Trends in Surface Oxygen Formation Energy in Perovskite Oxides.

Perovskite oxides comprise an important class of materials, and some of their applications depend on the surface reactivity characteristics. We calculated, using density functional theory, the surface O vacancy formation energy (E Ovac) for perovskite-structure oxides, with a transition metal (Ti-Fe) as the B-site cation, to estimate the catalytic reactivity of perovskite oxides. The E Ovac value correlated well with the band gap and bulk formation energy, which is a trend also found in other oxides. A low E Ovac value, which is expected to result in higher catalytic activity via the Mars-van Krevelen mechanism, was found in metallic perovskites such as CaCoO3, BaFeO3, and SrFeO3. On the other hand, titanates had high E Ovac values, typically exceeding 4 eV/atom, suggesting that these materials are less reactive when O vacancy formation is involved in the reaction mechanism.

Introduction

Defects can significantly influence the properties of metal oxides. The most representative defect is the O vacancy,[1−3] which can strongly affect the electrical, optical, magnetic, mechanical, and catalytic properties on intentional or unintentional introduction into the metal oxide structure.[4−6] O vacancies on the surface of metal oxide catalysts often act as reaction sites for heterogeneous catalysis;[2,7] thus, the formation energy of an O vacancy at the surface (denoted as EOvac in this paper) is often used as a descriptor of the catalytic activity of metal oxides.[8]

Experimental investigations of O vacancies are difficult, although research on O vacancies in the field of catalysis is obviously important.[9] Surface O vacancies also play an important role in polaron formation and stabilization in oxides such as CeO2[10] and TiO2.[11] Determination of the EOvac value requires highly sophisticated techniques, and its evaluation is not always possible.[12] On the other hand, there are recent theoretical studies on the formation of O vacancies in metal oxides,[4,13] but still the number of investigated surfaces remains limited. Therefore, studies on the physical principles determining EOvac and the development of guidelines to estimate EOvac using other properties that are much easier to obtain are highly desirable.

Perovskite structure oxides make up an important class of materials.[14,15] Applications to catalysis include ethane dehydrogenation by La0.8Ba0.2MnO3−δ,[16] NO adsorption/oxidation,[17] deoxygenation of coal bed methane on LaCoO3,[18] liquid-phase organic reactions,[19] and CaTiO3 nanosheets for photocatalytic hydrogen evolution.[20]

While there have been extensive computational studies of O vacancy formation energies in the bulk,[5,14,15,21] studies of surface EOvac are quite limited have been increasing recently.[3,22−25] The band gap, bulk formation energy, and electron affinity were reported to correlate well with EOvac in d0 and d10 binary oxides. Removal of neutral O results in two electrons being left behind. These electrons are excited from the valence band to the conduction band but typically relax and occupy defect states that may be lower than the conduction band minimum. Removal of O results in severing metal–O bonds, and the bulk formation energy provides a measure of the bond strength.[23] This paper reports calculated EOvac values for known perovskite structure oxides terminated by the (001) orientation. Relations between EOvac and the band gap or bulk formation energy is discussed together with strategies to reduce EOvac to obtain more reactive support materials.

Methodology

First-principles calculations were conducted using the projector augmented-wave method[26] and approximations as implemented in the VASP code.[27] The strongly constrained and appropriately normed (SCAN) meta generalized gradient approximation (meta-GGA)[28] was considered together with Dudarev’s formulation[29] for the Hubbard U correction. The effective U value, U – J, which is hereafter denoted as Ueff, was set at 2.7 eV on the valence d states of transition metals, including lanthanides. This Ueff value is based on a study on perovskite structure oxides by Wexler et al.[15] Spin-polarized calculations were conducted such that spins of an element all point in the same direction. When two cation species have nonzero spin, calculations were conducted where the spins of the two elements are parallel and antiparallel, respectively, and the lower energy spin configuration was adopted. The rationale for the selection of compounds discussed in this study is given in Supporting Information.

