Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “molecular dynamic (MD) simulation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 397 records · Page 22

Corrosion resistant hot melt adhesive to bind metals

Hot melt adhesives (HMAs) play an important role in many industries, and their demand is expected to grow. HMAs don't require any solvents, and their application results in the formation of strong bonds with the substrate upon cooling within seconds. These properties differentiate them from liquid glues and make them preferable for practical application. Currently, commercial HMAs are used in bonding lightweight materials such as paper, polymers, and cartons, and have limited usage in areas necessitating the bonding of heavier objects like metals. Here, in this study, we report a design and testing of versatile platform comprising an ion-coordinating polymer and ionic fillers for performance optimization and understanding of structure–property relationships, enabling the rational design of HMAs with improved adhesion to metal surfaces. All-atom Molecular dynamics (MD) simulations and various characterization methods are used to elucidate the adhesion mechanism in model composite system containing polyethylene oxide mixed with chemically diverse salt particles. The maximum adhesion strength is found in composites with Al(OH) 3 and FeCl 3 fillers. Interestingly, the presence of Al(OH) 3 also provides a multifunctional anticorrosion property as measured electrochemically using the Tafel method. The discovered path to formulations with improved adhesion to metal surfaces constitutes an important step toward advancing HMAs for use in the structural and semi-structural metal work domain.

Adhesive and cohesive forces↗

Resolving Lonsdaleite's decade-long controversy: Atomistic insights into a metastable diamond polymorph

Lonsdaleite, a theoretically proposed hexagonal diamond polymorph, has remained at the center of a five-decade scientific controversy since its 1967 identification. While some studies claim it exhibits superior hardness through compression-induced structural changes, others contend it is merely a stacking-faulted cubic diamond. Meteoritic samples and synthetic preparations have yielded conflicting evidence, with even advanced characterisation techniques like XRD and TEM failing to provide definitive proof. In this work, we employ first-principles density functional theory (DFT) and molecular dynamics (MD) simulations to generate unambiguous theoretical fingerprints through XRD, Raman, and SAED patterns that distinguish true Lonsdaleite from cubic diamond and its defective variants. Our atomistic approach quantifies the thermodynamic metastability of Lonsdaleite under realistic pressure-temperature conditions, reveals distinct spectral signatures through simulated Raman and resolves the structural ambiguity through generalised stacking fault energy analysis. By establishing clear criteria for definitive identification, this study provides long-awaited clarity to the Lonsdaleite debate while offering a robust computational framework for characterising metastable carbon phases in meteoritic, synthetic and industrial materials.

DFT↗

Ion-beam radiation-induced Eshelby transformations: The mean and variance in hydrostatic and shear residual stresses

Ion beam plays a pivotal role in ion implantations and the fabrication of nanostructures. However, there lacks a quantitative model to describe the residual stresses associated with the ion-beam radiation. Radiation-induced residual stress/transformation strain have been mostly recognized in the hydrostatic sub strain space. Here, in this study, we use molecular dynamics (MD) simulations to show that the response of a material to irradiation is generally anisotropic that depends on the ion-beam direction, and should be described using tensorial quantities. We demonstrate that accelerator-based ion beam irradiation, combined with the intrinsic lattice anisotropy and externally induced anisotropy (such as anisotropic mechanical loadings), causes radiation-actuated shear transformation strains in addition to hydrostatic expansion. We map out these complex correlations for several materials. Radiation-induced defects are shown to be responsible for residual shear stresses in the manner of Eshelby inclusion transformation. We propose such tensorial response model should be considered for accurate nanoscale fabrication using ion-beam irradiation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Insight into the nanostructure of “water in salt” solutions: A SAXS/WAXS study on imide-based lithium salts aqueous solutions

