From solid solution towards pyrochlore and kappa phases: introducing configurational entropy in ordered ceria–zirconia systems

Abstract

Following the example of well-known ceria–zirconia pyrochlore and kappa structures, the high-entropy rare-earth counterparts were synthesized. To synthesize ceria–zirconia-based solid solutions, a modified aqueous citrate sol–gel method was applied. In order to obtain pyrochlore phases, reduction by hydrogen (3% H₂ in Ar) was needed at a high temperature of around 1500 °C. The last step included mild re-oxidation at around 600 °C under atmospheric conditions to obtain kappa phases of a high degree of ordering. A direct comparison of different phases of CeZrO and its high-entropy counterpart LCPGY compounds was studied. Their structural similarities and differences were investigated using powder X-ray diffraction (PXRD), Raman spectroscopy, scanning electron microscopy with energy-dispersive X-ray spectroscopy (SEM–EDS), and physisorption measurements. Using thermogravimetric analysis (TGA), the thermal behaviour was inspected, which showed direct transformation of pyrochlore to the kappa phase due to oxygen uptake, i.e. mass gain. The surfaces of the compounds were analysed by X-ray photoelectron spectroscopy (XPS) to investigate Ce³⁺/Ce⁴⁺, O_ads/O_total, and Pr³⁺/Pr_total ratios. Temperature-programmed desorption (TPD) using 5% CH₄/Ar was conducted to show the catalytic activity of the synthesized compounds towards methane oxidation. Introducing configurational entropy in ordered ceria–zirconia systems showed that to obtain single-phase pyrochlore and kappa phases, it is also necessary to pay attention to the reduction/oxidation time and temperature in addition to the radius ratio, oxidation states, and atomic size disorder. Guided by this theory and experimental findings, we propose that the synthesized pyrochlore high-entropy compound is dual-phase pyrochlore and fluorite, while its kappa form is actually partially oxidized single-phase pyrochlore. High-entropy forms of the synthesized compounds showed much better catalytic performance towards methane oxidation than their non-high-entropy counterparts.

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Introduction

The ceria–zirconia (CeO₂–ZrO₂) system has attracted attention in the past decade due to its mechanical, electrical, and thermal properties¹ and also a wide variety of applications of zirconia–ceria-based materials in areas such as electronics,² engineering,³ catalysis,⁴ nanomedicine,⁵ fuel cells,⁶ etc. By adding a small amount (10–12 mol%) of cerium(IV) oxide, the tetragonal zirconia phase stabilizes over the fact that quite extensive Ce⁴⁺ ions expand the cation network.⁷ On the other hand, zirconium atoms are credited for the thermal stabilization of CeO₂ in terms of increased resistance to sintering^8,9 and structural stabilization.⁹ Due to their enormous chemical and thermal stability, CeO₂–ZrO₂-based materials are widely used as catalysts in the treatment of emission gases, which is justified by the fact that the oxygen storage/release capacity (OSC) of CeO₂ is enhanced by adding Zr into the structure.¹⁰ Another huge advantage is that Ce atoms can effortlessly change the oxidation state between Ce³⁺ and Ce⁴⁺ cations.¹¹

In previous years, mixed Ce–Zr (1 : 1) oxide, the so-called solid solution t-Ce_0.5Zr_0.5O₂, was shown to be more catalytically active and overall stable than pure CeO₂ or tetragonal ZrO₂.¹² Since the catalytic activity of these materials depends on oxygen storage capacity, transforming a solid solution t-Ce_0.5Zr_0.5O₂ to “kappa phase”, κ-Ce₂Zr₂O₈, enhances oxidation–reduction processes significantly.¹³ This high oxygen storage capacity is due to an ordered array of cations in a cubic lattice of κ-Ce₂Zr₂O₈, which is why 1/8 of the oxygen anions can freely be removed. In order to prepare “kappa phase” κ-Ce₂Zr₂O₈, the solid solution t-Ce_0.5Zr_0.5O₂ has to be reduced by hydrogen at high temperature, which is around 1500 °C,^14,15 to obtain the pyrochlore phase p-Ce₂Zr₂O₇. Pyrochlore Ce₂Zr₂O₇ could also be described as an anion-deficient distorted fluorite structure with two cations of different radii and 1/8 of empty tetrahedral anionic positions.^14,15 These empty positions are so-called oxygen vacancies, which smooth the way for the cations' ordering and consequently the ordering of the cationic sublattice.

High-entropy materials have been thoroughly investigated since their discovery in 2015 by Rost et al.¹⁶ and they have been the centre of scientific research in materials chemistry. The reason behind this is the diversity of possible elemental combinations that can be used to produce such materials. Another reason is that high entropy induces defects on the surface of such materials that open up new pathways to possible fundamental and applicative research.¹⁷ Introducing high entropy into ordered ceria–zirconia systems using rare earth elements gives a whole new class of materials known as high-entropy ceramics. In particular, high-entropy rare earth zirconates (RE₂Zr₂O₇) are widely known due to their extraordinary thermophysical properties, catalytic performances, irradiation resistance, etc.^18–20 Li et al.²¹ reported a study of single- and dual-phase rare-earth zirconate high-entropy ceramics, which showed that these types of materials could be used for thermal barrier coatings. The results showed that by incorporating multiple rare-earth elements onto the A site of pyrochlore structures, higher thermal expansions and mechanical properties are obtained compared to single rare-earth zirconates, RE₂Zr₂O₇. In order to obtain these kinds of compounds, three main conditions have to be satisfied. Firstly, the pyrochlore crystal structure is controlled by the cation radius ratio r_A/r_B, which has to be between 1.46 and 1.78,^22,23 where the A site in this case belongs to trivalent rare-earth cations and the B site is occupied by tetravalent zirconium cation. On the other hand, defective fluorite structures and monoclinic structures are obtained if the r_A/r_B ratio is lower or higher than this scale.^22,23 Secondly, to define these materials as high entropy, the single-phase system has to contain 5 or more cations, and the configurational entropy (S_conf) has to be greater than or equal to 1.5R,^24,25 where R is the ideal gas constant. The third, but also the most important factor influencing the formation of a single-phase pyrochlore structure, is atomic size difference (disorder), known as δ, which was first employed by Zhang et al.²⁶ It represents the ionic radius difference of the A site in high-entropy pyrochlore/fluorite oxides and gives an answer to whether a single or dual phase is formed in high-entropy rare-earth zirconates. The general formula is described by eqn (1):

where c_i and r_i represent the atomic percent and ionic radius of element i at the corresponding site, and r is the average ionic radius. In the case of pyrochlore, two cation sublattices exist, so it is mandatory to calculate the size disorder (δ) of the cations of both sites, A and B. When talking about zirconates, there is only a zirconium cation on the B site; thus, the prediction of structure type depends only on the size disorder of the A site. Wang et al.²² synthesized eighteen different 5-component equimolar rare-earth zirconates following these three main criteria. The size disorder for all the compounds was the main factor in obtaining single-phase zirconate since the study showed that a size disorder value greater than 5 forms a dual-phase compound in pyrochlore/fluorite systems regardless of the radius ratio.

