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At least 145 records · Page 8

Mechanistic insight of KBiQ 2 (Q = S, Se) using panoramic synthesis towards synthesis-by-design

Solid-state synthesis has historically focused on reactants and end products; however, knowledge of reaction pathways, intermediate phases and their formation may provide mechanistic insight of solid-state reactions. With an increased understanding of reaction progressions, design principles can be deduced, affording more predictive power in materials synthesis. In pursuit of this goal, in situ powder X-ray diffraction is employed to observe crystalline phase evolution over the course of the reaction, thereby constructing a “panoramic” view of the reaction from beginning to end. We conducted in situ diffraction studies in the K–Bi–Q (Q = S, Se) system to understand the formation of phases occurring in this system in the course of their reactions. Powder mixtures of K 2 Q to Bi 2 Q 3 in 1:1 and 1.5:1 ratios were heated to 800 °C or 650 °C, while simultaneously collecting diffraction data. Three new phases, K 3 BiS 3 , β-KBiS 2 , and β-KBiSe 2 , were discovered. Panoramic synthesis showed that K 3 BiQ 3 serves an important mechanistic role as a structural intermediate in both chalcogen systems (Q = S, Se) in the path to form the KBiQ 2 structure. Thermal analysis and calculations at the density functional theory (DFT) level show that the cation-ordered β-KBiQ 2 polymorphs are the thermodynamically stable phase in this compositional space, while Pair Distribution Function (PDF) analysis shows that all α-KBiQ 2 structures have local disorder due to stereochemically active lone pair expression of the bismuth atoms. The formation of the β-KBiQ 2 structures, both of which crystallize in the α-NaFeO 2 structure type, show a boundary where the structure can be disordered or ordered with regards to the alkali metal and bismuth. A cation radius tolerance for six-coordinate cation site sharing of ($\frac{r^+}{r^{3+}}$) ~ 1.3 is proposed. The mechanistic insight the panoramic synthesis technique provides in the K–Bi–Q system is progress towards the overarching goal of synthesis-by-design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

First-Principles Thermodynamic Assessments of Sr-Containing Secondary Phase Formation in La1-xSrxMnO3±δ Perovskites for Solid Oxide Cell Applications

Sr-secondary phase formation is a potentially significant degradation mode threatening solid-oxide cell (SOC) commercial viability. A first-principles thermodynamic study was performed for rhombohedral perovskite (La1-xSrx) MnO3±δ (LSM) to assess its stability against Sr secondary phase formation in SOC applications. In this work, the Sr secondary phase formation reaction free energies were determined by combining ab initio lattice dynamics calculations for the solid phases and an ab initio thermodynamics approach for the gas phases. Furthermore, this approach goes beyond previous thermodynamic modeling studies by integrating first-principles based point-defect equilibria into the analyses. The modeling results indicate an increased tendency to form SrO oxide from LSM upon decreasing the oxygen partial pressure. Additionally, enhancing factors to form the Sr-related secondary phase from the associated SrO activity in LSM are further quantified by considering the equilibrium of SrO reacting with contaminant gas species as a function of temperature and gas pressure.

Defect and phase stability↗

Exciton-driven antiferromagnetic metal in a correlated van der Waals insulator

Abstract Collective excitations of bound electron-hole pairs—known as excitons—are ubiquitous in condensed matter, emerging in systems as diverse as band semiconductors, molecular crystals, and proteins. Recently, their existence in strongly correlated electron materials has attracted increasing interest due to the excitons’ unique coupling to spin and orbital degrees of freedom. The non-equilibrium driving of such dressed quasiparticles offers a promising platform for realizing unconventional many-body phenomena and phases beyond thermodynamic equilibrium. Here, we achieve this in the van der Waals correlated insulator NiPS 3 by photoexciting its newly discovered spin–orbit-entangled excitons that arise from Zhang-Rice states. By monitoring the time evolution of the terahertz conductivity, we observe the coexistence of itinerant carriers produced by exciton dissociation and a long-wavelength antiferromagnetic magnon that coherently precesses in time. These results demonstrate the emergence of a transient metallic state that preserves long-range antiferromagnetism, a phase that cannot be reached by simply tuning the temperature. More broadly, our findings open an avenue toward the exciton-mediated optical manipulation of magnetism.

