Electrochemical Properties and Rate-Limiting Processes in Nd₂NiO_4+δ Cathode for Intermediate-Temperature Solid Oxide Fuel Cells

Abstract

Nd₂NiO_4+δ was investigated as a Ruddlesden–Popper (RP) cathode material for intermediate-temperature solid oxide fuel cells (IT-SOFCs), with particular emphasis on its electrochemical performance and oxygen reduction reaction mechanism. The material was synthesized via a polymeric sol–gel route derived from Pechini’s method and evaluated in symmetric cells using Ce_0.9Gd_0.1O_2−δ (GDC) as the electrolyte. X-ray diffraction confirmed the formation of a single RP phase and good chemical compatibility with GDC after thermal treatments at 800 °C. Cathode layers with thicknesses of 8–12 µm were deposited by dip-coating. Electrical conductivity measurements revealed a thermally activated semiconducting behavior governed by Ni²⁺/Ni³⁺ small-polaron hopping, with an activation energy of ~1.08 eV. Electrochemical impedance spectroscopy showed a strong temperature dependence of the area-specific resistance, decreasing from 9.18 Ω·cm² at 600 °C to 0.39 Ω·cm² at 800 °C. Distribution of relaxation times (DRT) analysis enabled the identification of the dominant electrochemical processes, indicating that oxygen surface exchange reactions are more favorable than charge transfer at the cathode–electrolyte interface, which remains the main limiting step. These results demonstrate that Nd₂NiO_4+δ is a promising cathode for IT-SOFC operation, while further optimization of the electrode–electrolyte interface is required to enhance its oxygen reduction kinetics.

1. Introduction

Cathode materials are a critical component in intermediate-temperature solid oxide fuel cells (IT-SOFCs), as they largely determine the overall electrochemical performance of the device [1,2,3]. An efficient cathode must promote the reduction of molecular oxygen into oxygen ions (O²⁻), which are transported through the electrolyte toward the anode, where fuel oxidation occurs [4,5]. Among conventional cathodes, La_1−xSr_xMnO_3−δ (LSM) has been extensively employed [6]; however, its purely electronic conduction, poor ion transport, and susceptibility to chemical reactivity and thermal degradation at the cathode–electrolyte interface restrict its application at reduced operating temperatures [7]. Furthermore, the oxygen reduction reaction (ORR) in LSM is confined to the triple-phase boundary (TPB), leading to high polarization resistance due to the limited active reaction sites.

To overcome these limitations, mixed ionic–electronic conducting (MIEC) cathodes have been proposed [8] because they extend the ORR zone beyond the TPB to the entire cathode surface and bulk, thereby enhancing oxygen reduction kinetics. The fundamental ORR processes occurring on MIEC cathodes can be described by the following reactions [1,9,10]:

O₂(gas) → 2O_ads

(1)

(adsorption of oxygen molecular and dissociation on cathode surface)

2O_ads + 4e⁻ → 2O²⁻

(2)

(oxygen reduced by electron)

2O²⁻→2O²⁻ (TPB)

(3)

(oxygen ion conduction to TPB on the interface)

O²⁻_TPB + Vö → O^xo

(4)

(exchange of oxygen ions throughout oxygen vacancies Vö on TPB)

Where O^xo is an oxygen ion occupying a lattice site in the electrolyte. The presence of both electronic carriers and oxygen vacancies in MIEC cathodes significantly improves the sluggish ORR kinetics in the intermediate-temperature range of 500–800 °C [11,12].

In this context, cathode materials of the Ruddlesden–Popper phases (RP) with the general formula A_n+1B_nO_3n+1 (A = La, Nd; B = Ni) have attracted considerable attention as promising cathode materials [13]. Their layered crystal structure, consisting of perovskite blocks interleaved with rock-salt AO layers, enables high oxygen mobility through interstitial sites and vacancies. Among them, La₂NiO_4+δ (n = 1) has been widely reported as an oxygen over-stoichiometric compound, where excess oxygen incorporated into interstitial sites leads to enhanced oxide-ion transport, predominantly along the ab-plane [6,14]. These materials also exhibit high oxygen surface exchange coefficients (k) and diffusion coefficients (D), outperforming conventional perovskite cathodes [15,16,17].

