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At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Lamellae of α phase in a metastable β -Ti alloy studied by small-angle x-ray scattering

The shapes and orientations of lamellae of the hexagonal close-packed α phase in single crystals of the body-centred cubic β phase in a metastable β -Ti alloy (Timetal LCB) were investigated by synchrotron small-angle x-ray scattering. Several steps of thermal treatment with various annealing times and temperatures were employed. The measured scattering data were fitted to a model of ellipsoidal lamellae of random sizes, and the mean lamella shapes and orientations of their axes with respect to the β -Ti matrix were determined from the fit. The number and relative volume of the lamellae were estimated from the integrated scattered intensity. The elastic energy of the lamellae as well as the energy of defects at the α / β interface (misfit dislocations) were calculated from the parameters of the lamellae. In conclusion, the results provide information on the kinetics of the β $ \rightarrow$ α transformation in metastable β -Ti alloys and allow assessing the degree of thermodynamic equilibrium of the final α / β composite.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Three-dimensional structure of a flavivirus dumbbell RNA reveals molecular details of an RNA regulator of replication

Abstract Mosquito-borne flaviviruses (MBFVs) including dengue, West Nile, yellow fever, and Zika viruses have an RNA genome encoding one open reading frame flanked by 5′ and 3′ untranslated regions (UTRs). The 3′ UTRs of MBFVs contain regions of high sequence conservation in structured RNA elements known as dumbbells (DBs). DBs regulate translation and replication of the viral RNA genome, functions proposed to depend on the formation of an RNA pseudoknot. To understand how DB structure provides this function, we solved the x-ray crystal structure of the Donggang virus DB to 2.1Å resolution and used structural modeling to reveal the details of its three-dimensional fold. The structure confirmed the predicted pseudoknot and molecular modeling revealed how conserved sequences form a four-way junction that appears to stabilize the pseudoknot. Single-molecule FRET suggests that the DB pseudoknot is a stable element that can regulate the switch between translation and replication during the viral lifecycle by modulating long-range RNA conformational changes.

Akiyama, Benjamin M.↗
DOE OSTI2026

Quasi-One-Dimensional Spin Excitations in the Iron Pnictide NaFe 0.53 ⁢Cu 0.47 ⁢As

Spectroscopic measurements in model 1D correlated systems offer insights for understanding their two-dimensional counterparts, which include the cuprate and iron pnictide/chalcogenide superconductors. A major challenge is the identification of such correlated systems with dominantly 1D physics. Here, in this Letter, inelastic neutron scattering measurements on NaFe 0.53⁢ Cu 0.47 ⁢As single crystal directly reveal quasi-1D spin excitations, resulting from atomic order that leads to magnetic Fe and nonmagnetic Cu chains. The dominant exchange interaction is antiferromagnetic along the chain [𝑆⁢𝐽 ∥ ≈ 90.1⁢(3) meV], whereas the inter-chain couplings are much weaker [𝑆⁢𝐽 ⊥ ≈ −2.4⁢(1) meV and 𝑆⁢𝐽 c ≈ 0.15⁢(5) meV]. The quasi-1D spin excitations in NaFe 0.53 ⁢Cu 0.47⁢ As stem from both the Néel and stripe vectors, with Néel excitations sensitive to Fe impurities on the Cu site. The spin excitations in quasi-1D NaFe 0.53 ⁢Cu 0.47⁢ As and quasi-2D FeSe exhibit a striking resemblance, suggesting a common origin for their coexistent stripe and Néel excitations. Our findings demonstrate magnetic dilution in NaFeAs leads to dimension reduction of its magnetic degree of freedom, presenting a strategy for discovering low-dimensional quantum materials.

