Thermochemistry of melilites I. Towards resolving an inconsistency in nebular condensation calculations

Abstract

A thermodynamic model is formulated for (Ca,Na)₂(Mg,Fe²⁺,Al,Fe³⁺)^T1 (Al,Fe³⁺,SiO₇ melilites. It employs the compositional vertices: åkermanite (Ca₂MgSi₂O₇, 1), gehlenite (Ca₂Al₂SiO₇, 2), iron åkermanite (Ca₂Fe²⁺Si₂O₇, 3), ferrigehlenite (Ca₂SiO₇, 4), sodium melilite (NaCaAlSi₂O₇, 5), and the convergent ordering variables: s = – and t = – to describe the distribution of Al³⁺, Fe³⁺ and Si⁴⁺ between T2 subsites T2a and T2b. It is calibrated for åkermanite–gehlenite melilites based on the calorimetric data of Charlu and others (1981), the assumption that the synthetic samples of Charlu and others approached “equilibrium” states of Al-Si tetrahedral ordering at 970 K, and analogy with the Al₂(MgSi)_− 1 substitution in CaMgSi₂O₆ – CaMg_1/2AlSiO₆ – CaAl₂SiO₆ fassaites (for example, Sack and Ghiorso, 2017). In this model gehlenite has a disordered Al-Si distribution on T2 sites above 1443 K (1170 °C), consistent with the crystallographic data on c/a ratios of lattice parameters as a function of annealing temperature (Woodhead and Waldbaum, 1974) and the high-temperature heat capacities inferred from drop calorimetric data (Pankratz and Kelley,1964). However, above this critical temperature a partially ordered Al-Si distribution persists between T2a and T2b sites in åkermanite – gehlenite solid solutions with intermediate X₂ (for example, 0.19 < < 0.89 at 1573 K). To a first approximation activity-composition relations of the gehlenite component approximate those of ideal mixing (that is, a_i = X_i), particularly in gehlenite-rich compositions, but those of åkermanite component display pronounced temperature dependence in intermediate compositions. Enthalpies of formation of åkermanite and gehlenite from the elements at 298.15 K, and , consistent with the experimental brackets on decarbonation equilibria of Walter (1963), Hoschek (1974), and Shmulovich (1974), the thermodynamic model for åkermanite-gehlenite melilites developed here, the thermodynamic properties of the other phases in these reactions tabulated by Berman (1988), and the revised estimates for and of diopside of Sack and Ghiorso (2017), are roughly 1 and 3 (kJ/gfw) more positive than those estimated by Berman (1988). More positive standard enthalpies of formation of both endmembers, together with a decrease in the vibrational heat capacity of gehlenite and less negative deviations from ideal mixing compared with previous calibrations, all contribute to reducing the stability of melilites in this model. Together these effects will decrease the predicted temperature of condensation of melilite from nebular vapors, bringing calculated temperatures of melilite condensation into closer alignment with those of MgAl₂O₄ spinel than the 80 to 100 K separating their appearances in previous calculations (for example, Yoneda and Grossman, 1995; Petaev and Wood,1998; Ebel and Grossman,2000). These effects, together with a possible increase in spinel stability due to non-negligible solubility of Al_8/3O₄ alumina component, may allow equilibrium models to match the observed condensation sequence of spinel before melilite in calcium-aluminum inclusions (CAIs) in carbonaceous chondrites, without the need to invoke kinetic effects.