To achieve a good performance of cathodes in IT-SOFC applications, the electrolyte must create enough oxygen vacancies (Vö) to be a fast O²⁻ conductor. GDC was chosen as the electrolyte because it has high oxygen ion conductivity in the intermediate-temperature range of 500–800 °C, which is significantly greater than that of conventional YSZ electrolytes under similar conditions. Additionally, GDC shows good chemical compatibility with layered nickelate cathodes, such as Nd₂NiO_4+δ. This compatibility facilitates stable electrode–electrolyte interfaces, making GDC a suitable electrolyte for assessing cathode performance in IT-SOFC [18]. Nd₂NiO_4+δ (Nd2) is a nickelate that, while having a similar RP structure, has received less attention compared to other RP nickelates. Nevertheless, it remains an attractive candidate for use as a cathode in IT-SOFC due to its mixed ionic and electronic conductivity. Additionally, the presence of interstitial oxygen enhances oxygen diffusion and surface exchange reactions. The substitution of La³⁺ with the smaller Nd³⁺ ion induces lattice distortion, modifies the Ni–O bond lengths, and changes the chemistry of oxygen defects. These alterations can significantly impact electrical transport and the kinetics of the oxygen reduction reaction (ORR) [19,20,21]. Previous studies have reported semiconducting behavior in Nd₂NiO_4+δ, governed by thermally activated small-polaron hopping between Ni²⁺/Ni³⁺ redox couples, as well as promising oxygen diffusion properties [16,22,23,24].

For IT-SOFC operation, electrolyte compatibility is also crucial. Ce_0.9Gd_0.1O_2−δ is considered a suitable electrolyte due to its high oxygen ion conductivity and thermal expansion coefficient (TEC) compatibility with RP cathodes in the 600–800 °C range [25]. Previous studies have shown acceptable chemical compatibility between GDC and La₂NiO_4+δ or La₄Ni₃O_10±δ at elevated temperatures, suggesting that RP/GDC interfaces are suitable for intermediate-temperature operation [11,26,27,28].

The electrochemical performance of RP cathodes is commonly assessed using symmetric cells through polarization resistance or area-specific resistance (ASR) analysis. ASR values strongly depend on synthesis route, microstructure, porosity, and cathode–electrolyte interfacial quality, which directly influence TPB density and oxygen transport pathways [29,30]. In recent years, layered RP nickelates have attracted increasing attention as promising cathode materials for IT-SOFC due to their mixed ionic–electronic conductivity and favorable oxygen transport properties. Liao et al. [31] demonstrated that La doping in Pr₂NiO_4+δ significantly enhances oxygen surface exchange kinetics and reduces polarization resistance, leading to improved ORR activity in SOFC cathodes. Similarly, recent studies on Nd₂NiO₄-based materials have shown that compositional modifications can strongly influence oxygen transport, and a-site substitution strategies have been reported to increase the concentration of oxygen vacancies and improve ORR kinetics, resulting in enhanced electrochemical activity in IT-SOFCs [32]. Nd_2−xPr_xNiO_4+δ cathodes studied by several authors exhibit improved electronic conductivity and significantly reduced polarization resistance, reaching values as low as ~0.035 Ω·cm² at 800 °C [33]. Furthermore, Sr and Cu co-doping in Nd₂NiO₄-based cathodes has been shown to enhance catalytic activity toward the ORR and improve electrical conductivity, leading to higher power densities in SOFC systems [21]. More recently, high-entropy Ruddlesden–Popper oxides have emerged as a new strategy to improve cathode performance, exhibiting enhanced structural stability and ORR activity [34]. These studies highlight the ongoing efforts to optimize RP-type cathodes and improve the understanding of oxygen reduction mechanisms in SOFC.

In this context, the present work investigates the electrochemical performance and kinetic processes of the Nd₂NiO_4+δ cathode through impedance spectroscopy and DRT analysis to better understand the rate-limiting processes of the oxygen reduction reaction, particularly using advanced analysis tools such as DRT remain scarce.

In this work, Nd₂NiO_4+δ cathodes were synthesized via a polymeric sol–gel route and deposited on GDC electrolytes using dip-coating to fabricate symmetric Nd2/GDC/Nd2 cells. Structural, thermal, electrical, and electrochemical properties were systematically investigated, with particular emphasis on impedance analysis and DRT deconvolution to identify the dominant ORR processes. The results provide new insights into the reaction mechanism and performance-limiting steps of Nd₂NiO_4+δ, contributing to a deeper understanding of RP cathodes for IT-SOFCs.

