Design principles of perovskites for solar-driven thermochemical splitting of CO₂

Abstract

Perovskites are attractive redox materials for thermo/electrochemical fuel synthesis. To design perovskites with balanced redox energetics for thermochemically splitting CO₂, the activity of lattice oxygen vacancies and stability against crystal phase changes and detrimental carbonate formation are predicted for a representative range of perovskites by electronic structure computations. Systematic trends in these materials properties when doping with selected metal cations are described in the free energy range defined for isothermal and temperature-swing redox cycles. To confirm that the predicted materials properties root in the bulk chemical composition, selected perovskites are synthesized and characterized by X-ray diffraction, transmission electron microscopy, and thermogravimetric analysis. On one hand, due to the oxidation equilibrium, none of the investigated compositions outperforms non-stoichiometric ceria – the benchmark redox material for CO₂ splitting with temperature-swings in the range of 800–1500 °C. On the other hand, certain promising perovskites remain redox-active at relatively low oxide reduction temperatures at which ceria is redox-inactive. This trade-off in the redox energetics is established for YFeO₃, YCo_0.5Fe_0.5O₃ and LaFe_0.5Ni_0.5O₃, identified as stable against phase changes and capable to convert CO₂ to CO at 600 °C and 10 mbar CO in CO₂, and to being decomposed at 1400 °C and 0.1 mbar O₂ with an enthalpy change of 440–630 kJ mol⁻¹ O₂.

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1. Introduction

The solar-driven thermochemical splitting of CO₂ into CO and O₂ operates at high temperatures and utilizes the entire solar spectrum and, thus, can potentially yield high solar-to-fuel energy conversion efficiencies.^1–11 It can be realized by a 2-step redox cycle, comprising the endothermic reduction of the metal oxide yielding O₂, followed by the exothermic oxidation of a metal oxide with CO₂ yielding CO. This is shown schematically in Fig. 1a for perovskite-type metal oxides of ABO₃ stoichiometry, with A and B representing metals at the twelve- and six-fold coordinated crystal lattice sites, respectively. Given its crystallographic stability, favorable oxidation thermodynamics, and fast fuel production kinetics, nonstoichiometric ceria (CeO_2−δ) has emerged as the benchmark redox material for the thermochemical splitting of CO₂ and H₂O.^3,5,12–23 The use of CeO_2−δ is however limited to solar reactors that can withstand the relatively high temperatures required for accessing moderate oxygen exchange capacities. Even at 1723 K and an oxygen partial pressures p_O2 below 10⁻³ bar O₂, oxygen nonstoichiometries δ remain typically below 0.03.^3,6,24,25 To circumvent these limitations, perovskites have recently attracted attention as an alternative class of redox materials with possibly higher oxygen nonstoichiometries and typically high oxygen vacancy conductivities.^5,24,26–38 The vast number of possible metal cation combinations in the perovskite structure may allow for control over the temperature and p_O2 requirements of the redox cycle.

Fig. 1 (a) Schematic representation of two-step solar-driven thermochemical splitting of CO₂ with nonstoichiometric perovskite redox materials. The oxygen nonstoichiometry after reduction and oxidation is denoted δ_red and δ_ox, respectively. These define the oxygen exchange capacity, Δδ = δ_red − δ_ox, which is equivalent to the specific fuel yield per redox cycle. (b) Schematic illustration of the number of computed (solid lines) and experimentally evaluated (dashed lines) perovskite compositions with respect to their thermodynamic properties (grey) and thermochemical stability (orange) discussed in the specified section of this article.

Previous experimental studies with perovskites have focused mostly on lanthanum manganites.^{24,26–28,30–33} For instance, McDaniel et al.²⁴ demonstrated that reduction of La_0.6Sr_0.4Mn_0.6Al_0.4O_3−δ at 1623 K and 0.2 mbar O₂ and re-oxidation at 1273 K under 40 vol% H₂O or CO₂ in Ar results in nine or six times greater H₂ and CO yields, respectively, relative to ceria.²⁴ Analogously, Takacs et al.³² showed that La_0.6Ca_0.4Mn_0.6Al_0.4O_3−δ reduced at 1700 K and 10⁻³ bar O₂ releases up to five times more O₂ per unit mass of redox material relative to ceria. However, the authors highlighted that although the reduction extents of the tested perovskites are higher than those of CeO_2−δ, oxidation extents with H₂O and CO₂ are lower.³² Choosing appropriate reduction and oxidation operating conditions for optimal performance is complicate since the thermodynamics and kinetics vary strongly with temperature, pressure, and the composition of the redox material.^32,33 Furthermore, given the vast amount of possible materials compositions, experimental evaluation of metal oxide redox materials is limited by trial-and-error.

A computational approach to the design of metal oxide redox materials was presented by Emery et al.,³⁹ calculating the thermodynamic stability and the oxygen vacancy formation energy for 5329 cubic and distorted ABO₃ perovskites via high-throughput density functional theory (HT-DFT). The stability of a perovskite was calculated by subtracting the convex hull energy for ABO₃ from the DFT-computed formation enthalpy of the perovskite, defined as the energy difference between the total energy of the ABO₃ structure and the chemical potentials of A, B and oxygen.³⁹ With this approach, the authors identified 139 compositions suitable for water splitting, such as CeCoO₃ and BiVO₃.³⁹ Other computational screening efforts for perovskite redox materials include the works by Deml et al.,^40,41 correlating the oxygen vacancy formation energy, the enthalpy of metal oxide formation, and the position of the band gap for binary (one cation-type oxides) and ternary systems (with two cations, such as perovskites). Michalsky et al.⁴² quantified scaling of the free energy and enthalpy of bulk metal oxide formation with the free energy of forming oxygen vacancies at the surface across various metal oxide structures, including three selected perovskites. Furthermore, Calle-Vallejo et al.⁴³ computed perovskite bulk formation energies using DFT and Meredig et al.⁴⁴ showed that a low enthalpy of reduction and a large positive entropy of reduction of the solid bulk metal oxide are thermodynamically favorable for two-step thermochemical splitting of CO₂ and H₂O. Noteworthy, Curnan et al.⁴⁵ showed that the oxygen vacancies formation across LaBO₃, SrBO₃, (B = 3d transition metals) and similar materials is thermodynamically more favorable in perovskite models with larger unit cell size.⁴⁵ The energetics of the oxygen vacancy formation are found less favorable in the non-cubic perovskites.⁴⁵

