Sr Doping and Oxygen Vacancy Formation in La_1−xSr_xScO_3−δ Solid Solutions: Computational Modelling

Abstract

Sr-doped lanthanum scandate La_1−xSr_xScO_3−δ (LSS) is a promising perovskite-type material for electrochemical applications such as proton conductors. Oxygen vacancy is a common defect in ABO₃-type perovskites. It controls ion transport as well as proton uptake. The energetic, structural, and electronic properties of oxygen vacancy in LSS are studied deploying the DFT method with meta-GGA functional. The vacancy formation energies in LSS were calculated for various Sr concentrations. Unlike other perovskites, in this material, the electrons are trapped at the oxygen vacancy site (the F-type centres, common in ionic oxides like MgO and Al₂O₃) rather than localised on the nearest to the vacancy B-cations. The process of oxygen vacancy formation is considered relative to Sr concentration x and oxygen nonstoichiometry factor δ. Three primary regimes are discussed: (I) localized at the vacancy electrons, x/δ < 2, (II) electron charge balanced system, x/δ = 2, and (III) delocalized electron holes, x/δ > 2. For x/δ ≥ 2 oxygen vacancy formation energy reaches the saturation level of ~3.5 eV, which is potentially beneficial for the proton uptake.

1. Introduction

Independently discovered in 1998 by Fujii et al. [1] and in 1999 by Lybye et al. [2], proton conductivity in lanthanum scandates made these materials a promising choice for Protonic-Ceramic Fuel Cells (PCFC) and Protonic Ceramic Electrolysis Cell (PCEC). As reported in ref. Nomura, K. et al. [3], Sr-doped lanthanum scandate-La_1−xS_xrScO_3−δ showed the highest proton conductivity of ca. 6 × 10⁻³ S cm⁻¹ at 873 K for x = 0.2. The high proton conductivity was attributed to the increased number of mobile protons due to the high concentration of oxygen vacancy at x = 0.2. Extensive studies on crystal structure, electrical conductivity, water incorporation, oxygen and hydrogen diffusivities of lanthanum-strontium scandate were performed [4,5,6]. Unlike acceptor-doped Ba(Zr,Ce)O₃ materials, La_1−xSr_xScO_3−δ (LSS) oxides demonstrate high stability and protonic conductivity not only in water-containing, but also in reduced and carbon-containing atmospheres [7,8]. This makes lanthanum scandates attractive and prospective not only for PCFC and PCEC applications but also for the electrochemical protonic ceramic membrane reactors for dimerization of methane and production of aromatics from methane, as well as fabrication of hydrogen electrochemical filters for gaseous hydrogen of high purity production and electrochemical separators for hydrogen isotopes.

The proton uptake requires the presence of oxygen vacancies in a host material while an oxygen atom of water molecule heals the vacancy, releasing two protons. The experimental study [9] suggests that oxygen deficiency in La_1−xSr_xScO_3−δ is provided by extended defects and formation of oxygen vacancy is rather unfavourable.

The study [10] of Sr doping in the ABO₃ perovskites have demonstrated a considerable decrease of the vacancy formation enthalpy and thus an increase of vacancy concentration. Acceptor doping into the LaScO₃ oxide causes oxygen deficiency, and recent studies indicate the presence of complex extended defects in the structure, as well as F-centres [11] of different types in reducing atmospheres [12]. The papers [9,13] discuss the possibility of the existence of even a double vacancy in related SrTiO₃ and LaScO₃ oxides. Recent Nuclear Magnetic Resonance (NMR) studies of the local symmetry in scandates [14,15] show that, contrary to A^IIB^IV-type perovskites, e.g., BaZr_1−xSc_xO_3−x/2, in LaScO₃ oxygen stoichiomentry relates to the surrounding of Sc cation. Particularly, in single B-cation perovskite-type compounds, Sc is solely six-fold coordinated. It implies the existence of various types of boundaries capable of segregating defects, including the oxygen sublattice defects, and the presence of electronic compensation mechanisms, potentially introduced by 3d-metals.

Being a common defect in perovkite-type materials, oxygen vacancy in lanthanum scandates needs to be considered as one of possible oxygen deficiency mechanisms. In this computational study, we investigate oxygen vacancy formation in undoped as well as Sr-doped lanthanum scandate.

2. Methods

For computational modelling of oxygen vacancy in lanthanum scandate we deployed the computer code VASP 6.1.2 The primary calculation details and the core potential details are given in

Table 1. Main calculation parameters.