36 MATERIALS SCIENCE↗

Episodic Magma Hammers for the 15 January 2022 Cataclysmic Eruption of Hunga Tonga‐Hunga Ha'apai

Understanding the forces and magma system dynamics on timescales of seconds to minutes remains challenging. In the January 2022 phreatoplinian Hunga Tonga-Hunga Ha'apai eruption, four remarkably similar seismic subevents within a 5-min interval occurred during the intensifying early eruptive phase. The subevents are similar in waveforms and durations (~25 s each). Each subevent begins with an unusual negative P-wave polarity which is inferred, using full-wave seismic modeling, to be caused by an upward single-force mechanism at the volcano created by a magma hammer likely in response to magma flow blockage/constriction during the early part of the eruption as discharge rapidly increased over orders of magnitude with concomitant conduit geometry evolution and instability. Our proposed episodic magma hammer model is consistent with thermodynamic and phase properties of the magmatic mixture, and yields an estimate of conduit mass flow in agreement with vent discharge rates derived from satellite imagery of plume heights.

58 GEOSCIENCES↗

Multiphase phase-field approach for solid–solid phase transformations via propagating interfacial phase in HMX

In this study, a thermodynamically consistent multiphase phase-field theory has been formulated to describe temperature-induced solid–solid phase transformations via an interfacial phase. This theory satisfies all thermodynamic equilibrium and stability conditions. It allows us to formulate the analytical solutions of the interface profile, energy, width, and velocity for each of the propagating solid–melt and solid–solid interfaces. The formation of the intermediate melt during solid–solid phase transformation has been studied hundreds of degrees below melting temperature in the HMX energetic crystal. The effect of the penalizing term in the phase-field model and two nanoscale material parameters on the appearance and degree of disordering of intermediate melt has been analyzed for the non-equilibrium interface. The developed approach is applicable to phase transitions in geological, pharmaceutical, ferroelectric, colloidal, and superhard materials where phase transformations occur via the intermediate phase.

Roy, Arunabha M. (ORCID:000000034790726X)↗

Thermodynamic Band Gap Model for Photoinduced Phase Segregation in Mixed-Halide Perovskites

Provided is a comprehensive description of a band gap thermodynamic model, which predicts and explains key features of photosegregation in lead-based, mixed-halide perovskites. The model gives a prescription for illustrating halide migration driven by photocarrier energies. Where possible, model predictions are compared with experimental results. Free energy derivations are provided for three assumptions: (1) halide mixing in the dark, (2) a fixed number of photogenerated carriers funneling to and localizing in low band gap inclusions of the alloy, and (3) the statistical occupancy of said inclusions from a bath of thermalized photocarriers in the parent material. Model predictions include excitation intensity (I exc )-dependent terminal halide stoichiometries (x terminal ), temperature-independent x terminal , excitation intensity thresholds (I exc,threshold ) below which photosegregation is suppressed, and reduced segregation in nanocrystals as compared to thin films. Here, the model also offers insight into kinetically manipulating photosegregation rates via control of underlying mediators and rationalizes asymmetries in forward and reverse photosegregation rate constants/activation energies. What emerges is a cohesive framework for understanding ubiquitous photosegregation in mixed-halide perovskites and a rational basis by which to manage the phenomenon.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Coupling solidification kinetics with phase-behavior computations in hydrodynamic simulations of high-pressure, dynamic-compression processes

In this study, we report a numerical scheme to integrate models for the kinetics of solidification processes together with phase-behavior computations in the context of continuum-scale hydrodynamic simulations. The objective of the phase-behavior computations is to determine the pressure and temperature, given the following three sets of inputs: (1) an appropriate equation of state to describe our system, (2) the phase fraction(s) produced by the kinetic models, (3) and the volume and internal energy obtained by solving the conservation equations that govern the hydrodynamic behavior. The kinetics are assumed to be governed by the Kolmogorov–Johnson–Mehl–Avrami equation, and the nucleation and growth rates that enter into that equation are functions of the pressure and temperature produced by the phase-behavior computations. Our formulation allows for the fluid and solid phases to be at different temperatures (thermal nonequilibrium) and pressures (arising from surface-tension-induced Laplace contributions). The formulation is presented in a fairly general setting that is independent of any particular material, although we demonstrate it in some examples related to high-energy-density science applications where materials are rapidly compressed to pressures exceeding several gigapascals in less than a microsecond. We conclude with a critical evaluation of our approach and provide suggestions for future work to improve the predictive capabilities and generality of the models.

