First principles analysis of oxygen vacancy formation and migration in Sr₂BMoO₆ (B = Mg, Co, Ni)

Abstract

Molybdenum-based double perovskites have been extensively studied as electrode materials in solid oxide fuel cells (SOFCs) due to their mixed ionic/electronic conductivity (MIEC) characteristics. Since the ionic conductivity in perovskite crystals arises primarily from oxygen ion diffusion via a vacancy-hopping mechanism, both the formation energy of the oxygen vacancy and the migration energy barrier play an essential role in the MIEC performance. In this work, we present a detailed first-principles investigation on the stoichiometric and oxygen-deficient structures of double perovskites, Sr₂BMoO₆ (B = Mg, Co and Ni), using the density functional theory (DFT) method plus Hubbard U for Co and Ni. The electronic ground states of the oxygen-stoichiometric cells exhibited apparent eigenvalue gaps which are consistent with the measured insulating features. The oxygen-deficient structures were studied by removing a neutral oxygen atom according to SOFC working conditions, and the minimum energy path (MEP) of oxygen ion migration was optimized using the nudged elastic band (NEB) method which produced the theoretical migration energy barriers at the DFT+U level. The vacant oxygen sites released electrons to the adjacent cation d states, coupled with the delocalization characteristics of the Mo 4d state, which led eventually to the transition from an insulator to the electronic conductivity of the oxygen-deficient crystals. The electronic structure analysis suggested that the outer shell electrons of Mg, Co and Ni significantly affected the energies of oxygen vacancy formation and migration. Our results elucidate the effect of B-site substitution elements on the electronic properties and MIEC characteristics which provides theoretical support for the enhancement of the MIEC properties for these Mo-based double perovskites.

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Introduction

Solid oxide fuel cells (SOFCs) are a promising electrochemical power source that are able to generate power from a wide array of flexible gaseous fuels.¹ A typical SOFC system is composed of three parts: anode, electrolyte, and cathode.² The oxidization of gaseous fuel occurs at the anode surface following the reaction:³

H₂ + O²⁻ = H₂O + 2e⁻ (1)

or

CH₄ + 4O²⁻ = CO₂ + 2H₂O + 8e⁻ (2)

which suggests the anode material should possess both catalytic activity and mixed ionic and electronic conductivity (MIEC). The conventional anode material used for SOFCs is Ni–YSZ cermet which exhibits great performance with H₂ fuel but also suffers from carbon deposition and sulfur poisoning.⁴ Although introducing an extra catalytic layer at the anode side could reform the gaseous fuel to pure H₂, it would increase the cost and impact the performance of SOFC devices.⁵ Therefore, exploring novel anode materials with high performance and robustness in the reducing anodic atmosphere is a key challenge in SOFC research.

The perovskite oxide ABO₃ has received considerable attention due to the excellent MIEC and stability and can be used as the electrode material in SOFCs.^6–8 Since the BO₆ octahedron ultimately determines the electronic properties of perovskites, B-site element substitution is a common approach to modify the electronic properties and catalytic activity by forming double perovskites, A₂BB′O₆.^9–11 One of the frequently used B-site elements is Mo owing to its multivalent features, which provide the Mo-based perovskites with a high oxygen vacancy concentration and excellent catalytic capacity. Sr₂MgMoO₆ has been reported as a potential anode material for SOFCs with high performance using a platinum collector and it also exhibits resistance to poisoning from sulfur impurities.^4,12 However, the electronic conductivity and electrocatalytic activity without a Pt paste are relatively low which will affect the power density of SOFCs. First-row transition metals usually possess great catalytic ability owing to their open-shell d state electronic configuration. Thus, the substitution of alkaline metal Mg with transition metal elements could enhance both the electronic properties and electrochemical performance.¹³ Previous investigations demonstrate the potential application of Sr₂FeMoO₆ (SFMO) in both the anode and cathode of SOFCs. The multivalent characteristics of Mo⁵⁺/Mo⁶⁺ and Fe³⁺/Fe⁴⁺ provide SFMO with excellent electronic conductivity, and a high oxygen vacancy concentration and ionic diffusion rate.^14–18 In addition to Fe, other transition metal elements (such as Co and Ni) also exhibit promising capabilities to improve the electronic performance of Mo-based perovskites in terms of their application as SOFC anode materials.^19–22 However, the development of the MIEC properties is still the biggest challenge for these double perovskite materials.

