Recent Progress in the Design, Characterisation and Application of LaAlO3- and LaGaO3-Based Solid Oxide Fuel Cell Electrolytes

Solid oxide fuel cells (SOFCs) are efficient electrochemical devices that allow for the direct conversion of fuels (their chemical energy) into electricity. Although conventional SOFCs based on YSZ electrolytes are widely used from laboratory to commercial scales, the development of alternative ion-conducting electrolytes is of great importance for improving SOFC performance at reduced operation temperatures. The review summarizes the basic information on two representative families of oxygen-conducting electrolytes: doped lanthanum aluminates (LaAlO3) and lanthanum gallates (LaGaO3). Their preparation features, chemical stability, thermal behaviour and transport properties are thoroughly analyzed in terms of their connection with the target functional parameters of related SOFCs. The data presented here will serve as a starting point for further studies of La-based perovskites, including in the fields of solid state ionics, electrochemistry and applied energy.


Introduction
The long-term goal of a large body of relevant scientific research is to find a solution to the problem of providing industrial and domestic human needs with renewable and environmentally friendly energy [1,2]. The main fields of sustainable energy concern both the search for renewable energy sources [3][4][5] and methods for the production of ecological types of energy [6][7][8][9], which differ from traditional types based on hydrocarbon fuel [10][11][12]. The tasks relating to sustainable energy also include the development of technologies for the use of non-renewable energy sources: efficient waste-processing [13][14][15], the construction of nuclear mini-reactors [16], and the creation of energy devices based on the direct conversion of various types of energy into electrical and thermal energy [17][18][19]. A well-known device for directly converting the chemical energy of fuels into electrical energy is a fuel cell [19][20][21]. If the electrolyte in the fuel cell is a ceramic material that is permeable to oxygen ions, it is referred to as a solid oxide fuel cell (SOFC) [21][22][23][24][25].
The advantages of SOFCs are the absence of noble metals in their composition and the flexibility of fuel types [24,26,27], while the disadvantages include high operating temperatures, which lead to chemical interactions between the parts of the SOFCs [28,29] and fast degradation [30][31][32]. The high temperatures required to operate SOFCs with conventional electrolytes on the basis of yttria-stabilized zirconia (YSZ) lead to the formation of metastable phases, sealing, and thermal and chemical incompatibility with electrode materials [33][34][35].
One of the ways to solve the described problem is to decrease the operating temperature of SOFCs and develop fuel cells operating at medium- [36][37][38] and low-temperature electrode materials [33][34][35].
One of the ways to solve the described problem is to decrease the operating temperature of SOFCs and develop fuel cells operating at medium- [36][37][38] and low-temperature ranges [39,40]. This has resulted in investigations into new classes of electrolytes [41][42][43][44] and the development of SOFCs enhanced with nanostructured materials [45,46]. The utilization of nanotechnologies, energy production and energy storage devices is extremely prospective due to their durability, sustainability, long lifetime, and low cost [47]. Among the alternative electrolytes used in low-and intermediate-temperature SOFCs, complex oxides with an ABO3-type perovskite structure have attracted specific attention due to their high efficiency in energy conversion [48][49][50]. Sr, Mg-doped lanthanum gallate (LaGaO3), possessing a high oxide ionic conductivity, which was established originally by Ishihara et al. in 1994 [51], was first used in SOFCs by Feng and Goodenough in 1996 [52]. Later, much more economical materials based on doped lanthanum aluminate LaAlO3 were reported by Fung and Chen in 2011 [53].
It is worth noting that previous generalizing works on lanthanum aluminate were aimed at the synthesis and characterization of LaAlO3 phosphors (published by Kaur et al. in 2013 [54]) and at some properties and applications of LaAlO3 not concerned with SOFCs (observed by Rizwan et al., in 2019) [55]. There is only one overview dedicated to Sr, Mg-doped LaGaO3 oxides as electrolytes for intermediate-temperature solid oxide fuel cells: this was published by Morales et al. in 2016 [56]. The present overview is dedicated to recent progress in the design, characterization and application of electrolyte materials for SOFCs based on the LaGaO3 and LaAlO3 complex oxides with a perovskite structure. Both these phases constitute a family of oxygen-conducting electrolytes, while other La-based perovskites (LaScO3, LaInO3, LaYO3, LaYbO3) exhibit protonic conductivity as well [49]. For this reason, scandates, indates, yttrates, and ytterbates are not considered within the present review.
A schematic image of an ABO3 perovskite structure is shown in Figure 1a,b. Typically, the size of A-site cations is larger than that of B-site cations, but is roughly close to that of the oxygen ions. The A-site cations are surrounded by 12 oxygen-ions in a cubo-octahedral coordination; the B-site cations are surrounded by 6 oxygen-ions in an octahedral coordination. In an ideal perovskite structure, BO6 octahedrons are linked at the corners, thus exhibiting the cubic Pm3m space group.  [57]; (c) a rhombohedral crystal structure (for example, LaAlO3). Reproduced from [58] with permission  [57]; (c) a rhombohedral crystal structure (for example, LaAlO 3 ). Reproduced from [58] with permission from the American Physical Society, 2016; (d) an orthorhombic crystal structure (for example, LaGaO 3 ) Reproduced from [59] with permission by Elsevier Ltd. (Amsterdam, The Netherlands), 2004.
