Oxygen Vacancy Defect Migration in Titanate Perovskite Surfaces

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Oxygen Vacancy Defect Migration in Titanate Perovskite Surfaces: Effect of the A-site Cation Joshua Brown, Zhuofeng Ke, Wei Geng, and Alister J. Page J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b03322 • Publication Date (Web): 24 May 2018 Downloaded from http://pubs.acs.org on May 24, 2018

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The Journal of Physical Chemistry

Oxygen Vacancy Defect Migration in Titanate Perovskite Surfaces: Effect of the A-site Cation Joshua J. Bown,a Zhuofeng Keb, Wei Gengb and Alister J. Page*a a

Priority Research Centre for Frontier Energy Technology and Utilisation, The University of

Newcastle, Callaghan 2308, NSW, Australia b

MOE Key Laboratory of Bioinorganic and Synthetic Chemistry, School of Chemistry and

Chemical Engineering, Sun Yat-sen University, Guangzhou 510275, P. R. China

ACS Paragon Plus Environment

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Abstract

Oxygen vacancy formation energies and migration barriers in (001) surfaces of CaTiO3, SrTiO3 and BaTiO3 have been investigated using first principles density functional theory. The degree of distortion within the TiO2 sublattice in the presence of defects, and consequently the defect formation energies in these titanate surfaces is determined by the size of the A-site cation (Ca2+ < Sr2+ < Ba2+). This is notably the case for CaTiO3, in which the presence of a vacancy defect leads to heavily distorted orthorhombic distortions within the (001) surface structure, despite the overall cubic symmetry of the material. This effectively leads to the TiO2 sublattice acting as a thermodynamic trap for oxygen vacancy defects. By contrast, calculated vacancy diffusion pathways in SrTiO3 and BaTiO3 indicate that vacancy diffusion with these larger A-site cations is kinetically, and not thermodynamically controlled. A detailed assessment of how the +U Hubbard correction influences these thermochemical and kinetic stability trends is also presented.


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1. Introduction Titanate perovskites such as SrTiO3 (STO) have been the focus of significant attention in recent years, in part as they are prototypical cubic perovskites. STO’s band gap of 3.2 eV (comparable to that of anatase TiO2) makes it potentially applicable in a number of areas such as high-k dielectrics,1 sensors2 and resistive switching random access memories.3-4 STO has also shown potential in nanoscale batteries,5 solid oxide fuel cell cathodes6 and new water splitting / CO2 reduction photocatalysts. The stability and mobility of oxygen vacancies is a key factor that determines the utility of STO and related titanate materials in such potential applications.7-9 For STO specifically, nonstoichiometric oxygen deficiency (i.e. SrTiO3-δ) is known to be the main origin of the visiblelight absorption and emission peaks.10-11 In STO, oxygen vacancies have lower formation enthalpy and higher diffusivity and mobility than oxygen ions themselves.12 Additionally it has been shown that reducing conditions above 700 °C will cause introduction of oxygen vacancies and electrons, which provides n-type conductivity.13 It has also been reported that, due to charge compensation effects, the migration of oxygen vacancies induces enhanced cation and electron migration.14 The diffusion coefﬁcient of oxygen in titanates, and ABO3 perovskite compounds more generally, can be characterized by the formation and migration of, and ion association with, oxygen vacancies.15 Marrocchelli et al.16 recently reported a first-principles investigation of the migration barriers associated with an oxide ion diffusing across a dislocation into a defect position in bulk STO. Bulk diffusion barriers of neutral and charged Vo in STO have also been studied theoretically by Zhang et al.17 A recent density functional theory (DFT) study by Choi et


