Oxygen nonstoichiometry and thermodynamic characterization of Zr doped ceria in the 1573–1773 K temperature range

The thermodynamics and defect chemistry of Zr⁴⁺-doped ceria is investigated and discussed in regards to the efficiency of solar thermochemical redox cycles.

Abstract

This work encompasses the thermodynamic characterization and critical evaluation of Zr⁴⁺ doped ceria, a promising redox material for the two-step solar thermochemical splitting of H₂O and CO₂ to H₂ and CO. As a case study, we experimentally examine 5 mol% Zr⁴⁺ doped ceria and present oxygen nonstoichiometry measurements at elevated temperatures ranging from 1573 K to 1773 K and oxygen partial pressures ranging from 4.50 × 10^–3 atm to 2.3 × 10^–4 atm, yielding higher reduction extents compared to those of pure ceria under all conditions investigated, especially at the lower temperature range and at higher p _O2. In contrast to pure ceria, a simple ideal solution model accounting for the formation of isolated oxygen vacancies and localized electrons accurately describes the defect chemistry. Thermodynamic properties are determined, namely: partial molar enthalpy, entropy, and Gibbs free energy. In general, partial molar enthalpy and entropy values of Zr⁴⁺ doped ceria are lower. The equilibrium hydrogen yields are subsequently extracted as a function of the redox conditions for dopant concentrations as high as 20%. Although reduction extents increase greatly with dopant concentration, the oxidation of Zr⁴⁺ doped ceria is thermodynamically less favorable compared to pure ceria. This leads to substantially larger temperature swings between reduction and oxidation steps, ultimately resulting in lower theoretical solar energy conversion efficiencies compared to ceria under most conditions. In effect, these results point to the importance of considering oxidation thermodynamics in addition to reduction when screening potential redox materials.

Introduction

Solar-driven thermochemical redox cycles utilizing nonstoichiometric metal oxides are capable of splitting H₂O and CO₂ to produce H₂ and CO (syngas), the precursors to the catalytic synthesis of conventional liquid fuels.^1,2 Ceria (CeO₂) is currently considered a state-of-the-art material because it displays rapid oxidation and reduction kinetics and is morphologically stable over a range of temperatures and reduction extents.³ The two-step thermochemical cycle using CeO₂ as reactive intermediate is represented by:

Reduction at T _red:

1

Oxidation at T _ox:

CeO_2–δ + αH₂O + βCO₂ = CeO₂ + αH₂ + βCO 2

where α + β = δ. In the endothermic first step, eqn (1), ceria is reduced typically under an atmosphere of low oxygen partial pressure (p _O2) at elevated temperatures, generally T _red > 1573 K, where the process heat is delivered by concentrated solar energy. In an exothermic second step, eqn (2), the reduced ceria is re-oxidized with H₂O or CO₂ at lower temperatures, generally T _ox < 1573 K, to produce H₂ or CO. The oxygen nonstoichiometry (δ) achieved during reduction depends strongly on T _red and p _O2 in the system^4,5 and is directly related to the maximum amount of H₂/CO capable of being produced per mole ceria in the second step. As ceria is not consumed within the process, the net reactions are H₂O = H₂ + 1/2O₂ and CO₂ = CO + 1/2O₂. In contrast to direct thermolysis, two-step redox cycles bypass the separation of fuel and O₂ at high temperatures. Contrary to photochemical processes, solar thermochemical processes utilize the entire solar spectrum and thus offer a thermodynamically favorable path towards fuel production.

Since the reduction extent of ceria is generally lower than those obtained by other appropriate redox materials (e.g. ferrite, zinc oxide), its specific fuel production per mass is low.^3,6 This has a direct implication on efficiencies because they are largely dictated by the ratio of fuel produced to that of the thermal energy required to heat the oxide between oxidation and reduction steps.⁷ Therefore, in an attempt to increase reduction extents, 4+ valence dopants such as Zr^4+ 8–12 and Hf^4+ 8,13 are often introduced into the ceria lattice. Cycling studies of Zr⁴⁺ doped ceria have shown favorable reduction extents during reduction, but slower re-oxidation kinetics with CO₂ ^8,11 or H₂O¹⁴ were observed compared to pure ceria. Scheffe et al. ⁸ showed that reduction extents of Zr⁴⁺ and Hf⁴⁺ doped ceria increase with increasing dopant concentration up to 15 mol% whereas re-oxidation is generally slower than pure ceria but appeared to be strongly dependent on available surface area. Call et al. ¹¹ concluded that reduction extents increase for dopant concentrations up to 22.5 mol%. Le Gal et al. ¹⁴ observed increasing oxygen release up to dopant concentrations of 25 mol% Zr⁴⁺ but the reduced forms could not be completely re-oxidized with steam at 1323 K. In summary, most of the above studies report consistent results, namely increasing reduction extents with 4+ valence dopant concentration but at the same time slower oxidation kinetics. Comparison between different works is difficult because the detailed experimental conditions (e.g. particle size) are generally not reported or controlled, and it is not clear from these studies whether thermodynamic limitations or inherent kinetics hinder the rates.