The surface of calculated slab models has a (001) orientation in the cubic setting. Calculations of defects, namely O vacancies, were conducted using a slab with 2√2 × 2√2 × 5 (=40) perovskite units separated by 15 Å vacuum (the PbTiO3 slab is shown as an example in Figure ). The cleavage energy is defined aswhere Eslab is the energy of the slab and Ebulk is that of the slab constituents when they are in a perfect bulk, respectively. Here, A is the in-plane area of the slab (blue parallelograms in Figure ; the coefficient 2 accounts for both sides of the slab), and Ebulk is obtained from a bulk calculation. The surface energy of one surface is not available because a strictly nonpolar slab that is stoichiometric and where all A-cation and B-cation layers are intact cannot be obtained. The nonexistence of a nonpolar slab means that the vacuum level is ill-defined, and thus the ionization potential, work function, and electron affinity cannot be calculated. The O vacancy formation energy EOvac is defined aswhere Eremoved and E(O2) are the energy of the slab after removal of an O atom from one side of the slab (A-site or B-site cation terminated layer, hereafter A-cation and B-cation layer, respectively) and the energy of an O2 gas molecule at 0 K, respectively.

Figure 1

200-atom slab of PbTiO3. Black, blue, and red balls represent Pb, Ti, and O atoms, respectively.

Results and Discussion

Tables and 2 summarize the results of first-principles calculations in this study. The space group number is provided in parentheses. Table S2 in the Supporting Information shows the space group symbol and number side by side. The bulk properties shown (Table ) are the volume per atom (v), minimum band gap (BG), bulk formation energy with respect to elementary metals and O2 gas (Eform), and net spin per five atoms in the bulk (nspin). Systems are identified where the Jahn–Teller effect is expected for transition metals in an octahedral coordination environment. Slab properties in Table , obtained for slab-and-vacuum model cells with 40 perovskite units, are Ecleave, the net spin of a slab (nspin_slab), EOvac, and difference in net spin (Δnspin) for O desorption from the A- and B-cation layers (denoted by A and B, respectively). Calculations where spin states far from the defect have changed significantly are removed from the table and not considered further. For example, the spin of the B-site cation on the surface without defects flipped after removal of O from the B-cation layer of BaMnO3 (221) and LaFeO3 (62).

Table 1

Bulk Properties of Systems Considered for Defect Calculationsa

system	v (Å3)	BG (eV)	Eform (eV/atom)	nspin (elementary charge/5 atoms)
BaFeO3 (221)	12.50	0.02	–2.31	4.19
BaFeO3 (123)	12.50	0.02	–2.31	4.19
BaMnO3 (221)	12.27	0.00	–5.84	3.25
BaTiO3 (221)	12.97	2.46	–3.58	0.00
BaTiO3 (123)	12.97	2.46	–3.58	0.00
BaTiO3 (99)	12.98	2.46	–3.58	0.00
BaTiO3 (38)	12.97	2.45	–3.58	0.00
BaVO3 (221)	12.42	0.01	–3.02	1.00
BiMnO3 (62)	12.09	0.65	–5.11	4.00
BiMnO3 (15)	12.42	0.57	–5.11	4.00
CaCoO3 (62)	10.58	0.01	–2.09	3.00
CaTiO3 (62)	11.30	3.24	–3.65	0.00
CdTiO3 (62)	11.08	3.06	–2.75	0.00
CdTiO3 (33)	11.07	3.06	–2.75	0.00
CdVO3 (62)	10.74	1.04	–2.28	1.00
ScCoO3 (62)	9.43	2.41	–2.72	0.00
LaFeO3 (62)	12.25	1.07	–3.09	5.00
SrFeO3 (221)	11.34	0.01	–2.42	4.01
SrFeO3 (123)	11.34	0.01	–2.42	4.01
MnTiO3 (62)	10.46	2.13	–6.52	5.00
MnVO3 (62)	10.11	0.38	–6.06	6.00
PbTiO3 (99)	12.56	2.37	–2.68	0.00
SrTiO3 (221)	12.10	2.62	–3.65	0.00
SrTiO3 (140)	12.08	2.69	–3.65	0.00
SrVO3 (221)	11.49	0.02	–3.11	1.00
YTiO3 (62)	12.00	1.85	–3.79	1.00

The parentheses following the compound name indicate the space group number.