"Water-in-salt " electrolyte (WISE) series have been studied for lithium-ion batteries and supercapacitor applications, but so far, most of the focus has been on the LiTFSI salt-based systems. Herein, we used small-angle X-ray scattering/wide-angle X-ray scattering (SAXS/WAXS) and molecular dynamics (MD) simulation to investigate the solvation structure of a series of lithium salts with four different symmetric anions: (bis(fluoro sulfonyl)imide (FSI), bis(trifluoromethane sulfonyl)imide (TFSI), bis(pentafluoroethane sulfonyl) imide (BETI) and bis(nonafluorobutane sulfonyl)imide (BNTI)), which have similar parent structures but different lengths of the fluorocarbon chains. Two competing structures were found in the four lithium salts aqueous solutions: anion solvated structure and anion network. The anion network plays a crucial role in obtaining a stable and enlarged electrochemical window. The d spacing of the anion solvated structure follows a linear correlation with the number of carbons in the fluorocarbon chains and an exponential correlation with the concentrations. Further, we also observed that the transition from one structure to another is predominantly controlled by the salt volume fraction for all imide-based aqueous solutions. This work provides a systematic study of the atomistic scale structures of a series of imide-based lithium salt aqueous solutions that could extend the knowledge of WIS electrolytes.

25 ENERGY STORAGE↗

Machine-learning and first-principles investigation of lightweight medium-entropy alloys for hydrogen-storage applications

The transition to a low-carbon economy demands efficient and sustainable energy-storage solutions, with hydrogen emerging as a promising clean-energy carrier and with metal hydrides recognized for their hydrogen-storage capacity. Here, we leverage machine learning (ML) to predict hydrogen-to-metal (H/M) ratios and solution energy by incorporating thermodynamic parameters and local lattice distortion (LLD) as key features. Our best-performing ML model provides improvements to H/M ratios and solution energies over a broad class of medium-entripy alloys (easily extendable to multi-principal-element alloys), such as Ti–Nb-X (X = Mo, Cr, Hf, Ta, V, Zr) and Co–Ni-X (X = Al, Mg, V). Ti–Nb–Mo alloys reveal compositional effects in H-storage behavior, in particular Ti, Nb, and V enhance H-storage capacity, while Mo reduces H/M and hydrogen weight percent by 40–50 %. We attributed results in molybdenum-rich alloys to slow hydrogen kinetics, as validated by our pressure-composition-temperature (PCT) isotherm experiments on pure Ti and Ti 5 Mo 95 alloys. Density functional theory (DFT) and molecular dynamics (MD) simulations also confirm that Ti and Nb promote H diffusion, whereas Mo hinders it, highlighting the interplay between electronic structure, lattice distortions, and hydrogen uptake. Notably, our Gradient Boosting Regression model identifies LLD as a critical factor in H/M predictions. Here, to aid material selection, we present two periodic tables illustrating elemental effects on (a) H 2 wt% and (b) solution energy, derived from ML, and provide a reference for identifying alloying elements that enhance hydrogen solubility and storage.

08 HYDROGEN↗

Modeling shock-induced void collapse in single-crystal Ta systems at the mesoscales

Understanding the role of microstructural heterogeneities on the shock wave propagation and defect evolution behavior is essential to predicting the dynamic response of metals. Heterogeneities, such as voids, provide challenges to understanding the wave propagation behavior as the shock-void interaction can collapse the void and result in large plastic strains and significant heating (hot spot formation) in the metal. Accurate modeling of this phenomenon requires predicting the void collapse mechanisms and the related heat generation and dissipation mechanisms (hotspot formation) that determine the microstructure evolution. While molecular dynamics (MD) simulations can model the void collapse behavior, the time/length scale capabilities pose a challenge to connect with continuum models or the experimental scales. Here, this study presents the capability of the newly developed quasi-coarse-grained dynamics (QCGD) method that extends the MD simulations to larger system sizes and longer times to model this phenomenon. This study uses QCGD simulations to investigate the mechanisms of shock wave interactions with pre-existing voids in single-crystal Ta microstructures for variations in shock pressures, void size, and loading orientations. For a given orientation, the plasticity contributions and rates of void collapse are observed to vary with shock pressures and void size. The larger void sizes and higher pressures result in increased temperatures (hot spots) and faster void collapse rates and unravel the variations in the plasticity contributions. In addition, QCGD simulations investigate the post-collapse microstructure evolution as a release wave travels through the hot spot region. The simulations reveal that the reduction in temperatures due to heat dissipation initiates the dynamic recrystallization behavior in the hotspot regions.

