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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Quartz Dissolution Effects on Flow Channelization and Transport Behavior in Three‐Dimensional Fracture Networks

We perform a set of reactive transport simulations in three-dimensional fracture networks to characterize the impact of geochemical reactions on flow channelization. Flow channelization, a frequently observed phenomenon in porous and fractured subsurface rock formations, results from the spatially variable hydraulic resistance offered by a geological structure. In addition to geo-structural features such as network connectivity, geometry, and hydraulic resistance, geochemical reactions, for example, dissolution and precipitation, can dynamically inhibit or enhance flow channelization. These geochemical processes can change the fracture permeability leading to increased flow channelization, which are localized connected regions of high volumetric flow rates that are seemingly ubiquitous in the subsurface. In our simulations, fractures partially filled with quartz are gradually dissolved until quasi-steady state conditions are obtained. We compare the flow field's initial unreacted and final dissolved states in terms of flow and transport observations. We observe that the dissolved fracture networks provide less resistance to flow and exhibit increased flow channelization when compared to their unreacted counterparts. However, there is substantial variability in the magnitude of these changes which implies that the channelization strongly depends on the network structure. In turn, we identify the interplay between the particular network structure and the impact of geochemical dissolution on flow channelization. The presented results indicate that geological systems that have been weathering or reactive for longer times in older landscapes are likely to have increased flow channelization compared to their equivalent but younger counterparts, which implies a time dependence on flow channelization in fractured media.

Hyman, Jeffrey D.↗
DOE OSTI2025

Quantifying dispersity in size and shape of nanoparticles from small-angle scattering data using machine learning based CREASE

Here, we use machine learning (ML) enhanced computational reverse engineering analysis of scattering experiments (CREASE) to interpret small-angle X-ray scattering (SAXS) data obtained from a system of nanoparticles without a priori knowledge of their exact shapes (e.g. spheres or ellipsoids), sizes (0.5–50 nm) and distributions. The SAXS measurements yielded three categories of scattering profiles exhibiting 'strong', 'weak' and 'no' features. Diminishing features (e.g. broadening or disappearing peaks) in scattering profiles have always been attributed to the presence of significant dispersity in the system. Such featureless SAXS data are not suitable for traditional analysis using analytical models. If one were to fit a relevant analytical model (e.g. the lmfit analytical model for polydisperse spheres) to these 'weak' and 'no' SAXS profiles from our nanoparticle systems, one would obtain non-unique interpretations of the data. Relying on electron microscopy to identify the distributions of nanoparticle shapes and sizes is also unfeasible, especially in high-throughput synthesis and characterization loops. In such situations, to identify the distributions of particle sizes and shapes that could be present in the sample, one must rely on methods like ML-CREASE to interpret the data quickly and output all relevant interpretations about the structure present in the system. The ML-CREASE optimization loop takes the experimental scattering profile as input and outputs multiple candidate solutions whose computed scattering profiles match the SAXS profile input. The ML-CREASE method outputs distributions of relevant structural features, such as the volume fraction of the nanoparticles in the system and the mean and standard deviation of the particle size and aspect ratio, assuming a type of distribution (e.g. normal, log-normal) for size and aspect ratio. We find that, for the SAXS profiles analyzed here, accounting for the shape dispersity along with size dispersity of the nanoparticles using ML-CREASE improved the match between the computed scattering profiles and input experimental profiles.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Molecular Origins of Temperature-Dependent X-ray Absorption in YAG:Dy

The absorption and emission of X-rays in dysprosium-doped yttrium aluminum garnet (YAG:Dy) has produced unexpected thermographic behavior, which is investigated using a combination of finite temperature ab initio molecular dynamic simulations, structural characterization, and electronic structure calculations of X-ray characteristics. Calculated average peak X-ray absorption spectra (XAS) from simulations between 300 and 600 K result in peak intensity loss due to thermalization effects, matching experimentally measured behavior of YAG:Dy. Here, investigation of atomic snapshots indicates structural factors that correlated with the X-ray behavior, with the first Y–O coordination sphere identified as the primary structural feature unique to high XAS intensity as calculated by radial and pair distribution functions.

