Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “hydrostaticity”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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

At least 559 records · Page 31

Pressure-induced creation and annihilation of Weyl points in T d - Mo 0.5 W 0.5 Te 2 and 1 T " - Mo 0.5 W 0.5 Te 2

By means of first-principles density-functional theory calculations, we investigate the role of hydrostatic pressure in the electronic structure of the T d (Pmn2 1 ) and 1T" (Pm) phases of the Weyl semimetal Mo 0.5 W 0.5 Te 2 , which is a promising material for phase-change memory technology and superconductivity. We particularly focus on changes occurring in the distribution of the gapless Weyl points (WPs) within the 0 to 45 GPa pressure range. Here we further investigate the structural phase transition and lattice dynamics of the T d and 1T" phases within the aforementioned pressure range. Our calculations suggest that both the T d and 1T" phases of Mo 0.5 W 0.5 Te 2 host four WPs in their full Brillouin zone at zero pressure. The total number of WPs increases to 44 (36) with increasing pressure via pair creation up to 20 (15) GPa for the T d (1T") phase, and beyond this pressure pair annihilation of WPs starts occurring, leaving only 16 WPs at 45 GPa in both phases. The enthalpy versus pressure data reveal that the 1T" phase is more favorable below the critical pressure of 7.5 GPa; however, beyond this critical pressure the T d phase becomes enthalpically favorable. We also provide the calculated x-ray diffraction spectra along with the calculated Raman- and infrared-active phonon frequencies to facilitate the experimental identification of the studied phases

36 MATERIALS SCIENCE↗

High-pressure inelastic neutron scattering study of the anisotropic S = 1 spin chain [ Ni ( HF 2 ) ( 3 - Clpyradine ) 4 ] B F 4

[Ni(HF 2 )(3-Clpyradine) 4 ]BF 4 (NBCT) is a one-dimensional, S=1 spin-chain material that shows no long-range magnetic order down to thermometer temperatures of 0.1 K. Previous ambient pressure inelastic neutron scattering experiments identified NBCT to be in the large-D quantum paramagnetic phase of the D/J phase diagram, where D is the axial single-ion anisotropy and J is the intrachain superexchange. In this work, we extend the previous experiments to a hydrostatic pressure of 0.9 GPa. By comparing to density matrix renormalization group calculations, we find D/J increases from 1.5 to 3.2 as pressure increases from 0 GPa to 0.9 GPa, which pushes the system further into the large-D phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Phase transitions in high-purity zirconium under dynamic compression

In this work, we present results from ramp compression experiments on high-purity Zr that show the α → ω, ω → β, as well as reverse β → ω phase transitions. Simulations with a multi-phase equation of state and phenomenological kinetic model match the experimental wave profiles well. While the dynamic α ! ! transition occurs ~ 9 GPa above the equilibrium phase boundary, the ω → β transition occurs within 0.9 GPa of equilibrium. We estimate that the dynamic compression path intersects the equilibrium ω – β line at P = 29:2 GPa, and T = 490 K. The thermodynamic path in the interior of the sample lies ~ 100 K above the isentrope at the point of the ω → β transition. Approximately half of this dissipative temperature rise is due to plastic work, and half is due to the non-equilibrium α → ω transition. The inferred rate of the α → ω transition is several orders of magnitude higher than that measured in dynamic diamond anvil cell (DDAC) experiments in an overlapping pressure range. We discuss a model for the influence of shear stress on the nucleation rate. We find that the shear stress s ji has the same effect on the nucleation rate as a pressure increase δP = cϵ ij s ji /(ΔV/V); where c is a geometric constant ~ 1 and, ϵ ij are the transformation shear strains. The small fractional volume change ΔV/V ≈ 0:1 at the α → ω transition amplifies the effect of shear stress, and we estimate that for this case δP is in the range of several GPa. Correcting our transition rate to a hydrostatic rate brings it approximately into line with the DDAC results, suggesting that shear stress plays a significant role in the transformation rate.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Boiling and cavitation caused by transient heat transfer in superfluid helium-4

