Fundamental material property trends in the La_0.8-xNd_xCa_0.2FeO_3-δ series: crystal structure and thermal expansion

A series of solid solutions La_0.8-xNd_xCa_0.2FeO_3-δ (0.1 \(\le\) x \(\le\) 0.7) was synthesised via a citric acid – ethylenediaminetetraacetate (EDTA) sol–gel process starting with stoichiometric amounts of the metal nitrates La(NO₃)₃.6H₂O, Nd(NO₃)₃.6H₂O, Ca(NO₃)₂.4H₂O and Fe(NO₃)₃.9H₂O (all chemicals obtained from Sigma-Aldrich, analytical grade quality). These were mixed with distilled H₂O in a stainless steel vessel. Anhydrous citric acid and EDTA (one mole each per mole cations) were added after the metal nitrates were completely dissolved. Subsequently, 25% aqueous NH₃ solution was added until pH = 8 was reached and a clear dark red solution was obtained. The temperature was slowly raised to evaporate water and form a gel. Self-ignition and combustion of the dried gel occurred at approximately 500 °C.

The raw ash was crushed in an agate mortar and calcined at 1000 °C for 4 h (5 K min⁻¹ ramps for heating and cooling) in air. According to XRD, single-phase compounds were obtained for La_0.8-xNd_xCa_0.2FeO_3-δ with x \(\le\) 0.6. Further increase in the Nd concentration to x = 0.7 led to the formation of the secondary phases CaO and Ca₂Fe₂O₅ (see Supplementary Material, Figure S-1 and Table S-1). The particle size distribution of the calcined powders was determined by use of a CILAS 1064L particle size analyser. After calcination, the d₅₀ values of the powders were in the range of 18.6 \(\le\) d₅₀/µm \(\le\) 22.4. A bench top roll-mill was used to grind the calcined powders until 0.5 \(\le\) d₅₀/µm \(\le\) 0.7 was reached.

For thermal expansion measurements, cylindrical pellets were fabricated by uniaxial pressing. After sintering at 1150 °C for 10 h with heating and cooling rates of 1 K min⁻¹, the samples were approximately 5 mm in diameter and 8 mm long. The relative densities of the sintered samples of La_0.8-xNd_xCa_0.2FeO_3-δ with x = 0 [7] and x = 0.3–0.6 (this study) were in the range of 97–99% of the theoretical densities. (Relative densities of La_0.8-xNd_xCa_0.2FeO_3-δ with x = 0.1–0.2 were determined with 92% of the theoretical densities; however, since these two samples were not ideally cylindrical, the relative densities may be underestimated.)

XRD of the calcined powders was performed with a diffractometer (BRUKER-AXS D8 Advance ECO) using a Cu K\(\alpha\) radiation source operated at 40 kV and 25 mA. The diffractograms were recorded at scanning rates of 0.01° s⁻¹. Rietveld refinement was performed by using the commercially available software TOPAS (Bruker) [27]. Lattice parameters were obtained from fits of the reflections’ positions to an orthorhombic unit cell (space group Pnma). Reflection broadening was described by convolution of a Voigt function with a modified pseudo-Voigt function according to Thompson–Cox–Hastings [28].

Sample preparation for the TEM investigation was carried out on a focused ion beam (FIB) microscope FEI NOVA 200 Nanolab. TEM analyses were performed with a TITAN³ G2 60–300 from FEI at 300 kV accelerating voltage in scanning transmission electron microscopy mode (STEM). The microscope is equipped with a C_S–probe corrector and a Super-X detector system (FEI). STEM images were acquired with a high-angle annular dark-field (HAADF) and a bright-field (BF) detector. The software packages GMS 3 (Gatan) and Velox 2 (Thermo Fisher Scientific) were used to acquire HAADF images and EDX spectrum images.

The cation stoichiometry (Table 1) was obtained by energy-dispersive X-ray spectroscopy (EDXS) measurements in a scanning electron microscope (Cambridge, STEREOSCAN 250 MK3) equipped with an Oxford Instruments Mod. 6272 detector. To confirm the homogeneity of cation distribution, area scans on polished samples with 10 mm diameters were measured.