Thermodynamic studies have been performed at temperatures below the range of interest for thermochemical cycles. For example, Kuhn et al. ¹⁰ reported oxygen nonstoichiometric measurements of Zr⁴⁺ doped ceria at T ≤ 1273 K and dopant concentrations between 5 and 80 mol%. Shah et al. ¹⁵ reported measurements for Zr⁴⁺ concentrations of 19 and 75 mol% at T ≤ 1173 K and p _O2 ≤ 10^–10 atm. Very recently, Hao et al. ¹² published nonstoichiometric measurements at higher temperatures for Zr⁴⁺ dopant concentrations up to 20 mol% in the range T = 873 K to 1763 K and p _O2 ≈ 10^–27 atm to 1 atm. All three studies^10,12,15 indicate a higher oxygen nonstoichiometry of doped ceria compared to pure ceria, which increases with increasing dopant concentration up to 20 mol%, and derive enthalpy and entropy values slightly lower than those for pure ceria.^4,5,16,17

In this work, we evaluate the thermochemical performance of Zr⁴⁺ doped ceria by using 5 mol% as a case study. Oxygen nonstoichiometry is reported in the operation range of solar reactors (1573 K ≤ T _red ≤ 1773 K, 2.3 × 10^–4 atm < p _O2 < 4.50 × 10^–3 atm) for 5 mol% Zr⁴⁺ doped ceria (CZO_5) and undoped ceria (CeO₂). We develop appropriate defect models to describe the defect chemical equilibria and in turn extract partial molar thermodynamic properties (Δh _O, Δs _O and Δg _O). From such data coupled with thermodynamic data from the literature, we determine equilibrium hydrogen yields and theoretical solar-to-fuel energy conversion efficiencies for dopant concentrations as high as 20 mol%. This analysis allows a straightforward and quantitative methodology for evaluating the potential of Zr⁴⁺ doped ceria used in solar thermochemical redox cycles.

Experimental section

Synthesis technique and sample characterization

5 mol% Zr⁴⁺ doped CeO₂ (CZO_5) powder was synthesized by sol–gel method as described by Scheffe et al. ⁸ Briefly, Ce(NO₃)₃·6H₂O (Aldrich, catalog number 238538), ZrO(NO₃)₂·6.3H₂O (Aldrich, catalog number 243493) and dry citric acid (Merck, catalog number 818707) in aqueous solution were used to carry out the synthesis. The ratio of the metal cations to the citric acid was 1 : 1.5. CeO₂ powder was purchased from a commercial distributor (Aldrich, catalog number 211575). CeO₂ and CZO_5 powders were uniaxially cold-pressed at 5 tons and sintered at 1873 K under air atmosphere for 5 hours into ∼1250 mg dense cylindrical pellets. The approximate dimensions after sintering were 7 mm diameter and 5 mm height. The CZO_5 dopant concentration was measured by inductively coupled plasma mass spectrometry (ICP-MS) analysis and was 4.5 mol%. Powder X-ray diffraction (XRD) was performed in the Bragg Brentano geometry using Cu Kα radiation (Philips, PANalytical/X′Pert MPD/DY636, λ = 1.5406 Å, 2Θ = 20–100°, 0.01° s^–1 scan rate, 45 kV/20 mA output). Scanning electron microscopy (SEM) of the dense pellets were conducted on a TM-1000 Microscope (Hitachi, 15 kV accelerating voltage). XRD patterns and SEM images are shown in ESI.†

Experimental measurements

Oxygen nonstoichiometry (δ) was measured using a thermogravimetric analyzer (TGA, Setaram Setsys Evolution). Samples were suspended to the scale with a custom-made platinum hook to ensure good exposure to the purge gas and eliminate gas diffusion limitations. Special care was taken to ensure that reduction and oxidation reactions were not limited by gaseous mass transfer but by solid-state diffusion and/or surface reactions. The p _O2 of the surrounding gas atmosphere was controlled by mixing Ar (Messer, Argon 4.6) with an O₂–Ar mixture (Messer, 0.5% O₂ 5.0 in Ar 5.0). Gases were mixed with electronic mass flow controllers (Brooks, Model 5850TR, accuracy ±1%) with a constant total flow rate of 200 ml min^–1. The gas species and concentrations at the outlet were monitored by mass spectrometry (Pfeiffer Vacuum, OmniStar GSD 320). Temperature was varied between 1573 K and 1773 K and p _O2 between 4.50 × 10^–3 atm and 2.3 × 10^–4 atm. In all measurements, the sample mass (m _s) was equilibrated at a constant temperature and p _O2. Following each equilibrium measurement, the p _O2 was rapidly changed by adapting the O₂–Ar gas mixture, resulting in a temporal weight change of the sample due to evolving or uptaking of oxygen until a new equilibrium was reached. To correct for buoyancy, blank runs were performed with Al₂O₃ sintered pellets of same dimensions. An additional correction was applied for a small amount of sample sublimation (<0.04 wt%) observed above 1723 K.

