Background

Complex oxides with perovskite structure RFeO3, where R is the rare earth(RE), represent an important class of functional materials. The RFeO3-based materials are used as electrodes in solid oxide fuel cells, as catalysts, gas sensory materials and semiconductor ceramics [1–6]. Complementary, the interest in the rare earth ferrites is stimulated by their interesting fundamental physical properties, such as spin-reorientation transitions at 80–480 K and the para- to antiferromagnetic transitions at 620–750 K [7–10]. Just recently, the interest to RE ferrite perovskites was renewed due to reported multiferroic properties of NdFeO3, SmFeO3 and other RFeO3 compounds [11–13]. At room temperature (RT), all RE orthoferrites adopt orthorhombic perovskite structure isotypic with GdFeO3 [14, 15]. No structural phase transitions were reported in the literature for RFeO3 compounds, with an exception of LaFeO3, which undergoes a high-temperature (HT) transition to rhombohedral structure at 1220–1280 K [16, 17]. Orthorhombic RFeO3 perovskites show strongly anisotropic thermal expansion: the expansivity in the b direction in the Pbnm setting is ca. two times lower than in the a and c directions. Subtle anomalies in the lattice expansion of PrFeO3 and SmFeO3 are observed in the b direction at 600–800 K, which is indicative for magnetoelastic coupling at the magnetic ordering temperature T N [18, 19]. In ref. [9], it was shown that the spin-reorientation transition in NdFeO3 between 100 and 200 K is associated with changes of the b-lattice parameter, which has a broad local minimum in the spin-reorientation region near 160 K. However, no lattice anomalies in NdFeO3 were found around the Néel temperature of 687 K in [10].

The aim of the present work is the detail study of the thermal behaviour of Sm0.5Pr0.5FeO3 and Sm0.5Nd0.5FeO3 in order to reveal the possible magnetoelastic coupling in these mixed perovskite ferrites.

Methods

Polycrystalline samples with nominal compositions Sm0.5Pr0.5FeO3 and Sm0.5Nd0.5FeO3 have been prepared from stoichiometric amounts of constituent oxides Sm2O3, Pr6O11, Nd2O3 and Fe2O3 by solid-state reaction technique according to the following reaction schemes:

$$ \begin{array}{l}3/2\mathrm{S}{\mathrm{m}}_2{\mathrm{O}}_3 + 1/2\mathrm{P}{\mathrm{r}}_6{\mathrm{O}}_{11} + 3\mathrm{F}{\mathrm{e}}_2{\mathrm{O}}_3\to\ 6\mathrm{S}{\mathrm{m}}_{0.5}\mathrm{P}{\mathrm{r}}_{0.5}\mathrm{F}\mathrm{e}{\mathrm{O}}_3 + 1/2{\mathrm{O}}_2\uparrow \hfill \\ {}1/2{\mathrm{Sm}}_2{\mathrm{O}}_3 + 1/2{\mathrm{Nd}}_2{\mathrm{O}}_3 + {\mathrm{Fe}}_2{\mathrm{O}}_3\to\ 2{\mathrm{Sm}}_{0.5}{\mathrm{Nd}}_{0.5}{\mathrm{Fe}\mathrm{O}}_3.\hfill \end{array} $$

Precursor oxides were ball-milled in ethanol for 5 h, dried, pressed into pellets and annealed in air at 1473 K for 20 h. The as-obtained product was repeatedly re-grinded and annealed at 1473 K for 20 h and, after that, slowly cooled to RT for 20 h.

X-ray phase and structural characterization of the samples was performed at room temperature by using imaging plate Guinier camera G670 (Cu Kα1 radiation, λ = 1.54056 Å). Thermal behaviour of Sm0.5Pr0.5FeO3 and Sm0.5Nd0.5FeO3 structures has been studied in situ in the temperature range of 298–1173 K by means of high-resolution X-ray synchrotron powder diffraction technique. The corresponding experimental powder diffraction patterns were collected with the temperature steps of 30 K at beamline B2 of synchrotron laboratory HASYLAB/DESY (Hamburg, Germany). Structural parameters of the samples were derived from the experimental diffractograms by using full-profile Rietveld refinement technique applying WinCSD program package [20].

