Defect chemistry and transport properties of perovskite-type oxides La_1−xCa_xFeO_3−δ

Abstract

Structural evolution, electrical conductivity, oxygen nonstoichiometry and oxygen transport properties of perovskite-type oxides La_1−xCa_xFeO_3−δ (x = 0.05, 0.10, 0.15, 0.20, 0.30 and 0.40) are investigated. All investigated compositions exhibit, under ambient air, a phase transition from room-temperature orthorhombic (space group Pbnm) to rhombohedral (space group R3̄c) at elevated temperature. The transition temperature is found to decrease gradually from 900 °C for x = 0.05 to 625 °C for x = 0.40. Analysis of the data of oxygen nonstoichiometry obtained by thermogravimetry shows that under the given experimental conditions the Ca dopant is predominantly compensated by formation of electron holes rather than by oxygen vacancies. Maximum electrical conductivity under air is found for the composition with x = 0.30 (123 S cm⁻¹ at 650 °C). Analysis of the temperature dependence of the mobility of the electron holes in terms of Emin–Holstein's theory indicates that small polaron theory fails for the compositions with high Ca contents x = 0.30 and x = 0.40. This is tentatively explained by the increased delocalization of charge carriers with increasing Ca dopant concentration. The oxygen transport properties of La_1−xCa_xFeO_3−δ in the range 650–900 °C are evaluated using the electrical conductivity relaxation (ECR) technique. Combined with data of oxygen non-stoichiometry, the obtained results enable calculation of the oxygen vacancy diffusion coefficient and associated ionic conductivity. Both parameters increase with increasing Ca content in La_1−xCa_xFeO_3−δ, while it is found that the effective migration barrier for oxygen diffusion decreases with decreasing oxygen vacancy formation enthalpy.

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1. Introduction

Mixed ionic–electronic conducting oxides are extensively investigated for potential application as air electrode in reversible solid oxide cells (RSOCs) that can be operated either as a solid oxide fuel cell (SOFC) or as a solid electrolyte electrolysis cell (SOEC).^1–3 The most popular electrodes considered to date are the perovskite-structured oxides La_0.6Sr_0.4CoO_3−δ (LSC) and La_0.6Sr_0.4Co_0.2Fe_0.8O_3−δ (LSCF), though many other compositions and structure types are currently being investigated.⁴ Oxygen ion transport in these oxides is mediated via a vacancy mechanism. A-site substitution of trivalent lanthanum with divalent strontium in the ABO₃ perovskite oxides serves to create oxygen vacancies and, hence, to enhance oxygen ionic conductivity. A drawback in the case of above compositions is the clear mismatch between the ionic radii of host and dopant ions, La³⁺ (XII) = 1.36 Å and Sr²⁺ (XII) = 1.44 Å, which is believed to be the cause of segregation of Sr²⁺ ions to the grain boundaries and to the surface. The latter has a detrimental effect on the surface oxygen exchange kinetics.^5–8 Apart from this, the long-term thermodynamic stability of materials under actual operating conditions is an issue. The poor stability of cobalt-containing perovskites under reducing atmospheres, reactivity towards commonly used electrolytes and – last but not least – the high price of cobalt have urged researchers to explore cobalt-free mixed conducting electrodes with high electrocatalytic activity.^9–11

In recent studies by Berger et al.,^12,13 La_0.8Ca_0.2FeO_3−δ (LCF82) has been put forward as a promising electrode for RSOCs. The choice for calcium (Ca²⁺ (XII) = 1.34 Å) rather than strontium not only reduces the mismatch between host and dopant ions, but also the lower basicity of Ca²⁺ compared to that of Sr²⁺ ions reduces vulnerability towards carbonation and, hence, surface degradation upon contact with CO₂. The thermal expansion coefficient of LCF82 is found in perfect match with that of state-of-the-art electrolytes,¹² whereas the material shows electrical conductivities in usual ranges of temperature and oxygen partial pressure (pO₂) in excess of 100 S cm⁻¹, which is often regarded as the threshold value for use as electrode.¹⁴ It is further found that LCF82 exhibits high surface exchange and chemical diffusion coefficients with values exceeding those of state-of-the-art materials like LSC and LSCF.¹²

In our preceding work, investigating the influence of the earth–alkaline–metal dopant on structure, electrical and oxygen transport of La_0.6A_0.4FeO_3−δ (A = Ca, Sr, Ba), we found that the kinetic parameters for La_0.6Ca_0.4FeO_3−δ (LCF64) resemble those of La_0.6Sr_0.4FeO_3−δ (LSF64).¹⁵ Compared to extensive reports in literature on structure, electrical conductivity and oxygen transport properties of La_1−xSr_xFeO_3−δ (LSF),^16–21 only a few reports are available on selected compositions in the series La_1−xCa_xFeO_3−δ.^12,22,23 This prompted us to conduct a more systematic study. In this study, the electrical conductivity and oxygen transport properties of La_1−xCa_xFeO_3−δ (x = 0.05, 0.10, 0.15, 0.20, 0.30 and 0.40) are investigated by means of electrical conductivity relaxation (ECR). Thermal evolution of the crystal structure and oxygen nonstoichiometry of the materials are investigated by high-temperature X-ray diffraction (HT-XRD) and thermogravimetric analysis (TGA).