If the complex oxide structure differs from the ideal perovskite structure by having rhombohedral or orthorhombic distortions due to the BO 6 octahedron arrangement, the stability of this oxide can be evaluated with the Goldsmith tolerance factor t equation [60] as follows: where r A , r B , r O are the ionic radii of the A-, B-cations, and oxygen ions, respectively. If t is equal to 1, an ideal cubic-type perovskite structure is formed. If t deviates from 1, various distortions occur in the ideal perovskite structure. The first reason for such distortions is the rotation of the BO 6 octahedron without axis deformation, which causes tilting around the large A-cations. Take, for example, the rhombohedral structure of LaAlO 3 at room temperature presented in Figure 1c. The second reason consists of the appearance of the irregularity in the BO 6 octahedrons due to the non-centrality of the B-site cations. Consider, for example, the orthorhombic structure of LaGaO 3 at room temperature presented in Figure 1d. 3
Employing conventional solid-state reaction technology, LaAlO 3 samples can be directly obtained from La 2 O 3 and Al 2 O 3 . In [61], these initial reactants were ground down, homogenized in a water media, desiccated and pressed into pellets annealed at a temperature range of 780-1100 • C. Such a temperature regime allows for single-phase LaAlO 3 samples to be prepared. A similar technology was used in work [62] to synthesize LaAl 1−x Zn x O 3−δ (here, δ is the oxygen nonstoichiometry; δ = x/2 in the case of oxidation-state stable cations and one charge state difference between the host and impurity cations). As initial reagents, stoichiometric amounts of aluminium and zinc oxides were milled in ethanol. The heat treatment included five 24-h stages at a temperature range of 700-1100 • C. Single-phased LaAlO 3 and LaAl 0.95 Zn 0.05 O 3−δ were obtained at 1250 and 1200 • C, respectively.
Fabian et al. [65] synthesised Ca-doped LaAlO 3 powders using the mechanochemical method. Oxide powders of La 2 O 3 , γ-Al 2 O 3 and CaO in appropriate proportions were milled in a planetary mill at 600 rpm. The prepared powders were pressed into disks with polyethylene glycol as a plasticizer. The LaAlO 3 and La 1−x Ca x AlO 3−δ pellets were sintered at 1700 and 1450 • C, respectively, to achieve a desirable ceramic densification. LaAlO 3 complex oxides were prepared starting from water solutions of aluminium and lanthanum chlorides with a molar ratio for the metal components of 1:1 [66]. Solutions with high and low concentrations of starting reagents were mixed with an ammonium solution serving as a precipitation agent. The obtained gels were filtered, washed with distilled water and dried twice, at 25 • C for 24 h and at 100 • C for 2 h. The prepared powders were calcined at a temperature range of 600-900 • C for 1 h. The powder obtained from the high-concentration solution was annealed at 900 • C for 2 h in air, then ground in a rotary mill with zirconia balls in dry ethanol, pressed and calcined at 1300-1500 • C for 2 h.
The most widely used technology for the preparation of LaAlO 3 and its doped derivatives is the pyrolysis of organic-nitrate compositions, known as the sol-gel [68,69,74] or autocombustion methods (or self-propagating high-temperature synthesis, and the Pechini method) [70][71][72][73]75]. Utilizing different fuels during the pyrolysis process coupled with various annealing temperatures affects the crystallinity, powder dispersity, and ceramics density, determining the functional properties of the obtained LaAlO 3 -based ceramic materials [74,76,77].
LaAlO 3 powders were prepared by Zhang et al. [68] from La(NO 3 ) 3 ·6H 2 O and Al(NO 3 ) 3 ·9H 2 O: they were dissolved in 2-methoxyethanol and then mixed with citric acid at a molar ratio of 1:1 to the total content of metal ions. The obtained solutions were  [69]. The molar ratio of glycine and EDTA to overall metal-ion content was 1.2:1:1; the ratio of NH 3 ·H 2 O to EDTA was adjusted to 1.15:1. The aqueous solution of metal nitrates was prepared and heated at 80 • C, and then the EDTA-ammonia solution and glycine were added. The colourless solution was dried, and the obtained brown resin was calcined at 350 • C; it was then ground down and calcined at 600-1000 • C for 3 h. The obtained powders were finally pressed into disks followed by sintering at 1600-1700 • C for 5 h.
According to Adak and Pramanik [70], LaAlO 3 was prepared from a 10% aqueous polyvinyl alcohol precursor that was added to a solution obtained from La 2 O 3 (99%) dissolved in nitric acid and Al(NO 3 ) 3 ·9H 2 O. The organic-nitrate mixture was evaporated at 200 • C until dehydration; then, spontaneous decomposition and the formation of a voluminous black fluffy powder occurred. The obtained powders were ground down and annealed at 600-800 • C for 2 h to form a pure phase.
Verma et al. [71]  O was used as an organic fuel. The metal nitrates and citric acid were dissolved in distilled water, resulting in the formation of a transparent solution. The pH value required for proper combustion was achieved by the addition of ammonia solution. The self-propagating synthesis method is shown in Figure 2a. The obtained powders were calcined at 700 • C for 4 h, then pressed into pellets and sintered at 1300 • C for 8 h to achieve 92-to-96% relative density, depending on the aluminate composition. ramic materials [74,76,77].
LaAlO3 powders were prepared by Zhang et al. [68] from La(NO3)3·6H2O and Al(NO3)3·9H2O: they were dissolved in 2-methoxyethanol and then mixed with citric acid at a molar ratio of 1:1 to the total content of metal ions. The obtained solutions were heated and dried at 80 °C until gelatinous LaAlO3 precursors were obtained, which were then calcined at 600-900 °C for 2 h.
According to Adak and Pramanik [70], LaAlO3 was prepared from a 10% aqueous polyvinyl alcohol precursor that was added to a solution obtained from La2O3 (99%) dissolved in nitric acid and Al(NO3)3·9H2O. The organic-nitrate mixture was evaporated at 200 °C until dehydration; then, spontaneous decomposition and the formation of a voluminous black fluffy powder occurred. The obtained powders were ground down and annealed at 600-800 °C for 2 h to form a pure phase.
