Patent Application
20230357046
This invention relates to metal-oxide perovskite materials used for thermochemical water and carbon dioxide splitting.
Reduction-re-oxidation thermochemical cycles for water and carbon-dioxide splitting use recyclable chemical compounds and high temperatures sourced from concentrated solar power or other renewable pathways to split water into hydrogen and oxygen and carbon dioxide into carbon monoxide and oxygen, with no direct greenhouse gas emissions. Some metal oxides, such as CeO2, have been used as recyclable reactants in these thermochemical cycles.
This disclosure describes a non-consumed reactant in a reduction-re-oxidation thermochemical cycle for water and carbon-dioxide splitting powered by a heat source. 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 Ca1-xCexTiyMn1-yO3, 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 Ca2/3Ce1/3Ti1/3Mn2/3O3 or CCTM2112.
In a first general aspect, a metal-oxide perovskite material has a general formula Ca1-xCexTiyMn1-yO3, 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.
Implementations of the first general aspect can include one or more of the following features.
In some cases, the metal-oxide perovskite material yields a reduced metal-oxide perovskite material in a reducing environment after heating to a reduction temperature, wherein 0.5>δr>0. The reduced metal-oxide perovskite material has a general formula Ca1-xCexTiyMn1-yO3-δr, wherein 0.5>δr>0. The reduction temperature is typically in a range of about 1600K to about 2000K. The reduced metal-oxide perovskite material yields a re-oxidized metal-oxide perovskite material and hydrogen when contacted with water at a re-oxidation temperature. The reduced metal-oxide perovskite material yields a re-oxidized metal-oxide perovskite material and carbon monoxide when contacted with carbon dioxide at a re-oxidation temperature. In some implementations, the reduced metal-oxide perovskite material yields a re-oxidized metal-oxide perovskite material and syngas when contacted with a re-oxidizing fluid including water and carbon dioxide at a re-oxidation temperature. The re-oxidized metal-oxide perovskite material has a general formula Ca1-xCexTiyMn1-yO3-δo, wherein 0<δo<δr. The re-oxidation temperature is typically in a range of about 900K to about 1500K.
In a second general aspect, producing hydrogen and oxygen includes a) heating a metal-oxide perovskite material; b) reducing the metal-oxide perovskite material to yield oxygen and a reduced metal-oxide perovskite material, 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; c) cooling the reduced metal-oxide perovskite material; and d) 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. The reduced metal-oxide perovskite material has a general formula Ca1-xCexTiyMn1-yO3-δr, wherein 0.5>δr>0. The re-oxidized metal-oxide perovskite material has a general formula Ca1-xCexTiyMn1-yO3-δo, wherein 0<δo<δr.
Implementations of the second general aspect can include one or more of the following features.
In some cases, heating the metal-oxide perovskite material includes heating to a temperature in a range of about 1600K to about 2000K. Heating the metal-oxide perovskite material can include heating with concentrated solar energy or a radiant heat lamp. In some cases, reducing the metal-oxide perovskite material occurs in a reducing environment having a partial pressure of oxygen less than 0.01 bar. The reducing environment typically includes nitrogen, argon, steam, carbon dioxide, or any combination thereof. In certain cases, cooling the reduced metal-oxide perovskite material includes cooling to a temperature in a range of about 900K to about 1500K. The re-oxidizing fluid can further include carbon dioxide, and contacting the reduced metal-oxide perovskite material with the re-oxidizing fluid further yields carbon monoxide. Some implementations include repeating a)-d), wherein heating the metal-oxide perovskite material comprises heating the re-oxidized metal-oxide perovskite material.
In a third general aspect, producing carbon monoxide and oxygen includes a) heating a metal-oxide perovskite material; b) reducing the metal-oxide perovskite material to yield oxygen and a reduced metal-oxide perovskite material; c) cooling the reduced metal-oxide perovskite material; and d) 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. The reduced metal-oxide perovskite material has a general formula Ca1-xCexTiyMn1-yO3-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. The re-oxidized metal-oxide perovskite material has a general formula Ca1-xCexTiyMn1-yO3-δo, wherein 0<δo<δr.