2. Experimental

2.1 Sample preparation

Powders of La_1−xCa_xFeO_3−δ (x = 0.05, 0.10, 0.15, 0.20, 0.30 and 0.40) were prepared via a modified Pechini method, as described elsewhere.²⁴ Stoichiometric amounts of La(NO₃)₃·6H₂O (Alfa Aesar, 99.9%), Ca(NO₃)₂·4H₂O (Sigma-Aldrich, 99%) and Fe(NO₃)₃·9H₂O (Sigma-Aldrich, ≥98%) were dissolved in water followed by the addition of C₁₀H₁₆N₂O₈ (EDTA, Sigma-Aldrich, >99%) and C₆H₈O₇ (citric acid, Alfa Aesar, >99.5%) as chelating agents. The pH of the solution was adjusted to 7 using concentrated NH₄OH (Sigma-Aldrich, 30 w/v%). After evaporation of the water, the foam-like gel reached self-ignition at around 350 °C. The obtained raw ashes were calcined at 900 °C for 5 h, using heating/cooling rates of 5 °C min⁻¹. The chemical composition of the powders was checked by X-ray fluorescence (XRF) using a Philips PW1480 apparatus. The obtained powders were pelletized by uniaxial pressing at 25 MPa followed by isostatic pressing at 400 MPa for 2 min. Subsequently, the pellets were sintered at 1120 °C for 5 h in air with heating/cooling rates of 2 °C min⁻¹. The relative density of the pellets was above 94% of their theoretical value as measured by Archimedes' method.

2.2 Characterization

The calcined powders were studied by room-temperature X-ray diffraction (XRD, D2 PHASER, Bruker) with Cu Kα₁ radiation (λ = 1.54060 Å) in air. Data were collected in a step-scan mode over the 2θ range 20–90 °C with a step size of 0.01° and a counting time of 8 s. The thermal evolution of the structures was investigated using high-temperature X-ray diffraction (HT-XRD, D8 Advance, Bruker) in air from 600 °C to 1000 °C with 25 °C intervals. The sample was heated to the desired temperature with a heating rate of 25 °C min⁻¹, followed by a dwell of 15 min to ensure equilibration. XRD patterns were recorded in the 2θ range of 20–90° with a step size of 0.015° and a counting time of 1.3 s. The FullProf software package was used for Rietveld refinements of the patterns.²⁵

The oxygen nonstoichiometry of the samples was determined by thermogravimetric analysis (TGA, Netsch STA F3 Jupiter). Data were collected during cooling from 900 °C to 650 °C, with intervals of 25 °C and a dwell time of 30 min at each temperature before data acquisition. The measurements were conducted in oxygen–nitrogen mixtures containing either 4.5%, 10%, 21%, 42% or 90% of O₂, corresponding to the pO₂ values maintained during ECR experiments (see below). Prior to data collection, the powder was heated under 4.5% O₂ to 900 °C, with a heating rate of 20 °C min⁻¹ and a dwell time of at least 2.5 h, in order to remove impurities like adsorbed water and CO₂. Following prior studies on La_1−xSr_xFeO_3−δ (0 ≤ x ≤ 0.6),¹⁷ all compositions in the present study were considered to be stoichiometric (δ = 0) at a pO₂ of 0.21 atm below 150 °C.

Samples for electrical conductivity relaxation (ECR) measurements were prepared by grinding and cutting dense sintered pellets to planar-sheet shaped samples with approximate dimensions 12 × 5 × 0.5 mm³. The sample surface was polished using diamond polishing discs (JZ Primo, Xinhui China) down to 0.5 μm. A four-probe DC method was used to collect data of electrical conductivity. Two gold wires (Alfa Aesar, 99.999%, Ø = 0.25 mm) were wrapped around both ends of the sample for current supply. Two additional gold wires were wrapped 1 mm remote from the current electrodes to act as voltage probes. To ensure good contact between the gold wires and the sample, sulphur-free gold paste (home-made) was applied on the sample surface directly underneath the gold wires. Finally, the sample was annealed at 950 °C in air for 1 h to sinter the gold paste and thermally cure the polished sample surface. Data of the transient electrical conductivity was collected following oxidation and reduction step changes in pO₂ between 0.100 and 0.210 bar. Measurements were conducted following stepwise cooling from 900 °C to 650 °C with intervals of 25 °C, heating/cooling rates of 10 °C min⁻¹ and a dwell time of 60 min at each temperature before data acquisition. The chemical diffusion coefficient D_chem and the surface exchange coefficient k_chem were determined by fitting the transient conductivity to the appropriate solution of Fick's second law using a non-linear least-squares program based on the Levenberg–Marquardt algorithm. Detailed descriptions of the ECR technique and the model used for data fitting are given elsewhere.^19,26

3. Results and discussion

3.1 Crystal structure

Fig. 1 shows the room temperature XRD patterns of La_1−xCa_xFeO_3−δ (x = 0.05, 0.10, 0.15, 0.20, 0.30 and 0.40). All patterns could be fitted using orthorhombic space group Pbnm. Corresponding lattice parameters and reliability factors from Rietveld refinements are listed in Table 1. Other structural parameters obtained from the refinements are listed in Table S1.† No impurity peaks are found in the patterns, suggesting that all compositions are single phase. The chemical composition of the powders appeared to be in good agreement with the intended nominal composition as was checked by XRF (see Fig. S1†).