The present work screens perovskites for thermochemical CO₂ splitting by: (1) choosing process conditions for perovskite reduction and oxidation comparable to those used for state-of-the-art ceria based materials; (2) computing the thermochemical stability of cubic perovskites relative to that of possibly formed binary metal oxides and metal carbonates; (3) expanding the range of screened perovskites generally to quinternary compositions; and (4) validating the computed trends in the redox activity and thermochemical stability for selected compositions experimentally. DFT is used to screen ABO₃, AA′BO₃, ABB′O₃ and AA′BB′O₃ perovskites for two-step temperature-swing and isothermal thermochemical splitting of CO₂ splitting. We considered combinations of non-toxic, inexpensive, and stable metals at the twelve-fold (A, A′ = Mg, Ca, Sr, Ba, Y, La, Ce) and six-fold (B, B′ = Ti, Cr, Mn, Fe, Co, Ni, Cu, Zr, Al) coordinated crystal lattice sites. As a guide, Fig. 1b illustrates which set or subset of perovskite compositions was chosen in a specific section of this article for computational screening (orange) and experimental evaluation (grey), respectively.

2. Electronic structure trends of perovskites

2.1 Redox activity

The redox energetics of 297 perovskites were computed for the thermochemical splitting of CO₂, of which 63 compositions had basic ternary ABO₃ stoichiometry, while the 77, 67, and 90 compositions contained metal cation dopants at the A and/or B lattice sites resulting in AA′BO₃, ABB′O₃, and AA′BB′O₃ stoichiometry, respectively. Fig. 2 shows the tendency of the most stable surfaces with (010) geometry to contain a specific B-cation, as an example for perovskites containing either Ca and Sr (cf.Fig. 2a) or Ce and La (cf.Fig. 2b) at the A-site, respectively. As a trend, we find that surfaces containing alkaline earth metals at the A-site (cf.Fig. 2a) frequently contain B-cations with intermediate periodic number, those with lanthanides at the A-site (cf.Fig. 2b) more frequently contain B-cations with relatively low periodic number.

Fig. 2 Tendency of the most stable perovskite surfaces with (010) geometry and with (a) Ca (dark blue) and Sr (light blue), and (b) Ce (orange) and La (red) at the A-site to contain a specific metal at the B-site (indicated on the x-axis), defined as t_B = (number of most stable surfaces containing the specified B cation)/(number of all surfaces containing the same A cation) × 100%.

Making use of scaling relations for the free energy of forming oxygen vacancies at metal oxide surfaces, ΔG_v[O], and the free energy and enthalpy of bulk metal oxide formation,⁴² we determined the Gibbs free energy changes for bulk perovskite reduction (liberating O₂) and oxidation (reducing CO₂ into CO). Generally, the more endergonic reaction limits the oxygen exchange capacity of a perovskite.⁴⁶Fig. 3 shows the limiting free energy change of a CO₂-splitting cycle (, at process conditions) as a function of the standard partial molar enthalpy change for metal oxide reduction (, at ambient conditions), estimated as the reaction of perovskites into their brownmillerite analogs and O₂. With other words, we employ the enthalpy change for metal oxide reduction, a measure of the bulk metal–oxygen bond strength, as a single general descriptor of the application-specific redox energetics. Given the resulting volcano-type curve for metal oxide redox materials,⁴² we find the materials with the least-endergonic limiting free energy changes at the intersection of both correlations. Dependent on reaction temperatures and pressures, balance of the redox energetics indicates a favorable intermediately strong binding of oxygen, that is, strong enough to facilitate oxide oxidation but weak enough to allow for reduction of the oxidized oxide. Ideally, this intersection is located in the exergonic reaction space. To approach this, Fig. 3 shows the redox energetics at reasonable process conditions, that is, oxide reduction between 1200 and 1800 K and 10⁻⁴ bar O₂ and oxide oxidation at 900 K in an atmosphere of either 1% CO in CO₂ (Fig. 3a) or 100% CO₂ (Fig. 3b). For the following discussion, the positions of YCo_0.5Fe_0.5O₃, La_0.5Sr_0.5Co_0.5Fe_0.5O₃ and La_0.5Sr_0.5MnO₃ are marked along with the position of CeO_2−δ as a reference. As indicated by their position relative to the top of the volcano-type curve, yields of redox cycles using YCo_0.5Fe_0.5O₃ and La_0.5Sr_0.5Co_0.5Fe_0.5O₃ are limited by the oxidation thermodynamics, while that of a process using La_0.5Sr_0.5MnO₃ is limited by the reduction thermodynamics.

Fig. 3 Limiting standard partial molar Gibbs free energy for thermochemical splitting of CO₂ as a function of the metal oxide reduction temperature (T_red) and the standard partial molar enthalpy of metal oxide reduction (). Oxide reduction is shown always at p_O2 = 10⁻⁴ bar, while oxide oxidation is always at a temperature (T_ox) of 900 K and (a) p_CO/p_CO2 = 0.01 (that is, 1% CO in CO₂), and (b) p_CO/p_CO2 = 0 (that is, 100% CO₂). La_0.5Sr_0.5Co_0.5Fe_0.5O₃, YCo_0.5Fe_0.5O₃, and La_0.5Sr_0.5MnO₃ are displayed at T_red of 1500, 1600 and 1700 K, respectively. For reference, the position of CeO_2−δ is computed for the reduction of the CeO₂(111) facet yielding stable oxygen vacancies in the subsurface of CeO_1.75(111) and O₂, indicated with dashed lines at of 606 kJ  mol_O2⁻¹.

