Nonstoichiometric Strontium Ferromolybdate as an Electrode Material for Solid Oxide Fuel Cells

Abstract

This review is devoted to the application of Sr₂FeMoO_6−δ (SFM) and Sr₂F_1.5Mo_0.5O_6−δ (SF_1.5M) in La_1−xSr_xGa_1−yMg_yO_3−δ (LSGM)-based SOFCs. We consider the most relevant physical properties (crystal structure, thermodynamic stability, iron and molybdenum valence states, oxygen vacancy formation and oxygen non-stoichiometry, electrical conductivity), A- and B-site ion substitution, and the performance of SF_1+xM SOFCs (polarization resistance, operation with hydrogen, operation with hydrocarbons and methanol). Their properties can be tailored to a particular application by the substitution of different metal cations into their lattices. SF_1+xM materials are excellent catalysts in hydrocarbon oxidation and can prevent carbon deposition due to the ability to exchange lattice oxygen with the gaseous phase. Moreover, they are sulfur tolerant. This opens the way to direct hydrocarbon-fueled SOFCs, eliminating the need for external fuel reforming and sulfur removal components. Such SOFCs can be greatly simplified and operate with much higher overall efficiency, thus contributing to the solution to the lack of energy problem in our modern world.

1. Introduction

Solid oxide fuel cells (SOFCs) convert chemical energy into electrical energy by oxidizing fuel in an electrochemical device. They are considered one of the most important power generation technologies because of their efficiency beyond 60%. SOFCs can utilize a wide variety of fuels, such as H₂, natural gas, liquid fuels, biofuels and gasified coal, with a relatively low sensitivity to fuel impurities compared with other types of fuel cells [1,2,3]. Current research focuses on the development of intermediate-temperature solid oxide fuel cells (IT-SOFCs), which are operated within 500–800 °C [4,5]. Lowering the operating temperature of high-temperature SOFCs suppresses component degradation, extends the range of acceptable materials, serves to improve cell durability and reduces the system cost [6]. However, as the temperature is reduced, the catalytic activity of cathode materials is reduced as well, leading to sluggish electrode kinetics for the oxygen reduction reaction and resulting in large interfacial polarization resistances [7]. This represents a barrier to IT-SOFCs’ commercialization.

A SOFC device usually consists of an electrolyte and two porous electrodes, an anode and a cathode. At the cathode, oxygen (O₂) is electrochemically reduced to two oxygen ions, O²⁻. At the anode, O²⁻ reacts with the fuel H₂ or hydrocarbons yielding H₂O or CO₂, respectively, thereby releasing electrons. The electrolyte conducts oxygen ions O²⁻ while its electronic conductivity should be kept as low as possible to prevent leakage currents. Many materials have already been used to make conventional SOFCs, including perovskite-type ABO₃ oxides and fluorites [4]. Double perovskites have been the subject of two recent reviews [8,9]. In the case of hydrocarbon fuels, double perovskites have attracted our attention due to the beneficial catalytic activity for methane oxidation reaching 80% at 530 °C [10]. In the following, we use the following notations for chemical elements, which are all introduced by corresponding chemical formulas: B—barium_, Ca—calcium, C—cobalt, Ce—cerium, F—iron, G—gallium, Gd—gadolinium, L—lanthanum, Mn—manganum, Mg—magnesium, M—molybdenum, N—niobium, Ni—nickel, O—oxygen, P—praseodym, S—strontium, Sc—scandium, Sm—samarium, Y—yttrium and Z—zirconium. No fractions of the element are given, e.g., B represents Ba2, Ba2₋xBax and Ba1₋x, and O represents On-δ with n = 2,3,6. Note that we are considering double perovskites A2BB’O6-δ, where the total number of ions at both A-site and B-site should be two.

Recently, a symmetrical SOFC has been reported using La_0.75Sr_0.25Cr_0.5Mn_0.5O_3−δ (LSCrMnO) as a redox (reduction-oxidation) stable material for both the anode and cathode. A redox-stable cathode is also advantageous for traditional SOFCs since some leakage might occur, and fuel is introduced into the cathode side [11]. In symmetrical SOFCs, sulfur poisoning or coke formation on the surface of the anode is eliminated, reversing fuel gas and air flow. The oxidant (typically air) flushed any sulfur or carbon species absorbed on the electrode, thereby regenerating the electrode from sulfur or coke deactivation. Another advantage of symmetrical SOFCs with redox-stable electrodes is the enhancement of the cathode durability since the O₂ partial pressure at the cathode triple phase boundary region can be quite low when SOFCs are operated at a low voltage. Moreover, a redox-stable electrode is a better choice in the case of some leakage [12]. In symmetrical SOFCs, the number of fuel cell components reduces from at least three materials to just two simplifying the production process, reducing manufacturing cost as well as improving thermal compatibility because only one type of interface is present. Nevertheless, materials requirements are much higher since electrodes for symmetrical cells must simultaneously maintain a stable structure and sufficient electrical conductivity in both air and fuel gas atmospheres. Moreover, symmetrical SOFCs provide balanced stresses and, thus, favorable mechanical properties for vibration and thermal cycling.

Typical SOFC cathode materials are transition metal-based perovskites such as La_0.8Sr_0.2MnO₃ (LSMn), La_0.8Sr_0.2Fe_0.8Co_0.2O_3−δ (LSCF) and Ba_0.5Sr_0.5Co_0.8Fe_0.2O_3−δ (BSCF) [6]. Commonly, LSMn is applied as a composite with yttria-stabilized zirconia (YSZ) electrolyte. This extends the triple-phase boundary, which is an active site for oxygen reduction and increases ionic conductivity [5,6]. LSMn has a high electrochemical activity for the O₂ reduction reaction at high temperatures, good thermal stability and chemical stability, and matches well with the electrolyte. Nevertheless, LSMn is a poor ionic conductor making it not suitable for intermediate-temperature SOFC operation [8]. The reason for this disadvantage is the absence of a sufficient number of oxygen vacancies [6]. Sr²⁺ doping is carried out at the La³⁺ site to introduce oxygen vacancies in the parent structure of LaMnO₃ due to the charge compensation mechanism [5]. On the other hand, the strontium doping on lanthanum introduces extra holes in the valence band of the p-type material and thus increases electronic conductivity. BSCF is an excellent oxygen permeation membrane material. Despite its excellent electrochemical performance, it has a high thermal expansion coefficient (TEC) of 20 × 10⁻⁶ K⁻¹ between 50 and 1000 °C [6]. LSCF does not react with ceria-based electrolytes and shows good electrical conductivity, high oxygen surface exchange coefficient and good oxygen self-diffusion coefficient between 600 and 800 °C. Its TEC may be lowered by A-site deficiency up to 13.8 × 10⁻⁶ K⁻¹ for La_0.6Sr_0.2Co_0.2Fe_0.8O_3−δ at 700 °C, matching with commonly used electrolytes [6]. Recently, a new cathode material, Ba_0.9Co_0.7Fe_0.2Nb_0.1O_3−δ (BCFN), was proposed for application with La_0.8Sr_0.2Ga_0.83Mg_0.17O_3−δ (LSGM) electrolyte in order to increase cathode stability [13]. For application as cobalt-free, redox stable and electrically conductive IT-SOFC interconnector, lanthanum strontium ferrite was doped with Sc yielding La_0.6Sr_0.4Fe_0.9Sc_0.1O_3−δ (LSFSc_0.1) [14]. Moreover, SmBaCo₂O_5+x (SmBC₂) was considered as an IT-SOFC cathode [5]. LSCF and SmBC₂ are mixed ionic electronic conductors (MIEC), permitting both oxide ion and electron mobility within the cathode material [4,5,8]. MIECs promote oxygen reduction by enhancing the charge transfer process and expanding the active reaction sites beyond the cathode/electrolyte physical interfaces.

SOFC electrolytes are oxygen ion-conducting ceramics. Yttria-stabilized Y_1−xZr_xO_2−δ, x = 8–10 mol %, YSZ) is the most used SOFC solid electrolyte due to its high chemical stability. It is chemically stable in a wide range of temperatures and oxygen partial pressures and is thermally matched to other SOFC components. However, its ionic conductivity below 800 °C becomes less than 3 × 10⁻² S cm⁻¹ [15]. When the SOFC operating temperature is lowered, an electrolyte material is required which possesses a high enough ionic conductivity. Strontium- and magnesium-doped lanthanum gallate La_1−xSr_xGa_1−yMg_yO₃ with x = 0.1–0.2, y = 0.13–0.2 (LSGM) exhibits an ionic conductivity of about 8.76 × 10⁻² S cm⁻¹ at 700 °C, negligible electronic conductivity and good chemical stability over a wide range of oxygen partial pressures [16]. Other promising electrolytes for IT-SOFCs are Ce_1−xGd_xO_2−δ, 0.1 < x 0.2, (Gadolinium doped ceria—GDC); Ce_1−xLa_xO_2−δ, x = 0.4, (Lanthanum doped ceria—LDC); and Ce_1−xSm_xO_2−δ, x = 0.2, (Samarium doped ceria—SDC) with conductivity values in the order of a few 10⁻² S cm⁻¹ at 700 °C, in some cases slightly higher than LSGM [15]. However, they are mixed ion–electron conductors suffering from a lower open-circuit voltage caused by an electron leakage current. At elevated temperatures above 500 °C, Ce⁴⁺ ions can be reduced at the anode to Ce³⁺ enhancing electronic conductivity and causing additional lattice expansion.

In this work, the considered Sr₂Fe_1.5Mo_0.5O_6−δ does not react with SDC even at 1200 °C while the interaction with YSZ electrolyte begins at 1000 °C. In the case of interaction with LSGM, no appreciable shift in the position of the diffraction peaks was observed at different sintering temperatures, and no new diffraction peaks assigned to reaction products were detected, indicating good chemical compatibility between LSGM and Sr₂Fe_1.5Mo_0.5O_6−δ, in the studied temperature range between 800 and 1200 °C [17].

The most common anode material is a nickel/yttria-stabilized (Ni-YSZ) cermet, usually in combination with YSZ electrolytes. The nickel provides electronic percolation at typically ~30 vol %. Ni was chosen, instead of Co and noble metals suitable at high temperatures for economic reasons. Moreover, a thick anode NiO-YSZ substrate and a thin YSZ electrolyte can be co-sintered, followed by in situ reductions in nickel oxide. This way, a good interlocking between the anode and electrolyte is achieved. YSZ provides mechanical support for the Ni particles, prevents coarsening of metallic particles, allows ionic transport and increases chemical as well as thermal compatibility with YSZ electrolyte. Ni-YSZ anodes exhibit excellent electrocatalytic properties for operation in H₂ fuel [15]. However, they are susceptible to nickel agglomeration, carbon formation and sulfur poisoning, leading to component degradation. Another undesirable feature of Ni-based compounds is redox instability [18]. In order to prevent reactions between a Ni-containing anode and an LSGM electrolyte, a doped ceria-based interlayer, e.g., SDC, should be placed between the Ni-SDC composite anode and the electrolyte [19].