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al.18 indicates that oxygen vacancies in the bulk and on/near the surface play different roles in the optical and magnetic properties of STO. Nevertheless, the practical utility of titanates such as STO as thin film and catalytic materials will be limited by the stability and mobility of defects near low index surface facets (notably the TiO2-terminated STO (001) surface).19 In this respect, characterization of vacancy defect formation energies and diffusion barriers at pertinent interfaces remain largely unexplored. Previous DFT studies have investigated the effect of oxygen defects on the metallic (001) surface state20 and the migration barriers associated with thin film growth of STO at the (110) surface.21 The influence of oxygen vacancies on water dissociation at the STO photoelectrode surface has also previously been demonstrated.22 Recent work by Plaza et al.23 demonstrated that training an STO electrode changes the surface structure from a double layer TiO2 termination to an oxygen-deficient, biaxially strained anataselike structure, as Sr2+ ions are progressively stripped from the surface. This implicates the A-site cation – largely considered to be the ‘structural’ cation (e.g. crystal structures, phase changes and electronic and thermal properties of AIITiIVO3 perovskites are known to change with A = Ba2+, Ca2+ and Pb2+)24 – as a determinant of oxygen vacancy defect stability and diffusion at titanate interfaces. Indeed, oxygen defect migration barriers have also been shown to be dependent on the A-site cation in bulk titanate perovskites (e.g. for STO, BaTiO3, LaTiO3, YTiO3 & PrTiO3).25-26 However, the impact of the A-site cation on oxygen defect stability and diffusion at perovskite interfaces has not been investigated, to our knowledge. In this work, we address this shortcoming with a first-principles investigation of the formation energies and diffusion barriers of neutral oxygen vacancy defects (Vo) in model (001) surfaces of


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cubic CaTiO3 (CTO), STO and BaTiO3 (BTO). We show that the A-site cation principally determines the degree of distortion when Vo reside in the TiO2 sublattice. This in turn determines the relative kinetic and thermochemical stabilities of oxygen vacancy defects at these (001) interfaces. The migration energy barrier of neutral defects shows a preference for Vo to drift to the immediate surface layer in BTO, while STO displays more consistent barrier heights from the surface into the subsurface and the bulk layers. CTO exhibited the most dramatic structural distortion in the presence of a vacancy defect, yielding near orthorhombic geometries in the defective TiO2 sublattice. In this case the TiO2 layers are effectively thermodynamic traps for oxygen vacancies, due to their relatively large stability. We anticipate therefore that cubic CTO will yield poorer ion mobility than STO. We also present a systematic investigation of the effect of the +U Hubbard correction (applied to the Ti 3d orbitals) on these trends.

2. Computational methodology 2.1. Density Functional Theory Calculations The Vienna Ab-initio Simulation Package27 (VASP) program was used for all results reported here. The revised Perdew–Burke–Ernzerhof PBEsol28 GGA exchange correlation functional in conjunction with projector augmented wave (PAW)29 pseudopotentials is used here, with and without rotationally invariant Hubbard-U / Hund-J corrections.30 All calculations employ (core)/valence configurations of Sr: ([Ar]3d)/4s4p5s; Ti: ([Ne]3s)/3p3d4s; O: ([He])/2s2p. A plane wave energy cutoff of 400 eV is used following reference.17,

31

The most common

Hubbard U and Hund J values applied to the Ti 3d orbitals in previous DFT+U investigations of STO17, 32-42 were originally proposed by Pavarini et al.31 (U = 5 eV, J = 0.64 eV) and Solovyev


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et al.43 (U = 3.2 eV, J = 0.9 eV). Both sets of corrections were chosen on the basis of the extent of electron localization in the Ti 3d orbitals, with the former yielding full localization. The former values are the most commonly employed in the literature for STO.17, 32-39, 41, 44 For these reasons, we apply corrections of U = 5 eV, J = 0.64 eV to the Ti 3d orbitals using Lichtenstein’s implementation of the DFT+U method.30 This choice makes the values reported here for the STO (001) interface consistent with a number of bulk STO investigations available in the literature.17, 38-39

However, we note that alternative non-empirical45 and empirical46-47 schemes for

determining appropriate +U and +J corrections have been recently reported for oxide materials. The value of the Hund exchange J correction in this case corresponds to full localization of electrons on Ti-3d orbitals and is believed to be the most widely used +U correction applied for studies of SrTiO3.31 PBEsol+U+J is abbreviated here as PBEsol+U for the sake of brevity. Following Alexandrova et al.,48 the oxygen vacancy formation energy is defined as, Eform(VO) = EVO + ½ µO2 - Epris