Ab initio molecular dynamics↗
DOE OSTI2025

Synthesis, Crystal Structure, and Optical Properties of the Barium meta -Pertechnetate Ba[TcO 4 ] 2

High-quality single crystals of the colorless title compound Ba[ 99 TcO 4 ] 2 were prepared from radioactive, isotope-pure 99 TcO 2 by oxidation with H 2 O 2 in an aqueous ammonia solution and subsequent cation metathesis using an ion-exchange column. Single-crystal X-ray diffraction revealed Ba[TcO 4 ] 2 to crystallize isotopically to Ba[MnO 4 ] 2 in the orthorhombic space group Fddd with the lattice parameters a = 747.34(5) pm, b = 1244.08(7) pm, and c = 1511.23(9) pm for Z = 8. Its crystal structure features [BaO 12 ] 22- icosahedra surrounded by ten [TcO 4 ] - tetrahedra connected via two edges and eight corners. The optical properties of Ba[TcO 4 ] 2 investigated by UV-vis spectroscopy show the broad O 2- → Tc 7+ ligand-to-metal charge transfer (2p → 4d) process within these discrete [TcO 4 ]- anions at an absorption maximum of around 350 nm.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

CuXASNet: Rapid and accurate prediction of copper L-edge x-ray absorption spectra using machine learning

In this work, we have developed CuXASNet, a dense neural network that predicts simulated Cu -edge x-ray absorption spectra (XAS) from atomic structures. Featurization of the Cu local environment is performed using a component of M3GNet, a graph neural network developed for predicting the potential energy surface. CuXASNet is trained on simulated spectra from FEFF9 at the multiple scattering level of theory, and can predict the and edges for Cu sites to quantitative accuracy. To validate our approach, we compare 14 experimental spectra extracted from the literature with the predictions of CuXASNet. The agreement of CuXASNet with experiments is shown by an average mean absolute error of 0.125 and an average Spearman's correlation coefficient of 0.891, which is comparable to FEFF9's values of 0.131 and 0.898 for the same metrics. As such, CuXASNet can rapidly predict a large number of -edge XAS spectra at the same accuracy as FEFF9 simulations. This can be used as a drop-in replacement for multiple scattering codes for fast screening of candidate atomic structure models of a measured system. This model establishes a general framework for Cu XAS prediction, and can be extended to more computationally expensive levels of theory and to other transition metal edges.

36 MATERIALS SCIENCE↗
DOE OSTI2025

X-ray Diffraction Studies of Single-Crystal Materials for Broad Battery Applications

Single-crystal materials have attracted growing interest in battery research due to their well-defined crystallographic orientation, absence of grain boundaries, and enhanced mechanical and electrochemical stability. This Review provides a comprehensive overview of recent advances in the synthesis, structural evolution, and performance optimization of single-crystal electrodes and solid electrolytes. Particular focus is placed on the application of advanced X-ray diffraction (XRD) techniques, including operando synchrotron diffraction, reciprocal space mapping, and Bragg coherent diffraction imaging, which have enabled in-depth investigations of lattice strain, cation disorder, phase transitions, and defect formation. Representative case studies across Ni-rich layered oxides, spinel-type cathodes, and garnet-based electrolytes are examined to highlight the structural features unique to single crystals. Additionally, the synergistic integration of XRD with machine learning, tomography, and spectroscopy is discussed as a powerful direction for real-time analysis and predictive modeling. Furthermore, these insights provide critical guidance for the rational design of high-performance single-crystal materials in lithium, sodium, and solid-state battery systems.

25 ENERGY STORAGE↗
DOE OSTI2025

Spin–Flop and Metamagnetic Transition in Monoclinic Eu 4 Bi 6 Se 13

This study explores an investigation of the crystallographic, electronic, and magnetic properties of the europium-based bismuth selenide compound Eu 4 Bi 6 Se 13 , with particular focus on its magnetic anisotropy. This compound adopts a monoclinic crystal structure classified under the P2 1 /m space group (#11). It exhibits distinctive structural features, including substantial Eu–Se coordination numbers (6 and 8), Bi–Se ladders, and linear chains of Eu atoms that propagate along the b-axis. Electronic resistivity assessments indicate that Eu 4 Bi 6 Se 13 exhibits metallic behavior. As the magnetic field is oriented along the b-axis, magnetic characterization reveals uniaxial magnetic anisotropy, with metamagnetic transitions appearing at approximately 12 kOe and a lower field. In the field below 10 kOe, the spin-flop transition is observed with possible domain-induced hysteresis. This behavior supports the identification of metamagnetic features in field-dependent measurements attributable to the europium spins.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Cryo-EM visualization of viruses from partially irrigated soils