In perovskite oxides, the ionic conductivity is mainly related to the diffusion of oxygen ions because the oxygen ion concentration far outweighs that of the cations. On the other hand, interstitial oxygen deficiency doesn’t extensively exist in perovskite oxides because of the large size of the oxygen ion compared to the crystal lattice.²³ Thus, oxygen ion diffusion in perovskites is mainly based on a vacancy-hopping mechanism, i.e., an oxygen ion will jump to its nearest vacant oxygen site by gaining an active energy to overcome the migration energy barrier (E_barrier). The oxygen ion diffusion coefficient (D_O) in perovskites can be described as:²⁴

D_O = C_VD_V (3)

where C_V is the oxygen vacancy concentration and D_V is the vacancy diffusion coefficient. The oxygen vacancy concentration is related to the vacancies formation energy (E_form) and the diffusion coefficient is dominated by the E_barrier. As a consequence, the E_form and E_barrier of the oxygen vacancy in perovskites play critical roles in the MIEC characteristics. An in-depth theoretical understanding of the electronic properties of double perovskites is conducive to assess the influence of B-site cations on the E_form and E_barrier of oxygen vacancies. A theoretical study on the oxygen-deficient features of B-site-ordered double perovskites Sr₂BMoO₆ (SBMO, B = Mg, Co and Ni), to the best of our knowledge, is not yet available from a density functional theory (DFT) perspective. In the present study, we aim to illustrate the oxygen vacancy formation and migration process in the double perovskite SBMO by using DFT with a Coulomb potential for the open-shell electrons of the Co and Ni 3d states. The electronic structures were calculated to evaluate the electronic conductivity while the E_form and E_barrier were calculated to clarify the effect of B-site elements on the ionic conductivity.

Computational details

All DFT calculations were performed using the Quantum ESPRESSO software package with a spin-polarized projector-augmented wave (PAW) approach.^25,26 The exchange correlation effects were described using the generalized gradient approximation with the Perdew–Burke–Ernzerhof (GGA-PBE) functional. PAW pseudopotentials were employed for the election-ion interactions with the following valence configurations: Sr (4s², 4p⁶ and 5s²), O (2s² and 2p⁴), Mo (4s², 4p⁶, 5s² and 4d⁴), Mg (2s², 2p⁶ and 3s²), Co (4s² and 3d⁷), and Ni (4s² and 3d⁸). A plane wave cutoff of 40 Ry was adopted for the expansion of the wave functions. A 4 × 4 × 4 Monkhorst–Pack k-mesh grid was used for sampling the supercell structures.²⁷

It is a well-known fact that the pure DFT method suffers from an inherent self-interaction error for transition metal oxides with open-shell 3d electrons.²⁸ An effective method to minimize this error is employing an intra-atomic Coulomb potential (U) and exchange interactions (J) for the d state electrons. In this study, we used the simplified parameter (U–J) introduced by Dudarev et al. for optimizing the electronic properties of these double perovskite oxides.²⁹ Effective (U–J) values of 4 and 3 eV were respectively considered for the 3d state electrons of Co and Ni which have been validated by previous electronic calculations.³⁰ For Mo 4d state electrons, we carefully tested the influence of (U–J)_Mo on the electronic properties and found that it was negligible in these double perovskites. Previous studies elucidated the delocalization of the Mo outer 4d state electrons due to the itinerant feature on the hybridized orbitals.^18,31 Therefore, we herein didn’t apply Hubbard U for the Mo 4d state electrons.

