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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Neutron Radiography and Computed Tomography of Biological Systems at the Oak Ridge National Laboratory's High Flux Isotope Reactor

Neutrons have historically been used for a broad range of biological applications employing techniques such as small-angle neutron scattering, neutron spin echo, diffraction, and inelastic scattering. Unlike neutron scattering techniques that obtain information in reciprocal space, attenuation-based neutron imaging measures a signal in real space that is resolved on the order of tens of micrometers. The principle of neutron imaging follows the Beer-Lambert law and is based on the measurement of the bulk neutron attenuation through a sample. Greater attenuation is exhibited by some light elements (most notably, hydrogen), which are major components of biological samples. Contrast agents such as deuterium, gadolinium, or lithium compounds can be used to enhance contrast in a similar fashion as it is done in medical imaging, including techniques such as optical imaging, magnetic resonance imaging, X-ray, and positron emission tomography. For biological systems, neutron radiography and computed tomography have increasingly been used to investigate the complexity of the underground plant root network, its interaction with soils, and the dynamics of water flux in situ. Moreover, efforts to understand contrast details in animal samples, such as soft tissues and bones, have been explored. This manuscript focuses on the advances in neutron bioimaging such as sample preparation, instrumentation, data acquisition strategy, and data analysis using the High Flux Isotope Reactor CG-1D neutron imaging beamline. The aforementioned capabilities will be illustrated using a selection of examples in plant physiology (herbaceous plant/root/soil system) and biomedical applications (rat femur and mouse lung).

Bilheux, Hassina↗
DOE OSTI2024

Structure and lattice excitations of the copper substituted lead oxyapatite Pb 9.06⁢(7)⁢ Cu 0.94⁢(6)⁢ (PO 3.92⁢(4) ) 6 ⁢O 0.96⁢(3)

The copper substituted lead oxyapatite, Pb 10-x⁢ Cu x (PO 3.92⁢(4) ) 6 ⁢O 0.96⁢(3) [x = 0.94(6)] was studied using neutron and x-ray diffraction and neutron spectroscopy techniques. The crystal structure of the main phase of our sample, which has come to be colloquially known as LK-99, is verified to possess a hexagonal structure with space group P6 3 /m, alongside the presence of impurity phases Cu and Cu 2 ⁢S. We determine the primary substitution location of the Cu as the Pb1 (6⁢ℎ) site, with a small substitution at the Pb2 (4⁢f) site. Consequently, no clear Cu-doping-induced structural distortion was observed in the investigated temperature region between 10 K and 300 K. Specially, we did not observe a reduction of coordinate number at the Pb2 site or a clear tilting of PO 4 tetrahedron. Magnetic characterization reveals a diamagnetic signal in the specimen, accompanied by a very weak ferromagnetic component at 2 K. No long-range magnetic order down to 10 K was detected by the neutron diffraction. Inelastic neutron scattering measurements did not show magnetic excitations for energies up to 350 meV. There is no sign of a superconducting resonance in the excitation spectrum of this material. The measured phonon density of states compares well with density functional theory calculations performed for the main LK-99 phase and its impurity phases. Our study may shed some insight into the role of the favored substitution site of copper in the absence of structural distortion and superconductivity in LK-99.

36 MATERIALS SCIENCE↗
DOE OSTI2022

M-STAR: Magnetism second target advanced reflectometer at the Spallation Neutron Source

M-STAR is a next generation polarized neutron reflectometer with advanced capabilities. A new focusing guide concept is optimized for samples with dimensions down to a millimeter range. A proposed hybrid pulse-skipping chopper will enable experiments at constant geometry at one incident angle in a broad range of wavevector transfer Q up to 0.3 A –1 for specular, off-specular, and GISANS measurements. M-STAR will empower nanoscience and spintronics studies routinely on small samples (~2 × 2 mm 2 ) and of atomic-scale thickness using versatile experimental conditions of magnetic and/or electric fields, light, and temperature applied in situ to novel complex device-like nanosystems with multiple buried interfaces. M-STAR will enable improved grazing incidence diffraction measurements, as a surface-sensitive depth-resolved probe of, e.g., the out-of-plane component of atomic magnetic moments in ferromagnetic, antiferromagnetic, and more complex structures as well as in-plane atomic-scale structures inaccessible with contemporary diffractometry and reflectometry. New horizons will be opened by the development of an option to probe near-surface dynamics with inelastic grazing incidence scattering in the time-of-flight mode. These novel options in combination with ideally matched parameters of the second target station will place M-STAR in the world’s leading position for high resolution polarized reflectometry.