36 MATERIALS SCIENCE↗

Dislocation cross-slip in precipitation hardened Mg–Nd alloys

An integrated experimental characterization and molecular dynamics (MD) simulation approach was used to explore the dislocation-precipitate interactions in a dilute Magnesium–Neodymium (Mg–Nd) precipitation hardened alloy. In situ indentation in a transmission electron microscope (TEM) and postmortem TEM characterization of deformed samples and MD simulations revealed that basal < a > type dislocations interacted differently with β 1 (Mg 3 Nd) and β"(Mg 3-7 Nd) precipitates. For β" precipitates, the basal dislocations directly shear the precipitates. For β 1 precipitates, such shearing becomes much more difficult because it requires the creation of antiphase boundaries in the ordered lattice of β 1 precipitates. Screw dislocations were observed to cross-slip from basal to the prismatic plane, which could be parallel to the broad facet of β 1 precipitates. It is postulated that double cross-slip (basal to prismatic to basal) via the Hirsch mechanism may enable screw dislocations to overcome the β 1 precipitates. MD simulations also revealed that an edge dislocation is unable to bypass the precipitate via the generation of screw dislocation segments plus the double cross-slip mechanism. The edge dislocation can bow around the precipitate, and the segment that adopts a screw character can cross-slip to the prismatic plane but with increasing applied stress, cross-slips back to the original basal plane to continue glide via precipitate shearing. Finally, the implication of glide dislocation - β 1 -precipitate interaction mechanisms on the strength and ductility of β 1 precipitate dominant microstructures is discussed.

36 MATERIALS SCIENCE↗

Intermetallic phase formation in Al-Si-Zr alloys during hot isostatic pressing revealed by experiments and molecular dynamics

Understanding phase transformations at alloy interfaces is critical for the design of advanced structural materials. Here, in this study, we investigate the formation mechanisms of the Al 2 SiZr intermetallic phase in the Al-Si-Zr system under hot isostatic pressing (HIP) using molecular dynamics (MD) simulations and thermodynamic analysis. A unique aspect of our approach in MD involves the replacement of a disordered Al 2 SiZr stoichiometry with an ordered phase at the Al-Zr interface once HIP results in the desired Al 2 SiZr stoichiometry, allowing us to compute the total energetic cost of transformation by accounting for both formation energies and diffusion barriers. Diffusion coefficients and activation energies, extracted across a range of temperatures, reveal that HIP substantially enhances atomic mobility, creating favorable stoichiometry for phase evolution. Our results show that Al 2 SiZr phase formation is kinetically unfavorable at lower temperatures but becomes feasible when the thermodynamic driving energy surpass a critical energy threshold.

Roy, Ankit [Pacific Northwest National Laboratory ↗

Understanding fluorine-free electrolytes via small-angle X-ray scattering

Fluorine-free electrolytes have attracted great attention because of its low-cost and environmental friendliness. However, so far, little is known about the solution structures of these electrolytes. Here, we compare the solvation phenomenon of sodium tetraphenylborate (NaBPh 4 ) salt dissolved in organic solvents of propylene carbonate (PC), 1,2-dimethoxyethane (DME), acetonitrile (ACN) and tetrahydrofuran (THF). Small-angle X-ray scattering (SAXS) reveals a unique two-peak structural feature in this salt concentrated PC electrolyte, while solutions using other solvents only have one scattering peak. Molecular dynamics (MD) simulations further reveal that there are anion-based clusters in addition to the short-range charge ordering in the concentrated NaBPh4/PC electrolyte. Raman spectroscopy confirms the existence of considerable contact ion pairs (CIPs). Here, this work emphasizes the importance of global and local structural analysis, which will provide valuable clues for understanding the structure performance relationship of electrolytes.

25 ENERGY STORAGE↗

Molecular dynamics study of primary damage in the near-surface region in nickel

In this work, we carried out a large-scale molecular dynamics (MD) simulation to elucidate the effect of the free surface on the defect production of displacement cascades in pure nickel. These MD simulations were performed both in the bulk and near-surface regions with primary knock-on atom (PKA) energies of E PKA = 1, 5, or 10 keV and at temperatures T = 300, 425, or 525 K. Additionally, for every (T, E PKA ), near-surface cascade simulations were performed as a function of depth. In the near-surface simulations, assuming isotropic neutron fluence, the PKAs were initiated in random directions, including toward and parallel to the free surface. For both the near-surface and bulk cascades, the effect of E PKA and T on the defect production is similar. In both cases, the defect production increases with E PKA , but the temperature has minimal effect. However, the production and clustering of vacancies are higher for near-surface cascades, and they decrease with increasing depth. In contrast, the production and clustering of self-interstitial atoms are lower and increase with depth. Eventually, the production and clustering of both defect types approach bulk cascade-like behavior, and the depth at which this occurs increases with E PKA , but is independent of temperature.

