**1. Introduction**

490 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

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The ABO3-type perovskite manganites, cobaltates, and ferrates (A= La, Sr, Ca; B=Mn, Co, Fe) are important functional materials which have numerous high-tech applications due to their outstanding magnetic and electrical properties, such as colossal magnetoresistance, half-metallic behavior, and composition-dependent metal-insulator transition (Coey et al., 1999; Haghiri-Gosnet & Renard, 2003). Owing to high electronic and ionic conductivities. these materials show also excellent electrochemical performance, thermal and chemical stability, as well as compatibility with widely used electrolyte based on yttrium-stabilized zirconia (YSZ). Therefore they are among the most promising materials as cathodes in solid oxide fuel Cells (SOFCs) (Fleig et al., 2003) and gas-permeation membranes (Zhou, 2009). Many of the above-mentioned applications require understanding and control of surface properties. An important example is LaMnO3 (LMO). Pure LMO has a cubic structure above 750 K, whereas below this temperature the crystalline structure is orthorhombic, with four formula units in a primitive cell. Doping of LMO with Sr allows one to increase both the ionic and electronic conductivity as well as to stabilize the cubic structure down to room temperatures - necessary conditions for improving catalytic performance of LMO in electrochemical devices, e.g. cathodes for SOFCs. In optimal compositions of b b <sup>3</sup> 1-x x La Sr MnO (LSM) solid solution the bulk concentration of Sr reaches xb0.2 .

Understanding of LMO and LSM basic properties (first of all, energetic stability and reactivity) for pure and adsorbate-covered surfaces is important for both the lowtemperature applications (e.g., spintronics) and for high-temperature electrochemical processes where understanding the mechanism of oxygen reduction on the surfaces is a key issue in improving the performance of SOFC cathodes and gas-permeation membranes at relatively high (~800 C) temperatures. First of all, it is necessary to determine which LMO/LSM surfaces are the most stable under operational conditions and which terminations are the energetically preferential? For example, the results of our simulations described below show that the [001] surfaces are the most stable ones in the case of LMO (as

Thermodynamics of ABO3-Type Perovskite Surfaces 493

wavefunctions of valence electrons on O atoms and valence and core-valence electrons on

We found that seven- and eight-plane *slabs* infinite in two (x-y) directions are thick enough to show convergence of the main properties. The periodically repeated slabs were separated along the z-axis by a large vacuum gap of 15.8 Å. All atomic coordinates in slabs were allowed to relax. To avoid problems with a slab dipole moment and to ensure having identical surfaces on both sides of slabs, we employed the symmetrical seven-layer slab MnO2(LaO-MnO2)3 in our plane-wave simulations, even though it has a Mn excess relative to La and a higher oxygen content. Such a choice of the slab structure however only slightly changes the calculated energies. For example, the energy for dissociative oxygen adsorption

is -2.7 eV for eight-layers (LaO-MnO2)4 slab and -2.2 eV for the symmetrical seven-layer MnO2-(LaO-MnO2)3 slab. The use of symmetrical slabs also allows decoupling the effects of different surface terminations and saving computational time due to the possibility to exploit higher symmetry of the slabs. The simulations were done using an extended 2√2 × 2√2 surface unit cell and a 2 × 2 Monkhorst-Pack k-point mesh in the Brillouin zone (Monkhorst & Pack, 1976). Such a unit cell corresponds to 12.5% concentration (coverage) of

The choice of the magnetic configuration only weakly affects the calculated surface relaxation and surface energies (Evarestov, et. al., 2005; Kotomin et al, 2008; Mastrikov et al., 2009). Relevant magnetic effects are sufficiently small (≈0.1eV) as do not affect noticeably relative stabilities of different surfaces; these values are much smaller than considered adsorption energies and vacancy formation energies. As for slabs the ferromagnetic (FM) configuration has the lowest energy, we performed all further plane-wave calculations with