47 OTHER INSTRUMENTATION↗
NASA NTRS1981

X-ray and gamma-ray observations of a white-light flare

Hard radiations (X-ray and gamma-ray) from a major solar flare observed by HEAO-1 on July 11, 1978, are discussed. It is noted that the observations showed gamma-ray line and continuum emission extending to the highest energy observed. The lines are identified with the 2.2 MeV line of deuterium formation and the 4.4 MeV line of inelastic scattering on C-12, both of which were previously observed in the flares of August 1972. The flare of July 11 is identified as a white-light flare. It therefore provides the first opportunity for a detailed examination of white-light flare theories that depend on proton heating of the photosphere. The line strength over a four-minute integration at 2.2 MeV is found to be 1.00 + or - 0.29 ph/sq cm-sec; the gamma-ray emission (excluding the 2.2 MeV line which was appreciably delayed) lagged by less than 20 sec approximately after the hard X-ray and microwave fluxes. It is concluded that the 'second-stage' acceleration of high-energy solar particles must commence promptly after the impulsive phase.

Hudson, H. S.↗
DOE OSTI2022

Modification of conventional peak shapes to accurately represent spectral asymmetry: High-Resolution X-ray photoelectron spectra of [C 4 C 1 Pyrr][NTf 2 ] and [C 8 C 1 Im][NTf 2 ] ionic liquids

X-ray photoelectron spectroscopy (XPS) is one of the most widely used techniques for surface characterization. Analysis of XPS data is challenging and requires the analyst to fit the data with synthetic line shapes to reach physically meaningful interpretations. Experimental spectral envelopes, however, are complex and display asymmetric features that are often ignored or attributed to additional chemical components. The high-resolution XPS spectra of [C 4 C 1 Pyrr][NTf 2 ] and [C 8 C 1 Im][NTf 2 ] all exhibit a degree of asymmetry which is systematically observed at the higher binding energy side of photoemission envelopes. Here, we present the development of a refined fitting procedure for XPS spectra of these ionic liquid-based systems which include (a) Shirley background offset necessary to account for the insulator-like region and (b) spectral asymmetry in C 1s and N 1s regions. Further, Shirley and trapezoid components are applied to compensate for inelastic scattering taking place during electron transitions as high as 7.8 eV above the start of the fitting region in C 1s high-resolution spectrum. To demonstrate the fitness of this model, we present an analysis of a 2:1 mixture of [C 4 C 1 Pyrr][NTf 2 ]: [C 8 C 1 Im][NTf 2 ].

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2000

Innovative Research Program: Supershields for Gamma-Ray Astronomy

The supershield project evaluated the importance of novel shield configurations for suppressing neutron induced background in new classes of gamma-ray detectors such as CZT. The basic concept was to use a two-part shield. The outer shield material heavily moderates the incoming neutron spectrum. This moderated neutron beam is then more easily absorbed by the inner material, which is an efficient neutron absorber. This approach is, in principle, more efficient than that in previous attempts to make neutron shields. These previous attempts involved biatomic, monlithic shields (eg. LiH) in which the shield consisted of a single material but with two types of atoms - one for moderating and one for absorbing. The problem with this type of monolithic shield is that moderating neutrons, without the efficient absorption of them, leads to the leakage into the detector of neutrons with a low energy component (approx. 10-100 KeV). These energy neutrons are particularly problematic for many types of detectors. The project was roughly divided into phases. In the first phase we attempted to carefully define the neutron source function incident on any space instrument. This is essential since the design of any shield depends on the shape of the incident neutron spectrum. We found that approximations commonly used in gamma-ray astronomy for photon background is inadequate. In addition, we found that secondary neutrons produced in any passive shield, and dominated by inelastic neutron scattering, are far more important than background due to neutron activation. The second phase of our work involved design of supershield geometries (one and three dimensional) in order to compare different shield configurations and materials for their effectiveness as neutron shields. Moreover we wanted to compare these supershields with previous neutron shields to confirm the performance differences between the supershield (two material) and monolithic (one material) designs and to understand the physics origins of these differences more clearly. The third phase of the supershield program involved the benchmarking of the supershield designs through direct experimental verification. This required fabricating various supershields and exposing them to beams of neutrons to directly characterize their performance. With explicit verification that our modeling procedures can be used with confidence, we are now in a position to design shields for realistic space geometries. Using the supershield modeling capacity developed as part of this program we are attempting to evaluate their utility for a specific proposed mission--the Energetic X-ray Imaging Survey Telescope (EXIST). It is anticipated that this experiment, which is limited by internal background at high energies, might benefit from a neutron shield.