(1)

where Epris is the total DFT energy of the defect-free supercell, EVO is the total DFT energy of the supercell with a single defect and µO2 is the gas-phase chemical potential of molecular oxygen (µO2 = -8.381 eV (-0.616 Ry) following Johnston et al.49). 2.2. Model (001) ATiO3 Interfaces Pristine and defective TiO2-terminated cubic (001) CTO, STO and BTO surfaces have been modelled with 2×2×4, 2×2×6, 3×3×4 slab models (Figure 1). A vacuum gap of 16 Å was used to separate the (001) slab in the unit cell from its periodic images. The base ATiO3 layer of atoms in each supercell was frozen, while all other atoms were fully relaxed. Cubic Pm-3m CTO, STO


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and BTO structures were taken from the International Crystal Structure Database (ICSD crystal IDs 91899, 95437 and 15317, respectively).50 Zhang et al.17 have previously demonstrated that the stability and migration barrier of oxygen vacancy defects in bulk STO depend sensitively on the size of the periodic unit cell; 2×2×2 cells lead to overestimations of migration barrier heights, while 3×3×3 cells can lead to an underestimation. Similarly, we examine the effect of lateral dimensions on surface vacancies by considering 2×2×4 and 3×3×4 model (001) surfaces. The 2×2×6 model surfaces enable us to comment in more detail on the formation energy and migration barrier profiles in the ATiO3 sub-surface regions, i.e. as the defect moves from the surface to the sub-surface region of the material. 5×5×1 k-points were used for the 2×2×N surface slabs, while 4×4×1 k-points were used for the 3×3×4 supercell using the Monkhorst– Pack scheme.51 The migration barriers of the neutral oxygen vacancy were computed using the climbing image nudged elastic band method (NEB)52 with 5 images for both the 2×2×6 and 3×3×4 supercells.


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Figure 1. (a) 6-layer STO surface slab model showing vacancy position numbering scheme. (b) 2×2 and (c) 3×3 extensions of the STO (001) unit cell. Blue polyhedral represent TiO2 subunits. For both slab and bulk calculations, structural relaxations were performed until all forces are smaller than 0.01 eV/Å. 2.3. Bulk ATiO3 Formation energies and migration barriers of neutral oxygen vacancies in bulk STO, BTO and CTO have been modelled using cubic 2×2×2 supercells. In the case of BTO and CTO, values are compared with native room temperature tetragonal BTO (P4mm, 2×2×2 supercell) and orthorhombic CTO (Pbnm, 2×2×1 supercell) phases. 6×6×6 k-points were used for all the bulk cells with the exception of Pbnm CTO where 6×6×8 was required.

3. Results and discussion 3.1. ATiO3 Vacancy Defect Formation Energy – Effect of +U Hubbard Correction We begin our discussion by considering the influence of the +U Hubbard correction to the PBEsol–predicted vacancy formation energies at the TiO2-terminated (001) surface of cubic STO. While such a comparison has been presented previously17 for bulk STO, it has not been considered to the (001) surface to our knowledge. It has been shown previously17 that PBE+U and PBEsol+U methods more accurately described the electronic structure of SrTiO3 supercells compared to PBE and PBEsol. We also consider the influence of the different model slab geometries in the manner of Zhang et al.17 The latter comparison enables us to elucidate (1) the influence of the lateral dimensions (i.e. by comparing the 2×2×4 and 3×3×4 model surfaces) and