Results and Discussion

X-ray powder diffraction examination revealed that both samples synthesized possess orthorhombic perovskite structure isotypic with GdFeO3. No extra crystalline phases were found. The unit-cell dimensions of Sm0.5Pr0.5FeO3 and Sm0.5Nd0.5FeO3 at room temperature are in good agreement with the structural data of the parent SmFeO3, PrFeO3 and NdFeO3 [14, 15] compounds, (Fig. 1), thus proving possible formation of continuous solid solutions Sm1 − x Pr x FeO3 and Sm1 - x Nd x FeO3 in the SmFeO3–PrFeO3 and SmFeO3–NdFeO3 systems.

Fig. 1
figure 1

Concentration dependence of the unit-cell dimensions in the SmFeO3–PrFeO3 and SmFeO3–NdFeO3 systems. The orthorhombic lattice parameters are normalized to the perovskite cell as follows: a p  = a o /√2, b p  = b o /√2, and c p  = c o /2

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Precise high-resolution X-ray synchrotron powder diffraction examination confirms phase purity of the Sm0.5Pr0.5FeO3 and Sm0.5Nd0.5FeO3 samples (Fig. 2). The values of full width at half maximum (FWHM) of the mixed samarium-praseodymium and samarium-neodymium ferrites are in the limits of 0.043°–0.089°, which is comparable with those of the “pure” SmFeO3 ferrite (Fig. 2, inset). Angular dependence of FWHM of Sm0.5Pr0.5FeO3 substantially resembles the behaviour of the parent SmFeO3 compound, whereas a rather scattered behaviour is observed for the Sm0.5Nd0.5FeO3 sample (Fig. 2, inset). To some extent, hkl-dependent anisotropic broadening of Bragg peaks points on the possible compositional, thermal and elastic microstrains presented in the Sm0.5Nd0.5FeO3 sample [21].

Fig. 2
figure 2

X-ray synchrotron powder diffraction patterns of Sm0.5Pr0.5FeO3 and Sm0.5Nd0.5FeO3 (λ = 0.53833 Å). For a comparison, the corresponding pattern of the “pure” SmFeO3 is given as well. Inset shows the angular dependence of HWFM for all three samples

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In situ high-temperature X-ray synchrotron powder diffraction investigations prove that Sm0.5Pr0.5FeO3 and Sm0.5Nd0.5FeO3 remain orthorhombic at least up to 1173 K. No structural phase transitions were detected in the whole temperature range investigated. Based on the experimental X-ray synchrotron powder diffraction data, the unit-cell dimensions and positional and displacement parameters of atoms in the Sm0.5Pr0.5FeO3 and Sm0.5Nd0.5FeO3 structures between RT and 1173 K were derived by full-profile Rietveld refinement technique. As an example, Fig. 3 represents the graphical results of Rietveld refinement of the Sm0.5Pr0.5FeO3 structure at 1173 K. Refined structural parameters of Sm0.5Pr0.5FeO3 and Sm0.5Nd0.5FeO3 at the selected temperatures are presented in Table 1.

Fig. 3
figure 3

Graphical results of Rietveld refinement of the Sm0.5Pr0.5FeO3 structure at 1173 K. Experimental X-ray synchrotron powder diffraction pattern (λ = 0.53833 Å) collected at 1173 K (dots) is shown in comparison with the calculated pattern (lines). The difference between measured and calculated profiles is shown as a curve below the diagrams. Short vertical bars indicate the positions of diffraction maxima in the space group Pbnm. Inset shows the view of the structure as corner-shared FeO6 octahedra with Sm/Pr species located between them

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Table 1 Lattice parameters, coordinates and displacement parameters of atoms in the Sm0.5Pr0.5FeO3 and Sm0.5Nd0.5FeO3 structures at RT, 753 and 1173 K
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Temperature dependencies of the unit-cell dimensions of Sm0.5Pr0.5FeO3 and Sm0.5Nd0.5FeO3 in comparison with the literature data for the “pure” ferrite perovskites SmFeO3 [19], PrFeO3 [18] and NdFeO3 [10] are presented in Fig. 4.