Hailey, Charles J.↗
DOE OSTI2022

Electromagnetic signals of inelastic dark matter scattering

Light dark sectors in thermal contact with the Standard Model can naturally produce the observed relic dark matter abundance and are the targets of a broad experimental search program. A key light dark sector model is the pseudo-Dirac fermion with a dark photon mediator. The dynamics of the fermionic excited states are often neglected. We consider scenarios in which a nontrivial abundance of excited states is produced and their subsequent de-excitation yields interesting electromagnetic signals in direct detection experiments. We study three mechanisms of populating the excited state: a primordial excited fraction, a component up-scattered in the Sun, and a component up-scattered in the Earth. We find that the fractional abundance of primordial excited states is generically depleted to exponentially small fractions in the early universe. Nonetheless, this abundance can produce observable signals in current dark matter searches. MeV-scale dark matter with thermal cross sections and higher can be probed by down-scattering following excitation in the Sun. Up-scatters of GeV-scale dark matter in the Earth can give rise to signals in current and upcoming terrestrial experiments and X-ray observations. We comment on the possible relevance of these scenarios to the recent excess in XENON1T.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Ion irradiation induced strain and structural changes in LiTaO 3 perovskite

LiTaO 3 crystals irradiated with 3 MeV and 1.162 GeV Au ions were studied by single crystal x-ray diffraction and Raman scattering measurements. The maximum lattice strains after 3 MeV Au ion irradiation to a fluence of 1.2 × 10 13 cm -2 were 1.2% and 0.6% along the c- and a-/b-axes, respectively. Two effects were observed in 1.162 GeV Au ion irradiated samples: (i) the (0006) and (1120) Bragg peaks were split into doublets, which suggested a subtle structural change due to slight modification of chemical composition; and (ii) the pre-damaged 1.2% lattice strain along the c-axis was relaxed to 0.9% after subsequent irradiation with 1.162 GeV Au ions, while relaxation along the a- or b-axis was not obvious. A distinct change in the Raman spectrum of the <0001> oriented LiTaO 3 crystals was observed after 1.162 GeV Au ion irradiation, but no obvious change was observed in the <1120> oriented samples or in 3 MeV Au ion irradiated samples. Strain and structural changes in crystalline LiTaO3, with or without pre-existing defects, upon ion irradiation are delineated in its responding to inelastic ionization and elastic nuclear collisions.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Magnetic structures and excitations in sawtooth olivine chalcogenides Mn 2 SiX 4 (X = S, Se)

