Sintering and Electrical Conductivity of Medium- and High-Entropy Calcium-Doped Four B-Site Cation Perovskite Materials

Abstract

La_1−xCa_x(Co_0.25Cr_0.25Fe_0.25Ni_0.25)O_3−δ perovskite powders were prepared via a sol-gel process. The A-site was doped with calcium, while four elements—cobalt, chromium, iron, and nickel—in equiatomic amounts made up the B-site. The configurational entropy was calculated to increase with the addition of calcium from medium to high entropy. The synthesized powders were heated to 1400 °C in air for 2 h to sinter them. The effect of doping on the resulting sintered materials was observed via density measurements and electron microscopy. The electrical conductivity was measured in air as a function of temperature to 900 °C. Conductivity versus composition indicates that an increase in entropy has a marked effect on electrical conductivity, leading to two distinct relationships with temperature.

1. Introduction

Perovskite materials using lanthanum as the A-site cation have been used in solid oxide fuel cell (SOFC) interconnects and cathodes. The general chemical formula for perovskite materials is ABO₃, where, for example, A is lanthanum and B is chromium, yielding LaCrO₃. The crystal structure, and thus the various other properties, can be altered by modifying the composition through doping [1]. Thus, compositions such as La(Cr_0.5Co_0.5)O₃ have been developed and studied [2]. Modifying the A-site and B-site composition by increasing the number of species present on each will increase the configurational entropy of the perovskite [3]. The densification behavior, high-temperature properties, and electrical conductivity [1,2,4,5,6] will also be affected. A-site doping can improve the low-temperature electrical conductivity, making these materials more desirable for SOFC applications [4,5].

Previous investigations have determined the effect of doping calcium onto the A-site in lanthanum perovskites [5,7,8]. The sintering temperature was reduced, as was the Seebeck coefficient [5]. Doping also alters conductivity, which in lanthanum-based perovskites is the result of small polaron hopping. When the concentration of these polarons is independent of temperature, the electrical conductivity is described by Equation (1) [5] as follows:

$$\sigma ={\displaystyle \frac{\mathrm{A}}{{\mathrm{T}}^{\mathrm{s}}}}{\mathrm{e}}^{-{\displaystyle \frac{{\mathrm{E}}_{\mathrm{c}}}{\mathrm{kT}}}}$$

(1)

where E_c is the activation energy for electrical conduction, k is Boltzmann’s constant (8.617 × 10⁻⁵ eV K⁻¹), T is temperature (in K), and A is a pre-exponential constant. The exponent s = 1 in the adiabatic limit and s = 1.5 in the non-adiabatic case.

High-entropy oxides (HEOs) have been studied since 2015 [9,10,11,12], when the high-entropy alloy concept was recognized to apply to non-metals, as well. A metric was established to characterize the relative amount of configurational entropy for an oxide material. This metric is based on the computation of the configurational entropy [13,14,15,16]. Low-entropy oxides are those with a configurational entropy (S) less than 1R (R is the universal gas constant). Oxides for which 1R < S < 1.5R are said to be medium-entropy oxides (MEOs), while those with S > 1.5R are high-entropy oxides. The formulation for calculating the configurational entropy is shown in Equation (2) as follows:

$$\mathrm{S} =-\mathrm{R}\left[{\left({\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{x}}_{\mathrm{i}}\ln {\mathrm{x}}_{\mathrm{i}}\right)}_{\mathrm{cation}}+{\left({\sum }_{\mathrm{j}=1}^{\mathrm{m}}{\mathrm{x}}_{\mathrm{j}}\ln {\mathrm{x}}_{\mathrm{j}}\right)}_{\mathrm{anion}}\right],$$