Oxygen nonstoichiometry

An exemplary experiment showing the dynamics of the reduction (decreasing p _O2) and oxidation (increasing p _O2) of CZO_5 and CeO₂ at 1573 K and 1773 K is shown in Fig. 1(a). Initially, their weights were stabilized at a constant p _O2, followed by a rapid p _O2 decrease to initiate reduction. After stabilization at the new m _s, p _O2 is increased back to its initial value to commence oxidation. At 1573 K, the reduction and oxidation of CZO_5 are noticeably slower than those of CeO₂. However, at 1773 K, the kinetic rates are similar for both materials. If surface reactions are assumed not to be limiting – a reasonable assumption at these length scales – this would imply that the activation energy for ambipolar diffusion is higher in the case of CZO_5.

Fig. 1. (a) Mass change in wt% as a function of time for the reduction and oxidation of CeO₂ (black) and CZO_5 (blue) at T = 1773 K where p _O2 was changed between 3.0 × 10^–4 atm and 2.3 × 10^–4 atm (solid lines) and at T = 1573 K where p _O2 was changed between 8.1 × 10^–4 atm and 2.3 × 10^–4 atm (dotted lines). (b) Mass change in wt% as a function of time for the reduction and oxidation runs of CeO₂ (black) and CZO_5 (blue) at T = 1673 K and O₂ partial pressure range p _O2 = 4.50 × 10^–3–2.3 × 10^–4 atm. (c) Mass change in wt% as a function of time for all the reduction and oxidation runs of CeO₂ and CZO_5 in the temperature range T = 1573–1773 K and O₂ partial pressure range p _O2 = 4.50 × 10^–3–2.3 × 10^–4 atm.

Fig. 1(b) shows the mass change in wt% of CeO₂ and CZO_5 as a function of time for T = 1673 K for a broader range of p _O2 and Fig. 1(c) shows all the reduction and oxidation runs over all temperatures and p _O2. Samples were heated to 5 different set point temperatures followed by isothermal reduction and oxidation by stepwise changing p _O2. As seen, CZO_5 released more oxygen than CeO₂ under all measurement conditions. The much slower oxidation of CZO_5 at 1073 K agrees well with the observation that its activation energy for ambipolar diffusion is higher than CeO₂ (cf. Fig. 1(a) and discussion above). A total sublimated mass of 0.40 mg and 0.32 mg at 1773 K was observed for CeO₂ and CZO_5, respectively.

Oxygen nonstoichiometry is calculated according to:

3

where Δm _s is the relative weight loss at equilibrium, M _s is the molar mass of the sample and M _O the molar mass of O. Measured δ versus p _O2 of CeO₂ and CZO_5 for all temperatures investigated are shown in Fig. 2(a) and (b), respectively. Open symbols show δ measurements of this work whereas literature data are shown by closed symbols (Panlener et al. ⁴) and crossed symbols (Iwasaki et al. ¹⁸). Lines indicate defect models used to describe δ, presented in the following section. As seen, δ of CZO_5 is higher over the whole measurement range investigated compared to CeO₂. Improvement in oxygen release is highest at low T _red and high p _O2. For example, at T = 1623 K and p _O2 ≈ 4.50 × 10^–3 atm, the improvement is almost 90% per mole of oxide (δ = 0.010 for CZO_5 and δ = 0.0055 for CeO₂) and around 27% at T = 1773 K and p _O2 ≈ 2.3 × 10^–4 atm (δ = 0.042 for CZO_5 and δ = 0.033 for CeO₂). Nonstoichiometry of CZO_5 at 1573 K is not shown because the sample weight did not equilibrate completely within the allotted time due to slower kinetics. δ values of pure CeO₂ measured in this work are slightly higher than the values reported in literature,^4,18 especially towards higher p _O2. The reason for the discrepancy is not clear but may be related to sample impurities and sublimation. Panlener et al. ⁴ performed oxygen nonstoichiometry measurements based on thermogravimetric analysis over a broad range of p _O2 from 0.01 atm to 10^–23 atm between 873 K and 1773 K while Iwasaki et al. ¹⁸ performed measurements only at temperatures up to 1573 K.

Fig. 2. Measured δ (open symbols) of CeO₂ (a) and CZO_5 (b) for T = 1573 K to 1773 K and p _O2 = 4.50 × 10^–3 atm to 2.3 × 10^–4 atm and a comparison to literature data: Panlener et al.:⁴ closed symbols, Iwasaki et al.:¹⁸ crossed symbols. Lines indicate defect models used to describe δ.