Superfluid helium-4 (He II) has been widely utilized as a coolant in various scientific and engineering applications due to its superior heat transfer capability. An important parameter required in the design of many He II based cooling systems is the peak heat flux $q^*$, which refers to the threshold heat flux above which boiling spontaneously occurs in He II. Past experimental and numerical studies showed that $q^*$ increases when the heating time $t_h$ is reduced, which leads to an intuitive expectation that very high $q^*$ may be achievable at sufficiently small $t_h$. Knowledge on how $q^*$ actually behaves at small $t_h$ is important for applications such as laser ablation in He II. Furthermore we present a numerical study on the evolution of the thermodynamic state of the He II in front of a planar heater by solving the He II two-fluid equations of motion. For an applied heat flux, we determine the heating time beyond which the He II near the heater transits to the vapor phase. As such, a curve correlating $q^*$ and $t_h$ can be obtained, which nicely reproduces some relevant experimental data. Surprisingly, we find that there exists a critical peak heat flux $q^*_c$, above which boiling occurs nearly instantaneously regardless of $t_h$. We reveal that the boiling in this regime is essentially cavitation caused by the combined effects of the first-sound and the second-sound waves in He II. Based on this physical picture, an analytical model for $q^*_c$ is developed, which reproduces the simulated $q^*_c$ values at various He II bath temperatures and hydrostatic head pressures. This work represents a major progress in our understanding of transient heat transfer in He II.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Pressure-temperature phase diagram of CaK ( Fe 1 – x Mn x ) 4 As 4 ( x = 0.024 )

Resistance measurements on single crystals of CaK(Fe 1–x Mn x ) 4 As 4 (x = 0.024) were performed under hydrostatic pressure up to 5.15 GPa. The pressure dependence of the magnetic and superconducting transition temperatures and that of the superconducting upper critical field are reported. Furthermore, our results show that upon increasing pressure, the magnetic transition temperature T N is suppressed, whereas the superconducting transition temperature T c first increases and then decreases, exhibiting a maximum at a pressure p c corresponding to the intersection of the T N (p) and T c (p) lines. In addition, a minimum in the normalized slope of the superconducting upper critical field as well as a change in the pressure dependence of the inferred superconducting coherence length are observed at p c , suggesting a difference in the Fermi surface of the paramagnetic and antiferromagnetic states. Finally, CaK(Fe 1–x Mn x ) 4 As 4 (x = 0.024) likely goes through a half-collapsed tetragonal phase transition at ~4.3 GPa, further demonstrating that the half-collapsed tetragonal transition pressure in the CaKFe 4 As 4 system is relatively insensitive to transition metal substitution.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Localized 𝑓-electron magnetism in the semimetal Ce 3 ⁢ Bi 4 ⁢ Au 3

Ce 3 ⁢Bi 4 ⁢ Au 3 crystallizes in the same noncentrosymmetric cubic structure as the prototypical Kondo insulator Ce 3 ⁢ Bi 4 ⁢Pt 3 . Here we report the physical properties of Ce 3 ⁢Bi 4 ⁢ Au 3 single crystals using magnetization, thermodynamic, and electrical-transport measurements. Magnetic-susceptibility and heat-capacity data reveal antiferromagnetic order below 𝑇 𝑁 =3.2K. The magnetic entropy 𝑆 mag reaches 𝑅⁢ ln⁡ 2 slightly above 𝑇 𝑁 , which suggests localized 4⁢𝑓 moments in a doublet ground state. Multiple field-induced magnetic transitions are observed at temperatures below 𝑇 𝑁 , which indicate a complex spin structure with competing interactions. Ce 3 ⁢Bi 4 ⁢ Au 3 shows semimetallic behavior in electrical resistivity in contrast to the majority of reported cerium-based 343 compounds which are semiconducting. Electrical-resistivity measurements under hydrostatic pressure reveal a slight enhancement of 𝑇 𝑁 under pressures up to 2.3 GPa, which supports a scenario wherein Ce 3 ⁢Bi 4 ⁢Au 3 belongs to the far left of the Doniach phase diagram dominated by Ruderman-Kittel-Kasuya-Yosida interactions. Using realistic many-body simulations, we confirm the semimetallic electronic structure of Ce 3 ⁢Bi 4 ⁢ Au 3 and quantitatively reproduce its local moment behavior in the paramagnetic state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Effects of pressure on the electronic and magnetic properties of bulk NiI 2

