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At least 1,549 records · Page 86
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Topological Hall effect in magnetic topological insulator films

Geometric Berry phase can be induced either by spin–orbit coupling, giving rise to the anomalous Hall effect in ferromagnetic materials, or by chiral spin texture, such as skyrmions, leading to the topological Hall effect. Recent experiments have revealed that both phenomena can occur in topological insulator films with magnetic doping, thus providing us with an intriguing platform to study the interplay between these two phenomena. In this work, we report on a numerical simulation of the anomalous Hall and topological Hall effects in a four-band model that can properly describe the quantum well states in the magnetic topological insulator films by combining Landauer–Büttiker formula and the iterative Green’s function method. Our numerical results suggest that spin–orbit coupling in this model plays a different role in the quantum transport in the clean and disordered limits. In the clean limit, spin–orbit coupling mainly influences the longitudinal transport but does not have much effect on topological Hall conductance. In the disordered limit, the longitudinal transport is determined by disorder scattering and spin–orbit coupling is found to affect strongly the topological Hall conductance. Here, this sharp contrast unveils a dramatic interplay between spin–orbit coupling and disorder effect in topological Hall effect in magnetic topological insulator systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Isotropic nanocrystalline Sm(Fe,Co) 11.3 Ti 0.7 magnets modified with B and Zr

Rare-earth-lean Sm(Fe,Co,Ti) 12 alloys with the ThMn 12 crystal structure and less than one Ti atom per formula unit have the potential of exceptionally powerful permanent magnets, but all prior attempts to develop high coercivity in bulk alloys, especially coercivity combined with crystallographic texture, have fallen short of the expectations. This study was aimed at improvement of the currently best Sm(Fe,Co,Ti) 12 magnets prepared through melt-spinning which are inherently isotropic. Modifications of the alloys with B and Zr, already demonstrated in earlier studies to be effective separately, have been implemented simultaneously. Here, a systematic study of Sm 1.1-x (Fe,Co) 11.3-y Ti 0.7 B y alloys melt-spun at a tangential speed of 50 m/s and annealed at 600–950 °C allowed for monitoring the continuous evolution of the two consecutive crystal structures, those of the TbCu 7 and ThMn 12 types. Zirconium was found to facilitate the formation of the 1:12 structure at the expense of the 1:7, whereas boron has the opposite effect, at certain concentrations completely suppressing the 1:12. When the two alloying elements are introduced simultaneously, they inhibit growth of the 1:12 crystallites at annealing temperatures higher than 800 °C, thus allowing for the development of a higher coercivity. Because of instrumental limitations, bulk magnets were prepared through a two-step process – compaction of the melt-spun ribbons at 650 °C and additional treatment at a higher temperature – and they were characterized by a reduced, 90–93%, density. Nevertheless, an isotropic Sm 0.9 Zr 0.2 (Fe,Co) 10.8 Ti 0.7 B 0.5 magnet exhibited fair values of the remanence (7.4 kG), maximum energy product (8.5 MGOe) and coercivity (5.4 kOe), as well as high Curie temperature of 525 °C and remarkably small temperature coefficient of the coercivity, -0.25%/°C.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Threshold behaviors of direct and Hall currents in topological spin-Hall effect

Here we study spin-dependent direct and Hall conductivities in the threshold region of Fermi energy, ε F = 2J, where J is the exchange integral between the conduction electron spins and the skyrmion spin texture. For ε F at the threshold value and above the spin-down electrons are allowed to exist. We find the two in the direct and four narrow peaks in the Hall conductivities for Fermi energies slightly below the threshold value. The found effects are dramatic because the electric current changes by approximately eight times in the narrow range of gate voltages (~4 meV). The values of the peaks strongly depend on skyrmion size. For small and very large skyrmion sizes the peak amplitudes are small compared to the conductivity absolute values. At the skyrmion radius a = 6 nm and very light conduction electrons, m* ~ 10 -2 m e , the extrema are the most pronounced. The temperature evolution reveals the strong smearing effect where the peak-wise behavior completely disappears at room temperatures. Spin transistor could be considered for possible applications where in the narrow region of gate voltage the sharp conductivity change occurs.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Metal-insulator transition temperature in EuO 1−x films as a function of exposure time in air