The thermal expansion behaviour of the materials was investigated between 30 and 1000 °C with heating rates of 1 K min⁻¹ using a single-rod dilatometer DIL 402/PC4 (NETZSCH). Atmospheres with different oxygen partial pressures in range of 1 × 10^–3 ≤ pO₂/bar ≤ 1 were obtained by O₂-Ar gas mixtures using mass flow controllers (Teledyne HFC-302) at flow rates of 10 l h⁻¹.

Differential scanning calorimetry (DSC) was performed on selected sintered (1100 °C, 2 h, air) and finely ground powders using a High Temperature DSC 404 C Pegasus (NETZSCH). The sample (approximately 20–30 mg) was placed in an 85 µl Pt–Rh crucible. To minimize the influence of adsorbed humidity or CO₂, the powders were heated in the calorimeter to 1000 °C, kept in 20% O₂ (rest Ar) and cooled to 20 °C before the actual experiments were started. The DSC measurements were performed between 20 and 1000 °C in 20% O₂ (rest Ar) with heating and cooling rates of 20 K min⁻¹ and gas flow rates of 50 ml min⁻¹.

XRD patterns of La_0.8-xNd_xCa_0.2FeO_3-δ (0 \(\le\) x \(\le\) 0.6) are shown in Fig. 1a. All reflections were assigned to the orthorhombic GdFeO₃ perovskite structure with the space group Pnma (SG#62). With increasing Nd content, the reflections shift towards higher diffraction angles. This effect is shown in detail for the reflections ascribed to the lattice planes (220) and (022) in Fig. 1(b), and for the lattice planes (321), (240), (123) and (042) in Fig. 1(c). The separation of these reflections increases with increasing Nd concentration. Rietveld refinement was performed for all compounds La_0.8-xNd_xCa_0.2FeO_3-δ (0 \(\le\) x \(\le\) 0.6). The lattice parameters of the orthorhombic unit cells are plotted as a function of Nd concentration in Fig. 2a. Linear dependences of the unit cell parameters of the solid solutions on the Nd concentration are observed, following Vegard’s law [29]. No change in space group is observed within the investigated range of compositions (see also the plot of the orthorhombicity, defined as 2(b −  a)/(a + b) [30], in Fig. 2b). The lattice parameters of the Nd-substituted compounds are given in Table 2, which also includes data of the unsubstituted materials LaFeO₃ [31], CaFeO₃ [32] and NdFeO₃ [33], and of La_0.8Ca_0.2FeO_3-δ [7]. Increasing substitution of La³⁺ with Nd³⁺ causes a linear decrease in the unit cell volume of La_0.8-xNd_xCa_0.2FeO_3-δ (Table 2 and Fig. 2(c)).

Goldschmidt’s tolerance factor t (Table 2), which describes the deviation from the ideal cubic perovskite structure (t = 1) and may be used as an indicator of the relative stability of the structure, was calculated according Eq. 1 [34, 35].

The variables \({\text{x}}_{{\text{A}}}\), \({\text{x}}_{{{\text{A}}^{\prime } }}\) and \({\text{x}}_{{{\text{A}}^{{^{\prime \prime } }} }}\) represent the occupancy of the A-sites of the perovskite lattice with A = La, A′ = Ca and A′′ = Nd (for example: \({\text{x}}_{{\text{A}}}\) = 0.2, \({\text{x}}_{{{\text{A}}^{\prime } }}\) = 0.2 and \({\text{x}}_{{{\text{A}}^{{^{\prime \prime } }} }}\) = 0.6 in La_0.2Nd_0.6Ca_0.2FeO_3-δ). The symbols r_i denote the ionic radii of the species i (A- and B-site cations, oxygen). The following ionic radii from [12] were used: r(La³⁺)(XII) = 1.36 Å; r(Ca²⁺)(XII) = 1.34 Å, r(Nd³⁺)(XII) = 1.27 Å, r(Fe³⁺(high spin))(VI) = 0.645 Å, r(O²⁻)(VI) = 1.40 Å. As indicated in Table 2, t decreases with increasing Nd concentration from LaFeO₃ (t = 0.9543) [31] over La_0.7Nd_0.1Ca_0.2FeO_3-δ (t = 0.9498) to CaFeO₃ (t = 0.9474), and subsequently to La_0.2Nd_0.6Ca_0.2FeO_3-δ (t = 0.9343) and NdFeO₃ (t = 0.9232).

