A COMPUTATIONAL INVESTIGATION OF MIGRATION ENTHALPIES AND ELECTRONIC STRUCTURE IN SrFeO 3-δ

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1 A COMPUTATIONAL INVESTIGATION OF MIGRATION ENTHALPIES AND ELECTRONIC STRUCTURE IN SrFeO 3-δ A. Predith and G. Ceder Massachusetts Institute of Technology Department of Materials Science and Engineering Room Massachusetts Avenue Cambridge, Massachusetts ABSTRACT SrFeO 3-δ displays fast oxygen ion conduction at high temperatures. First principles calculations found the calculated migration enthalpy to be 0.78 ev. Substitution of Sr 2+ with Ba 2+ indicates that the migration enthalpy increases with increasing radius of the A cation. Substitution of Fe 4+ with Mn 4+, Co 4+, or Ru 4+ shows a generally positive correlation between B radius size and migration enthalpy, but important exceptions exist. The calculated electronic structure confirms the metallic nature of SrFeO 3 as the Fermi level lies in bands with considerable width. INTRODUCTION High temperature perovskite oxides display the highest oxygen ion conductivities of any inorganic material. In many perovskites, the high ionic transport rate is accompanied by excellent electronic conductivity. While the electronic conductivity excludes them from use as solid state electrolytes, the high mixed conductivity makes them excellent materials for use as electrodes or oxygen gas separation membranes (1). The A ion in the ABO 3 perovskite is usually a lanthanide or earth-alkaline, and the B cation is usually a transition metal chosen to ensure good electronic transport. Optimization of conductivity, under the constraint of stability in both reducing and oxidizing environments, has so far been largely experimental. This short paper presents a first principles computation of the migration enthalpy for oxygen diffusion in selected perovskites and the electronic structure of SrFeO 3, chosen as a prototypical perovskite. While the migration enthalpy is not the only relevant parameter to obtain high permeation rates in membranes, it is definitely a key quantity in determining the oxygen diffusivity. A computational investigation of perovskite compounds provides an organized approach to isolating the effect of individual factors on the conductivity parameters. First principles calculations constitute a fundamental approach to computing material properties. Data presented in this proceeding are the result of solving the one-electron Schrödinger equation in the Generalized Gradient Approximation (GGA) to Density Functional Theory. The calculations used a soft pseudopotential representation of nuclei, as implemented in the Vienna Ab-initio Simulation Package (VASP) (2). These

2 calculations give a fully quantum mechanical description of the energy that allows for ionic as well as covalent effects, a key requirement for the description of covalent oxides (3). This investigation is different from previous computational studies of migration enthalpies in perovskites, which used energy models based on fitted interatomic potentials (4). The cutoff energy of the wave functions in the plane-wave basis set was 270 ev, and all cells were cubic perovskites with ABO 3 stoichiometry. Numerical errors are expected to be less than 1 to 2 mev. One promising perovskite compound for separation membranes is SrFeO 3. Often doped with lanthanum or cobalt, this material forms the basis for a family of compounds used as permeation membranes. The objective of this work is to determine the electronic structure SrFeO 3 and systematically investigate the effect of A and B cation replacement on the migration barrier for oxygen transport. OXYGEN MIGRATION ENTHALPY ( H mig ) Calculation of H mig in SrFeO 3 The migration enthalpy of a diffusing oxygen ion is the energy difference between a supercell with a diffusing oxygen ion is in its initial, stable position and a supercell with the oxygen in the position along the migration path with the maximum energy. Several potential pathways exist for the oxygen ion. A study by Cherry, et. al. of perovskite oxides found that interstitial diffusion is not favorable due to high energy barriers (5). Their study concluded that the oxygen migration followed a curved pathway of from one corner of a BO 6 octahedron to an adjacent vacant corner of the octahedron. The migration enthalpy of an oxygen ion diffusing along this path between adjacent octahedron corners is the difference between two supercell energies. The energy of the first supercell, 8 cubic perovskites of SrFeO 3 containing one oxygen vacancy at the corner of an oxygen octahedra, is E initial. The diffusing oxygen is in a stable position on the corner of the oxygen octahedron. The energy calculation used a 4x4x4 kpoint mesh. The energy of the second supercell is E activated. The diffusing oxygen ion is in its highest energy state in between its initial position on the corner of an octahedron and its final position in the vacancy on the adjacent corner. The second supercell has 8 cubic perovskites of SrFeO 3 with oxygen vacancies on two adjacent corners of an oxygen octahedron and with the diffusing oxygen ion half way along a curved trajectory between the two vacancies. The second energy calculation also used a 4x4x4 kpoint mesh. Figure 1 shows the path of the oxygen ion. H mig = E activated E initial [1] H mig (SrFeO 3 ) = 0.78 ev

