A new highly oxygen-deficient and cubic Pr_3ZrO_8-δ for intermediate-temperature thermochemical production of oxygen and hydrogen

Domain: chemistry
Published: 2026-02-23
Editorial outcome: major_revision

Abstract
Two-step thermochemical cycles offer a clean route for hydrogen and oxygen production but are typically limited to high temperatures exceeding 1500 °C. Lowering operating temperatures would enable the use of alternative heat sources such as industrial waste heat. Here, we report Pr3ZrO8-δ as a new enabling material for efficient intermediate-temperature redox cycling, with thermal reduction at 900 °C in argon and steam oxidation at 400 °C. Pr3ZrO8-δ adopts a face-centered cubic structure similar to CeO2 but exhibits significantly greater oxygen deficiency, achieving average oxygen and hydrogen fluxes of 331.7 and 70.3 µmol·g-1, respectively, over ten cycles at 20% H2O. These values surpass those of leading CeO2-δ and perovskite oxides under comparable or more severe conditions. In-situ neutron and X-ray diffraction determine the phase stability boundaries of Pr3ZrO8-δ, while density functional theory identifies O-H bond cleavage as the rate-limiting step. These results establish Pr3ZrO8-δ as a promising material for intermediate-temperature thermochemical oxygen and hydrogen production.

Introduction
The realization of a clean and sustainable energy future hinges on the availability of low-cost hydrogen on a large scale. The current benchmark technology for bulk H2 production, steam methane reforming (SMR) technology is cost effective and energy efficient but emits significant amounts of CO2 (~9 kg CO2 per kg H2 produced), which would impose a marked negative impact on the environment if allowed to release into the atmosphere without restriction1,2. While adding CO2 capture facilities to SMR plants is technically possible, it would considerably raise the cost of H2. Electrolytic production of H2 (green H2) from water is a clean technology, but it is still too expensive to be deployed at commercial scale. Similarly, the current commercial cryogenic distillation based bulk O2 production is also an energy intensive and costly process. Searching for clean, cost-effective, and scalable O2 and H2 production technologies is, therefore, of paramount importance to a sustainable clean energy future.

Solar-driven thermochemical (TC) approach stands out to be an appealing method for clean, scalable, and low-cost O2 and H2 production from water, using only solar heat as an energy source3–5. This approach leverages the entire solar spectrum for high temperature heat generation at desirable locations where the active material undergoes TC redox cycles for separate O2 and H2 productions6. Oxygen off-stoichiometric CeO2-δ is currently the benchmark TC material due to its reversible single-phase redox chemistry under the thermal and chemical cycling conditions7. The “two-step” thermal reduction and water splitting cycles can be represented by:

CeO2 = CeO2-δre + 0.5δre O2 ↑ (1)

CeO2-δre + (δre - δox)H2O = CeO2-δox + (δre - δox)H2 ↑ (2)

It is evident that the amount of oxygen released during the thermal reduction cycle is proportional to off-stoichiometry δre under a thermal reduction temperature (Ttr) and partial pressure of oxygen (pO2), whereas the hydrogen released during the steam splitting cycle is proportional to the difference between δre and oxygen off-stoichiometry δox under a steam splitting temperature (Twp) and pO2. Since CeO2 has a relatively low δre and δox, it must operate at a high Ttr (e.g., ~1500 °C) and Twp (e.g., ~1200 °C) to yield practically meaningful production rates of H2 and O2.

The strict requirement for high Ttr (heat demand) operation is undesirable for TC processes. This increases the solar energy demand and lowers the overall solar-to-fuel and solar-to-oxidant efficiencies. It also accelerates the sintering of redox materials, which causes reduction in active surface area and degradation in performance8–12. To reduce Ttr of reaction (1), one noticeable research effort is to remove O2 from the reactor during the cycle so that the equilibrium of reaction (1) can be shifted to the right. These methods include vacuuming10, chemical scavenging13, and oxygen transport membranes14. Challenges to implement these methods are the further-reduced solar-to-fuel (STF) efficiency (e.g., from ~5% to <1.73%) due to the low pumping efficiency (<1%) at low pressures (<10−5 atm)10,11 and increased system complexity and cost. Therefore, identification of new redox materials that can operate at lower Ttr is a preferred option to the development of commercially viable solar TC technologies.

Developing new redox active oxides (RAOs) with higher oxygen off-stoichiometry than CeO2-δ has been a focal area for the “two-step” TC research in recent decades. Given TCs’ harsh operating conditions15, RAOs need to (1) be chemically and thermally stable over a wide range of pO216; (2) exhibit large change in oxygen off-stoichiometry (Δδ) during the “two-step” cycles17; (3) show high mixed oxide-ion and electron conductivity18. Based on these criteria, off-stoichiometric oxides have attracted the most interests19. Representatives of this class of RAOs include transition-metal doped CeO211, iron aluminates20 and perovskites ABO3 (A=La, Ca, Sr, Ba, etc.; B=Mn, Fe, Co, etc.)20–25. While these materials exhibit greater δre over pure CeO2-δ, the overall TC cycling temperature window is still too high. Early studies have also considered volatile stoichiometric chemistries (e.g., ZnO/Zn and SnO2/SnO) for TC by leveraging the high entropy change of phase transformation during thermal reduction cycle26,27. However, one challenge for these volatile cycles is the difficulty of separating the reduced products from oxygen.

Here, we report a new RAO for intermediate temperature “two-step” TC production of O2 and H2. The new material has a composition of Pr3ZrO8-δ (PZO) with a high level of oxygen off-stoichiometry and face centered cubic (fcc) structure. We show that fcc-PZO substantially outperforms the benchmark CeO2-δ as well as other perovskites in δ and H2/O2 yields through TC cycle even under reduced temperatures and low steam concentrations, making it a promising class of RAO for new-generation reduced temperature TC processes driven by a variety of heat sources.

Results
Initial XRD check
A room-temperature lab XRD was first performed to quickly check the crystal structure of the as-synthesized PZO. Figure 1 shows the pattern that can be well indexed into the fcc structure with a lattice parameter of 5.43 Å. Therefore, PZO can also be viewed as a fluorite structured composition of Pr0.75Zr0.25O2 after doping ZrO2 into PrO2 in a stoichiometric ratio of Pr:Zr = 3:1.

VTND analysis
To precisely examine the evolutions of crystal structure and crystallographic parameters of PZO with temperature and atmospheres, we employed VTND (Variable Temperature Neutron Diffraction). The VTND patterns in 2D and 3D contour style collected in the range of RT-900 °C in argon (relevant to TC condition) are shown in Fig. 2a, b. The real-time phase evolution can be clearly visualized from the intensity contour plots. The refined crystal structure is shown in Fig. 2c along with refinement data listed in Table S1 of the Supplementary Information (SI).

At room temperature, the diffraction patterns can be well refined into space group Fm3¯m (No. 225) with very low Bragg-intensity R values (Rp) and weight-profile R value (Rwp). In this fluorite structure, Pr/Zr and O occupies (0, 0, 0) and (1/4, 1/4, 1/4), respectively. More importantly, Zr shares Pr position with 25% occupancy without showing a long-range ordering, which suggests that the original Pr3ZrO8-δ can be viewed as Pr0.75Zr0.25O2-δ. It is also interesting to note that 91.5% of the O-site in PZO is occupied at RT, suggesting 8.5% oxygen vacancies (δo=0.17) and the as-synthesized PZO composition as Pr0.75Zr0.25O1.83 at RT.

With the same fcc structure, we also refined VTND patterns at other temperatures. The original refined patterns and refined structure are provided in Fig. S1 with data in Table S1. From these data, we can conclude that PZO retains its fcc structure from RT to 900 °C in argon with neither phase transition nor impurity detected, indicating thermal stability of PZO in argon up to 900 °C. Similar datasets collected in air and refinement performed are provided in Figs. S2–S3 and Table S2. As evident from these results, there is no phase change from RT to 900 °C in air either.

The refined lattice parameter, unit cell volume and bond length between Pr(Zr) and O as a function of T in air and argon are compared in Fig. 3. In air, lattice parameter a (Å), unit cell volume (Å3) and Pr(Zr)-O bond length (Å) increase with T as expected. In argon, a similar trend with T is observed. However, the lattice parameter, unit volume and Pr(Zr)-O bond length of PZO are all larger in argon than in air. These increases are obviously caused by the loss of lattice oxygen that weakens Pr(Zr)-O interactions and formation of large Pr3+28,29, allowing lattice to expand and Pr-O bond to elongate.

It is interesting to point out that the lattice parameter measured in air exhibits a small contraction with time at 300 °C, signaling that there might be a small change in lattice oxygen content. In comparison, the lattice parameter measured at 300 °C in argon exhibits a significant increase in the later stage of the 300 °C-holding period, further inferring a possible change in lattice oxygen content. Our later TGA and TC cycling results suggest that this is likely related to the dynamics of oxygen release. While the lattice parameter measured in air remains normal at higher temperatures, they exhibit slightly different behaviors in argon. The first is from 400 to 500 °C, where there is a significant change in lattice parameter, followed by a slower change from 500 to 600 °C. Another occurs at 800 °C, where the expected plateau is taken over by a slower increase. Again, these lattice parameter abnormalities signal that there are some subtle changes in the PZO’s lattice oxygen content (and Pr oxidation state) with T, particularly in atmospheres with low pO2, although there is no clear evidence of phase transformation from all VTND patterns shown. With the data available, we hypothesize that Fig. 3a is the result of change in oxygen stoichiometry accompanied by the corresponding change in Pr-oxidation state and elongation of Pr-O bond. Oxygen occupancy cannot be precisely determined to further understand these subtle changes due to the short-time-bin data collection during the T-ramping period.

Phase stability of fcc-PZO
The phase stability of fcc-PZO under the working conditions of TC processes is critically important to the stability of H2/O2 yields. To determine the phase stability, we exposed the as-synthesized fcc-PZO samples in different T and pO2, followed by quenching the samples from high temperatures and analyzing the phase composition by XRD. According to the identified phases, we construct the phase stability diagram in Fig. 4. The original XRD patterns can be found in Fig. S4 in the SI. The impurities identified are Pr3+ compounds: Pr2O3 and Pr2Zr2O7. A general trend is that the higher the pO2, the higher the T that fcc-PZO is stable.

We also performed high-temperature XRD (HTXRD) in air (pO2 = 0.21 atm) and high vacuum (pO2 ~ 10−9 atm) from RT to 1100 °C as an independent verification. The original HTXRD patterns are shown in Fig. S5. Shown in diamond in Fig. 4 are the phases identified by HTXRD; they fall well within the phase regions constructed from ex-situ XRD data, indicating the accuracy of the phase diagram.

We also attempted to construct the phase stability diagram using hybrid DFT coupling spin-orbital interactions; the details about the approach are provided in the Experimental section. Figure S6 shows the calculated phase stability diagram of the PZO system using this method. With the consideration of temperature and configurational entropy, the calculations show that a stable PZO phase could be formed.