Computer Code.	VASP 6.1.2 [17]
Plane wave basis set cutoff energy	650 eV
Supercell extensions	$\left(\begin{array}{ccc}2& 0& 0\\ 1& 1& 1\\ 1& 1& -1\end{array}\right)$
K-points	Monkhorst-Pack [18] 2 × 2 × 2
Exchange-correlation functional	Strongly Constrained and Appropriately Normed Semilocal Density Functional (SCAN) [19]
External pressure	<1 kbar
Forces on atoms	<0.02 eV/Ǻ

and

Table 2. Projector Augmented Wave (PAW) [20] Perdew-Burke-Ernzerhof (PBE) [21] potentials for core electrons.

Potentials	Valence Electrons	Ecutoff, eV
La	5s25p66s25d1	219.292
Sr	4s24p65s2	229.353
Sc	3d14s2	154.763
O	2s22p4	400.000

, respectively. The ideal structure of undoped LaScO₃ was completely optimized (

Table 3. Experimentally measured and calculated LaScO₃ lattice constants in Å. Atomic coordinates are given in Table A1.

Scheme 0	a0	b0	c0
Clark, J. B. et al. [24]	5.7911	8.0923	5.6748
Farlenkov, A. S. et al. [16]	5.7913	8.0943	5.6793
present study	5.7841	8.0826	5.6680

,

Table A1. Atomic coordinates of LaScO₃.

		Atomic Coordinate
		x		y		z
Atom	Site	a*	b*	a*	b*	a*	b*
La	4c	0.43745	0.45054	0.25	0.25	0.01537	0.01127
Sc	4a	0	0	0	0	0	0
O apical	4c	0.5323	0.53270	0.25	0.25	0.5996	0.59797
O equatorial	8d	0.1988	0.20025	0.0528	0.05160	0.3044	0.30048

^*a -Ref. [24]; ^*b -present study.

, Figure A1). For Sr-doped material and vacancy calculations, the lattice constants were kept fixed. Experimental measurements [16] suggest that lattice constants for doped material (x ≤ 0.09) are only 0.02 Å larger, which is negligible for oxygen vacancy calculations. Although the electronic structure of the ideal compound suggests diamagnetic state, particularly for defect calculations spin-polarization was enabled.

It is known that the strongest structural perturbation caused by oxygen vacancy in perovskites occurs along the B-Vo-B chain [22]. In case of multiple oxygen vacancies, it is practical to build a supercell with the largest distances along all three mutually orthogonal B-Vo-B chain directions. The extensions [23] of our supercell (Figure A2) provide the smallest volume in a combination with the largest distance along the direction of the strongest interaction between the periodically translated images of oxygen vacancy.

Although the extensions of the supercell are large enough to limit the Brillouin zone sampling by a single K-point, we add one more point in each direction in order to facilitate the convergence.

SCAN exchange-correlation functional was chosen as a feasible alternative to computationally demanding hybrid functionals.

3. Main Results and Discussion

LaScO₃ is a perovskite-type single-phase material (Figure A1) with strongly pronounced orthorhombic distortion (Pnma space group).

Sr doping was modelled as A-cation substitution-Sr_La. Sr cations were placed as the 4th, the 5th and the 12th nearest neighbours (

Table A2. Radial Distribution Function of Sr-Sr, Sr-O_apical, Sr-O_equatorial, O_apical-O_apical, and O_equatorial-O_equatorial sublattices.

Sr-Sr	Distance, Å
4	5.44
5	5.62
12	8.05
Sr-Oap.
1	2.37
2	2.50
3	3.33
4	3.42
5	4.59
6	4.93
7	5.04
8	5.28
9	5.57
13	5.81
14	6.04
15	6.26
22	7.32
Sr-Oeq.
1	2.40
2	2.70
3	2.84
4	3.60
5	4.55
6	4.75
8	4.90
9	5.00
12	5.60
14	5.82
15	5.93
16	6.11
18	6.50
27	7.28
33	7.85
Oap.-Oap.
13	8.049
Oeq.-Oeq.
33	8.049

). This substitution is compensated by the electron holes delocalized over the oxygen sub-lattice, which determines the oxygen vacancies behaviour and defect formation energetics. There is a negligible, 0.01 and 0.04 eV per Sr_La, repulsive interaction between Sr_La atoms for x = 0.125 (

Table A3. Configurational Matrix (mutual interatomic distances in NN, as in Table A2) for x = 0.125.

	Sr1	Sr2
Sr1	0	Sr-Sr 12
Sr2		0

) and 0.25 (

Table A4. Configurational Matrix (mutual interatomic distances in NN, as in Table A2) for x = 0.25.