In order to predict stability and customize the synthesis path of rare-earth high-entropy oxides, it is indispensable to understand the interaction of parameters such as valence state, ionic size of the constituent cations, preferred coordination and thermal properties.²⁷ Rare-earth oxides commonly crystallize in fluorite or bixbyite forms, with CeO₂ serving as a standard fluorite-phase oxide. The main differences between these two structures are that the bixbyite structure is a derivative of the fluorite structure, having doubled lattice parameter and more unoccupied anion sites. Fluorite structure favors rare-earth cations with higher oxidation state (+4) and eightfold coordination, while bixbyite relies on lower oxidation state (+3) and sixfold coordination.²⁸ Sarkar et al.²⁹ synthesized equiatomic rare-earth oxides with up to seven different cations and showed that using rare-earth cations with higher oxidation state (+4) contributes to fluorite structure. Also, by increasing the concentration of the cerium cation, the fluorite structure is favored. All these parameters need to be satisfied in order to find the optimal synthesis conditions to produce rare-earth high-entropy oxides with fluorite structure, such as in CeO₂.³⁰

Since bixbyite and pyrochlore structures both favour the +3 oxidation state, it is possible to oxidize them, leading to formation of other different phases. Bixbyite structure is quite stable and its oxidation can lead to an increase of lattice disorder and oxygen vacancy concentration.^30,31 However, in high-entropy oxides, a phase transition could occur from bixbyite to fluorite structure as a result of increase of configurational entropy.^28,32

On the contrary, reduction of equimolar ceria–zirconia solid solution leads to formation of an ordered pyrochlore structure which is irreversible since re-oxidation of pyrochlore leads to symmetry breaking and formation of the oxygen-rich kappa phase.^14,15 To the best of our knowledge, there are no references in the literature regarding the high-entropy kappa form (A₂B₂O₈) of rare-earth zirconates.

Since nanocrystalline ceria–zirconia-based compounds exhibit oxygen-rich surfaces that can be used in oxidation reactions, they are often used in the methane oxidation process.^33–40 Methane is a greenhouse gas that affects the climate, so it is undesirable in the atmosphere even though it is a primary component of natural gas. It can be partially oxidized to methanol and carbon monoxide, or fully oxidized to carbon dioxide, which depends on the targeted use. Although carbon dioxide is also a greenhouse gas, it has found application in industry. It is mostly used in agriculture in urea production. It is also used to enhance fossil fuel recovery, as a food additive (especially in carbonated drinks, but also as an acidity regulator and propellant), in fire extinguishers and refrigerants, as a solvent in its supercritical state, etc. This is why it is important to have controlled carbon dioxide production as a raw material for further applications.

In this work, we synthesized solid solution Ce_0.5Zr_0.5O₂ and its high-entropy counterpart La_0.1Ce_0.1Pr_0.1Gd_0.1Y_0.1Zr_0.5O₂ using the citrate–nitrate route previously developed by our group.^41–47 Then, controlled reduction of the starting solid solution was performed to produce the pyrochlore form, A₂Zr₂O₇. Further, re-oxidation of the reduced pyrochlore form was conducted to produce the kappa phase, A₂Zr₂O₈. The obtained compounds were subjected to structural and microstructural analysis, and insight into the application of these compounds in methane oxidation was given.

Experimental

Materials and methods

Synthesis. The following chemicals were used without further purification: citric acid monohydrate (T. T. T., Croatia), concentrated ammonia solution (Gram-Mol, Croatia), cerium(III) nitrate hexahydrate (Acros Organics, USA), lanthanum(III) nitrate hexahydrate (Sigma Aldrich, USA), yttrium(III) nitrate hexahydrate (Alfa Aesar, USA), praseodymium(III) nitrate hexahydrate (Sigma Aldrich, USA) and gadolinium(III) nitrate hexahydrate (Acros Organics, USA). Zirconium oxynitrate hydrate (Sigma Aldrich, USA) was dried at 80 °C overnight in a drying oven (Instrumentaria ST-01/02) before use.

Powder X-ray diffraction. Powder X-ray diffraction was carried out using a PANalytical Aeris Research diffractometer with a CuKα (λ = 1.54059 Å) radiation source in an ambient atmosphere. The method for the collection of XRD data included a step size of 0.002°, 20.4 s per step, a divergence slit of 1°, and a fixed mask of 13 mm. The diffractograms were recorded in the 2θ range from 10° up to 90°.

Raman spectroscopy. Raman spectroscopy was performed using a Bruker Sentera II confocal microscope with a 532 nm wavelength source and a laser power of 2.50 mW. The spectral resolution was 4 cm⁻¹, optical objective 50×, aperture 50 × 1000 μm, and 3 co-additions of 10 000 ms for each measurement.

Scanning electron microscopy. The morphological characterization and elemental composition of powder samples were observed using the Thermo Fisher Scientific Apreo 2S field emission scanning electron microscope (FE-SEM). The optimal resolution was ensured by operating at an acceleration voltage of 2 kV and a working distance set to approximately 5.5 mm. Images were obtained by secondary electron (SE) and backscattered (BSE) detectors.

Energy-dispersive X-ray spectroscopy. Qualitative and quantitative analysis of the observed powders was performed at 20 kV using an Oxford X-Max SDD 100 mm² energy-dispersive detector (EDS) and AZtec X-ray microanalysis software, thereby facilitating comprehensive elemental mappings and compositions.

X-ray photoelectron spectroscopy. XPS analysis was carried out using a Supra+ instrument (Kratos, Manchester, UK) coupled with an Al K_α X-ray excitation source. The charge neutralizer was active during the measurements. The take-off angle was set at 90°. Powder samples were placed on a carbon tape mounted on a silicon wafer. Measurements were executed at a pass energy of 20 eV. Data acquisition and analysis were performed using ESCApe 1.5 software (Kratos). The binding energy scale was corrected to the C–C/C–H peak at 284.8 eV in the C 1s spectrum.

Thermogravimetric analysis. TGA measurements were performed using a Netzsch STA 449 F3 Jupiter system. The experimental protocol started with an isothermal phase at 30 °C for 1 h. Subsequently, the samples were subjected to a controlled heating phase to 600 °C using a 2.5 °C min⁻¹ heating rate and finalised in an isothermal step at peak temperature for 4 h. All segments were performed using an Ar 5.0 atmosphere with a 100 mL min⁻¹ flow rate and an Al₂O₃ crucible as reference material. Additionally, pyrochlore phase analysis was also conducted in an oxygen atmosphere under the same temperature conditions.

Temperature-programmed desorption. Thermal deposition with methane of powder samples was analysed in four steps, using 5 vol% CH₄/Ar 5.0 atmosphere with a 100 mL min⁻¹ flow rate. Starting with heating from an initial 50 to 400 °C using a heating rate of 10 °C min⁻¹, followed by the first thermostating at 400 °C for 30 min. The third phase was additionally heating to 700 °C with a heating rate of 10 °C min⁻¹ and finalized with the second isothermal step at 700 °C for 3 h. All measurements were simultaneously analysed for evolved gas analysis (EGA) using a quadrupole mass spectrometer (QMS) (model 403C Aëolos).

Specific surface area. Nitrogen adsorption–desorption isotherms for all powder samples were recorded at a temperature of −196 °C using an Autosorb IQ (Quantachrome Instruments USA) surface gas sorption analyser. Before starting the adsorption measurements, the samples were degassed at a temperature of 250 °C under vacuum for 12 h to remove all moisture and impurities from the pores.

Powder preparation

Synthesis of solid solution powders. A modified aqueous citrate sol–gel method was used for the synthesis of ceria–zirconia-based solid solutions Ce_0.5Zr_0.5O₂ and La_0.1Ce_0.1Pr_0.1Gd_0.1Y_0.1Zr_0.5O₂. Stoichiometric amounts of nitrate precursors (Table S1) of the involved cations were dissolved in a citric acid solution (w = 10%) using Milli Q water (prepared using a PURELAB Flex device). A pH value adjustment to 5 was carried out with a HANNA pH 211 device using concentrated ammonia solution (w = 25%). The prepared reaction solutions were heated up to 95 °C (solution temperature) on a magnetic hotplate stirrer (DLAB MS-H-S) under continuous stirring until a black resin was formed. The obtained black resin was dried in a drying oven (Instrumentaria ST-01/02) at 120 °C overnight to produce a xerogel-like mixture. Calcination of the xerogel-like mixture was performed up to 600 °C (heating rate 2 °C min⁻¹) for 8 h using a Nabertherm LT5/11/B410 muffle furnace.

