Knowledge about the formation energies of compounds is essential to derive phase diagrams of multicomponent phases with respect to elemental reservoirs. The determination of formation energies using common (semi-)local exchange-correlation approximations of the density functional theory (DFT) exhibits well-known systematic errors if applied to oxide compounds containing transition metal elements. In this work, we generalize, reevaluate, and discuss a set of approaches proposed and widely applied in the literature to correct for errors arising from the over-binding of the O2 molecule and from correlation effects of electrons in localized transition-metal orbitals. The DFT+U method is exemplarily applied to iron oxide compounds, and a procedure is presented to obtain the U values, which lead to formation energies and electronic band gaps comparable to the experimental values. Using such corrected formation energies, we derive the phase diagrams for LaFeO3, Li5FeO4, and NaFeO2, which are promising materials for energy conversion and storage devices. A scheme is presented to transform the variables of the phase diagrams from the chemical potentials of elemental phases to those of precursor compounds of a solid-state reaction, which represents the experimental synthesis process more appropriately. The discussed workflow of the methods can directly be applied to other transition metal oxides.
Determination of Formation Energies and Phase Diagrams of Transition Metal Oxides with DFT+U