Oxygen off-stoichiometry vs. T and pO2
Oxygen off-stoichiometry (δ) is a key parameter determining the performance of RAO in TC cycles. A precise determination of δ as a function of T and pO2 is critically important to understand the performance of PZO for TC applications. Therefore, we selected both VTND and TGA methods to evaluate δ of PZO. The VTND-derived δ values were taken as the twice the fraction of the unoccupied O-sites obtained from refinement; Tables S1 and S2 list these values measured in both air and argon and air, respectively. At RT, δo = 0.17, which is the same as δo = 0.17 estimated by XPS and XAS based on the oxidation state of Pr; see Figs. S7 and S8 in the SI.

To confirm the VTND-derived δ, we also performed TGA measurements; the original weight loss curves are shown in Fig. S9, from which δ = δ(T) is derived using δo = 0.17 as the starting value. Figure 5a compares the two sets of δ in the formula of Pr0.75Zr0.25O2-δ. Note that VTND-data are only available in air and argon. The VTND-derived δ consistently exhibits a slightly higher value than its TGA-derived counterpart in both atmospheres. Within the experimental error, the two sets of δ-values agree with each other. Correspondingly, the oxidation state of Pr is also plotted against T in the second y-axis in Fig. 5a. As is shown, the average oxidation state of Pr decreases as T increases and pO2 decreases, implying that more Pr3+ is formed while the lattice oxygen is being lost. A plot of log δ vs. 1/T shown in Fig. 5b confirms that the loss of oxygen or the formation of oxygen vacancies is a thermally activated process following Arrhenius relationship with a very low activation energy of 0.02−0.03 eV, suggesting that the thermal oxygen release in PZO is a very facile process. An early study has also confirmed in CeO2-ZrO2 system that Zr4+ facilitates reducibility of pure CeO230. Our DFT calculations also confirm the low formation energy of oxygen vacancies in fcc-PZO even at oxygen-rich condition, see Figs. S10–S11 in the SI; details about the DFT method are provided in the Experimental Methods section.

A simple conversion of Pr-oxidation state shown in Fig. 5a into Pr3+ concentration ([Pr3+]) using charge neutrality indicates that there is ~75% Pr3+ present in the fcc-PZO under 900 oC and N2, see Fig. S12, which is in striking difference from pure PrO2; the latter turns into Pr2O3 or other lower oxidation state intermediates (PrnO2n-2) under this condition31. Therefore, it is reasonable to believe that Zr4+ stabilizes Pr4+, likely due to its fixed-valence substitution.

To compare with the benchmark CeO2-δ, we further plot δ-pO2-T of fcc-PZO in Fig. 6. A first glance indicates that fcc-PZO exhibits much higher δ than CeO2-δ, particularly at lower T range. To put this into perspective, δ at 900 °C in argon and in air are 0.27 and 0.24, respectively. For the benchmark CeO2-δ, it is in the order of 10−4 and 10−3 in air and argon, respectively19,32. The significant advantage of PZO in δre over CeO2-δ strongly suggests that PZO is a promising RAO for intermediate temperature TC processes.

Understanding electrical conductivity vs. T and pO2
Electrical conductivity is a crucial indicator of bulk diffusion of ions/electrons and charge transfer kinetics at the surface of PZO. The measured total electrical conductivity σ of PZO as a function of pO2 and T is shown in Fig. 7. The level of conductivity over the entire pO2 and T ranges studied is rather low (10−2 to 10−3 S/cm) but comparable to CeO2-δ at much higher temperatures and lower pO2. Collectively, Fig. 7 indicates that PZO is a semiconductor with a low activation energy Ea = 0.34−0.43 eV (Fig. 7b). At high pO2 range (>10-4 atm), Fig. 7a indicates that fcc-PZO displays a p-type conducting behavior. As pO2 decreases, σ first experiences a plateau, an indicative of dominance of ionic defects, then a weak n-type conducting behavior.

To interpret the conductivity behavior described above, we developed a simplified defect-chemistry model based on the “dilute solution” approximation; full derivations are provided in the Supplementary Information. Briefly, the model adopts the fluorite (fcc) lattice as the reference framework and assumes Pr4+ (Pr×Pr) as the base oxidation state. Under a given T and pO2, oxygen loss generates oxygen vacancy (V••O), Pr3+ (Pr'Pr) species as described by reaction (S1) in the SI.

At high pO2 (>10−3 atm), oxygen vacancies are oxidized to produce electron holes (reaction (S2)), giving rise to p-type conductivity. Conversely, at low pO2 (<10−7 atm), lattice oxygen (O×O) is removed (reaction (S3)), generating free electrons and yielding n-type conductivity. In the intermediate pO2 range (~10−7 to 10−3 atm), ionic defects (V••O and Pr'Pr) dominate, while electronic carriers remain minority species. Consequently, overall conductivity becomes less sensitive to pO2. We note that both oxygen vacancies and electrons are present in fcc-PZO at comparatively high concentrations; however, because electrons possess much higher mobility, the total conductivity is still dominated by electronic charge transport even within the intermediate pO2 regime. Therefore, fcc-PZO is deemed a mixed electronic and oxide-ion conductor.

The above defect-chemistry picture is consistent with prior band-structure studies on Pr oxides. These studies show that the partially filled Pr4+ 4f1 band resides near the Fermi level and strongly hybridizes with the O-2p valance band, leading PrO2-δ, including fcc-PZO, to exhibit narrow-band semiconducting behavior with a band gap ~0.5 eV associated with mixed Pr3+/Pr4+ valance state33. This prediction agrees with the measured activation energy of ~0.4 eV in Fig. 7b. In contrast, Pr3+ contains strongly localized 4f2 electrons, and Pr2O3 behaves as a Mott insulator with a significantly large band gap (3.5–4.5 eV) between the O-2p valance band and Pr-5d/4f conduction band34. Because Pr4+ species provide the electronic states that facilitate charge transport, the conductivity naturally decreases as the Pr4+ concentration diminishes with decreasing pO2. Notably, a substantial amount of Pr4+ - approximately 25% even under 900 oC and N2 condition - is observed in the fcc-PZO system (Fig. S12).

Thermochemical performance of PZO
To search for the best TC working conditions, we first performed single-cycle testing on fcc-PZO under different T-window (i.e., between Ttr and Tws) and H2O contents. Note that the high T-value within the T-window represents the temperature (Ttr) for thermal reduction cycle, whereas the low T-value is the temperature (Tws) for water splitting reaction cycle. Figure 8a shows the effect of T-window on H2 generation flux under a fixed 20% H2O-Ar; the corresponding set of O2 flux is given in Fig. S14a. It is evident that there is a significant gain in H2 flux from 1100 to 900 °C window to 1100–500 °C window, but no significant gain is observed for 1100–400 °C window. On the other hand, cycling within 900–400 °C produces similar H2 flux as 1100–900 °C cycling. However, our phase diagram (Fig. 4) as well as the following post-test analysis indicate that exposure of fcc-PZO to argon above 1000 °C leads to its decomposition to Pr2O3. Therefore, 900–400 °C is selected as the T-window for TC cycling of fcc-PZO. On the other hand, the effect of H2O on H2 flux is shown in Fig. 8b along with the corresponding O2 flux shown in Fig. S14b, suggesting that H2O contents higher than 20% do not increase H2 flux significantly within the 400–900 °C window.

These selection of the above cycling conditions, i.e., 900–400 °C and 20% H2O is further supported by the post-test analysis. Figure 8c shows that at Ttr ≥ 1000 °C, fcc-PZO partially decomposes into Pr2O3, which is an oxide-ion and electron insulator and detrimental to TC performance. Upon exposure to 20% H2O for 4 h at 400 °C in the following oxidation cycle, Fig. 8d shows that the fcc-PZO exposed to Ar at Ttr ≤ 900 °C remains unchanged in phase compositions (red patterns). In contrast, for fcc-PZO exposed to 1000 °C in Ar (blue patterns), it is interesting to observe that the Pr2O3 secondary phase is reversed to the original fcc phase after H2O oxidation cycle, demonstrating the reversibility. A partial conversion of Pr2O3 impurity to Pr6O11 is also observed after H2O oxidation of fcc-PZO that was exposed to 1100 °C in argon (green patterns). These results suggest that the reoxidation of Pr2O3 into Pr6O11 or fcc-PZO is thermodynamically feasible but could be kinetically limited. Based on the above results, we, therefore, select 900 °C for thermal reduction cycles in argon and 400 °C for water splitting cycles in 20% H2O.

The original profiles of T, O2 and H2 concentrations collected under this condition over 10 consecutive TC cycles are shown in Fig. 9a, by which the O2/H2 fluxes are converted and plotted against cycle number in Fig. 9b. In general, this level of intermediate-temperature performance is better than most reported in the literature even under higher temperatures, see Table S3 for comparison, demonstrating the potential of fcc-PZO for reduced temperature TC applications. Note that fcc-PZO represents a fundamentally distinct material class from the extensively studied CeO2-ZrO2 solid solution systems; the latter has consistently underperformed the benchmark CeO2-δ 10,19,35–38. Unlike CeO2-ZrO2 solid solutions, fcc-PZO functions more like a compound, akin to CeO2. However, excessive reduction of Pr4+ to Pr3+ could lead to the undesirable formation of Pr2O3 and Pr2Zr2O7, see phase diagram Fig. 4. A key role of Zr in the system is stabilization of the Pr4+/Pr3+ redox couple within the fcc structure by limiting excessive oxygen release, thereby alleviating the formation of the unwanted Pr2O3 and Pr2Zr2O7 impurity phases. Compared to another similar system Ce0.8Pr0.2O2-δ (CPO, the “sweet-spot” composition in the CeO2-Pr2O3 series), where Pr3+ substitution is employed to stabilize oxygen vacancies and lower the reduction enthalpy39–42, fcc-PZO has a clear advantage in δ. For example, the Pr-rich fcc-PZO exhibits δ = 0.20–0.25 in air over 600–900 °C, vs. 0.02–0.08 for CPO39, largely due to suppressed Pr4+ to Pr3+ reduction by Zr4+.

It is evident from Fig. 9b that there is more O2 than H2 produced in each cycle, i.e., 331.7 µmol/g for O2 flux vs. 70.3 µmol/g for H2 flux (averaged from the 10 cycles), which significantly deviates from the theoretical ratio of H2/O2 = 2/1. The slow kinetics for water splitting reaction at lower temperature as evidenced by the longer cycle time than thermal reduction cycle, i.e., 2 h vs. 1 h, is likely the reason. In other words, it may take a much longer time for the water splitting cycle to occupy all available oxygen vacancies and reach the theoretical H2 flux. Accumulation of unfilled oxygen vacancies due to incomplete oxidation cycle could lead to a gradual loss of oxygen and hydrogen fluxes during the subsequent reduction cycle, resulting in the degradation shown in Fig. 9b.

It is worth noting that the steam utilization in this laboratory testing is very low, which leads to very low H2/H2O ratio during the water splitting cycle. One concern is whether fcc-PZO is still stable at lower pO2 (higher H2/H2O ratio). To test this possibility, we performed a separate study in which we directly expose fcc-PZO to 4% H2-Ar for 2 h at 900 °C. The XRD pattern of the tested sample is shown in Fig. S15, where the original fcc-PZO peaks remain without any detectable impurity phases. The XRD peaks are slightly shifted to the left, implying increased oxygen off-stoichiometry. Therefore, this study at least confirms that fcc-PZO is stable at 900 °C up to 4% H2.