Verma et al. [71] synthesized LaAlO3 and La0.9−xSr0.1BaxAl0.9Mg0.1O3−δ (x = 0.00, 0.01 and 0.03) samples from initial reagents composed of La(NO3)3·H2O, Sr(NO3)2, Ba(NO3)2, Al(NO3)3·6H2O and Mg(NO3)2·6H2O initial reagents. C6H8O7·H2O was used as an organic fuel. The metal nitrates and citric acid were dissolved in distilled water, resulting in the formation of a transparent solution. The pH value required for proper combustion was achieved by the addition of ammonia solution. The self-propagating synthesis method is shown in Figure 2a. The obtained powders were calcined at 700 °C for 4 h, then pressed into pellets and sintered at 1300 °C for 8 h to achieve 92-to-96% relative density, depending on the aluminate composition.  Reproduced from [71] with permission from Springer Nature (Berlin/Heidelberg, Germany), 2021; (b) XRD patterns for LaAlO 3 powders prepared and calcined at a temperature range of 600-900 • C for 1 h on each stage. Reproduced from [66] with permission by Elsevier Ltd., 2013; (c) pore size distributions of LaAlO 3 powder bodies calcined at 900 • C for 2 h. Reproduced from [66] with permission by Elsevier Ltd., 2013; (d) TEM image of LaAlO 3 powder calcined at 900 • C for 2 h. Reproduced from [66] with permission by Elsevier Ltd., 2013. The literature shows that the annealing temperature of the precursor powders plays a significant role in complex oxide synthesis: this regulates the density of the final polycrystalline ceramic samples [78]. For practical applications, it is important to obtain LaAlO 3 -based samples with a narrow distribution of fine-grained particles. These requirements were fulfilled in [66], where a fully converted LaAlO 3 phase was formed at relatively low temperatures. In more detail, the authors developed a co-precipitation technique enabling the formation of single-phase LaAlO 3 powders after its calcination in air at 900 • C for 2 h (Figure 2b). A narrow particle size distribution for LaAlO 3 powder was achieved in [66], where milling in an ethanol medium was conducted. As shown in Figure 2c, the milled LaAlO 3 powder exhibited mono-modal pore size distribution. The TEM image (Figure 2d) demonstrates that the calcined powder consisted of isometric particles of up to 15 nm in size. The use of a precursor solution with a high concentration of metal chlorides and ammonia allowed for the researchers to realize gel homogeneity and the direct synthesis of LaAlO 3 .
A Rietveld analysis of the XRD pattern confirmed the presence of a pure perovskite phase with a rhombohedral structure, referring to the R-3c space group. Reference [66] calculated unit cell parameters for the LaAlO 3 sample (a = 5.3556(1) Å and c = 13.1518(2) Å) agreed well with results from neutron powder diffraction [79]. The primitive LaAlO 3 cell consists of two formula units, as shown in Figure 1b. The rotation of AlO 6 octahedra is caused by changes to the θ angle (Al-O-Al). Above 540 • C, a phase transition from the rhombohedral to cubic structure was observed for LaAlO 3 [79]. The cubic lattice of LaAlO 3 with a unit cell parameter of a = 3.8106(1) Å corresponds to the Pm3m space group [79] (see Figure 1a).
Concluding the chapter about the synthesis methods of doped LaAlO 3 oxides, from the perspective of their use in SOFCs, the co-precipitation method should be noted as the most optimal synthetic method. The co-precipitation method with a subsequent sintering of samples at 900 • C is well-approved and allows for both single-phase powders with a narrow nano-size particle distribution and ceramic samples with high relative densities to be obtained.

Functional Properties
LaAlO 3 , a basic (undoped) lanthanum aluminate, has very low electrical conductivity, equal to around 1 × 10 −6 S cm −1 at 900 • C [75]. La-site doping of LaAlO 3 with strontium enhances electrical conductivity because it improves the oxygen vacancy concentration responsible for oxygen-ion transport (Equation (2), [80]). Al-site modification of LaAlO 3 with acceptor dopants (for example, magnesium) can also increase the total and ionic conductivities (see Figure 3a). The possibility of forming good oxygen-ionic conductivity by doping LaAlO3 oxides has promoted studies on their potential application in SOFCs [53,65,71,[82][83][84][85][86][87][88][89][90]. The The possibility of forming good oxygen-ionic conductivity by doping LaAlO 3 oxides has promoted studies on their potential application in SOFCs [53,65,71,[82][83][84][85][86][87][88][89][90]. The codoping strategy is a beneficial way to further increase ionic conductivity [80,82,83,87]; this is due to the fact that, along with Equation (2), an additional quantity of oxygen vacancies can be formed according to the following mechanism [80]: According to the results of [53], the simultaneous doping of LaAlO 3 with barium and yttrium drastically enhanced ionic transport. For example, the total conductivity of La 0.9 Ba 0.1 Al 0.9 Y 0.1 O 3−δ at 800 • C was close to that of YSZ (2 × 10 −2 S cm −1 ), as shown in Figure 3b. There are various ways to tailor the transport properties of LaAlO 3 -based materials. For example, the doping of (La,Sr)AlO 3 with manganese resulted in total conductivity rising due to the substitution of Mn 3+ ions, which were transformed into Mn 2+ and Mn 4+ ions at the Al 3+ position, enhancing an electronic contribution [75,84]. Therefore, co-doped (La,Sr)(Al,Mn)O 3 is attributed to mixed ionic-electronic conductors (MIEC). The Pr-doping of (La,Sr)AlO 3 had a positive influence on transport properties due to the suppression of grain boundary resistivity [85], and the isovalent substitution of La 3+ -ions with Sm 3+ -ions in (La,Sr)AlO 3−δ resulted in the formation of a pronounced mixed ion-electron conduction [88] due to the generation of more electrons than in the case of the aliovalent substitution of La 3+ ions with Ba 2+ ions.
The electrical conductivity values of LaAlO 3 -based ceramic materials are summarized in Table 1. Analysis of these data confirms that the simultaneous modification of both sublattices of LaAlO 3 results in improved conductivity compared to those reached using single doping approaches (see Figure A1). However, it should be noted that the Sr-and Mgco-doped LaAlO 3 materials exhibit mixed ionic-electronic conduction in air atmospheres over a wide temperature range (800-1400 • C, see Figure 3c), while predominant ionic transport occurs for more reduced atmospheres (for example, wet hydrogen). This is typical behaviour for various La-based perovskites [49] as well as for other perovskiterelated ion-conducting electrolytes [91].