(2)

where x_i and x_j are the mole fractions of cation and anion, respectively; and n and m are the number of cations and anions, respectively. For perovskites, the presence of multiple sites for cations allows for splitting the first summation of Equation (2) into two separate terms, as shown in Equation (3):

$$\mathrm{S}=-\mathrm{R}\left[{{\left(\sum _{\mathrm{h}=1}^{{\mathrm{n}}_{\mathrm{A}}}{\mathrm{x}}_{\mathrm{h}}\ln {\mathrm{x}}_{\mathrm{h}}\right)}_{\mathrm{cation}, \mathrm{A}\text{-}\mathrm{site}}+\left(\sum _{\mathrm{i}=1}^{{\mathrm{n}}_{\mathrm{B}}}{\mathrm{x}}_{\mathrm{i}}\ln {\mathrm{x}}_{\mathrm{i}}\right)}_{\mathrm{cation}, \mathrm{B}\text{-}\mathrm{site}}+{\left(\sum _{\mathrm{j}=1}^{\mathrm{m}}{\mathrm{x}}_{\mathrm{j}}\ln {\mathrm{x}}_{\mathrm{j}}\right)}_{\mathrm{anion}}\right],$$

(3)

where n_A and n_B are the number of cations on the A-site and B-site, respectively; x_h and x_i are the mole fractions of cations on the A-site and B-site, respectively; and the rest is as in Equation (2).

The presence of multiple cations, in addition to increasing the configurational entropy, will also distort the unit cell, in both shape and size [5,17,18,19,20]. The ideal cubic structure distorts in La-based perovskites due to the cations present. This can result in orthorhombic or rhombohedral structures, when there is only one B-site cation. By substituting multiple cations on the B-site, this structure will be distorted, due to the varying radii of the cations present, which in turn can vary based on the oxidation state of said cations. With an inconsistent set of radii, the lattice parameter will fluctuate from one unit cell to the next. The average lattice parameter, which one might obtain from X-ray diffraction, will not indicate the arrangement of atoms in the structure, only the aggregated result of their combined diffraction.

Table 1. Ionic radius (nm) of species present in current research as a function of oxidation state.

Cation	Ionic Radius (Oxidation State), nm
Lanthanum	0.117 (+3) [22]
Calcium	0.100 (+2) [23]
Chromium	0.073 (+2) [24], 0.0615 (+3) [25], 0.041 (+4) [26]
Cobalt	0.065 (+2) [27], 0.0545 (+3) [28], 0.053 (+4) [28]
Iron	0.077 (+2) [29], 0.0645 (+3) [30]
Nickel	0.78 (+2) [31], 0.56 (+3) [32]

lists the ionic radii for the cations possible from the elements used in this study, though the values shown can vary based on the oxidation state, coordination number, and external conditions [21]. Thus, these values are considered representative only. With the species present varying, and the ionic radius varying, it should be easily understood that the crystal structure does not have a single, uniform lattice parameter. This effect will be magnified as more cations are substituted/doped.

High-entropy oxides have shown promise due to improved dielectric constants [10] and electrical conductivity [33], increased low-temperature ionic conductivity [11], and decreased thermal conductivity [12], with potential applications including but not limited to energy storage [34,35,36], optics [37], and catalysis [38].

This paper presents results for doping calcium onto the A-site in concert to replace lanthanum, while four species are present in equal amounts on the B-site, to produce high-entropy materials. Calcium doping replaces up to 30 at% of the A-site lanthanum. The elements substituted onto the B-site in equal atomic amounts (that is, 25 at% each) were chromium, cobalt, iron, and nickel. The configurational entropy of these compositions was determined using Equation (3). After synthesis, powders were characterized with X-ray diffraction (XRD). The produced powders were uniaxially consolidated and then sintered. The sintering conditions were air at 1400 °C for 2 h. The density of the sintered materials was measured as a function of composition of the A-site. Electrical conductivity was measured at various temperatures to determine the effects of calcium-doping for these four B-site cation perovskites. Previous investigations on perovskites determined that calcium doping caused +2/+4 pairing of B-site cations. This reduced nearly to zero the high-temperature Seebeck coefficient and restrained the Verwey Mechanism to a degree [5]. The four perovskite formulations in this paper combine six total cations between the A- and B-sites, when calcium doping is considered. The resulting variation of cation location, and the corresponding variation of lattice parameter, for the high-entropy materials examined in this study, should eliminate this +2/+4 pairing phenomenon.

