Thermal Behaviour of Sm0.5R0.5FeO3 (R = Pr, Nd) Probed by High-Resolution X-ray Synchrotron Powder Diffraction

Mixed ferrites Sm0.5Pr0.5FeO3 and Sm0.5Nd0.5FeO3 with orthorhombic perovskite structure isotypic with GdFeO3 were synthesized by solid-state reaction technique in air at 1473 K. Structural parameters obtained at room temperature prove a formation of continuous solid solutions in the SmFeO3–PrFeO3 and SmFeO3–NdFeO3 pseudo-binary systems. Sm0.5Pr0.5FeO3 and Sm0.5Nd0.5FeO3 show strongly anisotropic nonlinear thermal expansion: thermal expansion in the b direction is twice lower than in the a and c directions. 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, which is close to the values reported for the parent RFeO3 compounds. Subtle anomalies in the lattice expansion of Sm0.5Pr0.5FeO3 and Sm0.5Nd0.5FeO3 detected at 650–750 K reflect magnetoelastic coupling at the magnetic ordering temperature TN.


Background
Complex oxides with perovskite structure RFeO 3 , where R is the rare earth(RE), represent an important class of functional materials. The RFeO 3 -based materials are used as electrodes in solid oxide fuel cells, as catalysts, gas sensory materials and semiconductor ceramics [1][2][3][4][5][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][8][9][10]. Just recently, the interest to RE ferrite perovskites was renewed due to reported multiferroic properties of NdFeO 3 , SmFeO 3 and other RFeO 3 compounds [11][12][13]. At room temperature (RT), all RE orthoferrites adopt orthorhombic perovskite structure isotypic with GdFeO 3 [14,15]. No structural phase transitions were reported in the literature for RFeO 3 compounds, with an exception of LaFeO 3 , which undergoes a high-temperature (HT) transition to rhombohedral structure at 1220-1280 K [16,17]. Orthorhombic RFeO 3 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 PrFeO 3 and SmFeO 3 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 NdFeO 3 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 NdFeO 3 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 Sm 0.5 Pr 0.5 FeO 3 and Sm 0.5 Nd 0.5 FeO 3 in order to reveal the possible magnetoelastic coupling in these mixed perovskite ferrites.

Methods
Polycrystalline samples with nominal compositions Sm 0.5 Pr 0.5 FeO 3 and Sm 0.5 Nd 0. 5   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 regrinded 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 K α1 radiation, λ = 1.54056 Å). Thermal behaviour of Sm 0.5 Pr 0.5 FeO 3 and Sm 0.5 Nd 0.5 FeO 3 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]. Precise high-resolution X-ray synchrotron powder diffraction examination confirms phase purity of the Sm 0.5 Pr 0.5 FeO 3 and Sm 0.5 Nd 0.5 FeO 3 samples (Fig. 2). The values of full width at half maximum (FWHM) of the mixed samarium-praseodymium and samariumneodymium ferrites are in the limits of 0.043°-0.089°, which is comparable with those of the "pure" SmFeO 3 ferrite (Fig. 2, inset). Angular dependence of FWHM of   Sm 0.5 Pr 0.5 FeO 3 substantially resembles the behaviour of the parent SmFeO 3 compound, whereas a rather scattered behaviour is observed for the Sm 0.5 Nd 0.5 FeO 3 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 Sm 0.5 Nd 0.5 FeO 3 sample [21]. In situ high-temperature X-ray synchrotron powder diffraction investigations prove that Sm 0.5 Pr 0.5 FeO 3 and Sm 0.5 Nd 0.5 FeO 3 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 Sm 0.5 Pr 0.5 FeO 3 and Sm 0.5 Nd 0.5 FeO 3 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 Sm 0.5 Pr 0.5 FeO 3 structure at 1173 K. Refined structural parameters of Sm 0.5 Pr 0.5 FeO 3 and Sm 0.5 Nd 0.5 FeO 3 at the selected temperatures are presented in Table 1.

Results and Discussion
Temperature dependencies of the unit-cell dimensions of Sm 0.5 Pr 0.5 FeO 3 and Sm 0.5 Nd 0.5 FeO 3 in comparison with the literature data for the "pure" ferrite perovskites SmFeO 3 [19], PrFeO 3 [18] and NdFeO 3 [10] are presented in Fig. 4.
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 SmFeO 3 and PrFeO 3 , a kink in the b-lattice expansion of Sm 0.5 Pr 0.5 FeO 3 and Sm 0.5 Nd 0.5 FeO 3 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 LaFeO 3 at T N = 735 K [17].
Similar to the "pure" RFeO 3 perovskites, thermal expansion of Sm 0.5 Pr 0.5 FeO 3 and Sm 0.5 Nd 0.5 FeO 3 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  [19], PrFeO 3 [18] and NdFeO 3 [10] is shown for a comparison is rather typical for the majority of perovskite oxides with a GdFeO 3 type of structure and is inherent for the families of rare earth aluminates, gallates [22][23][24][25] and other perovskites. The average linear thermal expansion coefficients of Sm 0.5 Pr 0.5 FeO 3 and Sm 0.5 Nd 0.5 FeO 3 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 LaFeO 3 [26,27] and other rare earth ferrites confirming the suggestion that the nature of rare earth ions does not influence the thermal expansion in RFeO 3 [15].
Subtle maxima at the TEC curves of Sm 0.5 Pr 0.5 FeO 3 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 Sm 0.5 Nd 0.5 FeO 3 , 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 LaFeO 3 by dilatometric measurements [16].
The lattice expansion of Sm 0.5 Pr 0.5 FeO 3 and Sm 0.5 Nd 0.5 FeO 3 could be also affected by a possible change of the oxygen defect structure during the heating of the samples, as it was detected in PrFeO 3 and SmFeO 3 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 SmFeO 3 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 samariumpraseodymium and samarium-neodymium ferrites Sm 0.5 Pr 0.5 FeO 3 and Sm 0.5 Nd 0.5 FeO 3 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 RFeO 3 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 Sm 0.5 Pr 0.5 FeO 3 and Sm 0.5 Nd 0.5 FeO 3 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 RFeO 3 compounds.