Oxygen-deficient Europium monoxide EuO 1-x shows a metal-to-insulator transition near the Curie temperature (T C ). A systematic transport study of EuO 1-x thin films as a function of exposure time in air reveals a gradually decreased T C from 140 K to 70 K as the concentration of the oxygen vacancies decreases, which is accompanied by a drastic increase in the resistance. Here we also find an unusual enhancement of magnetic anisotropy in the transport measurements, which results from the strong spin-orbit coupling at the interface between the film and substrate and possible presence of spin-textures like skyrmions in EuO 1-x .

36 MATERIALS SCIENCE↗
DOE OSTI2023

Observation of skyrmion bubbles in multilayer [Pt/Co/Cu] n using spin-polarized STM

Magnetic multilayers are a promising platform for storage and logic devices based on skyrmion spin textures, due to the large materials phase space for tuning properties. Epitaxial superlattice structures of [Pt/Co/Cu]n thin films were grown by molecular beam epitaxy at room temperature. Spin-polarized scanning tunneling microscopy (SP-STM) of these samples was used to probe the connection between surface structure and skyrmion morphology with nanoscale spatial resolution. Irregular-shaped skyrmion bubbles were observed, with effective diameters from 20 to 200 nm that are much larger than the nanoscale grain structure of the surface topography. Nucleation, annihilation, and motion of skyrmion bubbles could be driven using the stray field of the ferromagnetic tip in repeated imaging, and spin-polarized current/voltage pulses. Furthermore, our detailed comparison of STM topography and differential conductance images shows that there are no surface defects or inhomogeneities at length scales that could account for the range in skyrmion bubble size or shape observed in the measurements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Machine-learning modeling of magnetization dynamics in quasi-equilibrium and driven metallic spin systems

Here, we present a perspective on recent progress in machine-learning (ML) force-field approaches for large-scale Landau–Lifshitz–Gilbert (LLG) simulations of metallic spin systems. Building on a generalization of the Behler–Parrinello (BP) architecture originally developed for quantum molecular dynamics, we develop scalable and transferable ML models that faithfully capture the complex, environment-dependent electron-mediated exchange fields characteristic of itinerant magnets. A central ingredient of this framework is the implementation of symmetry-aware magnetic descriptors based on group-theoretical bispectrum formalisms. Leveraging these ML force fields, LLG simulations faithfully reproduce hallmark non-collinear magnetic orders—such as the 120° and tetrahedral states—on the triangular lattice, and successfully capture the complex spin textures emerging in the mixed-phase states of a square-lattice double-exchange model under thermal quench. We further discuss a generalized potential theory that extends the BP formalism to incorporate both conservative and nonconservative electronic torques, thereby enabling ML models to learn nonequilibrium exchange fields from computationally demanding microscopic approaches such as nonequilibrium Green’s-function techniques. This extension yields quantitatively accurate predictions of voltage-driven domain-wall motion and establishes a foundation for quantum-accurate, multiscale modeling of nonequilibrium spin dynamics and spintronic functionalities.

Descriptors↗
DOE OSTI2022

Effect of nitriding on mechanical and microstructural properties of Direct Metal Laser Sintered 17-4PH stainless steel

In this work, the effect of the nitriding process on microstructure and mechanical properties of additively manufactured (AM) 17-4PH stainless steel is investigated. The nitriding was performed at 530 °C, 560 °C, and 580 °C for 2 h. The nitriding process improves the hardness and surface roughness of the AM 17-4PH steel. Detailed microstructural characterizations of both as-built and nitride samples are performed using an optical microscope, scanning electron microscope (SEM) equipped with energy-dispersive X-ray spectroscopy (EDS), and X-ray diffraction technique. It reveals that the nitride layer thickness increases with nitriding temperature. A distinct transition layer between the substrate and nitride layer is observed in the 560 °C and 580 °C nitride samples. The nitriding process develops almost equiaxed grain microstructure with new secondary phase precipitates, whereas in the as-built material, the grains are primarily columnar along the AM process build direction. Specifically, the nitriding process introduces γ-Fe4N, ε-Fe3N, CrN, and Ni3N precipitates. The increase in Ni- and Cu-rich precipitates with the nitriding temperature explains the observed improvement in the hardness and surface roughness. Furthermore, the nitriding process does not alter the substrate's initial weak crystallographic texture.

