Effect of Gallium Doping on the Oxygen Exchange Kinetics in La₂SrFe₂O_7−δ Ruddlesden–Popper Phases

Abstract

This study investigates the oxygen exchange kinetics between O₂ and Ga-doped La₂SrFe₂O_7−δ, focusing on the role of gallium substitution in modifying the surface exchange properties of materials. Two compositions, undoped La₂SrFe₂O_7−δ and Ga-doped La₂SrFe_1.8Ga_0.2O_7−δ, were synthesised via conventional solid-state reaction. The phase composition and microstructure of the resulting powders were analysed using X-ray powder diffraction (XRPD), scanning electron microscopy (SEM), Brunauer–Emmett–Teller (BET) surface area analysis, and laser scattering techniques. Oxygen surface exchange kinetics between the oxides and O₂ was studied using the ¹⁸O/¹⁶O isotope exchange pulsed method across a temperature range of 400–900 °C under a He/¹⁶O₂ gas carrier mixture (19 vol. % O₂). The results reveal that both Ga doping and temperature significantly influence the exchange mechanism and rate-determining step, demonstrating tunable catalytic activity in oxygen reduction reactions relevant to solid oxide fuel cell (SOFC) cathodes.

1. Introduction

The development of solid-oxide fuel cells (SOFCs) and oxygen-permeable membranes operating in the intermediate temperature range (600–800 °C) requires novel electrode materials that combine high electrochemical efficiency, structural stability, and environmental safety [1,2,3,4,5]. Traditional cobalt-containing cathodes, such as La_1−xSr_xCo_1−yFe_yO_3−δ (LSCF), Ba_1−xSr_xCo_1−yFe_yO_3−δ (BSCF), and Sm_0.5Sr_0.5CoO_3−δ (SSC), exhibit excellent catalytic activity but suffer from critical drawbacks, including significant thermal expansion mismatch with common electrolytes, cobalt evaporation at elevated temperatures, and poor long-term chemical stability [6,7,8]. These limitations have spurred the search for cobalt-free alternatives capable of delivering comparable electrochemical performance without such drawbacks [9,10,11,12].

Among promising candidates, Ruddlesden–Popper (RP) oxides with the general formula A_n+1B_nO_3n+1 have gained particular attention [13,14,15]. Their unique layered structure comprises alternating perovskite blocks (ABO₃)_n and rock-salt layers (AO) that ensure high structural stability, enhanced oxygen mobility due to oxygen vacancies and interstitial oxygen, and catalytic activity associated with mixed-valence transition metals [15,16,17]. These properties make RP oxides attractive for applications as SOFC cathodes, oxygen-permeable membranes, and catalysts [17,18,19,20].

Iron-containing RP phases, such as Sr₂FeO_4−δ (n = 1), Sr₃Fe₂O_7−δ (n = 2), and Sr₄Fe₃O_10−δ (n = 3), have attracted significant research interest due to their tunable functional properties via cation substitution and oxygen non-stoichiometry control under varying oxygen partial pressures [21,22,23,24,25,26,27]. Recent studies on related systems, such as Sr_3−xLa_xFe_2−yCo_yO_7−δ and Sr_3−xLa_xFe_2−yNi_yO_7−δ, have demonstrated high oxygen permeability at temperatures below 900 °C, attributed to anisotropic structures and oxygen vacancy networks, which indicates the applicability of the materials for oxygen separation and partial oxidation processes [28,29,30,31]. Moreover, RP-based cathodes exhibit competitive polarisation resistance at intermediate temperatures, making the oxides promising cobalt-free alternatives for SOFCs [32,33].

Within this context, La₂SrFe₂O_7−δ, a derivative of Sr₃Fe₂O_7−δ with partial strontium substitution by lanthanum, stands out as a particularly promising candidate. Lanthanum incorporation enhances structural stability over a wide range of oxygen partial pressures, improves thermodynamic stability, and allows precise control over oxygen vacancy concentration [34,35,36,37,38,39]. The material’s functionality is closely linked to its crystal structure and defect chemistry: oxygen vacancies in perovskite layers facilitate oxygen transport, while mixed Fe³⁺/Fe⁴⁺ valence states enhance electronic conductivity and catalytic activity [40,41,42]. Additionally, La₂SrFe₂O_7−δ exhibits robust structural stability across temperatures and oxygen partial pressures, a critical requirement for long-term SOFC operation [35,39].

Partial substitution of iron with gallium in La₂SrFe₂O_7−δ (yielding La₂Sr(Fe_1−xGa_x)₂O_7−δ) further optimises its functional properties, enhancing compatibility with widely used solid-oxide electrolytes. Prior investigations [39] demonstrate that Fe³⁺ → Ga³⁺ substitution reduces the coefficient of thermal expansion (TEC) from ~12.5 · 10⁻⁶ K⁻¹ for undoped La₂SrFe₂O_7−δ to ~11.2 · 10⁻⁶ K⁻¹ at x = 0.2 for La₂SrFe_1.8Ga_0.2O_7−δ, mitigating thermal stress at electrode/electrolyte interfaces during operation (600–800 °C). Furthermore, Ga-doping aligns the cation composition of the electrode with high-conductivity electrolytes like La_0.8Sr_0.2Ga_0.8Mg_0.2O_3−δ (LSGM), reducing the risk of secondary phase formation such as LaSrGaO₄ or SrFeO_3−δ at the interface, which can otherwise degrade electrochemical performance [43].

Despite these advantages, the oxygen surface exchange kinetics of Ga-doped La₂Sr(Fe_1−xGa_x)₂O_7−δ materials remains poorly understood, particularly in the temperature range of 600–800 °C, which is a critical for intermediate-temperature SOFCs (IT-SOFCs), where high ionic conductivity, chemical and mechanical compatibility, and cost efficiency are of paramount importance. Key kinetic characteristics governing the oxygen surface exchange between the cathode material and the gas phase, such as the oxygen surface exchange coefficient (k), the interaction mechanism between O₂ and La₂Sr(Fe_1−xGa_x)₂O_7−δ, and the corresponding rate-determining steps of the oxygen exchange process, remain underexplored, hindering optimization of electrode compositions for IT-SOFCs.