2. Results and Discussion

2.1. XRD Analysis

According to the XRD patterns that are shown in Figure 1, the Nd2 powders were identified with the JPDS 01-089-0131 card file. The Nd2 cathode material was indexed with an orthorhombic structure with the Fmmm space group. The lattice parameters and space group obtained in this work are shown in comparison with those previously reported [11,35,36,37,38]. This aternative sol–gel method is a suitable synthesis to obtain the RP single phase at 1000 °C-2 h without impurity phases. Figure 2 illustrates the Rietveld refinement of Nd2, and the structural parameters collected are summarized in Table 1.

Figure 1. X-ray diffraction patterns of GDC, Nd₂NiO_4+δ (Nd2), and the Nd2–GDC mixture after thermal treatment at 800 °C for 50 h.

Figure 2. Rietveld refinement of Nd2 employed orthorhombic structure with Fmmm space group; R_p = 3.42, R_wp = 4.38, R_exp =2.51 and χ² = 1.87.

To identify the reactions occurring at the electrolyte/cathode interface that may affect the electrochemical properties, we analyzed a mixture of the cathode and electrolyte powders using X-ray diffraction (XRD). The Nd2 + GDC mixture showed no chemical reactivity after being subjected to 800 °C for 50 h. This indicates that it is viable to coat the cathode and subject it to thermal treatment to achieve good adhesion for IT-SOFC applications. XRD analysis is often used to assess phase stability and identify potential chemical reactions between SOFC electrode materials and electrolytes during thermal treatments, as reported in various previous studies [5,36,39,40].

Table 1. Structural parameters and oxygen non-stoichiometry of Nd₂NiO_4+δ and reference RP nickelates from the literature.

Cathode	Nd2 (This Work)	Nd2NiO4.22	La2	La4	La4Ni3O9.75	La2NiO4.16
a (Å)	5.367 (1)	5.367	5.457 (1)	5.409 (1)	5.413	5.466
b (Å)	5.465 (1)	5.464	5.464 (1)	5.458 (1)	5.468	5.467
c (Å)	12.389 (2)	12.385	12.689 (2)	28.015 (1)	27.95	12.668
V (Å3)	363.472 (1)	363.300	378.462 (1)	827.200 (2)	828.2	378.58
ẟ	0.23	0.22	0.22	−1	−0.25	0.16
Route	Sol–gel	Solid state reaction (21)	Sol-gel	Sol-gel	Nitrate (22)	Nitrate-citrate (20)

Data corresponding to La₂NiO_4+δ (La2) and La₄Ni₃O_10±δ (La4) were previously published by our team and are included here exclusively for comparison purposes [41].

Table 1. Structural parameters and oxygen non-stoichiometry of Nd₂NiO_4+δ and reference RP nickelates from the literature.

Cathode	Nd2 (This Work)	Nd2NiO4.22	La2	La4	La4Ni3O9.75	La2NiO4.16
a (Å)	5.367 (1)	5.367	5.457 (1)	5.409 (1)	5.413	5.466
b (Å)	5.465 (1)	5.464	5.464 (1)	5.458 (1)	5.468	5.467
c (Å)	12.389 (2)	12.385	12.689 (2)	28.015 (1)	27.95	12.668
V (Å3)	363.472 (1)	363.300	378.462 (1)	827.200 (2)	828.2	378.58
ẟ	0.23	0.22	0.22	−1	−0.25	0.16
Route	Sol–gel	Solid state reaction (21)	Sol-gel	Sol-gel	Nitrate (22)	Nitrate-citrate (20)

Data corresponding to La₂NiO_4+δ (La2) and La₄Ni₃O_10±δ (La4) were previously published by our team and are included here exclusively for comparison purposes [41].

The oxygen non-stoichiometry (δ) of the Nd₂NiO_4+δ cathode was determined by temperature-programmed reduction (TPR) under a 5% H₂/Ar atmosphere. As shown in Figure 3, the first weight loss at approximately 430 °C is attributed to the reduction of Ni³⁺ to Ni²⁺, associated with the release of interstitial oxygen typical of Ruddlesden–Popper nickelates. A second weight loss at higher temperatures corresponds to the thermal decomposition of the oxide, allowing an estimation of the total oxygen content. The oxygen non-stoichiometry value (δ) was calculated from the oxygen weight loss obtained from the TPR/TGA analysis using the following relation:

$$\delta ={\displaystyle \frac{(\Delta W)\left(M_{Nd2NiO4+\delta }\right)}{\left(100\right)\left(Mo\right)}}$$

(5)

where ΔW is the percentage weight loss associated with oxygen release, MNd₂NiO_4+δ is the molecular weight of Nd₂NiO_4+δ, and Mo is the molecular weight of oxygen (16 g/mol). Using this method, the oxygen non-stoichiometry value was estimated to be δ = 0.23.