The Mn lattice in olivine chalcogenide Mn 2 SiX 4 (X = S, Se) compounds forms a sawtooth, which is of special interest in magnetism owing to the possibility of realizing flat bands in magnon spectra, a key component in magnonics. In this work, we investigate the Mn 2 SiX 4 olivines using magnetic susceptibility, and X-ray and neutron diffraction. We have determined the average and local crystal structures of Mn 2 SiS 4 and Mn 2 SiSe 4 using synchrotron X-ray, neutron diffraction, and X-ray total scattering data followed by Rietveld and pair distribution function analyses. It is found from the pair distribution function analysis that the Mn triangle that constitutes the sawtooth is isosceles in Mn 2 SiS 4 and Mn 2 SiSe 4 . The temperature evolution of magnetic susceptibility of Mn 2 SiS 4 and Mn 2 SiSe 4 shows anomalies below 83 K and 70 K, respectively, associated with magnetic ordering. From the neutron powder diffraction measurements the magnetic space groups of Mn 2 SiS 4 and Mn 2 SiSe 4 are found to be Pnma and Pnm'a', respectively. Here, we find that the Mn spins adopt a ferromagnetic alignment on the sawtooth in both Mn 2 SiS 4 and Mn 2 SiSe 4 but along different crystallographic directions for the S and the Se compounds. From the temperature evolution of Mn magnetic moments obtained from refining neutron diffraction data, the transition temperatures are accurately determined as T N (S) = 83(2) K and T N (Se) = 70.0(5) K. Broad diffuse magnetic peaks are observed in both the compounds, and are prominently seen close to T N , suggesting the presence of a short-range magnetic order. The magnetic excitations studied using inelastic neutron scattering reveal a magnon excitation with an energy corresponding to approximately 4.5 meV in both S and Se compounds. Spin correlations are observed to persist up to 125 K much above the ordering temperature and we suggest the possibility of short-range spin correlations responsible for this.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Observation of a chiral wave function in the twofold-degenerate quadruple Weyl system BaPtGe

Topological states in quantum materials are defined by bulk wave functions that possess nontrivial topological invariants. While edge modes are widely presented as signatures of nontrivial topology, how bulk wave functions can manifest explicitly topological properties remains unresolved. Here, using high-resolution inelastic x-ray spectroscopy (IXS) combined with first principles calculations, we report experimental signatures of chiral wave functions in the bulk phonon spectrum of BaPtGe, which we show to host a previously undiscovered twofold-degenerate quadruple Weyl node. The chirality of the degenerate phononic wave function yields a nontrivial phonon dynamical structure factor, S(Q,ω), along high-symmetry directions, that is in excellent agreement with numerical and model calculations. Furthermore, our results establish IXS as a powerful tool to uncover topological wave functions, providing a key missing ingredient in the study of topological quantum matter.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

NaCo 2 (SeO 3 ) 2 (OH): competing magnetic ground states of a new sawtooth structure with 3d 7 Co 2+ ions

While certain magnetic sublattices have long been known theoretically to give rise to emergent physics via competing magnetic interactions and quantum effects, finding such configurations in real materials is often deeply challenging. Here we report the synthesis and characterization of a new such material, NaCo 2 (SeO 3 ) 2 (OH) which crystallizes with a highly frustrated sublattice of sawtooth Co 2+ chains. Single crystals of NaCo 2 (SeO 3 ) 2 (OH) were synthesized using a low-temperature hydrothermal method. X-ray single crystal structure analysis reveals that the material crystallizes in orthorhombic space group of Pnma (no. 62). Its crystal structure exhibits one-dimensional chains of corner-sharing isosceles triangles that are made of two crystallographically distinct 3d 7 Co 2+ sites (Co(1) and Co(2)). The chains run along the b-axis and are interconnected via [SeO 3 ] groups to form a three-dimensional structure mediating super-exchange interactions. The temperature dependent magnetization data show a ferromagnetic-like (FM) transition at 11 K (T 1 ) followed by an antiferromagnetic (AFM) transition at about 6 K (T 2 ). Neutron-powder diffraction measurements reveal that at T 1 = 11 K only the Co(2) site orders magnetically, forming ferromagnetic zigzag chains along the b-axis. Below T 2 = 6 K, both Co(1) and Co(2) sites order in a nearly orthogonal configuration, with Co(1) moments lying inside the plane of the sawtooth chain while Co(2) moments cant out of the plane. The canting of the magnetic moments leads to a net ferromagnetic component along b-axis, parallel to the chain direction. The ordered moments are fully compensated in the ac-plane. Inelastic neutron scattering measurements reveal crystal field excitations that are consistent with the presence of a spin–orbital entangled pseudo-spin state J eff = 1/2 for the Co 2+ ions. Low-energy spin-wave excitations are observed below the second magnetic transition. The analysis of powder excitation spectrum suggests complex exchange interactions that go beyond a Heisenberg Hamiltonian model with nearest neighbor couplings. Our results demonstrate the richness of the magnetic properties of sawtooth-type structures and encourage the study of similar structures with different oxyanion groups.

