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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Elastic moduli of hexagonal diamond and cubic diamond formed under shock compression

The relative stiffnesses and strengths of hexagonal diamond and cubic diamond constitute long standing unresolved issues, because relevant experimental results are lacking. Laser interferometry was used to experimentally determine the longitudinal sound speeds and moduli in hexagonal diamond and cubic diamond formed during the shock compression of graphite. The hexagonal diamond longitudinal moduli are significantly larger than the cubic diamond longitudinal moduli, and even exceed averaged cubic diamond single crystal values. Here, the measured hexagonal diamond longitudinal moduli, combined with high-pressure bulk moduli for cubic diamond single crystals, show that shock-formed hexagonal diamond shear moduli are larger than the shear moduli for cubic diamond single crystals.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Tuning the Néel Temperature of Hexagonal Ferrites by Structural Distortion

To tune the magnetic properties of hexagonal ferrites, a family of magnetoelectric multiferroic materials, by atomic-scale structural engineering, we studied the effect of structural distortion on the magnetic ordering temperature ( T N ) in these materials. Using the symmetry analysis, we show that unlike most antiferromagnetic rare-earth transition-metal perovskites, a larger structural distortion leads to a higher T N in hexagonal ferrites and manganites, because the K 3 structural distortion induces the three-dimensional magnetic ordering, which is forbidden in the undistorted structure by symmetry. We also revealed a near-linear relation between T N and the tolerance factor and a power-law relation between T N and the K 3 distortion amplitude. Following the analysis, a record-high T N (185 K) among hexagonal ferrites was predicted in hexagonal ScFeO 3 and experimentally verified in epitaxially stabilized films. Furthermore these results add to the paradigm of spin-lattice coupling in antiferromagnetic oxides and suggests further tunability of hexagonal ferrites if more lattice distortion can be achieved.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Structure Formation of Hexagonal Diamond: Ab Initio Calculations

The formation of structure of hexagonal diamond from graphite and cubic diamond is simulated with the density functional theory. Orthorhombic AB graphite transforms into hexagonal diamond under uniaxial compression at pressures above 61 GPa. The pressure should be higher than 57 GPa to form hexagonal diamond from AA graphite. Another possible way to obtain hexagonal diamond is uniaxial compression of cubic diamond under pressures from 300 to 380 GPa. The theoretical calculations were used to interpret the diffraction data obtained after X-ray diffraction and electron microscopic analysis of natural and synthetic diamond-like materials. We found that there are no crystals with ideal cubic and hexagonal structures in diamond-like carbon materials, and their structure is characterized by random packing of molecular layers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1985

Hexagonal uniformly redundant arrays for coded-aperture imaging

Uniformly redundant arrays are used in coded-aperture imaging, a technique for forming images without mirrors or lenses. The URAs constructed on hexagonal lattices, are outlined. Details are presented for the construction of a special class of URAs, the skew-Hadamard URAs, which have the following properties: (1) nearly half open and half closed (2) antisymmetric upon rotation by 180 deg except for the central cell and its repetitions. Some of the skew-Hadamard URAs constructed on a hexagonal lattice have additional symmetries. These special URAs that have a hexagonal unit pattern, and are antisymmetric upon rotation by 60 deg, called hexagonal uniformly redundant arrays (HURAs). The HURAs are particularly suited to gamma-ray imaging in high background situations. In a high background situation the best sensitivity is obtained with a half open and half closed mask. The hexagonal symmetry of an HURA is more appropriate for a round position-sensitive detector or a closed-packed array of detectors than a rectangular symmetry.

