Abstract
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.
Highlights
Due to their exceptional electronic, magnetic, or optical properties [1], transition metal oxide (TMO) compounds are key components of many modern technologies
This paper aims at providing a complete picture of the derivation of formation energies and phase diagrams of TMOs based on density functional theory (DFT)+U and the proposed correction schemes by evaluating, discussing, and generalizing the approaches proposed in the literature
With the exception of Tl2 O3 and PbO2, the points can be represented by a line, y = x + b, which confirms the generality of the approach of Wang et al [13], where six arbitrarily chosen compounds were taken into consideration for this analysis
Summary
Due to their exceptional electronic, magnetic, or optical properties [1], transition metal oxide (TMO) compounds are key components of many modern technologies. To many other applications, TMOs are utilized as active anode and cathode materials in Li- and Na-ion batteries [2,3,4,5] and as electrodes in solid-oxide fuel and electrolyzer cells [6,7,8] (SOFC and SOEC), where they enable the catalytic reactions with oxygen. The decisive functional parameters of a TMO, such as the catalytic activity and the electronic conductivity in the case of a solid-oxide cell electrode, can be tuned by varying the stoichiometry, e.g., by external doping or the incorporation of intrinsic lattice defects [9,10,11]. A phase diagram with respect to elemental reservoirs determines the ranges of the experimental synthesis conditions within which the desired compound can be stabilized and within which its composition can be varied without unwanted competing phases being formed.
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