Figure 3. Comparative TPR/TGA profiles of Nd₂NiO_4+δ (this work) and reference RP nickelates previously reported [41].

The Nd₂NiO_4+δ sample exhibits an oxygen excess of δ = 0.23, consistent with values in the literature, and crystallizes in an orthorhombic structure with the Fmmm space group. The incorporation of excess oxygen into the Nd–O layers leads to an expansion along the c-axis and a slight contraction of the a-axis, which is attributed to changes in the Ni–O bond lengths induced by partial Ni³⁺/Ni²⁺ reduction [38]. The obtained lattice parameters are in good agreement with previously reported data for Nd₂NiO_4+δ with similar δ values [22].

For reference, analogous trends related to oxygen incorporation and lattice distortion have been reported for La₂NiO_4+δ, while La₄Ni₃O_10±δ has been shown to exhibit oxygen non-stoichiometry strongly dependent on the synthesis route [42,43]. These comparisons confirm that the structural behavior observed in Nd₂NiO_4+δ follows the general trends of the RP nickelate family.

For comparison, previously published TPR/TGA profiles of La₂NiO_4+δ and La₄Ni₃O_10±δ are included in Figure 3 to illustrate the general reduction behavior within the RP nickelate family. While differences in reduction temperature and total oxygen release are observed among the RP phases, the reduction features of Nd₂NiO_4+δ follow the expected trend associated with oxygen-rich RP structures, reinforcing the role of oxygen non-stoichiometry in governing their structural and electrochemical behavior.

2.2. Microstructure

The SEM micrographs of the Nd2/GDC/Nd2 symmetric cells illustrate both the cross-sectional area and surface morphology, as shown in Figure 4. Additionally, chemical EDS analysis confirms the presence of the elements (Nd, Ni, and O) in the composition. The coating of Nd2 was precisely controlled and measured to have a thickness of 12.31 µm, as determined using a Gaussian function.

Figure 4. SEM microstructure of the cross-section and surface morphology (the arrow indicates the region selected for higher magnification) of Nd2/GDC/Nd2, showing the thickness layer Nd2 and EDS results.

The microstructure of the cathode layer exhibits excellent adhesion between the cathode and the electrolyte, showing no signs of delamination or cracks at the interface. Furthermore, the SEM images reveal a porous microstructure with interconnected grains, which is advantageous for oxygen transport and gas diffusion within the cathode layer. Grain size distribution analysis (see Figure 4) indicates an average grain size of approximately 12.31 µm, suggesting a microstructure that balances electronic conductivity with gas transport pathways. Such a porous and interconnected microstructure is known to facilitate oxygen diffusion and enhance the kinetics of the oxygen reduction reaction (ORR) in layered nickelate cathodes.

2.3. Thermal Expansion Measurements

The thermal expansion properties of the materials should have similar values to prevent internal stress during the SOFC operation. Nd₂NiO_4+δ has been studied from 200 to 900 °C to obtain cyclic thermal data (Figure 5). The TEC value for Nd2 is 12.41 × 10⁻⁶ K⁻¹, which is very close to that of the GDC reported in our group research, which is 11.1 × 10⁻⁶ K⁻¹ [44], and also consistent with the literature value of 13.08 × 10⁻⁶ K⁻¹ [45]. Therefore, within the operating range of the IT-SOFC, this cathode is compatible with the GDC electrolyte.

Figure 5. Thermal expansion of Nd2 between 200 and 900 °C in air.

2.4. Electrical Properties

The electrical conductivity of the Nd₂NiO_4+δ cathode exhibits a semiconducting behavior, increasing progressively with temperature and reaching a maximum value of ~51.2 S·cm⁻¹ at 500 °C, followed by a slight decrease at higher temperatures. This behavior is associated with thermally activated charge transport, as confirmed by the Arrhenius analysis (Figure 6), from which an activation energy of 1.08 eV was obtained. The conduction mechanism is attributed to charge transport through the Ni²⁺/Ni³⁺ redox couple via small-polaron hopping. With increasing temperature, partial oxygen loss from the lattice may occur, generating oxygen vacancies (Vö) and free electrons in accordance with the oxygen non-stoichiometry (δ). At elevated temperatures, the reduction of Ni³⁺ to Ni²⁺ decreases the effective charge carrier concentration, which contributes to the observed reduction in electrical conductivity.

$$O^{x}o \to O_2+\mathrm{V}\ddot{o}+ {2e}^{-}$$

(6)

$${Ni}^{3+}+e^{-} \to {Ni}^{2+}$$

(7)

Figure 6. Electrical conductivity of the Nd2 cathode as a function of the temperature (200–900 °C). Green symbols represent the experimental data, and the red line corresponds to the fitted curve. The inset shows the Arrhenius plot used to determine the activation energy.

