Role of intermediate 4f states in tuning the band structure of high entropy oxides

High entropy oxides (HEOs) were first reported in 2015,¹ and since then the topic has gained significant interest, which is evident from numerous published reports focusing on different aspects of HEOs.^2–10 HEOs can be broadly defined as single-phase solid solution oxides containing 5 or more cations in near-equiatomic compositions. The presence of multiple cations in comparable amounts leads to an enhanced configurational entropy of mixing (S_config), which is calculated using the Boltzmann statistical entropy equation.^1,3,11 The term “high entropy oxide” is typically used when the S_config of a given oxide system is above 1.5 R.^3,5,6,12 One of the most intriguing characteristics of HEOs is the phase purity despite their compositional complexity. Interestingly, the underlying principle for phase purity is distinct in different HEOs. For instance, in some systems a dominant role of entropy has been evidenced, which effectively overcomes the related enthalpic penalties and stabilizes a single-phase solid solution at high temperatures.^1,13,14

However, in the majority of HEOs a pertinent role of configurational entropy in stabilizing the phase composition and structure has not been observed, whereas factors such as the oxidation states of specific cations and lattice strain effects govern their phase composition.^3,5,6,15,16 Irrespective of the phase stability mechanisms, the high entropy based design approach in oxides offers an extended compositional flexibility along with retention of the phase purity. Hence, compositions close to the central regions of multi-component oxide phase diagrams can be studied, where interesting synergies can be anticipated. A wide range of crystal structures and functional features exhibited by HEOs can be linked to their unique composition and related synergies.^{4,6–10,17–24} Nevertheless, disentangling the role of individual elements is one of the major challenges in HEOs.

In our previous studies, we have explored the possibility to synthesize several single-phase fluorite type HEOs (F-HEOs) by populating the cationic sublattice with 5 or more rare-earth (RE) elements.^15,25 By comparing these compositions, we have observed that the presence of Pr in F-HEOs results in a lowering of the bandgap energy. Hence, we speculated that Pr due to its mixed 3+/4+ oxidation state in F-HEOs forms an intermediate unoccupied energy state, which facilitates lower energy electronic transitions of ∼2 eV.²⁵ Understanding the electronic band structure of conventional binary rare-earth oxides is still a subject of both theoretical and practical interest.^26–28 However, the theoretical band structure calculations for complex F-HEOs are not straightforward. Hence, in this current study, we use different spectroscopic techniques to investigate the validity of our hypothesized energy band diagram in a representative F-HEO composition, (Ce_0.2La_0.2Pr_0.2Sm_0.2Y_0.2)O_2-δ. Initially, by means of heat treatment under reducing (vacuum/hydrogen) or oxidizing atmospheres, we have observed reversible changes in bandgap energies. The changes in the oxidation states of the RE elements and related variations in the f and d electronic shell occupancy are studied using x-ray absorption spectroscopy (XAS) and electron energy loss spectroscopy (EELS), which primarily indicates the role of internal redox reactions in determining the electronic characteristics of F-HEOs. Although this kind of redox reaction driven bandgap tuning mechanism is known for simple metal oxides,^29,30 such a possibility has not yet been explored for HEOs. Furthermore, the accompanying physico-chemical changes such as large concentrations of oxygen vacancies, reversible disorder–order transition, and Raman features upon H₂-treatment make the F-HEO different. Hence, this study not only elucidates the dynamic band structure of the F-HEO but also provides a deeper structural insight into these compositionally complex systems.

The F-HEO, (Ce_0.2La_0.2Pr_0.2Sm_0.2Y_0.2)O_2−δ, was synthesized from water-based precursor solutions of the corresponding rare-earth nitrates using reverse co-precipitation (RCP) techniques. The precursor solution was added to a basic ammonia solution (pH = 10) in a controlled fashion along with continuous stirring of the mixture at ambient conditions. The formed precipitates were dried at 120 °C and further calcined at 750 °C in air to achieve the desired crystallographic phase. The temperature, 750 °C, has been determined based on the reports of the F-HEO synthesized by the nebulized spray pyrolysis method.¹⁵ The powders obtained after this first 750 °C heat-treatment step in air are defined as the as-synthesized (“as-syn”) samples. The as-synthesized samples were subsequently heat treated under different atmospheres, where the temperature, dwell time, and ramping rates (for both heating and cooling) were 750 °C, 2 h, and 10 °C/min, respectively. The heat-treatment conditions were as follows:

• Mildly reducing atmosphere: Vacuum heat treatment (VHT), corresponding to 10⁻⁷ mbar pressure.