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

Effects of mosaic crystal instrument functions on x-ray Thomson scattering diagnostics

Mosaic crystals, with their high integrated reflectivities, are widely employed in spectrometers used to diagnose high energy density systems. X-ray Thomson scattering (XRTS) has emerged as a powerful diagnostic tool of these systems, providing in principle direct access to important properties such as the temperature via detailed balance. However, the measured XRTS spectrum is broadened by the spectrometer instrument function (IF), and without careful consideration of the IF one risks misdiagnosing system conditions. Here, we consider in detail the IF of 40 and 100 μm mosaic Highly Annealed Pyrolytic Graphite crystals, and how the broadening varies across the spectrometer in an energy range of 6.7–8.6 keV. Notably, we find a strong asymmetry in the shape of the IF toward higher energies. As an example, we consider the effect of the asymmetry in the IF on the temperature inferred via XRTS for simulated 80 eV CH plasmas and find that the temperature can be overestimated if an approximate symmetric IF is used. We, therefore, expect a detailed consideration of the full IF will have an important impact on system properties inferred via XRTS in both forward modeling and model-free approaches.

47 OTHER INSTRUMENTATION↗
DOE OSTI2026

Spectral deconvolution without the deconvolution: Extracting temperature from x-ray Thomson scattering spectra without the source-and-instrument function

X-ray Thomson scattering (XRTS) probes the dynamic structure factor of the system, but the measured spectrum is broadened by the combined source-and-instrument function (SIF) of the setup. In order to extract properties such as temperature from an XRTS spectrum, the broadening by the SIF needs to be removed. Recent work [Dornheim et al. Nat. Commun. 13 , 7911 (2022)] has suggested that the SIF may be deconvolved using the two-sided Laplace transform. However, the extracted information can depend strongly on the shape of the input SIF, and the SIF is in practice challenging to measure accurately. Here, we propose an alternative approach: we demonstrate that considering ratios of Laplace-transformed XRTS spectra collected at different scattering angles is equivalent to performing the deconvolution, but without the need for explicit knowledge of the SIF. From these ratios, it is possible to directly extract the temperature from the scattering spectra, when the system is in thermal equilibrium. We find the method to be generally robust to spectral noise and physical differences between the spectrometers, and we explore situations in which the method breaks down. Furthermore, the fact that consistent temperatures can be extracted for systems in thermal equilibrium indicates that non-equilibrium effects could be identified by inconsistent temperatures of a few eV between the ratios of three or more scattering angles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Definition of a new (Doniach-Sunjic-Shirley) peak shape for fitting asymmetric signals applied to reduced graphene oxide/graphene oxide XPS spectra

The existence of asymmetry in X-ray photoelectron spectroscopy (XPS) photoemission lines is widely accepted, but line shapes designed to accommodate asymmetry are generally lacking in theoretical justification. Here in this work, we present a new line shape for describing asymmetry in XPS signals that is based on two facts. First, the most widely known line shape for fitting asymmetric XPS signals that has a theoretical basis, referred to as the Doniach-Sunjic (DS) line shape, suffers from a mathematical inconvenience, which is that for asymmetric shapes the area beneath the curve (above the x-axis) is infinite. Second, it is common practice in XPS to remove the inelastically scattered background response of a peak in question with the Shirley algorithm. The new line shape described herein attempts to retain the theoretical virtues of the DS line shape, while allowing the use of a Shirley background, with the consequence that the resulting line shape has a finite area. To illustrate the use of this Doniach-Sunjic-Shirley (DSS) line shape, a set of spectra obtained from varying amounts of graphene oxide (GO) and reduced GO on a patterned, heterogeneous surface are fit and discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Coherent γ *-nucleus scattering and coherent nuclear states

