PEROVSKITES FOR REDUCTION-RE-OXIDATION THERMOCHEMICAL WATER AND CARBON DIOXIDE SPLITTING

Abstract

A metal-oxide perovskite material having a general formula Ca.sub.1-xCe.sub.xTi.sub.yMn.sub.1-yO.sub.3, where x is in a range of about 0.3 to about 0.35 and y is in a range of about 0.25 to about 0.35. Producing hydrogen and oxygen includes heating the metal-oxide perovskite material; reducing the metal-oxide perovskite material to yield a reduced metal-oxide perovskite material; cooling the reduced metal-oxide perovskite material; and contacting the reduced metal-oxide perovskite material with a re-oxidizing fluid including steam to yield hydrogen and a re-oxidized metal-oxide perovskite material. Producing carbon monoxide and oxygen includes heating the metal-oxide perovskite material; reducing the metal-oxide perovskite material to yield a reduced metal-oxide perovskite material; cooling the reduced metal-oxide perovskite material, and contacting the reduced metal-oxide perovskite material with a re-oxidizing fluid including carbon dioxide to yield carbon monoxide and a re-oxidized metal-oxide perovskite material.

Claims

1. A metal-oxide perovskite material having a general formula Ca.sub.1-xCe.sub.xTi.sub.yMn.sub.1-yO.sub.3, wherein x is in a range of about 0.3 to about 0.35 and y is in a range of about 0.25 to about 0.35.

2. The metal-oxide perovskite material of claim 1, wherein the metal-oxide perovskite material yields a reduced metal-oxide perovskite material having a general formula Ca.sub.1-xCe.sub.xTi.sub.yMn.sub.1-yO.sub.3-δr in a reducing environment after heating to a reduction temperature, wherein 0.5>δr>0.

3. The metal-oxide perovskite material of claim 2, wherein the reduction temperature is in a range of about 1600K to about 2000K.

4. The metal-oxide perovskite material of claim 2, wherein the reduced metal-oxide perovskite material yields a re-oxidized metal-oxide perovskite material having a general formula Ca.sub.1-xCe.sub.xTi.sub.yMn.sub.1-yO.sub.3-δo and hydrogen when contacted with water at a re-oxidation temperature, wherein 0<δo<δr.

5. The metal-oxide perovskite material of claim 4, wherein the re-oxidation temperature is in a range of about 900K to about 1500K.

6. The metal-oxide perovskite material of claim 2, wherein the reduced metal-oxide perovskite material yields a re-oxidized metal-oxide perovskite material having a general formula Ca.sub.1-xCe.sub.xTi.sub.yMn.sub.1-yO.sub.3-δo and carbon monoxide when contacted with carbon dioxide at a re-oxidation temperature, wherein 0<δo<δr.

7. The metal-oxide perovskite material of claim 6, wherein the re-oxidation temperature is in a range of about 900K to about 1500K.

8. The metal-oxide perovskite material of claim 2, wherein the reduced metal-oxide perovskite material yields a re-oxidized metal-oxide perovskite material having a general formula Ca.sub.1-xCe.sub.xTi.sub.yMn.sub.1-yO.sub.3-δo and syngas when contacted with a re-oxidizing fluid comprising water and carbon dioxide at a re-oxidation temperature, wherein 0<δo<δr.

9. The metal-oxide perovskite material of claim 8, wherein the re-oxidation temperature is in a range of about 900K to about 1500K.

10. A method of producing hydrogen and oxygen, the method comprising: a) heating a metal-oxide perovskite material; b) reducing the metal-oxide perovskite material to yield oxygen and a reduced metal-oxide perovskite material having a general formula Ca.sub.1-xCe.sub.xTi.sub.yMn.sub.1-yO.sub.3-δr, wherein x is in a range of about 0.3 to about 0.35, y is in a range of about 0.25 to about 0.35, and 0.5>δr>0; c) cooling the reduced metal-oxide perovskite material; and d) contacting the reduced metal-oxide perovskite material with a re-oxidizing fluid comprising steam to yield hydrogen and a re-oxidized metal-oxide perovskite material having a general formula Ca.sub.1-xCe.sub.xTi.sub.yMn.sub.1-yO.sub.3-δo, wherein 0<δo<δr.

11. The method of claim 10, wherein heating the metal-oxide perovskite material comprises heating to a temperature in a range of about 1600K to about 2000K.

12. The method of claim 10, wherein cooling the reduced metal-oxide perovskite material comprises cooling to a temperature in a range of about 900K to about 1500K.

13. The method of claim 10, wherein heating the metal-oxide perovskite material comprises heating with concentrated solar energy or a radiant heat lamp.

14. The method of claim 10, wherein reducing the metal-oxide perovskite material occurs in a reducing environment having a partial pressure of oxygen less than 0.01 bar.

15. The method of claim 14, wherein the reducing environment comprises nitrogen, argon, steam, carbon dioxide, or any combination thereof.