36 MATERIALS SCIENCE↗

Diffusion of small anti-Schottky clusters in UO 2

The aggregation of irradiation-induced defect clusters in UO 2 leads to the formation of dislocation loops and cavities which contribute swelling and ultimately produce deleterious effects on the fuel. Despite their fundamental role in fuel evolution, the kinetics of these defect clusters are not currently well understood. In this work, we investigate the diffusive behavior of interstitial clusters via Molecular Dynamics (MD) simulations. In this work, our investigation considers a range of defect cluster sizes, each composed of N UO 2 units or anti-Schottky defects. We report a complex cluster size - mobility relation; increasing cluster size corresponds to an increase in mobility up until a critical size (N=4) where diffusivity reaches a maximum, after which the trend reverts and further increasing size corresponds to a decrease in mobility. The rapid migration observed correlates well with the very low barriers reported in a few historic experimental studies. Further analysis of the cluster shape and orientation reveals a strong structural preference for near-planar configurations oriented normal to the $\langle$100$\rangle$ direction. Rotational energy barriers are found to be similar in both magnitude and trend to the observed diffusion barriers. Lastly, connections are drawn to the behavior of large defect clusters including the formation of (1/3) $\langle$111$\rangle$ Frank dislocation loops.

36 MATERIALS SCIENCE↗

Mechanisms of ion irradiation induced ordering in amorphous TiO 2 nanotubes: Effects of ion mass and energy

Here, amorphous TiO 2 nanotubes were irradiated in-situ in a transmission electron microscope (TEM) with Kr + ions at energies of 46 keV, 150 keV, and 1 MeV and with 46 keV Xe + ions, to investigate the structural and morphological evolution of the nanotubes under irradiation. At all irradiation conditions, amorphous TiO 2 nanotubes exhibited significant morphological instability, and tended to undergo volumetric swelling with increasing ion counts, often until collapse of the original nanotube structure. Molecular dynamics (MD) simulations confirmed that irradiation-induced defects can explain the observed swelling. Structurally, nanotubes remain amorphous following all Kr + irradiation conditions, but irradiation with 46 keV Xe + leads to the formation of anatase nanocrystallites. Importantly, through systematically varying ion energy and ion species, we try to elucidate the influence of nuclear and electronic stopping power on ion irradiation induced changes. By contextualizing these results within the existing literature, we propose that the observed changes in TiO 2 nanotube morphology and structure could be due to a competition between two mechanisms: (1) disorder-induced swelling and (2) irradiation-induced amorphous-to-crystalline transformation.

36 MATERIALS SCIENCE↗

Engineering the fracture resistance of 2H-transition metal dichalcogenides using vacancies: An in-silico investigation based on HRTEM images

Vacancy engineering of 2H-transition metal dichalcogenides (2H-TMDs) has recently attracted great attention due to its potential to fine-tune the phonon and opto-electric properties of these materials. From a mechanical perspective, this symmetry-breaking process typically reduces the overall crack resistance of the material and adversely affects its reliability. However, vacancies can trigger the formation of heterogeneous phases that synergistically improve fracture properties. In this study, using MoSe2 as an example, we characterize the types and density of vacancies that can emerge under electron irradiation and quantify their effect on fracture. Molecular dynamic (MD) simulations, employing a re-parameterized Tersoff potential capable of accurately capturing bond dissociation and structural phase changes, reveal that isolated transition metal monovacancies or chalcogenide divacancies tend to arrest the crack tip and hence enhance the monolayer toughness. In contrast, isolated chalcogenide monovacancies do not significantly affect toughness. The investigation further reveals that selenium vacancy lines, formed by high electron dose rates, alter the crack propagating direction and lead to multiple crack kinking. Using atomic displacements and virial stresses together with a continuum mapping, displacement, strain, and stress fields are computed to extract mechanistic information, e.g., conditions for crack kinking and size effects in fracture events. The study also reveals the potential of specific defect patterns, “vacancy engineering,” to improve the toughness of 2H-TMDs materials.