Defect model

Defect models were used to describe the chemical equilibria of both CeO₂ and CZO_5. For small reduction extents (as small as δ = 0.01 for pure ceria and higher with dopant type and dopant concentration¹⁹) the reduction of ceria and doped ceria can be described in Kröger–Vink notation as:

4

where oxygen atoms on oxygen lattice sites () and cerium on cerium lattice sites () are in equilibrium with gaseous oxygen, doubly ionized oxygen vacancies () and electrons localized on cerium lattice sites (). Assuming there are no cluster formations between the various defects, δ can be described by:^10,20

5

which implies a slope of –1/6 when plotting log δ versus log p _O2.

For larger deviations from stoichiometry, the formation of oxygen vacancy–polaron associations should be accounted for, and is described as:

6

Assuming all defects form associations according to eqn (6),²⁰

7

As seen in the case of CeO₂ (Fig. 2(a)), the slope of log δ vs. log p _O2 best describing the data is close to –1/5, indicating that eqn (5) cannot adequately describe its defect equilibria, in agreement with previous investigations.^{4,16,19,21,22} A slope of –1/5 indicates that a combination of both defect models (eqn (4) and (6)) is needed to accurately describe ceria's defect chemistry, as evidenced by Otake et al. ¹⁹ who showed that the isolated defect model is only valid for very low nonstoichiometries (δ < 0.01). A slope of –1/6, on the other hand adequately describes the data of CZO_5 over the entire measurement range. This is consistent with observations of 3+ valence dopants such as Sm³⁺,^22,23 Gd^{3+ 22,24,25} and Y³⁺,¹⁹ but in such cases much higher concentrations are required to describe the measurement data with only a single defect model. For example, when doping ceria with 10 mol% Y³⁺, a single isolated defect model can only describe the data up to δ ≈ 0.02, whereas in the case of 20 mol% it is valid until δ ≈ 0.03. Here, with only 5 mol% Zr⁴⁺ a single model appears to adequately describe δ at least until δ ≈ 0.04.

The nonstoichiometry as a function of T and p _O2 may be modelled by fitting appropriate equilibrium constants from eqn (4) and (6) to the experimental data. To do so, the following site and charge relations for 4+ valence dopants and pure ceria¹⁹ are needed:

8

9

10

11

where X = 0.045 is the dopant concentration of Zr⁴⁺ in the case of CZO_5. Thus, the equilibrium constants K ₁ for eqn (4) and K ₂ for eqn (6) are given by:

12

13

K ₁ and K ₂ can be determined through a least square minimization of eqn (12) and (13) with the experimental nonstoichiometry data. Results are summarized in Fig. 3(a) and (b) for CeO₂ and CZO_5, respectively. As expected, K ₁ for CZO_5 is higher compared to that for CeO₂ because of its higher reduction extent. Additionally, the slope for CeO₂ is higher than that for CZO_5, indicating that its reduction enthalpy (at least at low δ where the reaction is dominated by K ₁) is higher and consistent with Kuhn et al. ¹⁰ K ₂ for CeO₂ is decreasing with increasing temperature meaning defect interactions become less predominant at higher temperatures. K ₂ for CZO_5 does not show a meaningful trend and values are much smaller than for CeO₂ because defect associations are probably not significant under the conditions investigated. In fact, in the case of CZO_5 at 1573 K, the best fit of K ₂ is orders of magnitude below the fits at higher temperatures. These findings directly support the conclusions drawn from Fig. 2, namely that a single isolated defect model appears to adequately describe the defect chemistry of CZO_5, whereas electron-vacancy associations should be additionally taken into account in the case of CeO₂. By fitting K ₁ and K ₂ over all experimental data, indicated by the lines in Fig. 2(a) and (b), it can be seen that the agreement is very good. When including both defect models, the RMS deviations of the fitted log p _O2 (cf. Fig. 2) are 0.013 and 0.005 in the case of CeO₂ and CZO_5, respectively. Both deviations are less than the uncertainty in the p _O2 setting, equal to 0.017. Considering only the isolated defect model (eqn (4)) the RMS deviations are 0.094 for CeO₂ and 0.038 for CZO_5. This reflects that defect associations are more important in the case of CeO₂ than in the case of CZO_5. The improvement in the RMS deviation for CZO_5 when including electron-vacancy associations may rather be a result of having an additional fitting parameter than having a more adequate physical model (cf. trend of K ₂ for CZO_5 in Fig. 3(b)).

Fig. 3. Equilibrium constants versus inverse temperature for CeO₂ and CZO_5: (a) K ₁; and (b) K ₂. Dashed lines indicate linear dependence of K ₁ and K ₂ on 1000/T (R ² > 0.99).

Based on computational investigations, Yang et al. ²⁶ concluded that an oxygen vacancy is most likely created close to a Zr⁴⁺-dopant which might serve as nucleation center for vacancy clustering. Based on these results, Kuhn et al. ¹⁰ proposed that the considerably smaller Zr⁴⁺, compared with Ce⁴⁺, prefers a 7-fold coordination (instead of 8-fold) with oxygen which can be achieved if an oxygen vacancy is created next to the smaller Zr⁴⁺ cation. Therefore, instead of associations were also tested, but this did not improve the isolated defect model within the δ-range investigated.