• Highly reducing atmosphere: Heat treatment with flow of a 5% hydrogen–argon mixture (H₂-HT), with a gas flow rate of 50 standard liters per minute.

• Re-heat treatment under air: This was carried out after the VHT or H₂-HT, using the respective VHT/H₂-HT powder. Hence, the samples obtained are termed as RHT (meaning “re-heat treated” in air).

The results obtained for heat treatment of (Ce_0.2La_0.2Pr_0.2Sm_0.2Y_0.2)O_2−δ-F-HEO in vacuum differ significantly to those obtained when heat-treated in a hydrogen atmosphere. Hence, two sub-sections specific to the heat-treating atmosphere are made.

The as-synthesized F-HEO powder has been subjected to vacuum heat treatment (VHT) followed by subsequent re-heat treatment (RHT) in air. An immediate indication of a reversible change can be observed by simple inspection of the powder color, as shown in Figs. 1(a)–1(c). The as-synthesized powder is dark brown in color [Fig. 1(a)], whereas VHT leads to a yellow powder [Fig. 1(b)], and upon further RHT, the initial brown color [Fig. 1(c)] is regained. Likewise, the diffuse reflectance spectra of the powders support this observation, and the corresponding changes in the bandgap energies have been estimated, as presented in Fig. 1(d). The bandgap energy of the as-synthesized powder is 1.93 eV. Upon VHT, an increase in the bandgap to 2.47 eV can be observed. The RHT of the powder in air leads to a reversal of the bandgap to 1.98 eV. This value is close to the bandgap of the as-synthesized system, and the difference (∼5%) falls within the experimental error of the measurement.

One of the main characteristics of HEOs is their phase purity; hence, it is important to investigate the effect of heat treatment on the phase composition of F-HEOs. Figure 2 presents the XRD patterns, HR-TEM micrographs, and selected area electron diffraction (SAED) patterns of the as-synthesized, VHT, and RHT samples. HR-TEM micrographs along with the XRD patterns reveal the presence of nano-sized crystallites, which aggregate to form micron sized particles. Structural details obtained from Rietveld refinement of the XRD patterns are presented in supplementary material, Fig. SI1. Importantly, no change in the crystal structure, phase composition, or elemental distribution (supplementary material, Fig. SI2) can be observed upon heat treatment under varying atmospheres. A marginal increase in the lattice parameter (∼0.4%, see Table I) along with broadening of the peaks due to strain effects can be observed upon VHT (Fig. 2). These observations hint toward the reduction in some of the constituent cations (resulting in larger ionic sizes) and related oxygen vacancy formation, which is the focus of Subsection III A 3.

In our previous report,²⁵ we inferred that the bandgap energy of ∼2 eV in F-HEOs is closely associated with the presence of multivalent Pr³⁺/Pr⁴⁺. Following this speculation, it can be expected that the change/reduction in the oxidation state of Pr will affect the occupancy of the Pr 4f states. Hence, a change in the bandgap energy of F-HEOs can be expected. In order to investigate the change in the oxidation of constituent elements upon VHT, EELS measurements have been carried out.