Wang, Yifan [Zhejiang Univ., Hangzhou (China)]↗
DOE OSTI2025

Magnetic properties of a staggered S = 1 chain with an alternating single-ion anisotropy direction

Materials composed of spin-1 antiferromagnetic (AFM) chains are known to adopt complex ground states that are sensitive to the single-ion-anisotropy (SIA) energy ( D ), and intrachain ( J 0 ) and interchain ( J 1 , 2 ′ ) exchange energy scales. While theoretical and experimental studies have extended this model to include various other energy scales, the effect of the lack of a common SIA axis is not well explored. Here we investigate the magnetic properties of Ni ( pyrimidine ) ( H 2 O ) 2 ( NO 3 ) 2 , a chain compound where the tilting of Ni octahedra leads to a twofold alternation of the easy-axis directions along the chain. Muon-spin relaxation measurements indicate a transition to long-range order at T N = 2.3 K and the magnetic structure is initially determined to be antiferromagnetic and collinear using elastic neutron diffraction experiments. Inelastic neutron scattering measurements were used to find J 0 = 5.107 ( 7 ) K , D = 2.79 ( 1 ) K , J 1 ′ = 0.00 ( 5 ) K , J 2 ′ = 0.18 ( 3 ) K , and a rhombic anisotropy energy E = 0.19 ( 9 ) K . Mean-field modeling reveals that the ground state structure hosts spin canting of ϕ ≈ 6 . 5 ∘ , which is not detectable above the noise floor of the elastic neutron diffraction data. Monte Carlo simulation of the powder-averaged magnetization, M ( H ) , is then used to confirm these Hamiltonian parameters, while single-crystal M ( H ) simulations provide insight into features observed in the data. Published by the American Physical Society 2025

Vaidya, S. (ORCID:000000033975497X)↗
DOE OSTI2024

Symmetry Breaking and Ascending in the Magnetic Kagome Metal FeGe

Spontaneous symmetry breaking—the phenomenon in which an infinitesimal perturbation can cause the system to break the underlying symmetry—is a cornerstone concept in the understanding of interacting solid-state systems. In a typical series of temperature-driven phase transitions, higher-temperature phases are more symmetric due to the stabilizing effect of entropy that becomes dominant as the temperature is increased. However, the opposite is rare but possible when there are multiple degrees of freedom in the system. Here, we present such an example of a symmetry-ascending phenomenon upon cooling in a magnetic kagome metal FeGe by utilizing neutron Larmor diffraction and Raman spectroscopy. FeGe has a kagome lattice structure with simple A-type antiferromagnetic order below Néel temperature T N ≈ 400 K and a charge density wave (CDW) transition at T CDW ≈ 110 K , followed by a spin-canting transition at around 60 K. In the paramagnetic state at 460 K, we confirm that the crystal structure is indeed a hexagonal kagome lattice. On cooling to around T N , the crystal structure changes from hexagonal to monoclinic with in-plane lattice distortions on the order of 10 − 4 and the associated splitting of the double-degenerate phonon mode of the pristine kagome lattice. Upon further cooling to T CDW , the kagome lattice shows a small negative thermal expansion, and the crystal structure gradually becomes more symmetric upon further cooling. A tendency of increasing the crystalline symmetry upon cooling is unusual; it originates from an extremely weak structural instability that coexists and competes with the CDW and magnetic orders. These observations are against the expectations for a simple model with a single order parameter and hence can only be explained by a Landau free energy expansion that takes into account multiple lattice, charge, and spin degrees of freedom. Thus, the determination of the crystalline lattice symmetry as well as the unusual spin-lattice coupling is a first step towards understanding the rich electronic and magnetic properties of the system, and it sheds new light on intertwined orders where the lattice degree of freedom is no longer dominant. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Spin Berry points as crucial for ultrafast demagnetization

Laser-induced ultrafast demagnetization has puzzled researchers around the world for over two decades. Intrinsic complexity in electronic, magnetic and phononic subsystems is difficult to understand microscopically. So far, it is not possible to explain demagnetization using a single mechanism, which suggests a crucial piece of information still missing. In this paper, we return to a fundamental aspect of physics: spin and its change within each band in the entire Brillouin zone. We employ face-centered cubic (fcc) Ni as an example and use an extremely dense k mesh to map out spin changes for every band close to the Fermi level along all the high symmetry lines. To our surprise, spin angular momentum at some special k points abruptly changes from [Formula: see text] to [Formula: see text] simply by moving from one crystal momentum point to the next. This explains why intraband transitions, which the spin superdiffusion model is based upon, can induce a sharp spin moment reduction, and why electric current can change spin orientation in spintronics. These special k points, which are called spin Berry points [M. V. Berry, Proc. R. Soc. Lond. A 393 (1984) 45], are not random and appear when several bands are close to each other, so the Berry potential of spin majority states is different from that of spin minority states. Although within a single band, spin Berry points jump, when we group several neighboring bands together, they form distinctive smooth spin Berry lines. It is the band structure that disrupts those lines. Spin Berry points are crucial to laser-induced ultrafast demagnetization and spintronics.