The thermodynamic equilibrium for the reduction and oxidation with CO₂ are given by eqn (1) and (2), respectively:

where the standard pressure, p°, is 1 bar. is the standard Gibbs free energy change of CO₂ dissociation (CO₂ = CO + 0.5O₂), and p_CO2 and p_CO are the partial pressures of CO₂ and CO, respectively. Evidently, the reduction of a metal oxide is favorable at high temperatures and low p_O2, while its oxidation is favorable at low temperatures and high p_CO2 and low p_CO. Fig. 3 quantifies this for perovskites, for which thermochemical data is typically not available from experiments. We note, while Fig. 3 gives the computed thermochemical trends at selected process conditions, the analysis can be reiterated for any set of process conditions using the raw data and scaling relations given with ESI.†

Guiding the design of perovskites, Fig. 3 identifies materials with the most-favorable redox activity (marked in dark red) with an enthalpy change for perovskite reduction of 440–630 kJ mol_O2⁻¹ at the chosen process conditions. As expected, CeO_2−δ with of 606 kJ mol_O2⁻¹, computed for reduction of the thermodynamically most stable mixed-terminated CeO₂(111) facet yielding stable oxygen vacancies in the subsurface of CeO_1.75(111),⁴⁹ is found favorably near the top of the volcano-type plot. While the exact location of this reference depends on the oxygen nonstoichiometry, we find ceria typically exhibits well-balanced redox energetics at high-temperature redox conditions. These trends in the redox energetics indicate further increasing the reduction temperature or decreasing p_O2 will yield exergonic limiting free energy changes with perovskites that are characterized by slightly stronger metal–oxygen bonding.

Comparison of Fig. 3a and b shows that for the perovskites is less endergonic in a pure CO₂ atmosphere, as compared to a more realistic environment of solar receiver–reactors for CO₂ splitting, i.e., 1% CO in CO₂.⁶ Analogously, we find at the selected conditions 63%, that is, the majority of the studied perovskites are characterized by oxide oxidation-limited redox energetics (cf. Fig. S17†). This confirms, as a trend, previous observations for selected perovskites, as outlined above.^{26,27,31–33} To validate these trends, we chose seven attractive perovskites (cf.Fig. 4, marked in blue), that are located near the top of the volcano-type curve with oxide reduction at 1600 K and 10⁻⁴ bar O₂ and oxide oxidation at 900 K and an atmosphere of 1% CO in CO₂. These conditions were chosen as realistic process conditions relevant to an industrial implementation.^26,27,31,32 In particular, we chose to investigate reduction at 1600 K, that is, below typically 1723 K with CeO_2−δ,⁶ since this would alleviate thermal and mechanical stresses in solar receiver–reactors and decrease volatilization of the redox material. For the seven chosen perovskites, Fig. 4 shows that YFeO₃, LaCo_0.5Fe_0.5O₃, LaFeO₃ and YMnO₃ exhibit reduction-limited energetics, while LaFe_0.5Ni_0.5O₃, LaCo_0.5Ni_0.5O₃ and YCo_0.5Fe_0.5O₃ are exhibit oxidation-limited energetics. Compositions marked with grey symbols were considered unstable, concluded from unsuccessful synthesis attempts. For example, synthesis of CeCoO₃ (with of about 500 kJ mol_O2⁻¹, resulting in of 97 kJ mol_O2⁻¹) was unsuccessful, as the solid synthesis product contained only CeO_2−δ and Co₃O₄ (cf. Fig. S1†), in line with previous studies.^47,48

Fig. 4 A detail of Fig. 3, limiting standard partial molar Gibbs free energy for thermochemical splitting of CO₂ for oxide reduction at 1600 K and 10⁻⁴ bar O₂ and oxide oxidation at 900 K and in an atmosphere of 1% CO in CO₂ plotted vs.. Perovskites shown with blue symbols (YFeO₃, LaCo_0.5Fe_0.5O₃, LaFeO₃, YMnO₃, LaFe_0.5Ni_0.5O₃, LaCo_0.5Ni_0.5O₃, and YCo_.5Fe_0.5O₃) are further examined experimentally. Perovskites shown with grey symbols were considered unstable, as discussed in Section 2.2.

2.2 Thermochemical stability of the perovskite phase

Thermochemical stability is fundamental for a stable performance of a metal oxide redox material throughout multiple fuel synthesis cycles. In this work, we differentiate between the stability of the cubic perovskite phase in general and the stability against metal carbonate formation in particular. To avoid time- and resource-demanding computations of solid-state entropies, we define as a descriptor of phase stability in an inert atmosphere r_phase = ∑E_p,phase/∑E_r,phase, with ∑E_p,phase and ∑E_r,phase being the sums of the DFT-calculated electronic energies of the stoichiometry-dependent reaction products (possible phases in the A–B–O ternary phase diagram, such as binary metal oxides) and reactants (the perovskite and the balance O₂) at 0 K. Analogously, we define as a descriptor of the thermochemical stability of a perovskite against carbonate formation in presence of CO₂r_carb = ∑E_p,carb/∑E_r,carb, with ∑E_p,carb and ∑E_r,carb being the sums of the DFT-calculated electronic energies of the stoichiometry-dependent reaction products (ACO₃ carbonates and binary metal oxides) and reactants (the perovskite and CO₂) at 0 K. Both stability descriptors indicate stronger stability of the perovskite with lower values. Details of this analysis are given with ESI† (cf. eqn (6) and (7)).

Fig. 5 shows r_phase for 63 ABO₃-type perovskites (cf.Fig. 5a) and r_carb for 36 ABO₃-type perovskites (cf.Fig. 5b) as a function of . Since experimental data for Y and La carbonates is very limited (neither the NIST nor Barin's database⁵⁹ provide thermochemical data for these compounds and their lattice constants are unknown to the best of our knowledge), we focused our analysis of carbonate formation on perovskites containing divalent alkaline earth metals (A = Mg²⁺, Ca²⁺, Sr²⁺ and Ba²⁺). We find perovskites with divalent A cations exhibit decreasing stability (Fig. 5a and b) with increasing . That is, a stable perovskite phase and an unstable carbonate phase correlate both with strong metal–oxygen binding within the perovskite. The stability of perovskites containing trivalent and tetravalent A cations do not show such a clear trend (red square symbols in Fig. 5a). Furthermore, we find both stability descriptors for perovskites with divalent A cations reach a plateau at of about 200 kJ  mol_O2⁻¹. That is, we can expect that the thermochemical stability of perovskites containing A²⁺ cations will not further increase when the metal–oxygen bond becomes stronger than 200 kJ  mol_O2⁻¹. Therefore, we consider perovskites containing divalent A cations and with r_carb < 0.66 and r_phase < 0.51 as thermochemically stable (cf. light blue circles round symbols in Fig. 5a and b). We note this self-consistent analysis is limited to the cubic perovskite phase. Other descriptors, such as the Goldschmidt tolerance factor, can be employed to further investigate perovskite stability.