Transition metal dihalides have recently garnered interest in the context of two-dimensional van der Waals magnets as their underlying geometrically frustrated triangular lattice leads to interesting competing exchange interactions. In particular, NiI 2 is a magnetic semiconductor that has been long known for its exotic helimagnetism in the bulk. Recent experiments have shown that the helimagnetic state survives down to the monolayer limit with a layer-dependent magnetic transition temperature that suggests a relevant role of the interlayer coupling. Here, we explore the effects of hydrostatic pressure as a means to enhance this interlayer exchange and ultimately tune the electronic and magnetic response of NiI 2 . We study first the evolution of the structural parameters as a function of external pressure using first-principles calculations combined with x-ray diffraction measurements. We then examine the evolution of the electronic structure and magnetic exchange interactions via first-principles calculations and Monte Carlo simulations. Further, we find that the leading interlayer coupling is an antiferromagnetic second-nearest-neighbor interaction that increases monotonically with pressure. The ratio between isotropic third- and first-nearest-neighbor intralayer exchanges, which controls the magnetic frustration and determines the magnetic propagation vector q of the helimagnetic ground state, is also enhanced by pressure. As a consequence, our Monte Carlo simulations show a monotonic increase in the magnetic transition temperature, indicating that pressure is an effective means to tune the magnetic response of NiI 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Designed metal-insulator transition in low-symmetry magnetic intermetallics

Compounds exhibiting half-metallic character and metal-insulator transitions draw considerable attention in condensed-matter and materials physics due to their potential use in spintronics. Here we show that specific electron doping plays a crucial role in tailoring thermodynamic, structural, electronic, and magnetic properties of materials derived from low-symmetry magnetic intermetallics, exemplified on triclinic Mn 4 Al 11 . Upon chemical doping of Al by Ge, we predict improved phase stability and adherence to a generalized “18-n rule” governing closed-shell configurations in intermetallic with narrow bandgaps. Validating experiments include measurements of phase stability and electronic transport properties of electron-doped Mn 4 Al 10 Ge that crystallizes in the Mn 4 Al 11 -type structure, confirming the bandgap opening as predicted by chemical analysis and density-functional theory. Here we also demonstrate theoretically that hydrostatic pressure enhances the predicted half-metallic gap in the up-spin channel, which leads to a ferrimagnetic-to-ferromagnetic transition driven by Mn-Mn charge ordering in the Mn 4 Al 11 parent. We have also discussed the generality of our approach in predicting the design of other classes of intermetallics including half and full Heusler compounds.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Electronic structure and magnetic tendencies of trilayer La 4 Ni 3 O 10 under pressure: Structural transition, molecular orbitals, and layer differentiation

Motivated by the recent observation of superconductivity in the pressurized trilayer Ruddlesden-Popper (RP) nickelate La 4 Ni 3 O 10 , we explore its structural, electronic, and magnetic properties as a function of hydrostatic pressure from first-principles calculations. We find that an orthorhombic (monoclinic)-to-tetragonal transition under pressure takes place concomitantly with the onset of superconductivity. The electronic structure of La 4 Ni 3 O 10 can be understood using a molecular trimer basis wherein n molecular subbands arise as the d z 2 orbitals hybridize strongly along the c axis within the trilayer. The magnetic tendencies indicate that the ground state at ambient pressure is formed by nonmagnetic inner planes and stripe-ordered outer planes that are antiferromagnetically coupled along the c axis, resulting in an unusual ↑, 0, ↓ stacking that is consistent with the spin density wave model previously suggested by neutron diffraction. Such a state is destabilized at the pressure where superconductivity arises. Despite the presence of d z 2 states at the Fermi level, the d x 2 –y 2 orbitals also play a key role in the electronic structure of La4Ni3O10. Finally, this active role of the d x 2 –y 2 states in the low-energy physics of the trilayer RP nickelate, together with the distinct electronic behavior of the inner and outer planes, resembles the physics of multilayer cuprates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Probing quantum criticality in ferromagnetic CeRh 6 Ge 4

