Open Access

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

  • Vasyl Hreb1Email author,
  • Leonid Vasylechko1,
  • Vitaliya Mykhalichko1 and
  • Yurii Prots2
Nanoscale Research Letters201712:442

Received: 16 March 2017

Accepted: 23 June 2017

Published: 5 July 2017


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.


Mixed cobaltites-chromites Perovskite Crystal structure Thermal expansion


Rare earth (R) cobaltites RCoO3 and chromites RCrO3 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) [13], thermoelectric and magnetocaloric materials [46], catalysts and humidity and gas sensors [79]. Currently RCoO3 and RCrO3 compounds and solid solutions on their basis are attracting renewed research interest aroused by their potential application as multifunctional materials [1013]. RCoO3-based materials are of particular interest, due to dependency of their transport, magnetic and other properties on spin state of Co3+ 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 ([1416] and references herein). These transitions in rare earth cobaltites RCoO3 are strongly affected by the chemical pressure caused by cation substitution either in A- or B-sites of perovskite structure [1719].

The present work deals with the study of crystal structure of new mixed cobaltite-chromite HoCo0.5Cr0.5O3 and its thermal behaviour in the temperature range of 300–1140 K by using high-resolution X-ray synchrotron powder diffraction technique. The HoCo0.5Cr0.5O3 was chosen for the detail structural investigations as a representative of the mixed cobaltites-chromites in view of the fact, that both parent compounds—HoCoO3 and HoCrO3, which are isostructural and isotypic with GdFeO3 [2023], 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 Pna21 structure, as it was recently suggested by X-ray powder diffraction of HoCrO3 at 80 and 160 K [12]. The authors assume that the polar oxygen rotations of CrO6 octahedra combined with the displacements of Ho in the non-centrosymmetric space group Pna21 engineer ferroelectricity in HoCrO3 below 240 K. For HoCoO3 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 [2426]. A negative expansion observed in b-direction (in Pbnm setting) below 150 K suggests a magnetoelastic coupling where short-range interactions between Ho3+ magnetic moments are established [24]. The high-temperature anomalies are associated with the transitions of the Co3+ ions to the higher spin states and coupled metal-insulator transition occurred in HoCoO3 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 HoCo0.5Cr0.5O3. 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].


HoCo0.5Cr0.5O3 was synthesized by a solid state technique. Precursor oxides Ho2O3, Co3O4 and Cr2O3 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 HoCo0.5Cr0.5O3 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 HoCo0.5Cr0.5O3 structure at the elevated temperatures. Corresponding structural parameters were derived by full-profile Rietveld method implemented in the program package WinCSD [27].

Results and Discussion

X-ray powder diffraction examination of new mixed cobaltite-chromite HoCo0.5Cr0.5O3 revealed almost pure perovskite structure isotopic with GdFeO3 (Fig. 1). The obtained values of unit cell dimensions are in excellent agreement with the corresponding data for the parent HoCoO3 and HoCrO3 compounds (Fig. 1, inset 1), thus proving an apparent formation of continuous solid solution HoCo1–x Cr x O3 with perovskite structure, similarly to the related RCoO3RCrO3 systems with La, Pr, Nd, Sm, Eu, Gd, Dy, Er and Y [18, 19, 2833].
Fig. 1

XRD pattern of HoCo0.5Cr0.5O3 at room temperature (Cu K α1 radiation, Guinier camera). Insets show concentration dependence of the unit cell parameters in the HoCoO3–HCrO3 system. The orthorhombic lattice parameters are normalized to the perovskite cell as follows: a p = a o/√2, b p = b o/√2, c p = c o/2, V p = V o/4

In situ high-temperature X-ray synchrotron powder diffraction revealed that HoCo0.5Cr0.5O3 remains orthorhombic up to highest investigated temperature of 1140 K. No symmetry-related structural changes were observed. Precise crystal structure parameters of HoCo0.5Cr0.5O3 in the temperature range of 300–1140 K including anisotropic displacement parameters for all atomic positions were derived by full-profile Rietveld refinement. In all cases, the refinement procedure performed in space group Pbnm led to the excellent agreement between experimental and calculated profiles. Selected examples of Rietveld refinement at 300 and 1140 K are presented on Fig. 2. Insets on Fig. 2 show corresponding projections of HoCo0.5Cr0.5O3 structure on (001) and (110) planes with thermal ellipsoids of atoms based on the refined structural parameters presented in Table 1.
Fig. 2