Reduction of solid solution powders. Solid solution powders were subjected to a reduction in a Carbolite Gero TF1 16/60/180 high-temperature tube furnace with a Eurotherm EPC 3016 controller to obtain pyrochlore phases. Small amounts of powder were placed in a rectangular crucible in the tube. Powders were then heated in an inert N₂ atmosphere (gas flow 300 mL min⁻¹) up to 800 °C (heating rate 4.5 °C min⁻¹) to eliminate the air from the tube. Then, the atmosphere was changed to 3% H₂ in Ar (gas flow 300 mL min⁻¹) from 800 °C to 1000 °C (4.5 °C min⁻¹). The heating was then continued from 1000 °C to 1500 °C under the same reducing atmosphere but with a heating rate of 1 °C min⁻¹. Then, the powders were left at 1500 °C in a reducing atmosphere (3% H₂ in Ar) for 10 h. After that, the cooling process took place: first from 1500 °C to 800 °C under a 3% H₂ in Ar atmosphere (10 °C min⁻¹) and finally from 800 °C to room temperature under a N₂ atmosphere.

Re-oxidation of the reduced powders. Re-oxidation of the reduced powders was performed to obtain κ-phases. The reduced powders were placed in a crucible in a muffle furnace (Nabertherm LT5/11/B410) and heated up to 600 °C with a heating rate of 2.5 °C min⁻¹ for 4 h (stabilization time). Cooling took place inside the furnace.

All of the above-mentioned steps are visualized in Scheme 1. The synthesized compounds were classified into three groups: (1) starting oxides (solid solutions), (2) reduced forms (pyrochlore phases), and (3) re-oxidized forms (kappa phases). Their code names are summarized in Table 1.

Scheme 1 Schematic representation of the step-by-step synthesis of ceria–zirconia systems: (1) schematic representation of the modified citrate–nitrate route; (2) reduction path of solid solution powders; (3) re-oxidation of pyrochlore phase powders to kappa phase.

Table 1 List of prepared compounds and their code names

Powder	Composition	Code name	Note
Starting oxide (solid solution)	Ce0.5Zr0.5O2	CeZrO	—
	La0.1Ce0.1Pr0.1Gd0.1Y0.1Zr0.5O2	LCPGY	High entropy
Reduced form (pyrochlore)	p-Ce2Zr2O7	p-CeZrO	—
	p-(La0.2Ce0.2Pr0.2Gd0.2Y0.2)2Zr2O7	p-LCPGY	High entropy
Re-oxidized form (kappa)	κ-Ce2Zr2O8	κ-CeZrO	—
	κ-(La0.2Ce0.2Pr0.2Gd0.2Y0.2)2Zr2O7+δ	κ-LCPGY	High entropy

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Results and discussion

Structural and microstructural analysis

Powder X-ray diffraction was performed to inspect the phase composition of the synthesized compounds. Using the FULLPROF software,⁴⁸ PXRD patterns were further investigated with the Rietveld refinement. Fig. 1 and Table 2 contain the Rietveld plots and refinement results of the synthesized solid solutions Ce_0.5Zr_0.5O₂ and La_0.1Ce_0.1Pr_0.1Gd_0.1Y_0.1Zr_0.5O₂, which are the starting compounds for the preparation of pyrochlore (p) and kappa (κ) phases. The refinement quality was evaluated by the discrepancy factor, R_wp, and goodness of fit, χ². The observed (black), the difference (blue), and the calculated (red) plots are shown along with Bragg reflections (green) for the fit of the PXRD patterns. The average crystallite size values for the prepared solid solution powders were obtained by microstructural analysis and vary between 2 and 8 nm. The values of ionic radii play the main role in lattice parameters and cell volume which are very similar for both tetragonal structures, but the average microstrain is higher for high-entropy solid solution compounds due to more than five elements in the crystal lattice.

Fig. 1 Rietveld plots of (a) Ce_0.5Zr_0.5O₂ and (b) La_0.1Ce_0.1Pr_0.1Gd_0.1Y_0.1Zr_0.5O₂.

Table 2 Results of the Rietveld refinement of the starting solid solution powders Ce_0.5Zr_0.5O₂ and La_0.1Ce_0.1Pr_0.1Gd_0.1Y_0.1Zr_0.5O₂

Chemical formula	Ce0.5Zr0.5O2	La0.1Ce0.1Pr0.1Gd0.1Y0.1Zr0.5O2
Crystal system	Tetragonal
Space group	P42/nmc
Z	2
Unit cell parameters (Å)	a = 3.73(2)	a = 3.73(2)
	c = 5.32(1)	c = 5.32(1)
Cell volume (Å^3)	74.08	74.08
Calculated density (g cm^−3)	6.58	6.46
Average crystallite size (nm)	7.31	2.82
Average microstrain (×10^−4)	42.59	128.62
Rp, Rwp, Re	11.0, 8.91, 7.36	12.6, 10.9, 7.94
χ^2	1.464	1.888

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Visualization of structures was performed using VESTA⁴⁹ software, as shown in Fig. S1. According to Rietveld refinement results, both compounds crystallize in the tetragonal crystal system, space group P4₂/nmc. Their XRD patterns are similar, with slight peak shifts that indicate the difference in unit cell parameters is not disturbed due to doping with rare-earth elements. Tables S2 and S3 show additional structural parameters of the starting solid solutions.

High-temperature reduction of solid solution powders reveals extremely sharp Bragg reflections for pyrochlore Ce₂Zr₂O₇ and pyrochlore–fluorite dual-phase (La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O₇, respectively. The average crystallite size differs from 66 nm for Ce₂Zr₂O₇ to 69 and 87 nm for the pyrochlore–fluorite dual phase (La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O₇. This indicates that by reducing the starting solid solution powders, the size of the unit cell expands due to the removal of oxide ions and compensating that with the increase in cations Ce and Pr size when changing the oxidation state from +4 (0.97 Å; 0.96 Å)⁵⁰ to +3 (1.14 Å; 1.13 Å),⁵⁰ respectively.

Fig. 2 and Table 3 show the Rietveld refinement results of the XRD patterns of the pyrochlore and kappa phases of both starting compounds. The reduced form of the non-high-entropy oxide consists of a single-phase pyrochlore Fd3̄m structure, while the high-entropy form consists of two phases: fluorite Fm3̄m and pyrochlore Fd3̄m. The pyrochlore structure can be seen as an ordered positioning of RE³⁺ (A site) and Zr⁴⁺ (B site) cations along the <110> direction. Here, Zr⁴⁺ ions have solid sixfold coordination by six identical Zr–O bonds.^14,15 An ordered pyrochlore Fd3̄m structure is characterised by the appearance of particular superstructure diffraction peaks applying Cu Kα radiation at the 2θ angles of 14° (111), 37° (331), 45° (511), and 51° (531), which are clearly visible in Fig. 2a and c. On the other hand, the high-entropy form consists also of the fundamental fluorite Fm3̄m phase with space group 225, indicated by the peaks at (200), (220), and (311), which are very close to those of the pyrochlore phase. This behavior has already been investigated in other rare-earth pyrochlore zirconates. According to Wang et al.,²² the cation radius ratio r_A/r_B is 1.528 and the size disorder in p-(La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O₇ is 4.96%, which is less than 5%, meaning that the pyrochlore structure is favoured with this combination of lanthanide cations.⁵¹ However, this combination involves Y³⁺ at the A site which has a small eightfold coordination radius and favours the formation of the fluorite phase regardless of size disorder being less than 5%.^22,51

Fig. 2 Rietveld plots of (a) p-Ce₂Zr₂O₇, (b) κ-Ce₂Zr₂O₈, (c) p-(La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O₇ and (d) κ-(La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O_7+δ (partially oxidized pyrochlore phase).