CeRh 6 Ge 4 is unusual in that its ferromagnetic transition can be suppressed continuously to zero temperature, i.e., to a ferromagnetic quantum-critical point (QCP), through the application of modest hydrostatic pressure. This discovery has raised the possibility that the ferromagnetic QCP may be of the Kondo-breakdown type characterized by a jump in Fermi volume, to which thermopower S measurements should be sensitive. Further, though S/T changes both sign and magnitude around the critical pressure P c ≈ 0.8 GPa, these changes are not abrupt but extend over a pressure interval from within the ferromagnetic state up to P c . Together with temperature and pressure variations in electrical resistivity and previously reported heat capacity, thermopower results point to the near coincidence of two sequential effects near P c , delocalization of 4f degrees of freedom through orbital-selective hybridization followed by quantum criticality of itinerant ferromagnetism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Effect of Ni substitution on the fragile magnetic system La 5 Co 2 Ge 3

La 5⁢ Co 2 ⁢Ge 3 is an itinerant ferromagnet with a Curie temperature T C of ~3.8K and a remarkably small saturated moment of 0.1µ B /Co. Here we present the growth and characterization of single crystals of the La 5 ⁢(Co 1–x⁢ Ni x ) 2 Ge 3 series for 0.00 ≤ x ≤ 0.186. Here we measured powder x-ray diffraction, composition as well as anisotropic temperature-dependent resistivity, temperature and field-dependent magnetization along with heat capacity on these single crystals. We also measured muon-spin rotation/relaxation (μ⁢SR) for some Ni substitutions (x = 0.027,0.036,0.074) to study the evolution of internal field with Ni substitution. Using the measured data we infer a low temperature, transition temperature-composition phase diagram for La 5 ⁢(Co 1–x ⁢Ni x ) 2 Ge 3 . We find that T C is suppressed for low dopings, x ≤ 0.014; whereas for 0.036 ≤ x ≤ 0.186, the samples are antiferromagnetic with a Néel temperature T N that goes through a weak and shallow maximum (T N ~ 3.4K for x~0.07) and then gradually decreases to 2.4 K by x = 0.186. For intermediate Ni substitutions, 0.016 ≤ x ≤ 0.027, two transition temperatures are inferred with T N >T C . Whereas the T–x phase diagram for La 5 ⁢(Co 1–x ⁢Ni x ) 2 Ge 3 and the T–p phase diagram determined for the parent La 5 ⁢Co 2 ⁢Ge 3 under hydrostatic pressure are grossly similar, changing from a low-doping or low-pressure ferromagnetic (FM) ground state to a high-doped or high-pressure antiferromagnetic (AFM) state, perturbation by Ni substitution enabled us to identify an intermediate doping regime where both FM and AFM transitions occur.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Anomalous elastic softening in ferroelectric hafnia under pressure

his study employs first-principles density-functional theory (DFT) calculations to explore the elastic and mechanical properties of ferroelectric hafnia (HfO 2 ) in its polar orthorhombic 𝑃⁢𝑐⁢𝑎⁢2 1 phase under varying hydrostatic pressure conditions up to 30 GPa. Utilizing a plane-wave basis set and Perdew-Burke-Ernzerhof generalized-gradient approximation for solids in our DFT calculations, we investigate both pure and yttrium-substituted HfO 2 . Our findings reveal an anomalous reduction in the 𝐶 33 component of the elastic tensor with increasing pressure, which becomes significant above 15 GPa and signals a potential pressure-driven structural phase transition at higher pressure. The analysis of atomic displacements under pressure sheds light on the unusual mechanical behavior and phase stability of this material. Additionally, we observe a transition from an indirect band gap to a direct band gap with increasing pressure, which could have significant implications for optical applications. Here, the effects of yttrium substitution on the mechanical and electronic properties are further examined, revealing that yttrium substitution softens the elastic response of this material and reduces the electronic band gap. These results enhance our understanding of elastic and mechanical responses of ferroelectric hafnia and its potential for applications in microelectronics, piezoelectric devices, and nonvolatile ferroelectric random-access memories. Further experimental validation is recommended to confirm our predictions and explore the practical implications of the observed phase transitions and electronic behavior of the ferroelectric hafnia under high-pressure conditions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Gravothermal phase transition, black holes and space dimensionality