Thermodynamic properties

Thermodynamic properties, namely partial molar enthalpy (Δh _O), partial molar entropy (Δs _O) and partial molar Gibbs free energy (Δg _O), defined per mole of monoatomic oxygen, can be determined as a function of δ, temperature and p _O2 according to eqn (14) and (15).

14

Δg_O = Δh_O – TΔs_O 15

By combining eqn (14) and (15) it is clear that Δh _O and Δs _O as a function of δ can both be solved by determining the slope and intercept of ln p _O2 versus 1/T for a constant δ, as shown in eqn (16).

16

Constant δ values are obtained by interpolating our defect models within the temperature range investigated (1573 K to 1773 K) and a slightly extrapolated p _O2 range (±20% of the measured –log p _O2 range). Results of Δh _O and Δs _O versus δ are shown in Fig. 4 and 5, respectively, for CeO₂ (open squares) and CZO_5 (open triangles) measurements from this work. For reference we have included CeO₂ data of Panlener et al.,⁴ Campserveux et al.,¹⁷ Bevan et al. ⁵ and Sørensen.¹⁶ Additionally, measurements of CZO_5 by Kuhn et al. ¹⁰ and Hao et al. ¹² are indicated by closed and crossed triangles, respectively. Measurements of 20 mol% Zr⁴⁺ doped CeO₂ (CZO_20) by Kuhn et al. ¹⁰ and Hao et al. ¹² are indicated by closed circles and crossed circles, respectively. In general, it can be observed that Δh _O increases with increasing dopant concentration. This is expected due to the ease with which Zr⁴⁺ doped ceria reduces compared to pure ceria.

Fig. 4. Partial molar enthalpy of CeO₂ (open squares) and CZO_5 (open triangles) as a function of δ and a comparison to literature data of CeO₂ (Panlener et al.:⁴ closed squares, Campserveux et al.:¹⁷ diagonally crossed squares, Bevan et al.:⁵ half closed squares, Sørensen:¹⁶ crossed squares), CZO_5 (Kuhn et al.:¹⁰ closed triangles, Hao et al.:¹² crossed triangles) and CZO_20 (Kuhn et al.:¹⁰ closed circles, Hao et al.:¹² crossed circles).

Fig. 5. Partial molar entropy of CeO₂ (open squares) and CZO_5 (open triangles) as a function of δ and a comparison to literature data of CeO₂ (Panlener et. al.:⁴ closed squares, Bevan et al.:⁵ half closed squares, Sørensen:¹⁶ crossed squares), CZO_5 (Kuhn et al.:¹⁰ closed triangles, Hao et al.:¹² crossed triangles) and CZO_20 (Kuhn et al.:¹⁰ closed circles, Hao et al.:¹² crossed circles).

Towards higher δ, the Δh _O values are in good agreement with literature data of CeO₂ ^4,5,16,17 and CZO_5.^10,12 However, at lower δ, they deviate. The same trend can be observed for Δs _O. Deviations can be attributed primarily to different measurement temperatures and to a lesser extent to differences in nonstoichiometry measurements. For example, the literature data shown in Fig. 4 and 5 were calculated based on measurements below 1573 K^5,10,16,17 or as an average of measurements at higher (>1573 K) and lower temperatures (<1573 K),^4,12 whereas values of this work are based on measurements only above 1573 K. Although it is often assumed that Δh _O and Δs _O are independent of temperature, this simplifying assumption is not always valid. For example, a temperature dependence of Δh _O is observed for the case of CeO₂ where two reactions dictate the defect chemistry. The degree of dependence varies in accordance with the magnitude of K ₂ in regards to K ₁. Sørensen¹⁶ has showed that the slope of Δg _O vs. T (see eqn (15)) is constant at T < 1623 K and δ < 0.08, but decreases at higher temperatures due to the formation of sub-phases. The more negative Δh _O values at low δ from this work are in agreement with Sørensen.¹⁶ Deviations in the measurements of CZO_5 can be additionally attributed to differences in Zr⁴⁺ dopant concentrations. For example, in this work the dopant concentration is 4.5 mol% compared to 5.2 mol% in the work of Hao et al. ¹²

The reduction of nonstoichiometric ceria is represented by:

17

The standard Gibbs free energy change of eqn (17), Δg _red, can be calculated by integrating Δg _O over the range of δ:¹⁶

18

where δ _ox is the nonstoichiometry before reduction and δ _red is the nonstoichiometry after reduction. Δg _red as a function of temperature for the reduction of CeO₂, CZO_5, and CZO_20 from δ _ox = 0 to δ _red = 0.05 (dashed lines) and from δ _ox = 0 to δ _red = 0.1 (solid lines) is shown in Fig. 6. For all materials, the reduction at standard pressure is thermodynamically favorable (Δg _red < 0) at T > 1950 K for δ _red = 0.05 and at T > 2100 K for δ _red = 0.1. At lower temperatures, where Δg _red > 0, reduction would only proceed if additional work is performed to the system, e.g. lowering p _O2 by vacuum pumping or flushing with inert gas. Therefore, this implies that at lower temperatures (<2000 K), CZO_20 can be reduced more easily compared to CZO_5 and CeO₂, which is related to its less negative Δh _O and consistent with experimental observations. For all materials, a higher Δg _red for δ _red = 0.1 compared to δ _red = 0.05 is related to the increasing Δs _O with increasing δ (cf. Fig. 5).