Implementations of the third general aspect can include one or more of the following features.
In some cases, heating the metal-oxide perovskite material includes heating to a temperature in a range of about 1600K to about 2000K. Heating the metal-oxide perovskite material can include heating with concentrated solar energy or a radiant heat lamp. In some cases, reducing the metal-oxide perovskite material occurs in a reducing environment having a partial pressure of oxygen less than 0.01 bar. In some implementations, cooling the reduced metal-oxide perovskite material includes cooling to a temperature in a range of about 900K to about 1500K. The reducing environment typically includes an inert gas (e.g., nitrogen or argon), steam, carbon dioxide, or any combination thereof. In some cases, the re-oxidizing fluid further includes steam, and contacting the reduced metal-oxide perovskite material with the re-oxidizing fluid further yields hydrogen.
Ca—Ce—Ti—Mn oxide perovskites can improve the efficiency of hydrogen production (from water splitting) and carbon-monoxide production (from carbon-dioxide splitting) by tuning or optimizing the reduction enthalpy, the reduction entropy, or both. Quantum-based modeling of Ca2/3Ce1/3Ti1/3Mn2/3O3 predicts that A-site Ce4+ reduction dominates the redox activity of the material. This metal-oxide perovskite also has desirable redox thermodynamics for metal-oxide water splitting and carbon-dioxide splitting for hydrogen and carbon dioxide production, respectively.
The details of one or more embodiments of the subject matter of this disclosure are set forth in the accompanying drawings and the description. Other features, aspects, and advantages of the subject matter will become apparent from the description, the drawings, and the claims.
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 Ca1-xCexTiyMn1-yO3, 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 Ca2/3Ce1/3Ti1/3Mn2/3O3 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.
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.
The reduced metal-oxide perovskite material is cooled in a low pO2 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.
As depicted in
The interior of
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.
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 CeO2. 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 Ce4+ reduction dominates the redox activity of the material.
The stability of CCTM2112 was computed as the energy above the convex hull (Ehull), 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 Ehull=39 meV/atom at 0 K.
The structure of CCTM2112 is a Pnma Ca2/3Ce1/3Ti1/3Mn2/3O3 solid solution, matching the Pnma structure of CaTiO3. 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
The energetics of oxygen vacancy (VO) formation in CCTM2112 and its dependence on the VO's nearest neighbors (NNs) were analyzed. All 216 VOs were categorized by their NN environment, and one VO was randomly sampled (i.e., one VO was introduced in the SQS, corresponding to δ=0.014) from each of the 13 unique VO 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 VOs. NN VO environments were defined using xCe and xMn, where xCe=NCe/(NCa+NCe), xMn=NMn/(NTi+NMn), and x (N) is the fraction (number) of the VO's four NN A-sites and two NN B-sites occupied by Ce (xCe=1−xCa and NCe=4−NCa) and Mn (xMn=1−xTi and NMn=2−NTi), respectively. The overall supercell structure maintained the same cation stoichiometry as that of bulk CCTM2112, with xCe and xMn strictly defining compositions that were local to the VO considered. Predictably, the VO 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 (xCe=0.25 and xMn=0.5 for the VO and xCe=⅓ and xMn=⅔ for the bulk). Two NN VO environments did not appear in the optimized SQS for CCTM2112 (namely those for xCe=1 and xMn≤0.5), however, VOs with these NN environments are unlikely to significantly influence the macroscopic reduction of CCTM2112 due to their scarcity (xCe=1 and xMn=0.5, and xCe=1 and xMn=0 make up 0.5% and 0.1% of the random alloy, respectively).