These double perovskites are reported to show tetragonal crystal structures with a space group I4/m at room temperature and undergo a phase transition from I4/m to Fm3m at around 500 K.^32–34 Given the high working temperature of SOFCs, we adopted the high-temperature Fm3m phase to probe the mechanism of oxygen vacancy formation and migration. These double perovskites are demonstrated to be long-range ordered owing to the variance of the oxidization state and ionic radius between the B-site Mo and substituted elements B (B = Mg, Co and Ni), hence we employed the rock-salt structure to construct the 40-atom supercells which are created by the VESTA program and displayed in Fig. 1.³⁵ The defective structure is constructed by removing a neutral oxygen atom to form a vacancy () and leaving two reducing transition metal cations (M′_TM):³⁶

Fig. 1 The schematic crystal structures of the double perovskites Sr₂BMoO₆ (B = Mg, Co and Ni).

A simple approximation of the formation energy can be extracted from the electronic energies:²³

where E(O₂) is a reference to the half energy of a free O₂ molecule in its triplet ground state. With regard to the E_barrier, we computed the energy profile of the transition states of oxygen ion migration to its nearest vacant site around the octahedron edge. The climbing-image nudged elastic band (CINEB) method was employed to determine the minimum energy pathway (MEP) of the oxygen anion migration with 5 simple linear interpolated images.³⁷ The spring force along the migration path was used to ensure the finding of the lowest energy path. The Bader charge approach was employed for the topological analysis of the electronic density in the oxygen-deficient structures.³⁸

Results and discussion

Stoichiometric Sr₂BMoO₆ (B = Mg, Co and Ni)

The structural parameters including cell volumes and atomic positions are fully optimized at the spin-polarized GGA+U level for the double perovskites Sr₂BMoO₆ (B = Mg, Co and Ni) which are listed in Table 1. As can be seen, the lattice parameters for all these compounds were slightly underestimated using the GGA+U approach. These underestimations can be attributed to the reason that the lattice parameters adopted in this study were extracted from their high-temperature phase structures for consistency under the operating conditions of SOFCs. In the high-temperature crystals, these double perovskites have undergone thermal expansion compared with their room-temperature phases.^32–34 Nevertheless, our estimated errors for these lattice parameters are within 1% at the GGA+U level for all these compounds indicating that these optimized supercells are adequate for the investigation of these double perovskites. Moreover, three tendencies can be observed from Table 1: (1) the predicted Mo–O bonds are very close for all these materials due to the same Mo–O bond characteristics; (2) the bond length between the substituted elements Mg, Co and Ni and oxygen are longer than that between Mo and O because Mo⁶⁺ has the shortest radius; (3) the bond length of Co–O along z-axis was predicted to be longer than that along the x–y plane due to the high-spin state of Co²⁺ (3d⁷4s⁰) mixed with the O 2p and Mo 4d orbitals which has been observed in previous experiments.³⁰

Table 1 Calculated lattice parameters and bond lengths in Sr₂BMoO₆ (B = Mg, Co and Ni)

Properties (Å)	Sr2MgMoO6		Sr2CoMoO6		Sr2NiMoO6
	Expt.	GGA+U	Expt.	GGA+U	Expt.	GGA+U
a	7.925	7.861	7.927	7.897	7.902	7.887
b	7.925	7.861	7.927	7.897	7.902	7.887
c	7.925	7.861	7.927	8.031	7.902	7.887
r xy (B–O)	2.056	2.019	2.045	2.031	2.027	2.028
r z (B–O)	2.056	2.019	2.045	2.101	2.027	2.028
r xy (Mo–O)	1.907	1.912	1.918	1.918	1.925	1.915
r z (Mo–O)	1.907	1.912	1.918	1.914	1.925	1.915

