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At least 271 records · Page 15

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NASA NTRS1989

Nucleation in the presence of long-range interactions

Unlike droplet nucleation near a liquid-gas critical point, the decay of metastable phases in crystalline materials is strongly affected by the presence of long-range forces. Field quench experiments performed on the ferroelectric barium titanate indicate that nucleation in this material is markedly different from that observed in liquids. In this paper, a theory for nucleation at a first-order phase transition in which the mediating forces are long range is presented. It is found that the long-range force induces cooperative nucleation and growth processes, and that this feedback mechanism produces a well-defined delay time with a sharp onset in the transformation to the stable phase. Closed-form expressions for the characteristic onset time and width of the transition are developed, in good agreement with numerical and experimental results.

Chandra, P.↗

NASA NTRS2013

The W-W02 Oxygen Fugacity Buffer at High Pressures and Temperatures: Implications for f02 Buffering and Metal-silicate Partitioning

Oxygen fugacity (fO2) controls multivalent phase equilibria and partitioning of redox-sensitive elements, and it is important to understand this thermodynamic parameter in experimental and natural systems. The coexistence of a metal and its oxide at equilibrium constitutes an oxygen buffer which can be used to control or calculate fO2 in high pressure experiments. Application of 1-bar buffers to high pressure conditions can lead to inaccuracies in fO2 calculations because of unconstrained pressure dependencies. Extending fO2 buffers to pressures and temperatures corresponding to the Earth's deep interior requires precise determinations of the difference in volume (Delta) V) between the buffer phases. Synchrotron x-ray diffraction data were obtained using diamond anvil cells (DAC) and a multi anvil press (MAP) to measure unit cell volumes of W and WO2 at pressures and temperatures up to 70 GPa and 2300 K. These data were fitted to Birch-Murnaghan 3rd-order thermal equations of state using a thermal pressure approach; parameters for W are KT = 306 GPa, KT' = 4.06, and αKT = 0.00417 GPa K-1. Two structural phase transitions were observed for WO2 at 4 and 32 GPa with structures in P21/c, Pnma and C2/c space groups. Equations of state were fitted for these phases over their respective pressure ranges yielding the parameters KT = 190, 213, 300 GPa, KT' = 4.24, 5.17, 4 (fixed), and αKT = 0.00506, 0.00419, 0.00467 GPa K-1 for the P21/c, Pnma and C2/c phases, respectively. The W-WO2 buffer (WWO) was extended to high pressure by inverting the W and WO2 equations of state to obtain phase volumes at discrete pressures (1-bar to 100 GPa, 1 GPa increments) along isotherms (300 to 3000K, 100 K increments). The slope of the absolute fO2 of the WWO buffer is positive with increasing temperature up to approximately 70 GPa and is negative above this pressure. The slope is positive along isotherms from 1000 to 3000K with increasing pressure up to at least 100 GPa. The WWO buffer is at a higher fO2 than the IW buffer at pressures lower than 40 GPa, and the magnitude of this difference decreases at higher pressures. This qualitatively indicates an increasingly lithophile character for W at higher pressures. The WWO buffer was quantitatively applied to W metal-silicate partitioning by using the WWO-IW buffer difference in combination with literature data on W metal-silicate partitioning to model the exchange coefficient (KD) for the Fe-W exchange reaction. This approach captures the pressure dependence of W metal-silicate partitioning using the WWO-IW buffer difference and models the activities of the components in the silicate and metallic phases using an expression of the Gibbs excess energy of mixing. Calculation of KD along a peridotite liquidus predicts a decrease in W siderophility at higher pressures that supports the qualitative behavior predicted by the WWO-IW buffer difference, and agrees with findings of others. Comparing the competing effects of temperature and pressure on W metal-silicate partitioning, our results indicate that pressure exerts a greater effect.

Shofner, G. A.↗

NASA NTRS1972

Magnetism, dimensional changes, and magnetic transitions in hydrated cesium manganese chloride

Dimensional changes (strain) along the three principal crystal axes of the antiferromagnet CsMnCl3-2H2O are studied as a function of magnetic field and temperature in the antiferromagnetic, spin flopped, and paramagnetic phases. Changes in dimensions through the phase transitions between the magnetic states are examined. By applying the molecular field model and utilizing all available information, magnetic properties of CsMnCl3-2H2O are determined. The possible usefulness of this material in a magnetic refrigeration cycle is evaluated.