Fig. 4
figure 4

Temperature dependencies of the lattice parameters (a-c) and unit cell volumes (d) of Sm0.5Pr0.5FeO3 and Sm0.5Nd0.5FeO3. Thermal evolution of the unit cell dimensions of SmFeO3 [19], PrFeO3 [18] and NdFeO3 [10] is shown for a comparison

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Temperature evolution of the lattice parameters of mixed Sm-Pr and Sm-Nd ferrites resemble for the most part the thermal behaviour of the parent compounds. In both cases, clear deviations from the “normal” trend are observed in the b direction at 650–750 K, whereas much less visible anomalies in the lattice expansion are observed in the a and c directions (Fig. 4a–c). It is evident that similar to SmFeO3 and PrFeO3, a kink in the b-lattice expansion of Sm0.5Pr0.5FeO3 and Sm0.5Nd0.5FeO3 is associated with the para- to antiferromagnetic transitions that occurred in these specimens at the Néel temperatures. Earlier, nonlinear lattice expansion across the antiferromagnetic to paramagnetic transitions was also observed in LaFeO3 at T N = 735 K [17].

Similar to the “pure” RFeO3 perovskites, thermal expansion of Sm0.5Pr0.5FeO3 and Sm0.5Nd0.5FeO3 shows a clear anisotropic behaviour. Calculated thermal expansion coefficients (TECs) in the b direction are in the limits of (5.3–6.2) × 10−6 K−1 which is twice lower than the values of (11.1–13.6) × 10−6 K−1 in the a and c directions (Fig. 5). Such anisotropic thermal expansion is rather typical for the majority of perovskite oxides with a GdFeO3 type of structure and is inherent for the families of rare earth aluminates, gallates [22–25] and other perovskites. The average linear thermal expansion coefficients of Sm0.5Pr0.5FeO3 and Sm0.5Nd0.5FeO3 in the temperature range of 298–1173 K are in the limits of (9.0–11.1) × 10−6 K−1. It is close to the TEC value of (10.8–11.8) × 10−6 K−1 reported for LaFeO3 [26, 27] and other rare earth ferrites confirming the suggestion that the nature of rare earth ions does not influence the thermal expansion in RFeO3 [15].

Fig. 5
figure 5

Temperature evolution of the linear thermal expansion coefficients of Sm0.5Pr0.5FeO3 (a) and Sm0.5Nd0.5FeO3 (b) The corresponding values of TECs in different crystallographic directions are derived by differentiation of the experimental values of the unit-cell dimensions in the temperature range of 298–1173 K. The dashed lines are quid for the eyes

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Subtle maxima at the TEC curves of Sm0.5Pr0.5FeO3 around 670 K (Fig. 5a) reflect the observed lattice anomalies at the Néel temperature. In spite of no obvious maxima observed on the TEC curves of Sm0.5Nd0.5FeO3, a change of the slope of the TEC(b) values occurs around 650–700 K (Fig. 5b). A similar step at the thermal expansion coefficient at 723 ± 50 K, corresponding with the Néel temperature, has been revealed in LaFeO3 by dilatometric measurements [16].

The lattice expansion of Sm0.5Pr0.5FeO3 and Sm0.5Nd0.5FeO3 could be also affected by a possible change of the oxygen defect structure during the heating of the samples, as it was detected in PrFeO3 and SmFeO3 by thermogravimetric measurements [15]. As it was shown, detectable weight loss due to the fast oxygen desorption begins in these ferrites above 573 K. As a consequence, thermal expansion behaviour of SmFeO3 shows a change of the slope at around 593 K close to the temperature of sharp weight loss detected by TGA [15].

Conclusions

Crystal structure parameters of the mixed samarium-praseodymium and samarium-neodymium ferrites Sm0.5Pr0.5FeO3 and Sm0.5Nd0.5FeO3 synthesized by solid-state reaction technique in air at 1473 K have been studied in a wide temperature range of 298–1173 K by means of high-resolution X-ray synchrotron powder diffraction technique. Close analysis of the temperature dependence of the unit-cell dimensions in comparison with the literature data for the parent RFeO3 compounds revealed strongly anisotropic lattice expansion and subtle anomalies associated with the para- to antiferromagnetic transitions at 650–750 K. The average linear thermal expansion coefficients of Sm0.5Pr0.5FeO3 and Sm0.5Nd0.5FeO3 derived from the experimental values of the unit-cell dimensions in the temperature range of 298–1173 K are in the limits of (9.0–11.1) × 10−6 K−1, which is close to the corresponding values reported for the parent RFeO3 compounds.