16. The method of claim 10, wherein the re-oxidizing fluid further comprises carbon dioxide, and contacting the reduced metal-oxide perovskite material with the re-oxidizing fluid further yields carbon monoxide.

17. The method of claim 10, further comprising repeating a)-d), wherein heating the metal-oxide perovskite material comprises heating the re-oxidized metal-oxide perovskite material.

18. A method of producing carbon monoxide and oxygen, the method comprising: a) heating a metal-oxide perovskite material; b) reducing the metal-oxide perovskite material to yield oxygen and a reduced metal-oxide perovskite material having a general formula Ca.sub.1-xCe.sub.xTi.sub.yMn.sub.1-yO.sub.3-δr, wherein x is in a range of about 0.3 to about 0.35, y is in a range of about 0.25 to about 0.35, and wherein 0.5>δr>0; c) cooling the reduced metal-oxide perovskite material; and d) contacting the reduced metal-oxide perovskite material with a re-oxidizing fluid comprising carbon dioxide to yield carbon monoxide and a re-oxidized metal-oxide perovskite material having a general formula Ca.sub.1-xCe.sub.xTi.sub.yMn.sub.1-yO.sub.3-δo, wherein 0<δo<δr.

19. The method of claim 18, wherein heating the metal-oxide perovskite material comprises heating to a temperature in a range of about 1600K to about 2000K.

20. The method of claim 18, wherein cooling the reduced metal-oxide perovskite material comprises cooling to a temperature in a range of about 900K to about 1500K.

21. The method of claim 18, wherein heating the metal-oxide perovskite material comprises heating with concentrated solar energy or a radiant heat lamp.

22. The method of claim 18, wherein reducing the metal-oxide perovskite material occurs in a reducing environment having a partial pressure of oxygen less than 0.01 bar.

23. The method of claim 22, wherein the reducing environment comprises nitrogen, argon, steam, carbon dioxide, or any combination thereof.

24. The method of claim 18, wherein the re-oxidizing fluid further comprises steam, and contacting the reduced metal-oxide perovskite material with the re-oxidizing fluid further yields hydrogen.

25. The method of claim 18, further comprising repeating a)-d), wherein heating the metal-oxide perovskite material comprises heating the re-oxidized metal-oxide perovskite material.

Description

BRIEF DESCRIPTION OF DRAWINGS

[0017] FIG. 1 depicts a general mechanism for thermochemical hydrogen production using a redox-active metal oxide.

[0018] FIG. 2 depicts the special quasirandom structure (SQS) for Pnma Ca.sub.2/3Ce.sub.1/3Ti.sub.1/3Mn.sub.2/3O.sub.3 (CCTM2112) optimized using Hubbard-U-corrected density functional theory (DFT) based on the strongly constrained and appropriately normed (SCAN) exchange-correlation functional. Lattice constants are labeled as (a, b, and c).

DETAILED DESCRIPTION

[0019] This disclosure describes a non-consumed reactant in a thermochemical cycle (TCC) for water and carbon-dioxide splitting that can be powered by renewable heat sources. The reactant is a redox-active metal-oxide perovskite material generally referred to as a Ca—Ce—Ti—Mn oxide perovskite. A general formula of the metal-oxide perovskite material is Ca.sub.1-xCe.sub.xTi.sub.yMn.sub.1-yO.sub.3, where x is in a range of about 0.3 to about 0.35 and y is in a range of about 0.25 to about 0.35. This metal-oxide perovskite material is generally referred to herein as Ca.sub.2/3Ce.sub.1/3Ti.sub.1/3Mn.sub.2/3O.sub.3 or CCTM2112, where “2112” indicates the relative composition of the material for three formula units or numerators of the fractional A- and B-site compositions for one formula unit.

[0020] Ca—Ce—Ti—Mn oxide perovskites can be employed in solar thermochemical reactors that use concentrated solar energy TCC redox reactions. Other examples of suitable heat sources include radiant heat lamps, low-carbon sources of electrically generated heat, and other renewable resources. The metal-oxide perovskite material is heated in an environment having a low partial pressure of oxygen to reduce one or more metals in the metal-oxide perovskite material and release molecular oxygen, producing oxygen vacancies in the material. After cooling, the reduced metal-oxide perovskite material can be contacted with steam, carbon dioxide, or both to re-oxidize the reduced metal-oxide perovskite material and yield molecular hydrogen (“hydrogen gas” or “hydrogen”), carbon monoxide, or syngas (hydrogen and carbon monoxide), respectively.