To facilitate the understanding of the observed degradation, we also examined the morphology of the tested fcc-PZO by SEM and compared it with the one before testing in Fig. S16. No significant change in fcc-PZO morphology can be detected after cycling, which is not surprising given the low temperature operation. Therefore, the degradation is likely due to the slow water splitting kinetics that causes the chain-reaction reducing the amount of available oxygen vacancies to sustain the thermochemical cycling.

Understanding the rate limiting step of the steam splitting cycle
To facilitate the understanding of the underlying reasons for the lower-than-anticipated H2 production in the water splitting cycle and identification of the rate limiting step (RLS), we conducted an analysis of the Gibbs free energy associated with the elementary steps using density functional theory (DFT) calculations. We first constructed three low index surfaces of fcc-PZO, namely, PZO (100), PZO (110), and PZO (111) from the optimized structure of the PZO bulk, as illustrated in Fig. S17. In accordance with the definition of surface energy, the calculated surface energies for PZO (100), PZO (110), and PZO (111) are 2.02, 0.51, and 0.24 J/m2, respectively. Generally, a thermodynamically stable crystal face is characterized by lower surface energy, indicating that the PZO (111) surface is the most stable surface. Consequently, we selected the PZO (111) surface for further DFT analysis. Figure S18 illustrates the construction process of the PZO (111) surface, including the optimized structure of the PZO unit cell, top and side views of the cleaved PZO (111) unit cell, and a 2x1x1 PZO (111) supercell.

The proposed elementary steps occurring on the surface of PZO (111) are as follows: (1) the formation of an oxygen-vacancy site (Ovac); (2) the adsorption of H2O onto an Ovac; (3) the splitting of H2O into two intermediate species (OH*); (4) the breakage of the OH bonds; and (5) the evolution of H2 molecule. Figure 10 illustrates both the top and side views of the reaction pathway along with the structural parameters, as well as the corresponding Gibbs free energy profiles for the H2O splitting process over the PZO (111) surface. Initially, an oxygen vacancy (Ovac) is generated by the release of one lattice oxygen from the pristine PZO (111) surface, which has an oxygen vacancy formation energy of -0.95 eV, see step b. Subsequently, an H2O molecule is adsorbed above the Ovac site, exhibiting an adsorption energy of −0.66 eV, see step c. It is noteworthy from Fig. 10b that, with the formation of the oxygen vacancy and the adsorption of the H2O molecule, the O1 atom in the subsurface gradually moves upward toward the surface. The distances between the O1 atom and the surface for steps a, b, and c are measured at 1.38 Å, 0.63 Å, and 0.10 Å, respectively. As the H atom (labeled as H2) approaches the adjacent O1 atom, a new H2-O1 bond is formed, resulting in its bond length from 1.44 to 1.02 Å. Concurrently, the H2-O3 bond within the H2O molecule breaks, leading to an elongation of its bond length from 1.07 to 1.66 Å. This sequence of events in the dissociation of H2O molecules requires a free energy change of −0.05 eV, forming two isolated OH* intermediates adsorbed on the surface. At step d, the dissociation of the H2O is complete. Subsequently, the two OH bonds, i.e., H2-O1 and H1-O3, are cleaved successively, with the corresponding Gibbs free energies being 0.60 eV and 1.67 eV, respectively. The high energy for H1-O3 cleavage indicates that this step is the RLS toward completing H2 evolution process. The reaction elementary steps and process energies are summarized in Table S4.

We observe that the oxygen vacancy formation energy in Table S4 is negative, implying that a lattice oxygen atom in the PZO (111) surface can be released spontaneously. Consequently, we conducted a further evaluation of the surface’s propensity for oxygen release at higher concentrations of oxygen vacancies. As illustrated in Fig. S19, the formation energies for the first and second oxygen vacancies are −0.95 eV and −0.25 eV, respectively. Moreover, the formation of oxygen vacancies facilitates the migration of subsurface oxygen atoms to the surface. These values indicate that the PZO (111) surface exhibits a strong tendency to release oxygen. Additionally, as illustrated in Fig. 9b, upon the completion of a H2O splitting cycle, we observe that the O1 atom in the subsurface migrates to the surface and forms oxygen molecule with O3, exhibiting an O1-O3 bond length of 1.29 Å. To further evaluate the oxygen release capacity of the PZO (111) surface, we calculated the desorption of this oxygen molecule. The results shown in Fig. S20 indicate a desorption energy of 0.26 eV, again suggesting that the PZO (111) surface can readily release oxygen. Overall, our computational results align well with experimental observations, i.e., the water splitting cycle is the RLS for PZO-based intermediate temperature TC processes, while thermal oxygen release cycle is facile. We are currently working to computationally identify effective surface catalysts that can promote O-H cleavage, followed by testing these catalysts in TC reactor.

In summary, we have demonstrated that PZO crystallizes in a face centered cubic (fcc) structure analogous to CeO2-δ yet exhibits significantly higher oxygen off-stoichiometry (δ), enabling hydrogen generation at lower temperatures. Under thermal reduction in argon at 900 °C, the 10-cycle averaged oxygen flux reaches 331.7 µmol g−1, while hydrogen production achieves 70.3 µmol g−1 at 400 °C with 20% H2O-performance that surpasses both benchmark CeO2-δ and most perovskite oxides under development. A comprehensive investigation combining in situ neutron diffraction, in situ XRD, and ex situ XRD has established the phase stability diagram of the fcc-PZO system, delineating its redox boundaries for thermochemical applications. Supported by experimental validation and hybrid DFT calculations including spin-orbit coupling interactions, a simplified defect chemistry model has been developed that integrates ionic (oxygen vacancies) and electronic (free electrons and holes) defects, providing key insights into charge-carrier transport mechanisms in fcc-PZO.

A remaining challenge for the practical deployment of fcc-PZO in intermediate-temperature TC processes lies in the kinetics of the steam-splitting reaction. Accelerating this step will be critical for realizing the full potential of fcc-PZO. Strategies such as applying surface catalysts or enhancing mixed oxide-ionic and electronic conductivity offer promising pathways to address this limitation. Preliminary DFT calculations indicate that the rate-limiting step (RLS) is the cleavage of the O-H bond on the PZO (111) surface. Overall, this study identifies PZO as a promising redox-active oxide (RAO) for low-temperature thermochemical hydrogen production, operable with a wide range of heat sources.

Methods
Sample preparation
The Pr3ZrO8-δ (PZO) powder was synthesized by Pechini method. In brief, stoichiometric amounts of high-purity starting materials - Pr(NO₃)₃·6H₂O (97%, Alfa) and ZrO(NO₃)₂·xH₂O (99.97%) - together with citric acid (CA) in a total metal:CA molar ratio of 1:1.5 were dissolved in deionized (DI) water, and a small amount of dilute nitric acid prepared by mixing commercial ~70 wt% HNO₃ with DI water in a 1:9 volume ratio was added to assist dissolution. The solution was then heated at 80 °C to vaporize the solution, followed by heating to 200 °C for autoignition. The resulting powder was first fired at 600 °C for 2 h to fully decompose the precursors into pure oxides. The powder was then dry-pressed into ϕ1″ pellets and sintered at 1050 °C for 10 h in air. To ensure a pure single phase, the sintering step was repeated twice. After sintering, the pellets were ground and ball-milled to obtain a fine powder with an average particle size of ~5.3 μm, which was then loaded into the fixed-bed reactor for thermochemical performance evaluation. The phase composition of the final powder synthesized was pre-checked by a lab powder X-ray diffractometer (Rigaku MiniFlex II) using graphite-monochromatized CuKα radiation (λ = 1.5418 Å) with a scan rate of 5° min−1 over a 2θ range of 10°–90°. Similarly, the post-cycled PZO was also checked with the lab-scale XRD.

Determination of crystal structure
To precisely determine the crystal structure of PZO and its evolution with temperature, we performed Variable Temperature Neutron Diffraction (VTND) at the VULCAN beamline43 at the Spallation Neutron Source at the Oak Ridge National Laboratory. The time-of-flight neutron diffraction at 30 Hz chopper setting and high-intensity mode covered a d-space range of 0.45–2.5 Å at the 90° detector bank. To run the VTND experiment, the PZO powders with a particle size of ~5 μm was loaded into a MgO crucible (about 12 mm diameter) to about 20 mm height. The 7 mm × 12 mm opening of neutron incident lights and the 5 mm receiving collimator defined the neutron gauge volume, which was aligned to the sample center to exclude the signals of the crucible and other backgrounds. The sample was moved into a controlled atmosphere furnace for the VTND experiments in both air and argon gas flows44. The diffraction patterns were continuously collected during the heating from the room temperature to 900 °C at a ramp rate of 10 °C/min with 1-h isothermal dwells at 300, 400, 500, 600, 700, 800 and 900 °C. Specifically, the last 40 min of data of the dwell at each temperature were selected for refinement45.

The Rietveld refinements were conducted using the GSAS program and the EXPGUI46 interface for enhanced usability and convenience45. The background was accurately modeled by employing a shifted Chebyscev function comprising 20 terms in GSAS. To refine the peak profiles, Gaussian width parameters (sig-1 and sig-2) and the Lorentzian width parameter (gam-1) were optimized in a profile function of the back-to-back exponentials with the pseudo-Voigt. Each data set independently underwent refinement for the lattice constant, atomic positions, thermal displacement parameters, and oxygen occupancies (oxygen stoichiometry). Throughout the refinement process, the instrument parameters that dictate the relationship between measured time-of-flight and d-spacing and the absorption correction parameters were consistently maintained across all temperature datasets.

Phase stability determination by XRD
To further elucidate the structural evolution and phase stability of fcc-PZO under different thermal and redox conditions, both ex situ and in situ X-ray diffraction (XRD) measurements were conducted as a complement to the VTND study.

For ex situ XRD experiments, the as-synthesized fcc-PZO powders were treated under different temperatures ranging from 700 to 1200 °C and pO2 varying from pure O2 to Ar-O2 and 5% H2-Ar mixtures using calibrated mass flow controllers (Alicat). Under each condition, a total of 4-h holding time was given to ensure phase equilibrium. To keep the high temperature phase composition as much as we could, the samples were quenched to RT for XRD analysis. Specifically, after being exposed to a target T and pO2 for 4 h, fcc-PZO samples were rapidly removed from the furnace and immediately quenched in air at room temperature to preserve the high-temperature phase.

We also used in situ XRD to verify the phase diagram constructed from ex situ XRD. The experiments were conducted on an Anton Paar XRK900 reaction chamber under stagnant air and vacuum (~10−9 atm). The samples were heated at a rate of 10 °C min⁻¹ with isothermal holds of 1 h at selected temperatures of 300, 500, 700, 900, and 1100 °C to ensure structural equilibrium at each condition. For each atmosphere, diffraction patterns were continuously acquired during heating and cooling cycles to monitor potential phase transitions and lattice parameter evolution.

All diffraction data were analyzed by Rietveld refinement using the GSAS and EXPGUI suite to extract lattice constants, thermal parameters, and oxygen site occupancies. Consistent refinement protocols were maintained across all datasets to ensure comparability with the VTND results.