Table 2

Bulk Properties of Systems Considered for Defect Calculationsa

system	Ecleave (eV/Å3)	nspin_slab (elementary charge/200 atoms)	EOvac (A, eV)	EOvac (B, eV)	Δnspin (A, elementary charge/defect)	Δnspin (B, elementary charge/defect)
BaFeO3 (221)	47.99	170.42	0.92	–0.40	7.75	6.22
BaFeO3 (123)	49.80	170.64	0.60	–1.14	7.85	3.53
BaMnO3 (221)	41.60	78.35
BaTiO3 (221)	60.19	0.00	5.53	4.72	0.90	1.18
BaTiO3 (123)	60.27	0.00	5.54	4.61	0.89	2.00
BaTiO3 (99)	61.39	0.00	5.53	4.30	0.45	1.01
BaTiO3 (38)	60.64	0.00	5.53	4.39	1.55	1.00
BaVO3 (221)	20.69	40.00
BiMnO3 (62)	22.85	160.00	1.94	2.12	2.02	2.02
BiMnO3 (15)	35.05	159.97	3.08	2.50	0.00	2.00
CaCoO3 (62)	52.35	100.01	0.02		4.01
CaTiO3 (62)	73.56	0.00	5.78	5.74	0.00	1.02
CdTiO3 (62)	72.81	0.00	3.17	4.56	0.00	0.72
CdTiO3 (33)	72.77	0.00	3.17	4.25	0.00	2.00
CdVO3 (62)	68.32	40.00	0.88	2.39	2.00	2.00
ScCoO3 (62)	105.40	3.63	3.70	0.79	3.63	1.63
LaFeO3 (62)	88.68	197.53	5.01		3.95
SrFeO3 (221)	59.89	164.68	1.19	0.10	2.27	0.64
SrFeO3 (123)	60.24	164.56	0.95	–0.22	1.98	0.67
MnTiO3 (62)	75.31	200.00	4.48	5.70	0.00	0.24
MnVO3 (62)	69.58	240.00	1.35	2.50	2.00	2.00
PbTiO3 (99)	47.01	0.00	4.31	4.40	0.00	2.00
SrTiO3 (221)	69.63	0.00	5.58	4.81	1.20	2.00
SrTiO3 (140)	69.38	0.00	5.62	5.27	1.28	1.02
SrVO3 (221)	43.23	40.00
YTiO3 (62)	100.95	40.00	4.98	4.64	0.00	2.00

The parentheses following the compound name indicate the space group number. A and B represent O removal from the A-cation and B-cation layer, respectively.

Figure plots the minimum EOvac value for O removal from the A-cation layer against the B-cation layer. There is a modest positive correlation with a coefficient of determination (R2) of 0.64 for all shown points. The points can be categorized into three groups: Ti-containing compounds, which are clustered at the top right (high EOvac), metals at the bottom left (low EOvac), and other nonmetals. Among the “other nonmetals”, O removal from the A-cation layer has lower energy when the B-site cation has fewer d electrons (V), while removal from the B-cation layer is favored in B-site cations with more d electrons (Co and Fe).

Figure 2

Plot of minimum EOvac values for A- against B-cation layers.

Figures S2–S4 show the partial electronic density of states (DOS) for bulk perovskites. The conduction band (CB) bottom is the B-site cation 3d states in all cases, which means that the defect state arising from electrons left in the slab after neutral O removal consists of mostly B-site cation 3d states. The nominal charge of Ti in titanates is 4+, with no 3d electrons. Notable charge states are the intermediate spin of Co4+ in metallic CaCoO3 (62), with four spin-up electrons and one spin-down 3d electron and high-spin Mn3+ (d5) and V4+ (d1) in MnVO3 (62).

