Vacancy Ordering in Fe-Deficient Iron Sulfide with the NiAs-Type Structure

An Fe-deficient iron sulfide thin film with a nickeline (NiAs) type structure has been reported with a stoichiometry close to greigite (Fe₃S₄) [Davis E. M.; Phys. Chem. Chem. Phys.2019, 21, 20204-20210]. We have investigated the Fe-vacancy ordering in the nonstoichiometric iron sulfide with the NiAs-like structure using density functional theory calculations with a Hubbard Hamiltonian and long-range dispersion corrections [DFT + <i>U</i> - D3(BJ)]. We applied canonical statistical mechanics to study the thermodynamics of ordering and in the most stable configuration we found the same concentration of Fe deficiencies in each layer along the <i>c</i> axis. We discuss the probabilities of the configurations and the averages of observables, such as lattice parameters and magnetic moments, as a function of temperature. At equilibrium, the Fe-deficient iron sulfide is expected to be fully ordered. The predicted electronic properties of the most stable configuration suggest that this material is antiferromagnetic. The simulated electronic structure shows that the most stable configuration of the Fe-deficient iron sulfide has semimetallic properties.