Physics↗
DOE OSTI2023

Neutron scattering study of fluctuating and static spin correlations in the anisotropic spin glass Fe 2 Ti O 5

The anisotropic spin-glass transition, in which spin freezing is observed only along the c axis in pseudobrookite Fe 2 TiO 5 , has long been perplexing because the Fe 3+ moments (d 5 ) are expected to be isotropic. Recently, neutron diffraction demonstrated that surfboard-shaped antiferromagnetic nanoregions coalesce above the glass transition temperature T g ≈55K, and a model was proposed in which the freezing of the surfboard magnetization fluctuations leads to the anisotropic spin-glass state. Given this model, we have carried out high-resolution inelastic neutron scattering measurements of the spin-spin correlations to understand the temperature dependence of the intrasurfboard spin dynamics on neutron (picosecond) timescales. Here, in this paper, we report on the temperature-dependence of the spin fluctuations measured from single-crystal Fe 2 TiO 5 . Strong quasi-elastic magnetic scattering, arising from intrasurfboard correlations, is observed well above T g . The spin fluctuations possess a steep energy–wave vector relation and are indicative of strong exchange interactions, consistent with the large Curie-Weiss temperature. As the temperature approaches T g from above, a shift in spectral weight from inelastic to elastic scattering is observed. At various temperatures between 4 and 300 K, a characteristic relaxation rate of the fluctuations is determined. Despite the freezing of most of the spin correlations, an inelastic contribution remains even at base temperature, signifying the presence of fluctuating intrasurfboard spin correlations to at least T/T g ≈0.1 , consistent with an energy landscape that is a hybrid between conventional and geometrically frustrated spin glasses.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Q-POP-Thermo: A general-purpose thermodynamics solver for ferroelectric materials

We report that Q-POP-Thermo is a program designed to compute thermodynamic monodomain equilibrium states and their properties for ferroelectric single crystals and thin films based on the Landau-Ginzburg-Devonshire (LGD) Theory. Utilizing symbolic manipulation with the SymPy Library, the governing equations along with appropriate boundary conditions are solved for speedy minimization of the free energy of a crystal. Utilizing the popular Differential Evolution algorithm, with appropriate hybridization, multiple phase diagrams, such as the pressure-temperature phase diagram for bulk single crystals and the common strain-temperature phase diagram for monodomain thin-film systems can be readily generated. Furthermore, a variety of material properties of stable ferroelectric phases, including dielectric, piezoelectric, and electrocaloric properties, can simultaneously be calculated. Validation studies are presented for both thin-film and single crystal systems to test the effectiveness and capability of the open-source program.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Electronic structure theory on modeling short-range noncovalent interactions between amino acids

While short-range noncovalent interactions (NCIs) are proving to be of importance in many chemical and biological systems, these atypical bindings happen within the so-called van der Waals envelope and pose an enormous challenge for current computational methods. We introduce SNCIAA, a database of 723 benchmark interaction energies of short-range noncovalent interactions between neutral/charged amino acids originated from protein x-ray crystal structures at the “gold standard” coupled-cluster with singles, doubles, and perturbative triples/complete basis set [CCSD(T)/CBS] level of theory with a mean absolute binding uncertainty less than 0.1 kcal/mol. Subsequently, a systematic assessment of commonly used computational methods, such as the second-order Møller−Plesset theory (MP2), density functional theory (DFT), symmetry-adapted perturbation theory (SAPT), composite electronic-structure methods, semiempirical approaches, and the physical-based potentials with machine learning (IPML) on SNCIAA is carried out. It is shown that the inclusion of dispersion corrections is essential even though these dimers are dominated by electrostatics, such as hydrogen bondings and salt bridges. Overall, MP2, ωB97M-V, and B3LYP+D4 turned out to be the most reliable methods for the description of short-range NCIs even in strongly attractive/repulsive complexes. SAPT is also recommended in describing short-range NCIs only if the δMP2 correction has been included. The good performance of IPML for dimers at close-equilibrium and long-range conditions is not transferable to the short-range. We expect that SNCIAA will assist the development/improvement/validation of computational methods, such as DFT, force-fields, and ML models, in describing NCIs across entire potential energy surfaces (short-, intermediate-, and long-range NCIs) on the same footing.