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(2) the influence of the total slab depth (i.e. by comparing Eform in 2×2×4 and 2×2×6 unit cells) on the calculated vacancy formation energies. Figure 2 presents vacancy formation energies of the (001) STO surface calculated with PBEsol with and without +U corrections for the 2×2×4, 2×2×6 and 3×3×4 model surfaces. For the smallest model interface considered here, 2×2×4, the PBEsol Eform values depicted in Figure 2(a) show that in defect positions 2 to 6, the formation energy ranges from between 5.70-6.13 eV. The defect formation energies in layers directly adjacent to the frozen layer are seen to be artificially elevated, presumably due constraint on atom relaxation so will not be considered further. Eform at the surface layer (position 1) in the 2×2×4 model surface is ~5.0 eV, and therefore markedly lower than for the other subsurface layers. This is because atoms in the TiO2 surface layer are less constrained, meaning their geometrical rearrangement around the defect site is more energetically favourable in the surface layer. We note that this trend is observed for all model (001) ATiO3 model slabs considered in this work, to varying extents (see Figure 3). We also see in Figure 2(a) increasing the depth of the model surface (i.e. 2×2×4 vs 2×2×6) decreases Eform slightly. Eform values for positions 1 to 4 in the 2×2×6 surface are within -0.2 eV of the corresponding values in the 2×2×4 surface (positions 5 and 6 are ignored here due to the evident influence of the frozen layer in the 2×2×4 surface). This is because the surface region in the vicinity of the vacancy defect in the 2×2×6 model surface is less constrained, compared to that in the 2×2×4 surface. The reduction in geometrical constraint in the deeper 2×2×6 surface is therefore a constant effect, and independent of the vacancy position. In the bulk regions of the 2×2×6 model surface, e.g. between positions 5-8, a zigzag trend of ~0.15 eV in the PBEsol Eform values is also evident in Figure 2(a). This is because the oxygen vacancy defect alternatively


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resides in SrO (higher Eform) and TiO2 layers (lower Eform) within the SrTiO3 structure. These results are consistent with PBEsol Eform values for bulk SrO (7.1 eV) and TiO2 (6.5 eV).17 The optimized geometries of the defective slab models also indicate that when an oxygen vacancy is present in a TiO2 layer, there is greater allowance for local distortion in the structure to accommodate the defect. Interestingly, the effect of increasing the lateral dimension of the unit cell (i.e. 2×2×4 vs 3×3×4) on PBEsol Eform values is, to a degree, comparable to the effect of increasing the depth of the surface (i.e. 2×2×4 vs 2×2×6); in both cases the PBEsol Eform values are decreased from those obtained with the 2×2×4 model surface (by ~0.5 eV for lateral expansion and by ~0.2 eV for longitudinal expansion).


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Figure 2. Vacancy formation energies Eform(VO) (eV) in 2×2×4, 2×2×6 and 3×3×4 model STO (001) surfaces as a function of depth calculated using (a) PBEsol and (b) PBEsol+U.


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Figure 3. (a) PBEsol and (b) PBEsol+U oxygen vacancy formation energies in TiO2 terminated 2×2×6 model STO, BTO and CTO (001) surfaces.

Figure 2 (b) summarizes the PBEsol+U results across the 2×2×4, 2×2×6 and 3×3×4 models of the STO (001) surface. The +U correction has two obvious effects on the PBEsol Eform values shown in Figure 2(a). Firstly, the effects of increasing the lateral dimension and depth of the model surface is negligible on PBEsol+U Eform values, with the 2×2×4, 2×2×6 and 3×3×4 models yielding essentially comparable results. Secondly the vacancy formation energy itself is