Table 3 Results of the Rietveld refinement of p-Ce₂Zr₂O₇, κ-Ce₂Zr₂O₈, p-(La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O₇ and κ-(La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O_7+δ

Chemical formula	p-Ce2Zr2O7	κ-Ce2Zr2O8	p-(La0.2Ce0.2Pr0.2Gd0.2Y0.2)2Zr2O7		κ-(La0.2Ce0.2Pr0.2Gd0.2Y0.2)2Zr2O7+δ partially oxidized pyrochlore phase	κ-(La0.2Ce0.2Pr0.2Gd0.2Y0.2)2Zr2O7+δ partially oxidized kappa phase
Crystal system	Cubic
Space group	Fd3̄m	P213	Fd3̄m	Fm3̄m	Fd3̄m	P213
Z	8	1	8		8	1
Unit cell parameters (Å)	a = 10.64(9)	a = 10.56(1)	a = 10.65(9)	5.3(2)	a = 10.62(9)	a = 10.62(1)
Cell volume (Å^3)	1205.42(8)	1178.38	1209.19(8)	148.99(7)	1196.45(8)	1196.86(8)
Calculated density (g cm^−3)	6.33	6.66	15.38	7.04	6.36	15.74
Phase content (wt%)	100	100	37.41	62.59	100	100
Average crystallite size (nm)	66.1(3)	82.9	69.4(5)	87.4(3)	64.3(5)	62.3(7)
Average microstrain (×10^−4)	11.24(9)	4.23	13.1(1)	10.2(3)	4.47(4)	4.23(1)
Rp, Rwp, Re	18.2, 12.9, 5.58	19.5, 14.2, 5.94	17.1, 11.1, 4.52		22.6, 16.2, 5.81	24.1, 17.2, 6.12
χ^2	5.38	5.71	6.05		7.76	7.94

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On top of that, it is also known that with the lowering of RE³⁺ radius, the intensity of the (200) fluorite phase peak gently increases, while the (400) peak symbolizing the pyrochlore phase progressively decreases.²³ Since the degree of disorder is still close to 5% and the combination of cations in our rare-earth zirconate includes yttrium, the formation of dual-phase fluorite–pyrochlore structures after reduction of the starting oxide (La_0.1Ce_0.1Pr_0.1Gd_0.1Y_0.1Zr_0.5O₂) can be expected. Fig. 2c shows a Rietveld refinement plot of XRD data belonging to p-(La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O₇. At higher 2θ angles, peak splitting can be observed. This is an indicator of the existence of a dual phase: fluorite and pyrochlore. According to the Rietveld refinement results, 37.41 wt% pyrochlore and 62.59 wt% fluorite phase are in the reduced form of the high-entropy compound. For both reduced forms, non-high entropy and high entropy, the extracted structural parameters are shown in Tables S4 and S5. As far as we know, there are no reports on the kappa form of high-entropy rare-earth zirconates (HE₂Zr₂O₈, HE = mixture of 5 equimolar metal cations) as opposed to non-high-entropy zirconates. κ-Ce₂Zr₂O₈, which is well-known, crystallizes in the cubic crystal system, space group P2₁3, with lower symmetry than the pyrochlore form, cubic Fd3̄m. Unlike the pyrochlore phase, this structure is described by the ordered arrangement of RE⁴⁺ and Zr⁴⁺ ions. Here, Zr⁴⁺ has an eightfold coordination with eight non-equivalent Zr–O bonds that form two polyhedra. This finding explains the ability of high oxygen storage capacity (OSC) to release oxygen in kappa phases by using chemical reduction by hydrogen, two tetrahedra can be formed with weaker Zr–O bonds. The transition between the pyrochlore and the kappa form in ceria–zirconia-based oxides occurs because of the remarkable redox properties of Ce^3+/4+.^14,15 Since in p-(La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O₇, La, Ce, Pr, Gd, and Y are all in the +3 oxidation state, it is reasonable to expect them to form a pyrochlore structure. However, for the kappa structure to be formed, these cations have to be oxidized to the +4 state, and the only cations that undergo such a reaction are Ce³⁺ and Pr³⁺. Thus, structurally we can propose the formation of two crystal structures of newly formed κ-(La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O_7+δ after re-oxidation:

(1) Partially oxidized pyrochlore phase (Fd3̄m)

(2) Partially oxidized kappa phase (P2₁3)

Taking this into account, Rietveld refinement was performed for both cases.

The kappa phase is formed when the 8b position in the pyrochlore Fd3̄m space group is fully filled, leading to distortion of the Fd3̄m space group to P2₁3.^14,15 However, we expect the 8b position to be only partially filled during re-oxidation of p-(La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O₇, so the question here is whether this amount is sufficient to distort the Fd3̄m space group. According to the Rietveld refinement results, a better fit was obtained taking into account the Fd3̄m space group, which would mean that the amount of incorporated oxygen (67%, 56%) was not enough to distort Fd3̄m to the P2₁3 space group. Also, there is no peak splitting at higher 2θ angles and lower value of goodness of fit, χ², which indicates the formation of single-phase partially oxidized pyrochlore κ-(La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O_7+δ (Fig. 2d). For kappa phases, the extracted structural parameters are presented in Tables S6 and S7. Moreover, the Rietveld plot of κ-(La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O_7+δ, refined as a partially oxidized kappa phase (cubic, space group P2₁3), is shown in Fig. S2.

Raman spectroscopy was used to investigate the structure of the synthesized compounds further. Fig. 3 shows the Raman spectra of all synthesized compounds. The solid solution Ce_0.5Zr_0.5O₂ spectrum in Fig. 3a clearly shows a typical Raman spectrum of a tetragonal solid solution.⁵² There is a triply degenerate F_2g mode at 468 cm⁻¹, which is the only mode allowed for the cubic fluorite-structured ceria.⁵³ There is also a peak at 628 cm⁻¹ that is often assigned to oxygen defects in cubic ceria.^14,54 However, the appearance of a mode at 305 cm⁻¹ is a clear sign of a tetragonal symmetry breaking and therefore presents the distinction between the cubic Fm3̄m and the tetragonal P4₂/nmc crystal structure.⁵² Urban et al.¹⁴ have already explained this in their research. However, their solid solution is almost cubic since the additional peaks are present only as broad, low-intensity shoulders rather than defined peaks. The reason behind this could be a difference in the synthesis procedure for obtaining solid solution powder.

Fig. 3 Raman spectra of (a) Ce_0.5Zr_0.5O₂ (black), p-Ce₂Zr₂O₇ (red) and κ-Ce₂Zr₂O₈ (blue) and (b) La_0.1Ce_0.1Pr_0.1Gd_0.1Y_0.1Zr_0.5O₂ (black), p-(La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O₇ (red) and κ-(La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O_7+δ (blue).

The high-entropy solid solution La_0.1Ce_0.1Pr_0.1Gd_0.1Y_0.1Zr_0.5O₂ spectrum in Fig. 3b displays a Raman spectrum similar to the one already reported for high-entropy ceria-based compounds.⁴⁶ The sharp F_2g mode is almost invisible, and the defect band at 610 cm⁻¹ dominates because of the addition of multiple elements in the fluorite structure of ceria. However, there is also a low-intensity broad shoulder at around 309 cm⁻¹ that might point toward symmetry breaking from the cubic to the tetragonal crystal structure, similar to that reported by Urban et al.^14,15

The pyrochlore-type cubic Fd3̄m crystal structure allows 6 Raman active modes, A_1g + E_g + 4F_2g.⁵³ There are 4 Raman active modes visible at 258 cm⁻¹, 372 cm⁻¹, 414 cm⁻¹, and 590 cm⁻¹ with shoulders at 220 cm⁻¹ and 513 cm⁻¹ (Fig. 3a). This is in accordance with the spectral active modes calculated from the crystallographic information file (.cif), a method described by Kroumova et al.⁵³