3 2.7 Å 1.7 Å Sr O 1.9 Å 3.3 Å Fe Figure 1. The calculation of migration enthalpy used supercells of 8 cubic perovskites and one missing oxygen ion. Shown here is the perovskite containing the oxygen vacancy. The diffusion path is from one corner of the oxygen octahedron to the adjacent corner. Effect of A and B Cation Radius on H mig As an oxygen ion diffuses through the interstice between two strontium ions and one iron ion, the size of the cations may affect the migration enthalpy. To investigate the effect of cation size, changing either the A site cation or B site cation while keeping all structures cubic perovskite isolates the effect of the cation on migration enthalpy. In the calculation, the volume of the perovskite and the coordinates of the ions relax while maintaining the cubic perovskite structure. Comparing BaFeO 3 to SrFeO 3 examines the effect of the A cation on H mig, and similarly comparing SrMnO 3, SrCoO 3 and SrRuO 3 to SrFeO 3 demonstrates the influence of the B cation on H mig. The resulting migration enthalpies in figure 2 show a clear trend with ionic size in the A-substituted case: a larger A cation leads to a higher oxygen migration barrier. In figure 3, the effect of the B cation is less clear, although the oxygen migration barrier also seems to generally increase with B-cation size.

4 ionic radii /Ang ionic radii migration enthalpy H migration /ev 1.4 Sr 2+ Ba 2+ A cations Figure 2. The perovskite AFeO 3 compounds show increasing migration enthalpy with increasing A cation radius (6) ionic radii /Ang ionic radii migration enthalpy H migration /ev Mn 4+ Co 4+ Fe 4+ Ru 4+ B cations Figure 3. The oxygen migration enthalpy in cubic perovskite SrBO 3 for various B ions shows that, overall, the migration enthalpy seems to increase with B cation size. Fe 4+ is a notable exception (6). To understand the trend between H mig with the A and B cation size, Kilner and Brook considered the effect the cations have on the amount of open volume in the perovskite structure (4). They found as the A cation increases in size, less volume is available through which an oxygen can diffuse; therefore, the migration enthalpy increases. The trend in their study of perovskites with interatomic potentials gave the same result as this first principles method for the A cation substitution.

5 Kilner used a similar argument to understand the trend between H mig and the size of the B cation. If the migration enthalpy depends largely on the amount of free volume, then an increase in B radius size would cause an increase in the amount of free volume available to the diffusing oxygen. The expected result would be that the migration enthalpy decreases with increasing B radius. Kilner and Brook found this general trend in their computational study (4). Since their study used potential models, their result largely reflects size and electrostatic interactions between ions. The result is not a definitive explanation of B cation site substitution (7). The quantum mechanical results in figure 3 do not follow the Kilner and Brook trend and even seem to point in the opposite direction. The migration enthalpy generally increases with increasing B radius with two exceptions: an increase in migration enthalpy from Mn 4+ to Co 4+ with no change in radius size and a decrease in migration enthalpy from Co 4+ to Fe 4+ with an increase in radius size. Reconsidering the free volume concept, the B cation radii are within 0.1 Å of each other, and changing the radius of the B site does not greatly influence the amount of free volume. Since the effect of the B ion on the oxygen activated state does not seem to follow simple electrostatic and size arguments, the trend between B radius size and migration enthalpy may be due to a rather covalent bond between the transition metal and oxygen. The d-states of octahedral transition metal ions undergo considerable hybridization with oxygen p-states, in particular when the transition metal is highly oxidized, which is the case for Fe 4+ (8). For a diffusing oxygen, the hybridized bond changes considerably as the oxygen travels along the path from one site to another. Such changes in hybridization would be specific to the electronic structure of each transition metal and would be unrelated to size or electrostatic effects. ELECTRONIC STRUCTURE Band Structure of SrFeO 3 Calculating the oxygen migration enthalpy of SrFeO 3 and the effect of the cation size on the migration enthalpy suggests SrFeO 3 can act as a good host material for ionic conduction. To understand the mixed conducting behavior of SrFeO 3 required for cathodes or oxygen separation membranes, an investigation of the electronic structure of the compound is useful. The band structure of SrFeO 3 in figures 4 and 5 show that the Fermi level crosses very wide bands. In the case of narrow bands, density functional theory does not reliably predict the electronic character of an oxide, but these wide bands at the Fermi level give a good indication that SrFeO 3 may be an intrinsic metallic conductor. A large amount of spin polarization present on the Fe 4+ can be observed from the difference between the up spin and down spin bands.