Fig. 1 Measured (red symbols) and calculated (black lines) of XRD powder patterns of La_1−xCa_xFeO_3−δ for (a) x = 0.05, (b) x = 0.10, (c) x = 0.15, (d) x = 0.20, (e) x = 0.30 and (f) x = 0.40. Data were recorded at room temperature in ambient air. The calculated positions of Bragg peaks and the residual plots are given under the patterns. Data for x = 0.40 were taken from our previous study.¹⁵

Table 1 Lattice parameters and reliability factors obtained from Rietveld refinements of room temperature XRD diffractograms of La_1−xCa_xFeO_3−δ (space group Pbnm). The numbers in parentheses denote standard deviations in units of the least significant digits

	x = 0.05	x = 0.10	x = 0.15	x = 0.20	x = 0.30	x = 0.40
a/Å	5.54765(4)	5.54089(11)	5.52984(11)	5.52167(15)	5.50262(10)	5.48822(12)
b/Å	5.55664(3)	5.54966(8)	5.54068(9)	5.53475(13)	5.52552(9)	5.51710(15)
c/Å	7.84294(5)	7.83187(13)	7.81634(14)	7.80452(19)	7.77789(13)	7.75721(17)
V/Å^3	241.769(2)	240.831(4)	239.485(4)	238.514(5)	236.486(4)	234.881(4)
R wp/%	4.96	6.33	7.33	7.19	5.72	6.29
R exp/%	1.99	4.55	4.89	4.06	2.41	2.52
R Bragg/%	1.275	1.769	1.868	2.050	1.875	2.237
χ ^2	6.22	1.93	2.25	3.14	5.65	6.23

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As is shown in Fig. 2, the lattice parameters show a clear negative dependence on Ca content, which suggests at first glance formation of Fe⁴⁺ (0.585 Å (XI)) as the primary compensating defect, noting that the Fe⁴⁺ ion has a smaller radius than Fe³⁺ (0.645 Å (XI) – high spin). The degree of electronic versus ionic compensation of the Ca dopant in La_1−xCa_xFeO_3−δ is further discussed below. The quoted ionic radii are taken from Shannon's compilation.²⁷ In general, a good agreement is found between the lattice parameters from this study and those of similar compositions reported by Price et al.²²

Fig. 2 Lattice parameters of La_1−xCa_xFeO_3−δ as a function of x from Rietveld refinements of room temperature XRD powder patterns (cf.Fig. 1). Orthorhombic (Pbnm) lattice parameters for LCF phases are presented as pseudo-cubic lattice parameters, calculated using , and .

The temperature dependences of the pseudo-cubic lattice parameters obtained from Rietveld refinements of the HT-XRD patterns of samples La_1−xCa_xFeO_3−δ are listed in Fig. 3. These give evidence of a structural phase transition from orthorhombic to rhombohedral (space group R3̄c), i.e., a slightly distorted cubic structure, occurring in all of the investigated compositions. The degree of distortion is found to decrease with temperature and Ca content. For example, at 1000 °C, the rhombohedral angle decreases in the order x = 0.05 (60.31°) > x = 0.10 (60.28°) > x = 0.15 (60.24°) > x = 0.20 (60.19°) > x = 0.30 (60.11°) > x = 0.40 (60.09°), noting that the value of 60° corresponds to ideal cubic symmetry. The observed transition temperatures are listed in Table 2 and compared, as far as available, with those found using differential scanning calorimetry (DSC) by Price et al.²² The lowering of the transition temperature with Ca content can be explained by the concomitant decrease of the deformation of the perovskite structure.

Fig. 3 Lattice parameters of La_1−xCa_xFeO_3−δ for (a) x = 0.05, (b) x = 0.10, (c) x = 0.15, (d) x = 0.20, (e) x = 0.30 and (f) x = 0.40 as a function of temperature from Rietveld refinements of HT-XRD patterns recorded in ambient air. For the orthorhombic (Pbnm) structure pseudo-cubic lattice parameters are given, calculated using , and . For the rhombohedral (R3̄c) structure, a = b = c ≡ a. Data for x = 0.40 were taken from our previous study.¹⁵

Table 2 Comparison of the transition temperature of the orthorhombic-to-rhombohedral phase transition in La_1−xCa_xFeO_3−δ from HTXRD (this study) with that estimated using differential scanning calorimetry (DSC) by Price et al.²²

	x = 0.05	x = 0.10	x = 0.15	x = 0.20	x= 0.30	x = 0.40
This work	900 °C	825 °C	775 °C	775 °C	725 °C	625 °C
Price et al.^22	—	834 °C	—	738 °C	688 °C	602 °C

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3.2 Oxygen nonstoichiometry

The oxygen nonstoichiometry (δ) of La_1−xCa_xFeO_3−δ was investigated as a function of temperature and pO₂ by thermogravimetric analysis. A typical measurement scheme is shown in Fig. S2.† Corresponding data plotted as a function of pO₂, at different temperatures, for each of the compositions are shown in Fig. 4. As can be inferred from these figures, δ, at a given temperature and pO₂, increases with increasing Ca mole fraction.

Fig. 4 Oxygen stoichiometry (3 − δ) of La_1−xCa_xFeO_3−δ for (a) x = 0.05, (b) x = 0.10, (c) x = 0.15, (d) x = 0.20, (e) x = 0.30 and (f) x = 0.40 as a function of log(pO₂) at different temperatures. Dashed lines are drawn to guide the eye. Data for x = 0.40 were taken from our previous study.¹⁵

Starting point in our discussion of the defect chemistry of La_1−xCa_xFeO_3−δ is the model developed by Mizusaki et al.^16–18 for La_1−xSr_xFeO_3−δ. Assuming localized and non-interacting defects, the oxidation reaction is described, in Kröger–Vink notation, as

with equilibrium constant in the ideal solution approximation

Under oxidizing conditions, coexists with , which is reflected in the reduced charge neutrality equation corresponding to this region, which reads

showing that the partial substitution of La³⁺ ions by Ca²⁺ is charge compensated by the formation of localized electron holes (Fe⁴⁺) and oxygen vacancies . Eqn (3) ignores the presence of localized electrons (Fe²⁺), arising from disproportionation of two Fe³⁺ ions in Fe²⁺ and Fe⁴⁺,

which electronic defects become predominant under reducing conditions, and that of structural vacancies on lanthanum and iron sites. Using eqn (3), the concentration of in La_1−xCa_xFeO_3−δ at a given temperature and pO₂ can be calculated from corresponding data of oxygen nonstoichiometry (Fig. 4). Fig. 5 shows the results of such calculations for pO₂ = 0.1 atm and pO₂ = 1 atm, at 800 °C, from which figure it can be inferred that under the given experimental conditions in each of the compositions electronic compensation of the Ca dopant dominates over ionic compensation.