Viruses are numerically the most abundant forms on Earth, and most are present in soil. Even though viruses are highly abundant in soil and critical to rhizosphere function, visualizing the diverse morphotypes within soil has been challenging. The difficulty is primarily due to the heterogenous nature of isolated suspensions that typically contain nanometer to micron scale debris which renders protein crystallography for structural studies unfeasible and hinders cryo-electron microscopy due to ice thickness and contrast issues. Here we employed and compared a simple spin filtration method to cleanup solutions of extracted viruses for direct observation with cryo-electron microscopy. The method employs common physical biochemical separation steps to remove large and small debris which dramatically improves image quality and preservation of structural features to permit visualizing morphotypes not typically seen with conventional negative stain approaches. In addition to tailed and non-tailed polyhedral phages, several under reported or novel morphotypes of soil viruses are directly visualized as a particle library with both 2D and 3D information.

cryo-EM↗
DOE OSTI2025

Higher-order Van Hove singularities in kagome topological bands

Motivated by the growing interest in band structures featuring higher-order Van Hove singularities (HOVHS), we investigate a spinless fermion kagome system characterized by nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping amplitudes. While NN hopping preserves time-reversal symmetry, NNN hopping, akin to chiral hopping on the Haldane lattice, breaks time-reversal symmetry and leads to the formation of topological bands with Chern numbers ranging from 𝐶 = ±1 to ±4. We perform analytical and numerical analysis of the energy bands near the high-symmetry points Γ, ±𝐊, and 𝐌 𝑖 (𝑖 = 1, 2, and 3), which uncover a rich and complex landscape of HOVHS, controlled by the magnitude and phase of the NNN hopping. We observe power-law divergences in the density of states (DOS), 𝜌⁡(𝜀)∼|𝜀| −𝜈 , with exponents 𝜈 = 1/2, 1/3, 1/4, which can significantly affect the anomalous Hall response at low temperatures when the Fermi level crosses the HOVHS. Additionally, the NNN hopping induces the formation of higher Chern number bands 𝐶 = ±2, ±4 in the middle of the spectrum obeying a sublattice interference whereupon electronic states are maximally localized in each of the sublattices when the momentum approaches the three high-symmetry points 𝐌 𝑖 (𝑖 = 1, 2, and 3) on the Brillouin zone boundary. Finally, this classification of HOVHS in kagome systems provides a platform to explore unconventional electronic orders induced by electronic correlations.

Chern insulators↗
DOE OSTI2024

Biosynthesis of Strained Amino Acids by a PLP‐Dependent Enzyme through Cryptic Halogenation

Abstract Amino acids (AAs) are modular building blocks which nature uses to synthesize both macromolecules, such as proteins, and small molecule natural products, such as alkaloids and non‐ribosomal peptides. While the 20 main proteinogenic AAs display relatively limited side chain diversity, a wide range of non‐canonical amino acids (ncAAs) exist that are not used by the ribosome for protein synthesis, but contain a broad array of structural features and functional groups. In this communication, we report the discovery of the biosynthetic pathway for a new ncAA, pazamine, which contains a cyclopropane ring formed in two steps. In the first step, a chlorine is added onto the C 4 position of lysine by a radical halogenase, PazA. The cyclopropane ring is then formed in the next step by a pyridoxal‐5′‐phosphate‐dependent enzyme, PazB, via an S N 2‐like attack at C 4 to eliminate chloride. Genetic studies of this pathway in the native host, Pseudomonas azotoformans , show that pazamine potentially inhibits ethylene biosynthesis in growing plants based on alterations in the root phenotype of Arabidopsis thaliana seedlings. We further show that PazB can be utilized to make an alternative cyclobutane‐containing AA. These discoveries may lead to advances in biocatalytic production of specialty chemicals and agricultural biotechnology.