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increased by ~1 eV by the addition of the +U Hubbard correction. The +U correction is observed to have the same effect on the PBEsol Eform in bulk cubic STO (Table 1), albeit to a lesser extent. Thus, PBEsol+U Eform values shown in Figure 2(b) are in closer agreement with a previously reported HSE06 bulk Vo formation energy (6.0 eV).53 The addition of the +U correction to the PBEsol functional also makes the zig-zag pattern observed for the 2×2×6 slab in Figure 2(a) more obvious, since the Vo in TiO2 layers (odd layers in Figure 2) becomes more stable relative to the Vo in the SrO layers. This is because the +U correction, which is applied to the Ti4+ 3d orbitals, stabilizes the lone electron pair (formed by the neutral defect site) in the Ti4+ t2g band when the vacancy resides in a TiO2 layer, i.e. equatorially to Ti4+. The same zig-zag pattern is observed to a lesser degree in the 2×2×4 model surface, however not observed in the larger 3×3×4 slab. Despite these differences, PBEsol and the PBEsol+U both predict the vacancy formation energy in the TiO2 surface layer to be ~1.0 eV lower in energy that for the subsurface and bulk layers. However, PBEsol+U predicts Eform in position 2 to be similar to that at position 1 for each model surface considered here. Thus, PBEsol and PBEsol+U evidently describe the transition from surface to sub-surface or bulk vacancy formation differently. In a similar vein, Haa et al. 48 have noted that the inclusion of the Hubbard +U can alter the prediction of whether a surface or subsurface Vo is the most stable in Anatase TiO2. Table 1. Neutral oxygen vacancy formation energies (eV) for bulk ATiO3 (A=Ca, Sr, Ba) in their cubic and (for CaTiO3) native room temperature phases.

CaTiO3 SrTiO3 BaTiO3

Phase Pm3m Pbnm Pm3m Pm3m P4mm

PBEsol 6.05 6.30 6.32 6.11 6.23

PBEsol+U 6.66 6.98 6.79 6.63 6.80


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3.2. ATiO3 (001) Vacancy Defect Formation Energy – Effect of the A-Site Cation On the basis of the results presented in the preceding section, we now consider the effect of the A-site cation on the vacancy formation energy profiles. Figure 3 presents Eform values for cubic STO, BTO and CTO TiO2-terminated (001) surfaces calculated using PBEsol and PBEsol+U with a 2×2×6 model surface. Analogous formation energy profiles for the AO-terminated (001) surfaces are presented in Supporting Information. While STO and BTO both exhibit room temperature cubic phases, the cubic phase of CTO is only observed at high temperatures (e.g. > 1634 K).54 However, we maintain a consistent crystalline phase here for the purpose of comparison, enabling us to elucidate the effect of the A site cation on oxygen vacancy formation energy profiles. Similarly, the 2×2×6 model surface is employed from this point as Eform values in this surface with the Hubbard+U correction are comparable to those in the larger 3×3×4 surface and the deeper 2×2×6 surface enables us to describe the migration of oxygen vacancy defects into the subsurface regions more extensively. Comparison of Figure 3(a) and (b) shows the effect of the +U Hubbard correction to PBEsol Eform values for CTO, STO and BTO. As established in the previous section, the +U correction stabilizes the vacancy defect in the TiO2 layer in STO, leading to a more pronounced zig-zag pattern in the formation energy profile for the STO (001) surface. Figure 3 shows the same trend for BTO within the subsurface region of the model slab (e.g. positions 3-8); PBEsol Eform values (Figure 3(a)) for the BaO layers in BTO range between 5.58-5.68 eV (excluding end effects), while Eform values for the TiO2 layers are notably higher, being 5.80-6.04 eV. We also note that the drop in Eform at the STO (001) surface is reproduced in BTO (001). By applying the +U


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correction (Figure 3(b)) the PBEsol Eform energies for BTO (001) generally increase by ~1 eV, similar to STO, and the Eform values in TiO2 layers are again stabilized relative to those in the BaO layers. For BTO, the +U correction produces more consistent Eform values between BaO and TiO2 layers in positions 3-10, compared to the profile shown in Figure 3(a) for PBEsol, which is the opposite trend of STO (001) discussed above. For CTO (001), Figure 3(a) shows PBEsol Eform values vary dramatically between the alternating CaO and TiO2 layers. For the CaO layers, PBEsol Eform values range between 4.685.39 eV, and the +U correction (Figure 3(b)) increases this consistently by ~0.5 eV. Figure 3(a) shows that Eform(CTO) < Eform(STO) < Eform(BTO) when the defect is in the AO layer using PBEsol. With the +U correction applied (Figure 3(b)), this trend generally remains in the subsurface layers of the (001) model surface. However, PBEsol+U Eform values are more consistent for these three titanates, again consistent with the trend shown in Table 1 for the respective bulk cubic structures. For reference,Table 1 additionally details the Eform values for the native room temperature phases of BTO and CTO. While there are small differences in the Eform values across the series, comparable trends are seen in the cubic form for PBEsol and PBEsol+U. The +U effect appears to increase the Eform values by between 0.5 to 0.8 eV. Additionally, in their respective native room temperature phases the Eform of BTO and CTO is seen to be higher as well. Much larger variation is seen in Eform for vacancies in the TiO2 layers of CTO, compared to STO and BTO which are comparable. Figure 4 shows that this correlates with the extent of the local structural rearrangement in the CTO (001) surface towards a local orthorhombic structure. By contrast, the structural deviation in STO and BTO (001) surfaces is relatively limited. Unsurprisingly, Figure S1 shows that these trends are independent of whether the (001) surface