17-4PH steel↗
DOE OSTI2024

Parameter development and characterization of laser powder directed energy deposition of Nb – Alloy C103 for thin wall geometries

This work focuses on the parameter development and microstructural characterization of Nb-based alloy C103 for thin wall structures produced via laser powder – directed energy deposition (LP – DED). Laser power and scanning speeds were varied as part of a design of experiments to identify adequate print parameters. Combinations were evaluated for relative density, porosity, and geometrical accuracy. A combination of a laser power of 1420 W and scanning speed of 14 mm/s resulted in a relative density >99%, exhibited a consistent weld bead profile and was used for further microstructural evaluation. A mix of optical and scanning electron microscopy (SEM) revealed small, slightly elongated grains along the edges and large epitaxial grains in the central region along the Build – Transverse view. Scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS) analysis revealed Hf rich columnar cells in the center that transition into an evenly spaced cellular structure towards the edges of the built sample. Electron backscatter diffraction (EBSD) scans show a sharp [001] texture when looking at the cross section of the sample along the build direction. The Build – Scan view revealed a zig – zag pattern that follows the back – and – forth deposition strategy that was used. Finally, microhardness measurements were taken in the as – built (AB) and stress relieved (SR) conditions to baseline preliminary mechanical properties. The AB condition exhibited a large amount of scatter in the data and averages up to 11% larger than the SR condition. The reduction in scatter upon applying the SR cycle are indicative of a large concertation of dislocations present in the AB condition.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Insights into elevated temperature tensile deformation mechanisms and kink banding in additively manufactured tungsten

Additive manufacturing (AM) potentially enables fabrication and repair of plasma facing components (PFCs) of tungsten. However, deformation mechanisms in AM-fabricated tungsten under service-relevant thermomechanical conditions remain unknown majorly due to challenges in achieving crack-free W. This study reveals the deformation mechanisms operative under tension at 800 °C and 1200 °C in the electron beam melting powder bed fusion (EBM-PBF) fabricated W. Textured columnar grains with mixed <001 >/<111 >|| build-direction were observed. Strong anisotropy in tensile properties persisted across test temperatures, and all specimens exhibited extensive deformation-induced banding phenomena. Grain boundary character analysis of the deformed specimens indicated that these deformation bands were kink bands with tilt grain boundaries prominently present at the band-matrix interface. Interestingly, the material within the kink bands rotated toward higher resolved shear stress, providing insights into the origins of kink band formation in body-centered cubic refractory metals. Intragranular misorientation axis analysis revealed that plasticity was dominated by {110} <111 > slip at 800 °C, whereas additional (213)[11⁢̄1] and (112)[11⁢̄1] slip systems activated at 1200 °C. A dense low-angle boundary networks observed near fractured surface indicated the onset of dynamic recrystallization. Results reveal plasticity governing mechanisms in AM-fabricated W under power plant-relevant conditions, and provide insights into kink band attributes in refractory metals.

Mayes, Riley [ORNL] (ORCID:000900089307010X)↗
DOE OSTI2022

Intense cyclic heating effects on thermo-fracture and thermal shock of solid tungsten and open-cell tungsten foam