Woollam, J. A.↗

NASA NTRS2018

Advancing Torpor Inducing Transfer Habitats for Human Stasis to Mars: II - Phase

SpaceWorks Enterprises, Inc. (SEI) has conducted an evaluation of an advanced habitat system designed to transportcrews between the Earth and Mars. This new and innovative habitat concept is capable of placing crew members ininactive, torpor states during transit phases of a deep space mission. This substantially reduces the mass and size ofthe habitat, which ultimately leads to significant reductions in the overall architecture size.Our approach for achieving this is based on extending the current and evolving medical practice of TherapeuticHypothermia (TH) - a proven and effective treatment for various traumatic injuries. TH is a medical treatment thatlowers a patient's body temperature by just 5 to 10 degrees Fahrenheit causing human metabolic rate to decreasesignificantly and the body to enter an unconscious state. This method avoids the intractable challenges often associatedwith cell metabolic cessation through cryogenic freezing and other highly speculative approaches.The initial results obtained from the research and analysis conducted in the Phase I effort warranted further study ofthis concept and technology. The specific objectives of the continued work include:1. Addressing critical medical aspects and risks for inducing torpor via Therapeutic Hypothermia and theapproach for providing nutrition and hydration for the crew during torpor. 2. Focusing on mitigation aspects and technology potential for solving key human spaceflight challenges. 3. Addressing critical engineering aspects of the design that may impact the initial performance and cost resultsobtained in Phase I. 4. Examining the broader extensibility and enabling capabilities of this concept through applicability toadditional exploration missions beyond Mars. 5. Establishing a technology development roadmap, addressing both medical and engineering aspects, thatindicate a logical and scientifically achievable path forward for maturation of this technology.

Stasis↗

NASA NTRSDate not supplied

A Machine Learning Approach to Predict Martensitic Transition Temperatures for Shape Memory Alloys

Shape memory alloys (SMAs) are a unique class of materials with several remarkable properties including shape recovery, superelasticity, etc. Especially important for many NASA applications is the ability to tune the martensitic phase transition temperature by varying the alloy composition. Nickel-titanium (NiTi) based alloys are the most widely studied of this class, with compositions involving ternary, quaternary, or higher additions being considered. Over the past several years, a significant database of SMA properties has been assembled by NASA researchers. Such a database is ideal for data science-based approaches including machine learning. We present results from a developed machine learning model capable of accurately predicting the transition temperature of SMAs across a wide range of compositions. Our model has the added benefit of interpretability and even provides confidence intervals for our predictions. This model will make rapid screening and design of new SMA materials possible. Predictions from the machine learning model can be validated by empirical and/or atomistic scale modeling.

Shreyas Honrao↗

NASA NTRS1977

Effects of high temperature and e-beam irradiation on the stability of refractory thin films

Refractory thin films of Al2O3, ZrO2, MgO, ThO2, and BN have been investigated in situ in an UHV transmission electron microscope. The electron transparent refractory films were prepared by electron-beam evaporation, anodization, RF sputtering, and thinning of bulk crystal materials. The study concentrates on monitoring the thermal and mechanical stability of the films, phase and structural changes, and electron irradiation effects as a function of film-preparation conditions. With increasing temperatures, five different crystallographic phases were observed for both anodized and electron-beam-evaporated alumina films. Zirconia films exhibited two phase transitions upon heating to 1200 C and electron-irradiation-induced crystallization of ZrO2 even at room temperature. MgO, ThO2, and BN films did not undergo any noticeable phase transformation but ruptured due to sintering below 1200 C.

Lee, E. H.↗

NASA NTRS1985

Comparison of predicted and measured drag for a single-engine airplane

Renewed interest in natural laminar flow (NLF) has rekindled designers' concerns that manufacturing deviations, (loss of surface contours or other surface imperfections) may destroy the effectiveness of NLF for an operational airplane. This paper reports on experimental research that compares predicted and measured boundary layer transition, total drag, and two-dimensional drag coefficients for three different wing surface conditions on an airplane typical of general aviation manufacturing technology. The three flight test phases included: (1) assessment of an unpainted airframe, (2) flight tests of the same airplane after painstakingly filling and sanding the wings to design contours, and (3) similar measurements after this airplane was painted. In each flight phase, transition locations were monitored using either sublimating chemicals or pigmented oil. As expected, total drag changes were difficult to measure. Two-dimensional drag coefficients were estimated using the Eppler-Somers code and measured with a wake rake in a method very similar to Jones' pitot traverse method. The net change in two-dimensional drag was approximately 20 counts between the unpainted airplane and the 'hand-smoothed' airplane for typical cruise flight conditions.