[0021] FIG. 1 illustrates a simplified TCC to generate thermochemical hydrogen. As depicted, a redox-active metal-oxide perovskite material (e.g., Ca.sub.2/3Ce.sub.1/3Ti.sub.1/3Mn.sub.2/3O.sub.3) is heated (e.g., by absorption of radiation from concentrated solar energy). The metal-oxide perovskite material is heated to a reduction temperature, and is reduced in a reducing environment. As used herein, “reduction temperature” generally refers to a temperature sufficient to reduce the metal-oxide perovskite material in a reducing environment with a low partial pressure of oxygen (pO.sub.2). In one example, a low pO.sub.2 environment has a pO.sub.2 of less than about 0.01 bar (e.g., between about 0.00001 bar and about 0.01 bar). The low pO.sub.2 environment can include an inert gas (e.g., nitrogen or argon), steam, carbon dioxide, or any combination thereof. In some cases, the total pressure of the low pO.sub.2 environment is less than 1 atmosphere. The reduction temperature is typically in a range of about 1600K to about 2000K. In some examples, heating to a reduction temperature includes following a predetermined heating profile. Heating the metal-oxide perovskite material to the reduction temperature results in oxygen vacancies in the metal-oxide perovskite material, yielding molecular oxygen (“oxygen gas” or “oxygen”) and a reduced form of the metal-oxide perovskite material (a “reduced metal-oxide perovskite material”). The reduced metal-oxide perovskite material has a general formula Ca.sub.1-xCe.sub.xTi.sub.yMn.sub.1-yO.sub.3-δr, wherein 0.5>δr>0.

[0022] The reduced metal-oxide perovskite material is cooled in a low pO.sub.2 environment to a re-oxidation temperature. As used herein, “re-oxidation temperature” generally refers to a temperature sufficient to re-oxidize the reduced metal-oxide perovskite material in the presence of steam (gaseous water), carbon dioxide, or both. The re-oxidation temperature is typically in a range of about 900K to about 1500K. In some examples, cooling to a re-oxidation temperature includes following a predetermined cooling profile. When the reduced metal-oxide perovskite material is at or above the re-oxidation temperature, it is contacted with a re-oxidizing fluid that includes steam, carbon dioxide, or both. In some cases, the re-oxidizing fluid includes small amounts (e.g., less than 0.5 vol %) of one or both of hydrogen and carbon monoxide.

[0023] As depicted in FIG. 1, contacting the reduced metal-oxide perovskite material with steam re-oxidizes the reduced metal-oxide perovskite material to yield a re-oxidized metal-oxide perovskite material, and also yields hydrogen during re-oxidation and yields oxygen during reduction. The re-oxidized metal-oxide perovskite material has a general formula Ca.sub.1-xCe.sub.xTi.sub.yMn.sub.1-yO.sub.3-δo, wherein 0<δo<δr. In some implementations, the reduced metal-oxide perovskite material is contacted with carbon dioxide. Contacting the reduced metal-oxide perovskite material with carbon dioxide re-oxidizes the reduced metal-oxide perovskite material to yield a re-oxidized metal-oxide perovskite material, and also yields carbon monoxide during re-oxidation and yields oxygen during reduction. The re-oxidized metal-oxide perovskite material has a general formula Ca.sub.1-xCe.sub.xTi.sub.yMn.sub.1-yO.sub.3-δo, wherein 0<δo<δr. In certain implementations, the reduced metal-oxide perovskite material is contacted with steam and carbon dioxide. Contacting the reduced metal-oxide perovskite material with steam and carbon dioxide re-oxidizes the reduced metal-oxide perovskite material to yield a re-oxidized metal-oxide perovskite material, and yields hydrogen and carbon monoxide (syngas) during re-oxidation and oxygen during reduction. The re-oxidized metal-oxide perovskite material has a general formula Ca.sub.1-xCe.sub.xTi.sub.yMn.sub.1-yO.sub.3-δo, wherein 0<δo<δr.

[0024] The interior of FIG. 1 shows an example of a plot of the logarithm of pO.sub.2 in a simplified TCC. The pO.sub.2 is a function at least in part, of the temperature and pressure of the environment and an amount of components such as an inert gas (e.g., nitrogen or argon), hydrogen, carbon monoxide, steam, and carbon dioxide. The lower dotted line in the plot depicts heating at a constant δo. The upper dotted line in the plot depicts cooling at a constant Sr.

[0025] An example synthesis of and experimental data related to the TCC performance of CCTM2112 is provided in “Multiple and nonlocal cation redox in Ca—Ce—Ti—Mn oxide perovskites for solar thermochemical applications” (Robert B. Wexler et al., Energy Environ. Sci., 2023, Advance Article, May 3, 2023), which is incorporated by reference herein.

[0026] CCTM2112 is an A-site redox-active perovskite with multiple redox-active cations in the same compound and on different sublattices, and it is predicted to have a lower reduction enthalpy than CeO.sub.2. Because reduction enthalpy influences redox capacity and water and carbon dioxide splitting efficiency, CCTM2112 is predicted to be an effective reactant in thermochemical reduction-re-oxidation cycles. Quantum-based modeling of CCTM2112 indicates that A-site Ce.sup.4+ reduction dominates the redox activity of the material.