In Fig. 3b, there are also 4 Raman active modes at 301 cm⁻¹, 385 cm⁻¹, 511 cm⁻¹, and 600 cm⁻¹ with a low-intensity shoulder at around 220 cm⁻¹. These modes are similar to the (La_0.2Nd_0.2Sm_0.2Eu_0.2Gd_0.2)₂Zr₂O₇ modes, recently studied by Luo et al.⁵⁵ Both pyrochlore phases in Fig. 3 have broad Raman modes. The broadening of Raman modes occurs due to the disorder in the oxygen sublattice.⁵¹ This could arise from the fact that oxygen position 8b in the structure of p-Ce₂Zr₂O₇ is empty.¹⁵ In p-(La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O₇, there is an additional structural disorder in the cationic sublattice introduced by the incorporation of multiple cations, which also impacts the A–O and B–O bond lengths.⁵⁵

The kappa phase, i.e. the cubic P2₁3 structure, contains 144 Raman active modes, 24A + 24E₁ + 24E₂ + 72F.⁵³ Many of them are not visible in Fig. 3, and it is difficult to resolve all of them.¹⁴ The peaks in Fig. 3a are narrow in frequency probably due to the large unit cell, which contains only a few different atomic species.¹⁴ However, the Raman spectrum of the kappa phase in Fig. 3b resembles the pyrochlore phase spectrum in the same figure. There are broad peaks at 296 cm⁻¹, 394 cm^−1, and 602 cm⁻¹ and shoulder peaks at 225 cm⁻¹ and 525 cm⁻¹. The reason behind this could be that oxygen position 8b is only partially occupied when Ce³⁺ and Pr³⁺ are oxidized to Ce⁴⁺ and Pr⁴⁺, respectively. Therefore, the disorder in the oxygen sublattice is preserved both due to the partially empty 8b position and the remaining disorder in the cationic sublattice. This would confirm the hypothesis that κ-(La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O₈ is actually a partially oxidized pyrochlore compound (La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O_7+δ.

The summary of observed Raman active modes for pyrochlore and kappa phases can be found in Table S8.

Raman spectroscopy can also be used to distinguish between Ce³⁺ and Ce⁴⁺ compounds because Ce³⁺ shows a characteristic scattering peak at around 2100 cm⁻¹.^56,57 This scattering peak represents ²F_5/2–²F_7/2 transitions⁵⁷ for Ce³⁺ and it usually occurs when Ce³⁺ is present in the structure of a compound, such as Ce₂O₃ or pyrochlore Ce₂Zr₂O₇.^58,59 However, this peak is not detected if surface Ce³⁺ makes no structural change (such as reduction of CeO₂ to Ce₂O₃).^58,60 Surface defects are usually detected by defect bands; for example, in CeO₂, they are present from 500 to 700 cm⁻¹.⁶⁰

Fig. S3 depicts the area between 2000 cm⁻¹ and 2300 cm⁻¹ in Raman spectra of both compounds in their solid solution, pyrochlore and kappa form. Only the pyrochlore form shows a scattering signal, at 2157 cm⁻¹ for p-Ce₂Zr₂O₇ and at 2123 cm⁻¹ for p-(La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O₇. This means that only pyrochlore-type compounds are Ce³⁺-based.

XPS was used to investigate the surface of the synthesized catalysts. The high-resolution C 1s spectra with four deconvoluted peaks for C–C/C–H, C–O, COO/COOH, and carbonate are visible in Fig. S4. Three peaks (C–C/C–H, C–O, COO/COOH) probably originate from carbonaceous species adsorbed on the surface of the material after preparation and during the sample transfer to the XPS spectrometer.^61–63 Rare-earth-based oxides tend to adsorb carbon dioxide when exposed to air and form carbonate species on the surface,^64–67 which is why the carbonate peak is detected. The high-resolution O 1s spectra in Fig. 4 for all samples show peaks corresponding to lattice oxygen (labelled O_L), surface-adsorbed oxygen species (O_ads),⁶⁸ adsorbed water, and oxidized adventitious carbonaceous species.⁶⁹ For CeZrO, LCPGY, p-LCPGY, and κ-LCPGY, probably some water remained on the surface (peak designated in Fig. 4). By comparing the surface atomic concentrations of O_ads for CeZrO catalysts, the highest surface concentration of O_ads relative to the surface atomic concentration of all O-containing species, i.e. O_total, was found for p-CeZrO (O_ads/O_total = 0.294), while CeZrO (O_ads/O_total = 0.063) and κ-CeZrO (O_ads/O_total = 0.114) phases have significantly lower amounts than p-CeZrO. This is due to the anion-deficient distorted fluorite structure of p-CeZrO with 1/8 empty tetrahedral anionic positions, known as oxygen vacancies, since O_L decreases significantly compared to the ordered structures of t-CeZrO and κ-CeZrO phases. On the other hand, p-LCPGY has a slightly lower O_ads/O_total ratio of 0.149 compared with p-CeZrO (O_ads/O_total = 0.294) due to phase duality, since it consists of both pyrochlore and fluorite phases. However, this ratio is similar for LCPGY (O_ads/O_total = 0.187) and κ-LCPGY (O_ads/O_total = 0.180). Tables S9–S11 show the relative surface atomic concentration ratios of O_ads/O_total, Ce³⁺/Ce⁴⁺, and Pr³⁺/Pr_total evaluated from the deconvoluted peaks. To calculate the amount of Ce³⁺, the fitted intensity of the v and u features was adapted. The peaks v, v′′, v′′′, u, u′′, and u′′′ correspond to cerium ions in the oxidation state +4, while v⁰, v′, u⁰, and u′ are assigned to Ce³⁺ ions.^47,70–72 The high-resolution Ce 3d XPS spectra in Fig. 5 show that the Ce³⁺/Ce⁴⁺ ratio in CeZrO compounds follows the trend kappa (0.32) < starting oxide (0.37) < pyrochlore (0.48). This is expected because the pyrochlore phase is the reduced form and therefore should contain the highest amount of Ce³⁺. The starting oxide has a significantly smaller crystallite size (around 7 nm) compared to the kappa phase (83 nm), resulting from sintering at high temperatures after reduction and re-oxidation. This is why the starting oxide also has more defects, i.e. oxygen vacancies, which are directly correlated to Ce³⁺ content. This is the reason for the larger amount of Ce³⁺ in the starting oxide compared to the kappa phase.

Fig. 4 Deconvoluted high-resolution O 1s XPS spectra of CeZrO, LCPGY, p-CeZrO, p-LCPGY, κ-CeZrO and κ-LCPGY.

Fig. 5 Deconvoluted high-resolution Ce 3d XPS spectra of CeZrO, p-CeZrO, and κ-CeZrO.

Deconvoluted high-resolution Ce 3d XPS spectra for high-entropy LCGPY compounds are shown in Fig. 6. High-entropy LCPGY compounds do not follow the same trend. In these compounds, the Ce³⁺/Ce⁴⁺ ratio decreases in the following order: pyrochlore (0.30) < kappa (0.51) < starting oxide (0.54). This is unusual behaviour since pyrochlore, as a reduced phase, should contain the highest amount of Ce³⁺. The reason for this could be in the dual-phase problem. According to Rietveld refinement, approximately 37 wt% pyrochlore phase is present in p-LCPGY, while the rest is fluorite. Fluorite ceria-based structures can be reduced, but they are also easily re-oxidized under ambient conditions after exposure to air, especially at the surface of RE-doped forms.⁷³ The fluorite phase in p-LCPGY has a significantly larger crystallite size (87 nm) compared to the starting fluorite oxide (around 3 nm). It also possesses a higher degree of crystallinity, which is inversely proportional to the concentration of defects, i.e. oxygen vacancies, and consequently, the concentration of Ce³⁺ ions. Further re-oxidation of the pyrochlore dual-phase compound leads to the formation of a single-phase partially oxidized pyrochlore structure.

Fig. 6 Deconvoluted high-resolution Ce 3d XPS spectra of LCPGY, p-LCPGY, and κ-LCPGY.