Fig. 5 Computed descriptors for the thermochemical stability of the cubic perovskite phase (a) in inert atmosphere, r_phase = ∑E_p,phase/∑E_r,phase computed for 63 ABO₃-type perovskites, and (b) in CO₂ atmosphere against metal carbonate formation, r_carb = ∑E_p,carb/∑E_r,carb computed for 36 ABO₃-type perovskites, plotted vs. the standard partial molar enthalpy change . Blue circles represent ABO₃ stoichiometry with divalent A cations (Mg²⁺, Ca²⁺, Sr²⁺, and Ba²⁺), red diamonds represent ABO₃ stoichiometry with trivalent or tetravalent A cations (La³⁺, Y³⁺, and Ce⁴⁺), and light blue circles represent materials with ABO₃ stoichiometry and divalent A cations that are thermochemically stable, as indicated by their stability descriptors discussed in Section 2.2.

In Section 2.1 we describe superior redox energetics for perovskites with in the range of 440–630 kJ mol_O2⁻¹ (cf.Fig. 3). This range describes materials with metal–oxygen bonding stronger than 200 kJ  mol_O2⁻¹, indicating that all analyzed perovskites that contain A²⁺ cations and that show attractive redox energetics are thermochemically stable at the chosen process conditions. This is assuming that the AA′BO₃-, ABB′O₃- and AA′BB′O₃-type compositions follow the correlation established here for ABO₃-type compositions.

2.3 Choosing a reasonable set of redox conditions

Choosing a reasonable set of process conditions is fundamental for consistent materials screening yielding results that are comparable to experiments with metal oxides tested at their specific set of favorable process conditions, as outlined in Section 2.1. For instance, given the often poor perovskite oxidation energetics, we find exergonic for reduction at 1600 K and 10⁻⁵ bar O₂ and oxidation at 900 K with a molar ratio of CO₂ feed to oxygen vacancies present in the solid of 10 000. At these conditions, LaNiO₃, CeNiO₃, and YCoO₃ reach desirably negative values of −6.40, −5.62 and −1.78 kJ  mol_O2⁻¹, respectively. However, these process conditions are unfavorable and would lead to a significant drop of the overall solar-to-fuel energy conversion efficiency of the redox cycle. Both, the low concentrations of O₂ during the reduction and the excess of oxidant imply additional energy penalties for gas separations and heat exchange, increasing the net-energy penalties.⁴⁹ Analogously, for realization of isothermal CO₂ splitting with perovskites we find exergonic redox energetics at T_red = T_ox = 1600 K, a molar CO₂ to oxygen vacancy ratio of 1000, and 10⁻⁷ bar O₂. This agrees well with the analysis by Meredig et al.,⁴⁴ who showed that large temperature differences between oxidation and reduction are required for thermodynamically favorable redox cycles. The authors further demonstrated that this advantage of relatively large temperature swings is material-independent and driven solely by the temperature difference and the entropy of the O₂.⁴⁴ The product of these two driving forces must be equal or larger than twice the free energy of formation of H₂O or CO₂, which is the barrier to a thermodynamically favorable two-step redox cycle.⁴⁴

In summary, perovskites do not outperform state-of-the-art nonstoichiometric ceria for solar thermochemical fuel production at the high-temperature process conditions which are required to render ceria redox-active. However, perovskites offer the possibility to decrease the maximum temperature of a redox cycle, which may alleviate thermal and mechanical stress in solar receiver–reactors and may diminish volatilization of solids. Realization of such redox cycles at lower temperatures with perovskite redox materials comes, however, at the costs of additional energy penalties for providing low O₂ partial pressures during oxide reduction and/or excess oxidant during oxide oxidation. An energy balance and calculation of the theoretical solar-to-fuel energy conversion efficiency assuming thermodynamic equilibrium is found in Takacs et al.³²

3. Experimental validation

3.1 Oxygen nonstoichiometry measurements

To assess the trends of the redox energetics established above via DFT, we evaluated the redox activity of selected perovskites (i.e., YFeO₃, LaCo_0.5Fe_0.5O₃, LaFeO₃, YMnO₃, LaFe_0.5Ni_0.5O₃, LaCo_0.5Ni_0.5O₃ and YCo_0.5Fe_0.5O₃, as marked with blue symbols in Fig. 4) by continuous redox cycling with a thermogravimetric analyzer (TGA). As all investigated perovskites are nonstoichiometric, Fig. S5† provides a detailed analysis of the oxygen nonstoichiometry, while we identify the discussed materials within the manuscript for simplicity with their stoichiometric compositions. In these studies perovskite reduction was at 1573 K and 1 bar of 10⁻⁴, 3.04 × 10⁻⁴, and 5.07 × 10⁻⁴ bar O₂ in Ar, respectively, and perovskite oxidation was at 873, 1073, and 1273 K and 1 bar of 1% CO in CO₂. To facilitate comparison with experiments that use O₂ as oxidant, we note these oxidation conditions correspond to O₂ partial pressures of 1.88 × 10⁻²¹, 3.79 × 10⁻¹⁵, and 7.75 × 10⁻¹¹ bar O₂, respectively, determined from the relation between the activities of CO₂, CO, and O₂.⁵⁰ The results of the TGA measurements are shown with Fig. S2 and S3† and are utilized here to calculate the oxygen nonstoichiometries with:where Δm_s is the relative weight change (in g/g), and M_s and M_O are the molar mass of the sample and of monoatomic oxygen, respectively (in g mol⁻¹). The oxygen exchange capacity is then defined as Δδ = δ_red − δ_ox (in mol O per mol ABO₃).

