Anomalous Thermal Expansion of HoCo0.5Cr0.5O3 Probed by X-ray Synchrotron Powder Diffraction

Mixed holmium cobaltite-chromite HoCo0.5Cr0.5O3 with orthorhombic perovskite structure (structure type GdFeO3, space group Pbnm) was obtained by solid state reaction of corresponding oxides in air at 1373 K. Room- and high-temperature structural parameters were derived from high-resolution X-ray synchrotron powder diffraction data collected in situ in the temperature range of 300–1140 K. Analysis of the results obtained revealed anomalous thermal expansion of HoCo0.5Cr0.5O3, which is reflected in a sigmoidal temperature dependence of the unit cell parameters and in abnormal increase of the thermal expansion coefficients with a broad maxima near 900 K. Pronounced anomalies are also observed for interatomic distances and angles within Co/CrO6 octahedra, tilt angles of octahedra and atomic displacement parameters. The observed anomalies are associated with the changes of spin state of Co3+ ions and insulator-metal transition occurring in HoCo0.5Cr0.5O3.


Background
Rare earth (R) cobaltites RCoO 3 and chromites RCrO 3 with perovskite structure due to their high electrical conductivity, specific magnetic properties, as well as significant electrochemical and catalytic activity are considered as prospective electrode and interconnect materials for solid oxide fuel cells (SOFC) [1][2][3], thermoelectric and magnetocaloric materials [4][5][6], catalysts and humidity and gas sensors [7][8][9]. Currently RCoO 3 and RCrO 3 compounds and solid solutions on their basis are attracting renewed research interest aroused by their potential application as multifunctional materials [10][11][12][13]. RCoO 3 -based materials are of particular interest, due to dependency of their transport, magnetic and other properties on spin state of Co 3+ ions, which can change with increasing of the temperature from low spin (LS, t 2g 6 e g 0 , S = 0), to intermediate (IS, t 2g 5 e g 1 , S = 1) and high spin (HS, t 2g 4 e g 2 , S = 2) configurations ( [14][15][16] and references herein). These transitions in rare earth cobaltites RCoO 3 are strongly affected by the chemical pressure caused by cation substitution either in A-or B-sites of perovskite structure [17][18][19].
The present work deals with the study of crystal structure of new mixed cobaltite-chromite HoCo 0.5 Cr 0.5 O 3 and its thermal behaviour in the temperature range of 300-1140 K by using high-resolution X-ray synchrotron powder diffraction technique. The HoCo 0.5 Cr 0.5 O 3 was chosen for the detail structural investigations as a representative of the mixed cobaltites-chromites in view of the fact, that both parent compounds-HoCoO 3 and HoCrO 3 , which are isostructural and isotypic with GdFeO 3 [20][21][22][23], show a variety of intriguing physical phenomena and properties. In particular, holmium chromite undergoes a low-temperature phase transition from centrosymmetric Pbnm to the non-centrosymmetric Pna2 1 structure, as it was recently suggested by X-ray powder diffraction of HoCrO 3 at 80 and 160 K [12]. The authors assume that the polar oxygen rotations of CrO 6 octahedra combined with the displacements of Ho in the non-centrosymmetric space group Pna2 1 engineer ferroelectricity in HoCrO 3 below 240 K. For HoCoO 3 no structural phase transitions are reported in a broad temperature range between 1.5 and 1098 K, although pronounced anomalies are observed both in low-and high-temperature lattice expansion [24][25][26]. A negative expansion observed in b-direction (in Pbnm setting) below 150 K suggests a magnetoelastic coupling where short-range interactions between Ho 3+ magnetic moments are established [24]. The high-temperature anomalies are associated with the transitions of the Co 3+ ions to the higher spin states and coupled metal-insulator transition occurred in HoCoO 3 above 780 K [15,25,26]. On the assumption of aforesaid extremely complicated structure, magnetic and electronic phase behaviour is expected in the mixed cobaltite-chromite system HoCo 0.5 Cr 0.5 O 3 . Analysis of the thermal expansion behaviour is a very useful tool for the investigation of diverse electronic and magnetic phase transformations occurring in the complex oxide perovskite systems [14,16,19].

Methods
HoCo 0.5 Cr 0.5 O 3 was synthesized by a solid state technique. Precursor oxides Ho 2 O 3 , Co 3 O 4 and Cr 2 O 3 were ball-milled in ethanol for 5 h, dried, pressed into pellet and annealed in air at 1373 K for 20 h. After regrinding, the product was repeatedly ball-milled in ethanol for 2 h, dried and annealed in air at 1373 K for 45 h with one intermediate regrinding.
