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At least 235 records · Page 13

Final Technical Report on Investigation of Short-range Ordering in Transition Metal Compounds by Diffuse Scattering

Future energy needs and sustainability require new materials with novel properties for such applications as energy production, storage and transport and microelectronics. Quantum materials with several competing interactions at the electronic level offer tremendous opportunity to discover, design and tune properties for such applications. Although it has been recognized that small deviations in atomic positions, driven by the competing electronic interactions, in crystalline materials can have significant impact on properties, it remains a challenge to accurately characterize such deviations (short-range order) due to the lack of advanced instruments and analysis tools to characterize them. This project used the powerful neutron and x-ray scattering instruments recently developed at the DOE user facilities to address this challenge. New methods and efficient analysis tools were employed to uncover the hidden ordering that is behind the unique properties of transition metal compounds. One example of hidden order revealed by this project comes from vanadium (IV) oxide (VO 2 ) and related compounds. The project found that the chemical bonds in VO 2 compete against each other, unlike most crystalline compounds where the chemical bonds cooperate to yield the ordered structure. This helps explain why different measurements yielded different, competing pictures about the nature of VO 2 , which has led to disagreement about where its physical properties come from. Another example from this project of hidden ordering comes from a class of compounds known as condensed Chevrel phases, which are superconducting compounds that are generally believed to be non-magnetic. The neutron scattering methods used in this project revealed evidence of magnetism, which usually does not coexist with superconductivity. In this case, magnetism is believed to be one part of a special type of electronic behavior that can occur in compounds that have one-dimensional bonding character.

36 MATERIALS SCIENCE↗

Tailoring the Reaction Heterogeneity for Robust Li‐Rich Cathodes

The practical application of Li-rich Mn-based layered oxides (LLO) cathode is hindered by severe capacity and voltage degradation resulting from severe oxygen release and irreversible phase transition. In this work, the reaction heterogeneity, which describes the spatially resolved electrochemical divergence within individual cathode particles, is engineered through compositional gradient design to couple Li + transport kinetics and the anion redox activity between particle interiors and surfaces. It is revealed that Co/Mn concentration gradient within particles creates heterogeneous phase content distribution and structural ordering, inducing surface-bulk reaction heterogeneity that significantly impacts the overall electrochemical performance. Specifically, Li 2 MnO 3 -poor and Co-enriched surface effectively mitigates the oxygen loss and enhances electrochemical reaction kinetics, benefited from the reduced surface redox reactivity and induced highly ordered intra-layered cationic arrangement. Meanwhile, the Li 2 MnO 3 -enriched core with slight Li/Ni intermixing provides high reversible capacity and strong mechanical stability. Consequently, the greatly enhanced anion redox reversibility, Li + diffusion dynamics, and structure stability endow LLO with exceptional electrochemical properties, showing a capacity retention of 86.0% and a reduced voltage decay of 0.518 mV per cycle after 500 cycles at 1 C. This work provides a valuable strategy to tailor the redox chemistry and achieve robust LLO.

25 ENERGY STORAGE↗

Metalorganic chemical vapor deposition of ZnGeN 2 films on GaN: effects of cation stoichiometry on surface morphology and crystallinity