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is AO-terminated or TiO2-terminated. These results are quantitatively corroborated by a geometrical energy decomposition analysis, which is provided in Supporting Information. These trends are consistent with STO and BTO exhibiting similar room-temperature cubic and tetragonal phases, respectively. We note that BTO also exhibits a higher energy cubic phase at 393 K,55 which is only slightly distorted from its room-temperature tetragonal structure. On the other hand, CTO at room temperature is orthorhombic, and can only access the cubic phase at high temperature (1634 K) via significant structural rearrangement (as shown in Figure 4).54 Such rearrangement is facilitated by the relative size of the the Ca2+ ion, which is the only ion of those considered here that is sufficiently small to allow such significant distortions in the lattice (e.g. the Shannon’s radii for 12 coordinated Ba2+, Sr2+ and Ca2+ are 1.61 Å, 1.44 Å and 1.34 Å respectively).

Figure 4. Examples of structural rearrangements at positions 5 (left, TiO2 layer) and 6 (right, AO layer) in 2×2×6 model surfaces of (a-b) CTO, (c-d) STO and (e–f) BTO using PBEsol+U. Circles denote the position of the oxygen vacancy defect. Orange, green, purple spheres indicate Ca2+, Sr2+ and Ba2+ cations; red spheres and blue polyhedral represent O2- anions and TiO2 octahedra.


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Equivalent trends to those established in the preceding discussion for TiO2-terminated STO, BTO and CTO (001) surfaces are obtained for the analogous AO-terminated (001) surfaces (Figure S1, Supporting Information). Previous experimental and computational studies have determined that Sr2+ ion migration in STO is mediated by oxygen vacancies and can lower the Sr2+ migration energy barrier by up to 1.0 eV.56-57 Our Eform results for AO-terminated and TiO2terminated (001) surfaces indicate that oxygen vacancies form more easily in STO in the presence of a TiO2-terminated surface, compared to both the bulk and AO-terminated surface. This is consistent with the equal loss of Sr2+ ions and O2- ions at the STO (001) electrode surface observed by Plaza et al.23 3.3. Vacancy Diffusion Barriers in ATiO3 (001) Surfaces – Effect of the A-Site Cation We now consider the effect of the A-site cation on the vacancy migration barriers in bulk CTO, STO and BTO and near the respective (001) surfaces. As noted previously, only STO and BTO both exhibit room temperature cubic phases (CTO exhibits a high temperature cubic phase54), and the consideration of cubic CTO here merely enables the elucidation of the effect of the A site cation on oxygen vacancy diffusion. Bulk diffusion barriers for cubic (2×2×2 unit cell) and orthorhombic (2×2×1 unit cell) are summarized in Table 2. Migration energy barrier profiles of CTO, STO and BTO calculated using the 2×2×6 (001) model surfaces are presented in Figure 5. For bulk cubic phase CTO, STO and BTO, Table 2 shows that the vacancy migration energy barrier is proportional to the size of the A-site cation. For instance, vacancy diffusion in CTO, STO and BTO are impeded by barriers of 0.71-0.75, 0.82 and 1.56-1.62 eV, respectively for PBEsol+U. For BTO and CTO the crystalline phase of the unit cell has a negligible impact on