Fig. S5 shows high-resolution Pr 3d XPS spectra for the high-entropy LCPGY compounds. The Pr environment is similar for all the compounds. It was shown previously⁷⁴ that the high-resolution XPS spectra for Pr₂O₃ do not exhibit the doublet for a′′/b′′; thus, it can be concluded that this doublet belongs only to Pr⁴⁺ ions.⁷⁴ On the other hand, doublets for a/b and a′/b′ are both present in PrO₂ and Pr₂O₃, so they cannot be assigned to a specific oxidation state. To estimate the amount of Pr³⁺ ions, a formula proposed by Sinev et al.⁷⁵ was used, which takes into account the peak ratio of a′′/a′ to calculate and estimate the surface concentration of a particular oxidation state of praseodymium ions. In this case, the highest surface concentration of Pr³⁺ has pyrochlore LCPGY, which corresponds to previous reports^76–78 since it is the only reduced form of the starting oxide, LCPGY, where Pr⁴⁺ is present, and the same in κ-LCPGY.

The high-resolution Zr 3d XPS spectra for all the compounds (Fig. S6) show Zr3d_5/2 and Zr3d_3/2 doublets, which correspond to ZrO₂. LCPGY shows an additional doublet, probably corresponding to sub-oxides.^79,80

High-resolution XPS spectra for La 3d, Gd, and Y are shown in Fig. S7–S9. The Y 3d spectrum was deconvoluted using constraints reported previously.^81,82 It consists of a doublet corresponding to Y 3d_3/2 (at around 159 eV) and Y 3d_5/2 (at around 157 eV). For LCPGY and κ-LCPGY, an additional Si 2s peak appears, which most likely originates from the carbon tape.

The deconvolution of the high-resolution La 3d, Gd 3d and Gd 4d XPS spectra is challenging due to the existence of charge-transfer satellites,^83,84 so they are only visualized in Fig. S7 and S8 showing La 3d_3/2 (at around 855 eV) and La 3d_5/2 (at 833 eV), Gd 3d_3/2 (at around 1219 eV) and Gd 3d_5/2 (at around 1187 eV), and Gd 4d_3/2 (at around 148 eV) and Gd 4d_5/2 (at around 143 eV), which is consistent with previously reported results.^{65,66,85–87} The magnitude of multiplet splitting in La 3d spectra of LCPGY, p-LCPGY, and κ-LCPGY is in the range of 4.8–5.0 eV, corresponding to lanthanum oxide.^65,83

The morphology of all the synthesized compounds was inspected using scanning electron microscopy. SEM images are shown in Fig. 7a–f. Fig. 7a and d show SEM images of the starting oxides. Since the calcination temperature used for their synthesis was only 600 °C, they appear to have smaller grain sizes than their reduced (Fig. 7b and e) and re-oxidized (Fig. 7c and f) counterparts. Also, they seem to be porous. Reduced and re-oxidized forms of starting oxides consist of larger grains, which is expected taking into account that they were additionally calcined at 1500 °C and 600 °C, respectively. This behaviour is expected due to sintering.⁸⁸ However, high-entropy forms of reduced and re-oxidized compounds seem to form a porous network. This could affect the increase of specific surface area, thus making them more efficient as catalysts.

Fig. 7 SEM images of (a) CeZrO, (b) p-CeZrO, (c) κ-CeZrO, (d) LCPGY, (e) p-LCPGY, and (f) κ-LCPGY.

Also, compared to the average crystallite size in Table 3, the average grain size shown in Fig. 7 is much larger. The reason behind this is that grains can contain one or multiple crystallites. Polycrystalline materials usually contain multiple crystallites inside larger grains, especially due to sintering at high temperatures.^{41,43–45,88,89} Fig. S10 shows these SEM images at low magnification where it is clear that these compounds are mostly porous sheet-like powders consisting of smaller grains. Fig. S11 shows an SEM image of LCPGY where it is visible that it consists of both smooth and porous surfaces. Smooth surfaces are present probably due to sintering.^88,89

The chemical content was investigated by energy-dispersive X-ray spectroscopy. When calculating the empirical formula, the oxygen content was normalized to 2 for the solid solutions (Ce_0.5Zr_0.5O₂ and La_0.1Ce_0.1Pr_0.1Gd_0.1Y_0.1Zr_0.5O₂), to 7 for the pyrochlore phases (Ce₂Zr₂O₇ and (La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O₇), and to 8 for the kappa phases (Ce₂Zr₂O₈ and (La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O₈). There are visible deviations from the desired chemical composition, but EDS quantification is not very precise, so these deviations are allowed. The summary of EDS quantitative analysis of solid solutions, pyrochlore, and kappa phases can be found in Tables S12 and S13. Elemental mapping was also performed for kappa forms of the synthesized compounds, and elemental maps are shown in Fig. S12 and S13.

In the case of κ-Ce₂Zr₂O₈, the distribution of involved elements (Ce, Zr, O) is homogeneous.

On the other hand, elemental maps of its high-entropy counterpart, κ-(La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O_7+δ, show that while the distribution of Ce, Pr, La, and Gd is uniform, Zr and Y seem to have a somewhat different distribution, different from Ce, Pr, La, and Gd, but similar to each other.

For all powder samples, nitrogen adsorption–desorption isotherms (Fig. S14) were accomplished at a temperature of −196 °C using Autosorb IQ (Quantachrome Instruments USA), a surface gas sorption analyzer. Solid solution and high-entropy solid solution adsorption isotherms belong to the group of type IV isotherms, which are characteristic of mesoporous materials. In contrast, pyrochlore and kappa compounds have quite different isotherm shapes and very small adsorbed volumes. This can be explained by the high reduction temperatures of solid solutions to obtain pyrochlore phases (1500 °C) since the crystallite size has remarkably increased. These types of problems can occur due to the cavitation effect or pore blocking.⁹⁰ The kappa phase is an oxidized pyrochlore phase, so the assumption is the same.

Using the Brunauer–Emmett–Teller (BET) and the nitrogen adsorption isotherm data, the specific surface areas of the obtained mesoporous materials were calculated.^91,92 The highest values were shown by starting solid solution Ce_0.5Zr_0.5O₂ and its high-entropy counterpart La_0.1Ce_0.1Pr_0.1Gd_0.1Y_0.1Zr_0.5O₂ of 57.55 m² g⁻¹ and 36.73 m² g⁻¹, respectively. The specific surface area of these oxides can vary from 30 to 400 m² g⁻¹, depending on which synthesis method has been used. For example, Dao and Luu⁹³ used the combustion method to prepare nanostructured Ce_0.5Zr_0.5O₂ using polyvinyl alcohol at 600 °C and obtained a value of 73 m² g⁻¹.⁹³ On the other hand, Hadi et al.⁹⁴ prepared CeZrO₂ nanoparticles using the water/oil microemulsion method at room temperature with and without the calcination process. The results showed that nanoparticles synthesized without calcination have a size under 10 nm and a high specific surface area of around 170 m² g⁻¹. In contrast, using the calcination process, the particle size increased, and the specific surface area dropped to around 47 m² g⁻¹.⁹⁴ Comparing the BET specific surface areas of pyrochlore and kappa phases of both types of compounds, high-entropy powders show greater values, which are proportional to their catalytic efficiency towards methane oxidation. Although a high-entropy solid solution has a higher specific surface area and pore volume than its oxidized kappa form, it can be assumed that high oxygen storage capacity improves catalytic activity. Pore sizes were calculated using the Barrett–Joyner–Halenda (BJH) test method.⁹⁵ Based on the appearance of the isotherm and the obtained data on the pore size of 3–5 nm, it can be presumed that these powders are mesoporous materials (2–50 nm).⁹⁶ Total pore volume was obtained from the amount of nitrogen adsorbed at the relative pressure (p/p₀) of 0.99 and shows superior advantages to starting solid solutions, which is to be expected due to the highest specific surface area. Table 4 shows values of specific surface area, pore size, and total pore volume of synthesized non-high entropy and high-entropy catalysts.

