Atomic Modeling and Electronic Structure of Mixed IonicâElectronic

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Atomic Modeling and Electronic Structure of Mixed Ionic-Electronic Conductor SrTi FeO Considered as a Mixture of SrTiO and SrFeO 1-x

x

3-x/2+#

3

2

2

5

Namhoon Kim, Nicola H Perry, and Elif Ertekin Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.8b04284 • Publication Date (Web): 06 Dec 2018 Downloaded from http://pubs.acs.org on December 7, 2018

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Chemistry of Materials

Atomic Modeling and Electronic Structure of Mixed Ionic-Electronic Conductor SrTi1−xFexO3−x/2+δ Considered as a Mixture of SrTiO3 and Sr2Fe2O5 Namhoon Kim,†,‡ Nicola H. Perry,¶,‡,§ and Elif Ertekin∗,†,‡,§ †Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 W. Green Street, Urbana, Illinois 61801, United States ‡Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 ¶Department of Materials Science and Engineering and Materials Research Laboratory, University of Illinois at Urbana-Champaign, 1304 W. Green Street, Urbana, Illinois 61801, United States §World Premier International Research Center Initiative - International Institute for Carbon Neutral Energy Research (WPI-I2 CNER), Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan E-mail: [email protected]

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Chemistry of Materials 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract As mixed ionic-electronic conductors (MIECs), ABO3 perovskite oxides and derivative compounds are candidates for applications such as solid oxide fuel and electrolysis cells. Understanding the atomic configurations and electronic structure of MIECs is important because they form the basis of ionic and electronic conductivity, but challenging because the materials tend to be non-dilute systems with substantial partial occupancies of the perovskite sublattices. In this work, we present a computational model for Fesubstituted SrTiO3 (STF, SrTi1−x Fex O3−x/2+δ ), a representative perovskite-derivative MIEC, by considering it as a mixture of perovskite SrTiO3 (x = 0, δ = 0) and brownmillerite Sr2 Fe2 O5 (x = 1, δ = 0). Our model accounts for disorder in the form of Ti and Fe species on the perovskite B-site sublattice and of O atoms and vacancies VO on the oxygen sublattice. The defect chemistry and electronic structure of STF across the full composition range 0 ≤ x ≤ 1 and for small |δ| is addressed within the framework of first-principles density functional theory. We find that this model of the STF solid solution reproduces experimentally known features such as short-range ordering between Fe and VO and thermodynamic influence on oxygen content in STF. We illustrate how the electronic structure of STF systematically evolves from the characteristics of end member compounds SrTiO3 and Sr2 Fe2 O5 , and establish the effects of non-zero δ on the type of electronic carriers present. These findings confirm that the SrTi1−x Fex O3−x/2+δ framework is a useful description for this material system, providing a systematic understanding of structure-property relations in the non-dilute perovskite mixture. Although this work focuses on STF, the underlying approach may be applicable to other mixtures of perovskite oxides and ordered oxygen vacancy compounds.

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Introduction Mixed ionic-electronic conductors (MIECs) play an important role in various electrochemical systems such as solid oxide fuel and electrolysis cells. Controlling the atomic and electronic structure of these materials is important, since these form the basis of ionic and electronic conductivity. 1 Perovskite oxides, derivative compounds, and their mixtures often form MIECs because their compositional variety leads to an ability to control the atomic and electronic structure. 2,3 Perovskites with general formula ABO3 can accommodate various atomic species, where the A-site is typically occupied by an alkaline or rare earth cation and the B-site is occupied by a transition metal cation. Moreover, the flexibility to accommodate partial substitutions on the A and/or B sublattices with cations of different valences provides a mechanism for tailoring ionic and electronic transport. 2,4 One representative example is SrTi1−x Fex O3−y (STF), in which the B-site titanium atoms in the perovskite strontium titanate (SrTiO3 ) are partially replaced by iron. STF is a functional material with a large mixed ionic-electronic conductivity, and thus has potential in a wide range of applications, including as cathodes 5–10 and anodes

10–12

for solid oxide fuel cells, gas sensors, 13–17 perme-

ation membranes, 18–20 and catalysts. 21–23 SrTi1−x Fex O3−y forms a continuous solid solution over the entire composition range of 0 ≤ x ≤ 1. 24 At low x (x < 0.01), the material can be thought of as Fe-doped SrTiO3 . As substitution of Ti4+ by Fe3+ enhances the hole and oxygen vacancy concentration, Fe-doped SrTiO3 behaves as an acceptor-doped large band gap material with enhanced electronic conductivity. 25 For dilute Fe, even though both holes and oxygen vacancies can compensate for Fe the electronic conductivity often outweighs the ionic conductivity because the electronic mobility is much higher. On the other hand, at high x (0.1 < x), the material becomes a good MIEC. 5,6,26–28 The multivalent Fe species form an impurity band that broadens and participates in electronic conduction for Fe concentrations exceeding 3%. 28,29 Moreover, the degree of oxygen deficiency y typically increases with x, the amount of Fe introduced, because the difference in the oxidation state between Ti+4 and Fe+3 can be compensated ionically by 3