2. Materials and Methods

2.1. Material Synthesis

La_1−xCa_x(Co_0.25Cr_0.25Fe_0.25Ni_0.25)O_3−δ materials were prepared via a sol-gel method [39,40], where x ranged from 0 to 0.3. The B-site cations were cobalt, chromium, iron, and nickel, each amounting to one-quarter of the total. The following Alfa Aesar powders were used for the synthesis: La₂(CO₃)₃·XH₂O, Cr(NO₃)₃·9H₂O, Fe(NO₃)₃·9H₂O, N₂NiO₆·6H₂O, Co(NO₃)₂·6H₂O, and CaCO₃. X in La₂(CO₃)₃·XH₂O was determined gravimetrically by weighing before and after a 1 h, 400 °C heat treatment; this was repeated for each batch of material. Starting powders were carefully weighed before mixing together. The mixture was placed into a beaker with citric acid and ethylene glycol and a magnetic stirrer. The beaker was placed on a stirring hot plate and heated to 60 °C and stirred for 4 h, then heated to 90 °C and stirred for 3 additional hours. The temperature was further increased to 450 °C, driving off excess water and forming a dark gray or black powder.

Post-synthesis, the powders were calcined at 950 °C for 8 h to remove any remaining water. Calcined materials were milled with polymer media in a polymer vial for 20 min. The resulting powders were then studied via X-ray diffraction (Rigaku D/Max-B Diffractometer, Rigaku Corp., Tokyo, Japan) using a copper source (λ = 1.54056 Å).

The produced perovskite powders were mixed with PVA using polymer media in a polymer vial for 20 min. PVA was used to improve the green density of pressed powders: the powders (2.5 g) blended with PVA were loaded into a stainless steel die. Powders were then compacted in a uniaxial hydraulic press (approximately 14 MPa) for 2 min. The resulting powder compacts were sintered for 2 h at 1400 °C in air. The sintering time was kept constant to eliminate that as a variable.

2.2. Sintering Characterization

The sintered pellets were imaged to observe the microstructure. The densified pellets were mechanically polished to a mirror finish, successively using polishing compounds of 45, 12, 9, 6, 3, and 1 μm. Polished pellets were thermally etched in a furnace for 2 h in air at 1200 °C. The grain structures were then imaged in a scanning electron microscope (SEM, FEI Quanta FEG450, Thermo Fisher Scientific, Hillsboro, OR, USA). The density of the pellets was also measured, using the Archimedes method with distilled water, in search of a correlation with composition.

2.3. Electrical Conductivity

The densified pellets were then measured for electrical conductivity. These tests used the four-wire method with an AC Resistance Bridge (LR-700, Linear Research, Inc., San Diego, CA, USA). The densified pellets were cut down to rectangular blocks using a diamond saw. Platinum was painted to each end; four coats of platinum paint were applied. Painted, cut-down pellets were then heated in air, with resistance measurements taken every 100 degrees from 100 to 900 °C, inclusive. Conductivity was determined using Equation (4) as follows:

$$\sigma ={\displaystyle \frac{\mathrm{l}}{\mathrm{R}\mathrm{A}}},$$

(4)

where l is the sample length, R is the measured resistance (in ohms), and A is the cross-sectional area of the sample.

3. Results

3.1. Configurational Entropy

To determine the configurational entropy of the perovskite oxides to be produced, Equation (3) was used. For La_1−xCa_x(Co_0.25Cr_0.25Fe_0.25Ni_0.25)O_3−δ, when x = 0, there are four cations on the B-site, and in equal amounts. There is only one cation on the A-site, reducing that term to zero. Similarly, there is only one anion; therefore, the third summation term also reduces to zero. This leaves only the middle summation term, where n_B is 4 and x_i = 0.25. This results in a configurational entropy of S = 1.386R. Thus, when x = 0, an MEO is produced. From x = 0.1 to 0.3, only the anion summation term reduces to zero. The summation for the B-site cations remains unchanged, while the A-site summation term varies, as nA is 2 and x_h varies from 0.9 to 0.7 for lanthanum and 0.1 to 0.3 for calcium. The configurational entropy is thus 1.711R (when x is 0.1), 1.887R (when x is 0.2), or 1.997R (when x is 0.3). Thus, for La_1−xCa_x(Co_0.25Cr_0.25Fe_0.25Ni_0.25)O_3−δ, with x > 0, high-entropy perovskite oxides are produced.