Sosa, Max B.↗
DOE OSTI2024

Small‐Molecule Mixed Ionic‐Electronic Conductors for Efficient N‐Type Electrochemical Transistors: Structure‐Function Correlations

Abstract The fundamental challenge in electron‐transporting organic mixed ionic‐electronic conductors (OMIECs) is simultaneous optimization of electron and ion transport. Beginning from Y6‐type/U‐shaped non‐fullerene solar cell acceptors, we systematically synthesize and characterize molecular structures that address the aforementioned challenge, progressively introducing increasing numbers of oligoethyleneglycol (OEG; g) sidechains from 1 g to 3 g, affording OMIECs 1gY, 2gY, and 3gY, respectively. The crystal structure of 1gY preserves key structural features of the Y n series: a U‐shaped/planar core, close π–π molecular stacking, and interlocked acceptor groups. Versus inactive Y6 and Y11, all of the new glycolated compounds exhibit mixed ion‐electron transport in both conventional organic electrochemical transistor (cOECT) and vertical OECT (vOECT) architectures. Notably, 3gY with the highest OEG density achieves a high transconductance of 16.5 mS, an on/off current ratio of ~10 6 , and a turn‐on/off response time of 94.7/5.7 ms in vOECTs. Systematic optoelectronic, electrochemical, architectural, and crystallographic analysis explains the superior 3gY‐based OECT performance in terms of denser n gY OEG content, increased crystallite dimensions with decreased long‐range crystalline order, and enhanced film hydrophilicity which facilitates ion transport and efficient redox processes. Finally, we demonstrate an efficient small‐molecule‐based complementary inverter using 3gY vOECTs, showcasing the bioelectronic applicability of these new small‐molecule OMIECs.

Cho, Yongjoon↗
DOE OSTI2024

Small‐Molecule Mixed Ionic‐Electronic Conductors for Efficient N‐Type Electrochemical Transistors: Structure‐Function Correlations

Abstract The fundamental challenge in electron‐transporting organic mixed ionic‐electronic conductors (OMIECs) is simultaneous optimization of electron and ion transport. Beginning from Y6‐type/U‐shaped non‐fullerene solar cell acceptors, we systematically synthesize and characterize molecular structures that address the aforementioned challenge, progressively introducing increasing numbers of oligoethyleneglycol (OEG; g) sidechains from 1 g to 3 g, affording OMIECs 1gY, 2gY, and 3gY, respectively. The crystal structure of 1gY preserves key structural features of the Y n series: a U‐shaped/planar core, close π–π molecular stacking, and interlocked acceptor groups. Versus inactive Y6 and Y11, all of the new glycolated compounds exhibit mixed ion‐electron transport in both conventional organic electrochemical transistor (cOECT) and vertical OECT (vOECT) architectures. Notably, 3gY with the highest OEG density achieves a high transconductance of 16.5 mS, an on/off current ratio of ~10 6 , and a turn‐on/off response time of 94.7/5.7 ms in vOECTs. Systematic optoelectronic, electrochemical, architectural, and crystallographic analysis explains the superior 3gY‐based OECT performance in terms of denser n gY OEG content, increased crystallite dimensions with decreased long‐range crystalline order, and enhanced film hydrophilicity which facilitates ion transport and efficient redox processes. Finally, we demonstrate an efficient small‐molecule‐based complementary inverter using 3gY vOECTs, showcasing the bioelectronic applicability of these new small‐molecule OMIECs.

Cho, Yongjoon↗
DOE OSTI2025

The structural basis for the broad aldehyde specificity of the aminoaldehyde dehydrogenase PauC from the human pathogen Pseudomonas aeruginosa