[0027] The stability of CCTM2112 was computed as the energy above the convex hull (E.sub.hull), which is the energy change upon decomposition of a material into stable compounds at the same composition. Hubbard-U-corrected density functional theory (DFT) calculations were performed with the strongly constrained and appropriately normed (SCAN) exchange-correlation functional. Based on a convex hull construction, CCM is thermodynamically metastable, with an E.sub.hull=39 meV/atom at 0 K.

[0028] The structure of CCTM2112 is a Pnma Ca.sub.2/3Ce.sub.1/3Ti.sub.1/3Mn.sub.2/3O.sub.3 solid solution, matching the Pnma structure of CaTiO.sub.3. To simulate an experimentally realistic CCTM2112 solid solution, an optimized special quasirandom structure (SQS) was constructed with 360 atoms (216 of which are O atoms) and lattice constants of a=16.70 Å, b=15.28 Å, and c=16.13 Å, corresponding to supercell dimensions of 3×2×3, as shown in FIG. 2. As described herein, “optimized” generally refers to optimization of the lattice constants and optimization of the particular SQS to mimic the random alloy. SCAN+U calculations show that CCTM2112 has an ≈15% lower E.sub.hull (=33 meV/atom, which is comparable to k.sub.B298.15 K≈26 meV/atom) than the previously predicted CCM material, indicating improved stability. Other contributions to the stabilization of CCTM2112 may include configurational entropy (which is >41 meV/atom at 1273 K).

[0029] The energetics of oxygen vacancy (V.sub.O) formation in CCTM2112 and its dependence on the V.sub.O's nearest neighbors (NNs) were analyzed. All 216 V.sub.Os were categorized by their NN environment, and one V.sub.O was randomly sampled (i.e., one V.sub.O was introduced in the SQS, corresponding to δ=0.014) from each of the 13 unique V.sub.O NN environments. This categorization also gave a tractable number of SCAN+U calculations from which to study the trends in the electronic and thermochemical properties of V.sub.Os. NN V.sub.O environments were defined using x.sub.Ce and x.sub.Mn, where x.sub.Ce=N.sub.Ce/(N.sub.Ca+N.sub.Ce), x.sub.Mn=N.sub.Mn/(N.sub.Ti+N.sub.Mn), and x (N) is the fraction (number) of the V.sub.O's four NN A-sites and two NN B-sites occupied by Ce (x.sub.Ce=1−x.sub.Ca and N.sub.Ce=4−N.sub.Ca) and Mn (x.sub.Mn=1−x.sub.Ti and N.sub.Mn=2−N.sub.Ti), respectively. The overall supercell structure maintained the same cation stoichiometry as that of bulk CCTM2112, with x.sub.Ce and x.sub.Mn strictly defining compositions that were local to the V.sub.O considered. Predictably, the V.sub.O with the highest frequency (f=44 or 44/216≈20% of the SQS) was the one with a NN environment closest to the bulk composition allowed by the A- and B-site NN fractions (x.sub.Ce=0.25 and x.sub.Mn=0.5 for the V.sub.O and x.sub.Ce=⅓ and x.sub.Mn=⅔ for the bulk). Two NN V.sub.O environments did not appear in the optimized SQS for CCTM2112 (namely those for x.sub.Ce=1 and x.sub.Mn≤0.5), however, V.sub.Os with these NN environments are unlikely to significantly influence the macroscopic reduction of CCTM2112 due to their scarcity (x.sub.Ce=1 and x.sub.Mn=0.5, and x.sub.Ce=1 and x.sub.Mn=0 make up 0.5% and 0.1% of the random alloy, respectively).

[0030] With this V.sub.O categorization protocol, five of the 13 V.sub.Os were predicted have E.sub.vs within (or within 0.06 eV of) the target range of 3.4-3.9 eV, including those with the first- and third-highest frequencies (f=44 or 44/216≈20% for x.sub.Ce=0.25 and x.sub.Mn=0.5, which is 17.6% in a random solid, and f=30 or 30/216≈14% for x.sub.Ce=x.sub.Mn=0.5, which is 13.2% of the sites in a random solid). To quantify the macroscopic reducibility of CCTM2112, the ensemble-averaged E.sub.v was calculated, with <E.sub.v>=Σ.sub.if.sub.iE.sub.v,i/Σ.sub.if.sub.i, where f.sub.i is the frequency of the i.sup.th unique NN V.sub.O environment, and Σ.sub.if.sub.i=216. −E.sub.v>=3.30 eV was obtained with a standard deviation of 0.36 eV which overlaps with the target range for water splitting. While E.sub.v depended weakly on x.sub.Ce, it systematically decreased with increasing x.sub.Mn. This trend can be rationalized based on crystal O.sup.2−-M.sup.n+ bond dissociation energies E.sub.b, an extension of molecular O-M bond dissociation energies to the solid state, defined as