Novel optoelectronic device designs based on the heterostructures of III-N and II-IV-N 2 are promising to advance device performance significantly. For example, by utilizing InGaN-ZnGeN 2 quantum well (QW) structures instead of pure InGaN, the band structure engineering in the QW active region can lead to improved electron-hole wavefunction overlap, and thus enhance the radiative efficiency for photon generation. These novel heterostructures have great potential to address the current challenge of low quantum efficiency in InGaN QW based light emitting diodes emitting in green and beyond. The materials development of ZnGeN 2 is still at an early stage as compared to the much matured GaN material system. In an ideal octet rule preserving ordered structure of ZnGeN 2 , every N atom is coordinated by exactly two Zn and two Ge atoms. However, local violation of octet rule can be caused by non-ideal coordination of N by the cations. The disordered structure is thermodynamically less favorable but can still be achieved, for example, in kinetics-limited growth regime. The ordered ZnGeN 2 has a bandgap very close to that of GaN (~3.4 eV) and a lattice mismatch of <0.1% with GaN. Interestingly, the valence band of ZnGeN 2 has been predicted to be ~1 eV above that of GaN, which has inspired novel designs for high efficiency light emitters. In this work, we investigated the metalorganic chemical vapor deposition (MOCVD) of ZnGeN 2 films on GaN/c-sapphire templates. Diethylzinc (DEZn), germane (GeH4) and ammonia were used as the precursors for Zn, Ge and N, respectively. A systematic study was conducted to investigate the cation stoichiometry as a function of growth temperature (TG), total reactor pressure (P) and DEZn/GeH 4 molar flow rate ratio (RII/IV). Under the investigated growth window, the Zn/(Zn+Ge) composition in the films, determined from energy dispersive X-ray spectroscopy, decreased monotonically with increase in TG but increased with increase in P and RII/IV. Atom probe tomography data did not indicate the presence of any secondary phases such as Zn 3 N 2 or Ge 3 N 4 . The surface morphology and crystallinity of the grown films had strong correlation with the Zn/(Zn+Ge) composition. The scanning electron microscopy images showed that the near-stoichiometric films have planar surfaces whereas Zn-rich films had crystallites on their surface and the Zn-poor films had faceted surface. Scanning transmission electron microscopy (STEM) imaging revealed that the Zn-rich and Zn-poor films have columnar and filament-like morphology, respectively, whereas the near-stoichiometric films have continuous film-like cross-sectional morphology. TEM nano-diffraction patterns as well as X-ray diffraction 2θ-ω scan profiles indicate that the near stoichiometric films are single crystalline. Nano-diffraction pattern of the stoichiometric films resembled that of a disordered ZnGeN 2 structure. Room temperature Raman spectra of near-stoichiometric films showed only the phonon density of states like features of a cation disordered ZnGeN 2 . Cathodoluminescence and photoluminescence spectra measured at different temperatures had similar features with peak emission wavelength at ~ 2 eV. In conclusion, the stoichiometry of ZnGeN 2 films can be widely tuned by tuning the MOCVD growth parameters. The surface morphology and the crystallinity of the films were found to have strong correlation with the Zn/(Zn+Ge) composition. The stoichiometric ZnGeN 2 films grown on GaN were demonstrated with uniform surface morphology and high crystalline quality. The results from this work will provide pathway to implement ZnGeN 2 in device structures.

Karim, Md Rezaul↗

Advancing the understanding of energy-energy correlators in heavy-ion collisions

We investigate the collinear limit of the energy-energy correlator (EEC) in a heavy-ion context. First, we revisit the leading-logarithmic (LL) resummation of this observable in vacuum following a diagrammatic approach. We argue that this route allows to naturally incorporate medium-induced effects into the all-orders structure systematically. As an example, we show how the phase-space constraints imposed by the static medium on vacuum-like emissions can be incorporated into the LL result by modifying the anomalous dimensions. On the fixed-order side, we calculate the $\mathcal{O}$(α s ) expansion of the in-medium EEC for a γ → $q\overline{q}$ splitting with arbitrary kinematics including, for the first time, subleading colour corrections. When comparing this result to previously used approximations in the literature, we find up to $\mathcal{O}$(1) deviations in the regime of interest for jet quenching signatures. Energy loss effects are also quantified and further suppress the EEC at large angles. These semi-analytic studies are complemented with a phenomenological study using the jet quenching Monte Carlo JetMed. Finally, we argue that the imprint of medium-induced effects in energy-energy correlators can be enhanced by using an alternative definition that takes as input Lund primary declusterings instead of particles.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Task Sharing of Proton Incorporation in Vertically Aligned Nanocomposite Triple Conductors: Growth, Structure, and Surface Exchange Kinetics