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Fig. 2 displays the projected density of states (DOS) for the stoichiometric structures of these double perovskites calculated using GGA with an on-site Coulomb potential U for Co and Ni 3d state electrons. Previous theoretical calculations on the SrMoO₃ electronic structure demonstrated that the conduction band, which is composed of the hybridization of Mo⁴⁺ t_2g with O 2p orbitals, crosses through the Fermi energy level suggesting metallic characteristics.³⁹ For the oxygen-stoichiometric structures of Sr₂BMoO₆ (B = Mg, Co and Ni), our results reveal that all these compounds, unlike the metallic features of SrMoO₃, exhibit eigenvalue gaps which correspond to the measured insulator features. When half of the B-site element Mo is substituted by alkaline metal Mg, the Mo⁴⁺ in SrMoO₃ loses the rest of the two electrons of the t_2g state and is further oxidized to Mo⁶⁺ (4d⁰5s⁰). Thus, the emptied d state of the Mo cation results in the Sr₂MgMoO₆ adopting a diamagnetic configuration. The fully filled O 2p orbital forms the valence band while the hybridization between the higher Mo e_g state with the O 2p state composes the conduction band with an electronic band structure gap of ∼2.0 eV. This electronic feature reveals the strong Mg–O ionic bond and the fractional covalent interaction between the Mo 4d and O 2p orbitals which may also be demonstrated by the charge density displayed in Fig. 3(a). For the case of Sr₂CoMoO₆, the anti-Ferromagnetic (AFM) configuration is predicted to be more stable than the ferromagnetic (FM) one at the GGA+U level which is in agreement with former experimental investigations.⁴⁰ The valence band maximum (VBM) is composed of the interaction of the Co e_g state with the O 2p state, whereas the lower density peak of the valence band is made up from the lower Co t_2g state and the O 2p state. These results also indicate that for the valence configuration of Mo⁶⁺ (4d⁰5s⁰) in Sr₂CoMoO₆ the contribution of the Mo 4d state electrons is negligible for the VBM. On the other hand, the hybridization of the Mo e_g state with the O 2p state composes the conduction band of Sr₂CoMoO₆ which is similar to that of Sr₂MgMoO₆. In addition, the GGA+U electronic properties of Sr₂NiMoO₆ are analogous to those of Sr₂CoMoO₆. The AFM arrangement for Sr₂NiMoO₆ is calculated to be the most stable state. However, the magnetic moment of Ni²⁺ (3d⁸) is expected to be smaller than that of Co²⁺ (3d⁷) due to the fully filled t_2g orbital of the former. The different electronic configurations of Co²⁺ and Ni²⁺ reflect different charge distributions as shown in Fig. 3(b) and (c). The VBM of Sr₂NiMoO₆ is composed predominantly of the Ni e_g state and O 2p state electrons, and the CBM is made up from the hybridization between the Mo e_g state and the O 2p state. Moreover, the Ni e_g state also shows interaction with Mo and O at the CBM which is different from the two others.

Fig. 2 The projected density of states at the GGA+U level for the oxygen-stoichiometric structures of Sr₂BMoO₆ (B = Mg, Co and Ni). The fermi energy levels have been set to zero.

Fig. 3 Contour plots of the charge density for Sr₂BMoO₆ (B = Mg, Co and Ni) calculated using the GGA+U method.

Oxygen-deficient structures of Sr₂BMoO₆ (B = Mg, Co and Ni)

As oxygen ion migration proceeds by way of jumping to the nearest oxygen vacant site via a vacancy-hopping mechanism, the vacancy concentration plays a crucial role in the MIEC characteristics of the perovskite materials. We evaluate the oxygen vacancy concentration by calculating the oxygen vacancy E_form using the approach outlined in the computational details section. The oxygen-deficient supercell is constructed by removing one neutral oxygen atom from the parental 40-atom cell corresponding to an oxygen-deficient structure of Sr₂BMoO_5.75 (B = Mg, Co and Ni). Although this small supercell indicates the high concentration of oxygen vacancies, previous literature has demonstrated that the 40-atom supercell is economical and adequate to study oxygen vacancy formation and oxygen ion migration in double perovskite materials.^23,24 Moreover, the B-site element stoichiometry in these double perovskites leads to the highly alternate order owing to the significant distinction in the ionic radius and oxidization state between Mo⁶⁺ and Mg²⁺, Co²⁺ or Ni²⁺. Thus, we in this work considered the oxygen vacancies which are generated between the Mo and the substituted element B (B = Mg, Co and Ni) in the rock-salt structure.