oxygen vacancy (VO ) formation to maintain charge neutrality. 28 Oxygen ion motion in STF occurs by a vacancy hopping mechanism and, consequently, an increase of the Fe concentration generally promotes oxygen ion transport through vacancy sites. 20,26 Therefore, with a reasonable amount of Fe, STF exhibits both significant ionic and electronic conductivity. 28,30 Several studies have focused on establishing the mixed conducting properties of STF as a function of Fe concentration 25,26 and experiments have revealed the material characteristics of STF such as electronic structure and magnetism, 25,26,28,31,32 surface oxygen exchange kinetics, 27,30,33,34 local atomic structure, 25,29,31–33 and oxygen non-stoichiometry. 35,36 There are also a large number of thermodynamic defect chemical models 27,28,36 and computational investigations 25,32,37–41 of the ionic and electronic properties of STF. Despite the progress, the electronic structure of STF remains not well-understood. In particular, there have been lengthy discussions on the oxidation state of Fe in bulk STF and the energy levels of the Fe bands relative to the valence or conduction band and their role in the reduced STF band gap. 28,32 The main shortcoming of most previous studies to date is the reliance on a model system involving dilute levels of substitutional Fe in SrTiO3 . Computationally, this is modeled by introducing one Fe atom into SrTiO3 supercell. This model cannot cover the wide composition range of STF, since Fe concentrations are not dilute in practice, and the effects of oxygen content on the electronic structure are not captured. To overcome these drawbacks, here we instead adopted a previously suggested 28 SrTi1−x Fex O3−x/2+δ (y = x/2 − δ) framework to describe STF and consider how the properties of STF emerge from this perspective. Within this composition space, the special case of δ = 0 represents the so-called “reference composition” of STF given by SrTi1−x Fex O3−x/2 . To maintain the reference composition, every two Fe atoms introduced are compensated by the introduction of one VO (the Fe introduced are fully ionically compensated). As x varies between 0 ≤ x ≤ 1, the reference compositions then correspond to a smooth transition between SrTiO3 and Sr2 Fe2 O5 , nominally enabling oxidation states for Ti4+ and Fe3+ respectively. Then, according to this description of STF, the atomic and electronic characteristics of STF are explained as being 4


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a mixture between the two end-member compounds, SrTiO3 (x = 0) and strontium ferrite, Sr2 Fe2 O5 (x = 1). Using this framework for STF, we model the defect chemistry and electronic structure using first-principles density functional theory (DFT) 42,43 and establish how they relate to those of the end members. First, we develop a computational model to simulate more realistic configurations. STF was reported as a solid solution without any long-range ordering of Ti/Fe ions or of VO . 28,29 To overcome the computational challenge of the large configuration space for these non-dilute systems, different configurations of Ti/Fe on the B-site sublattice and O/VO on the oxygen sublattice are considered. We find that Fe-VO -Fe chains represent low energy configurations amongst all possible ways of distributing Fe and VO in the lattice sites, and that such configurations are adequate to describe the electronic structure of the low-energy states of the real material system. Second, the defect chemistry and electronic structure of STF are evaluated with DFT calculations and the dependence of the electronic structure of STF on the Fe and VO composition are analyzed. The oxidation state of Fe is discussed when the system is oxidized or reduced relative to the reference composition δ = 0, and the role of Fe in reducing the band gap is elucidated by induced bands near the valence and conduction band. Our computational framework reproduces many experimentally known features of STF, such as x-ray absorption spectroscopy detection of Fe-VO complexes, thermogravimetric measurements of oxygen content, and optical absorption measurements of band gap reduction upon increasing Fe content.

Methods and Calibration of Simulation Parameters To address the complexity of the disordered solid solution, we first simulated SrTiO3 and Sr2 Fe2 O5 to establish the features of the end-member compounds. The corresponding atomic models are shown in Figure 1. A 3 × 3 × 3 SrTiO3 supercell is shown on the left and a 2 × 2 × 1 Sr2 Fe2 O5 supercell is shown on the right. The STF model shown in the middle will 5



Sr

Ti

Fe

SrTiO3

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O

SrTi1-xFexO3-x/2

Sr2Fe2O5

Figure 1: Atomic models of SrTiO3 (left), SrTi1−x Fex O3−x/2 (middle) and Sr2 Fe2 O5 (right) are shown. The position of an oxygen vacancy in SrTi1−x Fex O3−x/2 is indicated as a red dotted circle. be discussed in the following section. SrTiO3 exhibits the simple cubic perovskite structure, and the Sr A-sites show 12-fold coordination with oxygen anions, while the Ti B-sites show 6fold octahedral coordination. On the other hand, Sr2 Fe2 O5 adopts a brownmillerite structure with a general formula of A2 B2 O5 . Brownmillerite is a perovskite-like structure with a large degree of ordered oxygen vacancies. The ordering of the vacancies makes alternating layers of BO6 octahedra and BO4 tetrahedra. 44 Sr2 Fe2 O5 undergoes a phase transition to a disordered vacancy structure around 850◦ C. 45,46 The first-principles electronic structure simulations were performed within the framework of DFT. Our simulations invoke the Vienna Ab-Initio Simulation Package, 47,48 and projectoraugmented wave pseudopotentials 49,50 are used to remove the inert core electrons. Spinpolarization is included. For structural geometry relaxation, the positions of all the atoms are relaxed until the force on each atom is less than 0.01 eV/Å. All numerical results reported are converged to the number of significant digits shown with respect to Brillouin zone sampling and plane wave basis set cutoff. Within DFT, several approximations to the exchange-correlation functional are available nowadays, including conventional functionals, 51,52 DFT+U , 53,54 and hybrid functionals. 55–57 None of these are expected to perfectly reproduce all the aspects of the complicated material system. The selection of exchange-correlation functional can result in somewhat systematic errors to the degree of localization of the electronic states, and as a result, magnetic mo6


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Ti

Sr

Fe

O

(a) SrTiO3, HSE06

Projected Density of States

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(b) SrTiO3, PBE+U

(c) Sr2Fe2O5, HSE06

(d) Sr2Fe2O5, PBE+U −10 −8

−6

−4

−2

0

2

4

6

8

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Energy, E−Efermi (eV) Figure 2: Projected density of states for unit cells of SrTiO3 and Sr2 Fe2 O5 calculated by density functional theory with hybrid HSE06 or PBE+U functional. The green, blue, red, and black lines are projected states of Sr, Ti, Fe, and O, respectively.

