3738 | Phys. Chem. Chem. Phys., 2017, 19, 3738--3755 This journal is © the Owner Societies 2017 Cite this: Phys. Chem. Chem. Phys., 2017, 19, 3738 Thermodynamic stability of stoichiometric LaFeO 3 and BiFeO 3 : a hybrid DFT study† Eugene Heifets,* a Eugene A. Kotomin, ab Alexander A. Bagaturyants cd and Joachim Maier a BiFeO 3 perovskite attracts great attention due to its multiferroic properties and potential use as a parent material for Bi 1x Sr x FeO 3d and Bi 1x Sr x Fe 1y Co y O 3d solid solutions in intermediate temperature cathodes of oxide fuel cells. Another iron-based LaFeO 3 perovskite is the end member for well-known solid solutions (La 1x Sr x Fe 1y Co y O 3d ) used for oxide fuel cells and other electrochemical devices. In this study an ab initio hybrid functional approach was used for the study of the thermodynamic stability of both LaFeO 3 and BiFeO 3 with respect to decompositions to binary oxides and to elements, as a function of temperature and oxygen pressure. The localized (LCAO) basis sets describing the crystalline electron wave functions were carefully re-optimized within the CRYSTAL09 computer code. The results obtained by considering Fe as an all-electron atom and within the effective core potential technique are compared in detail. Based on our calculations, the phase diagrams were constructed allowing us to predict the stability region of stoichiometric materials in terms of atomic chemical potentials. This permits determining the environmental conditions for the existence of stable BiFeO 3 and LaFeO 3 . These conditions were presented as contour maps of oxygen atoms’ chemical potential as a function of temperature and partial pressure of oxygen gas. A similar analysis was also performed using the experimental Gibbs energies of formation. The obtained phase diagrams and contour maps are compared with the calculated ones. A. Introduction Both lanthanum and bismuth ferrates are limiting compounds for a set of very efficient cathode materials for solid oxide fuel cells (SOFCs) operating at intermediate temperatures (500–700 1C), while ordinary SOFCs operate at higher tempera- tures (700–1000 1C). In particular, lanthanum ferrate, LaFeO 3 (LFO), is the end member in solid solutions La 1x Sr x Fe 1y Co y O 3d , which are well-known highly efficient cathodes for SOFCs. 1–3 In its turn, bismuth ferrate, BiFeO 3 (BFO), is a parent material for the perovskite solid solutions Bi 1x Sr x FeO 3d and Bi 1x Sr x Fe 1y Co y O 3d , which were recently proposed as promising cathodes for the intermediate temperature SOFCs. 4–7 Simultaneously, BFO con- tinues to attract considerable attention due to its multiferroic properties 8 under ambient conditions. It has also been found that the photocatalytic 9 and photovoltaic 10 properties of BFO are enhanced due to its ferroelectricity. Independent of the area of application, understanding the thermodynamic stability of LFO and BFO is vital to provide a solid basis for future investigations of intrinsic defects, surface structures, and surface chemical reactions (e.g. oxygen reduction reaction), as well as the formation of solid solutions, like the above mentioned cathode materials, their possible structures and stability. The stability behavior also provides a valuable guidance to the appropriate conditions while synthe- sizing these materials. The LFO formation energies were estimated in several experimental studies 9–16 using various calorimetric and electro- chemical techniques. However, the range of Gibbs free energies of formation of LFO from La 2 O 3 and Fe 2 O 3 oxides obtained in different experiments is very wide: from 15 23 kJ mol 1 to 92 kJ mol 1 . 16 Such a difference comes out from the use of various electrochemical experiments, very likely due to neglect of oxygen vacancies at high temperatures and polarization of electrodes. 12 In turn, to the best of our knowledge, a single measurement of the energies of BFO formation has been attempted, using solution calorimetry and calvet calorimetric measurements. 17 a Max Planck Institute for Solid State Research, Heisenbergstr. 1, Stuttgart 70569, Germany. E-mail: eheif5719@sbcglobal.net, eheif5719@twc.com b Institute for Solid State Physics, The University of Latvia, Riga, 8 Kengaraga str., Riga 1063, Latvia c National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoye shosse 31, Moscow 115409, Russia d Photochemistry Center RAS Federal State Institution, Federal Research Center Crystallography and Photonics Russian Academy of Science, 7a Novatorov St., Moscow, 119421, Russia † Electronic supplementary information (ESI) available. See DOI: 10.1039/c6cp07986e Received 22nd November 2016, Accepted 20th December 2016 DOI: 10.1039/c6cp07986e www.rsc.org/pccp PCCP PAPER