EELS measurements have been performed on the as-synthesized, VHT, and RHT powders. The spectra for Ce and Pr M_4,5 edges are displayed in Fig. 3. The M_4,5 white lines in EELS spectra of the rare-earths (REs) result from electronic transitions between the initial state 3d and the 4f orbitals, such as 3d_3/2 → 4f_5/2 (M₄) and 3d_5/2 → 4f_7/2 (M₅). The relative intensity ratio (⁠$IM5$/$IM4$⁠) and chemical shift of the M_4,5 lines denote the change in valency (or the f-shell occupancy) of the respective RE cations.³⁷ The EELS spectra for Ce and Pr are of utmost importance as these two elements exhibit the highest tendency to vary between the 3+ and 4+ states, whereas La, Sm, and Y are known for their stable 3+ electronic configuration. For Ce, two white lines at 882 eV and 902 eV are observed, which are related to M₅ and M₄ transitions, respectively.^37,38 However, no noticeable chemical shifts of these lines have been observed after VHT or RHT. This finding is further supported by the fact that the $IM5$/$IM4$ ratio is relatively invariant with respect to heat treatment [Fig. 3(b)]. Unlike Ce, the scenario is different for Pr. For the as-synthesized system, Pr M_4,5 white lines are observed at 931 eV and 951 eV, respectively. A significant chemical shift (of ∼0.6 eV) toward low energies occurred upon VHT, which indicates a reduction in Pr from a pronounced 4+ state to 3+ dominated multivalent (3+/4+) state.³⁹ The formation of Pr³⁺ is supported by the pronounced shoulder at the left (or lower energies) of the Pr M₄ line. Additionally, an increase in $IM5$/$IM4$ of Pr is also observed upon VHT, further confirming the decrease in Pr⁴⁺ [Fig. 3(b)]. Likewise, upon subsequent RHT of the VHT sample in air, a reverse behavior, i.e., an oxidation of Pr toward the initial Pr⁴⁺ dominated mixed valence state, could be observed.

The reduction of Pr with VHT should be compensated internally. One way of charge compensation can be via oxidation of the other constituent cations, which is not the case here. Hence, the formation of oxygen vacancies can be expected. We have utilized Raman spectroscopy to study this possibility. Two characteristic bands centered at ∼452 cm⁻¹ and ∼580 cm⁻¹ in all samples are used for the estimation of the V_O concentration (see supplementary material, Fig. SI3). The ∼452 cm⁻¹ band corresponds to the F_2g stretching mode of the fluorite structure, while the latter corresponds to the presence of V_O.^40,41 The integral intensity ratio of V_O to F_2g can be used for a relative estimation of the V_O concentration in different systems.⁴² The inset of Fig. SI3 of the supplementary material, shows an increase in the amount of V_O concentration upon VHT, while V_O concentrations in the as-synthesized and RHT samples are nearly comparable (see the related discussion in supplementary material, Sec. 1). Although the V_O and the charge state of the elements are interlinked, it should be noted that the bandgap energy in the F-HEO is rather related to the presence of redox-active Pr and its unoccupied 4f intermediate band. This has been observed in our earlier report as well, where we compared various F-HEO compositions with varying amount of oxygen vacancies.²⁵ Nonetheless, we have probed samples using Raman spectroscopy as the change in the V_O concentration upon heat treatment supports the EELS data and indicates the reversible behavior in the F-HEO.

To summarize, we observe a reversible change in the bandgap upon VHT of the F-HEO followed by RHT. The increase in the energy gap upon VHT is expected due to the decrease in the number of unoccupied Pr 4f states, as evidenced from the EELS results. The reduction of Pr and resulting increase in V_O also support the increase in the lattice parameter and microstrain upon VHT. Furthermore, the fact that makes the F-HEO unique is the retention of the single-phase fluorite structure even upon VHT. The stability of a fluorite type oxide structure strongly depends on the presence of a 4+ cation, which in a VHT-F-HEO is only Ce and a minor part of Pr. Likewise, the V_O concentration (as shown from Raman spectroscopy) in VHT-(Ce_0.2La_0.2Pr_0.2Sm_0.2Y_0.2)O_2−δ is rather high compared to conventional binary or doped fluorite type oxides, and δ is expected to be ∼0.4. To further investigate the impact of stronger reducing atmospheres on physico-chemical features of F-HEO, heat treatment under a hydrogen atmosphere has been carried out.

