**5. Conclusions and perspectives**

In this Chapter, combining *ab initio* calculations of the atomic and electronic structure with chemical thermodynamics, we have described how to predict surface stabilities with different orientations and terminations for ABO3 perovskite materials and solid solutions. We considered also adsorption and formation of vacancies in the bulk and at the surfaces. The input data for such thermodynamic analyses are available from standard DFT calculations. We neglected vibrational contributions to the Gibbs free energies in present simulations, since there are good arguments that these contributions are quite small. However, the latest versions of the computer codes used here (VASP and CRYSTAL) are capable to perform the calculations of phonon spectra, which can be used to include vibration contributions into thermodynamic potentials. Despite currently such surface phonon calculations are computationally very expensive, with development of new algorithms and faster computers such analysis in near future could become a routine practice.

We have applied the described techniques to experimentally well studied SOFC cathode materials (LMO and LSM). The energies calculated by DFT techniques allow us to draw the surface stability diagrams showing that under the SOFC operational conditions MnO2 terminated surface of defect/dopant-free LMO is the most stable. The MnO2-terminated surface with adsorbed O atoms becomes more stable in a cubic phase of LMO. (The analysis based on results of calculations with hybrid functional gives higher precision of the obtained diagrams). Introduction of Sr dopant into LMO leads to a significant decrease of stability of MnO2-terminated surface with respect to stability of Sr-containing 1 *x x s s La Sr O* -terminated

surface. At elevated temperatures only the latter one can be found within an entire region of LSM stability which definitely should affect the LSM cathode performance due to our prediction that oxygen vacancies easily segregate from LMO bulk towards MnO2 terminated surface but not to the LaO-terminated one (Mastrikov et al, 2010).

Thermodynamic consideration of oxygen adsorption and formation of surface vacancies allowed us to move beyond the usual analysis of purely DFT electronic energy differences in these processes at zero K and to describe changes in the Gibbs free energies under realistic environmental conditions (high temperature and partial pressure of oxygen gas). In particular, we have shown that an oxygen adsorption from the gas phase is exergonic at low temperatures, but becomes endergonic at SOFC operational temperatures. Consideration of the energy differences between O atoms and O2 molecules in the gas phase and at surfaces makes it possible to determine theoretically preferred adsorption sites, adsorption energies and formation energies for vacancies (e.g. Kotomin et al., 2008, Mastrikov et al., 2010, and Piskunov et al, 2011). Thus the obtained data can be used for analysis of the kinetics of chemical reactions and investigation of their mechanisms. For example, we performed such an analysis (Mastrikov et al., 2010) in the study of oxygen reduction and incorporation into the LMO surfaces.

Note also that under realistic experimental conditions in a multinary crystal typically only one component is reversibly exchangeable so that only one chemical potential can be varied in-situ. Typically the others are varied under preparation conditions, and then soestablished sublattice stoichiometry is frozen under experimental conditions. This complex interplay of in-situ and ex-situ parameters has been discussed by Maier, 2003.

Various questions, where thermodynamic approach is necessary, are still open. One example is Sr segregation towards LSM surfaces which was experimentally observed e.g. by Fister et al., 2008 and Herger et al., 2008. In the study by Herger et al., 2008, the Sr segregation energy was estimated to be ~0.16 eV while preliminary theoretical estimate gave the segregation energy ~0.54 eV (Piskunov et al., 2008). Another question is, how vacancy formation and oxygen adsorption energies depend on surface Sr concentration. Lastly, our present simplified simulations assume that LMO and LSM have large flat surfaces. However, one can expect in reality much more rough surface structure containing many facets and steps. This is important also because SOFC cathode materials are polycrystalline. Therefore, there is a necessity to check, which kinds of steps and facets are the most stable ones and likely to exist at LMO and LSM surfaces and how their presence affects adsorption of oxygen atoms and molecules, vacancy formation and reactions occurring at the surfaces.