[00001]$\begin{array}{cc}{E}_b\left[O^{2-}-M^{n+}\right]=\frac{E_c\left[{MO}_{n/2}\right]}{N_b\left[O^{2-}-M^{n+}\right]}& \left(1\right)\end{array}$

where n is the oxidation state of the metal cation (M), E.sub.c[MO.sub.n/2] is the cohesive energy of the ground-state polymorph of the binary metal-oxide crystal MO.sub.n/2 containing M.sup.n+, and N.sub.b[O.sup.2−-M.sup.n+] is the number of O.sup.2−-M.sup.n+ bonds per MO.sub.n/2 formula unit. In short, E.sub.v∝−x.sub.Mn because O.sup.2−-Mn.sup.4+ (crystal bond dissociation energy E.sub.b=2.25 eV) and O.sup.2−-Mn.sup.3+ (1.97 eV) crystal bonds are weaker than O.sup.2−—Ti.sup.4+ (3.16 eV) and O.sup.2−—Ti.sup.3+ (2.62 eV).

[0031] It can be advantageous to obtain a mechanistic understanding of the high performance of CCTM2112 compared to the structurally related CaTi.sub.0.5Mn.sub.0.5O.sub.3-δ (CTM) and the Ce- and Mn-containing BCM perovskites. Because atomic magnetic moments (μ) are extremely sensitive measures of oxidation- and spin-state changes, these values were calculated for CCTM2112 and provided in Table 1. For fully oxidized CCTM2112, the mean magnetic moments imply that, rounded to the nearest integer, the average oxidation states of Ca, Ce, Ti, Mn, and O are 2+, 4+, 4+, 3+, and 2−, respectively, which leads to a charge neutral formula unit. Ce also can exist as Ce.sup.3+ and Mn as Mn.sup.4+ and Mn.sup.2+, where the latter suggests that disproportionation of two Mn.sup.3+ may occur in pristine CCTM2112.

TABLE-US-00001 TABLE 1 Magnetic moment summary statistics for fully oxidized CCTM2112.sup.1 Element Mean ± σ Minimum Maximum Ca 0.00 ± 0.00 (Ca.sup.2+) 0.00 (Ca.sup.2+) 0.00 (Ca.sup.2+) Ce 0.28 ± 0.23 (Ce.sup.4+) 0.06 (Ce.sup.4+) 0.68 (Ce.sup.3+) Ti 0.05 ± 0.02 (Ti.sup.4+) 0.03 (Ti.sup.4+) 0.08 (Ti.sup.4+) Mn 3.77 ± 0.24 (Mn.sup.3+) 3.10 (Mn.sup.4+) 4.50 (Mn.sup.2+) O 0.01 ± 0.01 (O.sup.2−) 0.00 (O.sup.2−) 0.05 (O.sup.2−) σ is the first standard deviation. All values are in μB.

[0032] To gain greater insight into the nature of the electronic reorganization in CCTM2112 upon V.sub.O formation in the thermal reduction step, the V.sub.O-induced changes in the absolute values of μ.sub.Ce, μ.sub.Mn, and to were computed. (The use of absolute values controls for changes in relative orientation, e.g., ferromagnetic or antiferromagnetic). These |μ| value changes were then summed separately for Ce, Mn, and O to quantify the extent to which the A, B, and O sub-lattices, respectively, were reduced (positive value) or oxidized (negative value). These sums were calculated because changes in μ roughly correspond to changes in oxidation states, excluding Ca and Ti because insignificant spin changes were observed on these sites. Thus, the quantification of the number of electrons added to or removed from a species comes from the calculated changes in |μ|. For example, when x.sub.Ce=0 and the change in |μ.sub.Ce|≠0, a V.sub.O without a NN Ce has reduced a non-NN Ce, thus resulting in nonlocal or delocalized reduction.

[0033] Computational results showed that reduction occurred primarily on the A-site Ce sub-lattice compared with that of Mn and O, regardless of the V.sub.O's NNs. In particular, the Ce sub-lattice reduced by 0.75 to 2.23 electrons depending on x.sub.Ce and x.sub.Mn, corresponding to an average decrease in Ce oxidation state of 0.031 to 0.093 electrons, respectively (average reduction of the 24 Ce in the unit cell). For Mn, no obvious net reduction or oxidation occurred during the formation of the V.sub.O, with both mild reduction (≤0.35 electrons accepted) and oxidation (≤0.42 electrons donated) of Mn occurring simultaneously. During V.sub.O formation, the O sublattice experienced weak-to-mild reduction (<0.52 electrons accepted in total by the O sub-lattice containing 216 atoms in the unit cell). The reduction of the O sub-lattice was indicative of empty O states in the pristine material, indicating that the Os were not fully ionized as O.sup.2− (as indicated by Bader charge analysis), with instead the M-O bonds exhibiting some singlet-coupled covalent character, which spin-averaged the electrons on O to appear nonmagnetic.

