschermaks, CATS, 4), aka fassaites. It is formulated for the assumptions of molecular mixing between AlBf and Di, Gr and CATS components, and that the reduction in configurational entropy resulting from short – range Al – Si ordering on tetrahedral sites may be described using, as a proxy, a long–range, convergent ordering parameter for ordering of Al and Si between A and B tetrahedral sites on the AlBf – free tetrahedral sublattice. Nine out of sixteen independent thermodynamic parameters are calibrated to be consistent with calorimetric measurements of Benisek and others (2007), spectroscopic and statistical mechanical constraints on tetrahedral Al – Si ordering in pyroxenes on the Di – CATS binary (Cohen, 1986; Vinograd, 2001; Warren and others, 2001), and phase equilibrium constraints on Di – AlBf miscibility gaps in the Di – AlBf – CATS ternary subsystem (Yang 1975, 1976). The remaining seven independent parameters (for Gr – bearing fassaites) are constrained to be consistent with the distribution of fassaite compositions in calcium – aluminum – rich inclusions in carbonaceous chondrites (CAIs), experimental determinations of fassaite single – phase regions produced at the extremely low oxygen fugacities prevailing during their primary condensation/crystallization (for example, Beckett, ms, 1986), and the assumption that secondary fassaites in Wark – Lovering rims enclosing CAIs were in local equilibrium with the outer surface layers of the earlier (canonical) AlBf – rich fassaites at their layer contacts at temperatures of around 1473 K (Wark and Lovering, 1982; Meeker and others, 1983; Murrell and Burnett, 1987; Ruzicka, 1997; Dyl and others, 2011). In this model there is a miscibility gap between Di–rich and AlBf–rich fassaites on the Di – AlBf join which displays only very limited extension into the fassaite tetrahedron. On the Di – AlBf – CATS face of this tetrahedron there is a second miscibility gap (upper buffonite gap, UBG) with 0.08 ≤ X4fas Within the fassaite tetrahedron at 1473 K the UBG is rapidly destabilized with addition of the Gr component, diminishing in dimension and collapsing to a critical endpoint at X2fas The model for fassaite thermochemistry is used to develop a Ti3+ – Ti4+ fassaite oxygen cosmobarometer based on experimental constraints (for example, Beckett, ms, 1986). Values of oxygen fugacity calculated with this cosmobarometer for fassaites and melilites, judged by Grossman and others (2008) to be coeval in refractory CAIs from the Allende carbonaceous chondrite, are more than three orders of magnitude below that of a gas of solar composition.