As protonic ceramic electrolysis cells emerge for efficient H 2 production, there is a need to develop air electrode materials enabling fast, durable steam splitting and proton incorporation. Single-phase triple conductors may fail to satisfy the myriad performance/stability requirements, and their critical charge-carriers (holes, oxygen vacancies, and protons) are in competition, limiting their concentrations. Instead, we propose task-sharing, vertically aligned nanocomposites (VANs), comprising a proton conductor (BaZr 0.9 Y 0.1 O 3-δ ) and a redox-active mixed ionic electronic conductor (Ce 0.9 Pr 0.1 O 2-δ ), that may enable rapid proton surface exchange at the solid–gas interface and transport along the solid–solid heterointerfaces. We grew VANs by pulsed laser deposition and investigated the interplay between their processing conditions, structure, and proton and oxygen surface exchange kinetics. We varied the substrate temperature, laser repetition rate, laser fluence, and processing oxygen pressure. The crystallinity and phases were characterized by grazing-incidence X-ray diffraction, and the strain and structural order as a function of depth were evaluated by angle-dependent synchrotron X-ray pair distribution function analysis. To evaluate the potential for interdiffusion, the formation energies of substitutional defects were simulated with density functional theory. Corresponding structural analysis and elemental mapping were performed by scanning/transmission electron microscopy, energy-dispersive X-ray spectroscopy, and electron energy-loss spectroscopy, indicating distinct nanoscale compositional regions with a hierarchical structure embedded in individual VANs columns and minimal interdiffusion across a bilayer film. Proton and oxygen surface exchange coefficients (k H , k O ) and polarization resistances were evaluated by electrical and optical relaxations and impedance spectroscopy of VAN-incorporated protonic ceramic electrochemical cells, respectively, at 400–500 °C, demonstrating values comparable to some of the best-known triple and mixed conductors.

36 MATERIALS SCIENCE↗

Extension of a new semiempirical method (BFS) and the study of ground state properties of binary alloys

We extend the method of Bozzolo, Ferrante and Smith (BFS) for the study of alloy energetics to include a description of the local environment in specific ordered structures. The concept of bond-diagrams is introduced and applied to fcc binary compounds. A simple example of the parameterization of the bond-diagrams is done with reference to available first-principles calculations of Ni-Pt ordered alloys.

Bozzolo, Guillermo↗

Experimental Robust Control of Structural Acoustic Radiation

This work addresses the design and application of robust controllers for structural acoustic control. Both simulation and experimental results are presented. H(infinity) and mu-synthesis design methods were used to design feedback controllers which minimize power radiated from a panel while avoiding instability due to unmodeled dynamics. Specifically, high order structural modes which couple strongly to the actuator-sensor path were poorly modeled. This model error was analytically bounded with an uncertainty model, which allowed controllers to be designed without artificial limits on control effort. It is found that robust control methods provide the control designer with physically meaningful parameters with which to tune control designs and can be very useful in determining limits of performance. Experimental results also showed, however, poor robustness properties for control designs with ad-hoc uncertainty models. The importance of quantifying and bounding model errors is discussed.

Cox, David E.↗

Computational design of thermoelectric alloys through optimization of transport and dopability

Alloying is a common technique to optimize the functional properties of materials for thermoelectrics, photovoltaics, energy storage etc. Designing thermoelectric (TE) alloys is especially challenging because it is a multi-property optimization problem, where the properties that contribute to high TE performance are interdependent. In this work, we develop a computational framework that combines first-principles calculations with alloy and point defect modeling to identify alloy compositions that optimize the electronic, thermal, and defect properties. We apply this framework to design n-type Ba 2(1–x) Sr 2x CdP 2 Zintl thermoelectric alloys. Our predictions of the crystallographic properties such as lattice parameters and site disorder are validated with experiments. To optimize the conduction band electronic structure, we perform band unfolding to sketch the effective band structures of alloys and find a range of compositions that facilitate band convergence and minimize alloy scattering of electrons. Here, we assess the n-type dopability of the alloys by extending the standard approach for computing point defect energetics in ordered structures. Through the application of this framework, we identify an optimal alloy composition range with the desired electronic and thermal transport properties, and n-type dopability. Such a computational framework can also be used to design alloys for other functional applications beyond TE.