This review is devoted to the application of Sr₂FeMoO_6−δ (SFM) and Sr₂Fe_1+xMo_0.5O_6−δ (SF_1+xM) in LSGM-based SOFCs. These materials are stable in both oxidizing and reducing atmospheres enabling the use of both not only as an anode but also as a cathode and also in symmetrical SOFCs. With regard to its cubic structure under SOFC operation conditions, a correct notation would be SrFe_1−xMo_xO_3−δ. However, in order to avoid reader’s confusion, the double perovskite notation Sr₂Fe_1+xMo_1−xO_3−δ (SF_1+xM) is used throughout this work. We consider the most relevant physical properties (crystal structure, thermodynamic stability, iron and molybdenum valence states, oxygen vacancy formation and oxygen nonstoichiometry, electrical conductivity), A- and B-site ion substitution and the performance of SF_1+xM SOFCs (polarization resistance, operation with hydrogen, operation with hydrocarbons and methanol).

2. Sr₂Fe_1+xMo_1−xO_6−δ Properties

2.1. Crystal Structure

The Goldschmidt tolerance factor t [20] is an indicator of the stability and distortion of the crystal structure. In the case of a double perovskite, such as Sr₂Fe_1+xMo_1−xO_6−δ, an average value of the two B-site radii (2 − x) × r_B and x × r_B′ should be used, yielding

$$t=\frac{r_{\mathrm{A}}+r_{\mathrm{O}}}{\sqrt{2}\left(\langle r_{\mathrm{BB}\prime }\rangle +r_{\mathrm{O}}\right)},$$

(1)

where r_A and r_O are the ionic radii of the A-site ion and oxygen, and r_BB′ is the average ionic radius of the B-site of an ABO₃ perovskite structure. Ionic radii are tabulated for various values of the coordination number, oxidation and spin states [21]. With regard to the Fe³⁺-Mo⁵⁺ fractions considered in Section 2.4 and assuming a high-spin state of Fe, the tolerance factor t amounts to 1.025, 0.971 and 0.940 for the double perovskites Ba₂FeMoO_6−δ (BFM), SFM and Ca₂FeMoO_6−δ (CaFM), respectively. The lattice symmetries obtained at room temperature are correspondingly cubic, tetragonal and orthorhombic. Assuming the same mixed valence states as in SFM, the value of t for SF_1.5M amounts to 0.955. Taking the Fe²⁺/Fe³⁺ and Mo⁶⁺/Mo⁵⁺ ratios given in [22], the value of t increases slightly to 0.962.

By doping SrFeO_3−δ (SFO) with a certain amount of Mo (about 5%, i.e., x = 0.95), doped SF_1+xM perovskites can be stabilized in a cubic structure [23,24,25]. The stabilization of the cubic form occurs due to the incorporation of Mo⁶⁺, a transition metal with a higher oxidation state than Fe³⁺ and Fe⁴⁺, leading to a filling of oxygen vacancies by oxygen in order to compensate for the high positive charge of Mo ions [23,26]. A cubic structure at SOFC operation temperatures exhibits better oxygen permeability than other structures, such as hexagonal and rhombohedral [27]. Therefore, it is beneficial to preserve the cubic structure of the electrode material after modification by ion substitution or doping.

The crystal structure of SF_1.5M at room temperature refined by Rietveld analysis from X-ray and neutron diffraction was attributed to several space groups: Cubic Fm-3m [28,29,30]; cubic Pm-3m with iron and molybdenum disordered on the B-site [25,31]; tetragonal I4/mcm of the tetragonal system [32]; and pseudocubic, orthorhombic Pnma [33]. These structural differences are due to the tilting of BO₆ octahedra. Consequently, different space groups are probably due to different synthesis methods of the samples. Variable temperature, powder X-ray diffraction measurements in the temperature range of 25–800 °C revealed a cubic Fm-3m space group without any phase transition [31]. Later, this result was revised, claiming a reversible tetragonal to cubic phase transition occurring between room temperature and 400 °C, both on heating and cooling in either oxygen or hydrogen [32]. A cubic structure was also obtained in SF_1.33M [29,34], Sr₂Fe_1.4Ni_0.1Mo_0.5O_6−δ (SF_1.4Ni_0.1M) and Sr_1.9Fe_1.4Ni_0.1Mo_0.5O_6−δ (S_1.9F_1.4Ni_0.1M) [35]. The cubic structure is associated with a structural B-site disorder. Below x = 0.2, the B-site ordering of SF_1+xM becomes noticeable, and the crystal structure changes from cubic Fm-3m to tetragonal I4/mmm [28,36].

In SF_1.5M, a cubic structure is preserved by A-site substitution of Sr²⁺ by Ba²⁺ up to 30% [37] and Sr²⁺ by Ca²⁺ up to 30% [38], and B-site substitution of Fe²⁺/³⁺ by Co²⁺/³⁺ up to 33% [39], Fe²⁺/Fe³⁺ by Ni²⁺ up to 26.6% [40,41], Fe²⁺/Fe³⁺ by Nb⁴⁺/Nb⁵⁺ by 6.7% [30], Fe²⁺/Fe³⁺ by Sc³⁺ up to 13.3% [42] and Mo⁵⁺/⁶⁺ by Sn²⁺/⁴⁺ up to 100% [43]. Contrarily, at room temperature, Sr_2−xCa_xFe_1.5MoO_6−δ (S_2−xC_xFM), x = 0–0.6, [44] and Sr₂Fe_1.5Mo_0.5−xNb_xO_6−δ (S₂F_1.5M_0.5−xN_x), x = 0–0.2 [45] were assigned to the space group Pnma.

2.2. Thermodynamic Stability

The SrFeO_3−δ (SFO) system exists over the oxygen composition range 0.16 ≤ δ ≤ 0 as four distinct compounds with the nominal composition Sr_nFe_nO_3n−1 (n = 2, 4, 8 and ∞). The end member SrFeO₃ (n = ∞) possesses a simple cubic perovskite crystal structure, whereas the oxygen-deficient (n = 2, 4 and 8) members each adopt a different vacancy-ordered perovskite crystal structure [46]. In the brownmillerite phase Sr₂Fe₂O₅ possessing the maximal oxygen nonstoichiometry (δ = 0.5), oxygen long-range ordering results in a regular alternation of layers of corner-connected FeO₄ tetrahedra and FeO₆ octahedra. The high oxygen non-stoichiometry of Sr_nFe_nO_3n−1 does not translate into a high oxygen ion conductivity. The formation of ordered oxygen vacancies drastically reduces oxide ion conduction, and oxygen deficiency decreases both mobility and carrier concentration [47]. Thus, only SFO (with n = ∞) is useful for SOFC applications. Under ordinary pressure, SFO is always oxygen-deficient, leading to a composition of samples slowly cooled in the air in the range of SrFeO_2.80 to SrFeO_2.85 [48].

SFe_1+xM is a solid solution of SFO with molybdenum substituting for iron. Double perovskite SFM is thermodynamically unstable in air due to insufficient Mo and Fe solubilities in SrFeO_3−δ and SrMoO₄ (SMO), respectively [49]. The solubility of SMO in SFO judged from oxygen non-stoichiometry is about 15 to 17 mol % (Sr₂Fe_1.40Mo_0.60O_6−δ to Sr₂Fe_1.32Mo_0.68O_6−δ) [49,50], that of SFO in SMO amounts to 2.2 mol % [49]. In 1% H₂/Ar, this solubility region is increased up to 27 mol % (i.e., up to Sr₂Fe_0.92Mo_1.08O_6−δ, including the stoichiometric composition) [51].

SFe_1+xM, 0.0 ≤ x ≤ 0.35, decomposes into SMO and SFO already at 850 °C, while a reduction at 800 °C in H₂—3 % H₂O restores the perovskite phase, whereas SF_1.5M was stable after calcining at 1100 °C for 5 h in air [52]. The synthesis of SFe_1.5M in the oxidizing environment at 1000 °C was also demonstrated in [12]. On the other hand, SFM could be synthesized only in a reducing environment. According to another report, S₂F_1.5M may be synthesized in air, while SF_1.33M needs a reducing treatment to form the perovskite structure [29]. SF_1.5M was found to be stable in H₂ up to 1400 °C [12,17] and in CO₂ in the studied range of 600–800 °C [17]. These data indicate that the Mo fraction had a significant influence on the stability of SFe_1+xM in air.

The solubility of iron-rich composition SFe_1.5M is slightly below maximum SMO solubility in the region of its thermodynamic stability both in air and in a reducing atmosphere of 1% H₂/Ar [12]. On the other hand, SFe_1+xM possesses a cubic structure for 0.2 < x < 1 [31,36,48,53], which in perovskites enhances oxygen permeability [27]. Note that in the compositions range of cubic structures, B-site Fe and Mo ions are highly disordered [31,36], diminishing carrier mobility. This can be overcome by selecting the Mo concentration slightly above the molybdenum percolation threshold in a material exhibiting nanoscale local ordering in a disordered matrix [53]. Experimentally, a percolation threshold value of x_p = 0.65 was obtained, while the theoretical value for a homogeneous composite containing randomly oriented spherical fillers of similar size amounts to x_p = 0.16 [54]. For ellipsoidal particles, the theoretical x_p value will be even lower since ellipsoidal fillers connect with each other more easily.

Substitution of Sr²⁺ by Ca²⁺ makes Ca₂FeMoO₆ (CaFM) thermodynamically more stable than SFM. The p_O2-region where CaFM is stable increases from 3.2042 × 10⁻⁹ ≤ p_O2 ≤ 1.6059 × 10⁻⁵ Pa for SFM to 3.2042 × 10⁻⁸ ≤ p_O2 ≤ 1.2756 × 10⁻⁵ Pa for Ca₂FeMoO_6−δ [55]. However, CaFM decomposes in nitrogen above 430 °C into CaMnO₄ and CaFeO_2.5. Therefore, it is incompatible as an anode material in SOFCs.