X-ray synchrotron powder diffraction patterns of HoCo0.5Cr0.5O3 at 300 and 1140 K. Experimental (dots) and calculated patterns, difference profiles and positions of the diffraction maxima are given. Insets show corresponding structures in projections on (001) and (110) planes. The displacement ellipsoids of atoms are shown at 90% probability level

Table 1

Coordinates and atomic displacement parameters in HoCo0.5Cr0.5O3 structure (space group Pbnm) at 300 and 1140 K


Ho, 4c

Co/Cr, 4b

O1, 4c

O2, 8d

300 K

1140 K

300 K

1140 K

300 K

1140 K

300 K

1140 K























B eq a









B 11









B 22









B 33









B 12









B 13







B 23







Lattice parameters

a = 5.19695(8) Å, b = 5.46911(8) Å, c = 7.45765(9) Å (at 300 K)

a = 5.28195(7) Å, b = 5.55944(7) Å, c = 7.56949(9) Å (at 1140 K)

a B iso/eq = 1/3[B 11(a*) 2 a 2+ … 2B 23 b*c*bc cosα]; displacement factors are defined as exp[−1/4(B 11 (a*) 2 h 2+ … 2B 23 b*c*k l)]

Crystal structure of HoCo0.5Cr0.5O3 is visualized as 3D framework of corner-shared MO6 octahedra (M = Co0.5Cr0.5) with the Ho atoms occupying hollows between them. The MO6 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 MO6 octahedra, as is depicted on insets of Fig. 2.

The ratio of the atomic displacement parameters (adps) observed in HoCo0.5Cr0.5O3 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 HoCo0.5Cr0.5O3 structure at room temperature are close to spherical shape, with minor contraction or elongation in b-direction: B 11≈ B 33> B 22 for Ho3+ and B 11≈ B 33< B 22 for Co3+/Cr3+. 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 MO6 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 Ho3+ 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 HoCo0.5Cr0.5O3 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 cobaltites-chromites LaCo1–x Cr x O3 [28] and RCo0.5Cr0.5O3 (R = Pr, Sm, Eu, Gd, Dy and Er) [19, 3133].
Fig. 3

Temperature evolution of the normalized unit cell parameters (a) and linear thermal expansion coefficients (b) of HoCo0.5Cr0.5O3. The orthorhombic lattice parameters are normalized to the perovskite cell as follows: a p = a o/√2, b p = b o/√2, c p = c o/2, V p = V o/4. The values on linear TECs in three crystallographic directions as well volumetric TEC were obtained by differentiation of experimental unit cell dimensions on the temperature. Inset on the right panel shows volumetric TEC of HoCo0.5Cr0.5O3 in comparison with literature data for HoCoO3 [25]

In the “pure” rare earth cobaltites RCoO3 abnormal thermal behaviour of the lattice expansion is associated with magnetic phase transitions and with a change of electronic configuration and spin state of Co3+ ions, which lead to the increment of the lattice parameters and unit cell volume due to increase of the radii of Co3+ 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 RCoO3 series from 535 K for LaCoO3 to 785 and 800 K for DyCoO3 and YCoO3, respectively [14].