Determination of oxygen off-stoichiometry
The oxygen off-stoichiometry (δ) is a critical indicator for the performance of RAO materials. The δ-value at room temperature (denoted as δo) in as-prepared fcc-PZO in air was determined by X-ray photoelectrons spectrometer (XPS), X-ray absorption Spectroscopy (XAS), Thermogravimetry Analysis (TGA) and VTND.

For XPS analysis, a Kratos Axis Ultra DLD instrument equipped with a monochromatic Al Kα X-ray source (15 kV, 10 mA) was employed. The beam was focused on a 0.7 mm × 0.3 mm area of the sample surface tilted at 45° to the analyzer. The electron energy analyzer was operated at a pass energy of 40 eV for high-resolution scans and 80 eV for survey scans. A step size of 0.05 eV was used, and each peak was scanned twice to ensure signal reliability. The relative proportions of Pr3+ and Pr4+ were determined from deconvoluted Pr 3d spectra, and δo was then calculated based on charge neutrality.

For XAS analysis, the δo in as-prepared fcc-PZO in air was calculated from the averaged Pr oxidation state determined by a lab XAS system (easyXAFS 300+) with energy range of 4.5 to 25 eV calibrated by Cr foil for Pr and Zr foil for Zr, respectively. The measurement mode is transmission and sample aperture is 11 × 3.4 mm. The XAS measurements were performed at Pr L3-edge. The ratio of Pr3+ to Pr4+ obtained from linear combination fitting of reference spectra was used to estimate δo through charge balance. The total measurement time is 1.5 h. During the measurements, three reference materials were used: ZrO2, Pr6O11 and Pr2O3 to ensure the accuracy of the data.

To directly determine δ as a function of temperature (T) and oxygen partial pressure (pO2), thermogravimetric analysis (TGA) was performed using a Netzsch STA 448 instrument. The weight change of fcc-PZO was continuously recorded at 300, 500, 700, 900, and 1050 °C under different controlled atmospheres, including ultrahigh-purity Ar, air, 50% O2/Ar, and 100% O2. The δ = δ(T, pO2) values were calculated from the measured weight loss, referenced to the initial δo. The comparison of TGA-derived δ values with those obtained from VTND showed good agreement, validating the combined approach for determining δ of fcc-PZO under variable redox conditions.

Electrical conductivity measurement
Electrical conductivity (σ) is an important indicator to the rates of bulk oxide-ion transport and surface oxygen exchange kinetics. To obtain σ = σ(T, pO2), we use a conventional four-probe technique and measure resistance of a cylindrical sample with a DC method. The cylindrical sample was made by pressing the powder into a dimension of ϕ1/4’’ × 1/2’’ and sintering into a dense body at 1050 °C in air for 10 h. Two pairs of silver paste/mesh were attached to both ends of the cylinder to ensure proper electrical contact for current passage, while another two sets of voltage tabs were adhered to the body of the cylinder with a pre-defined distance. The measurements were carried out from T = 400 to 900 °C and pO2 = 10−14 to 1 atm. The variation of pO2 was achieved by mixing pure O2 with Ar for pO2 ≥ 10-6 atm gases and mixing Ar-10% H2 with Ar and moisture for pO2 ≤ 10−14 atm gases. The final pO2 was determined by a home made tubular oxygen sensor placed next to the sample.

Defect chemistry modeling
The first step in building the model is to determine the base crystal structure of the material, Previous studies have shown that Pr1-xZrxO2-δ system can exhibit both pyrochlore and fluorite structures depending on the Zr content, as well as the presence of both 3+ and 4+ oxidation states for praseodymium47,48. Our XRD and VTND results confirm that Pr0.75Zr0.25O2-δ specifically exhibits fluorite structure which agrees with the finding from the literature47,48. Accordingly, we assume that structure in our model and set Pr4+ as our base oxidation.

The second step is to write the defect reactions to encompass various ionic and electronic point defects. With these reactions, mass action law is applied to express equilibrium constant (K). The defect chemistry modeling section in SI provides details on these defect reactions.

The third step is to solve these defect reaction equilibria. We adopted lsqnonlin function in MATLAB to do so. With the numerical solutions to the defect reaction, we obtain thermodynamic quantities of these defect reactions such as enthalpy (ΔH) and entropy (ΔS) from temperature-dependence of K. We also obtain transport properties such as diffusivities of charge carriers using Nernst-Einstein equation with charge carrier concentrations as the fitting parameters.

TC performance evaluation
A fixed bed flow reactor was employed to characterize the performance of fcc-PZO in TC cycling. Figure S21 shows the schematic of the reactor. A quartz tube with two-diameter (1/2’’ and 1/4’’) sections was used, where ~0.5 g of fcc-PZO powder was loaded in the 1/2’’-section connecting to the gas inlet, whereas the 1/4’’-section was connected to a Mass Spectrometer (MS, Pfeiffer OmniStar® GSD 350) at the outlet to analyze the gas composition. To minimize the potential sintering of fcc-PZO, a flow of 60 mL/min Ar was used to support the powder bed. After the thermochemical cycle, different temperature flows was used with different steam contents for the water splitting cycle. The temperature window for the TC cycling varied between 1100 to 400 °C and the steam contents varied from 3 to 50%. After the test, the phase and morphology of the fcc-PZO samples were examined by XRD and a field emission scanning electron microscope (FESEM, Zeiss Ultraplus).

DFT calculations of defect formation energy
The Vienna Ab-initio Simulation Package (VASP 6.5.1) code49 with the projector augmented wave (PAW) pseudopotentials50 was used in density functional theory (DFT) calculations. The cutoff energy for the plane wave expansion is 520 eV. To take into account the Coulomb correlation, we employed the Heyd–Scuseria–Ernzerhof (HSE)51 hybrid functional with 15% exact-exchange mixing and a screening parameter of 0.3 (HSE03)52. This yields a lattice parameter of 5.32 Å and a band gap of 1.73 eV. The former is close to the experimental 5.34 Å, reflecting the adequacy of the lattice constructed. The calculated defect-free bandgap is higher than 2Ea = 0.8-0.9 eV observed from electrical conductivity plot (Fig. 7). Applying a standard temperature (electron-phonon) renormalization yields a band gap ~1.1 ± 0.1 eV at 0 K. With the consideration of disorder/defect effect, the true quasiparticle gap could be higher, getting closer to the measured Ea.

Spin polarization and spin-orbit coupling (SOC) was included throughout all calculations. We adopted a 4×4×4 k-point grid for Brillouin zone (BZ) integration for the Pr3ZrO8 primitive cell. Regarding defect calculations, a larger 2×2 supercell with 96 atoms is built and BZ integration is performed based on a single Γ-point. All atoms are relaxed until the Hellmann-Feynman forces acting on individual atom becomes smaller than 0.01 eV/Å.

The formation energy Ef(Xq) of a defect X in charge state q is defined as53:

Ef(Xq) = Edef(Xq) - Ehost + Σ ni Δμi + q(ΔEF + ϵVBM) + Ecorr (3)

where Edef(Xq) is the total energy derived from a supercell calculation containing the defect X, and Ehost is the total energy for the perfect crystal using an equivalent supercell. The integer ni indicates the number of atoms of type i (here i could be Pr, Zr, or O) that have been added to (ni > 0) or removed from (ni < 0) the supercell. Ei are the total energy per atom of elementary substance of type i species. Δμi corresponds to chemical potentials of these species, referenced to Ei, with Δμi = 0 as the element-rich limit. The analog of the chemical potential for “charge” q is given by the chemical potential of the electrons, i.e., the Fermi energy ΔEF, using the valance band maximum (VBM) of host supercell ϵVBM as reference. Ecorr is charge correction.

Based on defect formation energy, the charge-state transition level ϵ(q1/q2) is defined as the Fermi-level position for which the formation energies of charge states q1 and q2 are equal53–55:

ϵ(q1/q2) = [Ef(Xq1; ΔEF=0) - Ef(Xq2; ΔEF=0)] / (q2 - q1) (4)

where Ef(Xq; ΔEF=0) is the formation energy of the defect X in the charge state q when the Fermi level is at the VBM (ΔEF = 0).

A thermodynamically consistent process for determining the bounds of chemical potentials is outlined below. The total energy of a stoichiometric unit of Pr3ZrO8 can be expressed as:

3μPr + μZr + 8μO = Eb(Pr3ZrO8) - 3Eb(Pr) - Eb(Zr) - 8Eg(O2) = ΔH(Pr3ZrO8) (5)

where ΔH(Pr3ZrO8) is the formation enthalpy of Pr3ZrO8. The stability of the system against decomposition into its constituent elements places upper limits on the chemical potential of each element in Pr3ZrO8. Therefore, additional restrictions are determined by:

μPr ≤ 0
μZr ≤ 0
μO ≤ 0 (6)

To ensure that the binary oxides (PrO2, ZrO2, and Pr2O3) do not precipitate from Pr3ZrO8, the following restrictions are also included:

μPr + 2μO ≤ ΔH(PrO2)
μZr + 2μO ≤ ΔH(ZrO2)
2μPr + 3μO ≤ ΔH(Pr2O3) (7)

where ΔH(PrO2), ΔH(ZrO2), and ΔH(Pr2O3) are the formation enthalpies of PrO2, ZrO2, and Pr2O3.

The above set of equations defines the range of chemical potentials consistent with the stability of Pr3ZrO8 against decomposition into binary oxides or into its elemental components. Given the bounds for the chemical potential of each element, a valid range for the formation energies of specific defects with various charge states can be examined.

DFT understanding of steam splitting process on the surface of fcc-PZO
To understand the reaction mechanism, we performed density functional theory (DFT) calculations using the Vienna Ab-initio Simulation Package (VASP 5.4.1)49,56. In the calculations, the projector augmented wave (PAW)57 method and the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE)58 functional were employed to describe ion-electron interactions and account for electronic exchange and correlation effects, respectively. To ensure the accuracy of the calculations, the energy cut-off for the plane waves was set to 450 eV, and the total energy and forces were set to 10-4 eV and 0.05 eV/Å, respectively. The first Brillouin zone was sampled using a 2×4×1 k-mesh for the PZO (111) supercell generated using the Γ-centered Monkhorst-Pack scheme59. A vacuum region of more than 17 Å was introduced along the z-direction to avoid interactions between periodically repeated images. The valence electron configurations considered were H 1s1, O 2s22p4, Zr 4s24p65s14d3, and Pr 5s25p66s25d1, respectively. Given that the systems include H2O molecular adsorption, the van der Waals (vdW) interactions between the H2O molecule and surface could be significant, thus, the DFT-D3 dispersion correction within the Grimme scheme was applied60. Spin polarization was considered in all calculations. In the present calculations, all atoms were fully relaxed for the unit cell optimization of PZO, while for the calculations of hydrogen evolution reaction (HER) and H2O-splitting over the PZO (111) surface, the bottom 12 atom layers were fixed to represent the bulk of PZO, with the top 6 atom layers and adsorbate fully relaxed.