Finger, M. H.↗
NASA NTRS1989

A hexagonal orthogonal-oriented pyramid as a model of image representation in visual cortex

Retinal ganglion cells represent the visual image with a spatial code, in which each cell conveys information about a small region in the image. In contrast, cells of the primary visual cortex use a hybrid space-frequency code in which each cell conveys information about a region that is local in space, spatial frequency, and orientation. A mathematical model for this transformation is described. The hexagonal orthogonal-oriented quadrature pyramid (HOP) transform, which operates on a hexagonal input lattice, uses basis functions that are orthogonal, self-similar, and localized in space, spatial frequency, orientation, and phase. The basis functions, which are generated from seven basic types through a recursive process, form an image code of the pyramid type. The seven basis functions, six bandpass and one low-pass, occupy a point and a hexagon of six nearest neighbors on a hexagonal lattice. The six bandpass basis functions consist of three with even symmetry, and three with odd symmetry. At the lowest level, the inputs are image samples. At each higher level, the input lattice is provided by the low-pass coefficients computed at the previous level. At each level, the output is subsampled in such a way as to yield a new hexagonal lattice with a spacing square root of 7 larger than the previous level, so that the number of coefficients is reduced by a factor of seven at each level. In the biological model, the input lattice is the retinal ganglion cell array. The resulting scheme provides a compact, efficient code of the image and generates receptive fields that resemble those of the primary visual cortex.

Watson, Andrew B.↗
NASA NTRS2019

Saturn Atmospheric Dynamics One Year After Cassini: Long-Lived Features and Time Variations in the Drift of the Hexagon

We examine Saturn's atmospheric dynamics with observations in the visible range from ground-based telescopes and Hubble Space Telescope (HST). We present a detailed analysis of observations acquired during 2018 obtaining drift rates of major meteorological systems from the equator to the North polar hexagon. A system of polar storms that appeared in the planet in March 2018 and remained active with a complex phenomenology at least until September is analyzed elsewhere [Sanchez-Lavega et al., 2019]. Many of the regular cloud features visible in 2018 are long-lived and can be identified in Saturn images in 2017, and in some cases, for up to a decade using also Cassini ISS images. Without considering the polar storms, the most interesting long-lived cloud systems are: i) A bright white spot in the Equatorial Zone that can be tracked continuously since 2014 with minimal changes in its zonal velocity, which was 444:3 +or- 3:1 ms(exp -1) in 2014 and 452:4 + or - 1:7 ms(exp -1) in 2018. This velocity is remarkably different from the zonal winds at the cloud level at its latitude during the Cassini mission, and is closer to zonal winds obtained at the time of the Voyagers flybys and to zonal winds from Cassini VIMS infrared images of the lower atmosphere. ii) A large long-lived Anticyclone Vortex, here AV, that formed after the Great White Spot of 2010-2011. This vortex has changed significantly in visual contrast, drift rate and latitude with minor changes in size over the last years. iii) A system of subpolar vortices at latitudes 60-65N present at least since 2011. These vortices and additional atmospheric features here studied follow drift rates consistent with zonal winds obtained by Cassini. We also present a study of the positions of the vertices of Saturn's North polar hexagon from 2015 to 2018. These measurements are compared with previous analyses during the Cassini mission (2007-2014), observations with HST in the 90s, and data from the Voyagers in 1980-1981 to explore the long term variability of the hexagon's drift rate. We find variations in the drift rate of the hexagon through these epochs that can not be fit by seasonal changes in the polar area. Instead, the different drift rates reinforce the role of the North Polar Spot that was present in the Voyager epoch and in the early 90s to cause a faster drift rate of the hexagon at that time compared with the current slower one.

R Hueso↗
DOE OSTI2016

Particle Image Velocimetry Measurements in a Wire-Wrapped 61-Pin Hexagonal Fuel Bundle