[0034] Computational results indicated that Ce reduced even when it was not a nearest neighbor to the V.sub.O. To better understand this phenomenon, the spatial dependence of the |μ| changes induced by a V.sub.O with a Ca- and Mn-rich local environment (i.e., x.sub.Ce=0 and x.sub.Mn=1) was analyzed. Calculations indicated that two Ce were reduced (Δ|μ|=0.44 μ.sub.B and 0.53 μ.sub.B), at distances of 4.32 Å and 7.04 Å from the V.sub.O, respectively. Ca and Ti are not redox active and only a few O were slightly reduced or became more ionic, mostly at distances of <5 Å from the V.sub.O. Additionally, the Mn sub-lattice was both reduced and—to a slightly lesser extent—oxidized, leading to a net mild reduction of 0.35 electrons, corresponding to a disproportionation. Given that the changes for Mn were modest, experimental validation is non-trivial. Ce reduction-at-a-distance was also indicated by the difference between the electron density (ρ) of CCTM2112 with and without (i.e., in its pristine state) this same neutral V.sub.O (Δρ=ρ.sub.vacancy−ρ.sub.pristine), as electron density gain was observed emerging from and surrounding the two Ce atoms 4.32 Å and 7.04 Å away from the V.sub.O. This nonlocal reduction allows a substantial fraction of the Ce present in the material to participate in oxygen vacancy formation and may partially explain the high extent of Ce reduction in CCTM2112.

[0035] The spatial dependence of V.sub.O-induced reduction can be used to explain the subtle x.sub.Ce dependence of E.sub.v at x.sub.Mn=0. The value of E.sub.v for x.sub.Ce=0 (4.25 eV) can be attributed to the localized reduction of Ce, and the electrostatic penalty associated with its distance (4.67-4.83 Å) from the holes localized on the V.sub.O. For x.sub.Ce=0.25, the E.sub.v≈3.58 eV is anomalously low because, while the reduction of Ce remains fairly localized (two Ce reduced at distances <5 Å to the V.sub.O), these electrons are closer to the V.sub.O-generated holes and therefore electrostatically stabilize the V.sub.O. Strain can have an indirect effect on E.sub.v by inducing or relaxing Jahn-Teller distortions on Mn but the strain effect is difficult to quantify.

[0036] The highest value of E.sub.v (4.35 eV) was reached for x.sub.Ce=0.5, which can result from the sum of the following: (1) an electrostatic penalty for delocalized reduction of Ce (four Ce reduced by >0.27 electrons at distances of 2.36 Å to 9.48 Å from the V.sub.O) and the delocalized electrons' resultant screening of electron-hole interactions; and (2) a penalty for oxidizing the Mn (|Δμ|=−0.55 μ.sub.B) at a distance of 10.01 Å from the V.sub.O. From x.sub.Ce=0.5 to x.sub.Ce=0.75, E.sub.v decreases from 4.35 eV to 4.07 eV which, considering the latter's fairly delocalized reduction of Ce, may derive from the absence of oxidized Mn (i.e., Mn for which Δ|μ|<0 μ.sub.B). Therefore, the subtle x.sub.Ce dependence of E.sub.v at x.sub.Mn=0 can be explained by the nature (localized versus delocalized) and location of V.sub.O-generated charge carriers interacting electrostatically with the V.sub.O.

[0037] The results of these computations indicate that Ce.sup.4+ functions as the primary acceptor of electrons even though it is generally less reducible than Mn.sup.4+ and Mn.sup.3+. To quantify the reducibility of Ce.sup.4+, Mn.sup.4+, and Mn.sup.3+, the enthalpy changes of the following solid-state reduction reactions were calculated: CeO.sub.2.fwdarw.0.5 Ce.sub.2O.sub.3+0.25 O.sub.2, MnO.sub.2.fwdarw.0.5 Mn.sub.2O.sub.3+0.25O.sub.2, and 0.5 Mn.sub.2O.sub.3.fwdarw.MnO+0.25O.sub.2, respectively. Mn.sup.4+ is the most reducible cation (ΔH=0.40 eV) followed by Mn.sup.3+ (ΔH=1.02 eV) and then Ce.sup.4+ (ΔH=1.82 eV). Additionally, since these reactions are normalized per one-electron reduction, their ΔHs are effectively crystal reduction potentials (V.sub.r), which are a key factor governing E.sub.v in ternary oxide perovskites. While this simple analysis suggests that Ce should not reduce, the unoccupied states closest to the Fermi level in metallic CCTM2112 are Ce 4f states. Therefore, even though Ce.sup.4+ is less reducible than Mn.sup.4+ and Mn.sup.3+ in their ground-state binary oxides, Ce does reduce in CCTM2112 because there is a lower energy penalty for the structure to put the V.sub.O-donated electrons in the Ce 4f states, even if the Ce atom is physically farther from the V.sub.O. Ce.sup.4+ reduction is also accompanied by delocalization of electrons (due to the degeneracy of 4f states contributed by several Ce atoms close to the Fermi level), while Mn reduction is almost always localized, evidenced by the presence or absence of Jahn-Teller distortions associated with Mn.sup.3+. The need for 4f states near the Fermi level to reduce Ce.sup.4+ in the presence of Mn.sup.3+ is consistent with the observation that Mn and not Ce reduces during thermochemical cycling of Ba(Ce,Mn)O.sub.3 (BCM) perovskite oxide (where Ba is on the A-site, and Ce and Mn occupy the B-site). Mn reduces in this example because BCM has a band gap and thus V.sub.O-induced reduction is driven by cation proximity and reducibility rather than the relative location of unoccupied states near the Fermi level. Thus, the density of states for CCTM2112 promotes Ce reduction.