Fig. 5 Electron hole concentration in La_1−xCa_xFeO_3−δ as a function of x, at 800 °C, at pO₂ = 0.1 atm and pO₂ = 1 atm. The dotted lines are drawn to guide the eye. The dashed line denotes the limiting case of electronic compensation of the Ca dopant. The blue and beige areas represent an artistic view of the degrees of electronic and ionic compensation, at pO₂ = 0.1 atm. Note that the degree of electronic compensation increases at the expense of ionic compensation upon increasing the pO₂ from 0.1 atm to 1 atm.

The use of eqn (2) to describe the equilibrium between oxygen in the gas phase and oxygen in the oxide relies on the assumption that the oxygen incorporation energetics is independent of the concentration of involved point defects, which are further taken to be randomly distributed among available lattice sites. The validity of this assumption in the experimental range of the measurements can be checked by estimating the standard enthalpy change (ΔH⁰_ox) involved in the oxidation reaction (reaction (1)). The relationship between the standard free Gibbs energy change (ΔG⁰_ox) and the equilibrium constant (K_ox) is

ΔG⁰_ox = ΔH⁰_ox − TΔS⁰_ox = −RT ln(K_ox) (5)

where ΔS⁰_ox is the standard reaction entropy change of the reaction and R is the universal gas constant. Assuming that ΔH⁰_ox is independent of temperature, ΔH⁰_ox can be calculated from the slope of ln(K_ox) vs. 1/T, according to

which is known as the van 't Hoff equation, while ΔS⁰_ox is calculated from the intercept. ln(K_ox) vs. 1/T plots, at constant pO₂, for La_0.7Ca_0.3FeO_3−δ are shown in Fig. 6a. The observed non-linearity and the observation that different plots are obtained at different pO₂ values indicate that K_ox is a non-ideal equilibrium constant. Fig. 6b shows ln(K_ox) vs. 1/T plots, at constant δ, for La_0.7Ca_0.3FeO_3−δ. Distinct from those presented in Fig. 6a, linear plots are obtained, with slopes that are a function of δ. Similar results were obtained for the other compositions investigated in this work. Values of ΔH⁰_ox and ΔS⁰_ox extracted from ln(K_ox) vs. 1/T plots, at constant δ, for the different compositions La_1−xCa_xFeO_3−δ are shown in Fig. 6c and d, respectively. Fig. 6c shows that for a given Ca dopant concentration x in the series La_1−xCa_xFeO_3−δ, ΔH⁰_ox becomes more exothermic with increasing δ, while at a fixed value of δ, ΔH⁰_ox becomes more endothermic (less exothermic) with increasing x.

Fig. 6 van 't Hoff plots of K_ox for La_0.7Ca_0.3FeO_3−δ at (a) constant pO₂ and (b) constant δ. (c) Enthalpy (ΔH⁰_ox) and (d) entropy (ΔS⁰_ox) of oxidation (reaction (1)) at given values of x in La_1−xCa_xFeO_3−δ as a function of δ. Data in (c) and (d) were extracted from ln(K_ox) vs. 1/T plots, at constant δ.

The isotherms in Fig. 4 allow evaluation of the chemical potential of oxygen relative to that in equilibrium with gaseous O₂ at 1 atm,

The partial molar enthalpy of oxygen, Δh_O, and the partial molar entropy of oxygen, Δs_O, can be deduced from ln(pO₂) vs. 1/T (or equivalent) plots, at constant δ, according to

Typical plots and resultant values of Δh_O and Δs_O for compositions La_1−xCa_xFeO_3−δ are shown in Fig. S3.† In view of eqn (3), i.e., ignoring charge disproportionation (reaction (4)), the slopes of ln(K_ox) vs. 1/T at constant δ relate to those derived from ln(pO₂) vs. 1/T plots. It follows

The partial molar entropy can be represented as

Δs_O = Δs⁰_O − s_conf (10)

where Δs⁰_O and s_conf are the non-configurational and configurational contributions, respectively. Analysis of the data of Δs_O obtained for the different compositions La_1−xCa_xFeO_3−δ, as shown in Fig. S3d,† indicates that significant departures occur from the ideal solution approximation, in which it is assumed that the configurational contribution to the entropy of the oxygen incorporation reaction (reaction (1)) is due to a random distribution of oxygen vacancies on the O sublattice and that of localized electron holes on the Fe sublattice. That is, the configurational contribution departs from the ideal form s_conf = ((3 − δ)/δ) × ((x − 2δ)/(1 − (x − 2δ)))² (cf.eqn (2)). A more proper analysis awaits data of oxygen nonstoichiometry of compositions La_1−xCa_xFeO_3−δ over more extended ranges in oxygen partial pressure and temperature than investigated in this study.