Liquid metal fast reactor fuel assemblies using sodium as a coolant typically utilize a tightly packed triangular lattice of fuel pins enclosed in a hexagonal duct. The fuel pins are typically wrapped with a helical wire spacer. The primary function of the wire spacers is to maintain a gap between neighboring fuel pins. They also mitigate vortex-induced vibration and enhance sub-channel mixing to increase convective heat transfer. Many experiments have been performed to study thermal-hydraulic characteristics, primarily pressure drops, of the wire-wrapped fuel bundles. Novendstern developed a semi-empirical model to predict pressure losses in a hexagonal array of wire-wrapped pins in the turbulent flow regime. Rehme proposed pressure drop correlations for a wide range of geometrical parameters, such as pitch-to-diameter ratio P/D from 1.125 to 1.417, lead-to-wire diameter ratio H / dm from 6 to 45, and number of pins n from 7 to 61. Cheng and Todreas introduced their hydrodynamic models for subchannel friction factors and mixing parameters in a 37-pin fuel bundle, which covered the laminar, transition and turbulent flow regimes. Computational fluid dynamics (CFD) offers an opportunity to validate the above correlations and investigate the flow characteristics in the subchannels. Several numerical studies of the wire-wrapped fuel bundles have been performed and most of them are Reynolds-Averaged Navier-Stokes (RANS) based simulations with various turbulence models. Ahmad and Kim performed RANS simulations of 7- and 19-pin bundles using the k-omega SST turbulent model, while Gajapathy et al. performed RANS simulations on 7-pin bundles using the k-epsilons model. Recently, Fischer et al. carried out large-eddy simulation (LES) calculations on wire-wrapped fuel bundles to obtain higher-resolution numerical solutions of subchannel behavior. The geometrical complexity of the hexagonal wire-wrapped fuel bundle has limited experimental activities to pressure drop measurements. A database of pressure drops and flow-field measurements in a 61-pin wire-wrapped hexagonal fuel bundle is not available to benchmark the existing correlations and validate the CFD calculations. Texas A and M University is conducting isothermal flow experiments in a wire-wrapped 61-pin hexagonal fuel bundle to support the research on advanced nuclear fuel development sponsored by the Department of Energy (DOE). The purpose of these tests is to perform high spatial and temporal resolution measurements of the flow and pressure measurements at different locations in the fuel bundle. The experimental facility employs matched-index-of-refraction (MIR) techniques and laser diagnostic velocity measurement techniques such as particle image velocimetry (PIV) and laser Doppler velocimetry (LDV). The result of this experimental activity will be an experimental database of pressure and flow-field measurements that will be suitable for validating CFD computer codes. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2014

Preparation of novel layer-stack hexagonal CdO micro-rods by a pre-oxidation and subsequent evaporation process

Graphical abstract: Layer-stack hexagonal cadmium oxide (CdO) micro-rods were prepared. - Highlights: • Novel hexagonal layer-stack structure CdO micro-rods were synthesized by a thermal evaporation method. • The pre-oxidation, vapor pressure and substrate nature play a key role on the formation of CdO rods. • The formation mechanism of CdO micro-rods was explained. - Abstract: Novel layer-stack hexagonal cadmium oxide (CdO) micro-rods were prepared by pre-oxidizing Cd granules and subsequent thermal oxidation under normal atmospheric pressure. X-ray diffraction (XRD) and scanning electron microscopy (SEM) were performed to characterize the phase structure and microstructure. The pre-oxidation process, vapor pressure and substrate nature were the key factors for the formation of CdO micro-rods. The diameter of micro-rod and surface rough increased with increasing of thermal evaporation temperature, the length of micro-rod increased with the increasing of evaporation time. The formation of hexagonal layer-stack structure was explained by a vapor–solid mechanism.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Evidence of hexagonal germanium grains on annealed monolayer MoS 2

Growing three-dimensional (3D) materials on two-dimensional (2D) van der Waals surface has shown its effectiveness in overcoming materials incompatibility for stacking transferrable membranes toward advanced device manufacturing. Herein, we demonstrate that the nucleation of hexagonal germanium (Ge) grains within a continuous crystalline film, which has been unfeasible through traditional epitaxy techniques, is realized by chemical vapor deposition on top of n-type monolayer molybdenum disulfide (MoS 2 ) substrates. Suggested by quantum molecular dynamics calculation, the hexagonal Ge nucleation is thermodynamically preferable to cubic Ge when growing on monolayer MoS 2 with sulfur vacancies. The strained hexagonal Ge grains have been confirmed by transmission electron microscopy analyses from both real space and reciprocal space. Scanning probe microscopy shows that the hexagonal Ge film possesses higher reflectivity in infrared spectral range, implying a higher carrier concentration resulted from the narrower band gap, as compared to cubic Ge.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Domain wall kinetics of lithium niobate single crystals near the hexagonal corner