Previous experiments have revealed the MIEC characteristics of the oxygen-deficient crystals of these double perovskites, indicating the transition from insulator to electronic conductivity.^4,21 In order to elucidate the effect of oxygen vacancies on the electronic structures, we calculated the electronic properties of the oxygen-deficient supercells with spin-polarized GGA+U, which are presented in Fig. 4. In oxygen-deficient Sr₂MgMoO_5.75, we can see that the Mg ions are still bivalent suggesting that the oxygen vacancy only changes the electronic configuration of Mo. As mentioned above, the O 2p state electrons dominate the VBM of stoichiometric Sr₂MgMoO₆ and its CBM consists of the hybridization between the Mo e_g state and the O 2p state. These features are preserved in the oxygen-deficient Sr₂MgMoO_5.75. Since the oxygen vacancy releases electrons to the Mo 4d state, the conduction band crosses through the Fermi energy level resulting in the electronic conductivity of the oxygen-deficient Sr₂MgMoO_5.75. For Sr₂CoMoO_5.75 and Sr₂NiMoO_5.75, the electronic properties are more complicated because of the open-shell 3d state electrons of Co and Ni. The eigenvalue gap predicted in Sr₂CoMoO₆ has vanished in the oxygen-deficient Sr₂CoMoO_5.75 accompanied by the Fermi level shifting upward into the conduction band. The same tendency can also be observed in the electronic structure of Sr₂NiMoO_5.75 in which the 3d state electrons of Ni play an important role in the VBM. The oxygen vacancies in these double perovskites affect the Fermi energy levels by shifting them into the conduction band which allows the Mo e_g states and O 2p states to be available both below and above the Fermi energy levels. These variations in electronic structure induce the transition from oxygen-stoichiometric insulators to the emerged electronic conductivity of the oxygen-deficient supercells for the double perovskites Sr₂BMoO_5.75 (B = Mg, Co and Ni).

Fig. 4 The projected density of states at the GGA+U level for the oxygen-deficient structures of Sr₂BMoO_5.75 (B = Mg, Co and Ni).

Now we describe the formation energy of oxygen vacancies calculated using GGA+U which are listed in Table 2. The is 4.85 eV, calculated using GGA+U, which is significantly higher than that of Sr₂CoMoO_5.75 and Sr₂NiMoO_5.75. As in the aforementioned electronic structures, the Mg²⁺ cations form relatively stable ionic bonds with their adjacent oxygen ions. Therefore, removing an oxygen atom between Mo and Mg demands more active energy to break the Mg–O bond compared with the Ni–O and Co–O bonds. The GGA+U calculated is 2.89 eV which is comparable to other Co-based perovskites.²⁸ Although Sr₂NiMoO₆ has similar electronic properties to Sr₂CoMoO₆, the calculated is 3.7 eV indicating that the oxygen vacancy concentration in Sr₂NiMoO₆ is lower than that of Sr₂CoMoO₆. The formation energies of oxygen vacancies in these Mo-based double perovskites are found to be higher than in the Co-based double perovskites LaSrCoFeO6 (LSCF) and BaSrCoFeO6 (BSCF), which are known as MIEC cathodes for SOFC.^41–43 For LSCF or BSCF, the unequal oxidization states of the cations and anions benefits oxygen vacancy formation. In addition, the large Ba ions lead to lattice expansion which further affects the redox energetics.^44,45 Therefore, it is an obvious strategy for tuning the oxygen vacancy formation energy in these Mo-based perovskites.

