A first-principles investigation on the enthalpy landscape for the hibonite solid solution: Implications for a nebular barometer

Hibonite, nominally CaAl₁₂O₁₉, is among the first minerals thermodynamically predicted to have formed in the early history of our solar system. It can incorporate significant amounts of Ti (≤15 wt%, ∼2 cations per formula unit) into its crystal structure, as both Ti⁴⁺ and Ti³⁺. The main pathways for Ti incorporation in the solar nebula include a direct substitution of Ti³⁺ replacing Al³⁺ and a coupled substitution in which Ti⁴⁺ and Mg²⁺ replace two Al³⁺. Additionally, the formation of oxygen vacancies can also reduce a Ti⁴⁺ cation to Ti³⁺ by trapping a free electron. The relative amounts of these cations potentially reflect the fugacity of oxygen fO2, $\left({{f}_{{{\text{O}}_{2}}}} \right),$ a fundamental thermodynamic parameter, that prevailed when hibonite first formed or last equilibrated. However, the Ti content and its oxidation state in hibonite does not depend solely on fO2. ${{f}_{{{\text{O}}_{2}}}}.$ The composition of the system is, thus, a key factor in changing the Ti⁴⁺/ςTi ratio of the structure concurrently with the fO2. ${{f}_{{{\text{O}}_{2}}}}.$ Therefore, it is necessary to understand the energetics, complex crystal chemistry, and substitution reactions of hibonite to relate the Ti oxidation state to the fO2 ${{f}_{{{\text{O}}_{2}}}}$ of the nebular system in which it condensed. To that end, we report DFT calculations (0 K) to determine the ground-state energies and the enthalpy of formation (ΔH) of hibonite solid solutions that span the range reported in meteorites. Our results show that coupled substitution is energetically favored (ΔH = -96.70 kJ·mol^-1, from oxides). In comparison, the formation of oxygen vacancies is energetically unfavorable, though similar to Ti³⁺ direct substitution for Al³⁺ (ΔH = ∼60 kJ/mol, from oxides), which is commonly observed in hibonite. It is therefore necessary to consider oxygen vacancies as a potential mechanism for controlling the incorporation of Ti³⁺ into hibonite, in addition to direct replacement reactions. We provide here the first reliable estimation of the formation enthalpies for the hibonite solid solution that includes solutes and point defects. The results presented herein constitute a significant advance toward the establishment of a comprehensive Gibbs free energy description of the hibonite solid solution, which is ultimately required for accurate modeling of its thermodynamic stability within the early solar nebula.