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ments and band gaps are not necessarily predicted well. These considerations are crucial for modeling STF because Fe has a large number of localized 3d electrons, which interact and hybridize with oxygen atoms upon bonding. Hybrid exchange-correlation functionals often improve the description of localized electronic states, 58,59 which has been shown to be the case for SrTiO3 and Fe-doped SrTiO3 . 37,41 However, they are computationally intractable for the STF system, because our simulations involve several disordered configurations of large supercells and also require energy-minimizing geometry relaxations. The DFT+U approach has been applied to transition metals to treat the strong on-site Coulomb interaction of localized electrons, 60,61 offering a compromise between accuracy and computational efficiency. Therefore, we first calculated the electronic structure of both end-member compounds by hybrid DFT (which we take here as the best available theory), and used the results to calibrate U parameters to be used for subsequent simulations. We tested the dependence of the band gap and the magnetic moment of Fe atoms on the parameter U . The Hubbard parameter U adjusts the strength of the on-site electronelectron interaction, resulting in a more localized description of electronic states better suited for many transition metals. 54 Figure 2 compares the projected density of states (DOS) for unit cells of SrTiO3 and Sr2 Fe2 O5 calculated by screened exchange hybrid Heyd-ScuseriaErnzerhof (HSE06) 55–57 and Perdew-Burke-Ernzerhof (PBE+U ) 51,52 functional. The dotted line at zero energy is set at the highest occupied energy level in all cases, obtained directly from the occupations of the DFT eigenvalues (Kohn-Sham energies). Amongst different possible combinations of U for Ti 3d and Fe 3d states, we found that selecting U = 3 eV for Ti and U = 5 eV for Fe in PBE+U recovers the important features of the electronic structure of the projected DOS compared to HSE06. (Note that we choose not to match the absolute value of the band gap, as this requires unphysically large values of U and distorts the electronic structure.) Figure 2a,b show the DOS for SrTiO3 calculated by HSE06 and PBE+U . The end-member SrTiO3 is a typical band insulator. The band gap appears across a set of states largely composed of O 2p orbitals (valence band) and a set of states largely 8


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composed of Ti 3d orbitals (conduction band). The gap appears across oxygen 2p valence bands and transition-metal 3d conduction bands, as is common in transition metal oxides. 41 Figure 2c,d show the DOS calculated by HSE06 and PBE+U for Sr2 Fe2 O5 , which is spinpolarized, and exhibits a more complex electronic structure. The formal charge of iron is Fe3+ , corresponding to a high-spin d5 configuration. 62 This is evident in the DOS, which shows a large spin splitting between the Fe 3d orbitals. In the majority spin, the 3d orbitals are completely filled, and lie well below the valence band which is composed of O 2p orbitals. In the minority spin, the 3d orbitals are completely empty, and form the conduction band. Table 1 summarizes the band gap of SrTiO3 and Sr2 Fe2 O5 in comparison to experiments. Hybrid DFT seems to reproduce the band gaps adequately, but the band gaps calculated by Perdew-Burke-Ernzerhof (PBE) functional or PBE+U are considerably smaller than those obtained from experimental measurements. As expected the gap depends on the U parameter used. With UT i = 3 eV and UF e = 5 eV, the band gaps are underestimated by ∼1.1 eV for SrTiO3 and by ∼0.5 eV for Sr2 Fe2 O5 . Even though the estimated band gaps are small, their ratio is similar to the experimental ratio. Table 1: Band gap of SrTiO3 and Sr2 Fe2 O5 calculated by density functional theory with PBE+U or HSE06 functional, and measured by experiments (unit: eV) SrTiO3 Sr2 Fe2 O5

PBE 1.8 0.7

PBE+U HSE06 2.2 (UT i = 3) 3.2 1.5 (UF e = 5) 2.3 a 26 b 63 Ref. Ref.

Experiments 3.2a 2.0b

For additional calibration of simulation parameters, the magnetic moments of Fe ions in Sr2 Fe2 O5 were calculated and the results are shown in Table 2. With hybrid DFT, the spin magnitudes are 4.12µB and 4.25µB for octahedrally and tetrahedrally coordinated Fe, respectively. The Fe ions with tetrahedral coordination of oxygen have higher spin magnitude. Interestingly, when the electronic structure of Sr2 Fe2 O5 is calculated in PBE with U = 0, the trend is opposite: 3.84µB for Fe ions in octahedra and 3.56µB for Fe ions in tetrahedra. Based on our tests, we found that U ≥ 3 eV is necessary to reproduce the 9



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relative ordering of the magnetic moments according to the hybrid functional. Table 2: Spin magnitude of iron atoms in Sr2 Fe2 O5 with octahedrally or tetrahedrally coordinated to oxygen atoms calculated by density functional theory with PBE+U (unit: µB ). Octahedron Tetrahedron

UF e = 0 3.84 3.56

UF e = 3 4.11 4.20

UF e = 5 4.27 4.38

HSE06 4.12 4.25

Based on these considerations, the results reported hereafter have been obtained with PBE+U with UT i = 3 and UF e = 5, which appears to reasonably capture the physical trends in a computationally tractable way. Using these parameters, computational models of STF are generated starting from an SrTiO3 supercell. Unlike dilute Fe-doped STF which can be modeled by substituting one Fe for one Ti atom into the supercell, for a given STF composition an appropriate number of Ti atoms are substituted by Fe atoms. To achieve the reference composition, half as many oxygen atoms are removed from the supercell (fewer or more oxygen are removed when considering compositions deviating from the reference). To select the particular configuration for Fe substitution and oxygen vacancies among the large number of possibilities, we estimate the electrostatic energy of different configurations using an ionic model, and select the lowest energy configuration for further analysis in DFT.