The PZO (111) surface was constructed from an optimized 5.43 Å × 5.43 Å × 5.43 Å PZO unit cell, which comprised 3 Pr, 1 Zr, and 8 O atoms, as shown in Fig. S16a. Initially, a 6-arrangement period in the c direction (18-atom layer) clean PZO (111) surface, terminating with Pr, Zr and O atoms, was generated by cleaving from the PZO unit cell, and subsequently expanded into a 2×1×1 supercell, see Fig. S16b, c. The surface formation energy of PZO (Esur) is defined as

Esur = (Eslab - (Nslab/Nbulk)Ebulk) / 2S (8)

where Eslab and Ebulk are the total energy of the slab and PZO bulk, respectively. Nslab and Nbulk are the number of PZO units contained in the slab and bulk, respectively. S is the area of the PZO surface.

The formation energy of oxygen vacancy (Ef) is calculated by

Ef = E(Ovac-PZO(111)) + 1/2 E(O2) - E(perfect-PZO(111)) (9)

where E(Ovac-PZO(111)) and E(perfect-PZO(111)) are the total energies of the defect PZO (111) surface and perfect PZO (111) surface, respectively. E(O2) is the total energy of free O2 molecules with triplet.

The adsorption energy of H2O molecule (Eads) is defined as

Eads = E(H2O-Ovac-PZO(111)) - E(H2O) - E(Ovac-PZO(111)) (10)

where E(H2O-Ovac-PZO(111)) and E(Ovac-PZO(111)) are the total energies of the defect PZO (111) surface with and without H2O molecule adsorption, respectively. E(H2O) is the total energy of free H2O molecules.

The Gibbs free energy is calculated by

G = E + ΔGDFT-cor (11)

where E represents the energy from DFT calculations, and ΔGDFT-cor denotes the free energy correction calculated using the VASP toolkit (vaspkit)61.

The desorption energy of oxygen molecules is calculated by

Edes = E(PZO(111)) + E(O2) - E(O2-PZO(111)) (12)