Thermal expansion coefficients (TECs) play an important role in material selection when seeking to avoid thermal incompatibilities between various parts of SOFCs. According to da Silva and de Miranda [75], the average TEC values for LaAlO 3 and La 0.8 Sr 0.2 AlO 3 were equal to around 11.4 × 10 −6 and 9.9 × 10 −6 K −1 , respectively. These data confirm that the TEC values of LaAlO 3 -based materials were close to those of the conventional YSZ electrolyte, i.e., 10.9 × 10 −6 K −1 [92].
The chemical compatibility of La 0.9 Sr 0.1 Al 0.97 Mg 0.03 O 3−δ as an electrolyte material with NiO-Ce 0.9 Gd 0.1 O 2−δ , Sr 0.88 Y 0.08 TiO 3−δ and La 0.75 Sr 0.25 Cr 0.5 Mn 0.5 O 3−δ as anode SOFC materials was thoroughly investigated in [87] using XRD analysis and scanning electron microscopy with energy-dispersive X-ray spectroscopy. The obtained results demonstrated that , confirmed that there were no chemical interactions between these components [93]. The authors noted that doped LaAlO 3 materials can serve as additives to the composite electrolytes and the anode-protective layers [93]. In addition, Mn-doped LaAlO 3 phases are considered a constituent part of the composite electrolytes, providing for the effective electrochemical oxidation of methane via ethylene and ethane [94]. Table 1. Total conductivity and activation energy values for LaAlO 3 ceramic materials. Figure A1 (see the Appendix A) provides a visualization of these data.

Sample
T

Applications in SOFCs
There are fragmentary data on the application of lanthanum aluminate electrolytes in SOFCs; see Figure 4.
For example, an SOFC was fabricated with 70% NiO-30% YSZ as an anode, SDC as an interlayer, La 0.9 Ba 0.1 Al 0.9 Y 0.1 O 3−δ (LBAYO) as an electrolyte and LSM as a cathode, and tested in [53]. LBAYO films with thicknesses of 63 and 74 µm were electrophoretically deposited on the LSM pellets with a diameter of 25 mm and a thickness of 2 mm. The LSM substrates and the deposited LBAYO films were then annealed at 1450 • C for 2 h to achieve full electrolyte densification. The thickness of the LBAYO film varied due to increases in the applied voltage. A NiO/YSZ anode with a thickness of 40 µm was screen-printed on the LBAYO/LSM sample and then sintered at 1500 • C for 6 h. To avoid chemical interactions between the NiO and the LBAYO film, an SDC buffer layer with a thickness of 10 µm was additionally screen-printed on the LBAYO film between the electrolyte and the anode. Humidified hydrogen was used as a fuel, while air was used as an oxidant. Figure 4a presents the SEM micrograph of the NiO-YSZ/SDC/LBAYO/LSM cell, indicating that after the annealing procedure, the LBAYO film was highly densified without cracks with a uniform thickness and a strong adhesion to the LSM substrate. The open-circuit voltage (OCV) values of the fabricated cells were 0.927 and 0.953 V, while the maximum power density values were 0.306 and 0.235 W cm −2 for the LBAYO electrolyte layers with thicknesses of 63 and 74 µm, respectively ( Figure 4b). The authors of the work attributed the sharp decrease in the cells' voltage at a small current to the slow oxygen reduction reaction kinetics for the LSM cathode. Nanomaterials 2022, 12,1991 8 of 32 addition, Mn-doped LaAlO3 phases are considered a constituent part of the composite electrolytes, providing for the effective electrochemical oxidation of methane via ethylene and ethane [94].

Applications in SOFCs
There are fragmentary data on the application of lanthanum aluminate electrolytes in SOFCs; see Figure 4. For example, an SOFC was fabricated with 70% NiO-30% YSZ as an anode, SDC as an interlayer, La0.9Ba0.1Al0.9Y0.1O3-δ (LBAYO) as an electrolyte and LSM as a cathode, and tested in [53]. LBAYO films with thicknesses of 63 and 74 μm were electrophoretically deposited on the LSM pellets with a diameter of 25 mm and a thickness of 2 mm. The LSM substrates and the deposited LBAYO films were then annealed at 1450 °C for 2 h to achieve full electrolyte densification. The thickness of the LBAYO film varied due to increases in the applied voltage. A NiO/YSZ anode with a thickness of 40 μm was screen-printed on the LBAYO/LSM sample and then sintered at 1500 °C for 6 h. To avoid chemical interactions between the NiO and the LBAYO film, an SDC buffer layer with a thickness of 10 μm was additionally screen-printed on the LBAYO film between the electrolyte and the anode. Humidified hydrogen was used as a fuel, while air was used as an oxidant. Figure  Another Ni-GDC/GDC/La0.9Sr0.1Al0.97Mg0.03O3-δ/GDC/La0.75Sr0.25FeO3−δ electrolyte-supported cell was tested in [87]. For this single cell with a La0.9Sr0.1Al0.97Mg0.03O3−δ electrolyte thickness of 550 μm, the OCV and Pmax values at 800 °C were found to be equal to 0.925 V and 19.5 mW cm −2 , respectively.  [87]. For this single cell with a La 0.9 Sr 0.1 Al 0.97 Mg 0.03 O 3−δ electrolyte thickness of 550 µm, the OCV and P max values at 800 • C were found to be equal to 0.925 V and 19.5 mW cm −2 , respectively. 3

Synthesis, Structure and Morphology
Historically, La 1−x Sr x Ga 1−y Mg y O 3−δ (LSGM) oxides were the first well-studied doped materials in the LaGaO 3 system. In 1998, Huang, Tichy and Goodenough determined the existence of single-phase La 1−x Sr x Ga 1−y Mg y O 3−0.5(x+y) perovskites while studying a LaO 1.5 -SrO-GaO 1.5 -MgO quasi-quaternary diagram [95] (see Figure 5a). This was possible due to variations in both x and y contents in a composition range of 0.05-0.30 with a step of 0.05. Sr-and Mg-co-doped LaGaO 3 samples were prepared from La 2 O 3 , SrCO 3 , Ga 2 O 3 , and MgO using solid-state reaction technology. The obtained powders were pressed into pellets and calcined at 1250 • C for 12 h. After remilling and repressing, the final pellets were finally sintered in air at 1470 • C for 24 h and quenched in a furnace at 500 • C.