[0038] The high reducibility of Ce.sup.4+ in CCTM2112 is both advantageous to its high water-splitting performance and substantially different than the behavior of CeO.sub.2 and other previously demonstrated Ce.sup.4+-containing off-stoichiometric redox-active materials. The existence of Ce.sup.4+ reduction is observed directly in modeling. One structural distinction of CCTM2112 is the 12-fold coordination of Ce.sup.4+ on the A-site, compared to the 8-fold coordination of Ce.sup.4+ in the CeO.sub.2 fluorite structure and 6-fold coordination on the B-site of BCM.

[0039] Computational Details. Neutral oxygen vacancy formation energies were calculated using spin-polarized DFT as implemented in the Vienna Ab initio Simulation Package (VASP) version 5.4.4. DFT calculations were performed within the SCAN+U framework, where U were fit to relevant oxidation energies for Ce, Ti, V, Cr, Mn, Fe, Co, and Ni oxides. This framework provides superior predictions of bulk thermodynamics, band gaps, and magnetic configurations in comparison to PBE, PBE+U, and SCAN. All-electron, frozen-core, projector augmented-wave (PAW) potentials were utilized to describe the ion-electron interactions, including the non-spherical contributions related to the electron density gradient and the kinetic energy density within the PAW spheres for the XC evaluation. The Accurate “precision” mode was used in VASP to avoid aliasing errors when setting fast-Fourier-transform and support grids. An additional support grid was employed for the more accurate estimation of augmentation charges and the projection operators were evaluated in real space using VASP's fully automatic optimization scheme. The electronic wave function was expanded in a plane-wave basis with a kinetic-energy cutoff of 520 eV and only the Γ-point of the Brillouin zone was sampled due to the large size of the supercell (360 atoms). A Gaussian smearing function was applied with a width of 0.05 eV to improve self-consistent-field convergence. Collinear, spin-polarized calculations were performed and the atomic magnetic moments were initialized for the bulk in a ferromagnetic configuration with values of 0.6 μ.sub.B for nominally nonmagnetic species (Ca.sup.2+, Ce.sup.4+, Ti.sup.4+, and O.sub.2) and 4μ.sub.B for Mn.sup.3+, which corresponds to its high spin state in an octahedral crystal field. For the vacancies, the atomic magnetic moments were initialized with bulk-optimized values.

[0040] Computational Prediction of Stability. To compute the stability of CCTM2112, its energy above the convex hull (E.sub.hull) was calculated, where E.sub.hull is the energy of decomposition into the set of most stable materials at its chemical composition. To calculate E.sub.hull, the phase diagram code in pymatgen and SCAN+U total energies (E.sub.tot) of materials containing Ca, Ce, Ti, Mn, and O were used. This code takes as input the total energies and compositions of these materials and returns the list of stable compositional coordinates in the phase diagram, where a stable compositional coordinate is a set of compounds in equilibrium that define the chemical potentials of Ca, Ce, Ti, Mn, and O and that are on the convex hull. The results show that CCTM2112 is metastable at 0 K, with an E.sub.hull of 33 meV/atom, i.e., a ΔE for its decomposition reaction of

Ca.sub.2Ce.sub.1Ti.sub.1Mn.sub.2O.sub.9.fwdarw.⅓Mn.sub.2O.sub.3+⅔CaMn.sub.2O.sub.4+⅓Ca.sub.4Ti.sub.3O.sub.10+CeO.sub.2  (2)

where the products are the solid phases stable at Ca, Ce, Ti, Mn, and O mole fractions of 2/15, 1/15, 1/15, 2/15, and 9/15, respectively, and 0 K. 33 meV/atom is approximately equal to thermal energy at 298.15 K (i.e., k.sub.BT=26 meV/atom).