X-ray powder diffraction (Huber imaging plate Guinier camera G670, Cu K α1 radiation) was used for the characterization of the sample at room temperature. Thermal behaviour of HoCo 0.5 Cr 0.5 O 3 crystal structure was studied in situ in the temperature ranges of 300-1140 K by using high-resolution X-ray synchrotron powder diffraction (beamline ID22 at ESRF, Grenoble, France). The data were collected upon the heating of the powdered sample filled into 0.3 mm quartz capillary with the temperature step of 50 K. The wavelength used λ = 0.35434 Å allows to collect the diffraction data until the maximum sinΘ/λ value of 0.849 ensuring reliable information on the positional and displacement parameters of atoms in HoCo 0.5 Cr 0.5 O 3 structure at the elevated temperatures. Corresponding structural parameters were derived by full-profile Rietveld method implemented in the program package WinCSD [27].
Crystal structure of HoCo 0.5 Cr 0.5 O 3 is visualized as 3D framework of corner-shared MO 6 octahedra (M = Co 0.5 Cr 0.5 ) with the Ho atoms occupying hollows between them. The MO 6 octahedra are rather distorted due to displacement of oxygen atoms from their "ideal" positions in the cubic perovskite aristotype. Mutual displacements of oxygen atoms are reflected in the cooperative antiphase tilts of MO 6 octahedra, as is depicted on insets of Fig. 2.
The ratio of the atomic displacement parameters (adps) observed in HoCo 0.5 Cr 0.5 O 3 structure both at 300 and 1140 K follow well the simple expectation based on the atomic masses, namely B iso/eq (O) > B iso/eq (Co/Cr) > B iso/eq (Ho). Thermal ellipsoids of cations in HoCo 0.5 Cr 0.5 O 3 structure at room temperature are close to spherical shape, with minor contraction or elongation in b-direction:  22 for Ho 3+ and B 11 ≈ B 33 < B 22 for Co 3+ /Cr 3+ . More pronounced anisotropic behaviour is observed for the displacement parameters of oxygen species, reflected in the remarkable contraction or elongation of the corresponding ellipsoids in c-direction (Table 1). Thermal ellipsoids of oxygen atoms both in equatorial (8d) and apical (4c) positions of MO 6 octahedra show near rotation-type behaviour along M-O bonds (Fig. 2, insets). At the elevated temperatures, the displacement ellipsoids for Co/Cr atoms become almost spherical, whereas those for Ho 3+ species exhibit considerable anisotropy, e.g. B 33 > B 11 > B 22 at 1140 K. The behaviour of adps of oxygen species located in 4c and 8d sites (B 11 ≈ B 22 > B 33 and B 11 ≈ B 22 < B 33 , respectively) does not change with the temperature (Table 1). However, it can be noticed that displacement parameters of apical O1 atoms located in 4c sites become more isotropic at the elevated temperatures (Fig. 2, insets).
Analysis of the thermal behaviour of HoCo 0.5 Cr 0.5 O 3 structure revealed pronounced anomalies in the lattice expansion, which are reflected in a sigmoidal temperature dependence of the unit cell dimensions and in significant increase of the thermal expansion coefficients (TECs) with broad maxima around 900 K (Fig. 3). Similar abnormal lattice parameter behaviour was earlier observed in the related mixed cobaltiteschromites LaCo 1-x Cr x O 3 [28] and RCo 0.5 Cr 0.5 O 3 (R = Pr, Sm, Eu, Gd, Dy and Er) [19,[31][32][33].
In the "pure" rare earth cobaltites RCoO 3 abnormal thermal behaviour of the lattice expansion is associated with magnetic phase transitions and with a change of electronic configuration and spin state of Co 3+ ions, which lead to the increment of the lattice parameters and unit cell volume due to increase of the radii of Co 3+ ions in the exited states (r(LS) = 0.545 Å, r(IS) = 0.560 Å, r(HS) = 0.610 Å). The maxima at the temperature dependence of the thermal expansion coefficients in rare earth cobaltites show clear correlation with the temperature of insulator-metal transition, obtained from resistivity measurements, which increases in the RCoO 3 series from 535 K for LaCoO 3 to 785 and 800 K for DyCoO 3 and YCoO 3 , respectively [14].