(Ce_0.2La_0.2Pr_0.2Sm_0.2Y_0.2)O_2−δ has been heat treated under a highly reducing 5% H₂ + Ar atmosphere (H₂-HT), followed by re-heat treatment (RHT) in air. A reversible change in the powder color can be observed after this treatment, as shown in Figs. 4(a)–4(c). Importantly, the change in the bandgap energy is larger than what was observed for VHT, i.e., increasing from 1.93 eV to 3.21 eV [Fig. 4(d)]. RHT of the H₂-HT powder in air leads to reversion of the bandgap to 2.04 eV. This bandgap tailoring of around 60% (∼1.3 eV) can be considered as significant, especially given that the change is reversible.

Figure 5 presents the XRD patterns along with SAED micrographs for the H₂-HT and RHT samples. Rietveld refinements of the XRD patterns are provided in supplementary material, Fig. SI4. Unlike for the as-synthesized and RHT samples, we observe additional peaks in the XRD patterns for the H₂-HT sample. These additional peaks are the superstructure reflections, indicating a structural transition from a fluorite (⁠$Fm3¯m$⁠) to C-type bixbyite (⁠$Ia3¯$⁠) structure. Evidence of faint superstructure reflections can also be observed in the SAED pattern (Fig. 5), which further confirms the formation of the bixbyite structure. Homogeneous cationic distribution, down to the nanometer length scales, further supports the phase purity of the bixbyite formed upon H₂-HT (supplementary material, Fig. SI5).

Bixbyite is a well-known low symmetry oxygen deficient body centered cubic variant of the fluorite family, where one out of every four oxygen ions is missing.^43,44 The symmetry relationship between fluorite (a) and bixbyite (2a) includes a twofold increase in the lattice parameter. Thus, for direct structural comparisons, the pseudosymmetric lattice parameter of the bixbyite structure (i.e., half of the actual lattice parameter) is considered. In fact, the as-synthesized (Ce_0.2La_0.2Pr_0.2Sm_0.2Y_0.2)O_2−δ sample undergoes a similar symmetry lowering when heat treated in normal atmospheric conditions (i.e., under air).^15,25 However, there are two subtle differences between the symmetry lowering happening upon normal heat treatment in air (as observed in our earlier studies) and the H₂-HT. First of all, upon H₂-HT, this phase transition happens at a much lower temperature, i.e., already at 750 °C, whereas the phase transition will happen only above 1000 °C if heat treated under a normal air atmosphere.^15,25 Second and a rather unusual phenomenon is that the phase transition to bixbyite upon H₂-HT is reversible, i.e., a single-phase fluorite structure can be regained when the H₂-heat treated sample is re-heated (RHT) in air at 750 °C (see XRD and SAED in Fig. 5). However, we observed^15,25 that the transition to a bixbyite phase is completely irreversible if the as-synthesized sample is heat treated above 1000 °C in a normal air atmosphere.^15,25 As mentioned above, the transition from fluorite to bixbyite is mostly governed by the presence of oxygen vacancies, which start to order above a certain temperature. One of the reasons for the structural transition already at 750 °C upon H₂-HT can be the formation of additional oxygen vacancies due to a stronger reducing atmosphere. This is supported by an increase (∼0.5%, Table I) in the pseudosymmetric lattice parameter upon H₂-HT. In fact, 750 °C under H₂ might already be sufficient to order the oxygen vacancies. However, the temperature might still not be large enough to result in a stable ordering, making the transition back to fluorite upon RHT possible. Further discussion of this point is presented in Sec. III C. Table I summarizes the structural and optical features obtained upon various heat treatments of F-HEOs.