42 ENGINEERING↗

A multiscale anisotropic polymer network model coupled with phase field fracture

The study of polymers has continued to gain substantial attention due to their expanding range of applications, spanning essential engineering fields to emerging domains like stretchable electronics, soft robotics, and implantable sensors. These materials exhibit remarkable properties, primarily stemming from their intricate polymer chain network, which, in turn, increases the complexity of precisely modeling their behavior. Especially for modeling elastomers and their fracture behavior, accurately accounting for the deformations of the polymer chains is vital for predicting the rupture in highly stretched chains. Despite the importance, many robust multiscale continuum frameworks for modeling elastomer fracture tend to simplify network deformations by assuming uniform behavior among chains in all directions. Recognizing this limitation, our study proposes a multiscale fracture model that accounts for the anisotropic nature of elastomer network responses. At the microscale, damage in the chains is assumed to be driven by both the chain's entropy and the internal energy due to molecular bond distortions. In order to bridge the stretching in the chains to the macroscale deformation, we employ the maximal advance path constraint network model, inherently accommodating anisotropic network responses. As a result, chains oriented differently can be predicted to exhibit varying stretch and, consequently, different damage levels. To drive macroscale fracture based on damages in these chains, we utilize the micromorphic regularization theory, which involves the introduction of dual local-global damage variables at the macroscale. The macroscale local damage variable is obtained through the homogenization of the chain damage values, resulting in the prediction of an isotropic material response. The macroscale global damage variable is subjected to nonlocal effects and boundary conditions in a thermodynamically consistent phase field continuum formulation. Moreover, the total dissipation in the system is considered to be mainly due to the breaking of the molecular bonds at the microscale. To validate our model, we employ the double-edge notched tensile test as a benchmark, comparing simulation predictions with existing experimental data. Additionally, to enhance our understanding of the fracturing process, we conduct uniaxial tensile experiments on a square film made up of polydimethylsiloxane (PDMS) rubber embedded with a hole and notches and then compare our simulation predictions with the experimental observations. Furthermore, we visualize the evolution of stretch and damage values in chains oriented along different directions to assess the predictive capacity of the model. In conclusion, the results are also compared with another existing model to evaluate the utility of our model in accurately simulating the fracture behavior of rubber-like materials.

42 ENGINEERING↗

Energetics of oxidation and formation of uranium monocarbide

To enable better implementation of uranium monocarbide (UC) as an advanced nuclear fuel for future high-temperature reactors, it is essential to have a thorough knowledge of its thermal and thermodynamic properties under reactor operational conditions. In this work, we studied thermal bulk oxidation of UC by simultaneous thermal analysis consisting of thermogravimetric analysis – differential scanning calorimetry coupled with evolved gas mass spectrometry (TGA-DSC-MS), and we examined the thermodynamic stability of UC using high temperature oxide melt drop solution calorimetry. Further, in air, our studied UC sample (which contains ~5 mol% UO 2 ) was found to undergo a step-wise thermal oxidation process consisting of consecutive oxidations and thermal decomposition reactions: 0.95UC·0.05UO 2 → UO 3 ·0.29(C x O y ) + 0.66CO 2 → UO 3 ·0.20(C x O y ) + 0.09CO 2 → UO 3 ·0.03(C x O y ) + 0.17CO 2 → U 3 O 8 + 0.03CO 2 + 0.166O 2 . DSC was further used to determine the enthalpies of reactions associated with this series of oxidation reactions. Synchrotron X-ray diffraction (XRD) and extended X-ray absorption spectroscopy (EXAFS) were performed to characterize both the long- and short-range structures of UC. The standard enthalpy of formation (ΔH° f ) of UC was determined to be –50.7 ± 10.8 kJ/mol·atom, in good agreement with previous values measured by bomb calorimetry. Lastly, the enthalpic landscape of U-C compounds, including UC, U 2 C 3 , and α-UC 1.94 , were established based on the enthalpy normalized per mole atom, which suggests that U-C phases are thermodynamically stable at lower C/U ratios.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Theoretical assessments of Pd–PdO phase transformation and its impacts on H 2 O 2 synthesis and decomposition pathways