Chemistry↗
DOE OSTI2025

Spin dynamics in natural multiferroic pyroxene NaFeSi 2 ⁢O 6

Spin dynamics in the natural mineral aegirine, NaFeSi 2⁢ O 6 , a member of the pyroxene family, was studied by elastic and inelastic neutron scattering. Magnetization and specific-heat measurements as well as single-crystal neutron diffraction maps, taken in the temperature range 2–20 K, confirm two successive magnetic transitions at 8.8 and 5.8 K, consistent with previous studies. The observed spin-wave excitations emerge from the incommensurate magnetic Bragg peaks corresponding to the propagation vector 𝑘 ICM = (0,0.77,0), and extend up to energies of about 1.5 meV. In the low-temperature helical phase, the spin dynamics of the Fe3+ ions is well described by a simple linear spin-wave model. The observed excitations can be modeled using a spin Hamiltonian that includes three primary exchange interactions—intrachain coupling 𝐽 = 0.142⁢(2) ⁢meV, and interchain couplings 𝐽 1 = 0.083⁢(1) ⁢meV and 𝐽 2 = 0.186⁢(1) meV—and an easy-plane anisotropy 𝐷 = 0.020⁢(6)⁢ meV. Furthermore, our results show that no single exchange interaction dominates the spin dynamics. The similar strengths of the intrachain and interchain couplings point to the fact that the magnetic interactions in aegirine are three dimensional rather than confined along one direction. As a result, the system cannot be considered quasi one dimensional, as previously suggested, and calls for further investigations.

Magnetic coupling↗
DOE OSTI2021

Understanding the plasticity contributions during laser-shock loading and spall failure of Cu microstructures at the atomic scales

A hybrid atomic-scale and continuum modeling framework is used to study the microstructural evolution during the laser-induced shock deformation and failure (spallation) of copper microstructures. A continuum two-temperature model (TTM) is used to account for the interaction of Cu atoms with a laser in molecular dynamics (MD) simulations. The MD-TTM simulations study the effect of laser loading conditions (laser fluence) on the microstructure (defects) evolution during various stages of shock wave propagation, reflection, and interaction in single-crystal (sc) Cu systems. In addition, the role of the microstructure is investigated by comparing the defect evolution and spall response of sc-Cu and nanocrystalline (nc) Cu systems. The defect (stacking faults and twin faults) evolution behavior in the metal at various times is further characterized using virtual in situ selected area electron diffraction and x-ray diffraction during various stages of evolution of microstructure. Here, the simulations elucidate the uncertain relation between spall strength and strain-rate and the much stronger relation between the spall strength and the temperatures generated due to laser shock loading for the small Cu sample dimensions considered here.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Tiny Sc Allows the Chains to Rattle: Impact of Lu and Y Doping on the Charge-Density Wave in ScV 6 Sn 6