To assess the thermodynamics of the oxygen exchange, Fig. 6 shows the oxygen exchange capacity for reduction at 1573 K in 10⁻⁴ bar O₂ and oxidation at 873 K in 1% CO in CO₂ (equivalent to 1.88 × 10⁻²¹ bar O₂), respectively. For comparison, Δδ of CeO_2−δ, marked with a grey line, was calculated from Panlener et al.²⁵ for oxidation at 1073 K in 3.79 × 10⁻¹⁵ bar O₂ (equivalent to 1% CO in CO₂) and reduction at 1773 K in 10⁻⁴ bar O₂, which are typical conditions for thermochemical splitting of CO₂ with CeO_2−δ. The analysis shows that all perovskites, except YCo_0.5Fe_0.5O₃, have a smaller Δδ than CeO_2−δ (found here with Δδ = 0.07, which is comparable to the values reported by previous experimental investigations of ceria²⁵). Furthermore, after perovskite oxidation, YCo_0.5Fe_0.5O₃ does not fully reoxidize using 0.2 bar O₂, (cf. Fig. S3 and S6†), which will result in smaller Δδ established in consecutive redox cycles. LaCo_0.5Fe_0.5O₃, LaFe_0.5Ni_0.5O₃, and LaCo_0.5Ni_0.5O₃ show nominally negative Δδ, owing to their strong loss of O₂ (that is, perovskite reduction) at oxidation conditions. The relatively large errors originate from drift corrections in the reduction and oxidation runs, from which the oxygen exchange capacities were calculated.

Fig. 6 Experimentally measured oxygen exchange capacity, Δδ, of LaCo_0.5Fe_0.5O₃, LaFe_0.5Ni_0.5O₃, LaCo_0.5Ni_0.5O₃, LaFeO₃, YMnO₃, YFeO₃, and YCo_.5Fe_0.5O₃ for oxide oxidation at 873 K in 1% CO in CO₂ (p_O2 = 1.88 × 10⁻²¹ bar) and oxide reduction at 1573 K in 10⁻⁴ bar O₂. As a reference, the grey area marks Δδ for CeO_2−δ, as calculated from Panlener et al.²⁵ for oxidation at 1073 K in 3.79 × 10⁻¹⁵ bar O₂ (corresponding to 1% CO in CO₂) and reduction at 1773 K in 10⁻⁴ bar O₂ (which are typical redox cycle conditions for ceria). Error bars are calculated as the sum of the experimental uncertainties for the oxidation and reduction runs, arising from minor mass changes of the samples at a stabilization temperature of 873 K and drift corrections.

To demonstrate how crucial the choice of a reasonable set of redox conditions is, we oxidized YCo_0.5Fe_0.5O₃, LaCo_0.5Ni_0.5O₃, and LaFe_0.5Ni_0.5O₃ at 873 K with 100% CO₂, which corresponds to a p_O2 (3.67 × 10⁻⁹ bar O₂) that is by several orders of magnitude higher than that of 1% CO in CO₂ at the same temperature (1.88 × 10⁻²¹ bar O₂). To assess the sensitivity of the perovskites to these oxidation conditions, Fig. 7 shows the oxygen nonstoichiometry for perovskite oxidation, δ_ox, measured in 1% CO in CO₂ and plotted as a function of that measured in 100% CO₂. Parity indicates materials that are insensitive to this difference in the oxidation potential of the gas composition. At all investigated temperatures, all investigated perovskites are located above parity, indicating a high sensitivity to the oxidation potential of the gas composition. This observation agrees well with the DFT-derived trends discussed above with Fig. 3. As a trend, we find perovskites with poor oxidation energetics are most sensitive to the presence of CO in the CO₂ oxidant. That is, YCo_0.5Fe_0.5O₃, LaCo_0.5Ni_0.5O₃, and LaFe_0.5Ni_0.5O₃ are (comparing the set of three perovskites) least, intermediately, and most sensitive to the presence of CO in CO₂ (cf.Fig. 7), and show positive, negative, and most negative Δδ (cf.Fig. 6), which correlates well with the average electronegativity of the metals at their B-type interstitials, that is 1.86, 1.87, and 1.90, respectively. Analogously, CeO_2−δ, with Ce having a much lower electronegativity of 1.12, exhibits redox energetics that are essentially insensitive to the presence of CO.^6,25 For example, oxidation of CeO_2−δ at 873 K in 100% CO₂ and 1% CO in CO₂ is reported with δ_ox = 0.0001 and δ_ox = 0.0006 mol_O mol_CeO2⁻¹, respectively.²⁵ Compared to this difference in δ_ox within the same order of magnitude for CeO_2−δ, we find an increase of δ_ox for YCo_0.5Fe_0.5O₃, LaCo_0.5Ni_0.5O₃, and LaFe_0.5Ni_0.5O₃ from −0.011, 0.004, and 0.003 mol_O mol_ABO3⁻¹ to 0.066, 0.190, and 0.392 mol_O mol_ABO3⁻¹ (for 873 K and 100% CO₂vs. 1% CO in CO₂), respectively. That is a difference in δ_ox by two to three orders of magnitude.

Fig. 7 Oxygen nonstoichiometry for perovskite oxidation, δ_ox, measured in 1% CO in CO₂ (δ_{ox,1% CO in CO2}) vs. δ_ox measured in 100% CO₂ (δ_{ox,100% CO2}) for YCo_0.5Fe_0.5O₃ (blue), LaFe_0.5Ni_0.5O₃ (green), and LaCo_0.5Ni_0.5O₃ (orange), and measured at 873 K (circles), 1073 K (triangles), and 1273 K (squares). The dashed line marks parity.

This inferior oxidation performance of the perovskites in the presence of CO in the CO₂ oxidant is a major downside, since the CO product is present in a solar receiver–reactor throughout the entire oxidation period at conditions relevant for industrial implementation.⁶ Alternatively, the oxidation performance of perovskites can be augmented by flooding the reactor with inert gas and/or excess CO₂ to decrease CO concentrations, but this may be energetically costly, as it introduces additional energy penalties for gas separation and heat exchange.

3.2 Fine-tuning the oxygen exchange capacity

To evaluate the possibility to fine-tune the oxygen exchange capacity of perovskites, the following discusses the trends in the redox energetics with varying metal cation concentrations. The discussion above focused on perovskite compositions with A : A′ and B : B′ cation ratios equal to unity. To estimate trends in the oxygen exchange capacity of perovskites with metal cation ratios that differ from unity, Fig. 8a shows the volcano-type curve for three selected materials: YFeO₃, YCo_0.5Fe_0.5O₃, and YCoO₃. The plot indicates oxidation-limited redox thermodynamics for YCo_0.5Fe_0.5O₃ and YCoO₃ (since both materials are located on the right side of the volcano) and reduction-limited redox thermodynamics for YFeO₃ (located on the left side of the volcano). Thus, we hypothesize increasing the concentration of the Fe dopant in YCo_0.5Fe_0.5O₃ stabilizes metal–oxygen bonds and, in turn, yields compositions located closer to the top of the volcano.