The direct synthesis of H 2 O 2 from O 2 and H 2 provides a green pathway to produce H 2 O 2 , a popular industrial oxidant. Here, in this study, we theoretically investigate the effects of Pd oxidation states, coordination environments, and particle sizes on primary H 2 O 2 selectivities, assessed by calculating the ratio of rate constants for the formation of H 2 O 2 (via OOH* reduction; k O–H ) and the decomposition of OOH* (via O–O cleavage; k O–O ). For Pd metals, the k O–H /k O–O ratio decreased from 10 -4 for Pd(111) to 10 -10 for the Pd 13 cluster at 300 K, indicating poorer H 2 O 2 selectivity as Pd particle size decreases and low primary selectivities for H 2 O 2 overall. As the oxygen chemical potential increases and metals form surface and bulk oxides, the perturbation of Pd–Pd ensemble sites by lattice O atoms results in selectivities that become dramatically higher than unity. For instance, at 300 K, the k O–H /k O–O ratio increases significantly from 10 -4 to 10 9 to 10 16 as Pd(111) oxidizes to Pd 5 O 4 /Pd(111) and to PdO(100), respectively. In contrast, such selectivity enhancements are not observed for surface and bulk oxides that persistently contain rows of more metallic, undercoordinated Pd–Pd ensemble sites, such as PdO(101)/Pd(100) and PdO(101). These Pd–Pd ensembles are also absent when smaller Pd nanoparticles fully oxidize, indicating that smaller PdO clusters can be more selective for H 2 O 2 synthesis. These trends for primary H 2 O 2 selectivities were found to inversely correlate with trends for H 2 O 2 decomposition rates via O–O bond cleavage, demonstrating that catalysts with high primary H 2 O 2 selectivity can also hinder H 2 O 2 decomposition. Ab initio thermodynamic calculations are used to estimate the thermodynamically favored phase among Pd, PdO/Pd and PdO in O 2 , H 2 O 2 /H 2 O, and O 2 /H 2 environments. These results are combined to show that smaller Pd nanoparticles are more prone to be oxidized at lower oxygen chemical potentials, upon which they become more selective than larger Pd particles for H 2 O 2 synthesis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Elemental segregation to lattice defects in the CrMnFeCoNi high-entropy alloy during high temperature exposures

The influence of small plastic pre-strains on the elevated-temperature stability and microstructure of the equiatomic CrMnFeCoNi FCC solid solution is investigated. Particular attention is given to whether any of the alloy elements segregate to individual dislocations. To that end, CrMnFeCoNi samples were first deformed in tension at room temperature to plastic strains of 0.2 and 2.3%, and subsequently annealed at 973 K for 800 hours. The pre-strains activated planar slip of 1/2<110>-type dislocations on {111}-type glide planes. Interactions of this planar slip with special Σ3 grain boundaries formed a large number of dislocation segments with a <110>-type crystallographic orientation suitable for a credible end-on analysis of dislocation cores in HR-STEM. The cores of the 1/2<110> dislocations pushed up against the investigated grain boundaries were found to be close to the compact configuration. Within the sensitivity of the Super-X EDS mapping, no concentration gradient was detected near dislocations that would indicate enrichment at dislocation cores of any of the elemental constituents of the alloy after the pre-deformation and annealing. However, a Cr-rich tetragonal sigma phase nucleated and grew at grain boundary triple junctions during this anneal, processes that were not accelerated by the enhanced dislocation density present after pre-strain. A clear chromium gradient was observed in the Cr-depleted zones near grain boundaries suggesting that Cr transport occurred by relatively slow diffusion from the bulk to the grain boundaries and then by relatively fast diffusion along the grain boundaries to the precipitates. Accompanying the Cr depletion near grain boundaries is a simultaneous Ni and Mn enrichment, which promotes formation of the L1 0 NiMn phase that is observed on the grain boundaries after prolonged annealing.

