Unraveling Anomalous Thermal Expansion in HoCo0.5Cr0.5O3 via High‑Resolution Synchrotron Diffraction

Background

Rare‑earth perovskite oxides of the form RCoO₃ and RCrO₃ have attracted sustained interest owing to their high electrical conductivity, distinctive magnetic behaviour, and catalytic activity. These properties make them promising candidates for solid‑oxide fuel cells, thermoelectric generators, magnetocaloric devices, gas sensors, and electrocatalysis (see reviews [1–9]). Recent studies have highlighted the rich phase space of RCoO₃, where the Co³⁺ ion can adopt low‑spin (LS, t_2g⁶e_g⁰), intermediate‑spin (IS, t_2g⁵e_g¹), or high‑spin (HS, t_2g⁴e_g²) configurations depending on temperature and chemical pressure [10–16]. The spin‑state evolution is closely linked to electronic bandwidth, lattice distortions, and magnetoelastic coupling, and it can trigger insulator‑metal transitions and magnetic ordering (see [15, 17–19]).

HoCoO₃ and HoCrO₃ are structurally isomorphic (GdFeO₃‑type) and display a wealth of temperature‑dependent phenomena. HoCrO₃ undergoes a low‑temperature centrosymmetric to non‑centrosymmetric transition, potentially enabling ferroelectricity below 240 K [12]. In contrast, HoCoO₃ shows no structural phase transition between 1.5 and 1098 K, but exhibits pronounced lattice anomalies and a high‑temperature insulator‑metal transition around 780 K [15, 25, 26]. The mixed system HoCo_1–xCr_xO₃ thus offers a unique platform to probe the interplay of spin, charge, and lattice degrees of freedom across a broad compositional range.

Here we present a systematic high‑temperature synchrotron diffraction study of HoCo_0.5Cr_0.5O₃, focusing on its thermal expansion, bond geometry, and displacement anisotropy. By correlating these structural metrics with known spin‑state transitions in the end members, we aim to elucidate the mechanisms driving the anomalous thermal behaviour in this mixed perovskite system.

Methods

HoCo_0.5Cr_0.5O₃ was prepared via conventional solid‑state reaction. Stoichiometric amounts of Ho₂O₃, Co₃O₄, and Cr₂O₃ were ball‑milled in ethanol for 5 h, dried, pelletized, and annealed at 1373 K for 20 h in air. The resulting powder was re‑grinded, milled again for 2 h, and annealed for an additional 45 h with one intermediate grinding step. The phase purity was confirmed by Cu K_α1 Guinier powder diffraction (Huber G670).

High‑temperature structural data were collected at ESRF beamline ID22 (λ = 0.35434 Å) using a 0.3 mm quartz capillary. Temperature increments of 50 K spanned 300–1140 K, and data were acquired upon continuous heating. The resulting diffraction patterns were refined by full‑profile Rietveld analysis using WinCSD, yielding lattice parameters, atomic positions, and anisotropic displacement parameters (ADPs) across the temperature range.

Results and Discussion

Room‑temperature XRD confirms that HoCo_0.5Cr_0.5O₃ crystallises in the orthorhombic GdFeO₃ framework (Fig. 1). The lattice parameters evolve linearly with composition, corroborating the formation of a continuous solid solution across the HoCoO₃–HoCrO₃ series. This behaviour aligns with previously reported RCo_1–xCr_xO₃ systems (La–Y) [18–33].

Synchrotron diffraction up to 1140 K shows that HoCo_0.5Cr_0.5O₃ remains in the Pbnm space group without any symmetry‑related phase change. Representative Rietveld refinements at 300 K and 1140 K (Fig. 2) demonstrate excellent agreement between observed and calculated patterns, confirming the stability of the orthorhombic perovskite framework across the entire temperature window.

The 3D perovskite framework consists of corner‑shared M(=Co_0.5Cr_0.5)O₆ octahedra and interstitial Ho cations. Significant octahedral tilting, evident from the displacement of O atoms, produces the observed orthorhombic distortion. The ADPs follow the expected mass dependence (B_iso(O) > B_iso(Co/Cr) > B_iso(Ho)). At elevated temperatures, Co/Cr ADPs become nearly isotropic, whereas Ho exhibits pronounced anisotropy (B₃₃ > B₁₁ > B₂₂ at 1140 K). Oxygen ADPs, particularly at apical sites, display a rotation‑type behaviour along the M–O bonds.

Temperature dependence of the lattice parameters (Fig. 3a) reveals a sigmoidal expansion, with a clear maximum in the linear thermal expansion coefficients (TECs) around 900 K (Fig. 3b). Such anomalies mirror those reported for LaCo_1–xCr_xO₃ and other RCo_0.5Cr_0.5O₃ compositions [19, 28–33]. In pure RCoO₃ compounds, the TEC peaks correlate with the onset of the Co³⁺ spin‑state transition and the accompanying insulator‑metal transition (see, e.g., HoCoO₃ at 782 K [15, 25]). For the mixed system, the peak shifts to higher temperature, indicating a stabilization of the LS state by Cr substitution.

Analysis of the M–O bond lengths (Fig. 4a) shows that both M–O1 (apical) and M–O2 (equatorial) distances remain constant up to ~600 K, followed by a gradual increase up to 850 K. This interval coincides with the expected temperature range for Co³⁺ spin‑state excitation from LS to IS/HS. The accompanying rise in the isotropic displacement parameters of oxygen (Fig. 4b) further supports the presence of dynamic lattice distortions linked to spin‑state fluctuations.

Bond‑angle analysis (Fig. 5a) reveals a divergence between the M–O1–M and M–O2–M angles. While the equatorial angles decrease with temperature, the apical angles increase, displaying a discontinuity between 770 and 900 K. These changes reflect a temperature‑dependent modulation of the octahedral tilt system, directly linked to the spin‑state transition.

The inverse bandwidth W⁻¹ increases monotonically with temperature, driven by the expansion of M–O bonds. Since the octahedral tilt angles remain largely temperature‑independent, this trend indicates an increasing population of higher‑spin Co³⁺ states. Such behaviour aligns with the electronic phase diagram of RCoO₃ (HoCoO₃ undergoes a paramagnetic dielectric transition at 486 K and an insulator‑metal transition at 782 K) [15]. The substitution of Cr, which prefers a low‑spin state, stabilises the LS configuration, shifting the spin‑state transition to higher temperatures and enhancing the overall thermal expansion anomaly.

Collectively, the lattice, bond, and displacement analyses reveal a strongly coupled electronic‑magnetic‑structural transition in HoCo_0.5Cr_0.5O₃ that is governed by the temperature‑induced spin‑state evolution of Co³⁺ and the concomitant insulator‑metal crossover. These insights are critical for tailoring the functional properties of mixed cobaltite‑chromite perovskites for high‑temperature applications.

Conclusions

We have characterised the thermal evolution of HoCo_0.5Cr_0.5O₃ from 300 to 1140 K using high‑resolution synchrotron powder diffraction. The crystal structure remains orthorhombic (Pbnm) throughout, yet exhibits pronounced anomalies in lattice parameters, thermal expansion coefficients, M–O bond lengths, octahedral tilt angles, and atomic displacement anisotropy. These anomalies are directly linked to temperature‑driven spin‑state transitions of Co³⁺ ions and the associated insulator‑metal crossover inherent to the HoCoO₃–HoCrO₃ solid solution. The published diffraction data (ICDD PDF cards NN 00‑066‑0678 and 00‑066‑0679) provide a comprehensive structural database for future computational and experimental studies.