Similar conventional techniques for synthesizing La 1−x Sr x Ga 1−y Mg y O 3−δ were used in other studies [96,97]. La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 3−δ samples were obtained from La 2 O 3 , SrCO 3 , Ga 2 O 3 and MgO sources, which were mixed and sintered in a platinum crucible at 1350 • C for 12 h [96]. The annealed powder was milled with zirconia balls and dried. Then, the powder was pressed into disks and sintered at 1350 • C in air, nitrogen or oxygen atmospheres for various times ranging from 20 min to 5 h. Moure 3 and MgO, which were mechanochemically activated in a Pulverizette 6 Fritsch planetary mill with stainless steel balls. The mixtures were synthesized at 1300 • C for 16 h; then after milling for 2 h and sieving with a 100-µm sieve, the powders were pressed into pellets and finally sintered at 1550 • C to form the desired ceramic samples. powder was pressed into disks and sintered at 1350 °C in air, nitrogen or oxygen atmospheres for various times ranging from 20 min to 5 h. Moure et al. [97] obtained La0.8Sr0.2Ga0.85Mg0.15O3-δ and La0.8Sr0.15Ga0.85Mg0.2O3-δ samples from La2O3, SrCO3, Ga2O3 and MgO, which were mechanochemically activated in a Pulverizette 6 Fritsch planetary mill with stainless steel balls. The mixtures were synthesized at 1300 °C for 16 h; then after milling for 2 h and sieving with a 100-μm sieve, the powders were pressed into pellets and finally sintered at 1550 °C to form the desired ceramic samples.  [98]. Mechanosynthesis was employed in a planetary mill (Retsch PM100, PM200) with tetragonal zirconia balls, according to a scheme presented in Figure 5b. The powders were pressed into disks that were sintered at 1300-1450 • C for 2-24 h.
As can be seen, the aforementioned methods (solid-state reaction synthesis and the mechanochemical route) that were conventionally used for the preparation of La 1−x Sr x Ga 1−y Mg y O 3−δ and its derivatives have two considerable disadvantages. First, high sintering temperatures (above 1450-1500 • C) are required for full densification of the pressed pellets [51]. This can influence the production cost of the final electrolyte materials. Second, the appearance of Sr 3 La 4 O 9 , SrLaGa 3 O 7 and/or SrLaGaO 4 impurity phases in La 1−x Sr x Ga 1−y Mg y O 3−δ samples was frequently observed. This was due to gallium evaporation [102], which resulted in the deterioration of the gallate material's ionic conductivity [51]. To solve the problems that arise during La 1−x Sr x Ga 1−y Mg y O 3−δ preparation, techniques based on co-precipitation [103,104], organic-nitrate precursors combustion [96,99,100,[105][106][107][108][109], self-propagating, high-temperature synthesis [110,111] and spray-pyrolysis [112] 3 and Mg(NO 3 ) 2 nitrates were used in these preparation methods. During synthesis with sol-gel technology, the required amounts of metal acetates and gallium nitrate solutions were mixed by stirring. An ammonia solution was then added, forming a white gel. This was aged at 25 • C for 72 h and heated at 150 • C for 8 h upon full water evaporation. The resulting product was fired at 300, 500 and 700 • C at varying times. Using the Pechini method, La 0.8 Sr 0.2 Ga 0.83 Mg 0.17 O 3−δ samples were prepared from a mixture of the necessary amounts of metal nitrate solutions at 25 • C: citric acid was then added. The citric acid was used to fulfil a mole ratio of citric acid/total cations around 1.5/1. After stirring the precursor solution, ethylene glycol was added in an equal amount to the citric acid. The obtained solution was heated at 150 • C for 12 h and resulted in a polymer-like solid material. This resin was slowly heated to 300 • C and, after several sintering stages, it was finally calcined at 1400 • C for 4 h [100]. The pressed La 0.85 Sr 0.15 Ga 0.8 Mg 0.2 O 3−δ samples were found to be single-phase after they were obtained via the Pechini method and annealed at 1400 • C for 6 h [105].
A La 0.8 Sr 0.2 Ga 0.85 Mg 0.15 O 3−δ sample was also obtained via the glycine-nitrate combustion method [106]. Ga, La 2 O 3 , MgO and SrCO 3 powders were dissolved in strong HNO 3 and mixed with water. Glycine was then added with a molar ratio of glycine/nitrate ions equal to 1:1. The glass beaker with the precursor glycine-nitrate solution was heated on a hot plate with spontaneous burning, which resulted in a white powder. Dense samples were formed at a temperature range of 1400-1550 • C for 6 h at each stage [106]. A similar method was used in [107] for the synthesis of La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 3−δ . The experimental procedure included the heating of the precursor glycine-nitrate solution at 550 • C upon combustion, initial calcination of voluminous oxide powders at 800 • C for 3 h, annealing the powders at 1000 • C and final annealing at 1300 • C for 2 h. It should be noted that the authors of [107] could not achieve single-phase sample. Huang and Goodenough also concluded that a La 0.8 Sr 0.2 Ga 0.83 Mg 0.17 O 3−δ single-phase material cannot be formed via hydrothermal treatment synthesis [100]. A typical diagram of La 1−x Sr x Ga 1−y Mg y O 3−δ synthesis via the glycine-nitrate combustion method described in [99] is presented in Figure 5c.