In this work, we investigate two RP-based materials: undoped La₂SrFe₂O_7−δ and its Ga-doped counterpart, La₂SrFe_1.8Ga_0.2O_7−δ. Our primary objective is to determine the oxygen surface exchange mechanism between the gas phase and the oxides, and to assess the impact of gallium doping on oxygen interfacial exchange kinetics.

2. Materials and Methods

Powders of La₂SrFe₂O_7−δ and La₂SrFe_1.8Ga_0.2O_7−δ were prepared using a conventional solid-state reaction method. Stoichiometric amounts of La₂O₃ (99.999%), SrCO₃ (99.99%), Fe₂O₃ (99.5%), and Ga₂O₃ (99.999%) precursor powders were thoroughly mixed in a zirconia-lined jar using 5 mm zirconia milling balls. The milling process was conducted in isopropanol at 300 rpm for 2 h using a planetary ball mill (model Retsch PM 100, Retsch GmbH, Haan, Germany). The resulting powder mixture was initially calcined at 1000 °C for 5 h in a muffle furnace (model SNOL 6.7/1300, SNOL, Utena, Lithuania), followed by re-milling under identical conditions to ensure homogeneity. Subsequently, the powder was subjected to a second calcination at 1450 °C for 5 h in a muffle furnace (model LHT 02/18, Nabertherm GmbH, Lilienthal, Germany). To ensure consistent granulometric composition and microstructural uniformity, the as-calcined powders were further processed through a sequence of re-milling (under the same conditions), followed by a final calcination at 1450 °C for 10 h, and a final homogenization step via planetary ball milling.

X-ray diffraction (XRD) analysis was conducted on a diffractometer (model D/MAX-2200, Rigaku Corporation, Akishima, Tokyo, Japan), equipped with a CuKα radiation source (λ = 1.5406 Å), to determine the phase composition of the synthesised powders. Measurements were performed in ambient air across a 2θ range of 10–90 °.

The specific surface area of the powder samples was measured using an analyser (model Sorbi N 4.1, META, Novosibirsk, Russia) via the Brunauer–Emmett–Teller (BET) technique. The BET method involves evaluating the material’s surface area through nitrogen adsorption measurements conducted under constant temperature conditions.

Particle size distribution analysis of powdered materials was performed via laser light scattering device (model Mastersizer 2000, Malvern Instruments, Worcestershire, UK).

The microstructural features of the powders were investigated using a scanning electron microscope (model EM8000, KYKY Technology, Beijing, China), which was coupled with an energy-dispersive X-ray (EDX) detector system (model INCA Energy 350/X-max 80, Oxford Instruments, Abingdon, UK).

The pulsed isotope exchange (PIE) method was employed to determine the mechanism of the oxygen surface exchange process over the La₂Sr(Fe_1−xGa_x)₂O_7−δ (x = 0, 0.2) oxides interacting with gaseous oxygen. The PIE measurements were conducted isothermally, across a temperature range from 300 to 900 °C, using a continuous flow of a He/¹⁶O₂ gas carrier mixture (19 vol. % O₂) at flow rates of 2, 3, and 4 L/h. Ultra-high-purity gases were employed: helium with 99.9999 vol. % purity, and oxygen with 99.999 vol. % purity. To remove surface-adsorbed species, such as water and residual gases, prior to the isotopic measurements, the powdered samples underwent a thermal pre-treatment. The samples were heated at 50 °C/h to 900 °C under a carrier gas flow of 1 L/h, then held isothermally at 900 °C for 1 h. Following this, the samples were cooled at a rate of 100 °C/h to the initial PIE experimental temperature. During the PIE experiments, isotopic pulses were introduced using a N₂/¹⁸O₂ gas mixture (19 vol. % O₂). The nitrogen carrier gas exhibited a purity of 99.9999 vol. %, while the ¹⁸O₂ tracer had a purity of 99.999 vol. % and an isotopic enrichment of 86.8 at. %. This enrichment level was achieved by blending ¹⁸O₂ gas (97 at. % ¹⁸O) with natural-abundance ¹⁶O₂ (natural isotope composition) to generate an oxygen isotope mixture with non-binomial isotope distribution, which is required for the precise analysis of the exchange kinetics. For further methodological details regarding the PIE procedure, see references [44,45].

3. Results

3.1. Sample Characterisation

The crystallographic and morphological properties of the synthesised La₂SrFe₂O_7−δ and La₂SrFe_1.8Ga_0.2O_7−δ powders were investigated using X-ray diffraction (XRD), laser diffraction, and scanning electron microscopy (SEM) methods. The results are summarised in Figure 1.

Figure 1. (A) XRD profiles of as-synthesised La₂SrFe₂O_7−δ and La₂SrFe_1.8Ga_0.2O_7−δ powders collected under ambient conditions; differential particle size distribution functions for (B) La₂SrFe₂O_7−δ and (C) La₂SrFe_1.8Ga_0.2O_7−δ; SEM-images of (D) La₂SrFe₂O_7−δ and (E) La₂SrFe_1.8Ga_0.2O_7−δ samples.

XRD measurements (Figure 1A) confirmed the formation of the layered Ruddlesden–Popper (RP) phase in the investigated oxides. The analysis of XRD data using the Whole-Pattern Profile Fitting (WPPF) method revealed that both La₂SrFe₂O_7−δ and La₂SrFe_1.8Ga_0.2O_7−δ samples crystallise in a tetragonal lattice system (sp. gr. I4/mmm). The lattice parameters were refined as follows: a = b = 3.9085(3) Å, c = 20.4716(4) Å for the undoped La₂SrFe₂O₇ phase; and a = b = 3.9083(3) Å, c = 20.4600(3) Å for the Ga-doped La₂SrFe_1.8Ga_0.2O_7−δ oxide, respectively. The parameters are in excellent agreement with previously reported values for La₂SrFe₂O_7−δ and La₂SrFe_1.8Ga_0.2O_7−δ oxide powders from prior investigations [39], as well as with the findings of Sharma et al. [37] and Gurusinghe et al. [38] for the based La₂SrFe₂O_7−δ composition.