We have used Raman spectroscopy to further investigate these systems due to its sensitivity to local chemical changes, especially related to light scatterers such as oxygen. It should be noted that the infrared laser, which we typically use to study the F-HEO, could not be used for the H₂-HT sample due to possible resonance effects (see supplementary material, Fig. SI6). Hence, a green laser (λ = 532 nm) has been used for comparison. It is shown in Fig. 6 that all the F-HEO systems show distinct Raman bands at ∼452 cm⁻¹, ∼1180 cm⁻¹, and ∼580 cm⁻¹. By comparing these with the parent binary (or doped) rare-earth based oxides (containing Ce/La/Pr/Sm/Y), we can draw correlations with CeO₂ based systems.^{40,42,45–47} The band at ∼452 cm⁻¹ can be associated with the triply degenerated F_2g vibration mode.⁴¹ The band at ∼1180 cm⁻¹ can be related to the second order 2LO Raman mode, which is generally observed in ceria or its doped variants.^40,41 The strong broad band at ∼580 cm⁻¹ can be best fitted using a two band model, which can be attributed to the presence of oxygen vacancies (V_O) and its related bonding with the 3+ and 4+ cations.⁴⁵ Given the fact that bixbyite (as in H₂-HT) is a superstructure of fluorite, additional vibration bands or strengthening/rupturing of some existing ones can be expected. After H₂-HT, three additional bands appear. The band at ∼358 cm⁻¹ [Fig. 6(a)] can be attributed to a second order Raman mode arising from a combination of A_1g, E_g, and F_2g scattering tensors.⁴⁰ However, we do not find a proper match for the two prominent additional bands at ∼1333 cm⁻¹ and ∼1610 cm⁻¹, which are observed only upon H₂-HT (see Fig. 6). Furthermore, these bands cannot be directly attributed to the crystal structural change as the bixbyite variant of Ce_0.2La_0.2Pr_0.2Sm_0.2Y_0.2)O_2−δ obtained upon normal air heat treatment does not exhibit these features (see the Raman spectra in supplementary material, Fig. SI7). Interestingly, both the bands disappear upon subsequent RHT of the H₂-HT sample in air, and a spectrum similar to the as-synthesized system is obtained. One of the plausible reasons for the appearance of the additional bands upon H₂-HT can be due to possible hydrogen incorporation in the F-HEO system. Hydrogen being a light element can lead to strong vibrational modes. Recently, it has been reported that H incorporation (even in the hydride form) is possible in the (bulk) fluorite type CeO₂ when it is heat treated above 350 °C in a H₂ atmosphere.⁴⁸ Such a H-incorporation cannot be ignored in the F-HEO as H₂-HT is done at 750 °C. Moreover, the presence of large V_O concentrations in the F-HEO might potentially facilitate H-incorporation. However, this is a speculation and finding concrete evidence of the presence of H is not simple. Hence, experiments sensitive to H, such as inelastic neutron scattering, are needed to support such a hypothesis.

In order to further understand the other physico-chemical changes happening upon H₂-HT, XAS has been performed.

XAS probes the (unoccupied) electronic density of states above the Fermi energy in an element specific way.^36,49 Hence, it offers the possibility to disentangle the element specific contributions in complex systems such as F-HEOs. Each of the XAS spectra has been normalized to the edge jump. In the following, the respective changes at the different absorption edges are discussed. In addition, an investigation concerning changes in the amount of unoccupied states has been performed.^50,51

At the M_4,5 edges, the transition from the 3d states into the unoccupied 4f states occurs (in a dipole approximation). The respective absorption spectra for the as-synthesized and H₂-HT sample are shown in Fig. 7. The La M_4,5 edges indicate that both the as-synthesized and H₂-HT samples are in the 3+ valence state, while a reduction in the free states by ∼3.5% can be determined by the difference of the integrated spectral area. We see a similar, intuitive behavior for Sm, which is also in a 3+ valence state in both cases, while the integrated spectral area is reduced by 3.9% upon H₂-HT. For Ce, a detailed fine structure occurs prior to both the M₅ and M₄ edges after H₂-HT (inset of Fig. 7). These additional peaks can be assigned to Ce³⁺, while the initial peaks can be assigned to Ce⁴⁺.^52,53 Therefore, it can be said that Ce is present in a 4+ dominated multivalent (3+/4+) state after H₂-HT. Due to the occurring multivalency in Ce, a change in the number of unoccupied states can only be determined from the integrated spectrum. From this analysis, an increase of 0.9% of the integrated white line intensity can be determined—such an increase can be neglected and can be explained by differences in the normalization procedure. Pr, on the other hand, is present in a multivalent 3+/4+ state (with a pronounced 4+ nature), as indicated by the prominent after edges⁵⁴ in the as-synthesized sample (see the inset of Fig. 7). It changes into a (fully) 3+ state upon H₂-HT. Furthermore, the unoccupied 4f states in Pr are reduced by ∼15%.

