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.

Oxygen vacancy formation energies play a major role in the electric field‐assisted abnormal grain growth of technologically relevant polycrystalline perovskite phases. The underlying effect on the atomic scale is assumed to be a redistribution of cationic and anionic point defects between grain boundaries (GBs) and the bulk interior regions of the grains due to different defect formation energies in the structurally different regions, accompanied by the formation of space charge zones. Using atomistic calculations based on classical interatomic potentials, optimized structures of the symmetric tilt GBs Σ5(210)[001] and Σ5(310)[001], and of the asymmetric tilt GB (430)[001]||(100)[001] in the electroceramic perovskite materials SrTiO₃, BaTiO₃, and BaZrO₃, are derived and discussed. Profiles of oxygen vacancy formation energies across those GBs are presented and their dependence on composition and GB type is discussed.

Oxygen vacancies have been identified to play an important role in accelerating grain growth in polycrystalline perovskite-oxide ceramics. To advance the fundamental understanding of growth mechanisms at the atomic scale, classical atomistic simulations were carried out to investigate the atomistic structures and oxygen vacancy formation energies at grain boundaries in the prototypical perovskite-oxide material $\mathrm{SrTi}{\mathrm{O}}_3$. In this paper, we focus on two symmetric tilt grain boundaries, namely, Σ5 (310)[001] and Σ5 (210)[001]. A one-dimensional continuum model is adapted to determine the electrostatic potential induced by charged lattice planes in atomistic structure models containing grain boundaries and point defects. By means of this model, electrostatic artifacts, which are inherent to supercell models with periodic or open boundary conditions, can be considered and corrected properly. We report calculated formation energies of oxygen vacancies on all the oxygen sites across boundaries between two misoriented grains, and we analyze and discuss the formation-energy values with respect to local charge densities at the vacant sites.

Artificial electrostatic potentials can be present in supercells constructed for atomistic simulations of surfaces and interfaces in ionic crystals. Treating the ions as point charges, we systematically derive an electrostatic formalism for model systems of increasing complexity, both neutral and charged, and with either open or periodic boundary conditions. This allows to correctly interpret results of classical atomistic simulations which are directly affected by the appearance of these potentials. We demonstrate our approach at the example of a strontium titanite (SrTiO₃) supercell containing an asymmetric tilt grain boundary. The formation energies of charged oxygen vacancies and the relaxed interface structure are calculated based on an interatomic rigid-ion potential, and the results are analyzed in consideration of the electrostatic effects.

A main source of capacity fading in lithium-ion batteries is the degradation of the active cathode materials caused by the series of volume changes during charge and discharge cycles. The quaternary colquiriite-type fluorides ${\mathrm{Li}}_x{\mathrm{CaFeF}}_6$ and ${\mathrm{Li}}_x{\mathrm{CaCoF}}_6$ were reported to have negligible volume changes in specific Li concentration ranges, making the underlying colquiriite structure a promising candidate for so-called zero-strain behavior. Using first-principles electronic structure calculations based on density functional theory with a Hubbard-$U$ correlation correction on the transition-metal ions, we systematically investigate the equilibrium volumes of the colquiriite-type fluorides ${\mathrm{Li}}_x{\mathrm{Ca}\mathit{M}\mathrm{F}}_6$ with $M=\mathrm{Ti}$, V, Cr, Mn, Fe, Co, and Ni at the Li concentrations $x=0$, 1, and 2. We elucidate the connection between the total volume of the structures and the local volumes of fluorine coordinated octahedra around the cations, and we find trends along the series of the 3d transition-metal elements. In the lithiation step from $x=1$ to $x=2$ we find volume changes of about 10%, and we discuss the discrepancy to the experimentally reported smaller value for ${\mathrm{Li}}_x{\mathrm{CaFeF}}_6$. The suitability as cathode material was furhter investigated by calculating the theoretical voltages and capacities. From $x=0$ to $x=1$ we describe the compensating structural mechanisms that lead to an exceptionally small volume change of ${\mathrm{Li}}_x{\mathrm{CaMnF}}_6$, which posseses a high theoretical voltage and moderate capacity. This compound is therefore a particularly promising zero-strain cathode material.