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DOE OSTI2021

Enhanced Hanford Low-Activity Waste Glass Property Data Development: Phase 4

This report summarizes and analyzes the data collected on a fourth test matrix of 25 low-activity waste glass compositions intended to expand the composition-property database and to validate the Vienna et al. (2020) property-composition models. The 25 low-activity waste glass compositions were statistically designed to be within the composition region of the 2020 models. The analyses performed on these glasses include chemical composition (for target compositional verification), density, viscosity, electrical conductivity, crystal fraction, canister centerline cooling with crystal identification, product consistency test response, vapor hydration test response, and sulfur solubility. This report discusses the results obtained from these tests.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

Enhanced Hanford Low-Activity Waste Glass Property Data Development: Phase 2

This report summarizes and analyzes the data collected on a second test matrix of 42 low-activity waste (LAW) glass compositions intended to expand the LAW glass composition region over which glass property-composition models are valid. The 42 LAW glass compositions were selected using a statistical layered experimental design approach to explore a new glass composition region that overlaps and expands beyond the previously explored LAW glass composition region. The layered design of 42 LAW glasses consisted of 21 outer-layer glasses, 15 inner-layer glasses, a center glass (three replicates), and two glasses previously tested at another laboratory. The outer-layer glass compositions include extrema based on current projections of the LAW feeds and melter operating temperatures. One of the outer-layer compositions was eliminated due to the inability to form a glass. Therefore, only 41 glasses were analyzed. The analyses performed on these glasses include chemical composition (for target compositional verification), density, viscosity, electrical conductivity, crystal fraction, canister centerline cooling with crystal identification, the Product Consistency Test, sulfur solubility, and the Vapor Hydration Test. This report discusses the results obtained from this testing.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

The Modified Void Nucleation and Growth Model (MNAG) for Damage Evolution in BCC Ta

A void coalescence term was proposed as an addition to the original void nucleation and growth (NAG) model to accurately describe void evolution under dynamic loading. The new model, termed as modified void nucleation and growth model (MNAG model), incorporated analytic equations to explicitly account for the evolution of the void number density and the void volume fraction (damage) during void nucleation, growth, as well as the coalescence stage. The parameters in the MNAG model were fitted to molecular dynamics (MD) shock data for single-crystal and nanocrystalline Ta, and the corresponding nucleation, growth, and coalescence rates were extracted. The results suggested that void nucleation, growth, and coalescence rates were dependent on the orientation as well as grain size. Compared to other models, such as NAG, Cocks–Ashby, Tepla, and Tonks, which were only able to reproduce early or later stage damage evolution, the MNAG model was able to reproduce all stages associated with nucleation, growth, and coalescence. The MNAG model could provide the basis for hydrodynamic simulations to improve the fidelity of the damage nucleation and evolution in 3-D microstructures.

36 MATERIALS SCIENCE↗
DOE OSTI2022

First Sagittarius A* Event Horizon Telescope Results. IV. Variability, Morphology, and Black Hole Mass

In this paper we quantify the temporal variability and image morphology of the horizon-scale emission from Sgr A*, as observed by the EHT in 2017 April at a wavelength of 1.3 mm. We find that the Sgr A* data exhibit variability that exceeds what can be explained by the uncertainties in the data or by the effects of interstellar scattering. The magnitude of this variability can be a substantial fraction of the correlated flux density, reaching ~100% on some baselines. Through an exploration of simple geometric source models, we demonstrate that ring-like morphologies provide better fits to the Sgr A* data than do other morphologies with comparable complexity. We develop two strategies for fitting static geometric ring models to the time-variable Sgr A* data; one strategy fits models to short segments of data over which the source is static and averages these independent fits, while the other fits models to the full data set using a parametric model for the structural variability power spectrum around the average source structure. Both geometric modeling and image-domain feature extraction techniques determine the ring diameter to be 51.8 ± 2.3 μas (68% credible intervals), with the ring thickness constrained to have an FWHM between ~30% and 50% of the ring diameter. To bring the diameter measurements to a common physical scale, we calibrate them using synthetic data generated from GRMHD simulations. This calibration constrains the angular size of the gravitational radius to be ${4.8}_{-0.7}^{+1.4}$ μas, which we combine with an independent distance measurement from maser parallaxes to determine the mass of Sgr A* to be ${4.0}_{-0.6}^{+1.1}\times {10}^{6}$ M⊙.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Hot Gravitons and Gravitational Waves From Kerr Black Holes in the Early Universe