36 MATERIALS SCIENCE↗

Thermal Stability of π-Conjugated n -Ethylene-Glycol-Terminated Quaterthiophene Oligomers: A Computational and Experimental Study

This work represents a joint computational and experimental study on a series of $\textit{n}$-ethylene glycol (PEO$\textit{n}$)-terminated quaterthiophene (4T) oligomers for 1 < $\textit{n}$ < 10 to elucidate their self-assembly behavior into a smectic-like lamellar phase. This study builds on an earlier study for $\textit{n}$ = 4 that showed that our model predictions were consistent with experimental data on the melting behavior and structure of the lamellar phase, with the latter consisting of crystal-like 4T domains and liquid-like PEO4 domains. The present study aims to understand how the length of the terminal PEO$\textit{n}$ chains modulates the disordering temperature of the lamellar phase and hence the relative stability of the ordered structure. In this work, a simplified bilayer model, where the 4T domains are not explicitly described, is put forward to efficiently estimate the disordering effect of the PEO domains with increasing n; this method is first validated by correctly predicting that layers of alkyl (PE)-capped 4T oligomers (for 1 < $\textit{n}$ < 10) stay ordered at room temperature. Both 4T-domain implicit and explicit model simulations reveal that the order-disorder temperature decreases with the length of the PEO capping chains, as the associated increase in conformational entropy drives a tendency toward disorder that overtakes the cohesive energy, keeping the ordered packing of the 4T domains.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Multi-scale investigation of heterogeneous swift heavy ion tracks in stannate pyrochlore

Er 2 Sn 2 O 7 pyrochlore was irradiated with swift heavy Au ions (2.2 GeV), and the induced structural modifications were systematically examined using complementary characterization techniques including transmission electron microscopy (TEM), X-ray diffraction (XRD), and neutron total scattering with pair distribution function (PDF) analysis. Each technique probes different aspects and length scales of the transformed material regions. TEM revealed a core–shell ion track structure—an amorphous core surrounded by a disordered, anion-deficient fluorite shell—which was confirmed by XRD. Neutron total scattering, with sensitivity to the oxygen sublattice, provided relative fractions of amorphous and disordered fluorite phases and confirmed the presence of a defective pyrochlore phase, which largely maintains its structural ordering but is clearly distinct from the pristine pyrochlore matrix. This defect-rich pyrochlore phase forms a halo extending radially beyond the well-characterized core–shell track morphology observed in electron micrographs. Despite their differing long-range periodicity, the short-range structures of the amorphous, disordered, and defective pyrochlore phases are all modeled well with a weberite-type configuration. Evolution of the phase fractions with increasing ion fluence was examined to ascertain the phase-to-phase pathways that occur during primary and secondary ion impact. Furthermore, this approach extends knowledge about the multi-scale response of stannate pyrochlores to swift heavy ion irradiation in the electronic energy loss regime and improves existing track-overlap models.

36 MATERIALS SCIENCE↗

Thermal conductivity of (Ge 2 Sb 2 Te 5 ) 1–x Cx phase change films

Germanium–antimony–telluride has emerged as a nonvolatile phase change memory material due to the large resistivity contrast between amorphous and crystalline states, rapid crystallization, and cyclic endurance. Improving thermal phase stability, however, has necessitated further alloying with optional addition of a quaternary species (e.g., C). In this work, the thermal transport implications of this additional species are investigated using frequency-domain thermoreflectance in combination with structural characterization derived from x-ray diffraction and Raman spectroscopy. Specifically, the room temperature thermal conductivity and heat capacity of (Ge 2 Sb 2 Te 5 ) 1–x C x are reported as a function of carbon concentration (x ≤ 0:12) and anneal temperature (T ≤ 350 °C) with results assessed in reference to the measured phase, structure, and electronic resistivity. Phase stability imparted by the carbon comes with comparatively low thermal penalty as materials exhibiting similar levels of crystallinity have comparable thermal conductivity despite the addition of carbon. The additional thermal stability provided by the carbon does, however, necessitate higher anneal temperatures to achieve similar levels of structural order.

42 ENGINEERING↗

Geometry of the charge density wave in the kagome metal A V 3 Sb 5

Kagome lattice is a fertile platform for topological and intertwined electronic excitations. Recently, experimental evidence of an unconventional charge density wave (CDW) is observed in a Z 2 kagome metal AV 3 Sb 5 (A=K, Cs, Rb). This observation triggers wide interest in the interplay between frustrated crystal structure and Fermi surface instabilities. Here, we analyze the lattice effect and its impact on CDW in AV 3 Sb 5 . Based on published experimental data, we show that the 2×2×2 CDW breaks the sixfold rotational symmetry of the crystal due to the phase shift between kagome layers and can explain the twofold symmetric CDW peak intensity observed by scanning tunneling spectroscopy. The coupling between the lattice and electronic degrees of freedom yields a weak first-order structural transition without continuous change of lattice dynamics. Our result emphasizes the fundamental role of lattice geometry in proper understanding of unconventional electronic orders in AV 3 Sb 5 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Dislocation dynamics in heterogeneous nanostructured materials