It is assumed that the observed structural anomalies in HoCo0.5Cr0.5O3 around 900 K are also associated with the magnetic and electronic phase transitions occurred at the elevated temperatures in the end members of this system. In particular, according to the electronic phase diagram of the RCoO3 perovskites [15], HoCoO3 undergoes a transition from nonmagnetic dielectric to paramagnetic dielectric state at 486 K and insulator–metal transition at 782 K. Detected anomalies in the lattice expansion of the mixed cobaltite-chromite HoCo0.5Cr0.5O3 are less pronounced than in the “pure” HoCoO3 [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 RCoO3RCrO3 systems, where increasing chromium content in NdCo1–x Cr x O3 and GdCo1–x Cr x O3 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 HoCo0.5Cr0.5O3 structure indicates additional structural anomalies, which are evidently associated with the electronic and magnetic phase transitions occurring in the HoCoO3–HoCrO3 system at elevated temperatures. Temperature evolution of the M–O bond lengths in the HoCo0.5Cr0.5O3 structure is presented on Fig. 4a. Initially, both M–O1 and M–O2 distances remain practically unchanged. Significant change in configuration of MO6 octahedra occurs between ~600 and 850 K, where an excitation to the higher spin states of Co3+ 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 HoCo0.5Cr0.5O3 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 MO6 octahedra (Fig. 4a). Thus, the shape of MO6 octahedra at the elevated temperatures differs considerably from the room temperature configuration.
Fig. 4

Temperature evolution of M–O bond lends (a) and isotropic displacement parameters of atoms (b) in HoCo0.5Cr0.5O3 structure

Temperature evolution of the M–O1–M and M–O2–M bond angles in HoCo0.5Cr0.5O3 structure reflecting the magnitude of MO6 octahedral tilt angles along [110] and [001] axis (Fig. 5a) displays clear divergence behaviour. The M–O2–M angles systematically decrease with increasing the temperature, whereas M–O1–M angles show increasing behaviour with detectable discontinuity between 770 and 900 K.
Fig. 5

Temperature evolution of the M–O–M angles (a) and inverse bandwidth W −1 (b) in HoCo0.5Cr0.5O3 structure. Inset shows thermal behaviour of the average bong length M–O and octahedral tilt angles

It is known that the M–O–M bong angles (θ) in RMO3 perovskite series characterize the M 3+–O2−M 3+ overlaps and govern the magnetic and transport properties of rare earth manganites, nickelates and cobaltites [34, 35]. In particular, increase of cooperative rotations of corner-shared CoO6 octahedra in RCoO3 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 RCoO3 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 CoO6 octahedra. The broadening of W in rare earth cobaltite series reduces the spin gap and decreases the onset of spin transition of Co3+ from LS to IS state [15]. Figure 5b demonstrates the temperature dependence of the inverse bandwidth, W −1 of HoCo0.5Cr0.5O3, 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 HoCo0.5Cr0.5O3 clearly illustrates an increasing population of the exited spin states of Co3+ ions with the temperature. It is apparent that the magnetic and electrical properties of HoCo0.5Cr0.5O3 will depend on the spin state of the Co3+ ions and a cation–anion–cation overlap, as it was reported for the related NdCo1–x Cr x O3 and GdCo1–x Cr x O3 systems [18, 30]. Increasing structural deformation in the last systems caused by the substitution of chromium by cobalt shifts the onset of Co3+ spin excitations and metal-insulator transition to the highest temperatures and led to the rising of electrical conductivity and Néel temperature in NdCo1–x Cr x O3 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.


Crystal structure parameters of the mixed holmium cobaltite-chromite HoCo0.5Cr0.5O3 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 HoCo0.5Cr0.5O3 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 Co3+ ions and coupled metal-insulator transition occurred in HoCoO3–HoCrO3 system.



The work was supported in parts by the Ukrainian Ministry of Education and Sciences under Project “RZE” and ICDD Grant-in-Aid program. The authors thank A. Fitch for the assistance with high-resolution synchrotron powder diffraction measurements at beamline ID22 at ESRF.

Authors’ Contributions

LV synthesized the sample, performed RT and HT structural characterization of the sample and wrote the manuscript. VH and VM contributed to the data evaluation, preparation of figures and tables and manuscript writing. YuP contributed to the in situ high-resolution X-ray synchrotron powder diffraction measurements at ESRF. All authors read and approved the final manuscript.

Competing Interests

The authors declare that they have no competing interests.

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Authors’ Affiliations

Lviv Polytechnic National University
Max-Planck-Institut für Chemische Physik fester Stoffe


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