where E(PZO(111)) and E(O2-PZO(111)) represent the total energies of the PZO (111) surface without and with oxygen molecule adsorption, respectively. E(O2) represents the energy of the free oxygen molecule.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript introduces Pr₃ZrO₈ (PZO) as a promising redox material for two-step thermochemical water splitting, a sustainable technology for the co-production of hydrogen and oxygen. This work lies in PZO’s ability to operate effectively at intermediate temperatures—specifically, 900 °C for thermal reduction (oxygen release) and 400 °C for chemical oxidation (hydrogen evolution). Structurally, PZO adopts a face-centered cubic lattice, analogous to CeO₂, yet demonstrates a significantly higher oxygen off-stoichiometry, a critical parameter governing its redox reactivity. The claims are supported by variable-temperature neutron diffraction (VTND) and thermogravimetric analysis (TGA).\n1. While the manuscript offers some insights into the development of intermediate-temperature redox materials, several key issues must be addressed and experimentally validated to fully assess the significance of this work.\n2. What are the maximum and minimum values of oxygen non-stoichiometry (δ) that PZO can accommodate without compromising its crystallographic stability? A precise understanding of δ boundaries under both oxidizing and reducing conditions is essential for evaluating and optimizing the redox performance of PZO. Currently, the lack of such data limits our ability to benchmark PZO against state-of-the-art redox materials and to optimize its operational parameters for improved energy efficiency.\n3. Although the manuscript emphasizes oxygen non-stoichiometry, it overlooks the potential role of Pr and Zr cation vacancies in influencing redox behavior. These defects may significantly affect oxygen mobility and catalytic performance. A discussion and supporting data regarding cationic defect chemistry are needed to provide a more comprehensive understanding of PZO's redox mechanism.\n4. Despite the detailed Rietveld refinement of VTND data—capturing temperature-dependent changes in lattice parameters, bonding, and oxygen vacancies—reciprocal space mapping (RSM) is crucial. RSM can reveal localized strain, defects, and phase transitions, which are indispensable for assessing the material’s thermal stability, defect dynamics, and catalytic performance under operational conditions. Unfortunately, such information is missing in this manuscript.\n5. The current characterization strategy lacks sufficient insight into local atomic environments and defect structures. A thorough investigation using XAS would allow quantification of local lattice distortions and vacancies (oxygen, Pr, and Zr), enabling a direct correlation between atomic-scale structure and macroscopic redox properties. This is important for identifying active sites and understanding structural transformations during cycling.\n6. The temperature profile employed during the VTND measurements must be clearly provided. In Figure 3, the change in lattice parameters at 300 °C suggests that the structure had not reached thermal equilibrium prior to the subsequent scan at 400 °C. To ensure meaningful analysis, neutron scans should be performed only after confirming structural stabilization at each temperature step.\n7. As XPS is inherently semi-quantitative, it is not suitable for accurately benchmarking stoichiometry. Therefore, the use of a standard reference sample with a well-defined composition is essential for calibrating TGA data, which plays a central role in quantifying oxygen exchange. Moreover, TGA analysis must be preceded by rigorous pre-oxidation and proper calibration of the sample. Without these critical steps, the resulting data may lead to misinterpretations of the material’s true oxygen storage capacity and redox behaviour.", "reviewer_2": "Useful extension of examination of ceria based oxides for intermediate temperature thermochemical productions of oxygen and hydrogen that selects elements that render ceria more readily reducible like PrxCe1-xO2-y and ZrxCe1-xO2-y. While the authors reference some of this work, I would ask them to reference PrxCe1-xO2-y given the similarity to the system chosen in this study. That being said, this represents examination of an additional interesting and promising offshoot of the others offering lower temperature operation, albeit some dangers in going too far in reduction and generating second phases that may create sluggish reoxidation pathways.\nMy major problems with the manuscript are suspect conductivity data and incorrect defect/transport models. To begin with, the general trends of conductivity vs pO2 are not unreasonable. However the abrupt shift from an ~1/8th slope in the log/log plot at 500C and above to ~1/4 at 475C and below makes no sense. Defect equilibria do not undergo such step changes over such small steps in temperature. The authors need to investigate what caused such a dramatic change in pO2 dependence.\nThe other, even more serious issue is there analysis of the defect equilibria and its impact on electron transport. In lines 184 and 185, they suggest a small polaron hopping model for electron transport similar to that ealier reported for PrxCe1-xO2-y in which electrons can hop from occupied Pr3+ ions to nearby unoccupied Pr4+ ions (e.g S. R. Bishop, et al, Electrical Conductivity and Defect Equilibria of Pr0.1Ce0.9O2-δ, Physical Chemistry Chemical Physics 13, 10165-10173 (2011)). Here the authors introduce 3 oxidation states for Pr 2,3 & 4+. The small polaran model assumes only 2 oxidation states and there is no reason to assume that Pr2+ exists, particularly if the crystal structure remains fluorite. The defect model needs to be rethought and redone.\nSome specific comments:\nLine 180: states in text: Figure 5(a) indicates that PZO is a semiconductor, i.e. conductivity increases with T. Yes but so does ionic conductivity!\nLine 190: Should be Pr3+ No evidence of Pr2+\nIn eq. 6 mixing up concentrations of defects [VO] with fractions of sites (cid:1). Not at all clear that Zr should be treated as an aliovalent element since fluorite structure is the reference.\nRecommendaton: Major revisions."}, "author_response": "Response to Reviewer’s Comments\nWe sincerely thank the reviewers for the thorough and constructive feedback, which has greatly\nhelped us enhance the clarity and impact of our work. In response to the comments, we have\ncarefully revised the manuscript, with all modifications clearly highlighted in the updated version.\nBelow, we provide detailed, point-by-point responses to the reviewers’ comments.\nReviewer #1:\n1. What are the maximum and minimum values of oxygen non-stoichiometry (δ) that PZO can\naccommodate without compromising its crystallographic stability? A precise understanding of δ\nboundaries under both oxidizing and reducing conditions is essential for evaluating and\noptimizing the redox performance of PZO. Currently, the lack of such data limits our ability to\nbenchmark PZO against state-of-the-art redox materials and to optimize its operational\nparameters for improved energy efficiency.\nReply: We appreciate the reviewer’s insightful comments. To address these points, we have\nconducted several new experiments as part of the revision:\n1. Thermogravimetric analysis (TGA) under a wider range of pO conditions;\n2\n2. Ex-situ XRD characterization of PZO samples exposed to different temperatures\nand pO ;\n2\n3. High-temperature XRD measurements performed under both air and vacuum.\nThese new experiments have resulted in two key relationship diagrams for the PZO system:\n1. Phase-T-pO diagram\n2\n2. δ-T-pO diagram\n2 2\nsingle-phase PZO stability. It clearly shows that as pO decreases, T range for PZO stability\n2\nalso shifts to lower values.\nIn addition, we have also constructed the δ-T-pO diagram of PZO and compared it with\n2\nthe benchmark CeO system in Figure R2. This comparison highlights PZO’s significant\n2-δ\nadvantage in oxygen nonstoichiometry (δ) within the intermediate temperature regime.\nFigure R2. The -T-pO Diagram of PZO system.\nmanuscript (pages 9 and 12, respectively).\n2. Although the manuscript emphasizes oxygen non-stoichiometry, it overlooks the potential role\nof Pr and Zr cation vacancies in influencing redox behavior. These defects may significantly\naffect oxygen mobility and catalytic performance. A discussion and supporting data regarding\ncationic defect chemistry are needed to provide a more comprehensive understanding of PZO's\nredox mechanism.\nReply: In response to the reviewer’s comments, we have revisited and significantly revised\nour original defect chemistry model. In the updated model, we adopt fluorite-structured\nPrO as the lattice reference framework, with Pr4+ as the base oxidation state of Pr-ion.\nFurthermore, based on variable-temperature neutron diffraction (VTND) results, which\nindicate that Pr and Zr occupy the same crystallographic site, we have included Pr3+\nsubstituting for Zr4+ as an ionic defect. This substitution creates a negatively charged\nantisite defect, denoted as 𝐏𝐫′ , which is incorporated into the charge neutrality\nZr\nrequriement.\nIn addition, the revised model considers free electrons and electron holes as intrinsic charge\ncarriers, not localized on Pr3+ that has a stable electronic configuration (Xe4f2). This new\ndefect chemistry model provides an excellent fit to the experimental conductivity-pO -T\n2\ndata (see revised Figure 7). From the model, we also derived the thermodynamic\nparameters of all defect reactions considered, including equilibrium constants, enthalpy\nchange (ΔH), and entropy change (ΔS) (see Figure S12 of the Supplementary Information).\nTo examine the potential involvement of cation vacancies, we performed hybrid DFT\ncalculations with spin-orbit coupling interactions to accurately capture the magnetic\nground state and electronic structure of PZO (see pages 14–15 of the Supplementary\nInformation for details). The results reveal that oxygen vacancy formation is energetically\nfavorable even under O-rich conditions, whereas Pr vacancy formation is highly\nunfavorable. Moreover, the Pr-on-Zr antisite defect also exhibits relatively low formation\nenergies in both its neutral and negatively charged states.\nTherefore, in the revised defect chemistry model, we consider oxygen vacancies, Pr3+\nsubstituting for Pr4+ and Pr3+ substituting for Zr4+ as the dominant ionic defects, while\nintrinsic free electrons and electron holes are considered electronic defects.\n3. Despite the detailed Rietveld refinement of VTND data—capturing temperature-dependent\nchanges in lattice parameters, bonding, and oxygen vacancies—reciprocal space mapping (RSM)\nis crucial. RSM can reveal localized strain, defects, and phase transitions, which are\nindispensable for assessing the material’s thermal stability, defect dynamics, and catalytic\nperformance under operational conditions. Unfortunately, such information is missing in this\nmanuscript.\nReply: We appreciate the reviewer’s suggestion regarding the use of reciprocal space\nmapping (RSM). The RSM technique is indeed well-suited for characterizing single crystals\nor highly textured samples when using constant-wavelength X-rays and two-dimensional\ndetectors. However, in our view, it is not particularly informative for powder or\npolycrystalline samples with random orientations, such as those investigated in this study.\nMoreover, obtaining relevant information is not feasible with our time-of-flight neutron\ndiffraction setup.\n4. The current characterization strategy lacks sufficient insight into local atomic environments\nand defect structures. A thorough investigation using XAS would allow quantification of local\nlattice distortions and vacancies (oxygen, Pr, and Zr), enabling a direct correlation between\natomic-scale structure and macroscopic redox properties. This is important for identifying active\nsites and understanding structural transformations during cycling.\nReply: We agree with the reviewer that X-ray absorption spectroscopy (XAS)\nmeasurements would further enhance our understanding of the local environment and\ndefect structures. However, due to the extended beamline access time (approximately one\nyear), we were only able to perform laboratory-based transmission-type XANES\nmeasurements in this study. Although the laboratory setup did not provide sufficient\nresolution to resolve detailed local atomic structures, it did allow us to determine the\naverage oxidation state of Pr-ions in PZO, assisted by several reference samples. The\ndetailed results are presented in Figure S7. The measured average oxidation state of Pr in\nPZO under ambient conditions is approximately +3.5, consistent with the composition\nPr Zr O identified from VTND and preliminary XPS analyses.\n0.75 0.25 1.83\nWhile the laboratory XAS results did not yield the desired local structural insights, the\nVTND experiments provided precise crystallographic information, including crystal\nsymmetry, atomic positions of Pr, Zr, and O, as well as Pr/Zr ratio and oxygen vacancy\nconcentration, from the local coordination between Pr-Pr, Pr-Zr and Pr(Zr)-O is easily\nresolved. These crystallographic parameters have been used to inform our defect chemistry\nmodeling, DFT calculations, and charge transport analysis.\n5. The temperature profile employed during the VTND measurements must be clearly provided.\nIn Figure 3, the change in lattice parameters at 300 °C suggests that the structure had not reached\nthermal equilibrium prior to the subsequent scan at 400 °C. To ensure meaningful analysis,\nneutron scans should be performed only after confirming structural stabilization at each\ntemperature step.\nReply: In response to the reviewer’s comments, we carefully revisited both our VTND and\nTGA data. Our analysis indicates that the variations in lattice parameters (reflecting\nchanges in oxygen content) observed between 300 and 500 °C are not attributable to\ntemperature nonequilibrium. In both experiments, the thermocouples were positioned in\nclose proximity to the samples, and each temperature point included a one-hour dwell\nperiod to ensure thermal equilibrium. Therefore, the observed anomalies are likely sample-\nrelated rather than instrumental.\nA more detailed examination of the VTND and TGA data further reveals that oxygen\nrelease occurs more rapidly within the 300-500oC range than at higher temperatures\n(>500oC). Table R1 summarizes the δ changes over consecutive 200°C intervals,\nhighlighting this trend.\nTable R1. Change of  in different temperature ranges.\n Temperature  in air  in air\n(oC) (TGA) (VTND)\n300-500 0.0198 0.0203\n500-700 0.0149 0.0157\n700-900 0.0140 0.0148\nAs shown in Figure 7, the conductivity vs. pO plots at different temperatures also depict a\n2\nchange in slope from below to above 500oC in the high-pO region. By incorporating this\n2\nobserved δ variation into our revised defect chemistry model, we are now able to reproduce\nthe slope change in the experimental data. The discussion of this updated defect chemistry\nmodel has been expanded and highlighted in the revised manuscript (pages 13-15).