In the framework of gravothermal evolution of an ideal monatomic fluid, I examine the dynamical instability of the fluid sphere in (N+1) dimensions by exploiting Chandrasekhar’s criterion to each quasi-static equilibrium along the sequence of the evolution. Once the instability is triggered, it would probably collapse into a black hole if no other interaction halts the process. From this viewpoint, the privilege of (3+1)-dimensional spacetime is manifest, as it is the marginal dimensionality in which the ideal monatomic fluid is stable but not too stable. Moreover, it is the unique dimensionality that allows stable hydrostatic equilibrium with positive cosmological constant. While all higher dimensional (N > 3) spheres are genuinely unstable. In contrast, in (2+1)-dimensional spacetime it is too stable either in the context of Newton’s theory of Gravity or Einstein’s General Relativity. It is well-known that the role of negative cosmological constant is crucial to have the Banados-Teitelboim-Zanelli (BTZ) black hole solution and the equilibrium configurations of a fluid disk. Owing to the negativeness of the cosmological constant, there is no unstable configuration for a homogeneous fluid disk to collapse into a naked singularity, which supports the Cosmic Censorship Conjecture. However, BTZ holes of mass M BTZ > 0 could emerge from collapsing fluid disks. The implications of spacetime dimensionality are briefly discussed.

79 ASTRONOMY AND ASTROPHYSICS↗

Robust Quantum Hall Ferromagnetism near a Gate-Tuned ν = 1 Landau Level Crossing

In a low-disorder two-dimensional electron system, when two Landau levels of opposite spin or pseudospin cross at the Fermi level, the dominance of the exchange energy can lead to a ferromagnetic, quantum Hall ground state whose gap is determined by the exchange energy and has skyrmions as its excitations. This is normally achieved via applying either hydrostatic pressure or uniaxial strain. Here, we study here a very high-quality, low-density, two-dimensional hole system, confined to a 30-nm-wide (001) GaAs quantum well, in which the two lowest-energy Landau levels can be gate tuned to cross at and near filling factor v = 1. As we tune the field position of the crossing from one side of v = 1 to the other by changing the hole density, the energy gap for the quantum Hall state at v =1 remains exceptionally large, and only shows a small dip near the crossing. The gap overall follows a $\sqrt{B}$ dependence, expected for the exchange energy. Our data are consistent with a robust quantum Hall ferromagnet as the ground state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Nodeless kagome superconductivity in LaRu 3 Si 2

We report muon spin rotation (μSR) experiments together with first-principles calculations on microscopic properties of superconductivity in the kagome superconductor LaRu 3 Si 2 with T c ≃ 7K. Below Tc, μSR reveals type-II superconductivity with a single s-wave gap, which is robust against hydrostatic pressure up to 2 GPa. We find that the calculated normal state band structure features a kagome flat band, and Dirac as well as van Hove points formed by the Ru-dz 2 orbitals near the Fermi level. We also find that electron-phonon coupling alone can only reproduce a small fraction of T c from calculations, which suggests other factors in enhancing T c such as the correlation effect from the kagome flat band, the van Hove point on the kagome lattice, and the high density of states from narrow kagome bands. Our experiments and calculations taken together point to nodeless moderate coupling kagome superconductivity in LaRu 3 Si 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Vacancy-mediated transport and segregation tendencies of solutes in fcc nickel under diffusional creep: A density functional theory study