Fig. 8 (a) Volcano-type curve for YFeO₃, YCo_0.5Fe_0.5O₃, and YCoO₃. (b) Oxygen exchange capacity, Δδ, for YFeO₃, YCo_0.1Fe_0.9O₃, YCo_0.3Fe_0.7O₃, and YCo_0.5Fe_0.5O₃ for oxide oxidation at 873 K in 1% CO in CO₂ at 873 K (p_O2= 1.88 × 10⁻²¹ bar) and oxide reduction at 1573 K in 10⁻⁴ bar O₂. As a reference, the grey area marks Δδ for CeO_2−δ (equivalent to that shown with Fig. 6). Error bars are the sum of the experimental uncertainties for the oxidation and reduction runs.

To evaluate this hypothesis, we performed TGA experiments for YFeO₃, YCo_0.1Fe_0.9O₃, YCo_0.3Fe_0.7O₃, and YCo_0.5Fe_0.5O₃ with reduction at 1573 K in 10⁻⁴ bar O₂ and oxidation at 873 K in 1% CO in CO₂ (1.88 × 10⁻²¹ bar O₂). Fig. 8b shows the oxygen exchange capacities obtained for these materials. We find increasing the Fe concentration in YCo_0.5Fe_0.5O₃ increases its oxygen exchange capacity from 0.07 mol_Omol_ABO3⁻¹ for YCo_0.5Fe_0.5O₃ to 0.11 mol_Omol_ABO3⁻¹ for YCo_0.3Fe_0.7O₃, which confirms our hypothesis. Further increasing the Fe concentration of YCo_0.3Fe_0.7O₃ decrease Δδ, which we suggest indicates increasing energetic limitations arising from the unfavorable thermodynamic equilibrium of the perovskite reduction, analogous to that of YFeO₃ (cf.Fig. 8a). This trend in the bonding strength of the lattice oxygen in metal-doped bulk perovskites is analogous to the trend in the adsorption energy of molecular fragments at bimetallic surfaces,⁵¹ which describes the similarity between the bonding of the gaseous reactant with varying coordination at the surface vs. in the bulk. Generally, these results demonstrate the utility of the presented electronic structure calculations to guide the rational design of perovskites. The presented methodology facilitates screening for redox-active materials at selected process conditions and fine-tuning of the oxygen exchange capacity for this highly versatile class of metal oxides for solar-driven thermochemical fuel synthesis.

3.3 Crystal phase stability and carbonate formation

This section validates the DFT-predicted trend that stronger endothermic perovskite reduction, that is, more positive values, indicates increasing thermochemical stability of the perovskite against a phase change yielding binary metal oxides and against carbonate formation. These electronic structure calculations are discussed in detail in Section 2.2, with trends in the metal carbonate formation predicted only for perovskites with ABO₃ stoichiometry. To this end, we evaluated the stability of selected perovskites using TGA, room-temperature X-ray diffraction (RT-XRD), high-temperature X-ray diffraction (HT-XRD), and transmission electron microscopy (TEM). The following discusses results that are representative for the investigated materials. The complete data is provided with ESI, including Fig. S9 and S10† showing HT-XRD spectra for SrTiO₃, SrCoO₃, SrMnO₃, LaAlO₃, BaCoO₃ and BaMnO₃ at 310, 675, 875, 1075, and 1275 K, in 100% CO₂ (to assess carbonate formation) and in 0.2 bar O₂ (to assess the stability of the cubic perovskite phase), respectively.

Regarding the thermochemical stability against decomposition of the cubic perovskite phase, the HT-XRD spectra, given with Fig. S9 and S10,† show segregation of SrCoO₃ into lower-symmetry metal oxides. As expected, SrTiO₃ remains stable, independent of temperature and pressure. This confirms the DFT-predicted stability trend, given that the lattice oxygen binds significantly stronger in SrTiO₃ (with of about 760 kJ mol_O2⁻¹) than in SrCoO₃ ( of 151 kJ mol_O2⁻¹). Similarly, SrMnO₃ ( of 314 kJ mol_O2⁻¹) and LaAlO₃ ( of 860 kJ mol_O2⁻¹) are thermochemically stable, as they do not show phase changes upon heating in either 0.2 bar O₂ or CO₂, opposed to less stable BaCoO₃ ( of 92 kJ mol_O2⁻¹) and BaMnO₃ ( of 237 kJ mol_O2⁻¹). The enthalpy change of BaMnO₃ reduction is near 200 kJ mol_O2⁻¹, which prohibits conclusive interpretation (cf. Section 2.2) within an uncertainty of this guide in the order of 10 kJ mol_O2⁻¹, partly due to the approximate nature of the perovskite models (that may converge to the actual extend and distribution of oxygen nonstoichiometries at infinitely large size) and structural differences between the synthesized perovskites (such as those in crystal phase or surface morphology).

Regarding the thermochemical stability against metal carbonate formation, Fig. 9a shows the mass gain for BaCoO₃, SrCoO₃, BaMnO₃, SrMnO₃ and SrTiO₃ exposed in a TGA to pure CO₂ at 973, 873, and 773 K (cf. Fig. S9†). We assume this mass gain is solely due to carbonate formation, which is discussed critically further below. As a general trend, we find the extent of apparent carbonate formation increases with less endothermic , as predicted. This can be seen in Fig. 9a, for instance by the relative weight changes for SrCoO₃ ( of 151 kJ  mol_O2⁻¹), BaMnO₃ ( of 237 kJ  mol_O2⁻¹) and SrTiO₃ ( of 760 kJ  mol_O2⁻¹) of +1.5, +0.15 and −0.047 wt%, respectively. SrCoO₃ and BaCoO₃ deviate from this trend, which may reflect differences in the crystal phase between the prepared samples (hexagonal BaCoO₃vs. cubic SrCoO₃, both shown with Fig. S12†) and the models (cubic perovskites), as well as differences in the oxygen nonstoichiometries between the prepared samples (possibly with δ > 0, as we reported previously for simpler compositions, such as BaCoO_2.58 and SrCoO_2.95)⁴⁶ and the models (which assume at oxidizing conditions δ = 0).