Any abundance of black holes that was present in the early universe will evolve as matter, making up an increasingly large fraction of the total energy density as space expands. This motivates us to consider scenarios in which the early universe included an era that was dominated by low-mass ($M < 5\times 10^8$ g) black holes which evaporate prior to primordial nucleosynthesis. In significant regions of parameter space, these black holes will become gravitationally bound within binary systems, and undergo mergers before evaporating. Such mergers result in three potentially observable signatures. First, any black holes that have undergone one or more mergers will possess substantial angular momentum, causing their Hawking evaporation to produce significant quantities of high-energy gravitons. These products of Hawking evaporation are predicted to constitute a background of hot ($\sim$eV-keV) gravitons today, with an energy density corresponding to $\Delta N_{\rm eff} \sim 0.01-0.03$. Second, these mergers will produce a stochastic background of high-frequency gravitational waves. And third, the energy density of these gravitational waves can be as large as $\Delta N_{\rm eff} \sim 0.3$, depending on the length of time between the mergers and evaporation. These signals are each potentially within the reach of future measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Superfluidity in Disordered Neutron Stars Crusts

Nonequilibrium conditions imposed by neutrino cooling through the liquid-solid transition lead to disorder in the solid crust of neutron stars. Disorder reduces the superfluid fraction, $\rho_s/\rho$, at densities above that of neutron drip, $\rho_d \approx 4\times 10^{11}\,g/cm^3$. For an amorphous solid crust the suppression of $\rho_s$ is small, except in the highest density regions of the crust. In contrast to the strong reduction in neutron conduction predicted for coherent Bragg scattering in a crystalline crust, the disordered solid crust supports sufficient neutron superfluid density to account for pulsar glitches.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Determination of the structure of lithium niobosilicate glasses by molecular dynamics simulation with a new Nb-O potential

A partial charge empirical potential for the Nb-O pair has been developed based on existing parameters of other pairs in a Teter potential to enable molecular dynamics simulations of both lithium niobate crystal and lithium niobosilicate glasses. The developed potential is capable of describing structural features of lithium niobosilicate glasses in a wide composition range, including niobium coordination number and bond length, density, bond angle distribution, polyhedral distribution and fraction of bridging oxygen. Furthermore, the results obtained using this new potential show good agreement with experimental data of density and structure from Raman spectroscopy of lithium niobosilicate glasses and X-ray absorption spectroscopy near Nb K-edge.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Activity of Silica-Alumina for the Conversion of Polyethylene into Tunable Aromatics Below Pyrolytic Temperatures

Plastic waste is a mounting problem that lacks global strategy, largely due to inadequate recycling capabilities. One alternative gaining traction in the heterogeneous catalysis community is the upcycling of polyolefins into value-added products, such as hydrogen-free conversion to alkylaromatic compounds over Pt/Al 2 O 3 . Here, we examined the activity of nominally metal-free, mesoporous silica-alumina mixed oxide materials (SiO 2 –Al 2 O 3 ) for the conversion of polyethylene into aromatic compounds at temperatures of and below 280 °C. Yields with the silica-alumina catalysts are comparable to those obtained over Pt(1 wt %)/Al 2 O 3 under identical conditions, and product selectivity can be tuned by altering reaction conditions or the acid site density of the SiO 2 –Al 2 O 3 . Notably, the fraction of polyaromatic products increases with the Brønsted acid site density of the catalyst, as does the degree of polymer deconstruction. These catalysts can be reused without regeneration, and their activity improves with each recycling event, producing soluble product yields up to 83%. Preliminary work on the mechanism of the reaction suggests that acid sites are responsible for initiating depolymerization and aromatization reactions, in analogy to previous work in the literature. Finally, this work showcases the activity of SiO 2 –Al 2 O 3 for polyolefin deconstruction/aromatization at subpyrolytic temperatures and lays the foundation for future studies involving solid acid and bifunctional catalysts.