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the magnitude of the diffusion barrier; 0.04 eV for CTO and 0.06 for BTO respectively. Experimentally, the activation enthalpy of vacancy diffusion for STO and BTO are reported to be similar, 0.62-0.67 eV and 0.70 eV, respectively.57-58 For CTO however, a recent review by de Souza et al.57 highlights the inconsistency of the recorded results for the comparable oxide selfdiffusion activation enthalpy, which has been reported to vary between 0.56 and 4 eV. Table 2. Bulk neutral oxygen vacancy diffusion energy barriers (eV) for ATiO3 (A=Ca, Sr, Ba) Phase PBEsol+U Pm3ma

0.71

Pbnmb

0.75

SrTiO3

Pm3ma

0.82c

BaTiO3

Pm3ma

1.62

P4mmb

1.56

CaTiO3

a

2×2×2 unit cell; b2×2×1 unit cell; cRef. 17

Figure 5(a) shows that for the 2×2×6 (001) model surface used here, vacancy diffusion barriers in CTO (001) are only observed within the subsurface region (e.g. between positions 5-8, Figure 1). Within this region, the barrier for a vacancy defect migrating from a CaO layer to the adjacent TiO2 layer is relatively small, ~0.2-0.3 eV. This is ~50% of the corresponding bulk value using PBEsol+U (Table 2), a reduction that is attributed to the ease with which the (001) surface may locally deform in the presence of a defect. The position of the vacancy migration transition state (relative to the adjoining CaO and TiO2 layers) indicates a late transition state; the transition state and CaO-layer defect structures are therefore comparable. Considering the prohibitively high defect formation energies for the CaO sublattice (Figure 3) relative to those in the TiO2 octahedra, and the fact that the diffusion of these defects is kinetically labile (Figure 5), it is likely that the TiO2 octahedra near the CTO (001) surface will act as “thermodynamic


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sinks”, effectively trapping defects. Figure 5(a) also shows that, in regions closer to the TiO2terminated surface, no migration barrier is observed. It is possible that vacancy migration in this region of the CTO (001) surface is barrierless, considering the extent of structural distortion to this surface in the presence of an oxygen vacancy, see Figure 4, and considering also that these deformations become exacerbated in layers closer to the surface. However, it is also possible that the climbing image NEB algorithm cannot locate the vacancy migration transition state here for the same reason. For the STO (001) surface, migration of a vacancy defect out of a SrO layer is impeded by a barrier of ~0.7 eV in the subsurface region, according to PBEsol+U. There is no significant difference between the migration barrier at the (001) and between underlying subsurface layers. We note also that these barrier heights are only marginally lower than the values reported for STO bulk reported independently (see Table 2).17 The kinetics of diffusion at the (001) surface and in bulk STO can therefore be expected to be comparable, but slightly more labile near the (001) interface. As observed for CTO (Figure 5(a)), the NEB path between adjacent SrO and TiO2 in the STO (001) subsurface (Figure 5(b)) is asymmetric, albeit not to the same extent as that observed in CTO. However, the position of the transition state is closest to the SrO sublattice; the structure of the transition state resembles the structure of the SrO-layer defect more than the TiO2-layer defect, as was the case in CTO (001). Nevertheless, diffusion barriers in the STO (001) surface are approximately three times larger than those in CTO (001), and so we conclude that vacancy diffusion in STO (001) is kinetically, and not thermodynamically controlled. For BTO (001) (Figure 5(c)), vacancy defect migration in the subsurface region is impeded by barriers of ~1.0-1.4 eV with respect to the BaO sublattice. This is comparable to the bulk diffusion barriers shown in Table 2. The migration barrier in the


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surface layer is lower (~0.86 eV) compared to that observed in the subsurface, and this is attributed to the increased capacity for structural deformation in the surface layer in the presence of a vacancy defect. Compared to the asymmetric NEB paths observed for CTO (001) and STO (001) subsurface regions, the NEB path in Figure 5 (c) for BTO is more symmetric. This means that the transition state structure does not resemble the BaO-layer defect structure to the same extent as do the respective transition states in STO and CTO, discussed above. Considering the fact that Eform for the BaO and TiO2 sublattices are comparable, vacancy diffusion near the BTO (001) surface is expected to be determined by kinetic, and not thermodynamic, factors. Notably, while defects are more likely to be found in the TiO2 sublattice in CTO (001) and STO (001)


