The effect of the regular solution model in the condensation of protoplanetary dust

We utilize a chemical equilibrium code in order to study the condensation process which occurs in protoplanetary discs during the formation of the first solids. The model specifically focuses on the thermodynamic behaviour on the solid species assuming the regular solution model. For each solution, we establish the relationship between the activity of the species, the composition and the temperature using experimental data from the literature. We then apply the Gibbs free energy minimization method and study the resulting condensation sequence for a range of temperatures and pressures within a protoplanetary disc. Our results using the regular solution model show that grains condense over a large temperature range and therefore throughout a large portion of the disc. In the high-temperature region (T >= 1400 K) hibonite and gehlenite dominate, and we find that the formation of corundum is sensitive to the pressure. The mid-temperature region is dominated by Fe(s) and silicates such as Mg2SiO4 and MgSiO3. The chemistry of forsterite and that of enstatite are strictly related, and our simulations show a sequence of forsterite-enstatite-forsterite with decreasing temperature and the abundance of the first high-temperature peak of forsterite is also pressure sensitive. In the low-temperature regions (T <= 600 K), a range of iron compounds (FeS, Fe2SiO3, FeAl2O3) form. We find that all the condensation sequences move towards lower temperature as the pressure decreases. We also run simulations using the ideal solution model and see clear differences in the resulting condensation sequences with changing solution model. In particular, we find that the turning point in which forsterite replaces enstatite in the low-temperature region is sensitive to the solution model. In this same temperature region, fayalite is the most stable compound for the regular solution, while magnetite replaces fayalite in the ideal solution model at the lowest values of temperature. Our results show that the ideal solution model is often a poor approximation to experimental data at most temperatures important in protoplanetary discs. We find some important differences in the resulting condensation sequences when using the regular solution model and suggest that this model should provide a more realistic condensation sequence.