A mesospheric approach based on a simple microscopic 2D Ising model in a hexagonal lattice plane is proposed to explain macroscopic “asymmetric in-out domain wall motion” observation in the (0001) plane of MgO-doped stoichiometric lithium niobate. Under application of an electric field that was higher than the conventional coercive field (E{sub c}) to the ferroelectric crystal, a natural hexagonal domain was obtained with walls that were parallel to the Y-axis of the crystal. When a fraction of the coercive field of around 0.1E{sub c} is applied in the reverse direction, this hexagonal domain is shrunk (moved inward) from the corner site into a shape with a corner angle of around 150° and 15° wall slopes to the Y-axis. A flipped electric field of 0.15E{sub c} is then applied to recover the natural hexagonal shape, and the 150° corner shape changes into a flat wall with 30° slope (moved outward). The differences in corner domain shapes between inward and outward domain motion were analyzed theoretically in terms of corner and wall site energies, which are described using the domain corner angle and wall slope with respect to the crystal Y-axis, respectively. In the inward domain wall motion case, the energy levels of the evolving 150° domain corner and 15° slope walls are most competitive, and could co-exist. In the outward case, the energy levels of corners with angles >180° are highly stable when compared with the possible domain walls; only a flat wall with 30° slope to the Y-axis is possible during outward motion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Vibrational renormalisation of the electronic band gap in hexagonal and cubic ice

Electron-phonon coupling in hexagonal and cubic water ice is studied using first-principles quantum mechanical methods. We consider 29 distinct hexagonal and cubic ice proton-orderings with up to 192 molecules in the simulation cell to account for proton-disorder. We find quantum zero-point vibrational corrections to the minimum electronic band gaps ranging from −1.5 to −1.7 eV, which leads to improved agreement between calculated and experimental band gaps. Anharmonic nuclear vibrations play a negligible role in determining the gaps. Deuterated ice has a smaller band-gap correction at zero-temperature of −1.2 to −1.4 eV. Vibrations reduce the differences between the electronic band gaps of different proton-orderings from around 0.17 eV to less than 0.05 eV, so that the electronic band gaps of hexagonal and cubic ice are almost independent of the proton-ordering when quantum nuclear vibrations are taken into account. The comparatively small reduction in the band gap over the temperature range 0 − 240 K of around 0.1 eV does not depend on the proton ordering, or whether the ice is protiated or deuterated, or hexagonal, or cubic. We explain this in terms of the atomistic origin of the strong electron-phonon coupling in ice.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Parallel transport sweeps on two-dimensional cartesian and hexagonal grids

This paper aims to provide a proof of concept for parallel transport sweeps on two-dimensional hexagonal grids for the discrete ordinates transport equation. While the method is an extension of the popular and well-established Koch-Baker-Alcoulffe (KBA) algorithm, there are significant differences between the cartesian and hexagonal grid and thereafter sweep. The most important is the three-way connectivity of hexagons within the grid which creates greater dependencies between the elements. The KBA method in structured orthogonal grids was first implemented in the DRAGON5 code and the method is first described here. The differences in implementation for the hexagonal grid are also described. Benchmark results are also presented, showing roughly 10 times speedup in computational times with roughly 100 processors, in both cases. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

Explicit Backscattering Coefficient for Ultrasonic Wave Propagating in Hexagonal Polycrystals with Fiber Texture