Abstract Despite significant differences in size and formal charge, the aldehyde dehydrogenasePaPauC (PA5312) fromPseudomonas aeruginosaPAO1 efficiently catalyzes the NAD + ‐dependent oxidation of the aminoaldehydes formed in polyamines degradation. We report here thatPaPauC also oxidizes 4‐guanidinebutyraldehyde, formed in one arginine degradation pathway, trimethylaminobutyraldehyde, of unknown metabolic origin, and indole‐3‐acetaldehyde, a precursor of the plant growth‐promoting hormone indoleacetic acid.PaPauC has been proposed as a potential target for combatingP. aeruginosa. However, understanding its structure–function relationships, crucial for developing specific inhibitors, is lacking. Using X‐ray crystallography, we identified the structural characteristics that determinePaPauC broad aldehyde specificity: a spacious aldehyde‐entrance tunnel and six active‐site residues. Docking simulations, site‐directed mutagenesis, and kinetic analyses support the interactions of Lys479 with glutamylated aminoaldehydes; Phe169, Trp176, and Phe467 with amino and guanidinium groups through cation–π interactions and with the indole group via NH–π and CH–π interactions; Asp459 with amino and indole groups; and Thr303 with amide and guanidinium groups. Exploiting the distinctive structural features of thePaPauC active site could aid in developing specific inhibitors to combatP. aeruginosainfections in humans and animals, as well as in preventing its colonization of plants, which are abundantP. aeruginosareservoirs and, therefore, a significant source of human infections.

Biochemistry & Molecular Biology↗
DOE OSTI2025

Uncovering Sequence and Structural Characteristics of Fungal Expansin‐Related Proteins With Potential to Drive Substrate Targeting

Expansins loosen plant cell wall networks through disrupting non-covalent bonds between cellulose microfibrils and matrix polysaccharides. Whereas expansins were first discovered in plants, expansin-related proteins have since been identified in bacteria and fungi. The biological function of microbial expansins remains unclear; however, several studies have shown distinct binding preferences toward different structural polysaccharides. Earlier studies of bacterial expansin-related proteins uncovered sequence and structural features that correlate to substrate binding. Herein, 20 fungal expansin-related sequences were recombinantly produced in Komagataella phaffii, and the purified proteins were compared in terms of substrate binding to cellulosic and chitinous substrates. The impact of pH on the zeta potential of prioritized substrates was also measured, and Principal Component Analysis was performed to uncover correlations between protein characteristics (e.g., pI, hydrophobicity, surface charge distribution) and measured substrate binding preferences. Whereas acidic proteins with a predicted pI less than 5.0 preferentially bound to chitin, basic proteins with pI greater than 8.0 preferentially bound to xylan and xylan-containing fiber. Similar to many cellulases, binding to cellulose was correlated to relatively high aromatic amino acid content in the protein sequence and presence of a carbohydrate binding module (CBM), which in the case of expansins is a C-terminal CBM63. Whereas overall sequence characteristics could be correlated to substrate binding preference, the identity of amino acids occupying conserved positions that impact protein activity was better correlated with loosenin versus expansin classifications.

chitin↗
DOE OSTI2024

Covalent Triazine-Based Frameworks with Ru-tda Based Catalyst Anchored via Coordination Bond for Photoinduced Water Oxidation

Light-induced water splitting (hν-WS) for the production of hydrogen as a solar fuel is considered a promising sustainable strategy for the replacement of fossil fuels. An efficient system for hν-WS involves a photoactive material that, upon shining light, is capable of separating and transferring charges to catalysts for the hydrogen and oxygen evolution processes. Covalent triazine-based frameworks (CTFs) represent an interesting class of 2D organic light-absorbing materials that have recently emerged thanks to their tunable structural, optical and morphological properties. Typically, catalysts (Cat) are metallic nanoparticles generated in situ after photoelectroreduction of metal precursors or directly drop-casted on top of the CTF material to generate Cat-CTF assemblies. Here, in this work, the synthesis, characterization and photocatalytic performance of a novel hybrid material, Ru-CTF, is reported, based on a CTF structure featuring dangling pyridyl groups that allow the Ru-tda (tda is [2,2':6',2'“-terpyridine]-6,6'”-dicarboxylic acid) water oxidation catalyst (WOC) unit to coordinate via covalent bond. The Ru-CTF molecular hybrid material can carry out the light-induced water oxidation reaction efficiently at neutral pH, reaching values of maximum TOF of 17 h -1 and TONs in the range of 220 using sodium persulfate as a sacrificial electron acceptor.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Synthesis, Structures, and Transport Properties of Quaternary Ba–Ag– Tr –As Materials ( Tr = Ga, In)