3.2. Structure (X-Ray Diffraction, XRD)

Figure 1 shows the XRD spectra for La_1−xCa_x(Co_0.25Cr_0.25Fe_0.25Ni_0.25)O_3−δ materials. All compositions formed a single-phase perovskite structure, as confirmed by XRD. A minor shoulder was observed on the highest-intensity peak in the x = 0 sample, which was not present in the Ca-doped samples (x = 0.1–0.3). This feature does not indicate the presence of a secondary phase but is instead attributed to a structural distortion associated with a rhombohedral-to-orthorhombic transition, which is commonly observed in La-based perovskites [40]. Such transitions can result in subtle peak splitting or shoulders within single-phase materials.

The disappearance of the shoulder upon Ca doping suggests that the addition of Ca stabilizes one predominant crystal symmetry, likely orthorhombic, by suppressing that particular structural distortion [6]. Similar behavior has been reported in other multicomponent and high-entropy perovskites, where increased configurational disorder can lead to structural stabilization [6,34,36].

3.3. Sintering Characterization

The SEM image of the thermally etched surface of La(Co_0.25Cr_0.25Fe_0.25Ni_0.25)O₃ is shown in Figure 2. The grains possess a noticeable angular shape indicative of a lack of liquid-phase sintering, as expected [41]. Significant porosity is evident, a consequence of pressureless sintering in the absence of a molten component.

Figure 3 shows the SEM image of the microstructure of La_1−xCa_x(Co_0.25Cr_0.25Fe_0.25Ni_0.25)O_3−δ where x = 0.1. Calcium doping reduced the grain size, and the grains have a more rounded shape than for the undoped material in Figure 2. There is also reduced porosity and no secondary phase present at the grain boundaries. This indicates that calcium formed a transient liquid phase during densification.

Figure 4 shows the SEM image of the microstructure for La_1−xCa_x(Co_0.25Cr_0.25Fe_0.25Ni_0.25)O_3−δ with x = 0.2. The grain structure appears similar to the x = 0.1 material, with further reduced porosity.

Figure 5 shows the thermally etched surface of the La_1−xCa_x(Co_0.25Cr_0.25Fe_0.25Ni_0.25)O_3−δ for x = 0.3. The increased A-site doping creates more liquid during the densification process, and thus more rounded grains. The lack of a Ca-rich phase on the grain boundaries indicates that Ca melted but was then reabsorbed onto the A-site as the temperature dropped.

Figure 2, Figure 3, Figure 4 and Figure 5 demonstrate that superior sintered microstructures, as evidenced by more rounded grains and fewer pores, are produced as the calcium content was increased.

Table 2. Relative density (%) for sintered La_1−xCa_x(Co_0.25Cr_0.25Fe_0.25Ni_0.25)O_3−δ materials, determined via the Archimedes immersion method and then compared to theoretical density. (Note: The theoretical density in this case was a simple rule of mixtures calculation based on the end-member densities. Due to the distortion of the unit cells in these medium- and high-entropy perovskites, this simple calculation is for relative comparison only. The Archimedes density measurement has inherent error, perhaps exceeding 1%).

Ca Doping Fraction, x	Relative Density (%)
0	90
0.1	~100
0.2	~100
0.3	~100

shows the relative density of the sintered pellets. The increased calcium content increased the density of pressureless sintered compacts to their estimated theoretical value. The presence of rounded grains in the Ca-doped samples (Figure 3, Figure 4 and Figure 5) indicates that liquid-phase sintering occurred, which correlates with the higher measured density values.

In this study, while the direct high-temperature phase analysis (such as in situ XRD or thermal analysis) was not conducted, and phase diagrams for this multicomponent La–Ca–Ni–Fe–Co–Cr–O oxide system are not available due to its compositional complexity, several microstructural observations strongly suggest the presence of a transient liquid phase during sintering. Specifically, statistical grain size analysis revealed that the average grain size increased from 1.32 μm for the undoped composition (x = 0) to 2.4 μm (x = 0.1), 2.3 μm (x = 0.2), and 2.9 μm (x = 0.3). In addition to the increase in grain size, SEM images of the Ca-doped samples clearly show more rounded grain morphology and full densification, in contrast to the angular grains and residual porosity in the undoped sample.