Table 2 Calculated oxygen vacancy formation energy E_form, magnetic moments μ and Bader charges q in stoichiometric and oxygen-deficient Sr₂BMoO₆ (B = Mg, Co and Ni)

	Sr2MgMoO6		Sr2CoMoO6		Sr2NiMoO6
	Stoichiometric	Deficient	Stoichiometric	Deficient	Stoichiometric	Deficient
E form (eV)	—	4.85	—	2.89	—	3.70
μ B (μB)	0.00	0.00	2.57	1.82	1.63	1.00
μ Mo (μB)	0.00	0.15	0.01	0.09	0.01	0.07
q B	1.70	1.66	1.49	1.06	1.38	0.89
q Mo	2.35	2.40	2.31	1.27	2.30	1.86
q Sr	1.52	1.58	1.60	1.60	1.53	1.60
q O	−1.26	−1.30	−1.22	−1.23	−1.20	−1.23

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The electronic structures of the oxygen-deficient supercells have demonstrated that the oxygen vacancies influence the electronic configurations of the adjacent B-site metal cations in these defective double perovskites. The magnetic moment μ provides a different theoretical insight into the rearrangement of the outer shell electrons which is presented in Table 2. In the oxygen-deficient Sr₂MgMoO_5.75 supercell, the small magnetic moment μ_Mg of the Mo cation neighboring the vacant oxygen site indicates that the 4d state of Mo has been partial filled with additional electrons released from the oxygen vacancy in the oxygen-deficient supercell. For the oxygen-deficient Sr₂CoMoO_5.75, the magnetic moment μ_Co shows a significant reduction from 2.57 μ_B in the stoichiometric supercell to 1.82 μ_B. In perfect Sr₂CoMoO₆, the B-site Co²⁺ is calculated to be in the high-spin state of 2.57 μ_B which is in accordance with the electronic configuration (t_2g⁵e_g²) of Co²⁺. But in the oxygen-deficient crystal, the released electrons from the oxygen vacancy occupy the Co t_2g state which leads to the reduction of the magnetic moment μ_Co. The calculated μ_Ni undergoes a similar change in the oxygen-deficient Sr₂NiMoO_5.75. The Ni²⁺ cation has a reduced magnetic moment of 1.00 μ_B compared with the value of 1.63 μ_B in the stoichiometric Sr₂NiMoO_5.75. As Ni²⁺ has a fully filled t_2g state and half-filled e_g state, the reduction of μ_Ni can be attributed to the reaccommodation of the additional electrons released from the oxygen vacancy.

The Bader charge q is calculated to investigate the charge distribution in the oxygen-deficient structures. Three trends can be observed from the Bader charge values: (1) the calculated Bader charge for Sr cations doesn’t change significantly before and after removing a neutral oxygen, indicating the relatively stable electronic state of the A-site cation; (2) The Mg and Mo cations in Sr₂MgMoO₆ have the largest Bader charge among these oxygen-stoichiometric double perovskites suggesting the more evident similarity of the chemical bonding in Sr₂MgMoO₆; (3) For the oxygen-deficient structures, oxygen vacancies increase the Bader charge q_Mo and decrease the Bader charge q_O, indicating the charge transition during oxygen vacancy formation. Given that Jahn–Teller distortion is nonexistent in the adopted high temperature phase, the delocalization of the Mo 4d state allows the additional electrons to travel in the whole crystal which gives rise to the electronic conductivity. In oxygen-deficient Sr₂CoMoO_5.75 and Sr₂NiMoO_5.75, the oxygen vacancies significantly alter the Bader charge values of the adjacent Mo and Co or Ni cations. The reduction of the Bader charge on Co and Ni demonstrates that the oxygen vacancies release electrons to the 3d states of the adjacent Co or Ni, corresponding to the change in the magnetic moment for Co and Ni.