As an example for the compounds from the LNCF series, La_0.2Nd_0.6Ca_0.2FeO_3-δ was analysed with atomically resolved STEM-EDX regarding the distribution of the cations La, Nd, Ca and Fe. The contrast in the STEM-HAADF image (Fig. 3, upper left image) results from the differences in the atomic numbers of the elements, with heavier elements appearing brighter than lighter ones. Due to the similar atomic numbers of La (57) and Nd (60), it is not possible to distinguish between those two elements solely based on the information from the HAADF image. However, the elemental distributions of La and Nd were determinable with STEM-EDX spectrum images. The elemental maps of La, Nd, Fe and Ca thus obtained are shown in Fig. 3. The Ca map is not as clear as those of La and Nd, due to the relatively low Ca signal intensities in the EDX spectra. However, the elemental distribution maps indicate that the cations are indeed homogeneously distributed on the A- (La, Nd, Ca) and B-sites (Fe) of La_0.2Nd_0.6Ca_0.2FeO_3-δ. Similar behaviour is assumed for the elemental distribution in the other compounds from the LNCF series.

Under consideration of these results, the atomic positions of the La-, Nd- and Ca-sites in the Rietveld refinement of the XRD data were set equivalent for all investigated compounds of the LNCF series. As an example, the refined XRD pattern and the crystal structure of La_0.2Nd_0.6Ca_0.2FeO_3-δ are shown in Fig. 4a and Fig. 4b. The atomic positions of La_0.8-xNd_xCa_0.2FeO_3-δ (0.1 ≤ x ≤ 0.6) are given in Table 3. Table 4 shows bond lengths and bond angles of materials from the LNCF series in comparison with the unsubstituted compounds LaFeO₃ [31], CaFeO₃ [32], NdFeO₃ [33] and the Nd-free analogue La_0.8Ca_0.2FeO_3-δ [7]. Bond lengths and bond angles of La_0.8-xNd_xCa_0.2FeO_3-δ (0 ≤ x ≤ 0.6) are also shown as a function of Nd concentration in Fig. 5. Substitution of 10% La with Nd decreases the bond length between Fe and the apical oxygen (Fe1-O1, Fig. 5f), followed by an increase in the bond length from x = 0.1 to 0.3 in La_0.8-xNd_xCa_0.2FeO_3-δ (Fig. 5(a)). An increase with different slopes is observed at higher Nd concentrations (x = 0.4 to 0.6). While the bond lengths Fe1-O2 (Fig. 5(b)) decrease with increasing x, the bond lengths Fe1-O2′ show similar trends to those of Fe1-O1 (Fig. 5c, decrease from x = 0 to x = 0.1 and increase with further increase in x). The presence of two different equatorial oxygen positions (O2 and O2′) is due to a distortion of the FeO₆ octahedra [31, 33, 36]. Although Fe1-O2 and Fe1-O2′ have different bond lengths, the bond angles of Fe1-O2-Fe1 and Fe1-O2′-Fe1 are equal. The bond angles Fe1-O2-Fe1 and Fe1-O2′-Fe1 (both shown in Fig. 5d), as well as Fe1-O1-Fe1 (Fig. 5e) increase from x = 0 to x = 0.1 and decrease from x = 0.1 to 0.6.

The high-resolution HAADF image shown in Fig. 6b was used to perform a Fast Fourier Transformation (FFT) (Fig. 6d) to analyse the changes in the crystal structure when substituting Nd with La within the perovskite structure. For this purpose, La_0.2Nd_0.6Ca_0.2FeO_3-δ was compared with the Nd-free compound La_0.8Ca_0.2FeO_3-δ. The reciprocal lattice spacings and angles measured from FFTs of La_0.2Nd_0.6Ca_0.2FeO_3-δ were compared with values obtained from simulations of electron diffraction patterns via JEMS [37]. Figure 6c depicts the simulated diffraction patterns of La_0.8Ca_0.2FeO_3-δ and La_0.2Nd_0.6Ca_0.2FeO_3-δ in [010] zone axis. A comparison of Fig. 6d with the simulations clearly reveals the changes in the crystal structure: spots from the (001), (00-1), (100) and (-100) lattice planes (marked in red squares) appear in the FFT as well as in the diffraction pattern simulation of La_0.2Nd_0.6Ca_0.2FeO_3-δ, but are not visible in the simulation of La_0.8Ca_0.2FeO_3-δ. The absence of further diffraction spots in La_0.8Ca_0.2FeO_3-δ (marked with dashed squares) is due to the fact that these reflections can be explained as orders of the inner missing spots.