Regarded in terms of the reverse of reaction (1), i.e., the oxygen reduction reaction, the present results show that the energetic cost of formation of oxygen vacancies in La_1−xCa_xFeO_3−δ is higher at higher oxygen nonstoichiometry, while smaller, at fixed δ, if La is partly substituted by Ca. These observations may be related, e.g., to an increase in the oxygen bond strength with increasing oxygen nonstoichiometry (due to the concomitant increase in the average oxidation state of the transition metal cation), a decrease in the oxygen bond strength with Ca content (Ca–O bonds are weaker than La–O bonds) and/or changes in the electronic structure. First principle calculations indeed confirm that the oxygen vacancy formation energy, Δh_V(= −Δh_O = −1/2ΔH⁰_ox) is significantly lowered with alkaline–earth metal dopant concentrations in La_1−xSr_xFeO_3−δ (ref. 28) and La_1−xCa_xFeO_3−δ (ref. 29) which is in line with the results shown in Fig. 6c. Both cited studies show that the electron holes induced by Sr or Ca substitution have significant O 2p character as has been confirmed by experimental studies using X-ray absorption spectroscopy.³⁰ These findings suggest that the electron holes in both series of oxides are (at least, to some extent) delocalized due to which the mass action law is expected to break down.³¹ Nonideal thermodynamic behavior of the defects as observed for La_1−xCa_xFeO_3−δ in this study has also been reported for a number of related perovskite oxides, including Ba_1−xSr_xFeO_3−δ (x = 0, 0.5),^32,33 (Ba_0.5Sr_0.5)_1.04Co_0.8Fe_0.2O_3−δ,³² Ba_0.5Sr_0.5Co_0.4Fe_0.6O_3−δ,³² La_0.4Sr_0.6Co_1−yFe_yO_3−δ (y = 0.2, 0.4),³⁴ SrCo_0.8Fe_0.2O_3−δ,³⁵ and La_1−xSr_xCoO_3−δ (0.1 ≤ x ≤ 0.7).^31,36 These and present findings are, however, in contrast with data of high-temperature drop calorimetry and thermogravimetry on La_1−xSr_xFeO_3−δ.^17,18,37 In these studies, ΔH⁰_ox for La_1−xSr_xFeO_3−δ is found virtually independent of the oxygen nonstoichiometry at an average value of −200 ± 50 kJ mol⁻¹ for 0 ≤ x ≤ 0.5 and at −140 ± 30 kJ mol⁻¹ for 0.5 ≤ x ≤ 1.0. Corresponding changes with x within the specified ranges are found to be within experimental error. Further work is required to understand the nonideal energetics of the defect species in La_1−xCa_xFeO_3−δ.

3.3 Electrical conductivity

Fig. 7a shows Arrhenius plots of the total electrical conductivity in air of the different compositions La_1−xCa_xFeO_3−δ. The conductivity includes both ionic and electronic contributions. Since under the given experimental conditions electron holes are the predominant charge carriers (Fig. 5) and their mobility will be much higher than that of oxygen vacancies, it can safely be assumed that the contribution of ionic conductivity to the total electrical conductivity is negligible.

Fig. 7 Arrhenius plots of the (a) electrical conductivity (σ_el), (b) concentration of electron holes and (c) mobility of electron holes (μ_h) for La_1−xCa_xFeO_3−δ, at pO₂ = 0.21 atm. The dashed lines are drawn to guide the eye.

Previous studies have suggested that electrical conduction in La_1−xA_xFeO₃ (A = Ca, Sr) at elevated temperatures occurs by p-type small polaron hopping,^16,20,38 and can be expressed as

where and μ_h are the concentration (mole fraction) and mobility of electron holes, respectively, is Avogadro's number, V_m is the molar volume, and e is the electronic charge. The charge carrier concentration p as a function of temperature for each composition La_1−xCa_xFeO_3−δ was determined from corresponding data of oxygen nonstoichiometry, while the mobility μ_h was calculated with the help of eqn (11). Arrhenius plots of both parameters for the different compositions La_1−xCa_xFeO_3−δ are shown in Fig. 7b and c, respectively. Fig. 7a shows that the electrical conductivity of La_1−xCa_xFeO_3−δ, at 650 °C, increases with Ca mole fraction up to a value of 123 S cm⁻¹ for x = 0.3. The results displayed in Fig. 7b make clear that this increase can be attributed to the concomitant increase in the charge carrier concentration. The lowering of electrical conductivity on going from composition x = 0.3 to x = 0.4 (Fig. 7a) is caused by the decreasing mobility, which is found much lower for x = 0.40 than for x = 0.30. The observed decrease of the electrical conductivity with temperature for both compositions x = 0.30 and x = 0.40 (Fig. 7a) can be attributed to a lowering of both the concentration and mobility of the charge carriers with increasing temperature.

To discriminate between adiabatic and non-adiabatic regimes of small polaron hopping, we have analyzed the electrical mobility in terms of Emin–Holstein's theory.^39–41 In the event of coincidence of local distortions of initial and final states, the temperature-dependent mobility in this theory is given by

where a is the hopping distance, ν₀ is the frequency of optical phonons, W_p is the polaron binding energy, J is the kinetic energy of the polaron, and k_B is Boltzmann's constant. The factor of 3/2 takes into account the fact that the polaron moves in a three-dimensional lattice.⁴¹ The factor of takes into account the probability that the adjacent site to which the polaron hops may already be occupied.⁴² Accordingly, the plot of vs. 1000/T should give a straight line with activation energy in the adiabatic regime. In the non-adiabatic regime,³⁹ the charge carrier moves too slowly to adjust to rapid lattice fluctuations and, hence, misses such ‘coincidence events’, lowering the net hopping rate. The mobility of electron holes is then given bywhere h is Planck's constant. In this case, the plot of vs. 1000/T should give a straight line with activation energy . Fig. 8a and b show corresponding data fitted to each model. The equations for the linear relationships along with the coefficients of determination (R²) are presented in Table 3. Both models fit the data for compositions x = 0.05, 0.10, 0.15 and 0.20 reasonably well. Based on the results, however, it is difficult to substantiate either model. Comparison of the obtained R² values indicates a slight favor for the non-adiabatic model. Clear departures from linear relationships are, however, obtained for compositions x = 0.30 and 0.40.

Fig. 8 Plots of (a) vs. 1000/T (adiabatic regime) and (b) vs. 1000/T (non-adiabatic regime) for La_1−xCa_xFeO_3−δ at pO₂ = 0.21 atm. The dashed lines are drawn to guide the eye.