Furthermore, the RE L₃ edges are also studied as the hard x rays in the transmission mode provide a better idea about the bulk nature of the sample. In the L₃ edge, the transition from the 2p_3/2 states to unoccupied 5d states occurs. Ce and Pr L₃ spectra are shown in Fig. 8. A complete spectrum including La and Sm is provided in supplementary material, Fig. SI8. For the L₃ absorption edge, the discussion is simpler compared to the M_4,5 edges. For La and Sm, a 3+ state is evident, while no significant change in the white line intensity is visible. For Ce, a 4+ state can be observed in the as-synthesized sample, while a reduction to a mixed valent state is evident upon H₂-HT. The presence of Ce³⁺ results in shoulder A,⁴⁷ as shown in the inset of Fig. 8. Nevertheless, a pronounced Ce⁴⁺ state is maintained even upon H₂ with no major change in the white line intensity. For Pr, a significant change in the spectral structure is visible. The as-synthesized sample shows a distinct multiplet spectrum (4f² and 4f¹ in the inset of Fig. 8). From the literature, it is known that such a spectrum is typically observed in multivalent Pr^3+/4+, where Pr⁴⁺ is ascribed to the 4f¹ peak.^55,56 After H₂-HT, the change in the spectral near-edge fine structure indicates a complete reduction to Pr³⁺. Accompanied with this change is a reduction in the spectral area by ∼3%. This can be explained either by a change in the unoccupied 5d states or structural changes due to the EXAFS signal from the La L₂ edge (⁠$E0,LaL2=5891$ eV). For this, a detailed EXAFS modeling would be necessary, which is difficult due to the relatively small available k-space for this complex system, as visible in supplementary material, Fig. SI8.

The mild reduction of Ce and strong reduction of Pr are in good agreement with the crystal structural transition to bixbyite observed upon H₂-HT. Ce⁴⁺ is known to play a pivotal role in stabilizing the fluorite lattice in F-HEOs.^15,25 Thus, even the mild reduction of Ce⁴⁺ most likely destabilizes the fluorite lattice. The accompanying strong reduction of Pr along with the presence of other 3+ cations leads to an enhanced V_O concentration. Hence, oxygen vacancy ordering (see Sec. III C 2) can be triggered at relatively lower temperatures (750 °C) compared to normal air heat treatment (1000 °C). As mentioned in Sec. III B 1, the ordering upon H₂-HT is most likely metastable, given the intensities of the superstructure reflections are rather weak (Fig. 5 and supplementary material, Fig. SI4) compared to XRD patterns of bixbyite obtained from air-heat treatment.^15,25 Thus, upon RHT, the fluorite structure can be regained.

Finally, we focus on the hybridization of the O 2p states with the RE neighbors by probing the O 1s → 2p transition at the O K edge. Unlike the RE cations, the XANES spectrum of the O K edge is rather complex as O hybridizes with all RE cations. Hence, disentangling all spectral features is not straightforward, given the fact that XANES of the F-HEO (or similar complex systems) has not been reported on before. Nevertheless, the changes happening in the RE M_4,5 and L₃ edges help us to identify the major spectral variation in O K edges upon heat treatment. The prominent features are observed at the photon energy E = 528.6 eV (A), 530 eV (B), 532 eV (C), 533 eV (D), 537 eV (E), and 539 eV (F), respectively (see Fig. 9). Feature A can be attributed to the Pr 4f-O 2p hybridization²⁷ (discussion pertaining to this feature is explained in Sec. IV). Features B, D, and E have been attributed to O 2p states, which hybridize with the 4f, 5d-e_g, and 5d-t_2g levels of Ce in stoichiometric CeO₂, respectively.^27,57 The splitting of the 5d–e_g and 5d–t_2g states occurs only if crystal field effects lift the degeneracy,^57,58 indicating that the changes in spectral features D and E are due to an alteration of the local structure (evident from Fig. 5). The relative increase in the peak intensity of feature D compared to feature E reveals a local ordering of the oxygen vacancies. This finding is in agreement with reports on doped CeO₂^38,44 and supports the formation of the C-type bixbyite structure upon H₂-HT. Feature F (539 eV) can be matched with the O 2p and Sm 5d hybridization^59,60 and hence does not change upon H₂-HT. Likewise, the presence of feature C can also be observed both in the as-synthesized and H₂-HT systems, which is possibly linked to the O 2p-RE 5d hybridization.