The energy barrier E_barrier of the oxygen ion migration is another important factor in the MIEC performance. In perovskite oxides, the energy barrier is primarily dependent on the interaction of oxygen ions with their adjacent B-site cations. The migration pathway is around the B-site cation along the octahedron edge as shown in Fig. 5. Because of the weaker Mo–O bond, the E_barrier for the oxygen ion migrating in the MoO₆ octahedron is apparently lower than in the BO₆ octahedron (B = Mg, Co and Ni). We optimized the minimum energy pathway (MEP) of oxygen ion migration by the CINEB method and the calculated corresponding energy profiles are depicted in Fig. 6. As can be seen, the energy barriers at the spin-polarized GGA+U level are calculated to be 1.29 eV, 1.20 eV and 1.47 eV for Sr₂MgMoO_5.75, Sr₂CoMoO_5.75 and Sr₂NiMoO_5.75 respectively. The lowest value of the energy barrier indicates the highest oxygen ion diffusion in Sr₂CoMoO_5.75. As stated above, the Co–O bond behavior plays an important role in the oxygen ion migration in the CoO₆ octahedron. To understand this characteristic, we calculated the magnetic moments of Co and Ni during oxygen ion migrations, which are presented in Fig. 6. We can find that the magnetic moments μ_Co are predicted to be in the low-spin configuration for both the initial and final migration states. For the intermediate migration states, the μ_Co increases to be at the high-spin configuration and remains nearly constant in the intermediate states which suggests a charge transfer process. When the oxygen ion deviates from its original site, the Mo–O bond is broken accompanied by the new Co–O bond formation through electron transfer between the Co t_2g and the O 2p state. For Sr₂NiMoO_5.75, the magnetic moment μ_Ni fluctuates during the transition states and reaches a peak at the middle image. This fluctuation indicates strong electron transfer at the migration midpoint, leading to the high migration energy barrier in Sr₂NiMoO_5.75. Given the previously stated oxygen vacancy formation energy, Sr₂CoMoO₆ is predicted to exhibit the best ionic conductivity among these Mo⁶⁺/B²⁺ double perovskites Sr₂BMoO₆ (B = Mg, Co and Ni). It is worth noting that the ion migration barriers in these materials are higher than common cathode materials (e.g., LSCF or BSCF).⁴⁴ However, considering the tolerance to the sulfur impurities of gaseous fuel, these materials can be seen as promising candidates for the Ni–YSZ cermet anode of SOFCs.

Fig. 5 The migration pathway of oxygen ions in oxygen-deficient Sr₂BMoO_5.75 (B = Mg, Co and Ni). Red spheres represent the oxygen ions.

Fig. 6 The calculated energy profiles for the oxygen ions migration and the magnetic moments for Co and Ni cations in the oxygen-deficient Sr₂BMoO_5.75; B = (a) Mg, (b) Co and (c) Ni.

Conclusions

In this work, we investigated the stoichiometric and oxygen-deficient structures of Sr₂BMoO₆ (B = Mg, Co and Ni) by using DFT plus the Coulomb potential U for the transition metals Co and Ni, with the focus on their application as SOFC anode materials. The oxygen vacancy formation energy and energy barrier for oxygen ion migration were calculated to evaluate the MIEC performance. The GGA+U electronic structures revealed the insulating behavior of the stoichiometric structures of these double perovskites which coincided with experiments. For the oxygen-deficient crystals, the removal of a neutral oxygen atom releases additional electrons to the adjacent B-site cations which shifts the Fermi energy level upward into the conduction band. The hybridized orbitals crossed the Fermi energy level eventually resulting in electronic conductivity for the oxygen-deficient structures of these double perovskites. The calculated energy profiles provide electronic insight into oxygen vacancy formation and oxygen ion migration for these double perovskites. The magnetic moment and Bader charge were also calculated to reveal the effect of the d state of the B-site transition metals on the oxygen vacancy concentration and oxygen ion diffusion rate. These calculated results provide a theoretical guide for the improvement of the MIEC properties of these Mo-based double perovskites.

Acknowledgements

This work was supported by the Grant-in-Aid for Scientific Research (KAKENHI) program, Japan (C, Grant Number 15K05597).

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