Here we investigate here the effects of transient (cyclic) arc-jet plasma and laser heating on fracture behavior of W-foam and solid tungsten. The two key parameters that control the foam thermomechanical response are its density and mean cell size expressed in Pores Per Inch (PPI). Tungsten foam samples were fabricated with Chemical Vapor Deposition (CVD) with variety of PPI and relative density. These were tested under two types of qualitatively different conditions: (1) high-enthalpy arc-jet, and (2) high-power cyclic laser heating. None of the foam samples showed macroscopic through-thickness cracks. However, distributed micro-cracks were observed on ligaments and their triple junctions. Under the same loading conditions, W-foam and solid tungsten showed similar crack network pattern and characteristic length-scale. However, Crack Opening Displacement (COD) was twice as large in solid W as compared to W-foam. Foam samples that have been previously exposed to a low-pressure helium plasma showed significant changes in their surface forming nano-texture fuzz which was removed by subsequent testing in the arc-jet. Extensive fracture and re-crystallization were observed in the thin solid W disk that was fully-constrained from expansion. Thicker and fully-constrained solid W disks did not display recrystallization, grain growth, and extensive cracking. However, thicker disks that were free to expand showed some recrystallization and extensive through-thickness cracks due to less effective cooling and thus higher temperatures. Laser beam testing showed no visible damage formation at 0.19 GW/m 2 and 0.38 GW/m 2 for both low-density (23%) and high-density (43%) foams at low pulses (100-1000). Micro-cracks were observed after 10,000 pulses at 0.19 GW/m 2 in both foams, and in low-density foam after 100,000 at 0.38 GW/m 2 . The nature of thermomechanical damage in W-foam exposed to extreme power (GW/m 2 ) short-duration laser pulses was found to be qualitatively similar to that of high power (MW/m 2 ) long-duration arc-jet.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Analysis of neptunium oxides produced through modified direct denitration

Production of neptunium-237 ( 237 Np) target materials for plutonium-238 ( 238 Pu) radioisotope thermoelectric generators (RTGs) for deep space exploration requires advanced chemistry and engineering development. Currently, the domestic Pu-238 Supply Program at Oak Ridge National Laboratory produces neptunium dioxide (NpO 2 ) for target material using a modified direct denitration (MDD) flowsheet. Although the chemistry, reaction mechanisms, and product characteristics of MDD are well understood for uranium, corresponding studies of the neptunium system are still needed to continue optimization of target material properties, production equipment design, and production flowsheets. Here, the objective of this work is to characterize crystalline phases, morphology, surface texture, and particle size of NpO 2 produced via MDD reactions. Solid-phase characterization techniques, including powder X-ray diffraction (pXRD) and scanning electron microscopy with energy-dispersive spectroscopy (SEM-EDS), were employed to achieve this objective. Subsequent data processing using the Morphological Analysis for Material Attribution (MAMA) software was performed to analyze particle morphology and size. Broadly, the powders were found to contain a mixture of NpO 2 and Np 2 O 5 after denitration with a variety of morphologies. After high-firing, the product was found to be NpO 2 with a typical polycrystalline oxide morphology and a grain size ranging from 0.72 to 0.94 µm. These analyses provide knowledge on the reaction pathway for a non-traditional NpO 2 synthesis method and offer additional unique insight into production-scale environments for transuranic materials.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

First-principles investigation of lanthanides diffusion in HCP zirconium via vacancy-mediated transport

The diffusion of lanthanide fission products plays an important role in the growth of the fuel-cladding chemical interaction (FCCI) region in metallic fuels. The use of a Zr interdiffusion barrier may mitigate the transport of lanthanides from the fuel to the cladding, but the efficacy of such a liner is not yet known. In this paper, the stability and vacancy-mediated diffusion of La, Ce, Pr, and Nd in hexagonal close-packed (HCP) Zr is investigated via density functional theory (DFT) calculations and self-consistent mean field (SCMF) analysis. DFT is used to calculate the formation, binding, and migration energies of vacancies and vacancy-solute pairs. The DFT energetics are used in the KineCluE code to calculate the Onsager transport coefficients. La is found to be the fastest diffusing species in HCP Zr and experiences an almost isotropic diffusion behavior. The other three species (Ce, Pr, and Nd) demonstrate anisotropic diffusion where the diffusion in the basal planes is significantly faster than that along the c-axis. Further, the calculated lanthanide diffusivities in HCP Zr are fitted to an Arrhenius relation and the activation energies and prefactors are reported for the first time. Furthermore, the vacancy drag and the segregation tendencies were analyzed using the calculated off-diagonal transport coefficients. According to our vacancy-mediated diffusion model, lanthanides are expected to be enriched at vacancy sinks at low temperatures, while at high temperatures, lanthanides are depleted at sinks and will preferably diffuse into the bulk. The enrichment/depletion transition temperature depends on the diffusion direction (basal or axial) and hence will be controlled by the grain texture and orientation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Enhanced Stress Relaxation Behavior via Basal ⟨a⟩ Dislocation Activity in Zircaloy-4 Cladding