Figure 1B,C display the particle size distribution (PSD) of La₂SrFe₂O_7−δ and La₂SrFe_1.8Ga_0.2O_7−δ powders, expressed in volumetric, surface-area, and number-based distributions. Both oxides exhibit PSDs of comparable shape, as illustrated in the figures. The mean particle diameters, represented by D[2,1], D[3,2], and D[4,3], were measured as 1.883 µm, 9.2 µm, and 79.98 µm for La₂SrFe₂O_7−δ, and 2.072 µm, 8.937 µm, and 60.206 µm for La₂SrFe_1.8Ga_0.2O_7−δ, respectively. The closely aligned D[3,2] values for both oxides suggest similarities in their specific surface areas, a conclusion corroborated by BET measurements, which yielded specific surface areas of 0.37 ± 0.03 and 0.28 ± 0.03 m²/g for La₂SrFe₂O_7−δ and La₂SrFe_1.8Ga_0.2O_7−δ, respectively. These results were used further in PIE studies, to obtain area-specified values of oxygen surface exchange rates.

Secondary-electron scanning electron microscopy images of the La₂SrFe₂O_7−δ and La₂SrFe_1.8Ga_0.2O_7−δ powder particles are presented in Figure 1D,E. Both powders consist predominantly of irregularly shaped, fragment-like particles. While the majority of particles are small in size, the Ga-containing sample exhibits a notable presence of larger particles within its bulk, a finding that is consistent with the laser scattering analysis results.

3.2. Oxygen Heterogeneous Exchange

The as-calculated temperature dependencies of oxygen isotopologue mole fractions (x_16O16O, x_16O18O, and x_18O18O) and mean ¹⁸O mole fraction (α = ½ x_16O18O + x_18O18O) in a pulse after its interaction with La₂SrFe₂O_7−δ and La₂SrFe_1.8Ga_0.2O_7−δ are presented in Figure 2. Both oxides demonstrate the beginning of exchange at 400 °C, which is justified by an increase in x_16O18O and a decrease in α compared to the values at lower temperatures. The total consumption of ¹⁸O in the pulse is achieved at 750 °C for La₂SrFe_1.8Ga_0.2O_7−δ, while in the case of La₂SrFe₂O_7−δ, the consumption was not achieved in the whole studied temperature range. This indicates that absolute surface exchange activity of La₂SrFe_1.8Ga_0.2O_7−δ is higher than that of La₂SrFe₂O_7−δ. The lower and upper limits of the kinetic activity revealed for the samples restrict the precise analysis of the exchange kinetics between O₂ and the oxides to the temperature ranges of 400–900 °C for La₂SrFe₂O_7−δ and 400–700 °C for La₂SrFe_1.8Ga_0.2O_7−δ, respectively.

Figure 2. Temperature dependencies of oxygen isotopologue mole fractions and α for (A) La₂SrFe₂O_7−δ and (B) La₂SrFe_1.8Ga_0.2O_7−δ, calculated from the results of PIE measurements at the gas-carried flow of 4 L/h and 1 mL of N₂/¹⁸O₂ pulse.

In order to obtain a quantitative estimation of the oxygen surface exchange rate, it is necessary to analyse the dependence of α on the time of pulse interaction with the oxides, which is equal to the residence time of the pulse. Figure 3 presents the time dependencies of α for La₂SrFe₂O_7−δ and La₂SrFe_1.8Ga_0.2O_7−δ, respectively. According to the figure, the kinetic profiles of α exhibit typical behaviour governed by exponential law. This suggests the absence of kinetic inequality of bulk oxygen atoms in the oxides, as well as the absence of bulk diffusion limitations, which often appear in kinetic profiles of α in the form of secondary exponential terms [46,47,48,49]. Thus, to estimate kinetic parameters of oxygen surface exchange it is possible to use the exponential kinetic model (1) to describe the time dependencies of α [50,51]:

$$\alpha ={\alpha }^{\infty }+\left({{\alpha }^0-\alpha }^{\infty }\right)e^{-{\displaystyle \frac{S}{N_g}}{r}_H\left(1+\lambda \right)t},$$

(1)

where t is time of interaction, r_H is oxygen heterogeneous exchange rate (surface exchange rate) representing the number of oxygen atoms exchanging between O₂ and the solid per unit surface and unit time [mole · m⁻² · s⁻¹]; λ is the ratio between number of oxygen atoms from the pulse in the packed bed microreactor and the number of exchangeable oxygen atoms in the oxide, calculated as $\lambda ={\displaystyle \frac{{\alpha }^{\infty }}{{{\alpha }^0-\alpha }^{\infty }}}$; α⁰ and α^∞ are the mean ¹⁸O fractions in the pulse before the exchange and under isotope equilibrium conditions; N_g is the number of oxygen atoms in pulse [mol.]; S is the total surface area of the oxide [m²]. The results of the fitting are presented in Figure 3A,B with solid lines and show a good agreement between the experimental data and the model of exponential kinetics.

Figure 3. Time dependencies of mean ¹⁸O mole fraction in a pulse (α) for (A) La₂SrFe₂O_7−δ and (B) La₂SrFe_1.8Ga_0.2O_7−δ, calculated from the results of PIE measurements at the gas-carrier flows of 2, 3, and 4 L/h, at 1 mL of N₂/¹⁸O₂ pulse; points—experimental data, solid lines—the model of exponential kinetics.

Figure 4A demonstrates the Arrhenius plot of r_H for La₂SrFe₂O_7−δ and La₂SrFe_1.8Ga_0.2O_7−δ, respectively. According to the figure, the effect of Ga doping on oxygen heterogeneous exchange is complex and depends on the temperature range. The values of r_H for La₂SrFe_1.8Ga_0.2O_7−δ are higher than those for La₂SrFe₂O₇ at temperatures ≥ 550 °C, which suggests that Ga doping increases r_H in the high-temperature range. Conversely, at temperatures < 550 °C the values of r_H for La₂SrFe_1.8Ga_0.2O_7−δ are comparable to or lower than those for La₂SrFe₂O_7−δ, indicating a decrease in r_H with Ga doping. The apparent activation energy of oxygen heterogeneous exchange increases with the Ga doping level: the value of E_a for La₂SrFe_1.8Ga_0.2O_7−δ is 1.66 times higher than that for La₂SrFe₂O_7−δ.

Figure 4. (A) Arrhenius plot of r_H and (B) temperature dependencies of x_exch. for La₂SrFe₂O_7−δ and La₂SrFe_1.8Ga_0.2O_7−δ, respectively.

In general, the effect of Ga doping on the apparent activation energy (E_a) can be associated with two factors: the first is a change in the local and overall defect structure of the surface and/or bulk of the oxides; the second is a change in the exchange mechanism, including rate-determining steps. The latter factor is discussed in detail in Section 3.3.