In conventional rare-earth (RE) oxides, the occupied oxygen 2p states are hybridized with RE 5d/4f states, resulting in the formation of the bonding and anti-bonding orbitals. The O 2p state with the occupied RE 5d/4f state forms the valence band, which is generally classified as the O 2p band. However, the anti-bonding states originating from the RE-O hybridization are the conduction bands, which are generally denoted in terms of the RE state related to the specific hybridization, such as RE 5d/4f. Thus, the electronic transition from the O 2p state to the unoccupied RE 5d/4f states determines the bandgap energy. In fact, the changes in the electronic structure of binary rare-earth oxides can be directly correlated with the changes observed in O K edges.⁶⁰ Likewise, in the case of the F-HEO, the analysis of the O K XANES edge provides a comprehensive understanding of the electronic band structure and valence states (which is also supported by the other spectroscopic techniques). The most interesting features in the O K edge of F-HEOs are A and B. As mentioned above, feature B corresponds to the Ce 4f-O 2p hybridization, while feature A corresponds to the Pr 4f-O 2p hybridization. Feature B is present in both cases; however, the intensity of feature A decreased to almost zero after H₂-HT. This indicates distinct changes in Pr 4f states that are related to the reduction in Pr valency or decrease in the unoccupied states in the 4f level (see Pr-M_4,5 edges in Fig. 7). Here, we would like to mention that the bandgap energy difference (see Fig. 4) between the as-synthesized sample and the H₂-HT sample is ∼1.3 eV. This value matches almost perfectly the energy difference between feature A (Pr 4f-O 2p, 528.6 eV) hybridization and feature B (Ce 4f-O 2p, 529.9 eV) hybridization. The weakening of feature A means an increase in the occupation of the Pr 4f band, thus prohibiting electronic transitions to the same. This finding validates our band energy diagram [see Fig. 9(c)], where we expect that the electronic transitions will occur from the O 2p state (valence bands) to Pr 4f (unoccupied) state in the case of the as-synthesized system. However, upon reduction of Pr, the 4f level will get filled; hence, the transition to unoccupied Ce 4f will determine the bandgap. This is exactly what we observed in the O K edge [see Fig. 9(c)] when the as-synthesized and the H₂-HT systems were compared. The fact that feature B becomes prominent upon H₂-HT, even upon the reduction of Ce⁴⁺, can be explained as follows: First, the reduction of Ce⁴⁺ to Ce³⁺ is rather mild as the predominance of Ce⁴⁺ can be observed from the Ce M_4,5/L₃ edges (Figs. 7 and 8). Additionally, no major changes in the white line intensity of Ce M_4,5 indicate only negligible changes in the Ce 4f occupancy.