Table 4 BET specific surface area, pore volume, and pore size of synthesized powders

Powder	BET specific surface area (m^2 g^−1)	Pore volume (cm^3 g^−1)	Pore size (nm)
t-CeZrO	57.553	0.131	3.4
p-CeZrO	10.275	0.007	4.9
κ-CeZrO	5.289	0.006	3.1
t-LCPGY	36.731	0.107	3.4
p-LCPGY	16.810	0.015	3.1
κ-LCPGY	21.510	0.016	3.4

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Oxygen uptake analysis

Thermogravimetric analyses were conducted in oxidative (O₂) and inert (argon) atmospheres. Fig. 8 shows the mass changes of the synthesized pyrochlore forms as a function of temperature. Mass change in the oxidative atmosphere can correspond to unit cell expansion or oxygen uptake due to oxidation.^97,98 Here, we observe a slight increase in the mass value (up to 0.3%) in an inert atmosphere that can be attributed to unit cell expansion.^97,98

Fig. 8 Mass change as a function of temperature for reduced forms of starting oxides (p-CeZrO and p-LCPGY) in oxidative (O₂) and inert (Ar) atmospheres.

However, there is a much larger mass increase in the non-high-entropy form (p-Ce₂Zr₂O₇) in the oxidative atmosphere of up to 2.2%, which can be the result of oxidation of Ce³⁺ to Ce⁴⁺, i.e. oxygen uptake. This is similar to previous findings.^14,15 Oxygen uptake here results in the phase transition from the pyrochlore to the kappa phase. As for the high-entropy form, there is only a slight increase in mass (0.5%) since there are only 0.2 mol of Ce³⁺ and Pr³⁺ in the compound, while other cations cannot be oxidized. Integrated mass change as a function of temperature is shown in Fig. 9.

Fig. 9 Integrated mass change as a function of temperature for reduced forms (p-CeZrO and p-LCPGY) of starting oxides in an oxygen atmosphere.

Mass change occurs rapidly and at lower temperatures in the non-high-entropy form of a reduced oxide (p-CeZrO) than in its high-entropy counterpart (p-LCPGY).

Temperature-programmed desorption

Temperature-programmed desorption (TPD) was conducted in a CH₄/Ar atmosphere using thermogravimetric analysis (TGA) for the increase in temperature and quadrupole mass spectrometry (QMS) for the detection of gaseous products. Methane oxidation can be written using eqn (2):

CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g) (2)

If methane reacts with the oxygen-rich surface of the catalyst, it is oxidized to carbon dioxide, and water (vapor) is formed. However, for this reaction to occur, energy is needed, which is why it takes place at higher temperatures. According to the QMS (Fig. S15), the only products that were detected were carbon dioxide and water, which means that the surfaces of the prepared compounds were sufficiently oxygen-rich to induce a complete oxidation of methane. Fig. 10a and b show the ion current change of carbon dioxide as a function of temperature. The methane oxidation for all used catalysts takes place at around 400 °C where adsorption of methane occurs, followed by carbon dioxide desorption. Ion current change increases proportionally with the increase in desorbed carbon dioxide. As seen from Fig. 10b, high-entropy forms of the starting oxide and its re-oxidized counterpart have the largest amount of ion current change. This means that they produce larger amounts of carbon dioxide than other forms of oxides, probably because of the larger amount of oxygen at the surface, i.e. larger oxygen storage capacity (OSC).

Fig. 10 (a) Ion current change and (b) derivation of ion current change as a function of temperature during the exposure of CeZrO, LCPGY, p-CeZrO, p-LCPGY, κ-CeZrO, and κ-LCPGY to methane flow (100 mL min⁻¹).

Integrated ion current change (Fig. 11) shows CO₂ desorption as a function of temperature and time. High-entropy forms of the starting and re-oxidized compounds show the highest CO₂ desorption rate (the largest slope), which starts slightly before 400 °C. This makes them more effective in methane oxidation. Also, the same trend can be observed in Fig. 9b, where it is evident that CO₂ formation occurs rapidly at the surface of the starting solid solution and the re-oxidized form of high-entropy compounds. After approximately 100 min (around 1.7 h), the production of CO₂ is terminated.

Fig. 11 Integrated ion current change as a function of temperature (a) and time (b) of CeZrO, LCPGY, p-CeZrO, p-LCPGY, κ-CeZrO, and κ-LCPGY.

Since the catalysts we presented here are metal oxides, it is generally considered that they catalyse the oxidation of methane via the Mars–van Krevelen mechanism⁹⁹ which follows 3 steps:

(1) initiation, where activation and dissociation of methane on the surface of the catalyst occurs;

(2) redox cycle, where surface oxygen species react with the adsorbed methane and oxidizes it while the catalyst reduces itself;

(3) formation of products, where they are desorbed from the catalyst surface (such as carbon dioxide and water when total oxidation occurs). In this mechanism, the rate-determining step is the activation of the first C–H bond in methane.^100,101 This is why external heating is required to overcome this barrier.

Most of the catalysts operate at temperatures of 500 °C or higher, and the aim over the years was to reduce the energy input.^102–104 According to the literature,^100,104 catalysts that operate at temperatures below 500 °C are considered low-temperature operating catalysts. The catalysts we present in this paper have started the oxidation process around 400 °C. The maximum ion current change for every synthesized compound occurs at different temperatures and is presented in Fig. 12a. These values represent the largest amount of detected carbon dioxide after the oxidation of methane. The most effective compound is κ-LCPGY, followed by LCPGY. The largest amount of detected carbon dioxide is in the range of 520–540 °C for these compounds. CeZrO produces the largest amount of carbon dioxide at around 680 °C, which is the highest operating temperature of all six compounds. The maximum ion current change (Fig. 10a) is around 500 °C. However, they could still be considered as low-temperature catalysts because C–H bond activation still occurs around 400 °C. Fig. 10b shows the ion current change (detected amount of carbon dioxide) at the beginning of the oxidation process (400 °C). Even if a catalyst possesses a large activity, its stability is also important. If the catalyst is still stable after the catalytic reaction, it can be reused in the same reaction. Therefore, XRD patterns of the catalysts after exposure to methane flow were inspected to investigate the stability of the used catalysts.

Fig. 12 Ion current change at 400 °C (a) and maximum ion current change versus temperature (b) of CeZrO, LCPGY, p-CeZrO, p-LCPGY, κ-CeZrO, and κ-LCPGY.

Solid solution CeZrO clearly decomposes after temperature-programmed desorption, while its high-entropy form (LCPGY) remains unchanged primarily (Fig. S16). LCPGY only shows sharper peaks as a result of additional sintering during the methane oxidation process (up to 700 °C). However, since pyrochlore and kappa forms could generally undergo structural changes due to oxidation and reduction, we have inspected these XRD patterns more closely, using Rietveld refinement (Fig. S17–S20). Rietveld refinement results are summarized in Table S14.

According to the refinement results, p-CeZrO undergoes partial phase transition from pyrochlore Fd3̄m to fluorite Fm3̄m. Thus, it is finally a dual-phase compound consisting of both pyrochlore (34.16 wt%) and fluorite forms (65.84 wt%), which can also be observed from peak splitting at higher 2θ angles. A similar thing occurs with its kappa form, κ-CeZrO. Peak splitting at higher 2θ angles revealed phase duality and the coexistence of the fluorite Fm3̄m structure. Since these catalysts oxidize methane, they should undergo a reduction process. Thus, we assumed that the kappa form could undergo a phase transition from kappa P2₁3 to pyrochlore Fd3̄m structure. However, a better fit was obtained for the kappa P2₁3 structure. As a result, κ-CeZrO also shows phase duality after the methane oxidation reaction, consisting of kappa P2₁3 (65 wt%) and fluorite Fm3̄m (35 wt%) structures due to partial phase transition.

In contrast, p-LCPGY, which consisted of pyrochlore (37 wt%) and fluorite (63 wt%) structures before the methane oxidation, is now a single-phase pyrochlore Fd3̄m compound. This phase transition probably occurred due to additional reduction of the compound during methane oxidation.