To estimate the influence of the former factor, it is necessary to consider the general defect structure of layered ferrites. Prior studies [35,41] have systematically analysed the defect structure of La-doped Sr₃Fe₂O_7−δ, demonstrating that its defect equilibria are governed by three key reactions, which may be expressed as Equations (2)–(4). The authors [41] found that the increasing La³⁺ content shifts the equilibrium of reaction (2) to the right, while simultaneously driving reactions (3) and (4) toward the left; a phenomenon attributed to the elevated concentration of Fe³⁺. Our results suggest that the Ga doping may exhibit the same effect as La doping. Since tetravalent Ga⁴⁺ does not exist under the experimental conditions employed, Ga cations cannot directly participate in the disproportionation reactions (3) and (4). Instead, the addition of Ga³⁺ induces a leftward shift in the equilibrium of these reactions via local charge-compensation effects. Consequently, the equilibrium of reaction (2) is driven to the right, effectively suppressing oxygen vacancy formation and increasing the binding strength of lattice oxygen. Regarding surface exchange at the gas–solid interface, the effect of Ga on the oxygen binding energies may increase E_a because of the higher binding energies of oxygen atoms in the outermost oxide layers. The Ga doping effect is discussed further in Section 3.3.

$${\displaystyle \frac{1}{2}}{\mathrm{O}}_2+{\mathrm{V}}_{\mathrm{O}1}^{••}+2{\mathrm{Fe}}_{\mathrm{Fe}}^{\prime }\begin{array}{c}\stackrel{⃑}{k}\\ \rightleftharpoons \\ \stackrel{⃐}{k}\end{array}{\mathrm{O}}_{\mathrm{O}1}^{\times }+{2\mathrm{Fe}}_{\mathrm{Fe}}^{\times },$$

(2)

$${\mathrm{Fe}}_{\mathrm{Fe}}^{\prime }\rightleftharpoons {\mathrm{Fe}}_{\mathrm{Fe}}^{″}+{\mathrm{Fe}}_{\mathrm{Fe}}^{\times },$$

(3)

$${\mathrm{V}}_{\mathrm{O}1}^{••}+{\mathrm{O}}_{\mathrm{O}3}^{\times }\rightleftharpoons {\mathrm{O}}_{\mathrm{O}1}^{\times }+{\mathrm{V}}_{\mathrm{O}3}^{••},$$

(4)

where ${\mathrm{V}}_{\mathrm{O}1}^{••}$ and ${\mathrm{V}}_{\mathrm{O}3}^{••}$ are oxygen vacancies in different structural positions of crystal lattice, with an effective charge of +2; ${\mathrm{O}}_{\mathrm{O}1}^{\times }$ and ${\mathrm{O}}_{\mathrm{O}3}^{\times }$ are structural oxygen atoms in the positions having effective zero-charge; ${\mathrm{Fe}}_{\mathrm{Fe}}^{\times }$ is a Fe⁴⁺ cation having effective zero-charge, ${\mathrm{Fe}}_{\mathrm{Fe}}^{\prime }$ is a Fe³⁺ cation, and ${\mathrm{Fe}}_{\mathrm{Fe}}^{″}$ is a Fe²⁺; $\stackrel{⃑}{k}$ and $\stackrel{⃐}{k}$ are the rate constants of forward and backward mass-transfer reactions.

While the Ga doping unambiguously increases the values of E_a, its effect on r_H values is more complex. To explain it, we need to consider the nature of r_H measured by isotope exchange methods. In contrast to various relaxation-based techniques, isothermal isotope exchange is carried out under isotope equilibrium/stationary conditions, which provide equilibrium values of exchange rates [44,50,52]. As discussed in [52] a general reaction rate (R) for a reversible process, expressed as the difference between the rates of the forward and backward reactions for the process ($R=\overrightarrow{R}-\overleftarrow{R}$), under equilibrium conditions is equal to zero, producing equal equilibrium rates of surface exchange rate $r_H=\overrightarrow{R}=\overleftarrow{R}$. Considering reactions (2)–(4), under our conditions, the relationship between r_H and the parameters is expressed as $r_H=\stackrel{⃑}{k}{C}_{V_{O1}^{••}}{p}_{O_2}^{1/2}{C}_{{\mathit{Fe}}_{\mathit{Fe}}^{\prime }}^2=\stackrel{⃐}{k}{C}_{O_{O1}^{\times }}{C}_{{\mathit{Fe}}_{\mathit{Fe}}^{\times }}^2=\sqrt{\stackrel{⃑}{k}\stackrel{⃐}{k}{C}_{V_{O1}^{••}}{p}_{O_2}^{1/2}{C}_{{\mathit{Fe}}_{\mathit{Fe}}^{\prime }}^2{C}_{O_{O1}^{\times }}{C}_{{\mathit{Fe}}_{\mathit{Fe}}^{\times }}^2}$, where C is the equilibrium concentration of the respective defects. Taking into account that the exchange reaction occurs in the adsorption layer between the gas phase and the oxygen atoms in the near-surface layers of the oxide, the equilibrium concentrations of the defects can, in general, be related to surface, bulk, or both types of defects, depending on the bulk diffusion limitations of the material. Thus, Ga doping may lead to both an increase and a decrease in r_H depending on its effect on the defect concentrations.

To determine the key factors responsible for the observed effect of Ga doping on r_H, the estimation of the relative fraction of exchangeable oxygen in the oxides was carried out using equation $x_{\mathit{exch}.}={\displaystyle \frac{{\lambda }_{\mathit{theor}.}}{{\lambda }_{\mathit{exp}.}}}$, where ${\lambda }_{\mathit{theor}.}={\displaystyle \frac{N_g}{N_O}}$ and represents λ at the conditions when all oxygen atoms in the sample (N_O) are considered to be exchangeable, and λ_exp. corresponds to λ obtained from the results of experimental data fitting.

Figure 4B shows the temperature dependencies of x_exch. for La₂SrFe₂O_7−δ and La₂SrFe_1.8Ga_0.2O_7−δ, respectively. The values of x_exch. increase with temperature for both oxides reaching the maximum at 850 and 700 °C for La₂SrFe₂O_7−δ and La₂SrFe_1.8Ga_0.2O_7−δ. At temperatures below 600 °C, the values are lower than 1%, suggesting that only oxygen atoms in near-surface layers of oxides are involved in the exchange process. The increase of temperature leads to a drastic increase in exchangeable oxygen fraction that indicates a growth in the accessibility of bulk oxygen for exchange.