SFO was observed to be insensitive to water. Alkaline earth metals such as strontium are known to be highly reactive in water-containing atmospheres. As a result, SF_1+xM is highly sensitive to water and would decompose into SMO, Sr(OH)₂ and FeO with Sr(OH)₂, further transforming into SrCO₃ by interaction with CO₂ [50]. At 800 °C, SF_1.5M is stable in water-containing atmospheres. SF_1.5M reacts with water at lower temperatures forming SrMo₄O₁₃·H₂O, Fe₃O₄, SMO, SrO and hydroxides such as Sr(OH)₂. However, the SF_1.5M phase was restored upon repeated heating to 800 °C [56]. SOFCs containing SFe_1.5M possess chemical stability and reasonable performance at the operating temperature [31]. When the SOFC is cooled down, Sr(OH)₂ forms, decreasing the conductivity and catalytic activity. When heated back to the operating temperature, reforming of SFe_1.5M does not occur due to the sluggish kinetics of solid-state reactions. Moreover, the decomposition products lead to a local increase in volume. This corresponding increase in volume cannot be accommodated by any other means than cracking, generating cumulative damage during cycling [56].

Partial substitution of Fe²⁺/Fe³⁺ by Nb⁵⁺ does not affect the formation of the perovskite phase in air. On the other hand, it hinders the reduction of iron to a metallic phase. Thus, SF_1.4N_0.1M has a more stable structure under a hydrogen atmosphere [30].

2.3. Iron and Molybdenum Valence States

SFO has an anomalous valence state, Fe⁴⁺, which does not appear in the simple Fe-O system [48]. With increasing oxygen nonstoichiometry, the formal charge state on Fe changes from Fe⁴⁺ in SrFeO₃ via a mixture of Fe³⁺ and Fe⁴⁺ to Fe³⁺ in SrFeO_2.5 [46]. Fe⁴⁺ reduction is also favored by heating and/or oxygen pressure decrease. At rather small oxygen pressure values, one can expect a partial reduction in both iron and molybdenum with the formation of Fe²⁺ and Mo⁵⁺ cations [23]. Another reason for the disappearance of Fe⁴⁺ and the simultaneous increase in the concentration of the larger Fe³⁺ cations is the incorporation of molybdenum in the crystal lattice. The origin of these effects is the charge compensation of Mo⁶⁺ ions via the concentration decrease in Fe⁴⁺ with a simultaneous filling of oxygen vacancy sites by oxygen [23,24].

When the Mo content is low, i.e., x of SF_1+xM takes a value of about 0.75, Fe is in the Fe³⁺ oxidation state and Mo adopts a Mo⁶⁺ state. With increasing Mo content, both the Fe and Mo cations are both partially reduced, resulting in a mixture of Fe³⁺, Fe²⁺, and Mo⁵⁺ and Mo⁶⁺ [57]. Here, reduction occurs to keep electro-neutrality. As the Fe²⁺/Fe³⁺ ratio increases in more Mo-rich compositions, the Mo⁵⁺/Mo⁶⁺ radio shows a peak in SFe_1.5M. A larger fraction of Fe²⁺ possesses a higher catalytic activity enhancing SOFC performance while the electrical conductivity of SFM decreases [22]. Thus, a balance between the activity, conductivity and stability exists in SFe_1.5M. Moreover, SFe_1.5M was reported to form the percolation path of the Fe-O-Fe bond for the charge carrier to move through the crystal in both hydrogen and air atmospheres [12].

The equilibrium reaction Fe³⁺ + Mo⁵⁺ ⇔ Fe²⁺ + Mo⁶⁺ is directly related to the resistive properties of SF_1+xM [51]. The contributions of the Fe²⁺–Mo⁶⁺ and Fe³⁺–Mo⁵⁺ configurations are quite different among A₂FeMoO_6−δ compounds. The mixed-valence state involves 21–34% Fe³⁺ (3d⁵; S = 5/2)-Mo⁵⁺ (4d¹; S = 1/2) and 79–66% Fe²⁺ (3d⁶; S = 2)-Mo⁶⁺ (4d⁰; S = 0) for SFM [58,59,60,61], about 14% Fe³⁺-Mo⁵⁺ and 86% Fe²⁺-Mo⁶⁺ for BFM [60] and about 40% Fe³-Mo⁵⁺ and 60% Fe²⁺-Mo⁶⁺ for CaFM [60]. Thus, as the A-site cation decreases, the valence balance of Fe³⁺+ Mo⁵⁺ ⇔ Fe²⁺ + Mo⁶⁺ gradually shifts closer to Fe³⁺-Mo⁵⁺, and the electronic conductivity increases [60]. It was observed that the contribution of the Fe³⁺-Mo⁵⁺ configuration to the XPS spectrum of double-perovskites A₂FeMoO_6−δ increases with decreasing A-site cation size [60].

An increase in the A-site cation size by substitution of the Sr²⁺ ion by the larger Ba²⁺ ion gradually shifts the valence balance of Fe²⁺/³⁺-Mo⁵⁺/⁶⁺ to Fe²⁺-Mo⁶⁺, which would promote B-site ordering [62,63]. On the other hand, barely any changes in Fe²⁺/Fe³⁺ and Mo⁶⁺/Mo⁵⁺ couples were obtained in Sr_2−xBa_xFe_1.5Mo_0.5O_6−δ, x = 0, 0.2, 0.4, 0.6 (SB_xFM) samples [37]. In the latter case, the changes were probably too small to be determined with certainty. Contrarily, Sr²⁺ substitution by Ca²⁺ increases the Fe³⁺/Fe²⁺ and Mo⁶⁺/Mo⁵⁺ ratios as a whole associated with a reduction in the δ value, i.e., with a decrease in the oxygen vacancy concentration [44]. A change in the Fe²⁺-Fe³⁺ and Mo⁶⁺-Mo⁵⁺ proportion by Ca-doping was also obtained in SCa_xF_1.5M [44]. Here, the decrease in Fe²⁺ with Ca doping correlates with the one Mo⁵⁺ and the increase in Fe³⁺ with Mo⁶⁺ since oxygen non-stoichiometry also increases. The valences of Fe and Mo change significantly with temperature. The Fe²⁺ and Mo⁵⁺ content increases with the increase in temperature, influencing the electronic conductivity [31].

At the B-site, Fe²⁺ substitution by Ni²⁺ affects the equilibrium between Fe³⁺/Mo⁵⁺ and Fe²⁺/Mo⁶⁺. The ratio of Fe²⁺/Fe³⁺ decreases from 1.46 for x = 0 to 0.81 for x = 0.4. The Fe²⁺/Fe³⁺ and Mo⁶⁺/Mo⁵⁺ decrease with Ni fraction, which indicates the amount of Fe³⁺ and Mo⁵⁺ cations increases. The ratios of the Fe²⁺/Mo⁶⁺ and Fe³⁺/Mo⁵⁺ redox couples increase with Ni fraction content as x increases. The optimal ratios are attributed to SF_1.4N_0.1M, which is directly related to the conductivity [40]. In another report, the Fe²⁺/Fe³⁺ ratio of SF_1.5−xNi_xM decreases from 1.22 at x = 0 to 0.97 at x = 0.1 and then increases up to 1.56 at x = 0.3. Similarly, the Mo⁶⁺/Mo⁵⁺ ratio changes from 1.11 at x = 0 to 0.94 at x = 0.1 and then up to 1.35 at x =0.3. The difference between the total Fe²⁺+Mo⁶⁺ and Fe³⁺+Mo⁵⁺ becomes the least when x = 0.1 [41]. The contribution of the Fe³⁺+ Mo⁵⁺ pair to conductivity was further confirmed by its enhancement in Ni-doped SF_1.4Ni_0.1M cathodes [40] and anodes [41]. For Sr₂Fe_1.5Mo_0.5−xNb_xO_6−δ (SF_1.5M_0.5−xN_x), the Fe²⁺/Fe³⁺ ratio is nearly constant while the Mo⁶⁺/Mo⁵⁺ ratio shows a minimum in the range x = 0.10–0.15 coupled with a maximum of the Nb⁵⁺/Nb⁴⁺ ratio at x = 0.10 [45]. The substitution of the Fe²⁺/Fe³⁺-site by high-valence Nb⁵⁺ induces an obvious reduction from Fe³⁺ to Fe²⁺ to achieve electrical neutrality. The increase in Fe²⁺ (which has a larger radius) results in an expansion of the crystal cell [30].

2.4. Oxygen Vacancy Formation Energy and Oxygen Non-Stoichiometry

The formation of an oxygen vacancy E_f(V_O) can be viewed as a process of breaking metal-oxygen bonds followed by the removal of a neutral oxygen atom and the subsequent redistribution of two extra oxygen electrons into the SFM lattice. Cubic SrFeO_3−δ, E_f(V_O) exhibits a constant low value (ca. 0.4 eV) for δ < 0.05, increases to ca. 0.5 eV for 0.05 < δ < 0.1, and further increases quickly with concentration when δ > ≈ 0.1 [64]. This increase is attributed to the local charge redistribution after V_O formation and to overlapping local lattice transformations. In stoichiometric SFM, first principle DFT (density-functional theory, which is a computational quantum mechanical modeling method used in physics) calculations predict that E_f(V_O) along metal–oxygen–metal bonds follows the trend Fe-O-Fe < Fe-O-Mo < Mo-O-Mo. Removing an oxygen atom from Fe-O-Fe costs ∼3.0–3.5 eV, and that from Mo-O-Mo bonds costs ∼4.5–5.0 eV. This is attributed to a much stronger metal–oxide bond of Mo compared to Fe [65]. The Fe−O bonds are easier to break in order to remove oxygen from the lattice to form a vacancy. The formation of an oxygen vacancy consists of not only the removal of a neutral oxygen atom but also the subsequent redistribution of the extra electrons from the oxide ion into the SF_1+xM lattice. Therefore, another origin of a low vacancy formation energy is a fully delocalized rearrangement of the extra charge delivered to the lattice upon removal of the neutral oxygen atom. In SF_1+xM, a partially occupied band with empty states is formed just above the Fermi level by a strong hybridization of the Fe and O states at the conduction band edge. The excess electrons left by the formation of the vacancy easily occupy just these empty states across the Fermi level. Additionally, this effect provides a high conductivity [33]. In fact, DFT calculations for SFe_1.5M confirm that E_f(V_O) along Mo-O-Mo bonds is higher than that along Fe-O-Fe bonds at all vacancy concentrations considered. Moreover, E_f(V_O) depends on oxygen non-stoichiometry, and it vanishes at δ ≈ 0.1, the value obtained in as-synthesized SFe_1.5M material [33]. For E_f(V_O) → 0, the oxygen migration barrier height governs oxide ion diffusion in this material. In summary, excess Fe in SF_1+xM provides SOFC materials with higher concentrations of oxygen vacancies that facilitate oxide ion diffusion. Oxygen vacancies in SF_1.5M are mainly transported along the Fe-O-Fe bonds and not along the Mo-O-Fe and Mo-O-Mo bonds. At the same time, the Fe-O bonds are relatively weak contributors to a high level of oxygen conductivity. The stronger Mo-O bond leads to a decrease in the value δ with the incorporation of Mo [25].