Fig. 6. Gibbs free energy change versus temperature for the reduction of CeO₂ (black), CZO_5 (blue) and CZO_20 (red) from δ _ox = 0 to δ _red = 0.1 (solid lines) and δ _ox = 0 to δ _red = 0.05 (dashed lines).

The oxidation of nonstoichiometric ceria and doped ceria with H₂O is described by:

19

Δg _ox, Δg _H2O, and Δg _ox,H2O are the standard Gibbs free energy change of ceria oxidation with oxygen (–Δg _red), of water dissociation, and of ceria oxidation with H₂O (eqn (19)). Thus, Δg _ox,H2O = Δg _ox + Δg _H2O, where Δg _H2O is obtained from NIST-JANAF thermochemical tables and Δg _ox = –Δg _red. Calculations indicate that oxidation with H₂O becomes thermodynamically less favorable as the Zr⁴⁺ concentration increases. This is shown in Fig. 7, where Δg _ox,H2O of CeO₂ (black), CZO_5 (blue), and CZO_20 (red) is plotted as a function of temperature for the oxidation with H₂O from δ _red = 0.1 to δ _ox = 0 (solid lines) and δ _red = 0.05 to δ _ox = 0 (dashed lines). Δg _ox,H2O is negative at T ≤ 1200 K for CeO₂, at T ≤ 1000 K for CZO_5, and at T ≤ 500 K for CZO_20. Above the mentioned temperatures, oxidation is thermodynamically favorable only if additional work is added to the system.

Fig. 7. Gibbs free energy change versus temperature for the oxidation of CeO₂ (black), CZO_5 (blue), and CZO_20 (red) with H₂O from δ _red = 0.1 to δ _ox = 0 (solid lines) and δ _red = 0.05 to δ _ox = 0 (dashed lines).

By combining the reaction equilibrium constant of water dissociation (K _W)

20

with eqn (14), equilibrium H₂ yields can be calculated according to:

21

where n _H2 is the molar amount of H₂ produced at equilibrium per mole oxide, and n _H2O,i is the initial molar amount of H₂O in the system per mole oxide. n _H2 is obtained by iteratively solving eqn (21) and is shown in Fig. 8 versus temperature for CeO₂ (black), CZO_5 (blue), and CZO_20 (red). n _H2O,i, is set equal to δ _red (solid lines) and 100 × δ _red (dashed lines), where δ _red is the nonstoichiometry achieved after reduction at T _red = 1773 K and p _O2 = 2.3 × 10^–4 atm. The calculations reaffirm that the oxidation with H₂O becomes thermodynamically less favorable with increasing Zr⁴⁺ dopant concentrations. For example, for n _H2O,i = δ _red, maximum n _H2 is reached at T ≤ 900 K for CeO₂, T ≤ 700 K for CZO_5, and T < 400 K for CZO_20. If n _H2O,i is increased by a factor of hundred, these oxides can be oxidized at higher temperatures but at the expense of heating excess H₂O. In this case, maximum n _H2 is obtained at as high as 1200 K for CeO₂, 1100 K for CZO_5, and 500 K for CZO_20. For CZO_20, n _H2 is only shown up to 0.042 moles because Δh _O and Δs _O are not available at δ ≤ 0.03. Because Δh _O and Δs _O of CeO₂ and CZO_5 are not measured over the range δ = 0 to 0.1, they are assumed to be constant for low δ and taken as the average from literature data^4,5,10,16,17 for high δ.

Fig. 8. Molar amount of H₂ produced by oxidation of CeO₂ (black), CZO_5 (blue) and CZO_20 (red) with H₂O as a function of temperature assuming n _H2O,i = δ _red (solid lines) and 100 × δ _red (dashed lines) where δ _red is the nonstoichiometry achieved after reduction at T _red = 1773 K and p _O2 = 2.3 × 10^–4 atm (δ _red = 0.0328 for CeO₂, δ _red = 0.0417 for CZO_5, and δ _red = 0.0725 for CZO_20).