	Sr1	Sr2	Sr3	Sr4
Sr1	0	Sr-Sr 12	Sr-Sr 4	Sr-Sr 4
Sr2		0	Sr-Sr 4	Sr-Sr 4
Sr3			0	Sr-Sr 5
Sr4				0

) concentrations, respectively, calculated relative to x = 0.0625 Sr-concentration. Such small interaction energy values suggest a homogeneous distribution of the dopant on the host lattice. Oxygen vacancy was introduced as a neutral defect-by removing the neutral atom from the neutral system. Note that in all cases in this study, despite the presence of charged defects, the whole system is kept electroneutral.

A detailed description of oxygen vacancy and Sr_La spatial distribution is given in interatomic distances (Appendix A). There are two nonequivalent oxygen atoms in undoped structure-apical and equatorial (Table A1). There are twelve nearest to A-cation oxygen anions in perovskite-type structure. Due to the orthorhombic distortion, in LSS we deal with eight coordination subspheres-four for each apical anion and four for each pair of equatorial oxygen anions (Table A2). In doped material, oxygen vacancy was created at all eight inequivalent nearest to Sr cation distances. Formation energy was calculated relative to oxygen molecule (Ref. [10]). Due to the strong dependence on the computational method, the experimental value of O₂ binding energy 5.12 eV [25] was used.

To satisfy the formal charge neutrality condition, the value of oxygen nonstoichiometry δ has to be twice smaller than the concentration of Sr dopant x-La_1−xSr_xScO_3-x/2. In many perovskite-type materials, e.g., A(Fe,Co)O_3−δ, oxygen stoichiometry is stabilized by the adjustment of the oxidation state of B-cation [26,27]. Some perovskite-type compounds may provide conditions for both accepting electrons to the d-orbitals of B-cations as well as trapping them at the vacancy site [10,28,29,30]. Sc cation, in its turn, demonstrates a strong resistance to accept additional electrons, remaining in the oxidation state 3+. A-cations La and Sr do not change their charge easily either. This leads to the formation of the F-type centres [11] in La_1−xSr_xScO_3−δ. Considering a relatively large band gap of LSS, localization of the electrons of the missing O at the vacancy site is energetically more favourable than on d-orbitals of the nearest to the vacancy Sc cations.

It is well known that Sr²⁺ ion substituting for La³⁺ is compensated by electron holes on oxygen p-orbitals or oxygen vacancy $V_{\mathrm{o}}^{••}$(Kröger-Vink notation [31]). Doping by Sr, as well as $V_{\mathrm{o}}^{••}$ formation alone, changes the electroneutrality of the system, which has to be compensated. Such $V_{\mathrm{o}}^{••}$ formation can be described as following

$$2\mathrm{SrO}\to 2{\mathrm{Sr}}_{\mathrm{La}}^{\prime }+V_{\mathrm{o}}^{••}+2{\mathrm{O}}_{\mathrm{O}}^x.$$

In parallel with the Kröger-Vink notation, we apply commonly accepted in optical physics F-type centre nomenclature. This way we would like to emphasize the material’s specific properties of oxygen vacancy. It is also a convenient approach to describe various vacancy formation regimes.

Oxygen vacancies are likely to prevail at high temperatures. In accordance with the present calculations in the electron charge neutral supercells:

(1)

two electrons, due to the $V_{\mathrm{o}}^{••}$ formation, reside at the vacancy site (the colour F⁰-centre [32]) if Sr is absent;

(2)

the substitution ${\mathrm{Sr}}_{\mathrm{La}}^{\prime }$ introduces an electron hole on oxygen p-orbitals;

(3)

Depending on the oxygen vacancy and Sr concentrations, electrons and holes are partially or completely compensated, giving rise to various combinations of F-type centres and electron holes. There are two, one and no electrons, trapped at the vacancy site in F⁰-, F⁺- and F⁺⁺-centre, respectively.

Therefore, the following cases were considered (

Table 4. Share of F-type centres and electron holes in La_1−xSr_xScO_3−δ (Figure 1).

x/δ Range	Defect	Defect Share	Defect	Defect Share
0 ≤ x/δ ≤ 1	F0-centre	1−x/δ	F+-centre	x/δ
1 ≤ x/δ ≤ 2	F+-centre	2−x/δ	F++-centre	x/δ−1
2 ≤ x/δ	F++-centre	1/(x/δ−1)	electron hole	(x/δ−2)/(x/δ−1)

, Figure 1):

(1)

formation of F⁰-centres for x/δ = 0;

(2)

simultaneous formation of both F⁰- and F⁺- centres for 0 < x/δ < 1;

(3)

formation of F⁺-centres for x/δ = 1;

(4)

simultaneous formation of both F⁺- and F⁺⁺- centres for 1 < x/δ < 2

(5)

formation of F⁺⁺-centres for x/δ = 2; all electron holes are compensated by the electrons left from the $V_{\mathrm{o}}^{••}$ for x/δ = 2

(6)

simultaneous formation of both F⁺⁺-centres and electron holes for x/δ > 2.