Results and Discussion Short-Range Ordering Between Fe and O Vacancies To obtain a good description of the electronic structure and related properties of STF, the first step is to properly represent the configurations of the disordered material. A continuous series of STF compositions between SrTiO3 and Sr2 Fe2 O5 have been reported experimentally, and structurally SrTi1−x Fex O3−y retains the perovskite lattice of SrTiO3 while the lattice constant varies significantly only when x ≈ 1. 24,25 Therefore, computational models of STF 10


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are generated based on a 3×3×3 SrTiO3 supercell containing 135 atoms. The compositional variations of STF are sampled by substituting Ti with Fe and by introducing VO to the SrTiO3 supercell. For example, for the STF system with x = 0.07 shown in the middle panel of Figure 1, the supercell has two Fe atoms (brown) that replaced two Ti atoms (blue), and one VO present (red dotted circle).

Total Energy, E−Emin (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Sr

1.0 0.8

(ii)

0.6 (iii)

0.4 0.2

Ti

Fe

O

(iv)

(i)

0.0

Atomic configurations Figure 3: DFT calculated energies of SrTi1−x Fex O3−x/2 (x = 0.07) supercell containing 135 atoms with different atomic configurations are plotted in ascending order. The energies are compared to the lowest energy value. Corresponding atomic configurations only near Fe atoms are shown. In general, for a given x, several configurations are possible for the distribution of Ti/Fe atoms in the B-site sublattice and the distribution of oxygen vacancies VO in the oxygen sublattice. Before analyzing larger degrees of Fe content, we first establish the features of a simpler system corresponding to a supercell with only two substitutional Fe atoms and one VO , which represents the smallest perturbation of SrTiO3 possible towards Sr2 Fe2 O5 while maintaining the reference composition. Insights obtained for this case serve as a bridge to understanding larger degrees of Fe incorporation. Among the large number of possible configurations in our 135 atom supercells containing two substitutional Fe atoms and one VO , 42 symmetry-unique configurations were identified using the software Supercell. 64,65 The total energy of the system was calculated using DFT for all candidate configurations, and their relative stability was compared. Figure 3 shows the relative energies of all 42 configurations. We found that the system with a Fe-VO -Fe chain configuration as shown in the middle 11



panel of Figure 1 and in Figure 3.i, in which the O vacancy is located between the two Fe atoms, is energetically most favorable. The Fe-VO -Fe chain can be thought of as a small local ‘patch’ of Sr2 Fe2 O5 within SrTiO3 . The energy of this configuration is 0.3 eV lower than the next lowest energy configuration, which contains a Fe-VO -Ti chain (Figure 3.ii). In general, the energies of the configurations without Fe-VO (Figure 3.iii) are 0.6 eV higher than those of the system with Fe-VO -Fe, and the configurations become even less stable when two neighboring Fe atoms are present without VO nearby (Figure 3.iv). These observations suggest a tendency for short-range ordering of VO around Fe ions, consistent with other computational studies. 32,37,66,67 The presence of VO in the first coordination shell of Fe ion has also been revealed through Fe K-edge x-ray absorption spectroscopy. 29 Therefore, our results are consistent with experiments showing that Fe atoms are largely 5-fold coordinated, whereas Ti atoms remain 6-fold coordinated. 28 Despite that the Fe-VO -Fe configuration results in the lowest energy, we note that Fe ions could still remain 6-fold coordinated in STF if either the composition varies from the reference value of δ = 0 or simply due to entropy/configurational sampling. The presence of both 5-fold and 6-fold coordinated Fe in STF has been observed by x-ray near edge structure methods. 25,66 In reality, deviations from δ = 0 and/or configurational sampling can result in different degrees of 5-fold coordinated and 6-fold coordinated Fe under different environments. The approach adopted in this work here onwards is to identify and highlight the trends present in the low energy configurations of STF, which can serve as a useful reference for experiment. However, we consider several examples of how the reported properties change for higher energy configurations, most of which is reported in the Supporting Information. To see how the presence of the isolated Fe-VO -Fe chain affects the electronic structure of the host SrTiO3 , Figure 4a shows a cross-sectional view of a plane containing the chain and Figure 4c shows the projected density of states. The dotted line at zero energy indicates the highest occupied energy level. Similar to the DOS of host SrTiO3 (Figure 2b), the completely filled valence band edge is largely composed of O 2p orbitals and the completely 12


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(c)

Fe - VO - Fe (b)

Sr

Ti

Fe

O

Density of States

(a)

(d)

Fe - O - Fe

Density of States

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


−2

Sr

Ti

Fe

O

0

2

4

Energy, E−Efermi (eV)

Figure 4: Cross-sectional views of SrTiO3 containing (a) an Fe-VO -Fe chain and (b) and an Fe-O-Fe chain, corresponding to SrTi1−x Fex O3−x/2+δ with x = 0.07, δ = 0 and x = 0.07, δ = 0.035 respectively. Projected density of states for each composition are shown in (c,d) respectively. The yellow clouds shown in (b) represent the total electron density of the empty states at the valence band maximum which is indicated by an arrow in (d).