The Ga introduction controversially affects the values of x_exch.. At temperatures < 650 °C the values of x_exch. for La₂SrFe₂O_7−δ are higher than that for La₂SrFe_1.8Ga_0.2O_7−δ, while the opposite trend is observed in high-temperature regions. A clear direct correlation is observed between r_H and x_exch., justifying that the key factor responsible for the impact of Ga on r_H is $C_{O_{O1}^{\times }}$. Thus, at lower temperatures, Ga doping reduces the number of exchangeable oxygen atoms, due to the effect of Ga on the activation barriers of oxygen vacancy formation. As temperature increases, more oxygen atoms from the oxides becomes exchangeable, while the total number of oxygen atoms in the oxide decreases due to the exothermic reaction (2). In this case, the effect of Ga on the activation barrier blocks the release of oxygen, which in turn results in a higher x_exch. for La₂SrFe_1.8Ga_0.2O_7−δ compared to La₂SrFe₂O_7−δ. Similar behaviour was observed in our previous study [45] on Ce- and Y-doped BaFeO_3−δ, where the increase in Ce doping level resulted in the increase of r_H due to the increase of oxygen content in the oxide.

3.3. Oxygen Surface Exchange Mechanism

To obtain comprehensive information on the effect of Ga doping on the oxygen surface exchange mechanism between the gas phase and oxides, the detailed analysis of the experimental data was performed within the model of three exchange types, independently proposed by Muzykantov et al. and Klier et al. in papers [53,54]. The model is a particular case of recently proposed general statistical theory of ideal isotope exchange (exchange without isotope effects) [49]. In terms of the theory, the isotope exchange process for any exchange participant (component) of an arbitrary system is the dynamic process of the change in the distribution function of the isotopes within the participant. The change corresponds to a discrete set of atom-transfer quasireactions, describing the transition between a distribution function of the given participant in the given time moment and other types of isotope distributions possible for the system. The quasireactions are classified as types and subtypes of exchange. The type of exchange shows the number of atoms transferred between exchange participants of different chemical composition during the act of quasireaction. The subtypes of exchange indicate the particular type of “product” distribution function within the given type of exchange.

The model of three exchange types considers the exchange in two-component systems of O₂–oxide, where the oxide is presented by one sort of one-atomic oxygen species. In this system, the three types of exchange are possible, presented by only one subtype each: r₀-type, representing the isotope redistribution between oxygen molecules without contributing of structural oxygen to the redistribution; r₁-type, corresponding to the isotope redistribution between O₂ and the oxide, with the contribution of one oxygen atom of the oxide to the redistribution; and r₂-type, representing the isotope redistribution between O₂ and the oxide, with the participation of two oxygen atoms from the oxide. In terms of general statistical theory of ideal isotope exchange, these types are described by three distinct atom-transfer quasireactions, expressed with Equations (5)–(7):

$$A_2\stackrel{r_0}{\rightleftarrows }2A,$$

(5)

$$A_2\stackrel{r_1}{\rightleftarrows }A+A_S,$$

(6)

$$A_2\stackrel{r_2}{\rightleftarrows }2A_S,$$

(7)

where A₂ denotes an arbitrary distribution function of ¹⁸O and ¹⁶O in O₂. Its elements are the probabilities of finding the three combinations of oxygen isotopes in O₂, i.e., ¹⁶O¹⁶O, ¹⁶O¹⁸O, and ¹⁸O¹⁸O, equal to the respective mole fractions. 2A, A + A_S, and 2A_S are the three types of oxygen isotope distribution. Type 2A represents a binomial distribution, indicating that the probability of finding the three combinations of oxygen isotopes depends only on the mean fraction of ¹⁸O in O₂ (α). Type A + A_S denotes a Poisson binomial distribution, indicating that the probability of finding the three combinations of oxygen isotopes depends on both the mean fractions of ¹⁸O in O₂ and in the oxide (α_S). Type 2A_S represents a binomial distribution in which the probability of finding the three combinations of oxygen isotopes is determined by the mean fraction of ¹⁸O in the oxide. The r₀, r₁, and r₂ are the rates of the quasireactions that, in the particular case of the model of three exchange types, are also equal to the rates of the three types of exchange.

The rate of oxygen heterogeneous exchange r_H is directly connected with the rates of the three exchange types by Equation (8), and the sum of the rates r_tot (9) corresponds to the total rate of isotope exchange in system, equal to the mean rate of oxygen dissociative adsorption.

$$r_H={\displaystyle \frac{1}{2}}{r}_1+r_2,$$

(8)

r_tot = r₀ + r₁ + r₂.

(9)

An equation, describing the kinetics of surface exchange within the model of three exchange types is written as (10):

$$y_2=\left({\displaystyle \frac{r_2·{\left(1+\lambda \right)}^2·{({\alpha }^0-{\alpha }^{\infty })}^2}{r-2r_H·(1+\lambda )}}·\left(e^{\left[r-2r_H·\left(1+\lambda \right)\right]·t}-1\right)+y_2^0\right)·e^{\left(-r_{\mathit{tot}}·t\right)},$$

(10)

where y₂ is an isotope variable for ¹⁸O₂, showing the difference between the mole fraction of ¹⁸O₂ in O₂ at a given moment of time, and the fraction governed by the binomial distribution function at a given moment of time, written as Equation (11); $y_2^0$ is the value of the variable at t = 0.

$$y_2=x_{18\mathrm{O}18\mathrm{O}}^{2A}-x_{18\mathrm{O}18\mathrm{O}}^{A_2}={\alpha }^2-x_{18\mathrm{O}18\mathrm{O}}.$$

(11)

Figure 5 presents the time dependencies of y₂ calculated from the experimental data by Equation (11), and fitted with Equation (10), with the refinement of r₂ and r_tot as fitting parameters. The figure demonstrates acceptable agreement between the data and the model of three exchange types.