[0041] Table 2 provides a comparison of the probability (Pr) and percentage (probability expressed as %) of all unique NN V.sub.O environments, where x.sub.S and N.sub.S are the mole fraction and number of species S in the NN V.sub.O environment, respectively, in the random alloy and the optimized SQS for Pnma CCTM2112 (% in SQS). If the site occupancy follows the binomial distribution, the probability of the V.sub.O having exactly k.sub.S NNs of species S in N noninteracting sites is given by

[00002]$\left(\begin{array}{c}N\\ k_s\end{array}\right){p_S^{k_S}\left(1-p_S\right)}^{N-k_S}.Math.\left(\begin{array}{c}N\\ k_S\end{array}\right)=\frac{N!}{k_S!\left(N-k_S\right)!}$

is the binomial coefficient and p.sub.S is probability of choosing S based on the composition (p.sub.Ce=⅓ and p.sub.Mn=⅔). Pr(A) and Pr(B) are the probability of the NN A- and B-site combination, respectively, and Pr=Pr(A)×Pr(B).

[00003]$\mathrm{Pr}\left(A\right)=\left(\begin{array}{c}4\\ 4x_{Ce}\end{array}\right){\left(\frac{1}{3}\right)}^{4x_{\mathrm{Ce}}}{\left(\frac{2}{3}\right)}^{4\left(1-x_{\mathrm{Ce}}\right)}$$\mathrm{and}\mathrm{Pr}\left(B\right)=\left(\begin{array}{c}2\\ 2x_{Mn}\end{array}\right){\left(\frac{2}{3}\right)}^{2x_{\mathrm{Mn}}}{\left(\frac{1}{3}\right)}^{2\left(1-x_{\mathrm{Mn}}\right)},$

where k.sub.Ce=4×.sub.Ce (because each V.sub.O has N=4 A-site NNs) and k.sub.Mn=2×.sub.Mn (because each V.sub.O has N=2 B-site NNs). The x.sub.Ce=1 and x.sub.Mn=0 NN environment does not appear in the SQS because its frequency in the random alloy is 0.30, i.e., <1 out of 216 atoms. The x.sub.Ce=1 and x.sub.Mn=0.5 NN environment does not appear in the SQS because it was randomly selected instead of the x.sub.Ce=1 and x.sub.Mn=1 NN environment, which has the same probability in the random alloy.

TABLE-US-00002 TABLE 2 Comparison of the probability (Pr) and percentage of all unique NN V.sub.O environments. x.sub.Ce x.sub.Mn N.sub.Ca N.sub.Ce Pr(A) N.sub.Ti N.sub.Mn Pr(B) Pr % % in SQS 0.00 1.00 4 0 0.20 0 2 0.44 0.09 8.8% 10.2% 0.00 0.50 4 0 0.20 1 1 0.44 0.09 8.8% 7.4% 0.00 0.00 4 0 0.20 2 0 0.11 0.02 2.2% 1.9% 0.25 1.00 3 1 0.40 0 2 0.44 0.18 17.6% 16.2% 0.25 0.50 3 1 0.40 1 1 0.44 0.18 17.6% 20.4% 0.25 0.00 3 1 0.40 2 0 0.11 0.04 4.4% 4.2% 0.50 1.00 2 2 0.30 0 2 0.44 0.13 13.2% 11.1% 0.50 0.50 2 2 0.30 1 1 0.44 0.13 13.2% 13.9% 0.50 0.00 2 2 0.30 2 0 0.11 0.03 3.3% 3.2% 0.75 1.00 1 3 0.10 0 2 0.44 0.04 4.4% 5.1% 0.75 0.50 1 3 0.10 1 1 0.44 0.04 4.4% 3.7% 0.75 0.00 1 3 0.10 2 0 0.11 0.01 1.1% 1.4% 1.00 1.00 0 4 0.01 0 2 0.44 0.01 0.5% 1.4% 1.00 0.50 0 4 0.01 1 1 0.44 0.01 0.5% 0.0% 1.00 0.00 0 4 0.01 2 0 0.11 0.00 0.1% 0.0%

[0042] Although this disclosure contains many specific embodiment details, these should not be construed as limitations on the scope of the subject matter or on the scope of what may be claimed, but rather as descriptions of features that may be specific to particular embodiments. Certain features that are described in this disclosure in the context of separate embodiments can also be implemented, in combination, in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments, separately, or in any suitable sub-combination. Moreover, although previously described features may be described as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can, in some cases, be excised from the combination, and the claimed combination may be directed to a sub-combination or variation of a sub-combination.

[0043] Particular embodiments of the subject matter have been described. Other embodiments, alterations, and permutations of the described embodiments are within the scope of the following claims as will be apparent to those skilled in the art. While operations are depicted in the drawings or claims in a particular order, this depiction should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed (some operations may be considered optional or modified), to achieve desirable results.

[0044] Accordingly, the previously described example embodiments do not define or constrain this disclosure. Other changes, substitutions, and alterations are also possible without departing from the spirit and scope of this disclosure.