The conductivity and activation energy obtained in this work are consistent with previously reported values for Nd₂NiO_4+δ cathodes measured under similar temperature ranges and atmospheres. Several studies report conductivities between 30 and 80 S·cm⁻¹ in the range of 500–800 °C and activation energies close to 0.9–1.2 eV, associated with the mixed ionic–electronic conduction typical of layered RP nickelates [46]. These results confirm that the electrical transport properties observed in this study are in good agreement with the literature.

For comparison, other oxide cathodes reported for IT-SOFCs exhibit significantly lower conductivities under similar conditions, such as Sr₂TiFe_0.8Mo_0.2O_6−δ (0.88 S·cm⁻¹) [47], SrFe_0.5Mn_0.25Mo_0.25O_3−δ (0.84 S·cm⁻¹) [48] and Sr₂Fe_1.4Nb_0.1Mo_0.5O_6−δ (27.61 S·cm⁻¹) [49], highlighting the favorable electronic transport properties of Nd₂NiO_4+δ for IT-SOFC cathode applications.

2.5. Electrochemical Properties

To evaluate the electrochemical properties of the symmetrical cells, a circuit equivalent was used to fit the impedance data at different temperatures.

The equivalent circuit is illustrated in Figure 7a. It includes an inductance (L), which does not contribute to the electrochemical process being studied. The next component is the resistance (R), which is related to the ohmic resistance of the electrolyte GDC. Following this, there are two resistances, each paired with a constant phase element in series: (R1-CPE1) and (R2-CPE2). The (R1-CPE1) pair corresponds to the medium frequency semicircle (MF), with capacitance values ranging from 10⁻⁶ to 10⁻⁵ F/cm² and a relaxation frequency between 10³ and 10⁶ Hz [23,29,50].

Figure 7. Electrochemical characterization of Nd2/GDC/Nd2 symmetrical cell. (a) Nyquist plot at 600–800 °C, (b) ASR values (inset the Arrhenius plot) and (c) Arrhenius plots of R, R1 and R2 (inset shows the activation energy).

This pair is associated with the charge transfer process at the electrolyte/cathode interface. In contrast, the (R2-CPE2) pair corresponds to capacitance values of 10⁻⁴ to 10⁻³ F/cm² and frequencies of 10–10³ Hz [51]. This element represents the low frequency semicircle (LF), which relates to the adsorption and dissociation of molecular oxygen, as well as the reduction of O²⁻ [52]. The fitted results are summarized in Table 2. This capacitance ranges align with those typically reported for charge transfer and surface oxygen exchange processes in layered nickelate cathodes, thereby supporting the assignment of the observed impedance arcs.

Table 2. Summary of the fitting parameters of the circuit equivalent of the Nd₂NiO_4+δ cathode.

Temperature (°C)	R (Ω cm2)	R1 (Ω cm2)	C1 (F/cm2)	R2 (Ω cm2)	C2 (F/cm2)
600	11.21	5.92	8.15 × 10−3	3.26	1.22 × 10−3
650	5.86	2.58	5.74 × 10−3	1.10	7.59 × 10−4
700	3.37	1.12	5.17 × 10−3	0.49	5.10 × 10−4
750	2.15	0.48	5.76 × 10−3	0.27	7.12 × 10−4
800	1.47	0.08	3.98 × 10−4	0.31	3.26 × 10−3

The electrochemical behavior of the Nd₂NiO_4+δ cathode was analyzed using electrochemical impedance spectroscopy over the studied temperature range (shown in Figure 7a). The ohmic resistance (R) is primarily related to the ionic resistance of the GDC electrolyte, with minor contributions arising from contact resistances within the cell. For the Nd₂NiO_4+δ symmetric configuration, this component reflects the inherent oxygen ion transport across the electrolyte. In contrast, the electrochemical phenomena associated with the oxygen reduction reaction (ORR) at the Nd₂NiO_4+δ/GDC interface are represented by the polarization elements of the equivalent circuit, which account for the charge transfer reactions and the oxygen surface exchange processes occurring at the cathode.