36 MATERIALS SCIENCE↗

HTESP (High-throughput electronic structure package): A package for high-throughput ab initio calculations

High-throughput ab initio calculations are the indispensable parts of data-driven discovery of new materials with desirable properties, as reflected in the establishment of several online material databases. The accumulation of extensive theoretical data through computations enables data-driven discovery by constructing machine learning and artificial intelligence models to predict novel compounds and forecast their properties. Efficient usage and extraction of data from these existing online material databases can accelerate the next stage materials discovery that targets different and more advanced properties, such as electron–phonon coupling for phonon-mediated superconductivity. However, extracting data from these databases, generating tailored input files for different ab initio calculations, performing such calculations, and analyzing new results can be demanding tasks. Here, in this work, we introduce a software package named “HTESP” (High-Throughput Electronic Structure Package) written in Python and Bash languages, which automates the entire workflow including data extraction, input file generation, calculation submission, result collection and plotting. Our HTESP will help speed up future computational materials discovery processes.

36 MATERIALS SCIENCE↗

Optically induced quantum transitions in direct probed mesoscopic NbSe 2 for prototypical bolometers

Superconducting transition-edge sensors (TES) have emerged as fascinating devices to detect broadband electromagnetic radiation with low thermal noise. The advent of metallic transition metal dichalcogenides, such as NbSe 2 , has also created an impetus to understand their low-temperature properties, including superconductivity. Interestingly, NbSe 2 -based sensor within the TES framework remains unexplored. In this work, direct-probed superconducting NbSe 2 absorbers led to a proof-of-concept demonstration for the transduction of incoming light to heat, where a thermodynamic superconducting phase transition in NbSe 2 was evident to switch it to the normal-state, when biased below its superconducting transition temperature. A wavelength-dependent response of its optical absorption properties was observed, based on the incident optical excitation source used. Furthermore, extensive optical characterization studies were conducted using Raman spectroscopy, where the in-plane and out-of-plane thermal conductivity was empirically determined. Our results open new possibilities for the use of NbSe 2 in superconducting radiation detectors, including in a TES framework

47 OTHER INSTRUMENTATION↗

The effects of ACRT on melt undercooling during the growth of CZT via the traveling heater method: Ekman versus Taylor-Görtler flows

For the first time, a comprehensive model for the traveling heater method, including detailed species transport and phase-change thermodynamics, is applied to understand the effects of accelerated crucible rotation (ACRT) on the growth of cadmium zinc telluride. Here, a rotation schedule that is designed from classical considerations does not completely mix the melt, rather undercooled regions of localized melt are swept periodically across the growth interface. Even without melt homogenization, these ACRT-driven flows disrupt the persistent undercooling that occurs during THM growth without rotation. An ACRT schedule designed to promote Ekman flows results in lower levels of melt undercooling than a schedule designed to promote Taylor-Görtler flows and greater mixing.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Interfacial and Confinement-Mediated Organization of Gas Hydrates, Water, Organic Fluids, and Nanoparticles for the Utilization of Subsurface Energy and Geological Resources

Harnessing the subsurface geologic environments in an efficient and environmentally sustainable manner is challenged by uncertainties associated with predicting the fate of fluids and sustaining porosity and permeability in subsurface geologic environments. Some of these uncertainties arise from confined and interfacially induced structures of fluids in subsurface geologic environments. The formation of gas hydrates, phase transitions of confined fluids, assembly and deposition of heavy hydrocarbons, and the agglomeration and fate of nanoparticles in confined environments are summarized in this review. Nanoscale confinement contributes to anisotropic structures and dynamics of fluids, which is the basis for anomalous phase transition thermodynamics, reactivity, transport, and geomechanical behavior. In this review, we discuss the structures of confined fluids and deviation in observed properties from bulk fluids. The factors influencing the structures of confined fluids can be generally divided into two groups: (a) pore characteristics including pore size, pore surface chemistry, and pore geometry and (b) confined fluid/solid characteristics such as molecular structure, concentrations, charges, pore filling, and presence of additives. Scientific advancements and knowledge gaps in our understanding of the structures of confined fluids and the associated differences in observed properties compared to bulk fluids are discussed. Here, the phenomena discussed in this review are of particular relevance to our efforts in harnessing the subsurface environments for a low carbon future by increasing the utilization of geothermal energy, using CO 2 as a working fluid, and storing CO 2 in subsurface geologic environments.