The vacancy formation energy of Co-substituted SF_1.5−xCo_xM was calculated by means of DFT in [39]. The corresponding values are listed in

Table 1. Oxygen formation energies along different bonds in SF_1.5−xCo_xM [39].

Bond Configuration	Ef(VO), eV
	x = 0	x = 0.5	x = 1.0	x = 1.5
Fe-O-Mo	2.95	2.89	2.58
Fe-O-Fe	2.30	2.19
Co-O-Mo		2.78	2.41	2.2
Co-O-Co			1.80	1.37
Fe-O-Co		2.08	1.74

. Moreover, E_f(V_O) along Fe-V_O–Mo is higher than that along Fe-V_O-Fe. It is also higher than E_f(V_O) along Co-V_O-Co and along Fe-V_O-Co. E_f(V_O) along Fe-V_O-Fe exceeds that along Fe-O-Co and all the values of E_f(V_O) decrease with increasing Co content. The latter means that vacancies are much easier to form at higher Co content.

DFT usually assumes oxygen-rich conditions where an upper limit of μ_O is chosen as half of the total energy of a free, isolated O₂ molecule in the triplet state at T = 0 K [66]. However, this upper limit can never be realized experimentally. On the other hand, the exact oxygen partial pressures in the fabrication processes of thin-film and bulk samples cannot be determined accurately, but their difference in film and bulk sample fabrication should be rather small. Introducing a combined DFT and thermodynamic model and using a temperature- and partial pressure-dependent value of the oxygen chemical potential, E_f(V_O) is reduced from about 4.5 eV in the oxygen-rich limit to about 2.9 eV at p_O2 = 2.1 × 10⁴ Pa (corresponding to air) and to about 1.7 eV at p_O2 = 10⁻⁴ Pa (corresponding to an atmosphere of ultrapure, i.e., 99.999 % Ar at 10 Pa) [67].

The lower E(V_O) value in Fe-rich compositions of SF_1.5M shifts the homogeneity region to higher values of δ. This is illustrated in Figure 1, which depicts a comparison of the homogeneity regions of both oxygen-deficient SF_1.5M and SFM. With the increase in δ, the oxygen permeation and lattice expansion in the reduction atmosphere become much more pronounced [68]. The latter causes larger internal stress to have harmful influences on SOFC operation, such as energy loss, cracking and breakage of the cell.

When summarizing crystal structure, thermodynamic stability, Fe and Mo valence state, and oxygen vacancy formation energy, SF_1.5M is a compromise that provides a cubic crystal structure, which generates an electronic structure as well as oxygen vacancies that promote suitable electrical transport properties and catalytic activity in oxidizing and reducing atmospheres. With regard to thermodynamic stability considered above, the ideal Fe to Mo ratio should be around two. The electrocatalytic properties of SF_1.5M may be further improved by partial substitution of A-site and B-site ions.

2.5. Electrical Conductivity

SFO exhibits the highest conductivity in a temperature range of 400 to 900 °C. Stoichiometric SrFeO₃ obtained by equilibration at high oxygen pressures and below room temperatures possesses a metallic conductivity of about 500 S cm⁻¹ (if not further specified, we consider the following electrical conductivities measured at environmental conditions) [70]. At 500 °C, a maximum conductivity of 181 S cm⁻¹ was obtained [25]. Slight Mo incorporation decreases the conductivity since the reduction of Fe⁴⁺ to Fe³⁺ reduces the number of charge carriers and the hole mobility [24]. The conductivity values at 800 °C drop with increasing Mo fraction from 62 S cm⁻¹ for SF to 22 S cm⁻¹ for SF_1.5M [25]. Values reported by other authors for SF_1.5M at 800 °C are in the range of 7 to 21 S cm⁻¹ [30,31,35,39,40,44]. The conductivity of SF_1.5M is much lower than that of SFM under similar conditions [60]. Here, the difference is a nearly random distribution of Fe and Mo at B-sites in SF_1.5M, while the B-site cation distribution in SFM is highly ordered. Ordering of SF_1+xM continuously increases in the range of 0.5 > x ≥ 0 [28,36]. However, total B-site ordering requires a thermodynamic equilibrium during synthesis, which in ceramic materials is reached by long-term annealing at 1200 °C [69]. Note that in this work, we disregarded unusually high conductivity data in [12], which do not match with data measured under similar conditions and also with the dependence of the conductivity on the Mo fraction in SF_1+xM. A probable reason for the differences could be that the specified Fe fraction does not correspond to the present one.

The low-temperature part of the SF_1+xM conductivities up to a transition temperature shifts to higher values with increasing Mo fraction. It is well described by the adiabatic small polaron hopping model [71]:

$$\rho ={\rho }_{0}T\exp \left(\frac{E_a}{kT}\right),$$

(2)

where E_a is the thermal activation energy. The decrease in conductivity at higher temperatures is related to a decreasing carrier concentration (holes in p-type materials) as the concentration of oxygen vacancies is increased due to the increasing loss of lattice oxygen. The generation of oxygen vacancies and electrons leads to a reduction in cations with high valence states to lower ones by electrons. Consequently, the effective charge carrier concentration will be reduced, causing a subsequent decrease in conductivity [72] and a corresponding decrease in the carrier density in this case [23,24]. This suggests that Mo-doped SFO has a stronger tolerance to reduction. For the same reason, the conductivity of Sr_1.9Fe_1.4Ni_0.1Mo_0.5O₆ drops below that of Sr₂Fe_1.5Mo_0.5O₆ when the temperature increases since the oxygen vacancies are easier formed in Sr_1.9Fe_1.4Ni_0.1Mo_0.5O₆ [35]. Note that the mobility of holes in SF_1+xM decreases in response to a decrease in oxygen content in the lattice or an increase in Mo fraction. The latter effect is explained by the blocking role of Mo⁶⁺ ions in the hole transfer via the Fe-O-Fe pathway [53]. Figure 2 illustrates the interplay of small adiabatic polaron hopping conduction at lower temperatures and loss of lattice oxygen at higher temperatures.

Similar behavior of the conductivity with a maximum in the temperature range 400–800 °C was also obtained for Ba substitution of Sr [37,44], Ni substitution of Fe [40], Co substitution of Fe [39,73] and Nd substitution of Mo [45] or of Fe [30]. Here, the low-temperature part was attributed to small adiabatic polaron hopping in [39,44,45,73,74]. Moreover, the temperature-activated behavior of hole mobility in SF_1+xM, 0.75 ≤ x ≤ 0.93, was characteristic of the polaron conduction mechanism [53].

Monocrystalline, half-metallic SFM exhibits a low-temperature resistivity ρ of ρ₀ = 1.8 × 10⁻⁶ Ω m increasing with temperature as:

$$\rho (T)={\rho }_0+R_{\nu }{T}^{\nu },$$

(3)

with ν = 2 near room temperature and the parameter R₂ = 2.16·× 10⁻¹¹ Ω m K⁻² for single crystal SFM [75,76]. The T² dependence suggests that electron–electron scattering [76,77] or spin-wave scattering [76] dominates the resistivity. At higher temperatures up to the Curie temperature T_C, other charge scattering mechanisms appear in perovskite thin films, transforming Equation (3) into

$$\rho (T)={\rho }_0+R_2{T}^2+{\displaystyle \sum _l{R}_l}{T}^l,$$

(4)

where an l = 2.5 term represents the combination of electron–electron scattering, electron–phonon scattering and electron–magnon scattering [78,79]; an l = 3 term stands for the scattering with anomalous single magnons in half-metallic systems [80]; l = 3.5 with spin-waves at low temperatures [81,82]; an l = 4.5 with electron–magnon scattering derived in the double-exchange theory at low temperatures [83] but experimentally observed at mediate (200–350 K) temperatures [77] or possibly for spin-wave scattering [84]; and l = 5 with acoustic phonons [85]. Additionally, there is a term due to optical phonon scattering:

$$\rho (T)\propto \frac{{\omega }_s}{{\sinh }^2(\hslash {\omega }_s/2kT)},$$

(5)

where ω_s is the average frequency of the softest optical mode, which is consistent with small polaron coherent motion involving relaxation [86]. Unfortunately, none of these models fit the experimental data of SFM thin films in the whole temperature range. However, the electron–electron scattering model is appropriate in a broader temperature range [87].

Above room temperature, the conductivity of SFM annealed in a vacuum is separated into three regions: (i) from 300 K up to the Curie temperature of about 405 K, where the electrical resistivity increases with temperature with metallic behavior; (ii) above 405 K up to approximately 590 K, where conductivity decreases with temperature due to a B-site disorder induced weak Anderson localization of the electrical carrier; and (iii) from 590 K up to 900 K, where the material becomes metallic again [88]. Another report on the electrical resistivity of SFM indicates metallic conduction behavior below 150 °C, localization of the carriers in the temperature range of 150–550 °C, and reversion to metallic conduction behavior between 550 and 850 °C [60]. A similar conductivity behavior with a maximum of σ at about 200 °C, far above the Curie temperature of ~60°C [89], was obtained for BFM, while CaFM shows solely metallic behavior in the whole temperature range of 50–850 °C. This correlates with the fraction of Fe²⁺-Mo⁶⁺ pairs discussed above [60]. The metallic resistivity of CaFM follows Equation (3) with ρ₀ = 0.65 mΩ cm, ν = 1.41 and Rν = 0.157 µΩ cm T^-ν. This can be attributed to an electron scattering process operating from temperatures of the order of the Debye temperature up to the melting point. Here, the resistivity is proportional to the mean squared amplitude of atomic vibrations in the crystals varying with temperature according to a T^1.5 power law [90].

On the other hand, a revision of the reported conductivity behavior of SFM and BFM above T_C [60,88] shows a convincing fit for the small adiabatic polaron hopping model [71] (cf. Equation (2)). The obtained E_a values are 0.07–0.08 eV for SFM and about 0.13 eV for BFM. They are in the order of the values of other double perovskites compiled in

Table 2. Activation energy of the adiabatic polaron hopping model of double perovskites measured under environmental conditions.

Compound	Temperature Range, °C	Ea, eV	Ref.
LSCF	100–500	0.10	[91]
BSCF	45–470	0.365	[92]
SMgM	450–850	0.279	[93]
S1.8Sm0.2MgM		0.195
S1.6Sm0.4MgM		0.113
S1.4Sm0.6MgM		0.080
S1.2Sm0.8MgM		0.087
SFO	400–500	0.204	[25]
SF1.9M	400–600	0.221
SF1.8M	400–600	0.164
SF1.6M	410–700	0.162
SF1.5M	400–750	0.156
SF1.5M	40–440	0.236	[39]
SF1.0C0.5M	40–530	0.193
SF0.5C1.5M	40–530	0.137
SF1.5M	300–450	0.067	[45]

.