Ward, D. T.↗

NASA NTRS1967

Ultrasonic properties of solids

Ultrasonic properties of solids studied to obtain information about bulk systems near phase transitions or critical points

PHASE CHANGE↗

NASA NTRS2020

Structural evolution, electrochemical kinetic properties, and stability of A-site doped perovskite Sr(1-x)Yb(x)CoO(3-δ)

Mixed ionic and electronic conducting (MIEC) perovskite SrCoO(3-δ) is a widely studied (electro)catalyst for the oxygen reduction reaction (ORR) and possesses different crystal structures at different temperatures. These temperature dependent phase transitions significantly impact the ordering of oxygen vacancies and electrochemical kinetic properties as well as the reliability of the related devices. Some of the crystal structures formed, e.g. hexagonal phases, turn out to be almost impermeable to oxygen gas. Therefore, it is important to stabilize the crystal structure of SrCoO(3-δ) that favors the ORR over a wide temperature range. Herein, the partial substitution of the A-site Sr with Yb is systematically studied, including synthesis, characterization and analysis of structural evolution, electrochemical kinetic properties, thermal stability, and stability in a CO2-containing atmosphere. The results indicate that Sr(0.90)Yb(0.10)CoO(3-δ) is able to stabilize the tetragonal crystal structure with less ordered oxygen vacancies, leading to polarization resistances of 0.051, 0.115 and 0.272 U sq.cm at 750, 700 and 650 °C, respectively, on symmetrical cells. Sr(0.90)Yb(0.10)CoO(3-δ) demonstrates a very stable surface oxygen vacancy distribution and electronic structure near oxygen vacancies but dissociation of adsorbed oxygen molecules into atomic oxygen is affected by surface Sr segregation, and polarization resistance degradation is mainly induced by surface Sr segregation. Furthermore, Sr(0.90)Yb(0.10)CoO(3-δ) exhibits excellent thermal stability as well as excellent recovery stability and improved polarization performance after a few pure air/CO2-containing air treatment cycles at 700 °C. However, a hysteresis behavior of polarization performance is observed at 650 °C during gas cycling treatment, which may cause long-term degradation of the Sr(0.90)Yb(0.10)CoO(3-δ) electrode. The different polarization behaviors during gas cycling treatment are induced by different sensitivities of the formed surface strontium carbonate and chemisorbed surface oxo-carbonaceous species to different operating temperatures.

electrochemical kinetic↗

NASA NTRSDate not supplied

Hydrodynamics of Two-Phase Flows through Porous Media in Microgravity: Packed Bed Reactor Experiment onboard of the International Space Station