Herein this work evaluates the stress relaxation behavior of textured Zircaloy-4 cladding to understand how mechanical anisotropy influences pellet-cladding interactions. Uniaxial and biaxial stress relaxation tests are performed using full-tube axial tension and internal pressurization, respectively, aiming to achieve 0.25%, 1%, and 2% equivalent strains in the cladding samples at a temperature of 300°C. Internal pressure relaxation test results display enhanced stress relaxation compared to axial testing results, particularly for samples loaded beyond yield. Results of electron backscatter diffraction indicate increased deformation microstructure during loading and increased strain homogenization and recovery during relaxation for samples loaded via internal pressurization. Analysis indicates that the increased production and activity of basal ⟨a⟩ dislocations play a significant role in the enhanced relaxation measured in samples subjected to internal pressurization.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Hot Hydrogen Exposure of U x Zr 1-x C y Nuclear Fuel: The Effect of Additional Carbon

Nuclear thermal propulsion (NTP) using hydrogen as propellant in a solid-state fission reactor to reach temperatures of up to 3000K can achieve significantly higher specific impulse than chemical propulsion. A promising fuel that is again considered for NTP is U x Zr 1-x C y . To reduce the overall mass loss as well as the uranium fuel loss, a range of experiments using additional carbon in hot hydrogen (2600 K, 6 SLPM flow rate) were performed for up to 5-6 h. Both a CH 4 addition (0.1 and 0.2 vol%) in the hydrogen stream and the use of sacrificial graphite pieces upstream of the samples were tested, with sample compositions from 5 at% UC to 30 at% UC. The results showed a strong reduction of mass loss, up to a factor of 3, as well as a reduction of surface uranium losses in the presence of additional carbon in the atmosphere. Even with additional carbon in the atmosphere, material with 30 at% UC was not stable, but material with 20 at% UC was stable for up to 6h. The sample surfaces showed texturing after processing, possibly by grain growth on the surface. This led to a separation into grains with high uranium content close to the (100)-orientation, and with low uranium content in grains close to the (111)-orientation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Strain rate sensitivity, microstructure variations, and stress-assisted β → α" phase transformation investigation on the mechanical behavior of dual-phase titanium alloys

In this study, the microstructures of three widely used dual-phase titanium alloys: Ti-6Al-4V, Ti-6Al-2Sn-4Zr-2Mo, and Ti-6Al-2Sn-4Zr-6Mo are characterized using backscatter electron imaging and the deformation behaviors in their individual α and β phases are investigated using in situ high-energy X-ray diffraction during uniaxial tension experiments. This is accompanied by calculation of the strain rate sensitivity (SRS) in these alloys, as a function of applied loading. The results of the calculated SRS and the mechanical response (in terms of lattice strains and hardening behaviors) are rationalized based on the local microstructure, composition, and texture of the alloy. A stress-induced β (BCC) to α" (orthorhombic) phase transformation is observed during the in-situ diffraction experiment, which permitted analysis of the lattice strain evolution during the phase transformation. Results from this study provide insights into the relationship between microstructure, composition, applied loading, and the deformation behavior, including effects on loading with time holds. Specifically, the results show that the microstructure, and not necessarily the chemical composition (Mo content), along with the applied loading have a dominant role in the observed SRS variation in titanium alloys. Further, the evolution of the α" (orthorhombic) phase is observed for the first time during deformation of an industrially relevant titanium alloy, Ti-6246.