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empty conduction band edge is largely composed of Ti 3d orbitals. However, there is a small but non-zero degree of Fe 3d states mixed in at both the valence and conduction band edge. The DFT predicted band gap reduces from 2.2 eV for SrTiO3 to 2.0 eV for the Fe concentration of 7% and VO concentration of 3.5%. Meanwhile Figure 4(b,d) considers the case of Fe-O-Fe instead for comparison. Now the two Fe ions are 6-fold coordinated, as opposed to 5-fold coordinated. The projected DOS of this model is shown in Figure 4d, and again the dotted line indicates the highest occupied energy level. The most distinctive feature of the PDOS is the presence of empty states at the valence band edge indicated by black arrow. When an oxygen atom is introduced to the vacancy site of the Fe-VO -Fe chain, the electronegative oxygen atom pulls electrons away from the Fe atoms and towards itself. If the electrons were completely transferred from the two neighboring Fe to the O, this would result in well-defined Fe4+ and O2− formal ionic charges. Instead, however, we observe only a partial charge transfer, corresponding to hybridization of high spin Fe states with oxygen partial holes. These redistributed electrons reside in the highest occupied energy level below the VBM in the PDOS. Because of the incomplete charge transfer, the new oxygen atoms is not fully ionized in the 2− state, leaving the uppermost valence bands empty. The charge density of the empty states is shown as yellow clouds in Figure 4b, and localized around the new O atom and the surrounding Fe. There have been extensive discussions of the oxidation state of Fe in STF. 25,28,29,31,32 Typically the oxidation state of Fe is indicated as Fe3+ when 5-fold coordinated and as Fe4+ when 6-fold coordinated by oxygen ions. 29,32,41 In experiment, Fe3+ is observed in STF under a range of pressures and temperatures, and Fe4+ is observed when the sample is oxidized. 25,28,29,32 Further, the material properties of STF, such as electronic conductivity and optical absorption, are often attributed to and explained by the concentration of Fe4+ . 27,37 Therefore, we investigated the oxidation state of Fe ions, for Fe atoms in the Fe-VO -Fe and in Fe-O-Fe configurations. To establish oxidation state, we used the calculated magnetic moment of the Fe atoms, since there are problems 41,62 with predicting oxidation states using 14


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Bader charge analysis. 68 The magnetic moment of Fe in Fe-VO -Fe and Fe-O-Fe are 4.26µB and 4.34µB , respectively. By comparison, the magnetic moment of Fe in Sr2 Fe2 O5 and SrFeO3 corresponding to Fe3+ and Fe4+ respectively, are ∼ (4.27, 4.38)µB and 3.95µB as shown in Table 3. Our calculated moments, as shown in Table 3, are more similar to those of Sr2 Fe2 O5 for both 5 and 6 -fold coordinated iron. 31 Table 3: Spin magnitude of iron atoms with octahedrally or tetrahedrally coordinated to oxygen atoms in Sr2 Fe2 O5 , SrTi1−x Fex O3−x/2 , and SrFeO3 calculated by density functional theory with PBE+U (unit: µB ).

Octahedron Tetrahedron

Sr2 Fe2 O5 (Fe3+ ) 4.38 4.27

SrTi1−x Fex O3−x/2 (x = 0.07) 4.34 (Fe-O-Fe) 4.26 (Fe-VO -Fe)

SrFeO3 (Fe4+ ) 3.95

The small difference in the oxidation state between Fe ions in 5-fold and 6-fold coordination can be explained by the nature of the bonding between Fe and O. Consistent with the covalent character of the Fe−O bond, the electrons appear to be shared by neighboring Fe and O atoms. Accordingly, the Fe atoms exhibit effective charges slightly larger than +3 but smaller than +4, and an average charge of the oxygen atom lower in magnitude than −2. 26,29,40 Given this, we suggest that Fe4+ states reported in experimental studies 25,29,31,32 at least for the case of dilute iron may more accurately be described as empty states of hybridized Fe−O bonding orbitals, which form the highest occupied energy levels and empty states at the VBM. (The effect of these states on the electronic structure and band gap will be discussed later.)

Dependence of Oxygen Content on Thermodynamic Environment To extend the modeling approach to higher Fe concentrations, it is critical to know not only the atomic configurations but also the appropriate compositions, i.e. how valid the concept of the reference composition is and how oxygen deficiency y in fact relates to the Fe content x in practice. The SrTi1−x Fex O3−x/2 (y = x/2) reference composition was suggested as a 15



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suitable description of STF solid solution based on electron counting of formal charges, and it relies on the assumption of fully ionic compensation of the introduced Fe. According to this, substitution of tetravalent Ti with trivalent Fe leads to one VO for every two Fe atoms. 24,28 However, STF alloys are often prepared in different environments with a wide range of temperatures and oxygen partial pressures, thus, the oxygen non-stoichiometry of the sample can vary in different environments particularly if electronic compensation is possible. Therefore, we next characterize the equilibrium oxygen deficiency y as a function of the thermodynamic environment. The stabilities are assessed using the mixed thermodynamic potential ΦST F as a function of temperature T and oxygen partial pressure P DF T DF T ΦST F (nSr , nT i , nF e , µO , T, P ) = EnV − Eperf ect + O

n µO (T, P ) . 2 2

(1)

This potential represents that of an STF system that has fixed numbers nSr , nT i , nF e of Sr, Ti, and Fe atoms but is open to exchange of O atoms with a thermodynamic reservoir. Here DF T DF T and Eperf EnV ect are the DFT-computed total energy of a supercell containing n oxygen O

vacancies and no oxygen vacancies (fully oxidized) respectively. The parameter µO2 denotes the chemical potential (partial molar Gibbs free energy) of an oxygen gas molecule. For solids, the temperature-dependent vibrational energy largely cancel when comparing defective and perfect structures, and the pressure dependence on total energy is ignored because it is normally weak. 69 The value of µO2 (T, P ) depends on the temperature and pressure of the environment and it is obtained using a combination of DFT and thermodynamics according to: T µO2 (T, P ) = EODF + ∆µ◦O2 (T ) + kB T ln 2

󰀓P 󰀔 P◦

.

(2)

T , the reference energy for O2 , because PBE is known We used the corrected value for EODF 2

to overbind the O2 molecule. 70 The temperature dependent thermodynamic function ∆µ◦O2 are obtained from tabulated data, 71 and the pressure dependence is considered in the last 16


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term of Eq. (2).