The fitting of the high-frequency arc (R₁–CPE₁) revealed capacitance values outside the typical range associated with interfacial charge transfer processes, which may be related to insufficient physical contact between the Nd2 cathode and the GDC electrolyte, resulting in a reduced number of TPBs. In contrast, the medium-to-low frequency response (R₂–CPE₂) showed capacitance and frequency values consistent with surface-related phenomena, such as oxygen adsorption and dissociation on the Nd₂NiO_4+δ surface. However, these processes appear to be partially limited by interfacial transport, restricting the overall ORR performance.

These results suggest that, although Nd₂NiO_4+δ exhibits active surface reactions toward oxygen species, the electrochemical performance is primarily constrained by interfacial charge transfer and oxygen ion diffusion through the cathode–electrolyte interface. Improvements in microstructural features, such as enhanced cathode–electrolyte contact and optimized porosity, could significantly enhance the electrochemical response of Nd₂NiO_4+δ in intermediate-temperature solid oxide fuel cell applications.

The area-specific resistance (ASR) normalized by the area of the cathode (ASR = A • Rp/2) is summarized in Table 3 and Figure 7b. The Rp represents the total polarization resistance (R₁ + R₂), which was measured for the three electrodes as a function of temperature.

Table 3. Results obtained from the Nd2 cathode at various temperatures.

T (°C)	ASR (Ω cm2)
600	9.18
650	3.67
700	1.61
750	0.75
800	0.39

The electrochemical performance of the Nd₂NiO_4+δ cathode can be directly correlated with its electrical conductivity, activation energy, and ASR. The semiconducting behavior and moderate electrical conductivity, governed by a thermally activated small-polaron hopping mechanism, contribute to charge transport during the oxygen reduction reaction. The Arrhenius analysis indicates that surface oxygen exchange is kinetically more favorable than interfacial charge transfer, whereas the relatively high activation energy associated with the electrolyte contribution reflects limitations in oxygen ion transport across the Nd₂–GDC interface. These kinetic constraints are reflected in the ASR values, which decrease systematically with increasing temperature, from 9.18 Ω·cm² at 600 °C to 3.67, 1.61, 0.75, and 0.39 Ω·cm² at 650, 700, 750, and 800 °C, respectively. The progressive reduction in ASR confirms the thermally activated nature of the electrochemical processes, while indicating that interfacial charge transfer and ionic transport remain the dominant limiting factors, particularly at lower operating temperatures.

The ASR values obtained from the Nd2 cathode across the entire temperature range show promising results compared to other cathodes previously reported: La_0.6Sr_1.4Co_0.2Fe_0.8O_4+δ (ASR = 0.42 Ω cm²) [7] and La_0.5Sr_1.5MnO_4±δ (ASR = 1.32 Ω cm²) [53].

Figure 7c presents the Arrhenius analysis of the different electrochemical contributions of the Nd₂NiO_4+δ cathode as a function of temperature. The activation energy associated with the oxygen surface exchange process (1.00 eV) is lower than that corresponding to the cathode–electrolyte interface (1.64 eV), indicating that surface processes predominantly control the oxygen reduction reaction. In contrast, the higher activation energy associated with electrolyte resistance (0.82 eV) suggests a limitation in oxygen ion transport across the Nd2–GDC interface, leading to charge accumulation at the interface. These results are consistent with the impedance analysis, confirming that interfacial charge transfer and oxygen ion diffusion are the main rate-limiting steps for the Nd₂NiO_4+δ cathode.

The distribution of relaxation times (DRT) analysis provides further insight into the electrochemical processes governing the oxygen reduction reaction (ORR) in the Nd₂NiO_4+δ cathode (Figure 8). Several relaxation peaks are observed across different frequency regions, which can be associated with specific electrode processes involved in the ORR mechanism. In the very-low-frequency region (~10⁻⁶–10⁻⁵ Hz), a pronounced contribution is observed, particularly at 600 °C. This process is commonly attributed to slow oxygen transport phenomena, including oxygen diffusion through the porous cathode structure and gas-phase diffusion limitations [54,55,56]. In layered nickelate cathodes such as Nd₂NiO_4+δ, this contribution may also be related to bulk oxygen transport facilitated by interstitial oxygen species characteristic of the Ruddlesden–Popper structure. The strong decrease in the intensity of this peak with increasing temperature indicates that oxygen transport becomes significantly enhanced at higher temperatures, reducing the associated mass transport limitations.

Figure 8. The DRT functions were calculated from the impedance spectra of Nd₂NiO_4+δ over the temperature range of 600 to 800 °C.