The kagome metals display an intriguing variety of electronic and magnetic phases arising from the connectivity of atoms on a kagome lattice. A growing number of these materials with vanadium–kagome nets host charge–density waves (CDWs) at low temperatures, including ScV 6 Sn 6 , CsV 3 Sb 5 , and V 3 Sb 2 . Curiously, only the Sc version of the RV 6 Sn 6 materials with a HfFe 6 Ge 6 -type structure hosts a CDW (R = Gd–Lu, Y, Sc). In this study, we investigate the role of rare earth size in CDW formation in the RV 6 Sn 6 compounds. Magnetization measurements on our single crystals of (Sc,Lu)V 6 Sn 6 and (Sc,Y)V 6 Sn 6 establish that the CDW is suppressed by substituting Sc by larger Lu or Y. Single-crystal X-ray diffraction reveals that compressible Sn–Sn bonds accommodate the larger rare earth atoms within loosely packed R–Sn–Sn chains without significantly expanding the lattice. We propose that Sc provides extra room in these chains crucial to CDW formation in ScV 6 Sn 6 . Our rattling chain model explains why both physical pressure and substitution by larger rare earth atoms hinder CDW formation despite opposite impacts on lattice size. Here, we emphasize the cooperative effect of pressure and rare earth size by demonstrating that pressure further suppresses the CDW in a Lu-doped ScV 6 Sn 6 crystal. Our model not only addresses why a CDW only forms in the RV 6 Sn 6 materials with tiny Sc but also advances our understanding of why unusual CDWs form in the kagome metals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Quantum simulation of an extended Dicke model with a magnetic solid

Abstract The Dicke model describes the cooperative interaction of an ensemble of two-level atoms with a single-mode photonic field and exhibits a quantum phase transition as a function of light–matter coupling strength. Extending this model by incorporating short-range atom–atom interactions makes the problem intractable but is expected to produce new physical phenomena and phases. Here, we simulate such an extended Dicke model using a crystal of ErFeO 3 , where the role of atoms (photons) is played by Er 3+ spins (Fe 3+ magnons). Through terahertz spectroscopy and magnetocaloric effect measurements as a function of temperature and magnetic field, we demonstrated the existence of a novel atomically ordered phase in addition to the superradiant and normal phases that are expected from the standard Dicke model. Further, we elucidated the nature of the phase boundaries in the temperature–magnetic-field phase diagram, identifying both first-order and second-order phase transitions. These results lay the foundation for studying multiatomic quantum optics models using well-characterized many-body solid-state systems.

Marquez Peraca, Nicolas↗
DOE OSTI2020

Se diffusion in CdTe thin films for photovoltaics

Manipulating CdSeTe bandgrading to enhance photocurrent and carrier lifetime is an essential part of high-performance CdTe photovoltaics (PVs). Here, we examine Se diffusion kinetics in single-crystal and polycrystalline CdTe during deposition, thermal annealing, and CdCl 2 treatments. Se distributions are determined by dynamic secondary-ion-mass spectroscopy and Auger electron spectroscopy depth profiling and coupled with electron backscatter diffraction images of the crystalline structure. Effective bulk and grain boundary diffusion coefficients are determined by analytical models and discussed in the context of processing and film morphology. Se is found to diffuse in CdTe at much higher rates during CdCl 2 treatments than with thermal processing alone. GB diffusion also occurs at a significantly faster rate than bulk diffusion. As a result of these two effects, the near interface bulk and GB Se diffusion during CdCl 2 treatments dominates the bandgrading profiles in CdTe PVs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Inferring relative dose-dependent color center populations in proton irradiated thoria single crystals using optical spectroscopy

In this work, we have utilized photoluminescence spectroscopy and optical ellipsometry to characterize the dose-dependence of the photoluminescence emission intensity and changes in optical absorption of thoria single crystals subject to irradiation with energetic protons at room- and elevated-temperatures. The photoluminescence peaks and the optical absorption bands are attributed to creation of new electronic states emerging from defects resulting from displacement damage. These bands are most likely associated with electrons trapped at the oxygen vacancy sites similar to color centers formed in other irradiated oxides and halides. Our experimental observations are supported by a standard density functional theory calculation of the electronic structure in pristine and oxygen vacancy-bearing thoria crystals. The dose-dependence of the intensity of the photoluminescence peaks is used to parameterize a rate theory model that estimates the concentration of color centers in the irradiated crystals. This parameterization provides optimized migration barrier parameters for oxygen interstitials and vacancies that simultaneously capture the optical response of the crystals irradiated at room- and elevated-temperature. These optical spectroscopy techniques offer a promising pathway to characterize the population of color centers formed at the sites of oxygen anion vacancies, particularly in irradiated nuclear fuels, where atomic-level defects cannot be readily imaged using electron microscopy. When combined with other direct and indirect characterization tools, our approach can provide new insight into defect formation and accumulation in energy materials over single atomic to extended length scales.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Comment on “STM study of the (111) and (100) surfaces of PdAg, Surf. Sci. 417 (1998) 292–300" and references therein