SFO is p-type only under oxidizing conditions (pO₂ > 10⁻⁶ atm) [53]. In reducing atmospheres, p-type conduction behavior is turned to n-type one. Thereby, the electron mobility is sufficiently lower than that of holes. It increases with rising Mo incorporation while the hole mobility decreases [23,24,53]. As shown above, the latter is explained by a blocking role of Mo⁶⁺ ions in the hole transfer via the Fe-O-Fe pathway [53]. The increasing electron mobility, the n-type carrier, is a result of partial molybdenum reduction to Mo⁵⁺ under reducing conditions which generates electrons. The Mo⁵⁺/Mo⁶⁺ ratio shows a peak in SF_1.5M [22]. Partial substitution of Fe at the B-site by an ion of a different radius affects the conductivity. In air, the highest conductivity is obtained as a result of substitution when the tolerance factor t adopts the ideal value t = 1 [26]. This was also observed by the substitution of A-site divalent ions by trivalent Nd³⁺ and Sm³⁺ in BSCF [92].

SF_1.33M shows a metallic behavior from 370 to 830 °C in 3% H₂O/H₂. At 800 °C, the conductivity amounts to about 16 S cm⁻¹ [34]. A fit to Equation (3) yields ρ(0) = 18.8·mΩ·cm, ν = 1.54 and R_ν = 1.482·µQ cm T^-ν. Moreover, in these cases, the temperature dependence of conductivity originates in the high-temperature electron scattering process exhibiting a T^1.5 power law [90].

Table 3. Parameters of metallic conductivity of SF_1+xM measured under reducing conditions.

Compound	ρ(0), mΩ cm	ν	Rν, µΩ cm T-ν	Ref.
SF1.33M	18.8	1.54	1.482	[34]
SFM	1.85	2.07	0.0013	[93]
SFM	3.01	1.75	0.014	[94]

lists the fits of experimental conductivity behavior of SF_1+xM samples possessing metallic conductivity to Equation (3).

At 800 °C and in reducing atmospheres, SF_1.5M conductivities of 8 to 40 S cm⁻¹ were obtained [22,29,30,31,41,56,95]. A reason for this data scatter is the strong dependence of the conductivity on the Fe-fraction. For example, it varies from 16 S cm⁻¹ for SF_1.4M to 75 S cm^-1 for SF_1.6M [22]. We attributed this increase to an increase for x < 0.5 in the B-site order of SF_1+xM [28,36]. The value of σ increases in strontium deficient Sr_1.9Fe_1.4Ni_0.1Mo_0.5O_6−δ up to about 29 S cm⁻¹ benefiting from the high conductivity of a cubic Fe-Ni metal alloy formed under reducing conditions [35]. Under reducing conditions, the temperature range of small adiabatic polaron hopping conduction widens to higher temperatures.

Table 4. Activation energy of the adiabatic polaron model of SF_1.5M-based ceramics under reducing conditions.

Compound	Temperature Range, °C	Ea, eV	Ref.
SF1.5M	475–800	0.167	[29]
SF1.5M	475–800	0.292	[35]
S1.9F1.4Ni0.1M	400–800	0.240
SF1.5M	200–800	0.225	[56]
SF1.5M	400–750	0.15	[32]
SF1.5M (SF1.4N0.1M)	300–800	0.115 (0.1)	[30]
SFM0.8N0.2	600–800	0.281	[96]
SFM0.65Ni0.35	250–700	0.05	[97]

compiles the activation energies of SF_1+xM ceramics obtained from experimental data, which are subjected to this conduction process. E_a values are of the order of 0.1 eV with a large scatter attributed to differences in sample synthesis and post-treatment.

Over the temperature range of 50–850 °C, the electrical resistivity of A₂FeMoO_6−δ in H₂ shows a clear increase by several orders of magnitude in the order: CaFM < SFM < BFM [60]. More detailed data were not provided. The conductivity of SFM sintered in 5 % H₂/Ar at 1000 °C for 5 h and measured in H₂ exhibits a small adiabatic polaron hopping conduction [94].

Under reducing conditions, the conductivity decreases with increasing ion radius of the ion partially substituting Fe in SF. It is maximum in the case of Mo⁶⁺ substitution and decreases with the ionic radii of the dopant from 4.5 S cm⁻¹ for Mo-doping to 0.4 S cm⁻¹ for Zr-doping at 800 °C [26].

3. A- and B-Site Substitution

The partial substitution of A and/or B site elements is an effective way to improve the performance of perovskite-type materials. The additional introduction of alkali earth metal elements on the A-site and transition-metal elements on the B-site affects the cation valence and oxygen-vacancy concentration and thus improves the electronic or ionic conductivity of the material as well as its catalytic properties.

3.1. A-Site Substitution

With a decrease in the A-site cation size in A₂FeMoO₆ (A = Ca, Sr, Ba), the Fe³⁺/Mo⁵⁺ electronic configuration increases resulting in an increase in the electrical conductivity of the material [60]. The thermal expansion coefficient does not change sufficiently with A-site substitution. The best performance of SOFCs with an A₂FeMoO₆ anode, a power density of 0.584 W cm⁻², was obtained for unsubstituted SFM (cf.

Table 5. Performance of S₂F_1+xM_1−x-based SOFCs operated with hydrogen fuel.

Configuration Anode-Electrolyte-Cathode	del, µm	T, °C	Pmax, W/cm2	Ref.
SFM/LSGM/SDC/SmBC2	300	850	0.831	[60]
		800	0.584
		750	0,412
SFM/LSGM/SDC/SmBC2	300	850	0.735 1	[60]
		800	0.476 1
		750	0.183 1
BFM/LSGM/SDC/SmBC2	300	850	0.561	[60]
		800	0.338
		750	0.206
CaFM/LSGM/SDC/SmBC2	300	850	0.186	[60]
SFM/LSGM/BSCF	300	850	0.864	[61]
		800	0.603
		750	0.436
SFN0.8M0.2/LSGM/PBCO	200	800	0.520	[96]
		700	0.375
		600	0.130
		550	0.061
SF1.33M/LGSM/LSCF	300	800	0.547	[34]
		750	0.392
		700	0.268
SF1.33M/LGSM/LSCF	300	800	0.472 1	[34]
SFM/LSGM/BSCF	300	850	0.864	[61]
		800	0.603
		750	0.436
SF1.33M/LGSM/LSCF	300	800	0.472 1	[34]
SF1.33M/LGSM/LSCF	265	850	0.532	[98]
		800	0.340
		750	0.200
SF1.33M/LGSM/LSCF SF1.5M/LGSM/LSCF	NA	800	0.588 0.474	[29]
SF1.33Mo0.66/LGSM/LSCF SF1.5M/LGSM/LSCF	NA	800	0.473 1 0.432 1	[29]
Ni-SF1.5M/LGSM/LSCF	300	800	1134	[99]
SF1.5M-GDC/CeGdO/BCFN	50	700	0.188	[100]
		650	0.100
		600	0.039
S1.9F1.4Ni0.1M/LSGM/CLO/LSCF	NA	850	1.160	[35]
		800	0.968
		750	0.730
SF1.5M-GDC/GDC/GDC-LSCF	35	700	0.22	[95]
		600	0.14
LSMn/YSZ-S2FM/YSZ/YSZ-LSFSc	24	800	0.462	[52]
		750	0.324
SF1.4M/LSGM/BSCF SF1.5M/LSGM/BSCF SF1.6M/LSGM/BSCF	300	800	0.514 0.508 0.482	[22]
SF1.4M/LSGM/BSCF SF1.5M/LSGM/BSCF SF1.6M/LSGM/BSCF	300	750	0.387 0.385 0.380	[22]
SF1.3Co0.3M0.4/LSGM/LSCF	170	850	1.09	[74]
		800	0.81
		750	0.50
		700	0.30
SF1.3Co0.3M0.4/LSGM/LSCF	170	850	0.981 2	[74]
		800	0.808 2
		750	0.604 2
Ni-LDC/LDC/LSGM/SF1.5M	300	850	0.613	[101]
		800	0.468
		750	0.349
Ni-LDC/LDC/LSGM/SF1.5M	265	850	0.613	[98]
		800	0.468
		750	0.349
Ni-YSZ/YSZ/SDC/S1.8B0.2F1.5M	700	800	1.63	[37]
		750	1.3
		700	0.87
		650	0.41
Ni-YSZ/YSZ/SDC/SF1.5Mo0.4N0.1	400	800	1.102	[45]
		750	0.920
		700	0.671
		650	0.421
Ni-YSZ/YSZ/SDC/S1.8B0.2F1.5M Ni-YSZ/YSZ/SDC/S1.6B0.4F1.5M Ni-YSZ/YSZ/SDC/S1.4B0.6F1.5M	400	800	1.06 1.26 0.94	[44]
Ni-YSZ/YSZ/SDC/SF1.4Ni0.1M	10	800	1.77	[40]
		750	1.21
		700	0.79
		650	0.33
Ni-YSZ/LSGM/SDC/SF1.5M Ni-YSZ/LSGM/SDC/SF1.45Sc0.05M	400	800	0.91 1.23	[42]
Ni-ScSZ/ScSZ/SDC/SF1.4Co0.1M Ni-ScSZ/ScSZ/SDC/S1.95F1.4Co0.1M Ni-ScSZ/ScSZ/SDC/S1.9F1.4Co0.1M	11	800	0.88 1.16 0.96	[73]
SF1.5M/LSGM/SF1.5M	265	900	0.835	[12]
SF1.5M/LSGM/SF1.5M	265	900	0.835	[98]
SF1.5M/LSGM/SF1.5M	243	800	0.531	[30]
		750	0.365
		700	0.244
		650	0.124
SF1.4N0.1M/LSGM/SF1.5M	236	800	0.374	[30]
		750	0.228
		700	0.156
		650	0.092
S1.4Ca0.6F1.5M/LSGM/S1.4Ca0.6F1.5M	35	800	1.050	[38]
		750	0.880
		700	0.660
		600	0.410
SF1.4Ni0.1M/LSGM/SF1.4Ni0.1Mo0.5	310	800	0.530 3	[41]
		750	0.380
		700	0.258
		650	0.164
SF1.5M/LSGM/SF1.5M0.2Sn0.3	400	800	0.618	[43]
		750	0.431
		700	0.262

¹ H₂S/H₂, ² syngas, ³ anode decomposes.

) [60]. The change in the Fe²⁺/Fe³⁺ and Mo⁵⁺/Mo⁶⁺ ratios in A-site substituted SFM (cf. Section 2.3) plays an important role in the conduction and electrochemical performance [37,44,60]. When x = 0.2, the conductivity of the SBa_0.2F_1.5M sample reaches the maximum value of 21.7 S cm⁻¹ at 550–600 °C where the dominant conductivity mechanism changes from small adiabatic polaron hopping to carrier diminution caused by oxygen lattice loss (cf. Section 2.5) [37]. This value is higher than that of the SF_1.5M (σ = 15.9 S cm⁻¹) sample [40]. SBa_0.2F_1.5M shows the lowest cathode polarization resistance and provides at 800 °C with Ni-YSZ anode and a YSZ electrolyte a maximum power density of 1.63 W cm⁻² at 800 °C (cf. Table 5) [37].