The only compound besides LCPGY that remained structurally unchanged after the methane oxidation was κ-LCPGY (partially oxidized pyrochlore Fd3̄m), with the same amount of incorporated oxygen (68%) at the 8b position, making it reusable and efficient in catalytic oxidation reactions, such as methane oxidation.

Guided by Rietveld refinement results, high-entropy forms show a surprising shift towards stability and single-phase structures. Comparing non-high-entropy and high-entropy pyrochlore forms after temperature-programmed deposition (methane oxidation), it can be seen that doping A sites with multiple rare-earth elements gives structure stability and therefore superior catalytic activity.

Besides methane oxidation, these compounds could be used in other oxidation reactions, such as the oxidation of carbon monoxide or volatile organic compounds (VOCs),^105–107 and also in electrochemical water splitting reactions.^108–117 These redox reactions could also be light- or temperature-assisted.^47,118,119

Conclusions

To sum up, we have successfully synthesized different phases of high-entropy rare-earth zirconates, counterparts of starting ceria–zirconia compounds, using a modified sol–gel method. In order to obtain κ-Ce₂Zr₂O₈ and κ-(La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O_7+δ partially oxidized pyrochlore phase, high-temperature reduction at 1500 °C of starting solid solutions, Ce_0.5Zr_0.5O₂ and La_0.1Ce_0.1Pr_0.1Gd_0.1Y_0.1Zr_0.5O₂, using hydrogen was needed. In this manner, pyrochlore phases, p-Ce₂Zr₂O₇ and p-(La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O₇, were formed, followed by their mild re-oxidation at 600 °C. These six samples were structurally characterized using PXRD, Raman spectroscopy, SEM–EDS, and BET specific surface area. According to Rietveld refinement, all three samples that consist only of cerium atoms on the A site and zirconium atoms on the B site show a single-phase structure. In the case of high-entropy counterparts, the starting solid solution showed remarkable similarities with the starting solid solution Ce_0.5Zr_0.5O₂. Regarding the pyrochlore phase, it was concluded that it exhibits a pyrochlore–fluorite dual phase, and that there is 37.41 wt% pyrochlore and 62.59 wt% fluorite phase. Interestingly, Rietveld refinement after temperature-programmed desorption of carbon dioxide showed that p-LCPGY is no longer a dual-phase but a pure single pyrochlore phase. In the literature mentioned above, the main criteria that must be satisfied are radius ratio, oxidation states, and atomic size disorder. Herein, it is visible that using 5% CH₄/Ar helps obtain a single pyrochlore phase, which means that the reduction time of 10 h and temperature of 1500 °C might not be enough to synthesize a single-phase pyrochlore compound despite all of the criteria being met. Regarding the kappa phase, all of the rare-earth cations on the A site have to be oxidized to the +4 state, and the only cations that undergo such a reaction are Ce³⁺ and Pr³⁺. We proposed two crystal structures of newly formed κ-(La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O_7+δ after re-oxidation, partially oxidized pyrochlore phase, and partially oxidized kappa phase. Considering this assumption, Rietveld refinement was performed for both cases. Since only these two cations have the ability to change oxidation state to +4, we expect the 8b position to be only partially filled during re-oxidation of p-(La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O₇. According to the Rietveld refinement results, a better fit was obtained for the Fd3̄m space group and showed no peak splitting at higher 2θ angles, which is proof of obtaining single-phase partially oxidized pyrochlore (La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O_7+δ. These results correspond to Raman spectroscopy data, which have shown similar scattering signals for both p-(La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O₇ and the so-called κ-(La_0.2Ce_0.2Pr_0.2Gd_0.2Y_0.2)₂Zr₂O₈. The scattering signal at around 2150 cm⁻¹ is characteristic only of the pyrochlore form, which is evidence that only pyrochlore-type compounds are Ce³⁺-based. Another evidence is that from TGA, comparing p-CeZrO and p-LCPGY in an oxidative atmosphere, only p-CeZrO has an enormous mass change of 2.2% which can be the result of oxidation of Ce³⁺ to Ce⁴⁺, i.e. kappa phase formation. Regarding methane oxidation, the greatest results showed high-entropy forms, solid solution LCPGY and κ-LCPGY (partially oxidized pyrochlore phase). This would mean that they produce larger amounts of carbon dioxide than other forms since structural analysis showed that they possess a larger amount of oxygen at the surface, i.e. larger oxygen storage capacity (OSC). After methane oxidation, κ-LCPGY (partially oxidized pyrochlore Fd3̄m) kept the same amount of incorporated oxygen (68%) at the 8b position, showing its reusability and productiveness in catalytic oxidation reactions. Another thing is that all other rare-earth elements can be successfully incorporated into the CeO₂–ZrO₂ system and thereby increase catalytic activity. Even though our conclusions form a solid framework, more in-depth research is needed to smoothly obtain a single-phase structure, maximize the efficiency of these catalysts, and diversify their applications.

Author contributions

S. Š.: synthesis, conceptualization, original draft preparation. D. T.: XRD measurements and formal analysis. T. S.: SEM–EDS measurements and elemental mapping, TPD measurements and analysis. C. B. P.: Raman spectroscopy measurements and analysis. I. S.: EDS elemental quantification. M. F.: XPS measurements. I. D.: project management funding acquisition. Á. K., M. M., and I. D.: review & editing. J. K.: conceptualization, formal analysis, review & editing.

Conflicts of interest

There are no conflicts to declare.

Data availability

Supplementary information: the details on reactants used during synthesis (Table S1), visualization of crystal structures (Fig. S1), structural parameters obtained from Rietveld refinement of XRD patterns (Tables S2–S7), Rietveld plot of κ-LCPGY refined as partially oxidized kappa phase (Fig. S2), Raman spectra in the range 2000–2300 cm⁻¹ (Fig. S3), the list of Raman signals (Table S8), deconvoluted high-resolution C1s XPS spectra (Fig. S4), deconvoluted high-resolution O 1s, Ce 3d and Pr 3d XPS spectra report (Tables S9–S11), deconvoluted high-resolution Pr 3d and Zr 3d XPS spectra (Fig. S5 and S6), High-resolution La 3d, Gd 3d and Gd 4d spectra (Fig. S7 and S8), deconvoluted high-resolution Y 3d spectra (Fig. S9), additional SEM images (Fig. S10 and S11), quantitative EDS analysis (Tables S12 and S13), EDS elemental maps (Fig. S12 and S13), physisorption isotherms (Fig. S14), temperature-dependent QMS profiles (Fig. S15), XRD patterns and Rietveld plots of synthesized compounds after methane oxidation (Fig. S16–S20) and Rietveld refinement results of synthesized compounds after methane oxidation (Table S14). See DOI: https://doi.org/10.1039/D5CE00736D.

The data supporting this article have been included as part of the SI file.

Acknowledgements

The authors acknowledge the Croatian Science Foundation project “The study of the role of rare earth metal promoters and ordering on the redox properties of CeO₂–ZrO₂ system” (PZS-2019-02-2467) and the Slovenian Research and Innovation Agency through research programme P1-0175 and The Centre for Research Infrastructure at the Faculty of Chemistry and Chemical Technology, University of Ljubljana (IC UL FCCT), for full financial support. The authors also acknowledge the financial support for this study received from the Slovenian Research Agency (Grant No. P2-0118, J7-4638), co-financed by the Republic of Slovenia, the Ministry of Higher Education, Science and Sport, and the European Union under the European Regional Development Fund. The authors also acknowledge the Croatian–Hungarian exchange partnership through bilateral project “The high-entropy oxides – promising catalysts for CO₂ reduction” (2024–2026) and the Croatian–Slovenian exchange partnership through bilateral project “Development of high-entropy oxides and the study of their environmental impact” (2025–2026) for connecting the scientists involved in this work through bilateral exchange.

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