Figure 5. Time dependencies of y₂-variable (A) La₂SrFe₂O_7−δ and (B) La₂SrFe_1.8Ga_0.2O_7−δ, calculated from the results of PIE measurements at the gas-carried flows of 2, 3, and 4 L/h, at 1 mL of N₂/¹⁸O₂ pulse; points—experimental data, solid lines—the model of three exchange types by Equation (10).

To determine the mechanism of isotope exchange between O₂ and the oxides using the model of the three exchange types, it is necessary to consider the probabilities of exchange by the types, calculated as ${\chi }_i={\displaystyle \frac{r_i}{r_{\mathit{tot}}}}$, where r_i is the rate of ith exchange type. According to studies [49,55,56], the probabilities are determined by the number of exchange steps, and the ratios between the rates of elementary steps for the mechanism. So far, several mechanisms were discussed in literature to describe isotope exchange between O₂ and complex oxides:

• A two-step model [55] suggests that the mechanism of oxygen surface exchange is composed of two subsequent steps: oxygen dissociative adsorption, corresponding to isotope exchange between O₂ and oxygen adsorbed atoms, O_a; and oxygen incorporation, corresponding to oxygen isotope exchange between oxygen adsorbed atoms and structural oxygen, O_S. This model governs exchange probabilities by the ratio $P_{\mathit{ih}}=2{\displaystyle \frac{\sqrt{{\chi }_0{\chi }_2}}{{\chi }_1}}=1$ In terms of oxygen mass-transfer reactions, the steps can be expressed with Equations (12) and (13), respectively.
• A statistical mechanism [56] considers the presence of kinetic inequality of adsorption and/or incorporation centres in the oxides, which creates multiple, parallel dissociative adsorption and incorporation steps with distinct rates. This model governs the exchange probabilities by the ratio P_ih > 1.
• A mechanism with partial kinetic inequality of active centres [44,55] governs exchange probabilities by the ratio P_ih < 1. The mechanism suggests the presence of a single dissociative adsorption step producing two oxygen adsorbed atoms with different incorporation capabilities, as well as the mechanism with multiple adsorption steps, but fast surface diffusion of adsorbed atoms, which allows recombination of adsorbed atoms with distinct activities within one molecule.

$${\mathrm{O}}_2\stackrel{r_{\mathit{ads}}}{\rightleftarrows }2{\mathrm{O}}_a,$$

(12)

$${\mathrm{O}}_a\stackrel{r_{\mathit{inc}}}{\rightleftarrows }{\mathrm{O}}_S,$$

(13)

where r_ads and r_inc are the rates of oxygen dissociative adsorption and incorporation steps.

Figure 6A demonstrates a probability of exchange diagram, showing the dependence of χ_i on the mean probability of surface exchange (${\displaystyle \frac{r_H}{r_{\mathit{tot}}}}$) for our data, in comparison with the theoretically calculated values predicted by P_ih for the above discussed mechanisms. The figure shows that for La₂SrFe₂O_7−δ the values of χ₀, χ₁, and χ₂ are closely aligned with the two-step model at the majority of ${\displaystyle \frac{r_H}{r_{\mathit{tot}}}}$ values. The decrease in ${\displaystyle \frac{r_H}{r_{\mathit{tot}}}}$ leads to shifting the values of χ₀, χ₁, and χ₂ to the mechanism with partial kinetic inequality (P_ih < 1). This suggests the slight change of the surface exchange mechanism. In the case of La₂SrFe_1.8Ga_0.2O_7−δ, in all studied temperature ranges, oxygen surface exchange follows the statistical mechanism (P_ih > 1), which indicates that Ga-doping splits the two-step model into multiple parallel two-step pathways having different rates of oxygen dissociative adsorption and incorporation. This suggests that the addition of Ga either modifies the kinetic activity of some of the existing adsorption centres or creates additional adsorption centres on the oxide surface having different kinetic activity towards the oxygen surface exchange reaction.

Figure 6. (A) Probability of exchange diagram in coordinates ${\chi }_i=f\left({\displaystyle \frac{r_H}{r_{\mathit{tot}}}}\right)$ with points denoting χ₀, χ₁, and χ₂ determined from experimental data using Equation (10), and lines representing theoretically calculated χ₀, χ₁, and χ₂ from the two-step model (solid lines), the statistical mechanism (dash-dot lines), and the partial inequality mechanism (dot lines); (B) the dependence of P_ih on x_exch.

The observed influence of Ga doping on the exchange mechanism may be explained from the same position as the effect of x_exch. on r_H. As discussed in Section 3.2 the oxygen/consumption release for the oxides is strongly connected with the change of oxidation state of Fe cations from +3 to +4 by Equation (2). Since Ga³⁺/Ga⁴⁺ transition is not possible, the outermost oxygen atoms bound to Fe and Ga atoms may exhibit different kinetic activity, which splits the two-step model into at least several parallel exchange pathways having different rates of oxygen dissociative adsorption and incorporation in different points of the oxide surface.

The effect of temperature on the exchange mechanism is likely to be connected with x_exch.. To illustrate this let us consider the dependence of P_ih on x_exch. presented in Figure 6B. According to the figure, the increase in x_exch. leads to a slight decrease in P_ih for La₂SrFe₂O_7−δ. This is in contradiction to the majority of perovskite-like oxides, exhibiting two-step mechanism of exchange [45,57,58]. However, the mechanisms of isotope exchange between O₂ and Ruddlesden–Popper oxides can be significantly more complex due to their layered structure. In particular, the study of oxygen surface on ceramic La₂NiO₄ [56] reveals P_ih > 1, which the authors explained by the distribution of active centres associated with pathways of oxygen migration within the crystal lattice. The study on powder La₂NiO₄ [44,57] with PIE, in contrast, shows the applicability of the two-step model, while the study of La₃Ni₂O_7−δ and La₄Ni₃O_10−δ [44] demonstrate the mechanism with P_ih = 0, associated with the presence of the two sorts of incorporation sites in the oxide, namely oxygen vacancies and oxygen interstitials, exhibiting drastically different kinetic activity. Our PIE results on La₂SrFe₂O_7−δ appear to be in between the discussed studies for layer nickelates and close to La₃Ni₂O_7−δ. This suggests that the layered structure of La₂SrFe₂O_7−δ may influence the exchange mechanism. In that case, in the low-temperature region where x_exch. is low, the different activation barriers of vacancy formation, associated with different structural layers of the crystal lattice, create kinetic inequality of adsorption/incorporation centres and lead to P_ih > 1. The increase in temperature leads to an increase in x_exch., which, in turn, unevenly increases the accessibility of oxygen atoms in the different layers of the oxide, effectively increasing the rate of oxygen incorporation only for specific pathways. This leads to decreasing P_ih to values below 1, similarly to La₃Ni₂O_7−δ, where one of oxygen incorporation pathways was immeasurably faster than others.