Fig. 9 (a) Percent mass change as a function of for BaCoO₃, SrCoO₃, BaMnO₃, SrMnO₃, and SrTiO₃. (b–e) Drift-corrected elemental maps and their overlays for BaCoO₃ obtained by TEM analysis.

To obtain evidence for the assumption that the weight gain recorded in presence of CO₂ is indeed due to metal carbonate formation, we analyzed selected samples using RT-XRD. This data is shown with Fig. S12,† which confirms formation of SrCO₃ by SrCoO₃ and of BaCO₃ by BaCoO₃. This is expected, in particular for these two perovskites that show the highest weight gains in the oxidation runs (cf.Fig. 9). To visualize and locate metal carbonate formation at the perovskite surface, TEM measurements are given with Fig. S13–S16.† As it can be concluded from the spatial distribution of the signals for carbon, oxygen, and the A-site metals, the analysis indicates formation of metal carbonates by SrCoO₃ and BaCoO₃, more so than by SrTiO₃ and SrMnO₃. This is shown with Fig. 9b–e, showing as an example the TEM data for BaCoO₃. We conclude apparent formation of BaCO₃ in surface regions with signals for Ba, C and O, but not for Co (as indicated in Fig. 9e). Equivalent regions we find for SrCoO₃ (cf. Fig. S15†), but neither for SrTiO₃ (cf. Fig. S14†) nor for SrMnO₃ (cf. Fig. S16†), which is in agreement with the trend in the weight changes discussed above (cf.Fig. 9a).

4. Conclusions

We used density functional theory to screen a large range of perovskites for their redox activity and thermochemical stability for solar-driven thermochemical splitting of CO₂. The computationally predicted trends are validated experimentally and employed for the fine-tuning of the oxygen exchange capacity of selected perovskite compositions. Our major findings are, firstly, perovskites with thermodynamically favorable redox energetics at reasonable process conditions can be identified with an enthalpy of metal oxide reduction at ambient conditions in the range of 440 to 630 kJ  mol_O2⁻¹. Secondly, ABO₃-type perovskites containing divalent metal cations at the A-site exhibit a stable cubic crystal phase in an inert atmosphere and thermochemical stability against metal carbonate formation in presence of CO₂, provided their enthalpy of metal oxide reduction is equal to or larger than 200 kJ  mol_O2⁻¹. This descriptor-based guide for the rational design of perovskites is useful for predicting redox-activity of a perovskite at a selected set of process conditions, fine-tuning of the oxygen exchange capacity via metal cation doping, and for assessing the thermochemical stability of the perovskite phase in an inert or CO₂ atmosphere. These properties of this class of highly versatile metal oxides is particularly important for designing redox materials for thermochemical fuel synthesis, but as well central to related high-temperature applications, such as carbonate-free solid oxide fuel cells.

Furthermore, we demonstrated the importance of choosing an appropriate set of redox cycle conditions for the screening of perovskite redox materials, as this class of materials with typically oxidation-limited redox energetics exhibits a significantly higher sensitivity to the composition of the oxidant, very different to the reduction-limited redox energetics of nonstoichiometric ceria. In this regard, we conclude perovskites do not outperform nonstoichiometric ceria for solar-driven thermochemical fuel synthesis applications at the high-temperature swing conditions used most beneficially with ceria. However, certain perovskites are found redox-active at lower oxide reduction temperatures, offering an option to alleviate thermal and mechanical stress in solar receiver–reactors and to diminish volatilization of solids. This, however, comes at the costs of additional energy penalties for providing low O₂ partial pressures and/or excess oxidant.

5. Experimental section

5.1 Electronic structure calculations

All DFT calculations were performed using the Grid-based projector-augmented wave (GPAW) code.^52,53 Atomic configurations were handled in the atomic simulation environment (ASE),⁵⁴ with exchange–correlation interactions treated by the revised Perdew–Burke–Ernzerhof (RPBE) functional.⁵⁵ The atomic geometries were optimized employing the line search Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm until the maximum force was less than 0.05 eV Å⁻¹. Convergence was achieved using a Fermi–Dirac smearing of 0.1 eV. The results were extrapolated to 0 K. Analogous to previous studies,^{33,42,46,56–58} all DFT calculations reported here use the generalized gradient approximation (GGA) without a Hubbard U correction, as previous studies demonstrated that this does not improve the description of surface activity with the employed perovskite models.⁴² AA′BB′O₃ perovskites were modeled with A₂B₂O₆ models containing two cubic ABO₃ unit cells with the same or two different metals (Mg, Ca, Sr, Ba, Y, La or Ce) at the twelve-fold coordinated A-site interstices, and the same or two different metals (Ti, Cr, Mn, Fe, Co, Ni, Cu, Zr or Al) at the six-fold coordinated B-site interstices. All atoms of the bulk models were allowed to optimize their positions (relax). In total, 297 compositions were modeled, with either ABO₃- (63 compositions), AA′BO₃- (77 compositions), ABB′O₃- (67 compositions), or AA′BB′O₃-type stoichiometry (90 compositions). The Brillouin zone of the bulk models with periodic boundary conditions in all directions was sampled with 4 × 4 × 4 k-points. Compositions containing Mn, Fe, Co, or Ni were modeled using spin-polarized calculations. The DFT-computed lattice constants are found within 0.07 to 2.17% of the experimental values. The minimum and maximum values of the computed lattice constants of the ABO₃, AA′BO₃, ABB′O₃ and AA′BB′O₃ perovskites are given along with the related magnetic moments with ESI.†

Perovskite surfaces were modeled using the (010) facet with AO-termination, which is geometrically symmetric with the (001) and (100) facet, dependent on composition, based on previous work suggesting that this is the thermodynamically most stable surface.⁴² The surface models contained the same number of atoms as the bulk models, that is with A₂B₂O₆ stoichiometry, of which the upper ABO₃(010) layer parallel to the surface was allowed to relax, while the lower ABO₃ layer was constrained to the bulk geometry. All surface models were periodically repeated in the directions parallel to the surface, used 10 Å of vacuum perpendicular to the surface, and employed a k-point sampling of 4 × 4 × 1. To model reduced perovskite surfaces, one third of the stoichiometric lattice oxygen in the upper surface layer was removed yielding A₂B₂O₅(010) stoichiometry with δ = 0.5.

