Activity–composition relations for phases in petrological calculations: an asymmetric multicomponent formulation

For petrological calculations, including geothermobarometry and the calculation of phase diagrams (for example, P–T petrogenetic grids and pseudosections), it is necessary to be able to express the activity–composition (a–x) relations of minerals, melt and fluid in multicomponent systems. Although the symmetric formalism—a macroscopic regular model approach to a–x relations—is an easy-to-formulate, general way of doing this, the energetic relationships are a symmetric function of composition. We allow asymmetric energetics to be accommodated via a simple extension to the symmetric formalism which turns it into a macroscopic van Laar formulation. We term this the asymmetric formalism (ASF). In the symmetric formalism, the a–x relations are specified by an interaction energy for each of the constituent binaries amongst the independent set of end members used to represent the phase. In the asymmetric formalism, there is additionally a "size parameter" for each of the end members in the independent set, with size parameter differences between end members accounting for asymmetry. In the case of fluid mixtures, for example, H₂O–CO₂, the volumes of the end members as a function of pressure and temperature serve as the size parameters, providing an excellent fit to the a–x relations. In the case of minerals and silicate liquid, the size parameters are empirical parameters to be determined along with the interaction energies as part of the calibration of the a–x relations. In this way, we determine the a–x relations for feldspars in the systems KAlSi₃O₈–NaAlSi₃O₈ and KAlSi₃O₈–NaAlSi₃O₈–CaAl₂Si₂O₈, for carbonates in the system CaCO₃–MgCO₃, for melt in the melting relationships involving forsterite, protoenstatite and cristobalite in the system Mg₂SiO₄–SiO₂, as well as for fluids in the system H₂O–CO₂. In each case the a–x relations allow the corresponding, experimentally determined phase diagrams to be reproduced faithfully. The asymmetric formalism provides a powerful and flexible way of handling a–x relations of complex phases in multicomponent systems for petrological calculations.     

Models of the dust envelope of the unique object FG Sagittae

We use JHKLM photometric data obtained in 1998–2001 to model the dust envelope of the unique object FG Sge, which formed around the star after several consecutive cycles of dust condensation beginning in Autumn 1992. Models with a spherically symmetric, extended envelope consisting of a mixture of spherical particles of amorphous carbon and silicon carbide with an MRN size distribution were fitted to match the mean observed spectral energy distributions of FG Sge during brightness maximum and minimum after 1998 for two values of the luminosity and effective temperature of the central star. The stellar-wind parameters and mass-loss rate have been estimated in each case. The observational data for the brightness maximum and minimum cannot be described by models with a fixed luminosity or fixed distance to the star. This is a consequence of the object’s unusual behavior, with synchronous flux decreases in all the observed bands. The inability of the model to adequately describe the minimum-brightness state is probably associated with the abrupt disruption of the spherical symmetry of the envelope due to the formation of a small, dense dust cloud in the line of sight.