Partial substitution of Sr²⁺ by Ca²⁺ changes the cathode polarization resistance in air, showing the lowest value at x = 0.4 and decreasing the thermal expansion coefficient toward a better thermal match with the electrolyte [44]. On the other hand, the substitution effectively enhances the anode catalytic activities, thereby reducing the anode polarization resistance, especially at lower temperatures [38].

In symmetrical SOFCs, the anode polarization resistances of SCa_xFM, x = 0, 0.2, 0.4, 0.6 and electrodes are significantly higher than that of the cathode. It decreases with an increasing value of x, while for the cathode, a minimum at compositions x = 0.2–0.4 occurs [38,44]. The lowest anode polarization resistance of SC_0.6M is coupled with slightly higher cathode polarization resistances than those of SF_0.4M. SOFC measurements showed the (up until now) highest power densities for symmetrical SC_0.6M electrodes and an LSGM electrolyte, 1.06 W cm⁻² at 800 °C (cf. Table 5) [38]. The thermal expansion coefficients were found to decrease when increasing the Ca content from 16.33 × 10⁻⁶ K⁻¹ to 15.08 × 10⁻⁶ K⁻¹ when the Ca-substitution increases from 0 to 0.6 [44]. This leads to a better match with LSGM values of 11.5 × 10⁻⁶ K⁻¹ for a wide range of temperatures (from room temperature to 1000 °C) [16]. In summary, the partial substitution of Sr²⁺ by Ca²⁺ improves the performance of the cathode of IT-SOFCs (cf. Table 5).

3.2. B-Site Substitution

Iron and cobalt oxides are well known for their excellent catalytic activity. On the other hand, Sr₂CoMoO_6−δ and Sr₂NiMoO_6−δ exhibit low resistance to carbonation in the intermediate temperature range of 600–800 °C but are unstable under a reducing atmosphere above 800 °C, decomposing partially into Sr₃MoO₆ and Co or Ni metals, respectively [17]. Recently, Sr₂Fe_1.5−xCo_xMo_0.5O_6−δ (SF_1+xC_xM) [39] and Sr₂Fe_1.5−xNi_xMo_0.5O_6−δ (SF_1+xN_xM) cathodes [40] have been reported. Both studies demonstrated that partial B-site substitution with transition-metal elements enhances the conductivity and electrochemical performance.

Fe²⁺/Fe³⁺ substitution by Co²⁺/Co³⁺ in SF_1.5−xCo_xM improves the conductivity, increases oxygen vacancy concentration and, consequently, enhances the surface exchange kinetics without deteriorating the structural stability. Unfortunately, it also significantly increases the thermal expansion coefficient from 15.8 to 19.8 × 10⁻⁶ K⁻¹[39]. The large TEC of the Co-containing perovskite (~20 × 10⁻⁶ K⁻¹) is due to the formation of oxygen vacancies and spin-state transitions associated with Co³⁺ [102].The temperature dependence of σ shows the typical behavior where the dominant conductivity mechanism changes from small adiabatic polaron hopping to carrier diminution caused by oxygen lattice loss (cf. Section 2.5). For x = 0, the maximum conductivity amounts to about 27 S cm⁻¹ at 645 °C, x = 0.5 to about 59 S cm⁻¹ at 535°C, while for x = 1, it increases to about 118 S cm⁻¹ at 450 °C [39]. The improvement of the surface exchange coefficient by about two orders of magnitude at 750 °C from 2.55 × 10⁻⁵ cm s⁻¹ for x = 0 to 2.20 × 10⁻³ cm s⁻¹ for x = 1.0 was similar to LaCoO₃ attributed to electron occupation of the crystal field d state near Fermi level and with the buildup of surface charge so as to enhance the electron transfer between a surface cation and a potentially catalyzed species [6]. Similar to SF_1.5M [103], the electrochemical performance of S_xF_1.4Co_0.1M can be further improved by Sr deficiency. Sr-deficiency shrinks the cubic crystal lattice. The TEC value first decreases from 16.40 × 10⁻⁶ K⁻¹ for x = 0 to the minimum of 15.62 × 10⁻⁶ K⁻¹ at x = 1.950 and then increases to 16.16 × 10⁻⁶ K⁻¹ for x = 1.900. The processes of Fe³⁺ + Mo⁵⁺ ⇔ Fe²⁺ + Mo⁶⁺ and Co³⁺ + Mo⁵⁺ ⇔ Co²⁺ + Mo⁶⁺ equilibriums were not obviously affected by increasing the number of Sr-site deficiencies. On the other hand, the conductivity increases slightly up to a maximum of ~27 S cm⁻¹ for S_1.95F_1.4Co_0.1M at 500 °C where the dominant conductivity mechanism changes from small adiabatic polaron hopping to carrier diminution caused by oxygen lattice loss (cf. Section 2.5) and when decreases with increasing x again to S_1.9F_1.4Co_0.1M. An anode-supported single cell with a thin scandia-stabilized yttria (ScSZ) electrolyte film (11 µm) on a Ni-ScSZ anode and a CSO interlayer to the S_1.95F_1.4Co_0.1M cathode showed a P_max of 1.16 W cm⁻² at 800 °C (cf. Table 5) [73].

Active cobalt metal nanoparticles are in situ exsolved in reducing atmosphere from the parent SF_1.3Co_0.2M. The maximum electrical conductivity in 5 %H₂/N₂ at 600 °C amounts to 13.9 S cm⁻¹. SOFCs achieved maximum power densities at 850 °C of 1.09, 0.981 and 0.29 W cm⁻² when hydrogen, syngas and methane were used as fuel, respectively (cf. Table 5 and

Table 6. Performance of SF_1+xM-based SOFCs operated with hydrocarbons.

Configuration Anode-Electrolyte-Cathode	Fuel	del, µm	T, °C	Pmax, W/cm2	Ref.
SFM/LSGM/BSCF	CH4	300	850	0.605	[61]
			800	0.429
SF1.33M/LGSM/LSCF	CH4	300	800	0.13	[34]
SF1.33M/LGSM/LSCF SF1.5M/LGSM/LSCF	CH4	NA	800	0.079 0.041	[29]
SF1.5M/LSGM/SF1.5M	CH4	265	900	0.23	[99]
SF1.5M/LSGM/SF1.5M	CH4	400	900	0.250	[31]
			850	0.125
Ni-SF1.5M/LGSM/LSCF	CH4	300	800	0.663	[99]
SF1.3Co0.3M/LSGM/LSCF	CH4	170	850	0.290	[74]
			750	0.151
			700	0.057
SFM-YSZ/YSZ/YSZ-LSFSc	C3H8	24	800	0.331	[52]
			750	0.173
SF1.4M/LSGM/BSCF SF1.5M/LSGM/BSCF SF1.6M/LSGM/BSCF	CH3OH	300	800	0.415 0.395 0.382	[22]
SF1.4M/LSGM/BSCF SF1.5M/LSGM/BSCF SF1.6M/LSGM/BSCF	CH3OH	300	750	0.341 0.297 0.205	[22]

). Continuous operation in hydrogen for 115 hs, in syngas for 190 hs and in methane for 300 hs did not show degradations [74].Substitution of Fe²⁺/Fe³⁺ by Co³⁺ in SFC_xM decreases B-site ordering and increases the conductivity monotonically up to a metallic behavior for x ≥ 0.15 with σ ≥ 135 S cm⁻¹. Thereby, the Co ion is in the trivalent, high-spin state [104].

Ni²⁺ substitutes Fe²⁺ because the ionic radius of Ni²⁺(69 pm] [21]) is smaller than that of Fe²⁺ (78 pm [21]) while larger than Fe³⁺ (64.5 pm [21]). It promotes oxygen vacancy formation on the SF_1.5M surface, which in turn improves the electrochemical performance toward fuel oxidation [105]. The conductivity reaches 60 S cm⁻¹ at 450 °C in air where the dominant conductivity mechanism changes from small adiabatic polaron hopping to carrier diminution caused by oxygen lattice loss (cf. Section 2.5). At the same composition, the lowest cathode polarization occurs, which is only 50 % of the SF_1.5M value. The thermal expansion coefficient increases from 15.6 × 10⁻⁶ K⁻¹ to 18.1 × 10⁻⁶ K⁻¹ with x varying from 0.05 to 0.4. This increases the thermal mismatch with the electrolyte. The polarization resistance of an SF_1.4Ni_0.1M cathode was approximately 50% of that of the SF_1.5M cathode. The maximal power density amounts to 1.77 W cm⁻² at 800 °C [40], exceeding the improvement achieved by A-site substitution (cf. Table 5). SF_1.5−xNi_xM, after reduction at 750 °C, possesses a single-phase perovskite structure up to x = 0.1. For higher Ni content (x = 0.2 and 0.3), a NiO impurity phase appears, while for x = 0.4, a Sr₃FeMoO_6.5 phase gives evidence of SF_1.5−xNi_xM decomposition. At 800 °C, Sr₃FeMoO_6.5 was also formed in the x = 0.1 sample. The conductivity of SF_1.4Ni_0.1M in H₂ monotonously increases in the temperature range 600 to 800 °C reaching a maximum value of 20.6 S cm⁻¹. The minimum anode polarization resistance occurs at the same composition. SOFCs show stable performance for 15 h providing a maximum power density of 0.380 W cm⁻² at 750 °C (cf. Table 5) [41]. Thus, similar to a Ni solubility limit of 13 to 18 % in the La_0.8Sr_0.2Cr_1−xNixO_3−δ lattice [106], a solubility of ~20% may be considered for SF_1.5M [41].

The introduction of a slight Sr-site deficiency favors the metal precipitation in reducing atmospheres. By this way a Ni-Fe alloy phase was created in S_1.9F_1.4Ni_0.1M which improved the catalytic activity, the redox stability and the SOFC maximum power density reaching 0.968 W cm⁻² at 800 °C with H₂ as a fuel and 0.277 W cm⁻² at 800 °C with C₃H₈ as a fuel (cf. Table 5 and Table 6) [35]. By dispersing a small amount of Ni (~2 wt%) on the SF_1.5M ceramic anode, the performance of SOFCs with LSGM as electrolyte and LSCF as a cathode has been significantly improved both in H₂ and CH₄ as the fuel and ambient air as the oxidant (cf. Table 5 and Table 6). It is very stable when operating with CH₄ fuel and provides the highest maximal power density, 0.663 W cm⁻², reported for CH₄ fuel at 800 °C (Table 6). This way, the carbon formation on the Ni surface can be suppressed by controlling the dispersion and loading of Ni on the SF_1.5M anodes [99].