Efficiency analysis

The theoretical solar-to-fuel energy conversion efficiency (η _{solar-to-fuel}) for the case of hydrogen production is defined as:

22

where HHV_H2 = 285.5 kJ mol^–1 is the higher heating value of H₂. Q _input,min is the minimum input of energy required to produce n _H2 and comprises the solar process heat for driving the reduction, for heating the redox material from T _ox to T _red, and for generating steam at T _ox, as well as the equivalent minimum work to drive the reduction for the case of Δg _red > 0. Assuming no heat recuperation between the redox steps,

23

where Δh _red is the enthalpy change of the reduction (eqn (17)),

24

is the thermal energy required to heat H₂O from ambient temperature to T _ox (obtained from NIST-JANAF tables), n _H2O,i is the initial molar amount of H₂O determined by eqn (21), and c _p is the specific heat capacity of pure ceria.²⁷ The excess H₂O needed is calculated for n _H2 approaching δ _red. Note that the maximum η _{solar-to-fuel} may not be attained by completely re-oxidizing the material, as shown by Chueh et al. ²⁸ and Furler et al.,²⁹ but an overall optimization routine is outside the scope of this work. Due to the low dopant concentration of Zr⁴⁺, c _p of CZO_5 and CZO_20 are assumed to be identical to that of pure CeO₂. Q _input,min is assumed to be delivered by concentrated solar energy. The solar absorption efficiency (η _absorption) for a blackbody cavity-receiver is given by:³⁰

25

where σ is the Stefan–Boltzmann constant, I = 1 kW m^–2 the direct normal irradiation (DNI) and C = 2000 the solar flux concentration ratio. The fourth term in eqn (23) is the minimum work required to drive the reduction at conditions for which Δg _red > 0; when Δg _red ≤ 0 this term is omitted. η _Carnot is the efficiency of an ideal heat engine converting solar heat at T _red to work.³⁰

A contour plot of η _{solar-to-fuel} shown as a function of δ _red and T _ox is shown in Fig. 9 for CeO₂ (a) and CZO_5 (b) respectively. p _O2 = 10^–6 atm is assumed for the efficiency calculations resulting in reduction temperatures of 1744 K for CeO₂ and 1741 K for CZO_5 needed to reach δ _red = 0.1 and 1564 K and 1510 K respectively to reach δ _red = 0.02. It is shown that the maximum efficiency for CeO₂ is slightly higher compared to CZO_5. η _{solar-to-fuel} is slightly greater than 17% at δ _red = 0.1 (T _ox = 1050 K) for CeO₂ and slightly greater than 16% at δ _red = 0.1 (T _ox = 880 K) for CZO_5. Simply stated, the energy savings during reduction of CZO_5 cannot compensate the additional energy inputs due to the less favorable re-oxidation with H₂O (lower T _ox and/or higher n _H2O,i compared to CeO₂). In general η _{solar-to-fuel} rapidly decreases towards higher T _ox as the re-oxidation with H₂O gets thermodynamically less favorable and an increasing amount of excess steam has to be heated in order to fully oxidize the reduced material. Towards lower T _ox, η _{solar-to-fuel} decreases as the temperature difference between oxidation and reduction increases and towards lower δ _red it decreases as the amount of H₂ produced (equal to δ _red) decreases compared to the sensible energy required to heat the oxide. Qualitatively these results are in agreement with calculations reported in literature for pure ceria,^7,31,32 and indicate the tradeoffs between an isobaric redox cycle driven by temperature swing and an isothermal redox cycle driven by pressure swing. Heat recovery, not accounted for in Fig. 9, can significantly boost η _{solar-to-fuel}.⁷ When heat recovery is used for generating steam at T _ox, η _{solar-to-fuel} peaks at 19% for CeO₂ and 18% for CZO_5. If, in addition, heat recovery is used to heat the redox material from T _ox to T _red, η _{solar-to-fuel} peaks at 41% and 44% for CeO₂ and CZO_5, respectively. Results for CZO_20 are not shown because thermodynamic data are not available at δ ≤ 0.03 and also because calculations always predict maximum η _{solar-to-fuel} at lowest T _ox (400 K) and highest δ _red (0.1).

Fig. 9. η _{solar-to-fuel} shown as contour lines for CeO₂ (a) and CZO_5 (b) as a function of δ _red and T _ox assuming reduction at p _O2 = 10^–6 atm and subsequent complete re-oxidation with steam.

Maximum η _{solar-to-fuel} as a function of p _O2 is shown in Fig. 10 for CeO₂ (solid lines), CZO_5 (dashed lines) and CZO_20 (dotted lines) where δ _red = 0.1 (a) and δ _red = 0.05 (b). Additionally, T _red where maximum η _{solar-to-fuel} is obtained is shown in Fig. 10. Estimates of T _red of CZO_20 were calculated according to the methodology described by Yang et al. ³³ using the thermodynamic data of Kuhn et al. ¹⁰ It is observed that CeO₂ shows the highest η _{solar-to-fuel} under all conditions investigated and CZO_20 shows the lowest η _{solar-to-fuel}. Although CZO_20 reduces at substantially lower temperatures compared to CZO_5 and CeO₂, the lower energy input during reduction cannot compensate the higher energy input during oxidation with H₂O. In general, η _{solar-to-fuel} increases with decreasing p _O2, meaning less energy is required to reduce the oxide by lowering p _O2 compared to increasing T _red.