Crystalline materials can be strengthened by introducing dissimilar phases that impede dislocation glide. At the same time, the changes in microstructure and chemistry usually make the materials less ductile. One way to circumvent the strength–ductility dilemma is to take advantage of heterogeneous nanophases which simultaneously serve as dislocation barriers and sources. Owing to their superior mechanical properties, heterogeneous nanostructured materials (HNMs) have attracted a lot of attention worldwide. Nevertheless, it has been difficult to characterize dislocation dynamics in HNMs using classical continuum models, mainly due to the challenges in describing the elastic and plastic heterogeneity among the phases. Here, in this work, we advance a phase-field dislocation dynamics (PFDD) model to treat multi-phase materials, consisting of phases differing in composition, structural order, and size in the same system. We then apply the advanced PFDD model to exploring two important but divergent materials design problems in HNMs: dislocation/obstacle interactions and dislocation/interface interactions. Results show that the interactions between a dislocation and distribution of obstacles varying in structure and composition cannot be understood by simply interpolating from their individual interactions with a dislocation. It is also found that materials containing interfaces with nanoscale thicknesses and compositional gradients have a much higher dislocation bypass stress than those with sharp interfaces, providing an explanation for the simultaneous high strength and toughness of thick interface-containing nanolaminates as observed in recent experiments.

36 MATERIALS SCIENCE↗

Building Durable Multimetallic Electrocatalysts from Intermetallic Seeds

When combined with earth-abundant metals, Pt-based alloy nanoparticles (NPs) can be cost-effective electrocatalysts. However, these NPs can experience leaching of non-noble-metal components under harsh electrocatalytic conditions. In this work, the Skrabalak group has demonstrated a novel NP construct in which Pt-based random alloy surfaces are stabilized against non-noble-metal leaching by their deposition onto intermetallic seeds. These core@shell NPs are highly durable electrocatalysts, with the ability to tune catalytic performance by the core@shell architecture, surface alloy composition, and NP shape. This versatility was demonstrated in a model system in which random alloy (ra-) PtM surfaces were deposited onto ordered intermetallic (i-) PdCu seeds using seed-mediated co-reduction (SMCR). In the initial demonstration, ra-PtCu shells were deposited on i-PdCu seeds, with these core@shell NPs exhibiting higher specific and mass activities for the oxygen reduction reaction (ORR) when compared to similarly sized ra-PtCu NPs. These NPs also showed outstanding durability, maintaining ~85% in specific activity after 5000 cycles. Characterization of the NPs after use revealed minimal loss of Cu. The activity enhancement was attributed to the strained surface that arises from the lattice mismatch between the intermetallic core and random alloy surface. The outstanding durability was attributed to the ordered structure of the intermetallic core. The origin of this durability enhancement was investigated by classical molecular dynamics simulations, where Pt atoms were found to have a lower potential energy when deposited on an intermetallic core than when deposited on a random alloy core. Also, ordering of Cu atoms at the core@shell interface appears to enhance the overall binding between the core and the shell materials. Inspired by this initial demonstration, SMCR has been used to achieve shells of different random alloy compositions, PtM (M = Ni, Co, Cu, or Fe). This advance is significant because ligand effects vary as a function of PtM identity and Pt/M ratio. These features also influence the degree of surface strain imparted from the lattice mismatch between the core and shell materials. Like the initial demonstration, standout features of these core@shell NPs were high durability and resistance to non-noble metal leaching. Moving forward, efforts have been directed toward integrating shape-control to this core@shell NP construct. This integration is motivated by the shape-dependent catalytic performance of NPs derived from the selective expression of specific facets. Considering the initial i-PdCu@ra-PtCu system, NPs with a cubic shape have been achieved by judicious selection of capping ligands during SMCR. Evaluation of these NPs as catalysts for the electrooxidation of formic acid found that the nanocubic shape enhances catalytic performance compared to similar core@shell NPs with a spherical morphology. We envision that SMCR can be applied to other NP systems to achieve highly durable catalysts as the syntheses of monodisperse and shape-controlled intermetallic seeds are advanced. This Account highlights the role of intermetallic cores in providing more durable electrocatalysts. More broadly, the versatility of SMCR is highlighted as a route to integrate architecture, alloy surfaces, and shape within one NP system, and how this achievement is inspiring new high-performance and robust catalysts is discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Strong enhancement of magnetic ordering temperature and structural/valence transitions in EuPd 3 S 4 under high pressure