In the case of La₂SrFe_1.8Ga_0.2O_7−δ the decrease in P_ih with x_exch. was also observed at x_exch. < 0.01, suggesting the same effect of the layered crystal structure on the reaction mechanism in this region as for La₂SrFe₂O_7−δ. However, the further increase in x_exch. results in drastic increase in P_ih. This observation may be associated with the combined structural and doping effect on the mechanism: the effect of layered structure increases the rate of specific incorporation pathways, while Ga doping increases activation barriers for oxygen adsorption and/or incorporation due to the impossibility of Ga³⁺/Ga⁴⁺ transition, compared to Fe³⁺/Fe⁴⁺. As x_exch. increases, more oxygen from the bulk becomes accessible for exchange at the centres of different kinetic activity connected with Fe and Ga cations. This results in further splitting of the reaction pathways to low- (Ga-related) and highly- (Fe-related) active, and leads to the increase in P_ih.

It should be noted that the proposed interpretation of the obtained reaction mechanisms and results is only based on the exchange kinetics and on similarities in structural and kinetic features between layered nickelates and the oxides under study. The finer aspects of the revealed exchange mechanism require additional studies with application of XPS, EXAFS, DFT, NMR, and other techniques to obtain detailed information on the structural–kinetic relationships for these oxides.

To conclude this section, let us analyse the effect of Ga doping on the rates of the elementary steps of the exchange process. Due to the fact that the exchange mechanism for both La₂SrFe₂O_7−δ and La₂SrFe_1.8Ga_0.2O_7−δ has a complex, multistep nature, the exact calculation of the rates for all elementary steps is impossible on the basis of only three independent parameters provided by the model of three exchange types. However, it is possible to estimate the effect of Ga doping on the mean rates of oxygen dissociative adsorption (<r_ads>=r_tot) and incorporation (<r_inc>=(<r_ads > ∙r_H)/((<r_ads > −r_H)) across all exchange pathways.

Figure 7 presents the Arrhenius plots of the mean rates of oxygen dissociative adsorption, <r_ads>, and incorporation, <r_inc>, for La₂SrFe₂O_7−δ and La₂SrFe_1.8Ga_0.2O_7−δ, respectively. The figure demonstrates that the increase in Ga content significantly affects oxygen dissociative adsorption rather than oxygen incorporation, and consequently the overall rate-determining process of exchange. The mean rates <r_ads> and <r_inc> have comparable values for undoped La₂SrFe₂O_7−δ, suggesting competition between the steps of adsorption and incorporation. Conversely, the rates for La₂SrFe_1.8Ga_0.2O_7−δ demonstrate the different rate-determining process at different temperature regions: at T below 500 °C oxygen dissociative adsorption is the rate-determining process, while at higher temperatures oxygen incorporation determines the oxygen surface exchange. The observed change in the rate-determining step of exchange for La₂SrFe_1.8Ga_0.2O_7−δ is likely to be partially responsible for the existence of low- and high-temperature regions in the temperature dependencies of r_H discussed in Section 3.2, where the rate of surface exchange for La₂SrFe_1.8Ga_0.2O_7−δ is the low-temperature region, and is higher in the high-temperature region than that for La₂SrFe₂O_7−δ.

Figure 7. Arrhenius plot of <r_ads> and <r_inc> for La₂SrFe₂O_7−δ and La₂SrFe_1.8Ga_0.2O_7−δ, respectively.

The observed impact of Ga doping on the rate-determining process of the exchange can be explained by its different effect on the <r_ads> and <r_inc>. According to the figure, an increase in Ga content results in a slight increase in both <r_inc> and the apparent activation energy of oxygen incorporation, while a pronounced drastic increase in the apparent activation energy and the values of <r_ads> with Ga content is observed in the case of oxygen dissociative adsorption. In Section 3.2, it was discussed that the impact of Fe substitution by Ga on oxygen surface exchange r_H and its apparent activation energy may be associated with a change in the thermodynamic parameters of reactions (2)–(4) induced by Ga doping, namely the increase in activations barriers of oxygen vacancies formation, which changes both E_a and the relative fraction of exchangeable oxygen in the oxides. In relation to <r_inc>, the explanation proposed in Section 3.2 can be responsible for the observed slight increase in both the values of <r_inc> and its activation energy.

It is clear that, in contrast to acceptor doping, which has been extensively studied in literature, the substitution of Fe³⁺ with Ga³⁺ cations does not produce excessive vacancies, which can facilitate oxygen incorporation. The impossibility of the Ga³⁺/Ga⁴⁺ transition indicates that Ga cannot participate directly in oxygen incorporation, which is strongly associated with the oxidation of Me³⁺ to Me⁴⁺, but only effects <r_inc> by means of the shift in the overall thermodynamic potentials for reactions (2)–(4) and, as a consequence, in the concentration of structural oxygen and its binding energies. The results showed marked agreement with the results of pressure relaxation studies of the oxides reported [39], where the authors showed that under non-equilibrium conditions close to vacuum (10⁻³ ≤ pO₂(atm) ≤ 3 · 10⁻²), the chemical surface exchange coefficient of the oxides is almost independent on Ga content. The values reported in paper [39] for the apparent activation energies of electrode polarization resistance, measured by EIS, for La₂SrFe₂O_7−δ and La₂SrFe_1.8Ga_0.2O_7−δ were 1.17 ± 0.09 and 1.15 ± 0.03 eV, while the apparent activation energies of the oxygen surface exchange coefficient measured by oxygen pressure relaxation at 0.017 atm were 0.71 ± 0.07 and 0.77 ± 0.09 eV, respectively. Both reported results demonstrate agreement with the determined effect of Ga doping on the apparent activation energy of oxygen incorporation, which may indicate that the oxygen incorporation process is mainly determined by the bulk properties of materials rather than surface properties.