Two concentrations of oxygen vacancies were tested in a combination with three concentrations of Sr (

Table 5. Oxygen vacancy (apical or equatorial, Table A1) formation energy in La_1−xSr_xScO_3−δ, in eV per one vacancy. Corresponding spatial distribution of Sr cations as in Table A3 and Table A4 and $V_{\mathrm{o}}^{••}$ as in Table A5, Table A6, Table A7 and Table A8. For δ = 0.0625 a single vacancy was introduced as in Table A5, Table A6 and Table A8. For δ = 0.125, a two vacancies were introduced as in Table A7 and Table A9.

		Configuration Matrix	Configuration Number (Table A10)
			$V_{\mathrm{o}}^{••} ap.$				$V_{\mathrm{o}}^{••} eq.$
x	δ		1	2	3	4	5	6	7	8
0	0.0625		7.89				7.97
0.0625	0.0625	Table A5	6.77	6.93	6.57	6.55	6.81	6.94	6.97	6.58
0.125	0.0625	Table A6	3.50	3.74	3.87	3.82	3.58	3.74	3.79	3.89
0.125	0.125	Table A7	3.17	3.51	3.53	3.56	3.52	3.45	3.56	3.38
0.25	0.0625	Table A8	6.72	6.88	6.59	6.58	6.77	6.91	6.92	6.59
0.25	0.125	Table A9	3.36	3.76	3.76	3.83	3.75	3.68	3.80	3.78

). One (x = 0.0625) and two (x = 0.125) oxygen vacancies were introduced at various distances from ${\mathrm{Sr}}_{\mathrm{La}}^{\prime }$ cations (Table A2), to estimate the deviation of the formation energy due to the ${\mathrm{Sr}}_{\mathrm{La}}^{\prime }$-$V_{\mathrm{o}}^{••}$ interaction. In undoped material vacancy formation energies are extremely high, reaching 8 eV. That makes the defect formation under the normal conditions extremely unfavourable. Even the low concentration of Sr (x = 6.25%) causes an immediate drop in formation energy down to 6.8–6.9 eV per vacancy. Note that vacancy formation energy does not depend solely on Sr concentration x or oxygen stoichiometry δ, but on the particular combination of defects (Table 4), governed by the x/δ ratio. In general, equilibrium oxygen vacancy concentration also strongly depends on oxygen partial pressure, temperature, as well as other factors [33] not considered in our model. The formation energies are still high for x/δ < 2. x/δ = 2 ratio provides the condition for moderate 3.5–3.8 eV oxygen vacancy formation energies while for x/δ > 2 the saturation is clearly reached (Figure 2). Similar saturation effect at x/δ > 2 was also observed by Mizusaki et al. [34] for La_1−xSr_xFeO_3−δ. However, there is a great difference between the materials. In La_1−xSr_xFeO_3−δ the electron holes localise on Fe cations, which facilitates the formation of oxygen vacancy with the energy of ~1eV [29,34].

To our best knowledge, there is no experimentally measured oxygen vacancy formation energy in LSS to compare the calculated values with. However, the authors of Ref. [35] assume that, among other factors, the contribution of the formation energy may be the reason for the the high oxygen diffusion apparent activation energy values for the undoped material. Farlenkov et al. showed that the apparent activation energy for the undoped material (2.7 eV) is much higher than for doped (x = 0.09, 0.04) ones (1.2, 1.3 eV).

The electronic properties analysis revealed that calculated band gap of 4.4 eV in comparison to the experimental values of 5.8 eV [36] is underestimated. This underestimate, however, does not affect the main conclusions. The Hubbard correction of U-J = 4 eV, expanding the gap by 0.2 eV, was discarded. Oxygen vacancies create distinct defect levels ~ at 0.8, 1.5 and 2.3 eV below the Conduction Band Minimum CBM (Figure 3). A similar peak in DOS was reported by Vlasov et al. in [12] for x/δ = 0 and 2. Our considerations suggest that in both cases there is a single defect level in the band gap, ca. 1.5eV below the CBM. The position of the defect levels in that study [12], however, is much closer to the valence band ~0.5eV, which can be attributed to the computational method applied.