36 MATERIALS SCIENCE↗

Machine learning prediction on the fractional free volume of polymer membranes

Fractional free volume (FFV) characterizes the microstructural level features of polymers and affects their properties including thermal, mechanical, and separation performance. Experimental measurements and theoretical analyses have been used to quantify the FFV of polymers, but challenges remain because of their limitations. Experimental measurements are laborious and based on semi empirical equations, while Bondi’s group contribution theory involves ambiguities like the determination of van der Waals volume and the choice of factor values in the theoretical equation. To efficiently evaluate the FFV of polymers, this study utilizes high-throughput molecular dynamics (MD) simulations to build a large dataset regarding polymer’s FFV. Based on this large dataset, we further build machine learning (ML) models to establish the composition-structure relation. Inspired by group contribution theory which correlates polymer’s functional groups to FFV, our ML models correlate polymer’s substructures or physico-chemical indexes to FFV. Here, our study first benchmarks the MD simulation protocol to obtain reliable FFV of polymers and then carries out high-throughput MD simulations for more than 6,500 homopolymers and 1,400 polyamides. Such a large and diverse dataset makes the well-trained ML models more generalizable, compared with the group contribution theory. The efficiency of a feed forward neural network model is further demonstrated by applying it to a hypothetical polyimide dataset of more than 8 million chemical structures. The predicted FFVs of hypothetical polyimides are further validated by MD simulations. The obtained FFVs of the 8 million polymers, plus their previously reported gas separation performances, demonstrate the promising capability of ML virtual screening for the discovery of polymer membranes with exceptional permeability/selectivity.

36 MATERIALS SCIENCE↗

Unraveling the solvation phenomena of Ln 3+ cations in room-temperature ionic liquids: A computational study

Rare-earth elements (REEs), classified as critical materials, are difficult to separate due to their similar chemical properties and slight differences in ionic radius. Room-temperature ionic liquids (RTILs) have gained significant attention for REE separation because of their unique physicochemical properties and environmental advantages. In this study, we have investigated the solvation mechanisms of two RE cations (Ln 3+ ), Nd 3+ (light REE) and Yb 3+ (heavy REE), in two 1-butyl-3-methylimidazolium ([BMIM] + )-based RTILs using bis(trifluoromethylsulfonyl)imide ([NTf 2 ] − ) and acetate ([OAc] − ) as the respective anions, employing classical molecular dynamics (MD) simulations and density functional theory (DFT) techniques. From MD simulations, it is evident that Ln 3+ cations are primarily solvated by RTIL anions in the first solvation shell, while [BMIM] + cations form the second solvation shell with their numbers depending on the size and composition of the first solvation shell. The neutralizing [NO 3 − ] counterions are mainly solvated by [BMIM] + cations in their first solvation shell. Relative free energy change of solvation calculations using thermodynamic integration (TI) method indicate that Yb 3+ is more strongly solvated than Nd 3+ in both RTILs, a trend further supported by DFT calculations. While both methods predict consistent qualitative behavior, differences in models and energy evaluations lead to variations in absolute values. Overall, this study provides a comprehensive understanding of the solvation behavior of Ln 3+ cations in RTILs, demonstrating a stronger solvation preference for the heavy Ln 3+ cation (Yb 3+ ). In conclusion, these findings have implications for the design of RTIL-based separation processes for REEs.

Ash, Tamalika [Ames Lab., and Iowa State Univ., Am↗

Effects of rejuvenation modes on the microstructures and mechanical properties of metallic glasses