The Gibbs free energy of oxygen vacancy formation (ΔG_v[O]) was computed with:⁴²

ΔG_v[O] = G_v − (G_s − G^r_O) (4)

with G_v and G_s being the Gibbs free energies of the perovskite surface models with and without oxygen vacancies, and with G^r_O being the reference energy of the liberated lattice oxygen, taken as the energy difference of stable H₂O and H₂ in the gas phase. Negative free energies correspond to exergonic reactions.

We employ the standard enthalpy of bulk metal oxide decomposition into the metals and O₂, computed at 298 K and 1 bar total pressure (Δh̄°), as a descriptor of redox-activity. For a limited number of mostly stoichiometric binary metal oxides, Δh̄° can be computed from tabulated thermochemical data.⁵⁹ To estimate Δh̄° for the investigated perovskites without the need for resource-demanding phonon calculations to determine solid-state entropies, we utilized previously established scaling relations describing the correction between Δh̄° and ΔG_v[O].⁴² As discussed in detail with ESI,† we employed:

Thermodynamic properties obtained using eqn (5) are per mole O₂. Detailed descriptions of converting the DFT-derived ΔG_v[O] values into Gibbs free energy changes at a specific set of reaction temperature and p_O2, and of the utilized reference energies are provided with ESI.†

5.2 Sample preparation

All perovskites were synthesized with a modified Pechini method, using stoichiometric amounts of La(NO₃)₃·H₂O (Sigma Aldrich, 99.999%), Sr(NO₃)₂ (Sigma Aldrich, 98%), Mn(NO₃)₂·4H₂O (Alfa Aesar, 98%), Al(NO₃)₃·9H₂O (Alfa Aesar, 98%), Ca(NO₃)₂·4H₂O (Alfa Aesar, 99%), Y(NO₃)₃·6H₂O (Alfa Aesar, 99.9%), Co(NO₃)₂·6H₂O (Sigma Aldrich, 98%), Ni(NO₃)₂·6H₂O (Sigma Aldrich, 97%), C₂H₆O (Alcosuisse, >96.1% vol) and C₆H₈O₇ (Fluka Chemika, ≥99.5%). The ratio between the metal cations and citric acid was 2 : 3. SrTiO₃ (99%) was purchased from Sigma-Aldrich. Solid products were ground using mortar and pestle and sintered for 24 h in air at 1573 K with heating and cooling at 2.5 K min⁻¹.

5.3 Solid-state analysis

RT-XRD and HT-XRD were performed in the Bragg Brentano geometry using Cu Kα radiation (20–80° 2θ, 0.01° min⁻¹ scan rate, 45 kV/20 mA output, PANalytical/X'Pert MPD/DY636, Philips). The HT-XRD experiments were performed at 673, 873, 1073, and 1273 K, with heating at 10 K min⁻¹ and a gas flow of 1 L min⁻¹. All volumes are given at standard conditions, here 1 bar and 20 °C. Before each HT-XRD scan, the temperature was held for one hour to establish thermodynamic equilibrium. TEM analyses were performed for SrTiO₃, SrCoO₃, SrMnO₃, and BaCoO₃ employing the high angle annular dark field detector used in scanning transmission electron microscopy (HAADF STEM) imaging mode and complemented by elemental distribution analyses using the SuperX EDX system of a FEI TalosF200X instrument, operated at 200 kV acceleration voltage. The surfaces of SrTiO₃, BaCoO₃, SrMnO₃, and SrCoO₃ were sampled at 17, 8, 9, and 9 different locations, respectively.

5.4 Thermal analysis

Perovskite reduction and oxidation were performed using a TGA (Setaram Setsys Evolution) to measure oxygen nonstoichiometries (δ). Samples with a mass of about 100 mg were finely ground and placed into an Al₂O₃ crucible which was covered with a platinum sheet. Heating and cooling were at 10 and 20 K min⁻¹, respectively. Reduction was carried out at 1573 K and used a gas flow of 175 mL min⁻¹ with a p_O2 of 10⁻⁴, 3.04 × 10⁻⁴, and 5.07 × 10⁻⁴ bar O₂, adjusted using a mixture of 500 ppm O₂ in Ar and pure Ar. Reduction conditions were held for 60 min. Oxidation was carried out at 873, 1073, and 1273 K and used a gas flow of 192 mL min⁻¹ with a p_O2 of 1.88 × 10⁻²¹, 3.79 × 10⁻¹⁵, and 7.75 × 10⁻¹¹ bar, respectively. These p_O2 values correspond to 1% CO in CO₂, simulating a typical gas composition at the end of the oxidation run in a solar receiver–reactor.⁶ To assess the sensitivity of the perovskites to the gas composition during oxidation, oxidation was carried out also in pure CO₂ and 873, 1073, and 1273 K, corresponding to a p_O2 of 3.67 × 10⁻⁹, 4.63 × 10⁻⁷, and 1.27 × 10⁻⁵ bar O₂. Oxidation conditions were held for 80 min. For complete re-oxidation before and after each reduction and oxidation experiment, the samples were exposed for 30 min at 873 K to a gas flow of 175 mL min⁻¹ with 0.2 bar O₂. The gas composition at the TGA outlet was monitored with a gas chromatograph (GC, CP-4900 System, Agilent Technologies). To account for buoyancy effects, blank runs were conducted for all specific measurement conditions without the perovskite samples.

Acknowledgements

We gratefully acknowledge the financial support by the Swiss National Science Foundation (Ambizione Energy Grant No. 166883), the Helmholtz-Gemeinschaft Deutscher Forschungszentren (Virtuelles Institut SolarSyngas), and the European Research Council under the European Union's ERC Advanced Grant (SUNFUELS-No. 320541). The DFT calculations were performed at the High-Performance Computation cluster of ETH Zürich.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7ta02081c

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