Thermodynamic potential, φ (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


5 0 −5 −10 −15

105 bar 105 bar 10-20 bar

0K 900 K 1300 K

10-20 bar

−20 −0.04

0

0.04 0.07 0.11 Oxygen nonstoichiometry, δ

0.15

Figure 5: Mixed thermodynamic potential of SrTi0.7 Fe0.3 O2.85+δ in terms of oxygen nonstoichiometry, δ. Atomic models with the lowest free energy for δ = 0 and δ = 0.15 are shown at the top. Each line corresponds to a specific temperature and oxygen partial pressure environment. Figure 5 shows ΦST F for a system SrTi0.7 Fe0.3 O2.85+δ (STF30) at a fixed Fe content of 30% (x = 0.3), for which the parameter δ on the x-axis indicates the deviation from the reference value SrTi0.7 Fe0.3 O2.85 . The 30% Fe composition is the closest achievable in our supercells to STF35 (35% Fe), for which experimental results 36 are available to compare our results. Experimentally, the 35% Fe composition has a reasonable balance between performance and stability: Ti gives better stability whereas Fe increases surface exchange coefficient, electronic and ionic conductivity, etc. In the simulated supercells, there are too many candidate configurations to be examined by DFT calculations. Instead, selected configurations were identified by calculating total electrostatic energy based on an ionic model, 64 and among them, the lowest energy configuration was selected for DFT simulations. The mixed thermodynamic potential ΦST F is shown in Figure 5 as a function of δ, for different values of temperature and oxygen partial pressure. Negative values of δ means that the system is reduced compared to the reference composition; as δ becomes more positive, 17



the system becomes more oxidized, and is fully oxidized (no vacancies present) at δ = 0.15. The fully oxidized case is defined here to have a potential ΦST F of zero. In Figure 5, the color of the lines represents different temperatures as shown in the legend, while solid/dashed lines represent oxygen partial pressure of 10−20 /105 bar respectively. For a given line, the value of δ which minimizes ΦST F indicates the expected oxygen content at equilibrium. For example, the red line for T = 0 K shows the DFT-simulated results and the minimum at δ = 0.15 indicates that at equilibrium the system should be fully oxidized. At T = 900 K, the minimum of ΦST F has shifted to δ = 0.04 at pressures of 105 bar, and is at the reference value of δ = 0 when oxygen partial pressure is decreased to 10−20 bar. At 1300 K, the minimum of ΦST F occurs at δ = 0 for 105 bar, but shifts to δ = −0.04 for 10−20 bar. These results indicate that the system can be reduced relative to the reference composition at sufficiently high temperatures and low pressures, and oxidized at low temperatures and high pressures. Notably however, we find that ΦST F is minimized at δ = 0 under a wide range of temperature and pressure conditions. In other words, at these conditions a combination of one VO per two Fe atoms is generally favorable, largely confirming the concept of the reference composition. Figure 6 shows a direct comparison of our computational predictions of δ, the deviation from the reference composition, and the same parameter previously measured in experiment. Figure 6a shows the value of δ that corresponds to the minimum value of ΦST F from Figure 5 as a function of oxygen partial pressure for different temperatures. The sharp jumps of the isothermal lines arise from the discrete sampling of the large, continuous configuration space in our 135 atom supercells, for which we are able to resolve δ in units of 1/27 only. To validate our results, we compared them to the oxygen non-stoichiometry δ of SrTi0.65 Fe0.35 O2.825 (STF35) previously measured by thermogravimetric analysis 36 shown in Figure 6b. The computational predictions capture several of the experimental trends. For a given temperature, there is an oxygen deficient region (δ < 0) at low oxygen partial pressure, followed by a reference region (δ = 0) at intermediate pressure, and oxygen-excess 18


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(a) Oxygen no-nstoichiometry, δ

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.07

STF30

0.04

900 K 1000 K 1100 K 1200 K 1300 K

0.00 −0.04 −30

−25

−20 −15 −10 −5 0 5 Oxygen partial pressure, log(PO2/bar)

10

(b)

Figure 6: Oxygen non-stoichiometry, δ, for SrTi1−x Fex O3−x/2+δ as a function of temperature and oxygen partial pressure environment. (a) Density functional theory estimation for SrTi0.7 Fe0.3 O2.85+δ (b) Thermogravimetric analysis 36 for SrTi0.65 Fe0.35 O2.825+δ (Reprinted with permission from M. Kuhn et al., Chem. Mater. 25 2970-2975 (2013). Copyright 2013 American Chemical Society)

19



region (δ > 0) at high pressure. The onset of the deviation from δ = 0 occurs at lower oxygen partial pressure as the temperature decreases. The spacing between lines of different temperature are similar in theory and experiment. However, the DFT results are shifted to higher oxygen partial pressure by about 105 bar overall compared to the experimental results, indicating that DFT predicts STF to be somewhat harder to oxidize than in experiment. The discrepancy may be due to systematic errors inherent in the DFT+U formalism. Alternatively it may be because all of the oxygen vacancy sites in our atomic model for STF are located between two Fe atoms, and thus to oxidize the system, Fe-VO -Fe configurations must be replaced by Fe-O-Fe. Therefore, the energy cost for introducing oxygen atom could be overestimated in our simulation, because real STF mixtures can exhibit different configurations with sites more favorable for the introduction of O atoms.