Fig. 10. Maximum η _{solar-to-fuel} and T _red versus p _O2 for CeO₂ (solid lines), CZO_5 (dashed lines) and CZO_20 (dotted lines) assuming δ _red = 0.1 (a) and δ _red = 0.05 (b).

Conclusions

Oxygen nonstoichiometry measurements of Zr⁴⁺ doped ceria at elevated temperatures presented in this work are largely in agreement with the trends observed in works performed at lower temperatures (<1573 K), namely: for a given T _red and p _O2 the reduction extent increases and the reduction enthalpy decreases with increasing Zr⁴⁺ concentration. Extracted thermodynamic properties are also largely in agreement with previous data, but they deviate at low nonstoichiometries especially for the case of pure ceria. This is likely due to the fact that they are slightly temperature dependent, especially at higher temperatures (>1623 K) where different sub-phases can be expected.¹⁶ Interestingly, in the case of 5 mol% Zr⁴⁺ doped ceria, a single defect model is capable of describing the nonstoichiometry data over the entire measurement range (δ = 0.01 to 0.04) and therefore the thermodynamic properties can be assumed to be independent of temperature. This is an important distinction when extrapolating nonstoichiometries to conditions that have not yet been measured experimentally.³³ Although the nonstoichiometry increases with increasing Zr⁴⁺ dopant concentration, oxidation with steam becomes thermodynamically less favorable and has to be conducted at lower temperatures or with excess amounts of steam. This ultimately results in lower theoretical solar-to-fuel energy conversion efficiencies compared to that for pure ceria. Therefore, when screening potential redox materials it is important to consider both steps of the cycle, i.e. the materials ability to release lattice oxygen and its oxidation potential with H₂O and CO₂. We have assumed that reduction and oxidation are driven to completion, but maximum efficiencies may be found at lower extents. In general, when we compare with the thermodynamic properties of pure ceria, a relatively lower partial molar enthalpy and a relatively higher partial molar entropy are desired, resulting in Δg _red < 0 at lower T _red and Δg _ox,H2O < 0 at higher T _ox, which in turn yields a smaller temperature swing between the redox steps. Besides thermodynamic aspects, fast reaction kinetics and long term chemical and morphological stability are obviously essential.

Nomenclature

C

Flux concentration ratio of incident radiation (—)

Cerium atom on cerium lattice site

Electron localized on cerium lattice site

Oxygen vacancy–polaron association

c_p

Heat capacity of CeO₂ (kJ mol^–1 K^–1)

Δg_H2O

Standard Gibbs free energy change of H₂O dissociation (kJ mol^–1)

Δg_O

Partial molar free energy (kJ mol^–1)

Δg_ox

Standard Gibbs free energy change of ceria oxidation (with O₂) (kJ mol^–1)

Δg_ox,H2O

Standard Gibbs free energy change of ceria oxidation (with H₂O) (kJ mol^–1)

Δg_red

Standard Gibbs free energy change of ceria reduction (kJ mol^–1)

Δh_H2O

Energy to heat water (kJ mol^–1)

HHV_H2

Higher heating value of H₂ (kJ mol^–1)

Δh_O

Partial molar enthalpy (kJ mol^–1)

Δh_red

Enthalpy change of reduction (kJ mol^–1)

I

Normal beam insolation (W m^–2)

K₁

Ideal solution model equilibrium constant (—)

K₂

Defect interaction model equilibrium constant (—)

K_W

H₂O dissociation equilibrium constant (—)

M_O

Molar mass of O (g mol^–1)

m_s

Weight of reactive sample (mg)

M_s

Molar mass of reactive sample (g mol^–1)

Δm_s

Relative weight loss of reactive sample (—)

n_H2

Molar amount of H₂ at equilibrium (mol)

n_H2O,i

Initial molar amount of H₂O (mol)

Oxygen atom on oxygen lattice site

p_O2

Oxygen partial pressure (atm)

Q_input,min

Minimum amount of input energy to produce H₂ (kJ mol^–1)

R

Universal gas constant (J mol^–1 K^–1)

Δs_O

Partial molar entropy (J mol^–1 K^–1)

T

Temperature (K)

T_ox

Oxidation temperature (K)

T_red

Reduction temperature (K)

Doubly ionized oxygen vacancy

X

Molar dopant concentration of Zr⁴⁺ (—)

α

Stoichiometric coefficient of H₂O (—)

β

Stoichiometric coefficient of CO₂ (—)

δ

Degree of oxygen nonstoichiometry (—)

δ_ox

Degree of oxygen nonstoichiometry after oxidation (—)

δ_red

Degree of oxygen nonstoichiometry after reduction (—)

η_absorption

Solar absorption efficiency (—)

η_Carnot

Carnot efficiency (—)

η_{solar-to-fuel}

Solar-to-fuel energy conversion efficiency (—)

σ

Stefan–Boltzmann constant (W m^–2 K^–4)