Investigation of isolated, single atoms on the surfaces of alloys is of great interest in the field of heterogeneous catalysis. Prior studies by Nieuwenhuys, etal. [Surf. Sci. 417 (1998) 292–300 and references therein] showed that annealing the (111) surface of a PdAg bulk alloy yielded a surface with ~5% Pd, predominantly in the form of single atoms, rendering it an ideal model for investigating the reactivity of single Pd atoms. Herein, new evidence is reported that establishes the bulk composition of the PdAg(111) alloy studied previously is 67 % Ag and 33 % Pd, whereas it was reported to be 33 % Ag and 67 % Pd in the prior studies. Furthermore, the bulk composition of a crystal derived from the same PdAg alloy boule used previously was determined using energy-dispersive X-ray spectroscopy (EDS)—a bulk sensitive technique. Surface-sensitive measurements, including X-ray photoelectron spectroscopy, were also performed and are in good agreement with the prior studies by Nieuwenhuys, etal.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Transuranium Sulfide via the Boron Chalcogen Mixture Method and Reversible Water Uptake in the NaCu T S 3 Family

The behavior of 5f electrons in soft ligand environments makes actinides, and especially transuranium chalcogenides, an intriguing class of materials for fundamental studies. Due to the affinity of actinides for oxygen, however, it is a challenge to synthesize actinide chalcogenides using non-metallic reagents. Using the Boron Chalcogen Mixture (BCM) method, we achieved the synthesis of the transuranium sulfide NaCuNpS 3 starting from the oxide reagent, NpO 2 . Via the same synthetic route, the isostructural composition of NaCuUS 3 was synthesized and the material contrasted with NaCuNpS 3 . Single crystals of the U-analog, NaCuUS 3 , were found to undergo an unexpected reversible hydration process to form NaCuUS 3 ·xH 2 O (x ≈ 1.5). Here, a large combination of techniques was used to fully characterize the structure, hydration process, and electronic structures, specifically a combination of single crystal, powder, high temperature powder X-ray diffraction, extended X-ray ab-sorption fine structure, infrared, and inductively coupled plasma spectroscopies, thermogravimetric analysis, and density functional theory calculations. The outcome of these analyses enabled us to determine the composition of NaCuUS 3 ·xH 2 O and obtain a structural model that demonstrated the retention of the local structure within the [CuUS 3 ] – layers throughout the hydration-dehydration process. Band structure, density of states, and Bader charge calculations for NaCuUS 3 , NaCu-US 3 ·xH 2 O, and NaCuNpS 3 along with X-ray absorption near edge structure, UV-vis-NIR and work function measurements on ACuUS 3 (A = Na, K, and Rb) and NaCuUS 3 ·xH 2 O samples were carried out to demonstrate that electronic properties arise from the [CuTS 3 ] – layers and show surprisingly little dependence on the interlayer distance.

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

Orientation-dependent mutual crystalline and amorphous order in a single phase solid

Amorphous materials distinguish themselves from crystalline materials by lacking long-range order while retaining structural order at the local scale (2–5 Å). However, the complexity in topological and chemical order prevents current characterization tools from fully unveiling the structure in disordered materials. Consequently, the nature of medium-range order in amorphous materials has remained elusive. The Zachariasen and crystal competing models have been proposed to describe disordered phases and have both been verified through synthesis and characterization. The main difference between them is thought to be whether the amorphous phase shows medium-range order. Here we demonstrate a form of organized inorganic matter that is amorphous in two dimensions, while exhibiting long-range order and a high degree of crystallinity in the third. The structure consists of periodically stacked 2-dimensional amorphous Nb-W-O monolayers without long-range in-plane order. The unique periodic and therefore crystalline stacking along one principal axis enables direct imaging and revealed that the amorphous Nb-W-O monolayers formed in agreement with the Zachariasen model for 2 dimensions. Our findings show that the gap between crystalline and amorphous materials does not only depend on medium-range order but can also apply to principal dimensions within the same solid.

Nanowires↗