Table 3 Linear equations used to fit vs. 1000/T (adiabatic regime) and vs. 1000/T (non-adiabatic regime) plots as shown in Fig. 8a and b, respectively, along with the coefficients of determination (R²)

	Adiabatic		Non-adiabatic
		R ^2		R ^2
x = 0.05	−1526.50/T + 6.72	0.99957	−2045.87/T + 10.68	0.99959
x = 0.10	−1409.57/T + 6.84	0.99884	−1943.11/T + 10.82	0.99917
x = 0.15	−1253.09/T + 6.65	0.99881	−1766.98/T + 10.64	0.99907
x = 0.20	−977.47/T + 6.33	0.99333	−1496.84/T + 10.29	0.99821

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Fig. S4a† shows the pO₂ dependence of the electrical conductivity of La_1−xCa_xFeO_3−δ, at 800 °C. For all compositions, it is found that the calculated electron hole mobility is suppressed by decreasing pO₂, suggesting that the presence of oxygen vacancies highly influences the apparent mobility, e.g., by disruption of Fe⁴⁺–O–Fe³⁺ migration pathways, oxygen vacancies acting as traps or as scattering centres for the electrons (Fig. S4b and S5†).

Above, we have analyzed the apparent hole mobility in La_1−xCa_xFeO_3−δ in terms of hopping of small polarons, which is a thermally activated process. As seen from Fig. 7c, the apparent hole mobility in the compositions with x = 0.30 and 0.40 is rather found to decrease with increasing temperature. As alluded to before, several studies based on density functional theory and X-ray adsorption spectroscopy have revealed that the Fe 3d and O 2p states in La_1−xA_xFeO_3−δ (A = Ca, Sr) and related perovskites are hybridized to some degree. The extent of hybridisation is proposed to increase with the oxidation state of the transition metal ion,⁴³ causing increased delocalisation of the charge carriers. Clearly, more research is warranted to clarify the nature of the charge carriers in these solids.

3.4 Electrical conductivity relaxation

The oxygen transport properties of phases La_1−xCa_xFeO_3−δ were evaluated using the ECR technique. It is recalled that measurements were conducted using small pO₂ steps, i.e., between 0.100 and 0.215 atm, ensuring conditions close to equilibrium. Fig. 9 shows normalized conductivity relaxation curves for a given sample obtained for oxidation steps at different temperatures along with the respective fits to the theoretical model. It can be seen that the time needed to reach equilibrium is longer as the temperature is reduced. Curve fitting allows simultaneous determination of the chemical diffusion coefficient, D_chem, and the surface exchange coefficient, k_chem, provided that fitting is sensitive to both parameters. Both parameters can be most reliably assessed from fitting if the sample length is close to D_chem/k_chem, as parameterized by the Biot number (Bi).⁴⁴ This number represents the ratio between the characteristic times for diffusion, τ_diff = l_z²/D_chem, and that for surface exchange, τ_exch = l_z/k_chem, l_z being the half-thickness of the sample,D_chem and k_chem can be most reliably assessed in the ‘mixed-controlled’ region. This confidence region is, however, determined by the accuracy of the measurements. A plot of the Biot number against temperature obtained from fitting of the conductivity relaxation curves as acquired for the series of La_1−xCa_xFeO_3−δ is shown in Fig. 10. Note from eqn (14) that the Biot number can only be calculated if both D_chem and k_chem are obtained from curve fitting.

Fig. 9 Typical normalized conductivity curves following a step change in pO₂ from 0.100 to 0.215 atm at different temperatures. Data shown were obtained for La_0.8Ca_0.2FeO_3−δ. The solid lines show the least-square fitting to the model equations. Corresponding values of D_chem and k_chem obtained from fitting are listed.

Fig. 10 Temperature dependence of the Biot number (Bi) for La_1−xCa_xFeO_3−δ. Error bars are within the size of the symbols. Following Den Otter et al.²⁵ the mixed-controlled region is found for 0.03 ≤ Bi ≤ 30.

Arrhenius plots of D_chem and k_chem for the different La_1−xCa_xFeO_3−δ compositions are shown in Fig. 11a and b, respectively. There is no significant difference between the results from oxidation and reductions runs. Obtained values of D_chem for x = 0.10 and x = 0.20 are in good agreement with corresponding values reported by Berger et al.^12,23 (Fig. 11a). The agreement is less good comparing values of k_chem for x = 0.20 with those reported by Berger et al.¹² (Fig. 11b). This may at least partly be due to the difficulty in determining k_chem as the materials exhibit exceptionally high surface exchange rates, as was noted before by Berger et al.²³ In the present study, values of k_chem could only be accurately assessed from the relaxation curves for compositions x = 0.15, x = 0.20, x = 0.30 and x = 0.40. Note from Fig. 11b that all these compositions show higher surface exchange rates than state-of-the-art La_0.58Sr_0.4Co_0.2Fe_0.8O_3−δ (LSCF).⁴⁵ Recent research has learned that the surface exchange rate on oxide surfaces may be highly influenced by, e.g., surface enrichment due to segregation, surface impurities and grain size.^5,6,45 The high exchange rates found for La_1−xCa_xFeO_3−δ deserve more focused research, but this is considered beyond the scope of this work.