In [110] 4 . An initial powder mixture was supplied to a self-propagating synthesis reactor: it was then ignited with a disposable carbon foil in contact with the sample. The obtained powders were washed with water to remove NaCl. The samples were pressed into disks in vacuum and then sintered at a temperature range of 1000-1500 • C for 6 h in air. An alternative process for La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 3−δ synthesis based on a preliminarily mechanically activated powder mixture was proposed by Ishikawa et al. [111]. The initial mixture was grinded in a planetary mill with stainless steel balls. The powder sample was pressed into a disk, which was placed in a self-propagating synthesis reactor: the aforementioned algorithm [110] was then used.
The literature points out that temperature of about 1400 • C (or more) is required for the synthesis of single-phase LSGM samples. Figure 5d presents the thermal evolution of the XRD pattern for a La 0. 8  It is worth noting that the crystal structure of the obtained LSGM samples depends on the strontium and manganese dopant contents. Basic LaGaO 3 at room temperature has an orthorhombic structure [113] but varying the doping contents can change the crystal structure symmetry [100,114]. Generally, the substitution of La 3+ -ions with Sr 2+ -ions increases the tolerance factor t (Equation (1)), while Ga-with-Mg substitution decreases it. Therefore, the t factor for La 1−x Sr x Ga 1−y Mg y O 3−δ is nearly equal to that calculated for undoped LaGaO 3 .
Comparative analysis of the microstructural parameters for La0.9Sr0.1Ga0.8Mg0.2O3−δ The crystal structure of LaGaO 3 and La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 3−δ samples was investigated via powder neutron diffraction at 25, 800 and 1000 • C in [116]. According to the Rietveld refinement analysis of the diffraction data collected at 25 • C, an orthorhombic structure was observed for both samples: fitting was provided in the Pnma space group for LaGaO 3 (unit cell parameters were equal to a = 5.4908(1), b = 7.7925(1) and c = 5.5227(1) Å) and in the Imma space group for La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 3−δ (unit cell parameters were equal to a = 5.5179(1), b = 7.8200(1) and c = 5.5394(1) Å). The high temperature measurements [116] show that the LaGaO 3 sample possessed a rhombohedral structure in the R-3c space group (unit cell parameters were equal to a = 5.5899(1) Å and a = 5.5987(1) Å at 800 and 1000 • C, correspondingly), whereas La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 3−δ exhibits a cubic structure in the Pm3m space group (unit cell parameters were equal to a = 3.9760(1) Å and a = 3.9866(1) Å at 800 and 1000 • C, correspondingly). Similar data at 25 • C (the Imma space group, a = 5.5056(9), b = 7.8241(7), c = 5.5387(5) Å) for a La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 3−δ sample obtained via solid-state route and sintered at 1350 • C for 2 h was reported in [115]. However, this sample consisted of an LSGM phase and a LaSrGa 3 O 7 impurity phase, as indicated by '*' in Figure 6b. This fact proves the necessity of sintering temperatures of 1400 • C for obtaining single-phase LSGM samples.
Comparative analysis of the microstructural parameters for La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 3−δ disks sintered at 1400 • C for 6 h obtained via the self-propagating high-temperature and solid-reaction synthesis techniques showed that the first sample was denser [110]. The relative densities of the samples were 98 and 92%, respectively, despite the fact that the sintering temperature for the first disk was 100 • C lower than that for the second one. Images in Figure 6c show the SEM micrographs of La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 3−δ samples obtained via self-propagating synthesis with and without mechanical activation of the starting mixture for 24 h [111]. These SEM images testify that mechanically activated self-propagating synthesis provided the high-grade powders with nano-size particles. The specific surface areas of the samples were 3.36 and 2.06 m 2 g −1 , respectively. Based on both studies, Ishikawa et al. [110,111] concluded that this proved the advantages of using self-propagating high-temperature synthesis (especially with mechanical activation of the starting mixture) in comparison with the solid-reaction method.
The evolution of a La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 3−δ sample's density against temperature was provided in by Batista et al. [115]. Based on dilatometry experimental results (Figure 6d), the authors separated the process into three steps: an insignificant increase of relative density at 25-1000 • C; gradual densification at 1000-1300 • C; and, finally, a fast densification above 1300 • C. According to [117], a relative density of over 99% was achieved after calcination at 1450 • C for 6 h.
Summing up the review section, which was devoted to the synthesis methods of Sr, Mg-doped LaGaO 3 oxides as electrolyte materials, the self-propagating high-temperature synthesis with mechanical activation of the starting mixtures can be identified as one of the most optimal techniques. The above-mentioned method can obtain the single-phase La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 3−δ powders with high specific surface areas, a narrow distribution of nano-size particles, and high relative densities for the sintered ceramic samples.

Functional Properties
In 1994, Ishihara et al. [51] were the first to show that the La-substitution of LaGaO 3 with strontium and gallium with magnesium increased the electrical conductivity of doped materials (Figure 7a,b) owing to the formation of oxygen vacancies in La 1−x Sr x Ga 1−y Mg y O 3−δ [118].
The measurements of Ishihara [51], Stevenson [119] and Goodenough [95] demonstrate that the La 1−x Sr x Ga 1−y Mg y O 3−δ samples possess maximal electrical conductivity values at x = 0.15/0.2 and y = 0.2, as can be seen in Table 2. It should be also noted that conductivity of nominally similar materials can be varied over a wide range (see Figure A2). This confirms that the microstructural parameters of ceramics, as well as the presence of insulating impurity phases, considerably affect the transport properties of gallates, encouraging the continuous search for their new synthesis and fabricating techniques.