DOS plots in Figure 3 demonstrate a continuous transition from the x/δ = 0 regime to x/δ = 2 regime via special (Figure 3a,e,i) as well as general (Figure 3b–d,f–h) cases. In the case of x/δ = 0 the single defect level is fully occupied (Figure 3a). The electron density distribution analysis shows that the electrons on this defect level are located right at the vacancy site (Figure 4a) rather than on the d-orbitals of the nearest B-cations as in Refs. [37,38,39]. This is also confirmed by a negligible (<0.05 e) deviation of electron charges (Bader) on A- as well as B-cations. So, the charge redistribution caused by oxygen vacancy occurs predominantly between oxygen p-orbitals and the vacancy site. There are two defect levels for x/δ = 1-occupied and unoccupied in the spin up and spin down channel, respectively (Figure 3e). A single unpaired electron is trapped at the vacancy site (Figure 4a). For x/δ = 1.5, with the equal numbers of F⁺- and F⁺⁺-centers in the system we observed a split of the central (F⁰-, F⁺⁺-centre) peaks, merging the F⁺-centre peaks (Figure 3g). For x/δ = 2 the vacancy site is unoccupied (Figure 3i) and Valence Band Maximum (VBM) is composed solely by the p-orbitals of all oxygen ions (Figure 4b). For x/δ = 4 the vacancy site remains unoccupied. In addition to that, two uncompensated electron holes appear.

The density of states analysis has confirmed that in a general case (Figure 3b–d,f–h) there is a superposition of two types of noninteracting defects, as described in Table 4 and shown in Figure 1. Note that in a combination of two defects (Figure 3b–d,f–h) the size of the defect peaks is proportional to the share of the corresponding defect (Table 4). In special cases (x/δ = 0, 1, 2) we can assume the presence of just one particular type of defects (F⁰-, F⁺- or F⁺⁺-centre) with one Figure 3a,i or two peaks Figure 3e. The positions of these three peaks relative to CBM remain practically the same for all combinations of defects.

Summing this Section up, we have shown that oxygen vacancy formation in La_1−xSr_xScO_3−δ solid solutions is controlled predominantly by the dopant Sr concentration x. Oxygen nonstoichiometry factor δ is very close to x/2 or slightly larger, for higher temperatures and lower $p_{{\mathrm{O}}_2}$. Large diviations from this value energetically are very costly. This makes oxygen vacancy formation in undoped material (F⁰-centre) extremely unfavourable (~8eV). For Sr-doped compounds the vast majority (x/δ-1) of vacancies will be presented as F⁺⁺-centres (~3.5eV) with an extremely small (2-x/δ) share of F⁺-centres (~7eV). This correlates with the available experimental data on oxygen diffusion coefficient [35]. For x/δ slightly smaller than 2, electrons, uncompensated by holes, convert F⁺⁺- into F⁺-centres. Detailed studies oxygen vacancy in commonly used perovkite-type materials (A = Sr, Ba, La, Pb; B = Ti, Fe, Co, Zr) revealed that two electrons are predominantly localized on d-orbitals of the nearest to the vacancy B-cations [10,29,30,40]. This is in contrast with LSS perovskites studied here, where electron localization within the vacancy itself (trapping) is similar to that in binary ionic oxides (MgO, Al₂O₃) [41,42,43,44]. This effect can be attributed to the Sc electron structure with completely unoccupied 3d-orbitals in 3+ oxidation state, making the electron transfer from the valence band energetically unfavourable.

Obtained data covers the whole range of x/δ values, predicting formation of the F-type colour centres with optical absorption in infrared (IR) region of 0.8–2.3 eV.

4. Conclusions

Controlled mainly by doping, e.g., Sr substituting for B-cation, oxygen deficiency in ABO₃ type perovskites usually affects the oxidation state of the transition metal B-cations. However, in contrast to other transition metals with open d-orbitals, scandium demonstrates predominantly a single oxidation state-3+, which follows from its electron structure-[Ar] 3d¹4s². In La_1−xSr_xScO_3−δ studied here, oxygen stoichiometry is controlled by mixing A³⁺- with A²⁺-cations (La with Sr). We have demonstrated, that unlike most of ABO₃ perovskites, electrons are trapped right at the oxygen vacancy site, like in MgO and other ionic oxides, rather than localise on the two nearest B-cations. We also predicted the optical absorption of the neutral vacancies (F⁰-centres with two trapped electrons) to be in the IR region. Lastly, we predicted that Sr doping strongly reduces the vacancy energy formation, which facilitates the proton uptake in this material.