This study systematically investigates the effects of three rejuvenation modes, namely biaxial loading, thermal pressure loading, and cryogenic thermal cycling, on the microstructures and mechanical properties of Cu 64 Zr 36 metallic glasses (MGs) using molecular dynamics (MD) simulations. The simulation results demonstrate that biaxial tension application during loading results in a rejuvenated glassy state with high strength. Specifically, we find that the yield stress, Young's modulus, and shear modulus of the rejuvenated glass obtained by biaxial tensile loading decreased by 2.8%, 2.1%, and 2.7%, respectively, compared to an as-cast MG reference. We also find that MGs achieve the greatest degree of rejuvenation, at the expense of strength, with the use of thermal pressure loading. Interestingly, the application of cryogenic thermal cycling results in a rejuvenated state with a lower strength drop compared to thermal pressure loading. Furthermore, analysis of the potential energy and medium-range-order (MRO) size indicates that the microstructures of MGs achieves a high-energy ordered glass state after thermal pressure loading, but a high-energy disordered glass state after biaxial tensile loading and cryogenic thermal cycling. Furthermore, these findings provide meaningful insights into the effect of rejuvenation modes on the microstructures and mechanical properties of MGs, as well as useful guidelines for designing MGs with high strength and superior plasticity for prospective applications in industry.

36 MATERIALS SCIENCE↗

Weakly solvating ester electrolyte for high voltage sodium-ion batteries

Ethyl acetate (EA) was identified as a promising electrolyte solvent for sodium-ion batteries (SIBs), exhibiting low viscosity, cost-effectiveness, and low toxicity. Despite a significant portion of aggregation being linked to the weak solvation of Na + /EA as revealed by molecular dynamics (MD) simulations, pulsed-field gradient nuclear magnetic resonance (pfg-NMR) analysis identified a noteworthy Na+ diffusion coefficient of 3.95×10 -10 m 2 s -1 at 25°C in the presence of 1 m NaPF 6 salt. Employing fluoroethylene carbonate (FEC) as a film-forming additive to create electrode-electrolyte interphase, this electrolyte surprisingly made ~210 mAh Na 0.97 Ca 0.03 [Mn 0.39 Fe 0.31 Ni 0.22 Zn 0.08 ]O 2 (NCMFNZO)/hard carbon (HC) pouch cells achieve a lengthy cycling lifetime of 250 cycles with ~80 % capacity retention, cycled up to 4.0 V at 40°C. X-ray photoelectron spectroscopy (XPS) revealed increasing interphasial organic species over cycling, augmenting charge transfer resistance on both cathode and anode, particularly during fast charging or low temperatures (<10°C), promoting Na plating. Finally, gas chromatography-mass spectrometry combined with density functional theory identified CO 2 as the major gas generated from charged cathode/electrolyte interactions, exhibiting temperature/voltage dependence.

25 ENERGY STORAGE↗

Mechanisms of direct and converse piezoelectricity in ferroelectric polymers

Within the linear regime of mechanical and electrical responses, it is commonly accepted that direct and converse piezoelectric coefficients should be the same. However, we observed a consistently higher converse d 31 (∼54 pm/V) than the direct d 31 (∼42 pC/N) for a quenched, stretched, annealed, and electrically poled poly(vinylidene fluoride-co-trifluorethylene) [P(VDF-TrFE)] 52/48 mol.% sample (abbreviated as coP-52/48QSAP). On the contrary, the direct and converse d 31 values were the same for coP-65/35QSAP and coP-55/45QSAP. Small-angle X-ray scattering results showed that coP-52/48QSAP had a higher amount of relaxor-like secondary crystals (SCs) in the oriented amorphous fraction (OAF) (SC OAF ) than coP-55/45QSAP and coP-65/35QSAP. To explain the experimental observation, we performed molecular dynamics (MD) simulation of the pure PVDF (without TrFE) to estimate direct and converse piezoelectricity for the PVDF OAF. Based on the MD simulation, the direct d 31 had a plateau value around 350 pC/N for the transverse (i.e., along the chain direction) strain up to 1 %, whereas the simulated converse d 31 could be lower (for electric field E < 0.8 MV/m), equal (for E = 0.8 MV/m), or higher (for E > 0.8 MV/m) than the direct d 31 , depending on the poling electric field. From the MD simulation, both mechano-electrostriction and electrostatic interaction were identified in the OAF as the driving force for enhanced piezoelectricity in ferroelectric PVDF. In conclusion, when ferroelectric domains were formed in the OAF by electric poling, the simulated converse d 31 became higher than the direct d 31 . Combining both experimental and MD simulation results, the higher converse d 31 than direct d 31 for coP-52/48QSAP was understood qualitatively.

36 MATERIALS SCIENCE↗