Fig. 11 Arrhenius plots of the (a) chemical diffusion coefficient (D_chem) and (b) surface exchange coefficient (k_chem) for La_1−xCa_xFeO_3−δ (0.100 ↔ 0.215 atm). Filled and open symbols represent data of oxidation and reduction step changes, respectively (for data from this study only). Error bars are within the size of the symbols. The dashed lines are from linear fitting of the data. Data for La_0.9Ca_0.1FeO_3−δ (0.10 ↔ 0.15 atm),²² La_0.8Ca_0.2FeO_3−δ (0.10 ↔ 0.15 atm),¹² and La_0.58Sr_0.4Co_0.2Fe_0.8O_3−δ (LSCF6428; 0.20 ↔ 0.40 atm)⁴³ from the cited literature are shown for comparison. The pressure range between brackets denotes the step change in pO₂ used in the ECR measurements.

Apart from x = 0.05, the temperature dependences of D_chem of compositions La_1−xCa_xFeO_3−δ exhibit non-Arrhenius behavior (Fig. 11a). The variation in slope with temperature is linked with the existence regions of the orthorhombic (space group Pbnm) and rhombohedral (space group R3̄c) phases as may be inferred by comparing the data in Fig. 11a with the structural data shown in Fig. 3. Apparent activation energies of D_chem in both temperature regions deduced from the data in Fig. 11a are listed in Table S2.† Note from this table that significantly higher activation energies are found in the temperature region of the orthorhombic phase. As D_chem is a lumped parameter, the different activation energies in both temperature regions may either have a kinetic or a thermodynamic origin.

3.5 Ionic conductivity and oxygen diffusivity

To further analyze the influence of Ca substitution on the oxygen transport properties of La_1−xCa_xFeO_3−δ, the oxygen self-diffusion coefficient, D_s, and vacancy diffusion coefficient, D_v, of the different compositions were calculated. D_s was calculated, using the relationship¹⁹

D_chem = γ_OD_s (15)

where γ_O is the thermodynamic factor, defined asand where c_O(= (3 − δ)/V_m) is the oxygen concentration, while D_v was calculated within the random walk diffusion theory framework, using the jump balance,⁴⁶

c_O × D_s = c_v × D_v (17)

where c_v(= δ/V_m) is the oxygen vacancy concentration. The temperature dependences of γ_O, at pO₂ = 0.147 atm, for the different compositions La_1−xCa_xFeO_3−δ investigated in this work are given in Fig. S6,† noting that the specified pO₂ corresponds to the logarithmic average of the pO₂ step change (0.100 ↔ 0.215 atm) used in the ECR experiments. Arrhenius plots of D_s and D_v are shown in Fig. 12a and b, respectively. Both plots are highly linear with coefficients of determination (R²) close to unity, which confirms not only that the observed non-Arrhenius behavior of D_chem (see previous section) has a sole thermodynamic origin, but also that the orthorhombic-to-rhombohedral phase transition has negligible influence on the diffusivity of oxygen in La_1−xCa_xFeO_3−δ. Calculated activation energies of D_s and D_v are listed in Tables S3 and S4,† respectively. For both parameters, good agreement is noted between the values deduced from data of oxidation and reductions runs. Values of D_v for La_1−xCa_xFeO_3−δ from this study are compared with literature data for La_1−xCa_xFeO_3−δ (x = 0.1, 0.2),^12,23 La_1−xSr_xFeO_3−δ (x = 0.1, 0.25, 0.5),^47,48 La_1−xSr_xCoO_3−δ (x = 0.2, 0.5)⁴⁹ and La_0.6Sr_0.4Co_0.2Fe_0.8O_3−δ (ref. 50) in Fig. S7.† This comparison shows that the differences in the values of D_v are relatively small, reinforcing the concept that in order to have high ionic conductivities in these perovskite-structured materials, the oxygen vacancy concentration must be high, as has been recognized previously by Mizusaki⁵¹ and Kilner.⁵²

Fig. 12 Arrhenius plots of the (a) oxygen self-diffusion coefficient (D_s) and (b) oxygen vacancy diffusion coefficient (D_v) for La_1−xCa_xFeO_3−δ, at pO₂ = 0.147 atm. The filled and open symbols represent the data of oxidation and reduction step changes, respectively. Error bars are within the size of the symbols. The drawn lines are from linear fitting of the data. The specified pO₂ corresponds to the logarithmic average of the step change in pO₂ (0.100 ↔ 0.215 atm) used in the ECR measurements.

Fig. 13 shows Arrhenius plots of the ionic conductivity, σ_ion, of La_1−xCa_xFeO_3−δ calculated using the Nernst–Einstein equation,

Fig. 13 Arrhenius plots of the calculated ionic conductivity (σ_ion) for La_1−xCa_xFeO_3−δ, at pO₂ = 0.147 atm. Lines are drawn to guide the eye. The specified pO₂ corresponds to the logarithmic average of the step change in pO₂ (0.100 ↔ 0.215 atm) used in the ECR measurements.

The obtained results clearly reveal that the isothermal value of σ_ion increases with the mole fraction x of the Ca dopant. This is due to the increase in the concentration of oxygen vacancies with x in La_1−xCa_xFeO_3−δ as can be inferred from the data presented in Fig. 4, but at least in part due to the concomitant increase in D_v as is shown in Fig. 14a. The results in the latter figure demonstrate that D_v at fixed temperature increases with Ca content to reach an almost constant value at x ≥ 0.20. The observed behavior is consistent with the concomitant decrease in the oxygen migration barrier, E_m, with increasing x in La_1−xCa_xFeO_3−δ as shown in Fig. 14b. E_m is found to decrease from 1.72 ± 0.02 eV for x = 0.05 to an average value of 1.08 ± 0.03 eV for x = 0.40 (Table S4†). The observed migration barriers at small values of x are distinctly larger than those reported for single crystals of La_1−xSr_xCoO_3−δ (77 ± 21 kJ mol⁻¹ (x = 0), 79 ± 25 kJ mol⁻¹ (x = 0.1))⁴⁷ and La_1−xSr_xFeO_3−δ (74 ± 24 kJ mol⁻¹ (x = 0), 79 ± 25 kJ mol⁻¹ (x = 0.1), 114 ± 23 kJ mol⁻¹ (x = 0.25) by Ishigaki et al.⁴⁷

Fig. 14 (a) Oxygen vacancy diffusion coefficient (D_v) and (b) migration energy (E_m) as a function of x in La_1−xCa_xFeO_3−δ as derived from data presented in Fig. 12b.