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

Simultaneous enhancement of tritium burn efficiency and fusion power with low-tritium spin-polarized fuel

This study demonstrates that using spin-polarized deuterium-tritium (D-T) fuel with more deuterium than tritium can increase tritium burn efficiency (TBE) by at least an order of magnitude without compromising fusion power output, compared to unpolarized fuel. Although previous studies show that a low tritium fraction can enhance TBE, this strategy resulted in reduced fusion power density. The surprising improvement in TBE at fixed power reported here is due to the TBE increasing nonlinearly with decreasing tritium fraction but the fusion power density increasing roughly linearly with D-T cross section. A study is performed for an ARC-like tokamak producing 481 MW of fusion power with unpolarized 53:47 D-T fuel, finding the minimum startup tritium inventory (I startup,min ) is 0.69 kg. By spin-polarizing half of the fuel and using a 60:40 D-T mix, I startup,min is reduced to 0.08 kg, and fully spin-polarizing the fuel with a 63:37 D-T mix further reduces I startup,min to 0.03 kg. Some ARC-like scenarios are predicted to achieve plasma ignition with relatively modest spin polarization. These findings indicate that, with advancements in helium divertor pumping efficiency, TBE values of approximately 10%–40% could be achieved using low-tritium-fraction and spin-polarized fuel with minimal power loss. This would dramatically lower tritium startup inventory requirements and reduce the amount of on-site tritium. More generally than just for spin-polarized fuels, increased plasma performance can be used to increase TBE. This strongly motivates the development of spin-polarized fuels and low-tritium-fraction operation for burning plasmas.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Direct observation of a magnetic-field-induced Wigner crystal

Wigner predicted that when the Coulomb interactions between electrons become much stronger than their kinetic energy, electrons crystallize into a closely packed lattice. A variety of two-dimensional systems have shown evidence for Wigner crystals (WCs). However, a spontaneously formed classical or quantum WC has never been directly visualized. Neither the identification of the WC symmetry nor direct investigation of its melting has been accomplished. Here we use high-resolution scanning tunnelling microscopy measurements to directly image a magnetic-field-induced electron WC in Bernal-stacked bilayer graphene and examine its structural properties as a function of electron density, magnetic field and temperature. At high fields and the lowest temperature, we observe a triangular lattice electron WC in the lowest Landau level. The WC possesses the expected lattice constant and is robust between filling factor ν ≈ 0.13 and ν ≈ 0.38 except near fillings where it competes with fractional quantum Hall states. Increasing the density or temperature results in the melting of the WC into a liquid phase that is isotropic but has a modulated structure characterized by the Bragg wavevector of the WC. At low magnetic fields, the WC unexpectedly transitions into an anisotropic stripe phase, which has been commonly anticipated to form in higher Landau levels. Furthermore, analysis of individual lattice sites shows signatures that may be related to the quantum zero-point motion of electrons in the WC lattice.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Origin of the $ν$ = 1/2 fractional quantum Hall effect in wide quantum wells

The nature of the fractional quantum Hall effect at ν = 1/2, observed in wide quantum wells al- most three decades ago, is still under debate. Previous studies have investigated it by the variational Monte Carlo method, which assumes that the transverse wave function and the gap between the symmetric and antisymmetric subbands obtained in a local density approximation at zero magnetic field remain valid even at high perpendicular magnetic fields; this method also ignores the effect of Landau level mixing. We develop in this work a three-dimensional fixed phase diffusion Monte Carlo method, which gives, in a single framework, the total energies of various candidate states in a finite width quantum well, including Landau level mixing, directly in a large magnetic field. This method can be applied to one-component states, and also to two-component states in the limit where the symmetric and antisymmetric bands are nearly degenerate. Our three-dimensional fixed-phase diffusion Monte Carlo calculations find that the one-component composite-fermion Fermi sea and the one-component Pfaffian states are very close in energy for a range of quantum well widths and densities, suggesting that the observed 1/2 fractional quantum Hall state in wide quantum wells is likely to be the one-component Pfaffian state. Furthermore, we hope that this will motivate further experimental studies of this state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Development and Integration of a Stochastic Clad Damage Propagation Model into PRONGHORN-SC Subchannel Analysis Code