With this VO categorization protocol, five of the 13 VOs were predicted have Evs 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 xCe=0.25 and xMn=0.5, which is 17.6% in a random solid, and f=30 or 30/216≈14% for xCe=xMn=0.5, which is 13.2% of the sites in a random solid). To quantify the macroscopic reducibility of CCTM2112, the ensemble-averaged Ev was calculated, with <Ev>=ΣifiEv,i/Σifi, where fi is the frequency of the ith unique NN VO environment, and Σifi=216. −Ev>=3.30 eV was obtained with a standard deviation of 0.36 eV which overlaps with the target range for water splitting. While Ev depended weakly on xCe, it systematically decreased with increasing xMn. This trend can be rationalized based on crystal O2−-Mn+ bond dissociation energies Eb, an extension of molecular O-M bond dissociation energies to the solid state, defined as
where n is the oxidation state of the metal cation (M), Ec[MOn/2] is the cohesive energy of the ground-state polymorph of the binary metal-oxide crystal MOn/2 containing Mn+, and Nb[O2−-Mn+] is the number of O2−-Mn+ bonds per MOn/2 formula unit. In short, Ev∝−xMn because O2−-Mn4+ (crystal bond dissociation energy Eb=2.25 eV) and O2−-Mn3+ (1.97 eV) crystal bonds are weaker than O2−—Ti4+ (3.16 eV) and O2−—Ti3+ (2.62 eV).
It can be advantageous to obtain a mechanistic understanding of the high performance of CCTM2112 compared to the structurally related CaTi0.5Mn0.5O3-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 Ce3+ and Mn as Mn4+ and Mn2+, where the latter suggests that disproportionation of two Mn3+ may occur in pristine CCTM2112.
To gain greater insight into the nature of the electronic reorganization in CCTM2112 upon VO formation in the thermal reduction step, the VO-induced changes in the absolute values of μCe, μMn, 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 xCe=0 and the change in |μCe|≠0, a VO without a NN Ce has reduced a non-NN Ce, thus resulting in nonlocal or delocalized reduction.
Computational results showed that reduction occurred primarily on the A-site Ce sub-lattice compared with that of Mn and O, regardless of the VO's NNs. In particular, the Ce sub-lattice reduced by 0.75 to 2.23 electrons depending on xCe and xMn, 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 VO, with both mild reduction (≤0.35 electrons accepted) and oxidation (≤0.42 electrons donated) of Mn occurring simultaneously. During VO 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 O2− (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.
Computational results indicated that Ce reduced even when it was not a nearest neighbor to the VO. To better understand this phenomenon, the spatial dependence of the |μ| changes induced by a VO with a Ca- and Mn-rich local environment (i.e., xCe=0 and xMn=1) was analyzed. Calculations indicated that two Ce were reduced (Δ|μ|=0.44 μB and 0.53 μB), at distances of 4.32 Å and 7.04 Å from the VO, 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 VO. 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 VO (Δρ=ρvacancy−ρpristine), as electron density gain was observed emerging from and surrounding the two Ce atoms 4.32 Å and 7.04 Å away from the VO. 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.
The spatial dependence of VO-induced reduction can be used to explain the subtle xCe dependence of Ev at xMn=0. The value of Ev for xCe=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 VO. For xCe=0.25, the Ev≈3.58 eV is anomalously low because, while the reduction of Ce remains fairly localized (two Ce reduced at distances <5 Å to the VO), these electrons are closer to the VO-generated holes and therefore electrostatically stabilize the VO. Strain can have an indirect effect on Ev by inducing or relaxing Jahn-Teller distortions on Mn but the strain effect is difficult to quantify.
The highest value of Ev (4.35 eV) was reached for xCe=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 VO) and the delocalized electrons' resultant screening of electron-hole interactions; and (2) a penalty for oxidizing the Mn (|Δμ|=−0.55 μB) at a distance of 10.01 Å from the VO. From xCe=0.5 to xCe=0.75, Ev 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 μB). Therefore, the subtle xCe dependence of Ev at xMn=0 can be explained by the nature (localized versus delocalized) and location of VO-generated charge carriers interacting electrostatically with the VO.