Thermal expansion coefficients \(\alpha\) of La_0.8-xNd_xCa_0.2FeO_3-δ (0 \(\le\) x \(\le\) 0.6) were obtained from the slopes of ΔL/L₀ vs. T curves (Figure S-2–S-5) in the temperature regions I (40 \(\le {\text{T}}/^\circ {\text{C}} \le\) 530) and II (530 \(\le {\text{T}}/^\circ {\text{C}} \le\) 990) and different oxygen partial pressures in the range of 1 × 10^–3 ≤ pO₂/bar ≤ 1 (Table 5 and Fig. 7). A three-dimensional representation of the T- and pO₂-dependence of the average \(\alpha\) values (50 \(\le {\text{T}}/^\circ {\text{C}} \le\) 1000) is given in Figure S-6. At constant pO₂, the effect of Nd-substitution in the series La_0.8-xNd_xCa_0.2FeO_3-δ on the thermal expansion coefficient is relatively small, and the \(\alpha\) values of La_0.8-xNd_xCa_0.2FeO_3-δ (0.1 \(\le\) x \(\le\) 0.6) are similar to those of La_0.8Ca_0.2FeO_3-δ [7]. At pO₂ = 1 bar, \(\alpha\) of La_0.8-xNd_xCa_0.2FeO_3-δ (0 \(\le\) x \(\le\) 0.6) is in the range of (12.8 ± 0.3) × 10^–6 K⁻¹ (region I) and (15.3 ± 0.5) × 10^–6 K⁻¹ (region II), and at 0.1 bar in the range of (13.0 ± 0.2) × 10^–6 K⁻¹ (region I) and (15.7 ± 0.2) × 10^–6 K⁻¹ (region II). At lower oxygen partial pressure, i.e. pO₂ = 0.01 bar, \(\alpha\) values are (13.4 ± 0.3) × 10^–6 K⁻¹ (region I) and (17.4 ± 0.9) × 10^–6 K⁻¹ (region II), and at 0.001 bar (13.2 ± 0.3) × 10^–6 K⁻¹ (region I) and (18.4 ± 0.4) × 10^–6 K⁻¹ (region II). The increase in \(\alpha\) with decreasing pO₂ (esp. at 1 × 10^–2 and 1 × 10^–3 bar) and increasing temperature (esp. in region II) is presumably due to the additional contribution of chemical expansion caused by the formation of oxygen vacancies as observed with similar perovskites [7, 22, 23].

The \(\alpha\) values of La_0.8-xNd_xCa_0.2FeO_3-δ (0 \(\le\) x \(\le\) 0.6), determined in temperature regions I and II at pO₂ = 0.1 bar, are similar to those of Nd-free lanthanum calcium ferrites like La_0.9Ca_0.1FeO_3-δ (13.1 × 10^–6 K⁻¹ [23]) and La_0.75Ca_0.25FeO_3-δ (15.1 × 10^–6 K⁻¹ [22]), but significantly smaller than those of the state-of-the-art SOFC cathode material La_0.6Sr_0.4CoO_3-δ (18.9 × 10^–6 K⁻¹ [38]). Further, the thermal expansion coefficients of La_0.8-xNd_xCa_0.2FeO_3-δ (0 \(\le\) x \(\le\) 0.6) are relatively close (especially in temperature region I) to those of common solid electrolytes like 8YSZ (10.8 × 10^–6 K⁻¹ [39]) or Ce_0.9Gd_0.1O_2-δ (12.5 × 10^–6 K⁻¹ [40]).

As previously reported in the literature, the Nd-free compound La_0.8Ca_0.2FeO_3-δ shows a reversible transition from the orthorhombic (SG: Pnma) to the trigonal (SG: R-3c) structural modification at approximately 740 °C [7, 25]. According to DSC measurements, substitution of La with Nd seems to suppress the structural transition in La_0.8-xNd_xCa_0.2FeO_3-δ (0.1 \(\le\) x \(\le\) 0.6) (Figures S-7 and S-8). While the DSC curve of La_0.8Ca_0.2FeO_3-δ shows an exothermal peak at approximately 740 °C (previously attributed to the structural transition [7, 25]), no comparable peaks were observed in the DSC curves La_0.8-xNd_xCa_0.2FeO_3-δ (0.1 \(\le\) x \(\le\) 0.6).