The failure of fuel pins in nuclear reactors is intrinsically stochastic. Typically, a combination of variation in manufacturing that affects the material characteristics and the fuel assembly dimensions, variation in operating conditions, such as local power, coolant flow rate, and irradiation induced changes in material properties lead to a large uncertainty in failure margin of the fuel pins. Failure, therefore, may occur in exceptional pins with adverse combinations of these variations. Upon a metal fuel pin (U-Pu-Zr/HT9) failure, depressurization of the fuel pin takes place by release of fission gas, liquid sodium bond, and potentially solid fuel particles or molten/eutectic fuel droplets through the hole in cladding. The effect of a fission gas jet on neighbor fuel pins and possible propagation of a clad damage during normal operation was studied experimentally in 1970s and it was found that the post-failure fission gas jet insulates the jet impingement area of the target fuel pin surface and could increase the target pin’s surface temperature by as much as 100 – 200 K during the failed pin depressurization. It was concluded that the effect should not lead to fuel pin failure propagation during normal operation. In accident scenarios of sodium and lead fast reactors such as Unprotected Loss-Of-Flow (ULOF) or Unprotected Transient Over Power (UTOP), the fuel pins can be subjected to higher clad temperatures and fuel pin pressures or fuel clad mechanical/chemical interaction where thermal creep margin becomes significantly lower compared to the normal operation conditions. Therefore, possible stochastic failure and the post-failure fission gas/fuel jet impingement could be critical in order to predict fuel pin failure propagation. Pin depressurization due to fission gas release may degrade the heat transfer by formation of a gas blanket on a neighboring pin surface, which is a local phenomenon, and by causing coolant flow deceleration and starvation, which could affect a surrounding region as well. Furthermore, the potential presence of solid fuel particles or molten fuel at the time of clad failure could boost post-failure jet induced degradation even further. The present study models the U-Pu-Zr/HT9 metal fuel pin failure and stochastic clad damage propagation by biased sampling based on a Cumulative Damage Fraction (CDF) type clad failure criterion and the normal distribution of fuel failure probability density as a function of logarithm of Cumulative Damage Fraction. In addition, the effect of post-failure fission gas jet on heat transfer degradation is modeled for the target pins. This model is called stochastic Clad Damage Propagation (CDAP). The CDAP model is now fully integrated into developmental version of PRONGHORN-SC subchannel analysis code, allowing for modeling local failures and its propagation potential. Section 2 describes the components of the CDAP models. Section 3 describes the model implementation to PRONGHORN-SC and input specifications. Section 4 describes the CDAP model validation coupled to PRONGHORN-SC.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Critical differences between electron beam melted and selective laser melted Ti-6Al-4 V

Effective optimization of the production of Ti-6Al-4 V using AM requires a fundamental understanding of the relative importance of different microstructural features to the deformation and failure mechanisms, particularly features that vary between production methods. In this study, the tensile response and deformation mechanisms of electron beam melted (EBM) AM Ti-6Al-4 V material loaded in different orientations and produced using various powder sizes were compared to those of selective laser melted (SLM) AM Ti-6Al-4 V material. The density and morphology of pores, phase fractions, prior-β grains, and defect microstructures were evaluated using scanning electron microscopy, X-ray computed tomography, electron backscatter diffraction, and transmission electron microscopy before and after deformation. The results were used to evaluate the relative importance of each feature on strengthening, deformation, and failure initiation mechanisms. Results focused primarily on coarse-powder EBM materials indicated that phase distribution and defect density were most influential for determining material yield strength as well as maximum possible strain to failure. Porosity was lower overall in EBM Ti-6Al-4 V than in SLM, allowing for occasional increases in part strain to failure, but remained a limiting factor determining overall part ductility.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Searching for heavy charged relics in the Earth