The Nabarro-Herring (NH) diffusional creep theory postulates the vacancy-mediated transport of atoms under a stress gradient as the creep mechanism under low-stress and high-temperature conditions. In multicomponent alloys, we premise that this stress-assisted flow of vacancies to and from grain boundaries will produce elemental segregation. An observation of such segregation, validated with theoretical predictions, can provide the necessary experimental evidence for the occurrence of NH creep. Theoretical calculations of the segregation tendencies via analyzing the dominant solute diffusion mechanisms and the difference in diffusivities of the elements are therefore essential. To this end, this study applies density functional theory calculations of migration barriers and solute-vacancy binding energies as input to the self-consistent mean-field theory to assess the vacancy-mediated diffusion mechanisms, transport coefficients, and segregation tendencies of Co, Cr, Mo, Re, Ta, and W solutes in face-centered-cubic Ni. We find Co, Re, and W to be slow diffusers at high temperatures and Cr, Mo, and Ta to be fast diffusers. Further analysis shows that the slow diffusers tend to always enrich at vacancy sinks over a wide range of temperatures. In contrast, the fast diffusers show a transition from depletion to enrichment as the temperature lowers. Furthermore, our analysis of the segregation tendencies under tensile hydrostatic strains shows that slow diffusers are largely unaffected by the strain and favor enrichment. On the other hand, the fast diffusers exhibit high sensitivity to strain and their segregation tendency can transition from depletion to enrichment at a given temperature. Finally, the transport coefficients calculated in this work are expected to serve as input to mesoscale microstructure models to provide a more rigorous assessment of solute segregation under NH creep conditions.

36 MATERIALS SCIENCE↗

Republished: Colossal density-driven resistance response in the negative charge transfer insulator MnS 2

The Mn chalcogenides show a remarkable variation in structural and physical properties with density. In MnS 2 we observe a pronounced difference with the effects of varying hydrostaticity with pressure inducing a structural transition at 300 K. Within the pyrite phase, a colossal electrical resistance drop of 10 8 Ohms is observed by 12 GPa of nonhydrostatic compression at 300 K. DFT simulations reveal the metallization to be unexpectedly driven by previously unoccupied S$^{2-}_2$ σ$^*_{3p}$ antibonding states crossing the Fermi level. This is a seldom seen variant of the charge transfer insulator to metal transition for negative charge transfer insulators which have anions with an unsaturated valence. Finally, by 36 GPa of nonhydrostatic compression, the single presence of the low-spin insulating arsenopyrite (P2 1 /c) phase is confirmed, and the bulk metallicity is broken with the system returning to an insulative electronic state.

36 MATERIALS SCIENCE↗

Pressure-Induced Superconductivity In Polycrystalline La 3 Ni 2 O 7 − δ

We synthesized polycrystalline La 3 Ni 2 O 7 − δ ( δ ≈ 0.0 7 ) samples by using the sol-gel method without postannealing under high oxygen pressure, and then measured temperature-dependent resistivity under various hydrostatic pressures up to 18 GPa by using the cubic anvil and two-stage multianvil apparatus. We find that the density-wave-like anomaly in resistivity is progressively suppressed with increasing pressure and the resistivity drop corresponding to the onset of superconductivity emerges at pressure as low as ∼ 6 GPa . Zero resistivity is achieved at 9 GPa below T c zero ≈ 6.6 K , which increases quickly with pressure to 41 K at 18 GPa. However, the diamagnetic response was not detected in the ac magnetic susceptibility measurements up to 15 GPa, indicating a filamentary nature of the observed superconductivity in the studied pressure range. The constructed T − P phase diagram reveals an intimate relationship between superconductivity, density-wave-like order, and the strange-metal-like behaviors. The observation of zero-resistance state in the polycrystalline La 3 Ni 2 O 7 − δ samples under high pressures not only corroborates the recent report of superconductivity in the pressurized La 3 Ni 2 O 7 crystals but also facilitates further studies on this emerging family of nickelate high- T c superconductors. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