Sample
Samples Obtaining Method; Annealing Temperature ( • C)  Step-wise current-limiting flash sintering process; 690 850 0.072 [133] It was shown in [119] that the ion-transfer numbers were nearly equal to 1. For La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 3−δ and La 0.8 Sr 0.2 Ga 0.8 Mg 0.2 O 3−δ ceramic samples, the oxygen-ion transference numbers were found to be equal 1 at 700-1000 • C [107], confirming the presence of electrolyte-type behaviour. Savioli and Watson [134] studied the defect structure of LaGaO 3 upon the use of various doping strategies using DFT calculations. They confirmed that Sr-, Ba-, and Mg-doping should result in the greatest improvements to the ionic conductivity of the LaGaO 3 parent phase, while the Ni 2+ -, Co 2+ -, Fe 2+ -, and Zn 2+ -doping is responsible for the generation of a mixed ionic-electronic conducting behaviour. Srand Mg-co-doped LaGaO 3 complex oxides are predominantly oxygen-ionic conductors, for which the electronic conductivity levels are 3-4 magnitudes lower compared to the oxygen-ionic conductivity levels [135].
According to [125], the dependence ln(σT) vs. 1/T had a break at 700 • C for La 0.85 Sr 0.15 -Ga 0.8 Mg 0.2 O 3−δ , which indicates that the activation energy value of oxygen-ion conductivity at a low-temperature range was higher than that at a high-temperature range.
A linear correlation between hardness and total ionic conductivity was revealed in [126] for La 0.  [123]. The LaSrGaO 4 phase exhibits a tetragonal structure K 2 NiF 4 -type and crystalizes in the I4/mmm space group; its conductivity is found to be around 2·10 −7 S cm −1 at 900 • C [136]. The LaSrGa 3 O 7 phase belongs to a melilitestructure described in the P421m space group; its ionic conductivity level is around 2·10 −6 S cm −1 at 800 • C [137]. The maximum values of ionic conductivity and hardness were achieved for single-phase La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 3−δ (LSGM1020) and La 0.85 Sr 0.15 Ga 0.8 Mg 0.2 O 3−δ (LSGM1520) samples with a high relative density, as shown in Figure 7d. With a significant amount of impurity phases at the grain boundaries, the samples exhibited a gradual decrease in hardness and the grain boundary conductivity, which resulted in a decreasing total conductivity. The data in Table 2 may also be analysed from the aforementioned perspective.
The expansion behaviour for La 1−x Sr x Ga 1−y Mg y O 3−δ is correlated with its crystal structure in the observed temperature range. Therefore, the presence of a phase transition from an orthorhombic phase to a cubic one for La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 3−δ [116] and the existence of an ideal perovskite cubic structure for La 0.8 Sr 0.2 Ga 0.8 Mg 0.2 O 3−δ [114] are responsible for the aforementioned variations in their thermal expansion behaviour.
Datta et al. [121] observed that the temperature of phase transition from an orthorhombic to a rhombohedral structure for La 1−x Sr x Ga 1−y Mg y O 3−δ increased as Mg content increased at a fixed Sr content, as shown in Figure 7f, and decreased with increasing Sr content at a fixed Mg content. The effect of Sr and Mg co-doping on TEC values was explained for La 1−x Sr x Ga 1−y Mg y O 3−δ in terms of the amount of generated oxygen vacancies. It was concluded that TEC values increased as oxygen vacancies increase, regardless of the dopant type. This was the result of the binding energy weakening as a result of oxygen vacancy formation.
Shkerin et al. [139] analysed the structure and phase transitions of La 0.88 Sr 0.12 Ga 0.82 -Mg 0.18 O 3−δ using dilatometry, XRD and Raman spectroscopy. According to the obtained data, La 0.88 Sr 0.12 Ga 0.82 Mg 0.18 O 3−δ exhibited two phase transitions of the second order at 502 and 607 • C. The first transition was attributed to a phase transition from an orthorhombic phase to a cubic one, while the second phase transition was attributed to the ordering of the oxygen vacancies.
Wu et al. [140] studied transport properties of La 0.85 Sr 0.15 Ga 0.8 Mg 0.2 O 3−δ upon the partial or full Sr-substitution with calcium or barium. Their analyses have shown that both types of substitution result in a decrease in ionic conductivity by 20-30%. However, at the same time, the Ca-substituted ceramic materials showed higher conductivities compared to the Ba-substituted analogues. This confirms that strontium is an ideal dopant (from the steric and energetic viewpoints) to be introduced into the La-sublattice of LaGaO 3 -based phases.
Chemical interactions between a La 0. 9 [141]. The LSGM/cathode powders were mixed at a weight ratio of 1:1, pressed into disks and annealed at 1300 • C for 3 h in air. The XRD data revealed that impurity phases were not formed in the LSGM mixed with Zhang et al. [154] showed that a La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 3−δ electrolyte reacted with the nickel component in a Ni-SDC anode. The chemical interaction between LSGM and the composite was due to the interface diffusion of nickel from the anode to the LSGM electrolyte; this led to the formation of La-based poor-conductive secondary phases, which block oxygen-ion transport. The unit cell design with a buffer layer of SDC was suggested as an effective way of avoiding the problem of interface diffusion [155]. However, chemical reactivity was observed between La 1−x Sr x Ga 1−y Mg y O 3−δ and buffer layers of Gd 0.1 Ce 0.9 O 1.95 , scandia-doped zirconia [156] and Gd 0.8 Ce 0.2 O 1.9 [157].
An alternate solution to the problem of nickel interface diffusion from a Ni-based anode is to find novel anode materials. A study of the chemical compatibility between La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 3−δ and Fe 2 O 3 , Co 2 O 3 , NiO as anode materials is provided in [158]. Powder mixtures of LSGM with metal oxides at a weight ratio of 1:1 were mixed in ethanol, pressed into pellets and annealed at 1150, 1250 and 1350 • C for 2 h. The obtained XRD data showed that the LSGM reacted with NiO and Co 2 O 3 at 1150 • C, while a detectable reaction with Fe 2 O 3 occurred only after calcination at 1350 • C.