Nb substitutes are either Mo or Fe since the ionic radii of Nb⁴⁺ (68 pm [21]) and Nb⁵⁺ (64 pm [21]) are only slightly larger than that of Mo⁵⁺ (61 pm [21]) and Mo⁶⁺ (59 pm [21]) and high-spin Fe³⁺ (64.5 pm [21]), expanding the lattice [21]. Under reducing conditions, Fe³⁺ is easily reduced. Here, high-spin Fe³⁺ (64.5 pm) substitution by Nb⁵⁺ increases the stability of SF_1.5M. On the other hand, the crystal lattice expands even though the cation size of Nb⁵⁺ is smaller than that of Fe³⁺. This was attributed to the reduction of Fe³⁺ ions in air Fe³⁺ to Fe²⁺ with a larger ion radius (76 pm) in order to achieve electrical neutrality. An increase in the Fe²⁺ fraction from 36.4% in SF_1.5M to 49.5% in SF_1.4N_0.1M was proved by XRD [30]. Although this is not direct evidence for Fe³⁺ substitution by Nb⁴⁺, we accept this explanation here. Note that for Mo substitution, Nb exhibits lower mixed valences (+4/+5) than that of Mo (+5/+6). When Mo is substituted by Nb, the value of δ increases, demonstrating an increase in the oxygen vacancy concentration. Unfortunately, the thermal expansion coefficient values of SF_1.5M_0.5−xN_x powders increase from 15.6 × 10⁻⁶ K⁻¹ to 16.7 × 10⁻⁶ K⁻¹ when x ranges from 0.05 to 0.20, increasing the thermal mismatch with the electrolyte. The maximum conductivity is obtained for SF_1.5M_0.4N_0.1, amounting to 31 S cm⁻¹ at 550 °C where the dominant conductivity mechanism changes from small adiabatic polaron hopping to carrier diminution caused by oxygen lattice loss (cf. Section 2.5). The same composition exhibits the lowest polarization resistance. The power density of a Ni-YSZ anode-supported SOFC consisting of an SF_1.5M_0.5−xN_x cathode reaches 1.1 W cm⁻² at 800 °C (cf. Table 5). No obvious performance degradation is observed over 15 h at 750 °C with wet H₂ (3 % H₂O) as fuel and ambient air as the oxidant [45]. The electrical conductivities of SF_1.4N_0.1M increase gradually with temperature up to the maximum value at 600 °C, where the dominant conductivity mechanism changes from small adiabatic polaron hopping to carrier diminution caused by oxygen lattice loss (cf. Section 2.5), and then decreases. At 600 °C, the substitution of 6.7 % Fe²⁺/Fe³⁺ by Nb⁵⁺ increases the conductivity from 17.62 to 27.61 S cm⁻¹ in air and from 11.11 to 15.86 S cm⁻¹ in 3 %H₂O/H₂. Furthermore, SFe_1.4N_0.1M exhibits a lower polarization resistance under both oxidizing and reducing atmospheres. A symmetrical SOFC showed excellent redox stability and provided at 800 °C a maximum power density of 0.531 W cm⁻² (cf. Table 5). SFe_1.4N_0.1M-based SOFCs maintained a stable output over ten redox cycles at 750 °C, while for SF1.5M one, the output declined obviously after seven cycles [30].

An SFM_0.8N_0.2 anode shows outstanding performances with high resistance against carbon build-up and redox cycling in hydrocarbon fuels. At 800 °C, it shows electrical conductivity of 5.3 S cm⁻¹ in 5% H₂ and provides maximum power densities of 0.520 and 0.380 W cm⁻² when using H₂ and CH₄ as the fuel, respectively (cf. Table 5 and Table 6). After six redox cycles, there is no degradation observed in the cell voltage. Under different current loads, the SOFC showed impressive performance stability [96].

Fe²⁺ (78 pm [21])/Fe³⁺ (64.5 pm [21]) substitution by Sc³⁺ (74.5 pm [21]) expands the lattice. Samples of SF_1.5−xSc_xM with x between 0.05 and 0.1 display the same initial cubic perovskite single-phase without no impurity. On the other hand, a Sc₂O₃ phase is observed when x is further increased up to 0.20. The substitution practically does not change the thermal expansion coefficient. The maximum conductivities of SF_1.5M and SF_1.45Sc_0.05M reach 17 S cm⁻¹ and 27 S cm⁻¹ in the temperature regions of 500–550 °C and 600–650 °C, respectively. The conductivity maximum is caused by a change in the conductivity mechanism from small adiabatic polaron hopping to carrier diminution caused by oxygen lattice loss (cf. Section 2.5). Enhancing the conductivity and oxygen vacancy by Sc³⁺ at the B-site of SFM promotes the reduction reaction of the adsorbed oxygen atom into an oxygen ion. Here, the dissociation of adsorbed molecular oxygen becomes the rate-limiting step. Ni-YSZ anode supported SOFCs with LSGM as an electrolyte, and an SDC layer at the cathode interface provides 800 °C maximum power densities of 1.23 and 0.91 W cm⁻² for SF_1.45Sc_0.05M and SF_1.5M, respectively. No obvious degradation of the SOFC performance occurred in a 100 h test at 750 °C [42].

Sn⁴⁺ favors the cubic structure of SrSnO₃. During the fabrication of Sr₂Fe_1.5Mo_0.5−xSn_xO_6−δ, tin adopts both the 2+ and 4+ valence. The substitution of Mo⁵⁺/Mo⁶⁺ by Sn²⁺/Sn⁴⁺ increases the TEC in the range of 20 °C to 900 °C from 16.26 × 10⁻⁶ to 20.32 × 10⁻⁶ K⁻¹ when x increases from 0 to 0.5 increasing the thermal mismatch with the electrolyte. An electrolyte-supported single cell, consisting of SF_1.5M anode, LSGM electrolyte and SF_1.5M_0.2Sn_0.3 cathode, provided a power density of 0.618Wcm⁻² at 800 °C which is comparable with the SOFC performance one of the other B-site substitutions but higher than the one of a symmetrical SF_1.5M-based cell (cf. [101] and Table 5). No obvious SOFC degradation was observed within the 200 h operation at 800 °C [43].

4. Performance of Sr₂Fe_1+xMo_1−xO_6−δ-Based SOFCs

4.1. Polarization Resistance

Polarization resistance (R_p) is the resistance at the interface between the electrodes and the electrolyte. It is caused by the electron transfer resistance and the gas diffusion resistance at the electrodes and reduces the open-circuit voltage of the SOFC. At high temperatures, the oxygen ion transport process is significantly accelerated. Consequently, reducing the SOFC operating temperature decreases the electrode kinetics and results in large interfacial polarization resistances. This effect is most pronounced for the oxygen reduction reaction at the cathode [6]. Thus, R_p is an effective parameter to probe the catalytic activity of SOFC cathode for the oxygen reduction reaction (ORR). The relatively low operation temperature of IT-SOFCs decreases the electrode kinetics and the catalytic activity of the ORR and inhibits the diffusion of oxygen [107]. In this case, the performance of the cathode becomes a limiting factor of IT-SOFC performance. Here, R_p is affected by the generation of oxygen vacancies at the electrode/electrolyte interface region induced by polarization [108], the increased concentration of oxygen vacancies by increasing the Fe/Mo ratio in SF_1+xM enhancing catalytic activity, and the sintering temperature [101]. In order to enhance the catalytic activity of the ORR, significant effort has been devoted to studying new cathode materials by metal element substitution or doping while keeping the cubic crystal structure of the SF_1+xM materials.

R_p generally varies with oxygen partial pressure. It accounts for a number of physicochemical reactions: (i) molecular oxygen adsorption on the catalyst surface, (ii) dissociation of adsorbed molecular oxygen, (iii) ionization of adsorbed oxygen atom, (iv) migration of oxygen ions to the triple phase boundary (TPB), (v) ionization of oxygen ions at the TPB and (iv) charge transfer at the TPB. Since R_p and oxygen partial pressure are connected by a power law specific for each of the physicochemical reactions, studying the effect of oxygen partial pressure on R_p allows analyzing the total reaction rate-limiting physicochemical reaction [42].

Electrochemical impedance spectroscopy (EIS) is an important diagnostic tool for the evaluation of polarization resistance. However, the impedance spectrum of a SOFC convolutes anode and cathode behavior, even when using reference electrodes. A simple equivalent circuit of a SOFC is a series connection of two constant phase elements CPE in parallel with a resistance R and an ohmic resistance R_ohm overall ohmic resistance including the electrolyte resistance, electrode ohmic resistance and lead resistance, i.e., (R_HF||CPE_HF)-R_ohm-(R_LF||CPE_LF) [101,109]. The resistance at the high-frequency R_HF is probably associated with the charge-transfer processes, which include the ion-transfer process occurring at the electrode/electrolyte interfaces and the electron-transfer process accompanying the oxygen reduction reaction. The low-frequency part (R_LF||CPE_LF) can be attributed to the diffusion processes, which include the adsorption–desorption of oxygen, oxygen diffusion at the gas–cathode interface and surface diffusion of intermediate oxygen species. The difference between real axes intercepts of the impedance plot represents the polarization resistance R_p = R_HF + R_LF [109]. This equivalent circuit yields two circular arcs shifted along the ReZ axis by the amount of R_ohm. Consequently, the high-frequency intercept on the real axis represents the ohmic resistance of the cell (R_ohm). The low-frequency intercept on the real axis represents the total cell resistance (R_total). The difference between the two is the electrode polarization resistance (R_p), including the contribution from both the anode and cathode (Figure 3).

Table 7. Polarization resistances of operational SOCFs consisting of SF_1+xM ceramics.