The results of these computations indicate that Ce4+ functions as the primary acceptor of electrons even though it is generally less reducible than Mn4+ and Mn3+. To quantify the reducibility of Ce4+, Mn4+, and Mn3+, the enthalpy changes of the following solid-state reduction reactions were calculated: CeO2→0.5 Ce2O3+0.25 O2, MnO2→0.5 Mn2O3+0.25O2, and 0.5 Mn2O3→MnO+0.25O2, respectively. Mn4+ is the most reducible cation (ΔH=0.40 eV) followed by Mn3+ (ΔH=1.02 eV) and then Ce4+ (ΔH=1.82 eV). Additionally, since these reactions are normalized per one-electron reduction, their ΔHs are effectively crystal reduction potentials (Vr), which are a key factor governing Ev 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 Ce4+ is less reducible than Mn4+ and Mn3+ in their ground-state binary oxides, Ce does reduce in CCTM2112 because there is a lower energy penalty for the structure to put the VO-donated electrons in the Ce 4f states, even if the Ce atom is physically farther from the VO. Ce4+ 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 Mn3+. The need for 4f states near the Fermi level to reduce Ce4+ in the presence of Mn3+ is consistent with the observation that Mn and not Ce reduces during thermochemical cycling of Ba(Ce,Mn)O3 (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 VO-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.
The high reducibility of Ce4+ in CCTM2112 is both advantageous to its high water-splitting performance and substantially different than the behavior of CeO2 and other previously demonstrated Ce4+-containing off-stoichiometric redox-active materials. The existence of Ce4+ reduction is observed directly in modeling. One structural distinction of CCTM2112 is the 12-fold coordination of Ce4+ on the A-site, compared to the 8-fold coordination of Ce4+ in the CeO2 fluorite structure and 6-fold coordination on the B-site of BCM.
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 μB for nominally nonmagnetic species (Ca2+, Ce4+, Ti4+, and O2) and 4μB for Mn3+, 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.
Computational Prediction of Stability. To compute the stability of CCTM2112, its energy above the convex hull (Ehull) was calculated, where Ehull is the energy of decomposition into the set of most stable materials at its chemical composition. To calculate Ehull, the phase diagram code in pymatgen and SCAN+U total energies (Etot) 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 Ehull of 33 meV/atom, i.e., a ΔE for its decomposition reaction of
Ca2Ce1Ti1Mn2O9→⅓Mn2O3+⅔CaMn2O4+⅓Ca4Ti3O10+CeO2 (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., kBT=26 meV/atom).
Table 2 provides a comparison of the probability (Pr) and percentage (probability expressed as %) of all unique NN VO environments, where xS and NS are the mole fraction and number of species S in the NN VO 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 VO having exactly kS NNs of species S in N noninteracting sites is given by
is the binomial coefficient and pS is probability of choosing S based on the composition (pCe=⅓ and pMn=⅔). Pr(A) and Pr(B) are the probability of the NN A- and B-site combination, respectively, and Pr=Pr(A)×Pr(B).
where kCe=4×Ce (because each VO has N=4 A-site NNs) and kMn=2×Mn (because each VO has N=2 B-site NNs). The xCe=1 and xMn=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 xCe=1 and xMn=0.5 NN environment does not appear in the SQS because it was randomly selected instead of the xCe=1 and xMn=1 NN environment, which has the same probability in the random alloy.
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.
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.
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.
This application claims the benefit of U.S. Patent Application No. 63/338,093 filed on May 4, 2022, which is incorporated herein by reference in its entirety.
This invention was made with government support under grant number DE-EE0008090 awarded by the Department of Energy. The government has certain rights in the invention.
| Number | Date | Country | |
|---|---|---|---|
| 63338093 | May 2022 | US |