We present a comprehensive study of the inhomogeneous mixed-valence compound, EuPd 3 S 4 , by electrical transport, X-ray diffraction, time-domain 151 Eu synchrotron Mössbauer spectroscopy, and X-ray absorption spectroscopy measurements under high pressure. Electrical transport measurements show that the antiferromagnetic ordering temperature, T N , increases rapidly from 2.8 K at ambient pressure to 23.5 K at ~19 GPa and plateaus between ~19 and ~29 GPa after which no anomaly associated with T N is detected. A pressure-induced first-order structural transition from cubic to tetragonal is observed, with a rather broad coexistence region (~20 GPa to ~30 GPa) that corresponds to the T N plateau. Mössbauer spectroscopy measurements show a clear valence transition from approximately 50:50 Eu 2+ :Eu 3+ to fully Eu 3+ at ~28 GPa, consistent with the vanishing of the magnetic order at the same pressure. X-ray absorption data show a transition to a fully trivalent state at a similar pressure. Our results show that pressure first greatly enhances T N , most likely via enhanced hybridization between the Eu 4 f states and the conduction band, and then, second, causes a structural phase transition that coincides with the conversion of the europium to a fully trivalent state.

36 MATERIALS SCIENCE↗

Nanolatticed Architecture Mitigates Damage in Shark Egg Cases

Structural versatility and multifunctionality of biological materials have resulted in countless bioinspired strategies seeking to emulate the properties of nature. The nanostructured egg case of swell sharks is one of the toughest permeable membranes known and, thus, presents itself as a model system for materials where the conflicting properties, strength and porosity, are desirable. The egg case possesses an intricately ordered structure that is designed to protect delicate embryos from the external environment while enabling respiratory and metabolic exchange, achieving a tactical balance between conflicting properties. Herein, structural analyses revealed an enabling nanolattice architecture that constitutes a Bouligand-like nanoribbon hierarchical assembly. Three distinct hierarchical architectural adaptations enhance egg case survival: Bouligand-like organization for in-plane isotropic reinforcement, noncylindrical nanoribbons maximizing interfacial stress distribution, and highly ordered nanolattices enabling permeability and lattice-governed toughening mechanisms. Furthermore, these discoveries provide fundamental insights for the improvement of multifunctional membranes, fiber-reinforced soft composites, and mechanical metamaterials.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Stochastic modal velocity field in rough-wall turbulence

Stochastically generated instantaneous velocity profiles are used to reproduce the outer region of rough-wall turbulent boundary layers in a range of Reynolds numbers extending from the wind tunnel to field conditions. Each profile consists in a sequence of steps, defined by the modal velocities and representing uniform momentum zones (UMZs), separated by velocity jumps representing the internal shear layers. Height-dependent UMZ is described by a minimal set of attributes: thickness, mid-height elevation, and streamwise (modal) and vertical velocities. These are informed by experimental observations and reproducing the statistical behaviour of rough-wall turbulence and attached eddy scaling, consistent with the corresponding experimental datasets. Sets of independently generated profiles are reorganized in the streamwise direction to form a spatially consistent modal velocity field, starting from any randomly selected profile. The operation allows one to stretch or compress the velocity field in space, increases the size of the domain and adjusts the size of the largest emerging structures to the Reynolds number of the simulated flow. By imposing the autocorrelation function of the modal velocity field to be anchored on the experimental measurements, we obtain a physically based spatial resolution, which is employed in the computation of the velocity spectrum, and second-order structure functions. The results reproduce the Kolmogorov inertial range extending from the UMZ and their attached-eddy vertical organization to the very-large-scale motions (VLSMs) introduced with the reordering process. The dynamic role of VLSM is confirmed in the –u'w' co-spectra and in their vertical derivative, representing a scale-dependent pressure gradient contribution.

42 ENGINEERING↗