Thermodynamic Landscape of Iron Vacancies in Troilite: Implications for Phase Stability and Electronic Properties

Troilite (FeS) is the stoichiometric end-member of the pyrrhotite (Fe_1–xS) mineral group, where x ranges from 0 to 0.125. While pyrrhotite is among the most abundant sulfide minerals on Earth, troilite is primarily found in meteorites and lunar rocks. The ordering of Fe vacancies in the hexagonal structure of troilite leads to the prevalent monoclinic Fe₇S₈ pyrrhotite phase. The electronic properties of troilite have attracted increasing interest due to their relevance in catalysis, spectroscopy, geochemistry, and planetary science. In this study, we investigate native Fe vacancies in troilite and their influence on the electronic and geometric structure of troilite. Vacancy formation introduces new electronic states within the band gap. Thermodynamic analysis reveals that the Helmholtz free energy of vacancy formation in troilite reaches a minimum at x = 0.125 at 800 K. To better understand the transformation of troilite into pyrrhotite, we extended our thermodynamic study to the nonstoichiometric phase. For pyrrhotite, a free energy minimum is found at x = 0.125 at 500 K, which is more favorable than that in troilite for the same defect concentration. These results agree with experimental observations that pyrrhotite forms around 500 K, while troilite requires higher synthesis temperatures (>1000 K). Topological analysis using QTAIM and the electron localization function reveals that Fe vacancies act as Lewis acid sites and that troilite exhibits a greater covalent character compared to other sulfide minerals.