The synthesis, structures, and properties of two quaternary barium–arsenide materials are presented. The first, Ba 4 Ag 2.3 In 1.7 As 8 , is a novel material with the monoclinic unit cell ( P 2 1 / m space group). The layered crystal structure of Ba 4 Ag 2.3 In 1.7 As 8 may be considered a lower‐symmetry, distorted analog of the LaCuSb 2 structure. The structure features a rare As fragment, cis‐trans As chains along the [010] direction. Large crystals of Ba 4 Ag 2.3 In 1.7 As 8 can be grown from Bi flux and are used for subsequent transport property measurements. Electrical resistivity and heat capacity properties are reported, establishing Ba 4 Ag 2.3 In 1.7 As 8 as a metallic phase. The second material, Ba 4 AgGa 5 As 8 , is a 3D material that crystallizes in the orthorhombic unit cell (noncentrosymmetric and polar Iba 2 space group). Expanding upon its original discovery, the optimized synthetic profile for single‐phase polycrystalline samples as well as transport properties relevant to thermoelectric applications are presented. Ba 4 AgGa 5 As 8 exhibits a high Seebeck coefficient of 290 μV K −1 at room temperature, indicative of lower carrier concentrations typical for nonmetallic phases. Electrical resistivity measurements also affirm conventional semiconducting behavior for Ba 4 AgGa 5 As 8 .

Kyveryga, Victoria [Department of Chemistry Iowa S↗
DOE OSTI2025

Iron-sulfur clusters: the road to room temperature

Abstract Iron-sulfur proteins perform a wide variety of reactions central to the metabolisms of all living organisms. Foundational to their reaction chemistry are the rich electronic structures of their constituent Fe-S clusters, which differ in important ways from the active sites of mononuclear Fe enzymes. In this perspective, we summarize the essential electronic structure features that make Fe-S clusters unique, and point to the need for studies aimed at understanding the electronic basis for their reactivity under physiological conditions. Specifically, at ambient temperature, both the ground state and a large number of excited states are thermally populated, and thus a complete understanding of Fe-S cluster reactivity must take into account the properties, energies, and reactivity patterns of these excited states. We highlight prior research toward characterizing the low-energy excited states of Fe-S clusters that has established what is now a consensus model of these excited state manifolds and the bonding interactions that give rise to them. In particular, we discuss the low-energy alternate spin states and valence electron configurations that occur in Fe-S clusters of varying nuclearities, and finally suggest that there may be unrecognized functional roles for these states. Graphical abstract

Skeel, Brighton A. (ORCID:000000018458088X)↗
DOE OSTI2025

Controllable oxygen vacancy defect engineering of BiVO 4 porous structures for room temperature NH 3 detection

Controlling structural features of sensing material while judiciously introducing vacancy defect states for revamping the electronic properties of the sample to obtain its superior gas sensing performance, is quite rare. Herein, we report for the first time, the room temperature (RT) ammonia (NH 3 ) detection of peanut-like porous bismuth vanadate (BiVO 4 ) with a stable monoclinic phase. The developed BiVO 4 possess abundant oxygen vacancies and porosity by virtue of calcinations (400–800 ℃). BiVO 4 calcined at 400 ℃ exhibits high selectivity towards NH 3 with a maximum response of 1421 @ 270 ppm at RT, which is 2.5 fold enhanced compared to without calcined BiVO 4 (response of 547 @ 270 ppm NH 3 ). The oxygen defective BiVO 4 appeared highly durable and stable even under high humid conditions (∼60 %). Besides, the porosity of BiVO 4 not only enhances the specific surface area (19.8 m 2 /g) but also results in fast diffusion of NH 3 molecules, leading to a reduction in the decay time (34 s for 90 ppm NH 3 ). The density functional theory (DFT) uncovers that the oxygen vacancy formation in BiVO 4 augments the NH 3 sensing capabilities by enhancing the adsorption energy of NH 3 . This work provides insight into the sensing mechanism of increased response caused by defect engineering and porosity, which will be favourable for fabricating high-performance NH 3 sensors at RT.

DFT analysis↗