The quality of plane-wave calculations can be illustrated by the results for the bulk properties (Evarestov, et. al., 2005; Mastrikov et al., 2009). In particular, for the lowtemperature orthorhombic structure the A-type antiferromagnetic (A-AFM) configuration (in which spins point in the same direction within each [001] plane, but opposite in the neighbor planes) is the energetically most favorable one, in agreement with experiment. The lattice constant of both the cubic and orthorhombic phase exceeds the experimental value only by 0.5%. The calculated cohesive energy of 30.7 eV is also close to the experimental

In our *ab initio* LCAO calculations we use DFT-HF (*i.e.*, density functional theory and Hartree-Fock) hybrid exchange-correlation functional which gave very good results for the electronic structure in our previous studies of both LMO and LSM (Evarestov et al., 2005; Piskunov et al., 2007). We employ here the hybrid B3LYP exchange-correlation functional (Becke, 1993). The simulations were carried out with the CRYSTAL06 computer code (Dovesi, et. al., 2007), employing BS of the atom-centered Gaussian-type functions. For Mn and O, all electrons are explicitly included into calculations. The inner core electrons of Sr and La are described by small-core Hay-Wadt effective pseudopotentials (Hay & Wadt, 1984) and by the nonrelativistic pseudopotential (Dolg et al., 1989), respectively. BSs for Sr and O in the form of 311d1G and 8–411d1G, respectively, were optimized by Piskunov et al., 2004. BS for Mn was taken from (Towler et al., 1994) in the form of 86–411d41G, BS for La is

the surface defects in calculations of vacancies and adsorbed atoms and molecules.


<sup>2</sup> 2 22 *<sup>x</sup> O Mn O Mn Mn ad Mn* (1)

metal atoms were explicitly evaluated in our calculations.

on the [001] MnO2-terminated surface

FM ordering of atomic spins.

value (31 eV).

compared to [011] and others). However, the [001] surfaces have, in turn, two different terminations: LaO or MnO2. We will compare stabilities of these terminations under different environmental conditions (temperature and partial pressure of oxygen gas). Another important question to be addressed is, how Sr doping affects relative stabilities of the LMO surfaces? These issues directly influence the SOFC cathode performance. Answering these questions requires a thermodynamic analysis of surfaces under realistic SOFC operational conditions which is in the main focus of this Chapter. Such a thermodynamic analysis is becoming quite common in investigating structure and stability of various crystal surfaces (Examples of thermodynamic analyses of binary and ternary compounds can be found in Reuter & Scheffler, 2001a, 2001b; Bottin et al., 2003; Heifets et al., 2007a, 2007b, Johnson et al., 2004).

The thermodynamic analysis requires careful calculations of energies for two-dimensional slabs terminated by surfaces with various orientations and terminations. The required energies could be calculated using *ab initio* methods of the atomic and electronic structure based on density functional theory (DFT). In this Chapter, we present the results obtained using two complementary *ab initio* DFT approaches employing two different types of basis sets (BS) representing the electronic density distribution: plane waves (PW) and linear combination of atomic orbitals (LCAO). Both techniques were used to calculate the atomic and electronic structures of a pure LMO whereas investigation of the Sr influence on the stability of different (001) surfaces was performed within LCAO approach.

After studying the stabilities of various surfaces, the next step is investigating the relevant electrochemical processes on the most stable surfaces. For this purpose, we have to evaluate the adsorption energies for O2 molecules, O atoms, the formation energies of O vacancies in the bulk and at the stable perovskite surfaces. These energies, together with calculated diffusion barriers of these species and reactions between them, allow us to determine the mechanism of incorporation of O atoms into the cathode materials. However, such mechanistic and kinetic analyses lie beyond the scope of this Chapter (for more details see e.g. Mastrikov et al., 2010). Therefore, we limit ourselves here only to the thermodynamic characterization of the initial stages of the oxygen incorporation reaction, which include formation of stable adsorbed species (adsorbed O atoms, O2 molecules) and formation of oxygen vacancies. The data for formation of both oxygen vacancies and adsorbed oxygen atoms and molecules have been collected using plane wave based DFT.