Conversely to the effect of Ga doping on the mean rates and apparent activation energy of oxygen incorporation, the effect on the values of oxygen dissociative adsorption is much more significant. The possible explanation for this may be associated with two factors: an uneven distribution of Ga across the oxide, or the direct participation of Ga cations in the adsorption reaction, but by a different mechanism of the adsorption step. The first factor suggests that the concentration of Ga in the near-surface layers of the oxide is higher than that in the bulk layers, which results in the more pronounced effect of Ga on the binding energies of chemisorbed oxygen than the bulk oxygen. The justification of this factor requires additional studies with XPS and DFT methods.

The second factor suggests that oxygen dissociative adsorption may occur by different mechanisms. Indeed, while oxygen incorporation is strongly associated with the transition of Me³⁺ to Me⁴⁺ and requires free oxygen vacancies, oxygen dissociative adsorption may, in general, occur on metal cations as active centres, including Ga³⁺ and Ga²⁺; the charge state of chemisorbed oxygen may also be different from the bulk oxygen [59]. The participation of Ga cations as an active centre of oxygen dissociative adsorption, with a different mechanism from the step, may drastically shift the activation energy of the overall dissociative adsorption reaction.

Nevertheless, both of these factors are in agreement with the revealed statistical mechanism of oxygen surface exchange for La₂SrFe_1.8Ga_0.2O_7−δ, but require additional XPS, EXAFS and DFT studies, which may motivate further research on Ga-doped layered ferrites.

Overall, the presented results show that Ga doping of layered ferrites can be a valuable tool for the selective modification of surface exchange mechanisms and the rate-determining step, with no or insignificant changes in the defect structure and bulk properties of the material. In this case, the co-doping of the oxides with Ga and other cations may be considered to be a promising method for fine tuning the catalytic properties of the materials towards oxygen mass-transfer between O₂ and the oxides, to achieve desirable reaction kinetics.

To demonstrate the high catalytic activity of the materials investigated in this study, the oxygen surface exchange coefficients (k, cm · s⁻¹) for La₂SrFe₂O_7−δ and La₂SrFe_1.8Ga_0.2O_7−δ were calculated from the measured r_H values by Equation (14) and compared with literature data for well-known iron-based mixed-conducting electrode materials measured at pO₂ = 0.21 atm using the PIE method [45,57,58]. The k values as a function of reciprocal temperature are presented in Figure 8.

$$k=r_H{\displaystyle \frac{M_r}{{(7-𝛿)·N}_A·\rho }},$$

(14)

where M_r is a molecular mass of an oxide; 𝛿 is the oxygen nonstoichiometry in an oxide; N_A is the Avogadro constant; and ρ is a sample crystallographic density.

Figure 8. Temperature dependencies of k for La₂SrFe₂O_7−δ and La₂SrFe_1.8Ga_0.2O_7−δ in comparison with existing literature data for a various mixed conducting oxide at pO₂ = 0.21 atm [45,57,58].

As depicted in Figure 8, the oxygen surface exchange kinetics of layered ferrites are competitive with, and in select cases exceed, those of the benchmark cathode materials Ba_0.5Sr_0.5Co_0.8Fe_0.2O₃ (BSCF) [57] and La_0.58Sr_0.4Co_0.2Fe_0.8O₃ (LSCF) [58]. This finding underscores the considerable promise of layered ferrites as viable alternatives for SOFC/IT-SOFC cathodes. Nevertheless, when evaluated against the state-of-the-art triple-conducting BaFe_0.8Ce_0.1Y_0.1O_3−δ cathode [45], the layered ferrites display lower oxygen exchange rates, with the k being approximately one order of magnitude smaller. Future research directions include the rational design of layered ferrite structures, optimization of synthesis protocols, and surface modification strategies, all of which may substantially improve their oxygen exchange capabilities and broaden their utility in electrochemical devices.

4. Conclusions

This study presents the first comprehensive analysis of oxygen surface exchange kinetics between O₂ and Ga-doped La₂SrFe₂O_7−δ using the pulsed isotope exchange technique under ambient oxygen partial pressures. The key results of the study are formulated as:

• Both La₂SrFe₂O_7−δ and La₂SrFe_1.8Ga_0.2O_7−δ powders exhibit oxygen surface exchange in the temperature range 400–900 °C under He/O₂ (19 vol. % O₂) flow.
• Ga doping has complex impacts on the rates of oxygen surface exchange (r_H) between O₂ and La₂SrFe₂O_7−δ, with r_H for La₂SrFe_1.8Ga_0.2O_7−δ lower than that for La₂SrFe₂O₇ at temperatures below 550 °C, and the values of r_H for La₂SrFe_1.8Ga_0.2O_7−δ were higher than those for La₂SrFe₂O_7−δ at temperatures higher than 550 °C. The results were explained by the effect of Ga doping on the defect structure and oxygen content of the materials.
• The correlation between the values of r_H and the relative fraction of exchangeable oxygen (x_exch.) was found for both materials, suggesting a connection between the defect structure of the materials and the surface exchange kinetics.
• The mechanism of oxygen surface exchange between O₂ and Ga-doped La₂SrFe₂O_7−δ was found to depend on temperature and Ga content: in the low-temperature region for undoped La₂SrFe₂O_7−δ, the mechanism comprises two subsequent steps, oxygen dissociative adsorption and incorporation. The increase in temperature leads to the splitting of the oxygen incorporation step into the two kinetically distinguishable steps with different rates, which may be associated with the complex layered structure of the oxide containing oxygen atoms in different inequivalent positions.
• The increase in Ga content leads to the splitting of the two-step mechanism into multiple parallel two-step pathways exhibiting different rates of oxygen dissociative adsorption and incorporation. The origin of the splitting is unclear but may be related to the different redox behaviour of Ga³⁺ and Fe³⁺ cations in the oxides, resulting in the existence of chemisorbed oxygen atoms with different binding energies. However, further studies with the application of XPS, EXAFS, and DFT techniques are required to obtain precise information about the nature of the splitting.
• The rate-determining exchange process was found to change with the Ga doping level: for undoped La₂SrFe₂O_7−δ, there was competition between oxygen dissociative adsorption and incorporation in the entire temperature region. In the case of La₂SrFe_1.8Ga_0.2O_7−δ, the rate-determining process is temperature-dependent: at temperatures below 500 °C, the process is oxygen dissociative adsorption, and at temperatures higher than 500 °C, the process relates to oxygen incorporation.