\n6. As XPS is inherently semi-quantitative, it is not suitable for accurately benchmarking\nstoichiometry. Therefore, the use of a standard reference sample with a well-defined composition\nis essential for calibrating TGA data, which plays a central role in quantifying oxygen exchange.\nMoreover, TGA analysis must be preceded by rigorous pre-oxidation and proper calibration of\nthe sample. Without these critical steps, the resulting data may lead to misinterpretations of the\nmaterial’s true oxygen storage capacity and redox behaviour.\nRely: We agree with the reviewer regarding the limitations of XPS in accurately\nquantifying stoichiometry and the importance of using reference samples for reliable\ncalibration. In this study, XPS was employed only as a preliminary qualitative check rather\nthan for determining . The oxygen stoichiometry at room temperature was determined by\nneutron diffraction and complemented by XPS and XANES analyses. The dependence of \non T and pO as shown in Figure 5 was further obtained from TGA and VTND.\n1. Useful extension of examination of ceria based oxides for intermediate temperature\nthermochemical productions of oxygen and hydrogen that selects elements that render ceria more\nreadily reducible like PrxCe1-xO2-y and ZrxCe1-xO2-y. While the authors reference some of\nthis work, I would ask them to reference PrxCe1-xO2-y given the similarity to the system chosen\nin this study. That being said, this represents examination of an additional interesting and\npromising offshoot of the others offering lower temperature operation, albeit some dangers in\ngoing too far in reduction and generating second phases that may create sluggish reoxidation\npathways.\nReply: In accordance with the reviewer’s suggestions, we have added additional references\nrelated to Pr Ce O and Zr Ce O systems to the discussion section (pages 17–18) of\nx 1-x 2- x 1-x 2-\nthe revised manuscript. We have also included a new paragraph comparing  (i.e.,\nreducibility) of Pr-doped CeO systems with our PZO material. In the revised text, we\n2\nfurther discuss the role of Pr3+ substitution in CeO in stabilizing oxygen vacancies, thereby\n2\nlowering the reduction enthalpy and enhancing redox kinetics at moderate temperatures.\n2. My major problems with the manuscript are suspect conductivity data and incorrect\ndefect/transport models. To begin with, the general trends of conductivity vs pO2 are not\nunreasonable. However the abrupt shift from an ~1/8th slope in the log/log plot at 500C and\nabove to ~1/4 at 475C and below makes no sense. Defect equilibria do not undergo such step\nchanges over such small steps in temperature. The authors need to investigate what caused such a\ndramatic change in pO2 dependence.\nReply: The reviewer’s points are well taken. To address this concern, we revisited our TGA\nand VTND data and observed an accelerated increase in oxygen nonstoichiometry (δ)\nbetween 300 and 500oC compared to temperatures above 500oC (see Table R1 below).\nTable R1. Change of  in different temperature ranges.\n Temperature  in air  in air\n(oC) (TGA) (VTND)\n300-500 0.0198 0.0203\n500-700 0.0149 0.0157\n700-900 0.0140 0.0148\nA previous study on the influence of the Pr4+/Pr3+ ratio on ionic transport has also reported\na similar behavior (DOI: 10.1016/j.ijhydene.2016.02.152). Therefore, we speculate that the\nobserved slope change is likely associated with the different rates of oxygen release below\nand above 500oC.\nBy incorporating this δ variation into our revised defect chemistry model, we successfully\nreproduce the slope change observed between the data sets above and below 500oC. The\ndetailed description of the revised defect chemistry model is provided in the revised\nmanuscript (pages 12-15) and in Figure S12 of the Supplementary Information.\n3. The other, even more serious issue is there analysis of the defect equilibria and its impact\non electron transport. In lines 184 and 185, they suggest a small polaron hopping model for\nelectron transport similar to that earlier reported for PrxCe1-xO2-y in which electrons can hop\nfrom occupied Pr3+ ions to nearby unoccupied Pr4+ ions (e.g S. R. Bishop, et al, Electrical\nConductivity and Defect Equilibria of Pr0.1Ce0.9O2-δ, Physical Chemistry Chemical Physics\n13, 10165-10173 (2011)). Here the authors introduce 3 oxidation states for Pr 2,3 & 4+. The\nsmall polaron model assumes only 2 oxidation states and there is no reason to assume that Pr2+\nexists, particularly if the crystal structure remains fluorite. The defect model needs to be\nrethought and redone.\nReply: We agree with the reviewer that the presence of Pr2+ is highly unlikely. In the\nrevised defect chemistry model, we use PrO as the reference lattice framework, where\n2\noxygen loss leads to the reduction of Pr4+ of Pr3+. However, due to the highly stable\nelectronic configuration of Pr3+ ([Xe]4f2), Pr3+ is not considered a host for additional\nelectrons (e.g. localized small polarons such as in the case of Co3+/Co4+ or Fe3+/Fe4+ in\nperovskite structure). Instead, our defect model includes intrinsic free electrons and\nelectron holes as electronic defects, together with oxygen vacancies, Pr3+ substituting for\nZr4+ and Pr3+ substituting for Pr4+ as the ionic defects.\nSome specific comments:\nLine 180: states in text: Figure 5(a) indicates that PZO is a semiconductor, i.e. conductivity\nincreases with T. Yes but so does ionic conductivity!\nReply: In response to the reviewer’s comments, we have revised the corresponding\nstatement to include the activation energy range of 0.34–0.43 eV, which is relatively low for\npure oxide-ion conduction. Therefore, given both the high concentration of oxygen\nvacancies and the low activation energy, PZO is likely a mixed oxide-ion and electronic\nconductor.\nLine 190: Should be Pr3+ No evidence of Pr2+\nReply: The reviewer is correct. We have removed Pr2+ from our revised defect model.\nIn eq. 6 mixing up concentrations of defects [VO] with fractions of sites 𝛿. Not at all clear that Zr\nshould be treated as an aliovalent element since fluorite structure is the reference.\nReply: The reviewer’s comment is well taken. We have corrected and highlighted it in the\nrevised defect chemistry model. In the revised defect chemistry model, Zr is treated as an\nintegral component of the fluorite lattice, consistent with the neutron diffraction data. Pr3+\nis considered to substitute for Pr4+ and Zr4+ within this framework. This clarification has\nbeen explicitly added to the revised manuscript on page 13-15."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have addressed most of the previous comments and have made the necessary improvements to the manuscript accordingly. The newly added Phase–T–pO₂ diagram (Figure 4) and δ–T–pO₂ diagram (Figure 6) provide valuable new insights, clearly delineating the material’s redox operating boundaries and enhancing the paper’s overall significance. However, several important details in the Experimental Methodology section require clarification to ensure reproducibility and accurate interpretation of the results. I would suggest the authors further clarify the following points:\n(1) The authors mention the use of “concentrated nitric acid (99.99 wt%)” diluted with DI water (1:9 volume ratio). A concentration of 99.99 wt% corresponds to fuming nitric acid, which is highly hazardous and uncommon for standard Pechini synthesis, particularly when diluted directly. Typically, concentrated nitric acid is ~68–70 wt%. This should be clarified.\n(2) In the “Sample preparation” section, the material was “dry pressed into φ1″ pellets and sintered.” However, in the “Thermochemical performance evaluation” section, it is stated that “~0.5 g of fcc-PZO powder was loaded.” Were the sintered pellets ground and sieved prior to loading into the reactor? If so, please specify the final particle size range used in the fixed-bed reactor. This information is critical for assessing potential heat and mass transfer limitations in kinetic studies. If powder was used for testing, please clarify the rationale for pellet sintering during synthesis.\n(3) The procedure for phase stability determination states that “we exposed the as-synthesized fcc-PZO samples under different T and pO₂, followed by quenching the samples.” It is recommended that the quenching process be described in detail in the Experimental Methods section.\n(4) In the XRD description, “step size of 5° min⁻¹” is reported. This value represents a scan speed, not a step size. Please correct the terminology to “scan rate” or clarify the actual step size (e.g., 0.02°) and dwell time.\n(5) Please check the temperature axis in Figure S5. It appears that some XRD spectra are duplicated, with the label “25 °C” appearing twice.", "reviewer_2": "I appreciate the authors attempts to clarify the defect and transport model for Pr3ZrO8 (PZO) and explain the source of the jump in pO2 dependences of the electrical conductivity just above and below 500C. Certainly, establishing the phase stability diagram of the PZO system as illustrated in Fig. 4 is very valuable. Also, Figure 6 shows that most of oxygen loss occurs below 500C, then it begins to saturate suggesting that simple defect relations based on mass action no longer apply. This would explain the weak pO2 dependences observed at the higher temperatures. See lines 258-259: This finding agrees with the experimental observation (Figure S8) that there is more oxygen release per temperature gradient (delta T) over 300 to 500oC than 500 to 900oC.\nUnfortunately, the defect and transport modeling is still, in my view incorrect. My detailed explanation of the problems with the authors' analysis is described in the attached document along with references that should be helpful in revising the models to be more appropriate. I also include a listing of more minor required corrections."}, "author_response": "Response to Reviewer’s Comments\nDear Editor,\nWe sincerely thank the reviewers for their thorough and constructive feedback, which has been\ninvaluable in further improving the quality and impact of our manuscript. Based on these\ncomments, we have revised the paper accordingly, with all modifications clearly highlighted\nin the updated version.\nBelow, we provide detailed, point-by-point responses to the reviewers’ comments.\nReviewer #1:\nComment-1: The authors mention the use of “concentrated nitric acid (99.99 wt%)” diluted\nwith DI water (1:9 volume ratio). A concentration of 99.99 wt% corresponds to fuming nitric\nacid, which is highly hazardous and uncommon for standard Pechini synthesis, particularly\nwhen diluted directly. Typically, concentrated nitric acid is ~68–70 wt%. This should be\nclarified.\nResponse: We appreciate the reviewer’s observation. In the revised manuscript, we have\nclarified that the nitric acid used in this study was commercial 70 wt% nitric acid, not\nfuming nitric acid. The value “99.99%” in the original text referred to the purity of the\nmetal nitrate precursors (Pr(NO ) ·6H O and ZrO(NO ) ·xH O), rather than to the nitric\n3 3 2 3 2 2\nacid itself.\nThis correction has been made and highlighted on page 26 of the revised manuscript.\nComment-2: In the “Sample preparation” section, the material was “dry pressed into φ1″ pellets\nand sintered.” However, in the “Thermochemical performance evaluation” section, it is stated\nthat “~0.5 g of fcc-PZO powder was loaded.” Were the sintered pellets ground and sieved prior\nto loading into the reactor? If so, please specify the final particle size range used in the fixed-\nbed reactor. This information is critical for assessing potential heat and mass transfer limitations\nin kinetic studies. If powder was used for testing, please clarify the rationale for pellet sintering\nduring synthesis.\nResponse: The PZO samples were synthesized from high-purity nitrate precursors using\nthe conventional Pechini method. After auto-ignition at ~200 °C, the resulting powder was\ndry-pressed into 1″ pellets and sintered at 1050 °C for 10 hours to ensure single-phase\nformation. The sintered pellets were then ground and ball-milled into a fine powder with\nan average particle size of approximately 5.3 μm, which was used for fixed-bed\nthermochemical testing.\nThis clarification has been added and highlighted on page 26 of the revised manuscript.\nComment-3: The procedure for phase stability determination states that “we exposed the as-\nsynthesized fcc-PZO samples under different T and pO₂, followed by quenching the samples.”\nIt is recommended that the quenching process be described in detail in the Experimental\nMethods section.\nResponse: After exposure to the target temperature and pO , fcc-PZO samples were\n2\nrapidly removed from the furnace and immediately quenched in air at room temperature\nto preserve the high-temperature phase.\nWe have added and highlighted this description on page 28 of the revised manuscript.\nComment-4: In the XRD description, “step size of 5° min⁻¹” is reported. This value represents\na scan speed, not a step size. Please correct the terminology to “scan rate” or clarify the actual\nstep size (e.g., 0.02°) and dwell time.\nResponse: We appreciate the reviewer’s attention to detail. The XRD measurements were\nconducted at a scan rate of 5° min⁻¹.\nThe terminology has been corrected and highlighted on page 27 of the revised manuscript.\nComment-5: Please check the temperature axis in Figure S5. It appears that some XRD spectra\nare duplicated, with the label “25 °C” appearing twice.\nResponse: Thank you for pointing this out. The “25 °C” label appears twice in Figure S5\nintentionally. The first “25 °C” in the pattern (near the end of the figure) represents the\nstarting temperature, while the second (near the beginning) corresponds to the final\ntemperature after thermal cycling.\nWe have added a note in the Figure S5 caption to clarify this distinction.\nReviewer #2:\nComment-1: While the stoichiometric fluorite structure of MO2 requires M to be 4+ valent,\nbecause Pr reduces so readily to 3+ (note reduction enthalpy derived in this study is nearly zero\n(0.02 -0.03 eV (line 192)), one expects to find it largely in the 3+ state even at relatively high\npO2 and reduced temperatures. Indeed, this is the reason the authors chose this material for\nthermochemical reduction.\nIn addition to the intrinsic ease of reduction of Pr from 4+ to 3+, the addition of the smaller Zr\nion leads to further reductions in reduction enthalpy- Please reference: D. Chen,et al, Defect\nand Transport Model of Ceria-zirconia Solid Solutions:Ce0.8Zr0.2O2-δ - an Electrical\nConductivity Study, Chem. Mater. 26 [17], 5143–5150 (2014).\nResponse: We thank the reviewer for this insightful comment. We emphasize that the\nvariation of [Pr³⁺] in the fcc-PZO system as a function of T and pO is distinct from that\n2\nin CeO -Pr O and CeO -ZrO systems previously studied. A replot of Figure 5(a) in\n2 2 3 2 2\nterms of lattice Pr3+ concentration ([Pr³⁺], see below) indicates that approximately 25%\nPr4+ ( or 75%Pr3+) remains even at 900 °C under N . We propose that substitution of\n2\nsmaller Zr4+ ions on the Pr-lattice hinders Pr4+→Pr3+ reduction by impeding electron\ntransfer between Pr sites - a steric hindrance effect.\nThe low activation energy (0.02-0.03 eV) obtained from oxygen nonstoichiometry\nvariations with T (as reported in line 192) reflects the ease of oxygen vacancy formation\nin PZO and may not directly correspond to the [Pr³⁺] concentration.