These microstructural changes are consistent with a transient liquid-phase sintering (TLPS) mechanism [42]. It is proposed that a Ca-rich intermediate phase may have formed and partially melted during sintering at high temperature, enabling rapid grain growth and densification. Upon cooling, this transient liquid could have been reabsorbed into the perovskite lattice, leaving no residual secondary phase—an effect observed in related systems such as Ca-doped LaCrO₃ [6,42]. While this TLPS hypothesis aligns well with experimental evidence, we acknowledge that other mechanisms may also contribute to the observed densification behavior. These include (A) the formation of oxygen vacancies due to the charge compensation from Ca²⁺ substituting La³⁺, which can enhance diffusion kinetics [43]; (B) the possible formation of Schottky defects, which lower the energy barrier for mass transport; [44,45] (C) lattice distortion induced by increased configurational entropy from multi-element B-site occupancy [6]; and (D) the formation and dissolution of an easily sintered intermediate phase, similar to densification pathways reported in composite ceramic systems [41,46,47,48,49]; a similar mechanism may also be observed in the present study. Although the mechanisms A and B were not directly evaluated in this work, they represent plausible contributing factors and warrant further investigation in future studies to elucidate the sintering behavior of this high-entropy perovskite system.

3.4. Electrical Conductivity

The conductivity measured for sintered La_1−xCa_x(Co_0.25Cr_0.25Fe_0.25Ni_0.25)O_3−δ from 100 to 900 °C is found in Figure 6. Conductivity is presented in a semi-logarithmic plot versus temperature (10,000 K⁻¹). All four perovskites show increased electrical conductivity with increased temperature. The slopes for the four materials varied with the Ca content. In particular, the slopes for x = 0.1 and x = 0.2 (−0.0822 and −0.0879, respectively) were steeper than the x = 0 and x = 0.3 materials (−0.0424 and −0.0636, respectively). This varying temperature dependence suggests a change in the conduction behavior, as increased temperature dependence (greater slope) correlates with non-adiabatic conduction. It seems that the undoped material and the x = 0.3 material follow adiabatic behavior, and the others non-adiabatic. This is distinct from the behavior noted for three-cation B-site substituted perovskites doped with calcium [6], which tended toward similar slopes. This shifting behavior is probably due to the increasing entropy in the present materials. The x = 0.1 and x = 0.2 materials exhibited reduced conductivity over nearly the entire temperature range compared to both the undoped and x = 0.3 materials. At low temperatures, the undoped material delivered the highest electrical conductivity, and only at temperatures above 400 °C did the x = 0.3 material exceed it.

Table 3. Electrical conductivity (S cm⁻¹) at 800 °C for sintered La_1−xCa_x(Co_0.25Cr_0.25Fe_0.25Ni_0.25)O_3−δ and end-member perovskites for comparison.

Material	x = 0	x = 0.1	x = 0.2	x = 0.3
La1−xCax(Co0.25Cr0.25Fe0.25Ni0.25)O3−δ	28.2	20.6	29.3	46.9
LaCoO3 [50]	1000
LaCrO3 (700 °C) [51]	0.34
LaFeO3 [52]	0.1
LaNiO3 [52]	40

shows the electrical conductivity for all four materials at 800 °C, with the conductivity of the end-member perovskites for comparison. At 800 °C, there is no conductivity improvement for the perovskites doped with 10–20 at% Ca over the undoped material. The x = 0.3 material, however, shows a marked increase in conductivity compared to the undoped material. It seems that the increased entropy, correlated to the increasing Ca content, exhibits a variable effect on the electrical properties. This suggests that the properties can be tailored based on the fraction of calcium doped onto the A-site. The smaller fractions of calcium might prevent a stable structure from forming, while higher amounts would allow for a degree of uniformity of the A-site that enables higher conductivity while still possessing high configurational entropy.