We propose a method for detecting an ambient density of heavy, electrically-charged particles. Such particles would impact the Earth, lose energy in terrestrial matter, and become trapped. We study the accumulation of these rare particles in multiple target materials that provide large exposure, such as water and geological rocks. We discuss strategies for concentrating the particles by centrifugation or gravitational settling, along with particle identification using mass spectrometry. This method enables the discovery of charged relics with masses $1-10^{12}\,{\rm TeV}$ comprising a tiny fraction of the local dark matter density, reaching down to $f_X\sim 10^{-20}$ at the lowest masses. A pathfinder experiment using only a liter of water and one centrifuge (or $\sim \text{m}^3$ and no centrifuge) operating for a month can already reach $f_X\sim 10^{-10}$ and probe new parameter space.

Ebadi, Reza [Johns Hopkins U.; Delaware U.] (ORCID↗
DOE OSTI2023

Elucidating Biomass-Derived Pyrolytic Lignin Structures from Demethylation Reactions through Density Functional Theory Calculations

Pyrolytic lignin is a fraction of pyrolysis oil that contains a wide range of phenolic compounds that can be used as intermediates to produce fuels and chemicals. However, the characteristics of the raw lignin structure make it difficult to establish a pyrolysis mechanism and determine pyrolytic lignin structures. Herein this study proposes dimer, trimer, and tetramer structures based on their relative thermodynamic stability for a hardwood lignin model in pyrolysis. Different configurations of oligomers were evaluated by varying the positions of the guaiacyl (G) and syringyl (S) units and the bonds βO4 and β5 in the hardwood model lignin through electronic structure calculations. The homolytic cleavage of βO4 bonds is assumed to occur and generate two free radical fragments. These can stabilize by taking hydrogen radicals that may be in solution during the intermediate liquid (pathway 1) formation before the thermal ejection. An alternative pathway (pathway 2) could occur when the radicals use intramolecular hydrogen, turning themselves into stable products. Subsequently, a demethylation reaction can take place, thus generating a methane molecule and new oligomeric lignin-derived molecules. The most probable resulting structures were studied. We used FTIR and NMR spectra of selected model compounds to evaluate our calculation approach. Thermophysical properties were calculated using group contribution methods. The results give insights into the lignin oligomer structures and how these molecules are formed. They also provide helpful information for the design of pyrolysis oil separation and upgrading equipment.

09 BIOMASS FUELS↗
DOE OSTI2025

An extension of the localized artificial diffusivity method for immiscible and high density ratio flows

The localized artificial diffusivity (LAD) method is widely regarded as the preferred multi-material regularization scheme for the compact finite difference method, because it is conservative, easy to implement, and generally robust for a wide range of multi-material problems. However, traditional LAD methods face significant challenges when applied to flows with large density ratios and when maintaining thermodynamic equilibrium across material interfaces. These limitations arise from the formulation of the artificial diffusivity flux and the reliance on enthalpy diffusion for interface regularization. Additionally, traditional LAD methods struggle to ensure stability under large density ratio conditions, fail to maintain a finite interface thickness, and are therefore unsuitable for modeling immiscible interfaces. Here, in this work, we discuss the origins of these issues in traditional LAD methods and propose modifications which enable the simulation of large density ratio and immiscible flows. The proposed method targets the artificial diffusion fluxes at gradients and ringing in the volume fraction, rather than the mass fraction in traditional methods, to consistently regularize large density ratio interfaces. Furthermore, the proposed method introduces an artificial bulk density diffusion term to enforce equilibrium conditions across interfaces. To address the challenge of modeling immiscible flows, a conservative diffuse interface term is incorporated into the formulation to ensure a finite interface thickness. Specific consideration is taken in the design of the method to ensure that these crucial properties are maintained for N -material flows. The effectiveness of the proposed method is demonstrated through a series of canonical test cases, and its accuracy is validated by comparison with experimental data on micro-bubble collapse in water. These results highlight the method’s robustness and its ability to overcome the limitations of traditional LAD approaches.