36 MATERIALS SCIENCE↗
DOE OSTI2021

An automated procedure built on MTEX for reconstructing deformation twin hierarchies from electron backscattered diffraction datasets of heavily twinned microstructures

Here we present a set of algorithms built on the MTEX and MATLAB graph toolboxes for automatic reconstruction of deformation twin hierarchies from Electron Backscatter Diffraction (EBSD) datasets with a focus on developing methods for heavily twinned microstructures (twin fractions >0.5). The algorithms address key issues arising at large strains, mainly: missing twin relationships, grouping of heavily deformed grain fragments into families of similar orientation originating from a single initial grain, identification of parent fragments for large twin volume fractions, and classification of families having twin relationships with multiple families. To facilitate the development of these algorithms, large-grained ultra-high purity α-Ti deformed in compression along two directions is investigated. Graphs are utilized to handle non-local geometric merging and to represent relationships throughout the reconstruction process. When determining if a grain fragment is from the undeformed microstructure, the combined metrics of the fragment's orientation volume fraction in the initial texture and the directed graph centrality measure of out-closeness (the number of nodes reached in a graph from a given node) are essential. To address automation in reconstructing the sequence of twinning and relating fragments originating from a single grain in the initial microstructure, the twin family tree is formulated as a minimum spanning tree emanating from the initial grain family. A scheme constructing the distances associated with twin relationship comprising the spanning tree is developed, and a novel quasi-directional Prim spanning tree algorithm is used to determine the twin family tree. The procedure is demonstrated to significantly improve the level of automation in reconstructing twin hierarchies in heavily twinned microstructure compared to other methodologies in literature. The procedure can readily be applied to analyses of twinning in metals, as well as provide an approach for routinely extracting twin statistics at larger deformation levels than previously possible. Significantly, the procedure is demonstrated to be capable of identifying third generation twinning in α-Ti microstructures.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Scan strategies in EBM-printed IN718 and the physics of bulk 3D microstructure development

Three-dimensional (3D) characterization provides opportunities for understanding processing-structure relationships in additively manufactured (AM) materials. Bulk samples of Inconel 718 were fabricated via electron beam melting (EBM) in order to study microstructural development as a function of energy input and beam scan strategy. TriBeam tomography of bulk Inconel 718 microstructures built under steady-state growth conditions reveals the sensitivity of microstructure formation and evolution to machine process parameters. Here, samples manufactured using a narrow range of energy input per unit build area result in varied grain morphologies and crystallographic textures. Using TRUCHAS, a thermal simulation software, the thermal history of bulk scan strategies was predicted, and combined with a calibrated microstructure-processing map to accurately predict bulk grain morphologies. The solidification parameters and the 3D measured nucleation density are used to predict the transition between columnar and equiaxed grain morphologies, providing a process map to guide AM parameter choices to locally control as-printed microstructure. A two-dimensional metric for characterizing bulk grain morphology was also found to agree well with predictions from the process map calibrated by 3D data. Combined with 3D tomography and thermal modelling, the physics of structure development were understood at a new level of detail with respect to the competing processes of grain nucleation and epitaxial growth.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Reconstructing parent microstructures in martensitic and pearlitic Ti-Cu

Evaluating the microstructural evolution of parent phases has long been a challenge in metals with a partial or complete solid state transformation. Most parent microstructure evolution has to be inferred from the product microstructure, with some information permanently lost. Parent microstructure reconstructions relying on orientation relationships and EBSD data are a useful tool to overcome this challenge, though much background knowledge is required to do so. Here, this work introduces a reconstruction process for a eutectoid composition Ti-Cu binary alloy to evaluate the high temperature β-Ti phase from martensitic and pearlitic product microstructures. Martensitic microstructures were accurately reconstructed, enabling elucidation of β-Ti grain size and texture, and the employed script included for scientific reference. Pearlitic microstructures did not reconstruct effectively with the current process. However, new insight into the interfacial crystallographic orientations of pearlitic Ti-Cu microstructures was gleaned via this analysis, and future investigations of interest are discussed accordingly. Ultimately, these findings demonstrate tools widely implemented on conventional titanium and ferrous alloys can also be applied to understand parent microstructures in Ti-Cu and other alloys of emerging interest. This is especially of use as new manufacturing processes for such materials require understanding how parent phase microstructures respond to new, novel material processing such as AM.

36 MATERIALS SCIENCE↗