In the intermediate-frequency region (10⁻⁴–10⁻² Hz), the relaxation peaks are associated with surface-related processes, including oxygen adsorption, dissociation, and surface exchange reactions occurring on the cathode surface. These processes play a key role in the ORR kinetics for mixed ionic–electronic conducting cathodes. The progressive decrease in peak intensity with increasing temperature suggests improved surface exchange kinetics and enhanced catalytic activity of Nd₂NiO_4+δ toward oxygen reduction.

At higher frequencies (10⁻¹–10¹ Hz), smaller relaxation peaks are observed and are typically associated with charge transfer processes occurring at the cathode/electrolyte interface, where oxygen ions are incorporated into the electrolyte lattice. The decrease in the intensity of these peaks and their slight shift toward higher frequencies as the temperature increases indicate faster interfacial reaction kinetics [39,57,58,59].

The interpretation of the DRT spectra is consistent with the activation energy analysis shown in Figure 7c. The intermediate-frequency contribution associated with oxygen surface exchange exhibits an activation energy of approximately 1.00 eV, which is characteristic of surface-controlled ORR processes in layered nickelate cathodes. In contrast, the higher activation energy obtained for the cathode–electrolyte interfacial process (1.64 eV) indicates that the charge transfer reaction at the Nd₂NiO_4+δ/GDC interface requires greater thermal activation, explaining the more pronounced high-frequency contribution at lower temperatures. Furthermore, the activation energy associated with the electrolyte resistance (0.82 eV) is consistent with the typical oxygen ion transport behavior of GDC electrolytes. The combined DRT and Arrhenius analyses therefore indicate that the overall ORR kinetics in the Nd₂NiO_4+δ cathode are governed by a combination of oxygen surface exchange, interfacial charge transfer reactions, and oxygen transport processes, with mass transport limitations becoming dominant at lower temperatures and progressively diminishing as the temperature increases.

3. Materials and Methods

3.1. Sample Preparation

The Nd2 cathode and GDC electrolyte powders previously had been synthesized via a polymeric route of the sol–gel-modified Pechini method. The precursor materials, i.e., nickel and neodymium, were dissolved in deionized water with a constant stirring to obtain a homogeneous sol. Hexamethylenetetramine (HMTA, C₆H₁₂N₄) and acetylacetone (ACAC, C₄H₈O₂) were selected as polymeric precursors. HMTA and ACAC in a molar ratio (1:1) were added to acetic acid (C₂H₄O₂) and stirred at room temperature to form an organic polymeric gel. The two solutions (sol and gel) were mixed with continuous stirring and heated at 80 °C for 15 min to form a polymeric resin. This solution changed the color from transparent to brown. Subsequently, the Nd2 cathode was calcined at 1000 °C for 2 h. Moreover, the same preparation was employed for the GDC electrolyte, which was calcined at 800 °C for 1 h, as previously reported by the group [44].

3.2. Symmetrical Cells Preparation

The symmetrical cells were fabricated as Nd2/GDC/Nd2 to study the complex impedance to obtain their electrochemical properties. In this study, the GDC powders were uniaxially pressed (11.5 mm in diameter and 1.7 mm in thickness) with 1 ton for 16 s to obtain the green pellets where these were sintered at 1400 °C for 2 h in air. Cathode inks were prepared by mixing the additives, such as a dispersant (terpineol), a binder (PVB), or a plasticizer (dioctyl phthalate), into an azeotropic mixture, with methylethylketone (Mek) and ethanol (Etoh) as solvents. These inks were stirred for 2 h. The electrolyte GDC pellets were coated with Nd2 ink by dip-coating technical. The withdrawal speed was controlled at 40 mm/min to prevent the formation of drops on GDC. The electrolytes with cathode ink were heated with a heat speed of 1 °C/min with two ramps at 230 °C and 430 °C with stability of 20 min to eliminate organic compounds from the ink, and after that the symmetric cell was sintered at 1000 for 2 h. The coating presents a good adhesion at the cathode/electrolyte interface. The active area is 0.26 cm², and it was taken from coating of each cathode area. Finally, the faces of the symmetric cells were coated with a paintbrush and platinum ink, and after that it was calcined at 900 °C for 2 h to serve as a current collector.