Artificial diffusivity↗
DOE OSTI2021

Structure prediction of epitaxial inorganic interfaces by lattice and surface matching with Ogre

We present a new version of the Ogre open source Python package with the capability to perform structure prediction of epitaxial inorganic interfaces by lattice and surface matching. In the lattice matching step, a scan over combinations of substrate and film Miller indices is performed to identify the domain-matched interfaces with the lowest mismatch. Subsequently, surface matching is conducted by Bayesian optimization to find the optimal interfacial distance and in-plane registry between the substrate and the film. For the objective function, a geometric score function is proposed based on the overlap and empty space between atomic spheres at the interface. The score function reproduces the results of density functional theory (DFT) at a fraction of the computational cost. The optimized interfaces are pre-ranked using a score function based on the similarity of the atomic environment at the interface to the bulk environment. Final ranking of the top candidate structures is performed with DFT. Ogre streamlines DFT calculations of interface energies and electronic properties by automating the construction of interface models. The application of Ogre is demonstrated for two interfaces of interest for quantum computing and spintronics, Al/InAs and Fe/InSb.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Mathematical Modeling of Hydroxide-Exchange-Membrane Water Electrolyzer

Water electrolyzers can transform intermittent renewable energy like solar energy and wind energy into the chemical energy of hydrogen with zero greenhouse-gas emissions. The hydroxide-exchange membrane electrolyzer (HEME) combines the capability to produce pressurized hydrogen with the advantage of being able to use low or non-platinum group metal (PGM) electrocatalysts in the alkaline environment.1 Hydroxide salts, for example, KOH, are added to the HEME water feed on both anode and cathode to improve its performance. However, the specific mechanism of performance improvement still needs to be further understood. In addition, at high current densities, bubble evolution can result in mass-transport limitations, a less well studied phenomena. Mathematical modeling is ideal to explore these issues as it is cost and time efficient and can deconvolute the physics, processes, and observed phenomena and study the applied-voltage breakdown. In this work, we extend our previously developed 1D two-phase continuum model2 to study the varies processes in the HEME and provide insights on performance optimizations. First, the oxygen evolution reaction (OER) and hydrogen evolution reaction (HER) kinetics at different hydroxide concentrations have been studied by rotating disk electrodes (RDE) and implemented in the model. Then, the model is calibrated and validated against experimental HEME polarization curves for different KOH concentrations as a liquid electrolyte. The model clearly shows a performance increase with increasing KOH concentrations, which is consistent with the experimental results. The reduced ohmic resistance and increased electrochemical active surface area (ECSA) are the two main reasons for performance increase. The large amount of hydroxide in the liquid electrolyte not only helps to distribute the reactant hydroxide throughout the catalyst layer (CL), which reduces ohmic loss, but also enables reaction at the interface between the liquid electrolyte and electrocatalyst, which increases the ECSA. Applied-voltage breakdown demonstrates that the electrolyzer performance is dominated by anode kinetics and ohmic loss. A comparison with the DI water feed shows a more uniform current distribution in the anode CL when KOH is added, which indicates a higher utilization of the CL. Second, we present modeling on the effects of bubble coverage. As gas evolves, part of the ECSA is minimized due to bubble coverage. To account for this effect, an empirical relationship between the fractional bubble coverage and the current density is implemented in the model.3 The model shows this bubble coverage effect is more pronounced at large current densities with DI water feed. Acknowledgements This work was funded under the HydroGEN Consortium by the Energy Efficiency and Renewable Energy, Hydrogen and Fuel Cell Technologies Office, of the U. S. Department of Energy under contract number DE-AC02-05CH11231. References R. Abbasi, B. P. Setzler, S. Lin, J. Wang, Y. Zhao, H. Xu, B. Pivovar, B. Tian, X. Chen, G. Wu and Y. Yan, 31, 1805876 (2019). L. N. Stanislaw, M. R. Gerhardt and A. Z. Weber, ECS Transactions, 92, 767 (2019). H. Vogt and R. J. Balzer, Electrochimica Acta, 50, 2073 (2005).

Liu, Jiangjin↗