The objective of the Packed Bed Reactor Experiment was to develop a fundamental understanding of the hydrodynamics of two-phase flow with no phase transition through porous media in microgravity. This work describes two experimental campaigns flown on the International Space Station (ISS) that were designed to achieve the objective. This work presents the results on flow patterns observed, two-phase flow pressure drop in porous media, and the impact of capillary effects on pressure drop at various gas and liquid flow rates. This work is the first to present predictive correlations of the two-phase friction factor for the different regimes identified based on the superficial liquid and gas velocity in microgravity, the first to hypothesize the different regimes based on the change in slope of the pressure gradient versus flow rate plots, the first to address the effects of the capillarity on the pressure gradient and the first to measure column holdup and assess the effective porosity based on the packing and the trapped gas bubbles. Experimental data on pressure drop in gas (N2) – liquid (water) flow show the presence of four different flow regimes in microgravity. Dispersed bubble flow (DB) and pulse (P) flow regimes are detected at high liquid flow rates, whereas at low liquid flow rates “large bubble” or elongated bubble (LB) and “gas channeling” (GC) regimes are observed. For these different flow regimes, different two-phase flow friction factor and pressure gradient correlations are presented for the first time as a function of the gas and liquid modified Reynolds numbers and Suratman number. Within the viscous-capillary (V-C) regime, it is found that the capillary contribution is the dominant force that contributes to the pressure drop for the wetting case (glass). However, for the non-wetting packing (Teflon), the viscous contribution dominates. It was found that the gas hold-up and pressure drop are functions of bed history at low liquid and gas flow rates with the magnitude of the hysteresis decreasing with increasing flow rates. PBRE-2 results show that the capillary force is a strong function of the superficial liquid velocity but is a much weaker function of the superficial gas velocity and varies inversely with the particle diameter. Within the Viscous-Capillary (V-C) regime, over 90% of the pressure gradient is attributed to the capillary contribution in the gas continuous regime. However, in the large bubble regime, the viscous and capillary contributions were comparable. After the completion of PBRE-2 with glass spherical beads, another bed packed with alumina was installed. Pressure gradient data for the alumina packed bed (PBRE-Water Recovery) were transferred to the PI and were not analyzed by the authors of this work. The Packed Bed Reactor Experiment concluded its on-orbit operation after two successful campaigns of testing in 2017 and in 2021. The flight hardware was brought back from orbit and is being reconditioned for a series of future experiments referred to as PBRE-WRS in support of water recovery (WRS). The WRS series consists of testing different two-phase fluid system components and packed beds to assess their pressure gradient characteristics, which will be used for designing packed bed reactors for various applications relevant to life support. Although there is so much relevance of the experimental results obtained from the two PBRE campaign in microgravity to life support, these findings also apply to other applications that involve two phase flow in porous medium such as fuel cells, transport of nutrient to plants in space and other chemical and materials processing that involve two phase flows. These systems operate differently in microgravity because, due to the lack of buoyancy, the density difference between the phases becomes irrelevant and no longer leads to phase separation.

Packed Bed↗

NASA NTRS1984

Surface roughening as a precursor to the polymorphic transition in CBr4

The morphology of CBr4 crystals was microscopically studied at temperatures near the polymorphic transition (Ttr = 47 C) during growth from the vapor. The observations presented here give evidence that surface roughening is occurring with increasing temperature as an apparent precursor of the solid state phase transition.

Ming, Nai-Ben↗

NASA NTRS2012

Coronagraph Focal-Plane Phase Masks Based on Photonic Crystal Technology: Recent Progress and Observational Strategy

Photonic crystal, an artificial periodic nanostructure of refractive indices, is one of the attractive technologies for coronagraph focal-plane masks aiming at direct imaging and characterization of terrestrial extrasolar planets. We manufactured the eight-octant phase mask (8OPM) and the vector vortex mask (VVM) very precisely using the photonic crystal technology. Fully achromatic phase-mask coronagraphs can be realized by applying appropriate polarization filters to the masks. We carried out laboratory experiments of the polarization-filtered 8OPM coronagraph using the High-Contrast Imaging Testbed (HCIT), a state-of-the-art coronagraph simulator at the Jet Propulsion Laboratory (JPL). We report the experimental results of 10-8-level contrast across several wavelengths over 10% bandwidth around 800nm. In addition, we present future prospects and observational strategy for the photonic-crystal mask coronagraphs combined with differential imaging techniques to reach higher contrast. We proposed to apply a polarization-differential imaging (PDI) technique to the VVM coronagraph, in which we built a two-channel coronagraph using polarizing beam splitters to avoid a loss of intensity due to the polarization filters. We also proposed to apply an angular-differential imaging (ADI) technique to the 8OPM coronagraph. The 8OPM/ADI mode avoids an intensity loss due to a phase transition of the mask and provides a full field of view around central stars. We present results of preliminary laboratory demonstrations of the PDI and ADI observational modes with the phase-mask coronagraphs.

coronagraphy↗

NASA NTRS2013

The Herschel* PEP-HERMES Luminosity Function- I. Probing the Evolution of PACS Selected Galaxies to z approx. equal to 4