\nWe thank the reviewer for sharing the work of D. Chen et al. (Chem. Mater. 26, 5143–\n5150, 2014). Based on insights from this reference, we have expanded the discussion on\nthe role of Zr4+ in modulating [Pr3+] on page 11 of the revised manuscript.\nThe new plot shown below has been added as new Figure S12.\nNew Figure S12. A replot of Figure 5(a) with [Pr3+] as a function of T and pO .\nintermediate pO2s between ~ 10-10 and 10-3 atm in Fig. 7. In the closely related PrxCe1-xO2-δ\nsystem, this conductivity plateau is ascribed to ionic conductivity due to the high oxygen\nvacancy concentration induced by Pr reduction - [𝑃𝑟Ce] = 2[𝑉o∙∙]. The reason it is largely\nionic is because when nearly no Pr4+ sites exist, small polaron hopping of electrons or in this\ncase holes is blocked. This is contrary to the assumption of the authors’ defect and transport\nmodel assuming “intrinsic electron and hole conduction. The increasing conductivity above 10-\n3 atm is consistent with increasing formation of Pr4+ sites upon increasing levels of oxidation\nleading to increased electron hopping and thereby electronic conduction. Similar phenomena\nwere observed in the PrxCe1-xO2-δ system. Indeed, the activation energies in this high pO2\nregion of ~ 0.4 eV is very similar to that observed in the PrxCe1-xO2-δ system. See reference:\nS. R. Bishop, et al, Electrical Conductivity and Defect Equilibria of Pr0.1Ce0.9O2-δ, Physical\nChemistry Chemical Physics 13, 10165-10173 (2011).\nFurthermore, if the electron-hole generation were intrinsic, it would not show a pO2\ndependence, nor is the estimated band gap of ~1.1±0.1 eV at 0K large enough to explain the\nred color induced by transitions from the O2p valence band to the Pr 4f band – see J.-J. Kim,\net al, Optically Derived Energy Band Gap States of Pr in Ceria, Solid State Ionics. 225, 198-\n200 (2012).\nResponse: We agree with the reviewer that describing the electronic conduction\nmechanism using intrinsic electron and hole terms alone is inadequate for fcc-PZO. The\nhole and electron generation reactions proposed in the manuscript are both pO -\n2\ndependent:\nAt high pO range: 𝟏 𝐎 +𝑽∙∙ ⇌ 𝐎𝐗 +𝟐𝒉∙ (5)\n2 𝟐 𝐎 𝐎\n2 𝐎 𝟐 𝐎\nPr\nthe defect chemistry model. The measured activation energy (Eₐ ≈ 0.45 eV) associated\nwith electrical conductivity aligns closely with half of the estimated intrinsic band gap\n(~1.1 eV at 0 K under defect-free conditions; see SI, Figures S10–S11).\nThe pO -indepdent conductivity plateau in the intermediate range (10-10–10-3 atm) is a\n2\ncharacteristic of ionic conduction and can be analytically explained by the charge\nneutrality condition:\n[𝐏𝐫′ ]+[𝒆′] = 𝟐[𝑽∙∙ ]+[𝒉∙] (7)\n𝐏𝐫 𝐎\nUnder intermediate pO , where [𝐏𝐫′ ] ≫ [𝒆′] and 𝟐[𝑽∙∙ ] ≫ [𝒉∙] , the above charge\n2 𝐏𝐫 𝐎\nneutrality condition can be simplified into:\n[𝐏𝐫′ ]𝟐[𝑽∙∙ ]\n𝐏𝐫 𝐎\nThus, the concentration of oxygen vacancies is governed by [Pr³⁺], where\n[𝐏𝐫′ ] = 𝟎.𝟕𝟓−[𝐏𝐫 ]\n𝐏𝐫 𝐏𝐫\nWhile the above relationships are derived with assumptions, all results presented in the\npaper were obtained numerically from full defect-chemical equilibrium calculations\nwithout assumptions.\nThese clarifications along with suggested references have been added and highlighted on\npages 7, 11, 13-15 of the revised manuscript.\nComment-3: Interestingly there is a weakly increasing conductivity below ~ 10-10 atm in Fig.\n7. This does suggest the beginning of some reduction of Pr to the 2+ oxidation state, perhaps\nnot so surprising given that Pr3+ ([Xe]4f2) and so only requires removal of one of the\nremaining 4f electrons, likely feasible at highly reducing conditions.\nResponse: We appreciate the reviewer’s comment. In our initial defect model, we\nconsidered Pr2+ as a potential free electron carrier via Pr3+/Pr2+ charge transfer with Pr3+\nas the reference framework and Pr4+ as the electronic hole. Following reviewer feedback\non the physical possibility of Pr2+, in the first round, we conducted an extensive literature\nreview and found that Pr2+ ([Xe]4f3) is energetically unfavorable and readily oxidized\nback to Pr³⁺ under most conditions. Among all oxidation states of Pr-ions, Pr3+ is the most\nstable, followed by Pr4+. The n-type conductivity observed at low pO , therefore, can only\n2\narise from oxygen lattice reduction and oxygen vacancy formation rather than from\nPr3+/Pr2+ redox couple.\nMinor Corrections:\nComment (Line 100): fluorite structured not fluoride\nResponse: Corrected “fluoride” to “fluorite”.\nComment (Line 122): Pr0.75Zr0.25O1.83 at RT\nResponse: Corrected to “Pr Zr O at RT”.\n0.75 0.25 1.83\nComment (Line 125): retains\nResponse: Corrected to “retains”.\nComment (Lines 134-135):Chemical expansion associated with formation of Pr3+. Authors\nshould Reference: Bishop et al., J. Euro. Ceram. Soc. 2011, 31, 2351-2356; Marrocchelli et al.,\nPhys. Chem. Chem. Phys. 2012, 14, 12070-12074.\nResponse: Added the suggested references (Bishop et al., J. Eur. Ceram. Soc. 2011;\nMarrocchelli et al., Phys. Chem. Chem. Phys. 2012) to the discussion on page 7.\nComment (Line 171): are provided\nResponse: Corrected to “are provided”.\nComment (Line 236): Pr doesn’t occupy Zr sites, it just occupies its own sites; ZrO2 is the\nminority additive. Therefore, with respect to Equation 11 𝑛𝑜 𝑛𝑒𝑒𝑑 𝑓𝑜𝑟 [Pr_Zr']\nResponse: Removed [Pr ′] from the defect model per reviewer’s comment, and\nZr\nrecalculated defect concentrations and thermodynamic/transport properties. The new\nresults are shown in Figure 7(a) and Figure S13.\nComment (Line 260): Change to: Thermochemical performance of PZO\nResponse: Changed to “Thermochemical performance of PZO”.\nComment (Line 273): do not\nResponse: Corrected to “do not”.\nComment (Line 307): Pr doping on Zr sites make no sense; it’s the reverse as stated that Zr is\nused as dopant to stabilize PrOx from becoming too reduced.\nResponse: Revised the statement to clarify that Zr acts as a dopant stabilizing PrO (pages\nx\n13–15).\nComment (312): is more O"}, {"round": 3, "reviewer_comments": {"reviewer_1": "The authors have addressed my comments satisfactorily. I am now happy to recommend the revised manuscript for publication in Nature Communications.", "reviewer_2": "I appreciate the efforts of the authors to respond to my concerns regarding their interpretation of the defect and electrical properties of their Pr3ZrO8-δ material. While some clarifications have been made, there remain some problmes with their analysis that I summarize in the following.\nLines 201-203: the observed stabilization of the fluorite phase for PrO2-x by partial substitution of fixed valent Zr cannot be related to a transport issue, i.e. blocking electron transfer between Pr4+ and Pr3+. This is a thermodynamic not kinetic feature, i.e. the increased stability against reduction is due to substitution of fixed valent Zr4+. The authors should correct this sentence.\nLine 230 if Pr4+ is the base oxidation state, standard defect notation should be PrPrx or just PrPr without a superscript. The symbol that the authors use is confusing.\nLines 232-233. The authors insist that Pr3+ is a highly stable oxidation state and therefore the localized small polaron state is not appropriate. At the same time, they point out in line 199 that there is ~75% Pr3+ present in the fcc-PZO under 900oC and N2 . Clearly a significant fraction of Pr presumably remains in the 4+ state. In any case, whether one reaches a condition where most of a multivalent ion is one state or the other has nothing to do with the degree of electron localization but rather with the electronic band width and the 4f band is known to be quite narrow.\nEq 6; e’ - prime should be superscript for clarity\nRegarding the analysis of the log conductivity vs log pO2 curve in Fig. 7, I am afraid it still does not make sense to me. If we examine the defect reaction in the blue region at the top of the figure, it refers to the reduction of the material by removing oxygen from the lattice to form oxygen vacancies and converting 2 Pr ions from 4+ to 3+. This should show a show the conductivity following a P_(O_2)^(-1⁄6) dependence not pO2 independence. On the other hand, they conclude (see Eq 8’) that the concentration of Pr3+ is independent of pO2 and thus the oxygen vacancy concentration as well, explaining the pO2 independence of the conductivity in this regime. They explain that this conductivity is strictly ionic although the activation energy in this regime of ~0.35 eV a)which is half the migration energy of oxygen vacancies in the best fluorite structured oxygen ion conductors and b) remains nearly the same in the regions at both low and high pO2 which is assigned to electronic carriers. My suspicion is that we have both high concentrations of electronic and ionic carriers, but the much higher electron mobility ensures that the conductivity is predominantly electronic even in this intermediate pO2 regime. Perhaps the problem is trying to describe the observed pO2 dependence based on defect chemical principles based on the dilute solution approximation. I hate to see this nice work held up due to problems with defect modeling which is not the main point of the work, rather its utility in photothermal water splitting. I suggest that they move this section to the supplementary section, note the low activation energies suggesting predominantly electronic conduction and the negative slopes at low pO2 consistent with extra electron generation under highly reducing conditions and positive slopes a high pO2 consistent with extra hole generation, but the exact defect analysis hindered by the high concentrations of defect species."}, "author_response": "Response to Reviewer’s Comments\nDear Editor,\nWe sincerely thank the reviewer 2 again for his/her thorough and constructive feedback. Based on\nthese comments, we have revised the paper accordingly, with all modifications clearly highlighted\nin the updated version.\nBelow, we provide detailed, point-by-point responses to the reviewer’s comments.\nReviewer #2:\nComment: Lines 201-203: the observed stabilization of the fluorite phase for PrO2-x by partial\nsubstitution of fixed valent Zr cannot be related to a transport issue, i.e. blocking electron transfer\nbetween Pr4+ and Pr3+. This is a thermodynamic not kinetic feature, i.e. the increased stability\nagainst reduction is due to substitution of fixed valent Zr4+. The authors should correct this\nsentence.\nReply: Per reviewer’s comment, we have changed the sentence to “likely due to its fixed-\nvalence substitution” on page 12 of the revised MS.\nComment: Line 230 if Pr4+ is the base oxidation state, standard defect notation should be PrPrx\nor just PrPr without a superscript. The symbol that the authors use is confusing.\nReply: We thank reviewer for pointing out this typo. We have corrected it in line 230 on page\n13 and make sure that all Pr4+ in the model is expressed as 𝑷𝒓× throughout the paper.\n𝑷𝒓\nComment: Lines 232-233. The authors insist that Pr3+ is a highly stable oxidation state and\ntherefore the localized small polaron state is not appropriate. At the same time, they point out in\nline 199 that there is ~75% Pr3+ present in the fcc-PZO under 900oC and N2 . Clearly a significant\nfraction of Pr presumably remains in the 4+ state. In any case, whether one reaches a condition\nwhere most of a multivalent ion is one state or the other has nothing to do with the degree of\nelectron localization but rather with the electronic band width and the 4f band is known to be quite\nnarrow.\nReply: We agree with the reviewer. Based on the comments, we have added and highlighted\na couple of paragraphs on page 13-14 of the revised MS.\nIn this new addition, we emphasize the mixed electron and oxide-ion conduction in fcc-PZO\nover a wide pO and T range. We also clarify why Pr O is a wide-band Mott insulator and\n2 2 3\nPrO is a narrow-band semiconductor with mixed conductivity.\n2-\nComment: Eq 6; e’ - prime should be superscript for clarity.\nReply: Per reviewer’s suggestion, we have corrected it to 𝒆′ in eq. (S2) and (S3) in the\nrevised SI after they were moved into SI section.\nComment: Regarding the analysis of the log conductivity vs log pO2 curve in Fig. 7, I am afraid\nit still does not make sense to me. If we examine the defect reaction in the blue region at the top\nof the figure, it refers to the reduction of the material by removing oxygen from the lattice to form\noxygen vacancies and converting 2 Pr ions from 4+ to 3+. This should show the conductivity\nfollowing a P_(O_2)^(-1⁄6) dependence not pO2 independence. On the other hand, they conclude\n(see Eq 8’) that the concentration of Pr3+ is independent of pO2 and thus the oxygen vacancy\nconcentration as well, explaining the pO2 independence of the conductivity in this regime. They\nexplain that this conductivity is strictly ionic although the activation energy in this regime of ~0.35\neV, a) which is half the migration energy of oxygen vacancies in the best fluorite structured oxygen\nion conductors and b) remains nearly the same in the regions at both low and high pO2 which is\nassigned to electronic carriers. My suspicion is that we have both high concentrations of electronic\nand ionic carriers, but the much higher electron mobility ensures that the conductivity is\npredominantly electronic even in this intermediate pO2 regime.\nReply: We agree with the reviewer that there are concurrent electronic conduction with\noxide-ion even in the intermediate pO regime. We have emphasized this mixed conductivity\n2\nreality on page 14 of the revised MS with additional discussion on the band structure and\nbandgap of Pr-oxides to support the assumption.\nPer reviewer’s following suggestion, we have also moved the majority of defect-chemistry\nmodeling section into the SI. In the revised defect model, we have removed the original eq.\n(8)’ (simplified charge neutrality) questioned by the reviewer and only used eq. (8) (now eq.\n(S4) of full charge-neutrality) in our numerical simulations.\nComment: Perhaps the problem is trying to describe the observed pO2 dependence based on defect\nchemical principles based on the dilute solution approximation. I hate to see this nice work held\nup due to problems with defect modeling which is not the main point of the work, rather its utility\nin photothermal water splitting. I suggest that they move this section to the supplementary section,\nnote the low activation energies suggesting predominantly electronic conduction and the negative\nslopes at low pO2 consistent with extra electron generation under highly reducing conditions and\npositive slopes a high pO2 consistent with extra hole generation, but the exact defect analysis\nhindered by the high concentrations of defect species.\nReply: We appreciate the reviewer’s constructive suggestion. In the revised MS, we have\nmoved the majority of the defect-chemistry modeling into the SI, and only briefly\nsummarized the key understanding of -pO -T behavior. In addition, the reviewer’s points\n2\non the limitation of “dilute solution approximation” and mixed electronic and oxide-ion\nconduction over the entire pO range have also been stressed in the shortened “electrical\n2\nconductivity section” on page 13-14."}, {"round": 4, "reviewer_comments": {"reviewer_2": "I find the revisions made by the authors to be adequate in responding to my earlier comments."}, "author_response": ""}]

Decision letter