Hexagonal polycrystalline materials such as titanium, zirconium and magnesium are common in engineering structures like car bodies and airplane engines. These components are usually specially designed in microstructure level to guarantee desired mechanical properties, so microstructure characterization is of great importance to the optimization of manufacturing processes. Compared with traditional destructive characterization methods like scanning electron microscopy (SEM), the ultrasonic approach is nondestructive and cost-effective. Although some progress has been made in ultrasonic microstructure characterization of polycrystal aggregates of hexagonal grains, some factors like macro texture and grain size distribution associated with realistic microstructures were not accounted for yet. Targeting one common texture component for hexagonal polycrystalline materials, {0001} basal fiber texture, this paper derived the explicit backscattering coefficient for aggregates of ellipsoidal grains through one texture parameter and obtained an analytical backscattering coefficient for microstructures with various grain size distributions. In this study, the basal fiber texture was quantified by the 1D Gaussian orientation distribution function (ODF), which merely includes one texture parameter, and its relationship with generalized spherical harmonics ODF was also addressed. Moreover, explicit expressions for effective elastic moduli and elastic constant covariances were derived. Furthermore, some computational examples were given to demonstrate the impacts of texture, frequency, grain geometry and grain size distribution on backscattering behavior. The theoretical results in this study will greatly benefit the later ultrasonic microstructure characterization of hexagonal polycrystalline materials.

42 ENGINEERING↗
DOE OSTI2019

Assessment of surface and bulk-dominated methodologies to measure critical resolved shear stresses in hexagonal materials

We present that crystallographic slip in hexagonal metals involves a number of geometrically distinct slip families characterized by their slip direction and slip plane (basal, prismatic, and pyramidal). Owing to the low symmetry of hexagonal lattices, each of these slip families only have a few symmetrically equivalent slip systems (family members). Furthermore, different slip families become active at different resolved shear stress, i.e., they have different critical resolved shear stress values (CRSS). The plastic anisotropy of hexagonal materials makes the numerical prediction of their plastic behavior challenging and depends critically on the knowledge of CRSS values. The present contribution assesses the reliability of three proposed methods (with additional variations) to quantify CRSS values of the different hexagonal slip families. Those methods (a to c) rely on: (a) the statistics of observed surface slip traces in a (slightly) deformed polycrystal; (b) an iterative adjustment of CRSS values until a simulated single crystal indentation matches the corresponding experiment in terms of load–displacement response and residual surface topography of the indent; (c) in-situ high-energy X-ray diffraction to measure the evolution of resolved stress (from lattice strains) in grains for which single-family slip is probable based upon specific lattice reorientation conditions. Virtual experiments are performed on synthetic microstructures such that the (extracted) CRSS values resulting from simulating the different methodologies can be rigorously compared against the (target) CRSS values that are installed in the phenomenological constitutive material description used in the simulations. The resulting CRSS values of methods (a) exhibit a strong dependence on, and deterioration with, decreasing level of slip trace observability, which is an uncertain quantity in experimental measurements. For the inverse indentation method (b), the predicted CRSS values are within 8 % of their reference CRSS values for the two investigated cases. Lastly, the high-energy X-ray diffraction method (c) most reliably determines CRSS values for basal and prism slip, but lacks a strict grain selection criterion to assess pyramidal slip.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Advances in hexagon mesh-based flow direction modeling

Watershed delineation and flow direction representation are the foundations of streamflow routing in spatially distributed hydrologic modeling. A recent study showed that hexagon-based watershed discretization has several advantages compared to the traditional Cartesian (latitude–longitude) discretization, such as uniform connectivity and compatibility with other Earth system model components based on unstructured mesh systems (e.g., oceanic models). Despite these advantages, hexagon-based discretization has not been widely adopted by the current generation of hydrologic models. One major reason is that there is no existing model that can delineate hexagon-based watersheds while maintaining accurate representations of flow direction across various spatial resolutions. In this study, we explored approaches such as spatial resampling and hybrid breaching-filling stream burning techniques to improve watershed delineation and flow direction representation using a newly developed hexagonal mesh watershed delineation model (HexWatershed). We applied these improvements to the Columbia River basin and performed 16 simulations with different configurations. The results show that (1) spatial resampling modulates flow direction around headwaters and provides an opportunity to extract subgrid information; and (2) stream burning corrects the flow directions in mountainous areas with complex terrain features.