3.5. Activation Energy for Conduction

Figure 7 shows Arrhenius plots of Log σT vs. 10,000 T⁻¹ for La_1−xCa_x(Co_0.25Cr_0.25Fe_0.25Ni_0.25)O_3−δ materials. This plot represents adiabatic conduction (when s = 1 in Equation (1)) [5]. A linear fit to the data allows one to determine the activation energy. The quality of these fits, as determined by the R² value, was 99.5% or better, making them viable for calculating the activation energy. The linearity of these plots indicates that small polaron hopping is the conduction mechanism [5]. The slope of the linear fit is proportional to the activation energy divided by the Boltzmann constant [2].

Table 4. Activation Energy (eV) for sintered La_1−xCa_x(Co_0.25Cr_0.25Fe_0.25Ni_0.25)O_3−δ, calculated from the data in Figure 7 and Figure 8.

Ca Doping Fraction, x	Activation Energy, Adiabatic (Figure 7)	Activation Energy, Non-Adiabatic (Figure 8)
x = 0	0.059974	0.071685
x = 0.1	0.094356	0.106063
x = 0.2	0.099182	0.110888
x = 0.3	0.078242	0.090037

shows the activation energy determined from the slopes in Figure 7. The activation energy experiences an increase in the x = 0.1 and x = 0.2 materials, with the lowest value being for the x = 0 material. This correlates with the reduced electrical conductivity values for the x = 0.1 and x = 0.2 materials, as seen in Figure 6. This suggests that the increased configurational entropy generates a barrier to conduction, as even the x = 0.3 material has a higher activation energy than the undoped material.

Figure 8 shows Arrhenius plots of Log σT^3/2 vs. 10,000 T⁻¹ for La_1−xCa_x(Co_0.25Cr_0.25Fe_0.25Ni_0.25)O_3−δ materials. This graph represents non-adiabatic conductivity (when s = 1.5 in Equation (1)) [5]. Figure 8 was analyzed in the same way as Figure 7 to obtain the activation energy for conduction. The activation energy values are shown in Table 4. The same trend as the adiabatic case is present for the non-adiabatic values. However, for all values of x, the activation energy is higher for the non-adiabatic case. The quality of the linear fits to both cases were effectively the same. Thus, the adiabatic case is dominant for conduction in these materials, as the activation energy is lower, and the conduction mechanism is small polaron hopping [5].

The inconsistent behavior of the electrical conductivity indicates that the conduction begins as an adiabatic process, switches to non-adiabatic, and then returns to adiabatic behavior for the highest amount of calcium doping. This switching behavior was not seen in Ca-doped perovskites with three cations on the B-site [5]. As those materials were not high-entropy perovskites, it seems that the increased configurational entropy causes a composition-dependent behavior of the conduction mechanism.

3.6. Effect of Configurational Entropy

The lower values for activation energy in the adiabatic case, as seen in Table 4, indicate that electrical conductivity in these materials obeys an adiabatic mechanism. This is true for all values of calcium doping on the A-site and for the undoped material. Note: the medium-entropy perovskite (x = 0) possesses the minimum activation energy for electrical conductivity, while the high-entropy materials (x > 0) require additional energy for the onset of conduction. This is a measurable effect of increased entropy. The lower values of Ca doping (x = 0.1 and x = 0.2) have the highest values, while the activation energy for x = 0.3 has decreased slightly, but remains higher than the undoped material. Because of the increased Ca content, there is less randomness on the A-site for x = 0.3. In other words, there may be a range of values for which the Ca content distorts the unit cell more significantly. Above that level, the distortion becomes less random and the structure more uniform, leading to a lower activation energy. That value lies somewhere between x = 0.2 and 0.3. Additional research is required to determine the arrangement of cations in these high-entropy materials. High-energy synchrotron X-ray analysis would be required for this purpose.

The entropic effect also explains the 800 °C conductivity values in Table 3, where the x = 0.1 conductivity exhibits a decrease from x = 0, and x = 0.2 is only slightly higher than x = 0 (which only occurred for 800 °C and above). While the material retains some conductivity, the magnitude has been decreased due to the distortion of the crystal structure. Once the value of x is increased to 0.3, this effect has been overcome due to the greater stability of the structure, yielding the highest conductivity value at 800 °C.