We exploit the deep and extended far-IR data sets (at 70, 100 and 160 μm) of the Herschel Guaranteed Time Observation (GTO) PACS Evolutionary Probe (PEP) Survey, in combination with the Herschel Multi-tiered Extragalactic Survey data at 250, 350 and 500 μm, to derive the evolution of the rest-frame 35-, 60-, 90- and total infrared (IR) luminosity functions (LFs) up to z ∼ 4.We detect very strong luminosity evolution for the total IR LF (LIR ∝ (1 + z)(sup 3.55 +/- 0.10) up to z ∼ 2, and ∝ (1 + z)(sup 1.62 +/- 0.51) at 2 less than z less than approximately 4) combined with a density evolution (∝ (1 + z)(sup −0.57 +/- 0.22) up to z ∼ 1 and ∝ (1 + z)(sup −3.92 +/- 0.34) at 1 less than z less than approximately 4). In agreement with previous findings, the IR luminosity density (ρIR) increases steeply to z ∼ 1, then flattens between z ∼ 1 and z ∼ 3 to decrease at z greater than approximately 3. Galaxies with different spectral energy distributions, masses and specific star formation rates (SFRs) evolve in very different ways and this large and deep statistical sample is the first one allowing us to separately study the different evolutionary behaviours of the individual IR populations contributing to ρIR. Galaxies occupying the well-established SFR-stellar mass main sequence (MS) are found to dominate both the total IR LF and ρIR at all redshifts, with the contribution from off-MS sources (≥0.6 dex above MS) being nearly constant (∼20 per cent of the total ρIR) and showing no significant signs of increase with increasing z over the whole 0.8 < z <2.2 range. Sources with mass in the range 10 ≤ log(M/solar mass) ≤ 11 are found to dominate the total IR LF, with more massive galaxies prevailing at the bright end of the high-z (greater than approximately 2) LF. A two-fold evolutionary scheme for IR galaxies is envisaged: on the one hand, a starburst-dominated phase in which the Super Massive Black Holes (SMBH) grows and is obscured by dust (possibly triggered by a major merging event), is followed by an AGN-dominated phase, then evolving towards a local elliptical. On the other hand, moderately star-forming galaxies containing a low-luminosity AGN have various properties suggesting they are good candidates for systems in a transition phase preceding the formation of steady spiral galaxies.

Herschel↗

NASA NTRS1991

Aspects of reheating in first-order inflation

Studied here is reheating in theories where inflation is completed by a first-order phase transition. In the scenarios, the Universe decays from its false vacuum state by bubble nucleation. In the first stage of reheating, vacuum energy is converted into kinetic energy for the bubble walls. To help understand this phase, researchers derive a simple expression for the equation of state of a universe filled with expanding bubbles. Eventually, the bubble walls collide. Researchers present numerical simulations of two-bubble collisions clarifying and extending previous work by Hawking, Moss, and Stewart. The researchers' results indicate that wall energy is efficiently converted into coherent scalar waves. Also discussed is particle production due to quantum effects. These effects lead to the decay of the coherent scalar waves. They also lead to direct particle production during bubble-wall collisions. Researchers calculate particle production for colliding walls in both sine-Gordon and theta (4) theories and show that it is far more efficient in the theta (4) case. The relevance of this work for recently proposed models of first order inflation is discussed.

Watkins, Richard↗

NASA NTRS1992

Observations of a new SAGE II aerosol extinction mode following the eruption of Mt. Pinatubo

In the aftermath of the eruption of Mt. Pinatubo, multiwavelength stratospheric aerosol extinction measurements by the satellite-borne Stratospheric Aerosol and Gas Experiment (SAGE II) revealed the presence of a previously unobserved mode of aerosol that exhibited high extinction but a small inferred particle size. This mode may represent a transitional phase between the very small aerosol created by gas-to-particle conversion and a quasi-steady state, post-volcanic aerosol that exhibits both large extinction and large particle size. The presence of a transitional small aerosol mode may have a significant impact on chemical and radiative processes in the stratosphere.