It is assumed that the observed structural anomalies in HoCo 0.5 Cr 0.5 O 3 around 900 K are also associated with   are less pronounced than in the "pure" HoCoO 3 [25], whereas the maximum at TEC curve is shifted to the higher temperatures (inset of Fig. 3b). Similar effect of cationic exchange was observed in the related RCoO 3 -RCrO 3 systems, where increasing chromium content in NdCo 1-x Cr x O 3 and GdCo 1-x Cr x O 3 series led to increase of the temperature of metal-isolator transitions [18,30]. Thorough analysis of the selected bond length, atomic displacement parameters and octahedral tilt angles in HoCo 0.5 Cr 0.5 O 3 structure indicates additional structural anomalies, which are evidently associated with the electronic and magnetic phase transitions occurring in the HoCoO 3 -HoCrO 3 system at elevated temperatures. Temperature evolution of the M-O bond lengths in the HoCo 0.5 Cr 0.5 O 3 structure is presented on Fig. 4a. Initially, both M-O1 and M-O2 distances remain practically unchanged. Significant change in configuration of MO 6 octahedra occurs between~600 and 850 K, where an excitation to the higher spin states of Co 3+ ions begins. Detectable deviation from the "normal" behaviour in this temperature range is also observed for the temperature dependence of the displacement parameters of oxygen species in HoCo 0.5 Cr 0.5 O 3 structure (Fig. 4b). Further increasing of the temperature led to the increase of all M-O distances and to the convergence of both sets of M-O2 bond lengths in the equatorial plane of MO 6 octahedra (Fig. 4a). Thus, the shape of MO 6 octahedra at the elevated temperatures differs considerably from the room temperature configuration.
Temperature  [34,35]. In particular, increase of cooperative rotations of corner-shared CoO 6 octahedra in RCoO 3 perovskites led to reducing of Co-O-Co bond angles and the bandwidth of Co(3d)-O(2p) interactions, which are correlated with the increasing spin-state transition temperature, T onset [15]. According to ( [15,35] and references herein), in the RCoO 3 cobaltite series the σ*-bonding e g bandwidth W ∝ cosω/〈Co-O〉 3.5 , where ω = (180 -〈θ〉)/2 is the average octahedral tilting angle, and 〈Co-O〉-the mean bond length inside CoO 6 octahedra. The broadening of W in rare earth cobaltite series reduces the spin gap and decreases the onset of spin transition of Co 3+ from LS to IS state [15]. Figure 5b demonstrates the temperature dependence of the inverse bandwidth, W −1 of HoCo 0.5 Cr 0.5 O 3 , which increase with the temperature solely due to increase of the average bond lengths inside octahedra, whereas the octahedral tilt angles are practically temperature independent (Fig. 5b, inset). Observed increasing behaviour of the inverse bandwidth of HoCo 0.5 Cr 0.5 O 3 clearly illustrates an increasing population of the exited spin states of Co 3+ ions with the  [25] temperature. It is apparent that the magnetic and electrical properties of HoCo 0.5 Cr 0.5 O 3 will depend on the spin state of the Co 3+ ions and a cation-anion-cation overlap, as it was reported for the related NdCo 1-x Cr x O 3 and GdCo 1-x Cr x O 3 systems [18,30]. Increasing structural deformation in the last systems caused by the substitution of chromium by cobalt shifts the onset of Co 3+ spin excitations and metal-insulator transition to the highest temperatures and led to the rising of electrical conductivity and Néel temperature in NdCo 1-x Cr x O 3 series. It is evident that the coupling of the electronic and magnetic transitions combined with the anomaly of the lattice behaviour will result in extremely complicated magnetic and electronic phase diagram of the mixed cobaltite-chromite systems.

Conclusions
Crystal structure parameters of the mixed holmium cobaltite-chromite HoCo 0.5 Cr 0.5 O 3 synthesized by solid state reaction in air at 1373 K have been studied in the temperature range of 300-1140 K by using high-resolution X-ray synchrotron powder diffraction technique. Experimental X-ray synchrotron powder diffraction patterns and crystal structure parameters of HoCo 0.5 Cr 0.5 O 3 structure at room temperature and 1140 K are published by the International Centre of Diffraction Data (ICDD) in the last release of the Powder Diffraction File (PDF cards NN 00-066-0678 and 00-066-0679, respectively). Detailed analysis of the temperature dependence of structural parameters revealed pronounced anomalies in thermal behaviour of the unit cell dimensions and thermal expansion coefficients with clear maxima at around 900 K. Extra structural anomalies are also observed on temperature dependencies of the M-O bond lengths, octahedral tilt angles and atomic displacement parameters, which are evidently caused with the temperature induced changes of spin configuration of Co 3+ ions and coupled metalinsulator transition occurred in HoCoO 3 -HoCrO 3 system.