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surfaces, defects can be expected to be more evenly distributed between BaO and TiO2

sublattices in BTO (001). Figure 5. PBEsol+U oxygen vacancy migration barrier profiles (eV) for 2×2×6 (001) model surfaces of (a) CTO (b) STO (c) BTO. Dashed lines show Eform for each surface for comparison. Note the different energy scale in (a). 4. Conclusions We have presented a first-principles investigation of the thermochemical and kinetic stability of oxygen vacancy defects near the (001) surface of a class of titanate perovskites. A detailed assessment of how the +U Hubbard correction influences thermochemical stability of oxygen


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vacancy defects is also presented. Our results demonstrate that the defect formation energies are proportional to the degree of geometrical distortion within the defective TiO2 sublattice, and this correlates with the size of the A-site cation (Ca2+ < Sr2+ < Ba2+). This is most obvious for the smallest cation considered here, Ca2+. In this case vacancy defects in the (001) surface yield dramatic structural distortions, whereby TiO2 octahedra rotate towards an orthorhombic arrangement. In CTO the TiO2 sublattice effectively acts as a thermodynamic trap for oxygen vacancy defects, which incur prohibitively high formation energies, but relatively small migration barriers. On the other hand, our results indicate that vacancy diffusion in STO and BTO (which have larger A-site cations) is kinetically controlled, since the migration energy barriers are significantly higher than those for CTO.

Supporting Information Vacancy formation energies of CaO, SrO, BaO – terminated (001) titanate surfaces, geometrical energy decomposition analysis. This material is available free of charge via the Internet at http://pubs.acs.org.

Acknowledgements AJP acknowledges support from the Australian Research Council (INTERSECT, LE170100032). JJB acknowledges an Australian Postgraduate Award. This research was undertaken with the assistance of resources provided at the NCI National Facility systems at the


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Australian National University and INTERSECT systems, through the National Computational Merit Allocation Scheme supported by the Australian Government. Corresponding Author *[email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

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TOC graphic


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Figure 1. (a) 6-layer STO surface slab model showing vacancy position numbering scheme. (b) 2×2 and (c) 3×3 extensions of the STO (001) unit cell. Blue polyhedral represent TiO2 subunits. For both slab and bulk calculations, structural relaxations were performed until all forces are smaller than 0.01 eV/Å. 90x121mm (300 x 300 DPI)


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Figure 2. Vacancy formation energies Eform(VO) (eV) in 2×2×4, 2×2×6 and 3×3×4 model STO (001) surfaces as a function of depth calculated using (a) PBEsol and (b) PBEsol+U 90x136mm (300 x 300 DPI)



Figure 3. (a) PBEsol and (b) PBEsol+U oxygen vacancy formation energies in TiO2 terminated 2×2×6 model STO, BTO and CTO (001) surfaces 90x178mm (300 x 300 DPI)


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Figure 4. Examples of structural rearrangements at positions 5 (left, TiO2 layer) and 6 (right, AO layer) in 2×2×6 model surfaces of (a-b) CTO, (c-d) STO and (e-f) BTO using PBEsol+U. Circles denote the position of the oxygen vacancy defect. Orange, green, purple spheres indicate Ca2+, Sr2+ and Ba2+ cations; red spheres and blue polyhedral represent O2- anions and TiO2 octahedra. 90x78mm (300 x 300 DPI)



Figure 5. PBEsol+U oxygen vacancy migration barrier profiles (eV) for 2×2×6 (001) model surfaces of (a) CTO (b) STO (c) BTO. Dashed lines show Eform for each surface for comparison 90x181mm (300 x 300 DPI)


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Oxygen Vacancy Defect Migration in Titanate Perovskite Surfaces

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