58 GEOSCIENCES↗
DOE OSTI2019

Consistent spatial expansion functions on hexagonal surfaces for use in radiation transport methods

Some of the radiation transport solvers that are based on expansion function methods in hexagonal geometry generally use projection techniques that transform the spatial dependence of the angular flux in hexagonal geometry to Cartesian geometry by mapping and then expanding in terms of expansion functions (e.g., Legendre polynomials). However, this approach usually requires a relatively higherorder expansion in space for accurate representation of the spatial distribution of the flux. To overcome this limitation, a set of consistent spatial expansion functions have been developed in hexagonal geometry in this paper. These functions satisfy the orthogonality condition on hexagonal surfaces and guarantee the conservation of currents after expansion regardless of the truncation order. The latter is an important property for preservation of neutron balance. The new spatial expansion method has been implemented into the coarse mesh radiation transport (COMET) code and tested in both the single assembly and the full core Advanced High Temperature Reactor (AHTR) benchmark problems. The eigenvalues and assembly-averaged and stripe-wise fission density distributions predicted by the new method with 2nd order spatial expansion functions were found to exhibit similar accuracy as those computed by the current mapping method with 4th order spatial expansion functions. This indicates that the angular fluxes in AHTRs can be predominantly represented by a low order expansion if the new spatial expansion functions are used. As a result, to maintain the same accuracy, the computational efficiency of COMET is improved significantly (2–5 times) by using the new spatial expansion method.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Accommodating a hexagonal ζ- phase Mn 2 N film on a cubic MgO (001) substrate

The thin films of c -plane dominated hexagonal ζ- phase Mn 2 N were successfully grown on a cubic MgO (001) substrate directly using plasma-assisted molecular beam epitaxy. The surface was comprehensively studied through experimental and theoretical approaches. Reflection high energy electron diffraction revealed two pseudo-cubic domains along [100] MgO and [110] MgO , and one hexagonal domain, which is 30° apart from the [100] MgO direction. Scanning tunneling microscopy was used to image and resolve the high-quality surface, revealing a distorted hexagonal surface structure. Furthermore, atomic resolution of the hexagonal domain with a 2 × 2 reconstructed surface is presented. For c-plane surface, theoretical investigations were carried out using first principles studies to determine the surface formation energy for various reconstructed surfaces. The theoretical study shows that the nitrogen terminated 2 × 2 structure with a manganese adatom on the surface as the most stable reconstruction that reproduces the experimental results. A corresponding simulated scanning tunneling microscopy model is also presented, providing strong support for the experimentally observed in-plane lattice structures. Furthermore, the manganese: nitrogen stoichiometry within the bulk and surface is in good agreement with the expected ratio of 2:1.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Pressure-induced phase transitions of hexagonal perovskite-like oxides

We have stabilized two new cubic (3C structured) A{sub 2}B′B′′O{sub 6}-type double-perovskite phases, Ba{sub 2}CoSbO{sub 6} and Ba{sub 2}ZnTeO{sub 6}, by means of a high-pressure heat-treatment of corresponding hexagonal (6H and 12R structured, respectively) non-perovskite phases at 4 GPa and 1000 °C. Similar treatments on hexagonal Ba{sub 2}TiMnO{sub 6} (12R) and Ba{sub 2}NiTeO{sub 6} (12R) phases did not yield the 3C double-perovskite structure but converted the 12R structure to the 6H structure. The pressure-induced phase conversion in each A{sub 2}B′B′′O{sub 6} system apparently goes from the 12R structure towards the 6H and 3C structures with increasing pressure, where the pressure ranges required most likely depend (among other possible factors) on the tolerance factor for the particular combination of A, B′ and B′′. We foresee that yet a number of novel B-site ordered double-perovskite compounds are to be discovered through the high-pressure high-temperature treatment. - Graphical abstract: High-pressure (HP) heat-treatment is an efficient tool to synthesize novel B-site ordered double-perovskite materials. This is demonstrated for two new cubic (3C structured) perovskite phases, Ba{sub 2}CoSbO{sub 6} and Ba{sub 2}ZnTeO{sub 6}, obtained through a HP conversion of corresponding hexagonal (6H and 12R structured, respectively) non-perovskite phases at 4 GPa and 1000 °C. Similar treatments on hexagonal Ba{sub 2}TiMnO{sub 6} (12R) and Ba{sub 2}NiTeO{sub 6} (12R) phases yield the intermediate 6H structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