In the context of a McLerran-Venugopalan (MV) model for a large nucleus, coherent scattering of a virtual photon on that nucleus is evaluated in the A − = 0 gauge, the gauge appropriate for the target nucleus. The evaluation of the scattering in A − = 0 gauge is very intricate compared to the usual A + = 0 gauge evaluation natural for the scattering process, but has the advantage of directly giving the scattering in terms of a partonic description of the nucleus. In the limit where a tagged forward jet puts the dipole-nucleus scattering in the saturation regime the coherent reactions are equal to the inelastic reactions. In terms of the nuclear wave function the coherent reactions come from color singlet and zero total transverse momentum quark-antiquark pairs in the wave function and in the saturation regime the nuclear wave function is a coherent state for these pairs. In the saturation region half of all quarks (or antiquarks) come from zero momentum and color charge pairs.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Gamma-ray imaging of inertial confinement fusion implosions reveals remaining ablator carbon distribution

The joint LANL/LLNL nuclear imaging team has acquired the first gamma-ray images of inertial confinement fusion implosions at the National Ignition Facility. The gamma-ray image provides crucial information to help characterize the inertially confined fuel and ablator assembly at stagnation, information that would be difficult to acquire from neutron or x-ray observations. Gamma imaging visualizes both gamma radiation emitted directly in deuterium–tritium (DT) fusion reactions as well as gamma rays produced when DT fusion neutrons scatter inelastically on carbon nuclei in the remaining ablator of the fuel capsule. The resulting image provides valuable information on the position and density of the remaining ablator and potential contamination of the hot spot—a powerful diagnostic window into the capsule assembly during burn.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Optimization of the gamma reaction history diagnostic for double-shell pusher areal density and reaction history measurements on the National Ignition Facility

The double-shell inertial confinement fusion campaign, which consists of an aluminum ablator, a foam cushion, a high-Z pusher (tungsten or molybdenum), and liquid deuterium–tritium (DT) fuel, aims for its first DT filled implosions on the National Ignition Facility (NIF) in 2024. The high-Z, high density pusher does not allow x-rays to escape the double-shell capsule. Therefore, nuclear diagnostics such as the Gamma Reaction History (GRH) diagnostic on the NIF are crucial for understanding high-Z implosion performance. To optimize the GRH measurement of fusion reaction history and the pusher’s areal density, the MCNP6.3-based forward model of the detector was built. When calculating the neutron-induced inelastic gamma ray production, the interaction of neutrons with the compressed fuel was additionally included. By folding the calculated gamma ray spectrum output and the previously calibrated GRH detector responses, the optimum set of GRH energy thresholds for measuring the pusher areal density is determined to be 2.9 and 6.3 MeV for DT double-shell experiments. In addition, the effect of the down-scattering of neutrons on the gamma ray spectrum, the minimum required yield for measurements, and the attenuation of the gamma rays through the pusher are analyzed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Exploiting dissipative reactions to perform in-beam γ-ray spectroscopy of the neutron-deficient isotopes 38,39 Ca

The neutron-deficient Ca isotopes continue to attract attention due to their importance for testing isospin symmetry and their relevance in capture reactions of interest for nova nucleosynthesis and the shape of light curves in Type I x-ray bursts. To date, spectroscopic information on 38,39 Ca is largely limited to data on lower-spin excited states. Here, we report in-beam γ-ray spectroscopy of complementary higher-spin, complex-structure states in 39 Ca populated in fast-beam-induced, momentum-dissipative processes leading to neutron pickup onto excited configurations of the projectile, 9 Be( 38 Ca*, 39 Ca + γ)X. Such a dissipative reaction was recently characterized for the case of inelastic scattering of 38 Ca off 9 Be, 9 Be( 38 Ca, 38 Ca + γ)X. Additional data and discussion on the nuclear structure of 38 Ca is also presented. Furthermore, an explanation for the more-complex-structure states, populated with small cross sections in one-nucleon knockout reactions, and observed in the tails of their longitudinal momentum distributions, is also offered.

20 ≤ A ≤ 38↗