The motion of oxygen ions through the oxide lattice is described by an activated hopping process and involves the breaking of cations bonds with oxygen and partial charge transfer from oxygen to the adjacent transition metal or the Fermi level (i.e., resembling the process of oxygen vacancy formation) and migration along the minimum energy pathway to the next nearest-neighbor site, thereby migrating through a critical A₂B triangle (formed by two A cations and one B cation). Many researchers have attempted to correlate the experimentally observed migration barriers with various descriptors, like the free lattice volume, oxygen bond strength, lattice distortion, critical radius, etc.^53–56 Using ab initio methods, Mayeshiba and Morgan⁵⁷ found that descriptors like the O p-band center energy and oxygen vacancy formation energy correlate well with the oxygen migration barrier for a group of over 40 perovskite oxides. Both descriptors are related to the metal–oxygen bond strength, which obviously raises the question whether one of the used descriptors is redundant. The O p-band center energy (which is defined as the centroid of the projected density of states (PDOS) relative to the Fermi level) is found to correlate well with the oxygen vacancy formation enthalpy, which suggests that electronic contributions are highly important to oxygen vacancy formation in perovskite oxides.^57–60

Assuming that all oxygen sites are equivalent, random walk theory of diffusion predicts that the vacancy diffusivity D_v is directly proportional to the fraction of occupied sites and, hence, to the oxygen concentration c_O which, for small values of the oxygen vacancy concentration c_v, is virtually constant.⁶¹ For this reason, measured activation energies of D_v are commonly interpreted as the migration energy (E_m), assuming that all other atomistic parameters, including the characteristic lattice frequency and hopping distance, remain constant with changes in c_v. Fig. 15 shows the migration barriers thus obtained for La_1−xCa_xFeO_3−δ (Table S4†) plotted against the oxygen vacancy formation energies, Δh_V, at two different values of δ, as evaluated from corresponding van 't Hoff plots (Fig. 6b). Both curves exhibit a trend similar to that observed for the group of perovskite oxides by Mayeshiba and Morgan⁵⁷ in the sense that the migration barrier in La_1−xCa_xFeO_3−δ is found to decrease with decreasing Δh_V. As discussed in Section 3.2, values of Δh_V for La_1−xCa_xFeO_3−δ depend both on x and δ. A more detailed analysis of the correlation between E_m and Δh_V in La_1−xCa_xFeO_3−δ must therefore await evaluation of the migration barriers in compositions La_1−xCa_xFeO_3−δ as a function of both x and δ.

Fig. 15 Migration energy (E_m) vs. oxygen vacancy formation energy (Δh_V). E_m was evaluated at constant pO₂ (extracted from data presented in Fig. 12b), while Δh_V = −1/2ΔH⁰_ox was evaluated at constant oxygen nonstoichiometry (extracted from data presented in Fig. 6c), at δ = 0.003 and at δ = 0.013. Data presented by open symbols were obtained by extrapolation.

4. Conclusions

In this work, we have shown that:

(i) Perovskite-type oxides La_1−xCa_xFeO_3−δ (x = 0.05, 0.10, 0.15, 0.20, 0.30 and 0.40) exhibit a phase transition, under ambient air, from room-temperature orthorhombic (space group Pbnm) to a rhombohedral (space group R3̄c), i.e., a slightly distorted cubic, structure at elevated temperature. The transition temperature decreases gradually from 900 °C for x = 0.05 to 625 °C for x = 0.40.

The combined data of thermogravimetry, electrical conductivity and electrical conductivity relaxation measurements on La_1−xCa_xFeO_3−δ reveal that:

(ii) the Ca dopant is predominantly compensated by the formation of electron holes (electronic compensation) rather than by oxygen vacancies (ionic compensation). The enthalpy of oxidation is found to decrease with increasing oxygen nonstoichiometry δ, while it becomes more endothermic (less exothermic), at constant δ, with increasing x.

(iii) Maximum electrical conductivity of value 123 S cm⁻¹ at 650 °C is found, under air, for x = 0.30. The temperature dependence of the calculated mobility of electron holes x = 0.10, 0.15, 0.15 and 0.20 is found to be in accordance with Emin–Holstein's theory (adiabatic and non-adiabatic regimes), but fails for the compositions with high Ca contents x = 0.30 and x = 0.40. This is tentatively explained by the increased delocalization of charge carriers with increasing the Ca dopant concentration.

(iv) The effective migration barrier for oxygen diffusion in La_1−xCa_xFeO_3−δ decreases with decreasing oxygen vacancy formation enthalpy (less negative enthalpy of oxidation). The latter is found to depend both on Ca content and the level of oxygen nonstoichiometry. The ionic conductivity increases with increasing Ca content in La_1−xCa_xFeO_3−δ due to the resultant increases in oxygen nonstoichiometry and vacancy diffusivity.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Financial support from the Dutch Technology Foundation (STW, now part of NWO; Project Nr. 15325) and the Chinese Scholarship Council (CSC 201406340102) are gratefully acknowledged.

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d0ta07508f

‡ Separation and Conversion Technology, Flemish Institute for Technological Research (VITO), Boeretang 200, Mol 2400, Belgium

§ Center for Information Photonics and Energy Materials, Shenzhen Institutes of Advanced Technology (SIAT), Chinese Academy of Sciences, Shenzhen 518055, P. R. China

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