Furthermore, as shown in Fig. 9(a), both the Pr 4f-O 2p and the Ce 4f-O 2p hybridization are actually pre-edge features, while the main absorption corresponding to the RE 5d-O 2p hybridization starts above 531 eV. This is equivalent to our hypothesized energy band diagram [Fig. 9(c)] with the two intermediate energy bands at lower energy gaps, while the gap between O 2p and unoccupied RE 5d is much larger. The energy difference between features A and C is ∼3.5 eV (so is the energy difference between the onset of edge A to edge C). This means that the effective gap between O 2p and RE 5d is ∼5.5 eV. In fact, this value is in good agreement with our earlier hypothesis²⁵ and is close to the expected energy gap in rare-earth oxides without intermediate 4f states.^26,60 Hence, it can be summarized that in F-HEOs, Ce and Pr lead to the formation of intermediate energy states, resulting in narrow bandgaps, whereas the other 3+ cations add to the main energy gap of ∼5.5 eV. Depending upon the heat treatment condition, i.e., reducing/oxidizing atmospheres, each of these electronic structures in F-HEOs can be achieved reversibly.

This work attempts to provide a comprehensive understanding of the tunable electronic band structure in a fluorite type rare-earth based high entropy oxide (F-HEO). Owing to the element specific techniques used here, it is possible to disentangle the individual effects of the constituent cations, which can be directly correlated to the observed reversible changes in the optical features. Reversible changes (∼0.5 eV) in the bandgap energies are achieved in the F-HEO upon vacuum heat treatment followed by reheating in air. Importantly, the single-phase fluorite type structure of (Ce_0.2La_0.2Pr_0.2Sm_0.2Y_0.2)O_2-δ is maintained even upon vacuum heat treatment with Ce being the sole element, which is purely 4+. This shows the potential of the F-HEO to accommodate a large amount of oxygen vacancies. A stronger reduction of F-HEO, achieved via hydrogen heat treatment, allows for a larger change (∼1.2 eV) in the bandgap energy, which can be reverted back to the initial state upon subsequent annealing in air. In addition, a reversible structural transition from fluorite to a single-phase oxygen vacancy ordered C-type bixbyite structure has been observed. Raman spectroscopy further strengthens this reversible behavior as local chemical features before and after reheat treatment are identical. X-ray absorption near-edge spectra (XANES), using soft and hard x rays, indicate that the crystal structure transition can be correlated to the reduction of Ce⁴⁺, while tuning of the bandgap energy is related to the reduction of Pr and related changes in the Pr 4f-O 2p hybridization.

Although practical applications using the F-HEO are yet to materialize, the unique combination of narrow and tunable bandgap energies along with large concentrations of oxygen vacancies in the F-HEO might be beneficial for applications related to mixed electronic–ionic conduction, catalysis, etc. In this context, understanding the exact nature of oxygen vacancy ordering and the related fluorite to bixbyite transition is important. Hence, comprehensive high temperature investigations (above 750 °C) under different atmospheres will be crucial. An electrochemical approach to tune the bandgap in the F-HEO can be another prospective research direction. In any case, further experiments and most importantly support from theoretical studies are essential to exploit the complete potential of the F-HEO.

The supplementary material includes the Rietveld refinements of the XRD patterns, TEM–EDS maps, Raman spectra (of vacuum heat treated F-HEO and bixbyite HEO), and XANES of La and Sm L3 edges.

The data that support the findings of this study are available within the article and its supplementary material.

A.S. and H.H. acknowledge financial support from the Deutsche Forschungsgemeinschaft (DFG) under Project No. HA 1344/43-1. B.E. and H.W. acknowledge financial support from the Deutsche Forschungsgemeinschaft (DFG) under Project No. WE 2623/14-1. X.M. and L.V. acknowledge the support of Karlsruhe Nano Micro Facility (KNMF) for the access to the TEM. A.S. thanks Soumabha Bag (INT, KIT) for fruitful discussions. We thank the Helmholtz-Zentrum Berlin for the allocation of beamtime at the beamline UE46 PGM₁ (Proposal No. 192-08578-ST/R) and Eugen Weschke for the support during the beamtime. We acknowledge DESY (Hamburg, Germany), a member of the Helmholtz Association, for the provision of experimental facilities. Parts of this research were carried out at PETRA III (Proposal No. 20190485), and we would like to thank Ruidy Nemausat for assistance in using the beamline P65. We acknowledge support by the KIT-Publication Fund of the Karlsruhe Institute of Technology.