Thomason, Larry W.↗

NASA NTRS1991

Applying state diagrams to food processing and development

The physical state of food components affects their properties during processing, storage, and consumption. Removal of water by evaporation or by freezing often results in formation of an amorphous state (Parks et al., 1928; Troy and Sharp, 1930; Kauzmann, 1948; Bushill et al., 1965; White and Cakebread, 1966; Slade and Levine, 1991). Amorphous foods are also produced from carbohydrate melts by rapid cooling after extrusion or in the manufacturing of hard sugar candies and coatings (Herrington and Branfield, 1984). Formation of the amorphous state and its relation to equilibrium conditions are shown in Fig. 1 [see text]. The most important change, characteristic of the amorphous state, is noticed at the glass transition temperature (Tg), which involves transition from a solid "glassy" to a liquid-like "rubbery" state. The main consequence of glass transition is an increase of molecular mobility and free volume above Tg, which may result in physical and physico-chemical deteriorative changes (White and Cakebread, 1966; Slade and Levine, 1991). We have conducted studies on phase transitions of amorphous food materials and related Tg to composition, viscosity, stickiness, collapse, recrystallization, and ice formation. We have also proposed that some diffusion-limited deteriorative reactions are controlled by the physical state in the vicinity of Tg (Roos and Karel, 1990, 1991a, b, c). The results are summarized in this article, with state diagrams based on experimental and calculated data to characterize the relevant water content, temperature, and time-dependent phenomena of amorphous food components.

Non-NASA Center↗

NASA NTRSDate not supplied

Composition-property correlations in NiTi-based shape memory alloys from the first principles

Development of shape memory alloys (SMA) has been traditionally accomplished by means of extensive empirical efforts, with a very limited support from phenomenological models and related tools. We present a theoretical framework based on the Hamiltonian formalism, which connects important thermodynamic properties directly to the relative energies (the eigenvalues of the Hamiltonian), computed from the first principles using density functional theory. The estimates based on this formalism allow to establish correlations between composition and physical properties, such as relative energies, phase transition temperatures, hysteresis, thermal expansion, and other thermodynamic information. Importantly, estimates and correlations not only provide a fast answer, but also elucidate underpinning of thermodynamic features in terms of the electronic structure. Using this framework, we consider phase transformations and correlations between the selected properties and composition in the NiTi-based ternary and multicomponent shape memory alloys. Our theoretical guidance facilitates design and development of future alloys.

shape memory alloys↗

NASA NTRSDate not supplied

Sources of Uncertainty in Ultrasonic Phase-Based Assessment of Interfacial Stiffness in Adhesive Joints

Quantitative nondestructive evaluation (NDE) of adhesive joint strength is critical for certifying fastener-free bonded aerospace structures. Unfortunately, available adhesive NDE approaches are only suitable for detecting gross defects and delamination and cannot reliably detect variations in strength in intact bonds. Intact (i.e., nominally defect free) bonds are challenging to inspect because they, by definition, contain no macroscopic defects that would produce a strong NDE signature. Even in the absence of obvious defects, however, bond strength can vary substantially due to factors such as contamination, variations in the adhesive cure processes, and environmental exposure. For ultrasonic bond inspections, the effect of interactions from an imperfect adhesive interface are subtle and may include changes in the frequency content or phase of the ultrasonic signal. The bond condition can be deduced from these subtle changes in the acoustic response using an accompanying physics-based model of adhesive joint interaction. For example, researchers have used the spring network adhesion model of Baik and Thompson [1] to determine the interfacial stiffness of the joint from its ultrasonic response (e.g., [2]). This interfacial stiffness metric describes the bonds resistance to separation between the adhesive and adherent and has shown a strong correlation with joint strength. In this study, interfacial stiffness is assessed using the ultrasonic phase change associated with bond interaction in varying bond conditions. The phase change is measured precisely using a phase-locked-loop instrument over a swept range of frequencies. The phase transition at resonance, where the bond thickness is half the acoustic wavelength, produces a unique signature with which to fit a physics-based model. Interfacial stiffness is determined by minimizing the difference between the theoretical and experimental phase response. Experimental results are presented for glass specimens bonded with aerospace adhesives and a sensitivity analysis is performed to examine the effects of parameters that may be uncertain in the industrial inspection environment – namely bond thickness, adhesive and adherent properties, and porosity. The results are a first step toward an uncertainty quantified version of the measurement technique, show correlation between interfacial stiffness and bond strength, and are another key step toward maturing this approach for use in complex materials and joint geometries. [1] Baik, J.M. and Thompson, R.B., 1984. “Ultrasonic scattering from imperfect interfaces: a quasi-static model”. Journal of Nondestructive Evaluation, 4. [2] Haldren, H.A., Perey, D.F., Yost, W.T., Cramer, K.E., and Gupta, M.C., 2019. “Swept-frequency ultrasonic phase evaluation of adhesive bonding in tri-layer structures”. Journal of the Acoustical Society of America, 145.

Matt Webster↗