These results indicate that the composition of La-based perovskite materials can be tailored to a specific configurational entropy, and that entropy in turn yields tunable electrical properties of the resulting materials. These tunable properties are absent when there is no A-site doping, and they are present only for limited amounts of Ca doping on the A-site. Once the amount of calcium reaches ~30 at%, the distortion of the structure has been decreased and a new uniformity has been instituted. Thus, one can limit the amount of Ca doping on the A-site to leverage effective control of the electrical properties of these HEO materials.

3.7. Discussion of Conduction Mechanism and Practical Implications

To enhance clarity on the conduction behavior, the activation energies derived from the Arrhenius plots in Figure 6 have been explicitly extracted and reported. These values correspond to the slopes of the log(σT) versus 1/T and log(σT³ᐟ²) versus 1/T plots, representing adiabatic and non-adiabatic small-polaron hopping models, respectively. For each composition, the adiabatic model consistently produced lower activation energies (e.g., 0.06 eV for x = 0, 0.10 eV for x = 0.2), indicating that it is the dominant conduction mechanism. The assignment of conduction mechanism is based on this trend in activation energy magnitude, supported by linearity in both models across the measured temperature range.

Although the electrical conductivity values of the Ca-substituted solid solutions are lower than that of LaCoO₃, these compositions offer distinct advantages. In particular, LaCoO₃ suffers from a high coefficient of thermal expansion (CTE) that is mismatched with commonly used electrolytes like YSZ, potentially leading to mechanical instability during operation [41,42]. The present materials, with partial Ca substitution and equimolar B-site cation disorder, are expected to exhibit reduced CTE and improved chemical compatibility with YSZ, as reported in similar systems. Moreover, replacing a portion of cobalt with Fe, Ni, and Cr offers benefits in terms of material cost and thermal robustness, which are valuable for long-term SOFC operation [53,54,55].

The consistent observation that adiabatic activation energies are lower than non-adiabatic ones aligns with the proposed small-polaron conduction mechanism [1,46]. While intermediate Ca contents (x = 0.1 and 0.2) show higher activation energies than x = 0 and x = 0.3, this is interpreted as a result of the increased lattice disorder due to the rising configurational entropy. Such disorder can increase the hopping barrier, making conduction temporarily less favorable. However, at x = 0.3, a saturation or structural stabilization effect appears to reduce the activation energy again. This non-monotonic trend supports the notion that entropy-driven distortion affects charge transport but does not fundamentally alter the adiabatic nature of the hopping process [1,2,46].

Finally, the ~10 vol% porosity in the undoped sample (x = 0), as indicated in Table 2, is expected to suppress its measured electrical conductivity. In contrast, Ca doping significantly improves densification, yielding fully dense pellets (≈100% theoretical density) due to liquid-phase sintering. The SEM analysis revealed fewer pores and more rounded grains in the Ca-containing samples, consistent with enhanced mass transport during sintering. The improved conductivity observed in these compositions is therefore attributed not only to changes in charge carrier concentration and hopping behavior, but also to reduced porosity and improved microstructural uniformity [1,2,47,48].

4. Conclusions

Perovskite properties, from the unit cell to the grain structure to the electrical properties, may be controlled by controlling the elements present on both the A-site and B-site. Doping calcium onto the A-site of lanthanum-based perovskites while substituting equal atomic amounts of cations on the B-site, causes several effects. First, the increased calcium content lowers the necessary temperature and increases the resulting density when densifying in air without external pressure application. This is due to the transient liquid phase that forms due to the increased calcium content. Since this liquid phase is reabsorbed, no secondary phase exists upon cooling. Second, the sufficiently high calcium content increases the electrical conductivity at elevated temperatures. Third, calcium doping increased the activation energy for conduction. These results indicate the varying effects of high entropy on La-based perovskite materials. Calcium doping on the A-site increased the activation energy for conduction, most likely due to the disruption of the crystal structure. Higher levels of Ca doping began to overcome this by imposing increased stability on the crystal structure and reducing the activation energy for conduction compared to the materials with less calcium doping. Thus, the properties of high-entropy La-based perovskites can be tailored by altering the doping concentration.