Evolution of Density of States with Fe Concentration at Reference Composition Having established that the reference composition is energetically favorable over a wide range of thermodynamic environments, we now consider how the electronic structure of STF for δ = 0 evolves for increasing iron content x at the reference composition. Figure 7 shows how the projected DOS evolves across a series of compositions corresponding to x = 0, 0.3, 1 at the reference composition. The DOS shown are aligned with respect to the deep, low energy O 2s levels (not visible in the plotted range), as they are expected to be fixed for all three compositions. The dotted lines indicate the highest occupied energy level in all cases. In simulating the intermediate alloy x = 0.3, whose DOS is shown in Figure 7b, we again determined the configuration that minimizes the total electrostatic energy based on an ionic model, and used it for the DFT simulations of the DOS. Remarkably the DOS of STF30 largely resembles a mixture of the two end-member compounds. It exhibits properties of both end-members: the completely filled valence bands are composed of the O 2p orbitals, while the completely empty conduction bands are derived from the metal 3d states. The Fe 20


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Sr

Ti

O

Fe

x=0


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a) SrTiO3 x = 0.3

(b) SrTi0.7Fe0.3O2.85 x=1

(c) Sr2Fe2O5 −10 −8

−6

−4

−2

0

2

4

6

8

10

Energy, E−Efermi, SrTiO3 (eV) Figure 7: Projected density of states for SrTi1−x Fex O3−x/2 supercells. (a) SrTiO3 (x = 0), (b) SrTi0.7 Fe0.3 O2.85 (x = 0.3), and (c) Sr2 Fe2 O5 (x = 1). The green, blue, red, and black lines are projected states of Sr, Ti, Fe, and O, respectively.

21



atoms remain spin-polarized and remnants of the large exchange splitting present in Sr2 Fe2 O5 are visible in the DOS. For the lowest energy configuration of STF30 shown here, we see no states arising inside the gap and the material remains an intrinsic semiconductor (DFT band gap = 1.8 eV). If STF at the reference composition can be considered a mixture of SrTiO3 and Sr2 Fe2 O5 , it is expected that the primary gap decrease with increasing Fe content. This is reflected in the DOS shown in Figure 7. The band gap reduction has been reported in previous experimental studies. 22,25,26,28,36 Some of these find that the reduction is linear with Fe content, while others find that the reduction occurs more rapidly at low Fe content, which would make the band gap of STF35 closer to the gap of Sr2 Fe2 O5 . Most of the experimental studies concluded that the band gap narrowing arises from additional energy levels above the valence band and/or defects states within the band gap. In our simulations focusing on low-energy configurations at the reference composition, we observe from the DOS in Figure 7 that as Fe is introduced, both the energy of the VBM increases and the energy of the CBM decreases, causing the reduction of the gap. The energy of the VBM increases with the Fe concentration as Fe-derived bands appear near the top of the valence band and form hybridized Fe-O bonding orbitals. The energy of the conduction band minimum (CBM) decreases as hybridized Ti 3d and Fe 3d states broaden the conduction band. Moreover, as shown in Figure 7, there are no electronic states present inside the gap due to the introduction of Fe and VO , in contrast to several of the experimental analyses. This can be reconciled by noting that we do, however, observe defect states for less stable STF configurations which result in more dramatic changes to the band gap even at low Fe concentration. An example of the DOS for a higher energy configuration of STF30 with states distributed throughout the gap is given in the supporting information (Figure S1). Therefore, in reality the reduced band gap with increasing Fe content largely can be viewed as arising primarily from a transition from SrTiO3 (Eg = 3.2 eV) to Sr2 Fe2 O5 (Eg = 2.0 eV) associated with a broadening of the band edges, but further perturbed by local atomic configurations which can introduce mid 22


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Page 23 of 37

gap states.

Effect of the Oxygen Non-stoichiometry on DOS Sr

Ti

O

Fe

δ = 0.15


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a) SrTi0.7Fe0.3O3 δ=0

(b) SrTi0.7Fe0.3O2.85 δ = −0.15

(c) SrTi0.7Fe0.3O2.7 −10 −8

−6

−4

−2

0

2

4

6

8

10

Energy, E−Efermi, SrTi0.7Fe0.3O2.85 (eV) Figure 8: Projected density of states for SrTi0.7 Fe0.3 O2.85+δ supercells. (a) SrTi0.7 Fe0.3 O3 (δ = +0.15), (b) SrTi0.7 Fe0 .3O2.85 (δ = 0), and (c) SrTi0.7 Fe0.3 O2.7 (δ = −0.15). The green, blue, red, and black lines are projected states of Sr, Ti, Fe, and O, respectively. To assess the effects of varying the oxygen stoichiometry, Figure 8 illustrates how the electronic structure evolves as the composition becomes oxidized (δ > 0) or reduced (δ < 0) relative to the reference composition. These simulations were performed at a fixed Fe content of 30% (SrTi0.7 Fe0.3 O2.85+δ ), while the oxygen content was varied from the prior reference value δ = 0 (middle panel) to δ = +0.15 (top panel) and δ = −0.15 (bottom panel). We considered oxygen contents that nominally would correspond to fully oxidized (Fe4+ ) and 23



fully reduced (Fe2+ ) systems. The DOS are again referenced to the O 2s levels, and the dotted line indicates the highest occupied energy level in all cases. We emphasize again that these results are specific to the low energy configurations of STF. At the reference composition, the most stable atomic configurations are ones for which all oxygen vacancies are present as first nearest neighbors to the Fe ions. Therefore, when the system is oxidized, the new O atoms are introduced at these vacancy sites adjacent to the Fe ions. On the other hand, when the system is reduced, there is the option to remove oxygen atoms either directly adjacent to an Fe ion or not directly adjacent to an Fe atom. For the oxidized case (δ = +0.15), oxygen atoms are introduced into the supercell, thus modifying the Fe-VO -Fe chains to Fe-O-Fe as illustrated in Figure 4(a,b). The DOS for the oxidized system (Figure 8a) reveals the presence of empty O 2p states above the valence band edge, with considerable degree of Fe 3d character mixed in (Figure S2 in the Supporting Information shows a zoomed in view of the states near the VBM). The presence of empty VBM states suggests that the oxidized system becomes p-type in nature. The mixed O 2p−Fe 3d character of the empty states shows that the holes are not fully localized on the multivalent Fe, but are distributed around the Fe-O-Fe region (Figure 4b). Interestingly, the empty states towards the top of the VBM can be explained by extension of the known defect levels present in dilute Fe-doped SrTiO3 . Isolated Fe impurity levels above the VBM have been observed in Fe-doped SrTiO3 . 39,40 These Fe-derived defect states would be expected to broaden with increasing Fe concentration, and to hybridize with the VBM O 2p states of SrTiO3 , 25,28,41 resulting in a DOS very similar to that shown in Fig. 8a. For the reduced case (δ = −0.15), we removed additional oxygen atoms from the supercells beyond the reference composition. Due to the large oxygen vacancy concentration, several candidate configurations are possible. We considered several possible configurations using DFT and generally found that it is energetically more favorable to create the additional oxygen vacancies at sites adjacent to Fe rather than those only neighboring Ti atoms. The DOS for the reduced system for such a low energy configuration is shown in Figure 8c. 24