The spin states of B-site cations in “other nonmetals” are d1 in V4+ (MnVO3 and CdVO3), high-spin d4 in Mn3+ (BiMnO3), high-spin d5 in Fe3+ (LaFeO3), and low (no)-spin d6 in ScCoO3. Removal of O from the A-cation layer results in severing of one O–“B-cation” bond from a 6-fold coordinated B-cation, and removal from the B-cation layer causes severing of two O–“B-cation” bonds from two 5-fold-coordinated B-cations. O removal causes changes in the number of d electrons in B-cation(s), which is accompanied by a change in of the bonding environment, especially a change in the distribution of bond lengths. Removal of O from the B-cation layer results in a higher flexibility because a bond is severed from B-cations with already missing bonds. This could be the reason for the smaller spread in EOvac values for O removal from the B-cation layer in comparison to the A-cation layer for “other nonmetals” in Figure . In particular, Fe–O and Co–O bond lengths in LaFeO3 (62) and ScCoO3 (62) are almost all the same. Adding extra electrons from O removal from the A-cation layer forces Jahn–Teller distortion to the Fe or Co that bonded to the removed O, which would force large local changes in bond lengths and/or unfavorable electronic states in Fe or Co. The lack of mitigating mechanisms could lead to the high EOvac values for O removal from the A-cation layer in LaFeO3 (62) and ScCoO3 (62).

Figure gives a plot of BG versus minimum EOvac. The space group number is shown together with the chemical formula. There is a positive correlation trend in both the A- and B-site terminated layers, with the lowest EOvac value being found in metallic systems. This trend was also found in binary carbide, nitride,[24] and d0 and d10 binary oxide systems,[23] but not in zinc-containing normal spinels.[25] On the other hand, Figure shows plots of Eform versus minimum EOvac. A negative correlation is found, which is consistent with d0 and d10 binary oxide systems[23] as well as the (100) and (110) surfaces of Zn-containing normal spinels.[25]EOvac from the B-cation layer of ScCoO3 (62) appears to be an extreme layer for the BG plot (Figure b) but is not in the Eform plot (Figure b). The high EOvac in titanates comes from the electronic structure; all titanates have BG values exceeding 1.5 eV, and all nontitanates except for ScCoO3 have BG values below 1.5 eV (Figure ).

Figure 3

BG versus EOvac for O removal from (a) A- and (b) B-cation layers.

Figure 4

Eform versus EOvac for O removal from (a, top) A- and (b, bottom) B-cation layers.

Figure shows the DOS of the bulk, slab, and slab with O removed from the A- and B-cation layers of CdTiO3 (33) and ScCoO3 (62). The formation of surfaces results in the formation of surface states within the band gap. The formation of O vacancies results in additional defect states. In CdTiO3 (33) (Figure (a,c,e,f)), the defect state is closer to the valence band in O removal from the A-cation layer in comparison to that from the B-cation layer, and this is reflected in the lower EOvac in the former. On the other hand, the Fermi level after O removal is at the top of the valence band in ScCoO3 (62) (Figure (b,d,f,h)). Variations in the defect state position among various compounds was also observed in d0 and d10 binary oxides.[23]

Figure 5

DOS of (a, b) bulk, (c, d) slab, and slabs with O removed from the (e, f) A- and (g, h) B-cation layers of (a, c, e, f) CdTiO3 (space group number 33) and (b, d, f, h) ScCoO3 (62). The EOvac value is also shown.

Summary

We calculated the EOvac values for perovskite-structure oxides with a transition metal (Ti–Fe) as the B-site cation. The EOvac correlates well with the band gap and bulk formation energy, which is a trend also found in other oxides. A low EOvac value, which is expected to result in higher catalytic activity, is found in metallic perovskites such as CaCoO3, BaFeO3, and SrFeO3. On the other hand, titanates had high EOvac values, typically exceeding 4 eV/atom.