Du and Sammes [159] reported good chemical compatibility between La 0.8 Sr 0.2 Ga 0.8 -Mg 0.2 O 3−δ and an alternative La 0.75 Sr 0.25 Cr 0.5 Mn 0.5 O 3 anode at a temperature range of 1100-1500 • C. However, the authors note that a low-conductivity phase formed if the annealing time was more than 6 h or the annealing temperature was greater than 1500 • C.
According to Takano et al. [165], La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 3−δ did not react with Ce 0.8 La 0.2 O 1.8 after annealing at 1300 • C for 1 h; therefore, it was concluded that La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 3−δ and Ce 0.8 La 0.2 O 2−δ might be recommended as SOFC electrolyte and buffer materials, respectively, with Sr 2 MgMoO 6−δ used as the anode material. However, a comprehensive investigation of the chemical compatibility between various compositions of La 1−x Sr x Ga 1−y Mg y O 3−δ and lanthanum-doped CeO 2 , provided in [169], showed that only a La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 3−δ / Ce 0.6 La 0.4 O 2−δ mixture did not result in additional phases after being annealed twice at 1350 • C for 2 h at each stage.

Applications in SOFCs
The problem of reactivity between the LSGM and SOFC electrode materials during sintering can be solved by reducing sintering temperatures or/and using the SDC buffer layer as a barrier, eliminating lanthanum-and nickel-cation diffusion. Several unit cell designs have been proposed in the literature. Table 3 presents a summary of electrochemical performances for different types of hydrogen-fuelled SOFCs with LSGMbased electrolytes. These data testify that enhanced power densities were achieved for electrolyte-supported SOFCs when the LSGM electrolyte thickness was in a range of 100-300 µm. Buffer layers of doped ceria were used between the electrolyte and anode: Ce 0.8 Sm 0.2 O 2−δ [144,145,149,155,160,167], Ce 0.8 Gd 0.2 O 2−δ [170] and Ce 0.6 La 0.4 O 2−δ [171,172].   [167] Considering the details in Figure A3, one can see that the SOFCs' power density tends to increase with a decrease in the electrolyte's thickness (due to a corresponding decline in the ohmic resistance) despite the existence/absence of CeO 2 -based buffer layers. Nevertheless, the performance of the compared SOFCs varies greatly, even for close electrolyte thicknesses, indicating that other functional components (cermets, oxygen electrodes) have a significant effect on the achievable output characteristics.
A diagram of a typical LSGM-supported cell with a barrier layer between the anode and the electrolyte, using a Ni-Fe/Ce 0.6 La 0.4 O 2−δ /La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 3−δ /Sm 0.5 Sr 0.5 O 3−δ cell, is presented in Figure 8a. In [171], it was shown that the OCV values were equal to 1.07 and 1.15 V at 800 • C and 700 • C, respectively, and there was no significant difference in the thickness of the Ce 0.6 La 0.4 O 1.8 interlayer. This LSGM-supported cell yielded up to 2200 and 1350 mW cm −2 at 850 and 800 • C, respectively. The typical I-V curve and power densities at different temperatures for the LSGM-supported cell are shown in Figure 8b, which is based on the Ni-  Table 3 shows that, for electrode-supported SOFCs with thin-film LSGM electrolytes, a barrier layer between the electrolyte and the electrodes is not necessary [174][175][176]184,185]. An anode-supported cell containing a La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 3−δ film deposited on an anode supported substrate using radio-frequency magnetron sputtering was fabricated in [174]. The anode substrate was composed of a Ni-Sm 0.2 Ce 0.8 O 2−δ functional layer and a Ni collector layer; an LSGM-La 0.6 Sr 0.4 Co 0.2 Fe 0.8 O 3−δ composite layer was used as a cathode. The obtained SOFC revealed no cracking, delamination or discontinuity, as shown in Figure 8c. The polarization resistance of an anode-supported cell containing a La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 3−δ film decreased from 0.41 to 0.05 Ω cm 2 as the temperature increased from 600 to 800 • C. The OCV and P max values were in the range of 0.85-0.95 V and 650-1420 mW cm −2 , respectively, at a temperature range of 600-750 • C. based on the Ni-Ce0.8Gd0.2O2−δ/Ce0.8Gd0.2O2−δ/(La0.9Sr0.1)0.97Ga0.9Mg0.1O3−δ/ La0.6Sr0.4Fe0.8Co0.2O3−δ cell tested in [170]. The maximum power density of the aforementioned cell reached 540 mW cm −2 at 800 °C, while the maximum power density of a cell containing a La0.9Sr0.1Ga0.9Mg0.1O2.9 electrolyte reached 450 mW cm −2 at 800 °C. The electrode polarization resistance values of the La0.9Sr0.1Ga0.9Mg0.1O3−δ and (La0.9Sr0.1)0.97Ga0.9Mg0.1O3−δ based cells were equal to 0.34 and 0.30 Ω cm 2 at 800 °C, respectively.  Table 3 shows that, for electrode-supported SOFCs with thin-film LSGM electrolytes, a barrier layer between the electrolyte and the electrodes is not necessary [174][175][176]184,185]. An anode-supported cell containing a La0.9Sr0.1Ga0.8Mg0.2O3−δ film deposited on an anode supported substrate using radio-frequency magnetron sputtering was fabricated in [174]. The anode substrate was composed of a Ni-Sm0.2Ce0.8O2−δ functional layer and a Ni collector layer; an LSGM-La0.6Sr0.4Co0.2Fe0.8O3−δ composite layer was used as a cathode. The obtained SOFC revealed no cracking, delamination or disconti-

Conflicts of Interest:
The authors declare no conflict of interest. Appendix A Figure A1. Total conductivity of the LaAlO3 ceramic materials at 700-900 °C depending on doping strategies. These data are taken from Table 1. Figure A1. Total conductivity of the LaAlO 3 ceramic materials at 700-900 • C depending on doping strategies. These data are taken from Table 1.    Table 2.