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Nominally, one might assume that the removal of additional oxygen atoms beyond the reference composition would reduce the Fe3+ to Fe2+ . The magnetic moments of the Fe atoms in the reduced STF were found to be ∼3.74µB , lower than the value of 4.26µB found in the reference composition. The reduced magnetic moment arises as the Fe atoms gain and localize the electrons of the removed oxygen atoms. The reduction of Fe3+ to Fe2+ would imply occupying the lowest unoccupied 3d states, which in this case are located in the conduction band, would render the material n-type. There is experimental evidence of n-type conductivity in STF at low oxygen partial pressure condition. 18,26,28 However, based on our DOS (Figure 8c), instead the highest occupied state remains at the top of the valence band while the magnitude of the DOS decreases near the VBM. The reduction of the magnitude of the DOS itself is a direct result of the reduction in the number of O atoms contributing to the O 2p band, thereby producing a more pronounced Fe character at the VBM particularly in the minority spin. On the other hand, the material does become n-type when the additional removal of oxygen atoms occurs at sites far away from Fe atoms. The DOS for this higher energy configuration is shown in Figure S3 in the Supplementary Material. In this case there is a partial charge transfer between the removed O atoms and neighboring Ti atoms, and the redistributed electrons reside in defect levels mainly composed of O 2p and Ti 3d states close to the conduction band minimum. A possible implication of the degree of p or n -type character of STF as predicted relates to surface exchange kinetics. Understanding and controlling oxygen surface exchange is important when selecting STF compositions for use in various electrochemical systems including solid oxide fuel and electrolysis cells. There is evidence that exchange at the STF surface is limited by the transfer of conduction band electrons to the antibonding energy levels of the adsorbate oxygen molecules across the full solid solution composition space. 34 In this case, it should be possible to enhance surface exchange by increasing the concentration of n-type carriers, which may occur in reducing environments as shown here. It would be most insightful to control and decouple the n-type carrier concentration from the VO 25



concentration, such as through incorporation of external dopants. This would enable better assessment of whether surface exchange rates are governed by electron transfer (and thus n-type carrier concentration) or by the presence of surface VO , which has also been suggested to be important. 38

Conclusions We present an improved first principles modeling approach for the disordered solid solution STF. The approach considers STF as a mixture of SrTiO3 and Sr2 Fe2 O5 , and the configuration and composition of iron and oxygen vacancies are explicitly considered. Through DFT analysis of local atomic structure, we find that short-range ordering of Fe and VO stabilizes the mixture. Using a mixed thermodynamic potential with open boundaries to oxygen, the introduction of one VO formation per two Fe atoms is generally favorable under a wide range of temperature and oxygen partial pressure environments although oxidation and reduction are possible at high pO2 / low T or low pO2 / high T respectively. Therefore, the SrTi1−x Fex O3−x/2+δ framework can serve as a good description of the STF solid solution. Further analysis of the effects of Fe concentration and the oxygen non-stoichiometry on the electronic structure illustrate how the properties of low-energy configurations of STF systematically evolve from the characteristics of end member compounds SrTiO3 and Sr2 Fe2 O5 . The reduction in the band gap with increasing Fe content can be attributed to this evolution. When the system is oxidized relative to the reference composition, electron transfer from Fe to introduced oxygen creates empty states at the top of the valence band derived from Fe-O bonding orbitals. Our computational framework reproduces experimentally known features of STF including x-ray absorption spectroscopy evidence of the presence of the Fe-VO complexes, thermogravimetric measurements of oxygen content, and optical measurements of band gap reduction at higher Fe content. Moreover, our model explains p-type and n-type conductivities of the STF under oxidized and reduced conditions, respectively. While this

26


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work is focused on the STF system, the underlying approach may also be applicable to other disordered solid solutions. Therefore, it may shed light on the atomic and electronic structure of perovskite oxides and derivative compounds and their resulting ionic and electronic conductivity.

Acknowledgement The authors gratefully acknowledge the support of the NSF and JSPS under the JSPSNSF Partnerships for International Research and Education (PIRE), U.S. NSF Grant No. 1545907. We also acknowledge the support of the International Institute for Carbon Neutral Energy Research (WPI-I2CNER), sponsored by the Japanese Ministry of Education, Culture, Sports, Science and Technology. Computational resources were provided by the Illinois Campus Computing Cluster. We are grateful to Professor Harry L. Tuller in Department of Materials Science and Engineering at Massachusetts Institute of Technology for comments and useful discussions.

Supporting Information Available Density of states for higher energy configurations of SrTi0.7 Fe0.3 O2.85 at the reference composition, zoomed in density of states of oxidized composition SrTi0.7 Fe0.3 O3 showing empty valence band states, and density of states of reduced composition SrTi0.7 Fe0.3 O2.7 .

27



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Graphical TOC Entry Sr

Ti

Fe

O [Fe] [VO]

Density of States

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


SrTiO3

SrTi1-xFexO3-x/2

O

Sr2Fe2O5 Ti Fe

Fe

Energy

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