6 8 6 up bands energy /ev E Fermi ½ 0 ½ ½ ½ ½ ½ 0 ½ 0 delta_k /Ang.^-1 Figure 4. The calculated up spin bands of SrFeO 3 show the Fermi level crosses wide bands down bands 6 energy /ev E Fermi ½ 0 ½ ½ ½ ½ ½ 0 ½ 0 delta_k /Ang.^-1 Figure 5. The calculated down spin bands of SrFeO 3 show the Fermi level crosses a dense region of bands. Density of Electronic States in SrFeO 3 The density of states of SrFeO 3 shows that the Fermi level lies in a dense region of states (Fig. 6). Since the material has available energy sites close in energy to the Fermi level, the plot suggests that perfectly stoichiometric SrFeO 3 is a metallic conductor.

7 (Energy - E_Fermi) /ev up states down states Fermi level Figure 6. The electronic density of states in cubic perovskite SrFeO 3 shows the Fermi level in a dense region of states. The abscissa is normalized with respect to the Fermi level. CONCLUSION The first principles investigation of cubic perovskite SrFeO 3 shows that H mig = 0.78 ev. Substitution of Sr 2+ with the larger cation Ba 2+ shows that increasing A cation size increases the migration enthalpy. The increasing A cation size decreases the available free space for oxygen diffusion thereby increasing the migration enthalpy. Substituting Fe 4+ with smaller Mn 4+ or Co 4+ or larger Ru 4+ shows no clear trend between B cation size and migration enthalpy, indicating that this effect may be dominated by covalent bonding. The electronic band structure and density of states shows the Fermi level to cross wide bands, which explains the metallic conductivity observed in these materials. ACKNOWLEDGMENTS We would like to thank discussions with our colleagues A. C. Palanduz, H. Tuller, and the members of the Scientific Computational Research and Analysis of Materials group. AP acknowledges a Graduate Fellowship from the National Science Foundation. Support for this work came from the Department of Energy through the University of Alaska, Fairbanks (contract number UAF ).

8 REFERENCES Journals 1. U. Balachandran, et. al., American Ceramic Society Bulletin, 74, 71 (1995). 2. G. Kresse, J. Furthmuller, Physical Review B, 54, (1996). 3. A. F. Kohan and G. Ceder, Computational Materials Science, 8, 142 (1997). 4. J. Kilner and R. Brook, Solid State Ionics, 6, 237 (1982). 5. M. Cherry, M. Islam, C. Catlow, Journal of Solid State Chemistry, 118, 125 (1995). 6. R. Shannon, Acta Crystallographica, A32, 751 (1976). 7. J. Kilner, Solid State Ionics, 129, 13 (2000). 8. G. Ceder, Y.-M. Chiang, D. R. Sadoway, M. K. Aydinol, Y.-I Jang, B. Huang, Nature, 392, 694 (1998).

9 Key Words perovskite, Sr, Fe, migration enthalpy, electronic structure, density of states, bands, oxygen diffusion, strontium, iron, oxide, activation energy, radius