Configuration Anode-Electrolyte-Cathode	T, °C	Rp, Ω cm2	Ref.
SFM/LSGM/SDC/SmBC2	850	0.284	[60]
	800	0.327
	750	0.583
SFM-YSZ/YSZ/YSZ-LSFSc0.1O	750	0.52 2.11 1	[52]
SFM-YSZ/YSZ/YSZ-LSFSc0.1 SF1.2M-YSZ/YSZ/YSZ-LSFSc0.1 SF1.35M-YSZ/YSZ/YSZ-LSFSc0.1 SF1.5M-YSZ/YSZ/YSZ-LSFSc0.1	800	0.152 0.176 0.193 0.235	[52]
SF1.33M/LGSM/LSCF	800	~0.2	[34]
	750	0.26
	700	0.45
SF1.5M/LGSM/LSCF	850	0.40	[98]
	800	0.76
	750	1.73
SF1.3Co0.3M/LSGM/LSCF	850	0.152	[74]
	800	0.223
	750	0.369
	700	0.575
SF1.3Co0.3M/LSGM/LSCF	850	0.442 2	[74]
	800	0.842 2
	750	1.979 2
Ni-LDC/LDC/LGSM/SF1.33M	800	0.32	[101]
Ni-YSZ/YSZ/SDC/SF1.5M	750	0.42	[37]
	700	0.92
Ni-YSZ/YSZ/SDC/SF1.5M0.4N0.1	800	0.168	[45]
SDC-SF1.65M/LGSM/SF1.5M	750	0.11 0.27	[111]
S1.4C0.6F1.5M/LSGM/S1.4C0.6F1.5M	800	0.155	[38]
	750	0.179
	700	0.220
	650	0.359
SF1.2Co0.3M/LSGM/SF1.2Co0.3M	850	0.152	[74]
	800	0.223
	750	0.369
	700	0.575
SF1.5M/LSGM/SF1.5M0.2Sn0.3	800	0.22	[43]
	750	0.35
	700	0.71

¹ C₃H₈, ² CH₄.

lists the polarization resistances of operational SOFCs, i.e., including the contribution from both the anode and cathode under their corresponding operational conditions. Values determined under symmetrical atmospheres (without potential chemical gradient) were not considered since the oxygen chemical potential gradient between the cathode and anode of the SOFC and the current across the cell decreased the polarization resistance [17,110]. The lowest R_p value at 800 °C, i.e., 0.152 Ω cm², was obtained for an SFM-impregnated YSZ anode in an SFM-YSZ/YSZ/YSZ-LSFSc_0.1 SOFC configuration [53]. At lower temperatures, the S_1.4C_0.6F_1.5M/LSGM/S_1.4C_0.6F_1.5M SOFC configuration with 35 µm thick electrolytes shows low polarization resistances. Decreasing the electrolyte thickness will further enhance the fuel cell performance [38].

Feeding the SOFC with hydrocarbons increases R_p at 800 °C by about a factor of four [52,74]. A similar value at the same temperature was also found in a (PrBa)_0.95(Fe_0.9Mo_0.1)₂O_5+δ/LSGM/PrBaCo₂O_5+δ(PBCO) SOFC configuration when the fuel was switched from H₂ to 3% H₂O/CH₄ [112]. This factor increases with decreasing temperature as a consequence of different activation energies of the involved electrochemical reactions [74].

Generally, the combined area-specific resistivity (ASR) of a SOFC (electrolyte, anode and cathode) should be below 0.5 Ωcm², ideally approaching 0.1 Ωcm² to ensure high power densities. Thereby, about 60% is attributed to the electrolyte [1]. Thus, the R_p values listed in Table 7 are still far from the targets.

4.2. Sr₂Fe_1+xMo_1−xO_6−δ-Based SOFCs Operated with Hydrogen Fuel

Initially, SF_1.33M and SF_1.5M were studied as anodes in parallel [29,34]. A single-phase double perovskite of SF_1.33M is formed by treatment in a reducing environment at 800 °C. SF_1.33M is compatible with LSGM and a ceria interlayer and shows remarkable electrochemical activity, carbon resistance with CH₄ as a fuel and sulfur tolerance in 100 ppm H₂S/H₂ [34]. Contrarily to S₂F_1.33M, S₂F_1.5M has already formed a single perovskite phase after the calcination in air. S₂F_1.33M shows a better single-cell performance than SF_1.5M, with H₂ and CH₄ as fuel attributed to a higher catalytic activity, but it suffers from redox stability [29].

Table 5 compiles the performance of SF_1+xM-based SOFCs operated with hydrogen fuel. The maximum power of SOFCs using A₂FeMoO_6−δ anodes and H₂ as fuel increases in the order: CaFM < BFM < SFM. These SOFCs use a thin CSO buffer layer between the electrolyte and anode to prevent the interdiffusion of ionic species. The poor cell performance of the CaFM anode is attributed to its decomposition at high temperatures and the low oxygen vacancy concentration. SFM exhibited a particularly favorable combination of high electrical conductivity, good thermal stability and thermal compatibility, and electrochemical performance [60]. Neither a composition of SF_1+xM_1−x [29,34,98] nor B-site substitution [96] significantly changes the SOFC performance. Improvement is achieved by dispersing a small amount of Ni (~2 wt%) on the SF_1.5M0.5 ceramic anode [99] and for a Sr-deficient anode material [35]. The best performance shows an SF_1.4M composition [22], corresponding approximately to the solubility of SMO in SrFeO_3−δ in air at 1200 °C [49,50]. Exsoluted Co nanoparticles boost the P_max value [74].

Concerning application as SOFC cathodes, an increase in performance was achieved by A-site substitution of Sr by Ba [37,44], B-site substitution of Fe by Ni [40], Fe by Sc [42], Fe by Co [74], Mo by Nb [45] and by a Sr deficiency [74]. In the case of nearly symmetrical (one of the electrodes modified) SOFCs, a substantial increase in P_max can be achieved by the A-site substitution of Sr by Ba at the cathode [38]. A noticeable improvement of P_max was demonstrated by a direct comparison of SF_1.5M and SF_1.4N_0.1M anodes [30] and by the application of SF_1.5M_0.2Sn_0.3 electrodes [43].

4.3. Sr₂Fe_1+xMo_1−xO_6−δ-Based SOFCs Operated with Hydrocarbon Fuel

The intended fuel of a SOFC is hydrogen. In this case, other fuels, such as natural gas and biomethane, should be first converted to hydrogen in the fuel cell’s reformer. With liquid hydrocarbon fueling, SOFCs have essentially the same specific energy as that of the fuel (~1 kWh kg⁻¹) [113]. Currently, most hydrogen is produced from fossil fuels, specifically natural gas. The production of H₂ requires additional external processes, e.g., steam-methane reforming or partial catalytic oxidation, water splitting by electrolysis, partial combustion of fuel–air or fuel–oxygen mixtures resulting in hydrogen- and carbon monoxide-rich syngas, as well as membrane separation or preferential oxidation. However, each of these steps requires energy. This decreases the overall system efficiency. On the one hand, SOFCs can oxidize essentially any fuel, from hydrogen to hydrocarbons to even carbon, because the electrolyte transports an oxygen ion, O²⁻. On the other hand, any available hydrocarbon-based resource (which includes not only fossil fuels but also, potentially, biomass and municipal solid waste) may be considered as a fuel. Double perovskites have attracted attention due to their beneficial catalytic activity for methane oxidation, reaching 80% at 530 °C [10]. An SFM_0.8N_0.2 anode shows outstanding performances with high resistance against carbon build-up and redox cycling in hydrocarbon fuels [97]. The mixed-valence Mo⁵⁺/Mo⁶⁺ and Fe³⁺/Fe⁴⁺ couples provide electronic conductivity, and the characteristic high oxygen vacancy concentration, as well as low oxygen ion migration barriers in SFMO, lead to a high ionic conductivity [33]. The ionic conductivity of SFMO is significantly higher than that of the commonly used La_0.8Sr_0.2MnO₃ cathode, and its electrical conductivity in both air and hydrogen environments meets the conductivity requirements for both anodes and cathodes [29]. The anode materials that operate directly with hydrocarbon fuels should be chemically stable in the CO₂ atmosphere because this is the main oxidation product formed in the anode compartment. SrF_1.5M is stable both under H₂ and pure CO₂ atmospheres [17]. SOFCs are able to convert the energy stored in any hydrocarbon fuel directly into electricity. However, sulfur species in the available hydrocarbon fuels will unfavorably react with the Ni catalyst in conventional nickel-yttrium-stabilized zirconia (Ni-YSZ) anode, resulting in severe anode sulfur poisoning and, thus, significant cell performance loss. SF_1+xM electrodes show an excellent low level of sulfur poisoning [31,95,114]. From all these points of view, half-metallic double-perovskites with a double-exchange conduction mechanism seem to be perfect candidates in fuel cells using hydrocarbons or alcohols as fuel. Table 6 compiles the performance of SF_1+xM-based SOFCs operated with hydrogen fuel.

The performance of SF_1+xM-based SOFCs with CH₄ and methanol as fuels is comparable with the state-of-the-art [115]. For instance, in [116], a novel on-cell micro-reformer, i.e., a noble-metal free NiSn/Al₂O₃ catalyst embedded Ni foam, was designed for efficient internal reforming of biogas in SOFCs. The NiSn bimetallic alloys were developed and characterized as the potential anode material and biogas reforming catalyst. Sn remained preferentially on the surface of the NiSn alloy to enhance both the carbon deposition resistance and sulfur tolerance NiSn/Al₂O₃ deposited on Ni foam and functioned as a catalyst layer, which proved with high catalytic activity as well as great stability toward biogas reforming reactions. In the button cell with the configuration NiSn/Al₂O₃|NiSn–Y_0.08Zr_0.92O₂|Y_0.08Zr_0.92O₂|Y_0.08Zr_0.92O₂–(La_0.8Sr_0.2)_0.95MnO₃, the peak power density of 0.946 W/cm² was achieved at 850 °C with the inlet gas of CH₄–CO₂–200 ppm H₂S, and conversion rate to methane reached around 95% with the discharge current density of 1.25 A/cm². This performance is comparable with the data in Table 6.

5. Conclusions

In this work, we reviewed the application of Sr₂FeMoO_6−δ (SFM) and Sr₂Fe_1−xMo_1−xO_6−δ (SF_1+xM) in LSGM-based SOFCs. These materials are stable in both oxidizing and reducing atmospheres enabling the use of both not only as an anode but also as a cathode and also in symmetrical SOFCs. They provide both electron and ionic conductivity extending the triple phase boundary compared to purely electronic or purely ionic conductors. Their properties can be tailored to a particular application by the substitution of different metal cations into their lattices. SF_1+xM materials are excellent catalysts in hydrocarbon oxidation and can prevent carbon deposition due to the ability to exchange lattice oxygen with the gaseous phase. Moreover, they are sulfur tolerant. This opens the way to direct hydrocarbon-fueled SOFCs eliminating the need for external fuel reforming and sulfur removal components. As such, SOFCs can be greatly simplified and operate with much higher overall efficiency, thus contributing to the solution to the lack of energy problem in our modern world.

Nevertheless, there are still some problems that need to be solved for commercial application: (i) A vapor phase deposition technology for SF1+xM deposition with a reproducible composition has to be developed. (ii) The composition of an SF1+xM cathode should be adapted to the used electrolyte. It will be different in the case of LSGM and YSZ electrolytes. (iii) A vapor phase deposition method of porous, composite anode deposition is required. Catalytic properties may be further improved by impregnation and exsolution methods. (iv) An appropriate carrier material of the SOFC thermally matched to the electrodes and the electrolyte must be selected.