42 ENGINEERING↗

Permutationally Invariant Networks for Enhanced Sampling (PINES): Discovery of Multimolecular and Solvent-Inclusive Collective Variables

The typically rugged nature of molecular free energy landscapes can frustrate efficient sampling of the thermodynamically relevant phase space due to the presence of high free energy barriers. Enhanced sampling techniques can improve phase space exploration by accelerating sampling along particular collective variables (CVs). A number of techniques exist for data-driven discovery of CVs parameterizing the important large scale motions of the system. A challenge to CV discovery is learning CVs invariant to symmetries of the molecular system, frequently rigid translation, rigid rotation, and permutational relabeling of identical particles. Of these, permutational invariance has proved a persistent challenge in frustrating the data-driven discovery of multi-molecular CVs in systems of self-assembling particles and solvent-inclusive CVs for solvated systems. In this work, we integrate Permutation Invariant Vector (PIV) featurizations with autoencoding neural networks to learn nonlinear CVs invariant to translation, rotation, and permutation, and perform interleaved rounds of CV discovery and enhanced sampling to iteratively expand sampling of configurational phase space and obtain converged CVs and free energy landscapes. Here, we demonstrate the Permutationally Invariant Network for Enhanced Sampling (PINES) approach in applications to the self-assembly of a 13-atom Argon cluster, association/dissociation of a NaCl ion pair in water, and hydrophobic collapse of a C 45 H 92 n-pentatetracontane polymer chain. We make the approach freely available as a new module within the PLUMED2 enhanced sampling libraries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Synthesis, Magnetic Properties, and Electronic Structure of Magnetic Topological Insulator MnBi 2 Se 4

The intrinsic magnetic topological insulators MnBi 2 Te 4 and MnBi 2 Se 4 support novel topological states related to symmetry breaking by magnetic order. Unlike MnBi 2 Te 4 , the study of MnBi 2 Se 4 has been inhibited by the lack of bulk crystals, as the van der Waals (vdW) crystal is not the thermodynamic equilibrium phase. In this study, we report the layer-by-layer synthesis of vdW MnBi 2 Se 4 crystals using nonequilibrium molecular beam epitaxy. Atomic-resolution scanning transmission electron microscopy and scanning tunneling microscopy identify a well-ordered vdW crystal with septuple-layer base units. The magnetic properties agree with the predicted layered antiferromagnetic ordering but disagree with its predicted out-of-plane orientation. Instead, our samples exhibit an easy-plane anisotropy, which is explained by including dipole–dipole interactions. Angle-resolved photoemission spectroscopy reveals the gapless Dirac-like surface state, which demonstrates that MnBi 2 Se 4 is a topological insulator above the magnetic-ordering temperature. These studies show that MnBi 2 Se 4 is a promising candidate for exploring rich topological phases of layered antiferromagnetic topological insulators.

36 MATERIALS SCIENCE↗

Heterogeneous and Framework-Bound Copper Species Contribute to Catalytic Partial Methane Oxidation in Cu–Chabazite Zeolites

The relationship between continuous partial methane oxidation (PMO) rates and Cu site speciation in Cu-CHA zeolite catalysts is explored through differential rate measurements across a series of samples of varying compositions combined with density functional theory, first-principles thermodynamics, and statistical models that characterize Cu speciation. Under continuous PMO conditions (573 K, 0.07 kPa O 2 , 3 kPa H 2 O), Cu ions are shown to anchor to the CHA framework in both monomeric (Z 2 Cu and Z 2 CuH 2 O) and dimeric (O- and OH-bridged Cu) forms that are sensitive to the identity of the local framework anchoring site. Consequently, across the studied compositional range, Cu-CHA catalysts are predicted to contain a mixture of monomeric and dimeric Cu sites. Cu-normalized CH 3 OH formation rates extrapolated to zero conversion reflect contributions from multiple site types. Predicted CH 3 OH formation rates indicate that the Cu site reactivity toward CH 4 is influenced by zeolite composition and is likely limited by the reduction half-cycle.

03 NATURAL GAS↗