3.3. Characterizations

The calcined powders were ground using a Restch-S100 planetary ball mill (Retsch S100, RETSCH GmbH, Haan, Germany) operated at 350 rpm for 4 h. Ethanol was used as the grinding medium with zirconia balls (diameter 10 mm). The phases of the calcined cathode and electrolyte powders were identified by X-ray diffraction (XRD) using a Bruker Advanced X-Ray Solutions D8 diffractometer (D8 Advance, Bruker AXS GmbH, Karlsruhe, Germany) with CuKα radiation. Data were recorded on the angular region of 2θ = 20–90° and were collected in a step-scanning mode with 0.01° steps and a step-counting time of 8 s. The phase material was correlated with the PDF-2 database from ICDD.

DRX patterns of Nd2 were refined with the Rietveld technique using the FULLPROF Refinement Program (version 2.05) to determinate the crystal profile refinement.

Chemical reactivity between the Nd2 cathode and GDC electrolyte were mixed in ethanol with a 1:1 weight ratio; then, the powders were subjected to thermal treatment at 800 °C for 50 h in air and analyzed by XRD.

The stoichiometry oxygen of the Nd2 cathode was employed by the thermogravimetric (TG) analyzer under a 5% Ar/N₂ atmosphere, using Mettler TA3000 equipment (TA3000, Mettler-Toledo GmbH, Greifensee, Switzerland). The measurements were collected in the temperature range of 30–1000 °C with a heating rate of 5 °C/min.

The calcined powders were analyzed by scanning electron microscopy using a FEI-NovananoSEM-450 electron microscope equipped to know the microstructure. The grain size values of the cathode powders were determined by image analysis with the JMicroVision software version 1.2.2 [60].

The thermal expansion coefficient (TEC) data values were obtained to determine the temperature required for assessing powder expansion. To calculate the TEC, cathode powders were pressed using the same process applied to the electrolyte mentioned earlier, resulting in the formation of green pellets. These green pellets were subsequently sintered at 1000 °C for 2 h in air. The TEC values were recorded through dilatometric analysis, utilizing an alumina dilatometer (L75/1550C, LINSEIS Messgeräte GmbH, Selb, Germany), which heated the samples from 25 °C to 1000 °C at a rate of 5 °K·min⁻¹.

The four-probe DC technique was employed to determinate the electrical conductivity of the cathode at temperatures ranging from 200 to 900 °C with intervals of 50 °C; a current load of 500 mA was applied using potentiostat/galvanostat (AUTOLAB PGSTAT30 with FRA2 module, Metrohm Autolab B.V., Utrecht, The Netherlands), and the potential was recorded by a digital multimeter (Fluke 179 True RMS, Fluke Corporation, Everett, WA, USA).

The electrochemical characterization of the symmetrical cells was performed using impedance spectroscopy (IS) were performed using a potentiostat/galvanostat (AUTOLAB PGSTAT30 with FRA2 module, Eco Chemie B.V., Utrecht, The Netherlands). in an air atmosphere, applying a 5 mV signal over a frequency range from 1 to 10 MHz and from 600 to 800 °C [41,44,61,62]. Impedance data were analyzed using a parallel resistance–capacitance electrical circuit in Zview 2.1 software to determine the electrical values. The resistance values were divided by two to take into account the sample geometry (cylindrical symmetrical half-cell) to obtain a normalized ASR values of the cathodes. The distribution of relaxation times (DRT) for the symmetrical cell was analyzed using the RelaxIS DRT software (version 3, rhd instruments GmbH & Co., KG, Darmstadt, Germany).

A regularization parameter (λ) of 10⁻³ was applied, and the Gaussian method was employed to assess the electrochemical performance in SOFC [56,63].

4. Conclusions

Nd₂NiO_4+δ exhibited a thermally activated electrochemical response between 600 and 800 °C, characteristic of layered Ruddlesden–Popper nickelates. The electrical conductivity is governed by the Ni²⁺/Ni³⁺ small-polaron hopping mechanism, while the presence of interstitial oxygen contributes to mixed ionic–electronic conduction and facilitates oxygen transport. Arrhenius analysis indicates that surface oxygen exchange processes primarily control the oxygen reduction reaction (ORR), whereas ionic transport limitations arise mainly at the cathode–electrolyte interface. The area-specific resistance (ASR) decreased significantly from 9.18 to 0.39 Ω·cm² as temperature increased, demonstrating improved ORR kinetics under intermediate-temperature SOFC conditions. DRT analysis further allowed the identification of the main electrochemical contributions associated with charge transfer, oxygen adsorption–dissociation, and oxygen diffusion processes. These results confirm the potential of Nd₂NiO_4+δ as a promising cathode material for intermediate-temperature SOFCs, while further improvements may be achieved through interface engineering and microstructural optimization to reduce interfacial polarization and enhance oxygen transport.