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DOE OSTI2020

Clathrate XI K 58 Zn 122 Sb 207 : A New Branch on the Clathrate Family Tree

Abstract The compositional screening of K‐Zn‐Sb ternary system aided by machine learning, rapid exploratory synthesis using KH salt‐like precursor and in situ powder X‐ray diffraction yielded a novel clathrate type XI K 58 Zn 122 Sb 207 . This clathrate consists of a 3D Zn‐Sb framework hosting K + ions inside polyhedral cages, some of which are reminiscent of known clathrate types while others are unique to this structure type. The complex non‐centrosymmetric structure in the tetragonal space group was solved by means of single crystal X‐ray diffraction as a 6‐component twin due to pseudocubic symmetry and further confirmed by high‐resolution synchrotron powder X‐ray diffraction and state‐of‐the‐art scanning transmission electron microscopy. The electron‐precise composition of this clathrate yields narrow‐gap p ‐type semiconductor with extraordinarily low thermal conductivity due to displacement or “rattling” of K cations inside oversized cages and as well as to twinning, stacking faults and antiphase boundary defects.

Cox, Tori↗

DOE OSTI2020

Clathrate XI K 58 Zn 122 Sb 207 : A New Branch on the Clathrate Family Tree

Cox, Tori↗

DOE OSTI2024

Electrochemical and Optical Spectroscopic Probing of Transition–Sized Au 130 (SR) 50 Nanoclusters

Ultrasmall metal nanoclusters (NCs) exhibit a quantized conduction band, hence, a distinct HOMO-LUMO gap (E g ). Such a quantized electronic structure gives rise to multiple discrete peaks in the optical absorption spectrum of the NCs. As the size grows to 130 gold atoms (Au 130 protected by ligands), electrical charging and optical behaviors seem to show certain metal-like features (hence, transition-sizes). To probe such behaviors, especially the potential ligand effect, we have devised the synthesis of Au 130 NCs protected by phenylethanethiolate and naphthalenethiolate, respectively, with the former having a nonconjugated separation between the aromatic molecular group and the metal core while the latter being in direct bonding. A careful comparison of these two Au 130 nanoclusters with the earlier reported analogues is carried out, including the structurally characterized Au 130 (pMBT) 50 and the aqueous counterpart. While all of these nanoclusters possess the same 80 free electron counts in the core, some notable differences in electrochemical and optical properties are found, which are attributed to the ligand effects. The obtained insights may stimulate further interest in the transition-sized nanoclusters and also promote their applications in optics, energy conversion, and biomedicine.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Monte Carlo Explicitly Correlated Second-Order Many-Body Green’s Function Calculations of Semiconductor Band Gaps

A systematically converging series of ab initio, post-density-functional, size-consistent, electron-correlated approximations is desired for predictive computing of felectronic band structures of insulating, semiconducting, and metallic solids. A series that meets all of these desiderata (except the applicability to metals) is ab initio many-body Green's function theory based on Gaussian-type-orbital (GTO) basis sets. Here, its leading-order approximation, the second-order Green's function (GF2) method in the diagonal and frequency-independent approximations with the aug-cc-pVDZ basis set, is applied to the fundamental band gaps of three semiconductors (diamond, silicon, and silicon carbide in the zincblende structure) using cluster models. Corrections are made to the basis-set-incompleteness errors by the explicit-correlation (F12) ansatz (GF2-F12) for the valence band edges. The crystals are modeled as surface-passivated clusters of increasing sizes, whose wave functions are expanded by up to 2709 GTO basis functions. Immense computational costs of these calculations are overcome by the highly scalable stochastic algorithm of the Monte Carlo GF2-F12 method, whose operation cost per state increases only as a cubic power of system size, which has a tiny memory footprint and easily achieves near-perfect parallel efficiency on thousands of CPUs or on hundreds of GPUs. The correlated, F12-corrected highest-occupied and lowest-unoccupied molecular-orbital energy (HOMO-LUMO) gap is 5.78 ± 0.07 eV for C 87 H 76 as compared with the experimental value of the fundamental (indirect) band gap of bulk diamond at 5.48 eV. The correlated, F12-corrected HOMO-LUMO gaps for Si 75 H 76 and Si 32 C 43 H 76 are 2.56 ± 0.15 eV and 3.50 ± 0.12 eV, respectively, which are expected to decrease further with increasing cluster sizes. As a result, the experimental fundamental (indirect) band gaps of bulk silicon and silicon carbide are 1.17 eV and 2.42 eV, respectively.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Colloidal AInSe 2 (A = K, Rb, Cs) Nanocrystals with Tunable Crystal and Band Structures

Wide band gap AInSe 2 (A = K, Rb, Cs) is an important interlayer material for improving the efficiency of Cu(In,Ga)(S,Se) 2 (CIGS) solar cells. Compared to high-vacuum deposition and solid-state synthesis, a less energyintensive method is of interest for its fabrication. Herein, we present the rapid, low-temperature colloidal synthesis of AInSe 2 nanocrystals that opens a pathway for convenient solution processing. The crystal structures and electronic band structures of the nanocrystals were studied, and their particle morphology was found to be dependent on the choice of alkali metal and selenium precursors. Homogeneous solid solution (K,Rb,Cs)InSe 2 nanocrystals were synthesized using a mixture of alkali metal precursors. Their compositions, lattice parameters, and band gaps were easily tuned based on the K:Rb:Cs precursor ratio, providing potential for interface engineering of CIGS nanocrystal-based solar cells.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Possible Spin-Triplet Excitonic Insulator in the Ultraquantum Limit of HfTe 5

More than 50 years ago, excitonic insulators formed by the pairing of electrons and holes due to Coulomb interactions were first predicted [A. N. Kozlov and L. A. Maksimov, Sov. J. Exp. Theor. Phys. 21, 790 (1965); L. V. Keldysh and Y. V. Kopaev, Sov. Phys. Solid State 6, 2219 (1965); D. Jérome, T. M. Rice, and W. Kohn, Phys. Rev. 158, 462 (1967)]. Since then, excitonic insulators have been observed in various classes of materials, including quantum Hall bilayers, graphite, transition metal chalcogenides, and more recently in moiré superlattices. In these excitonic insulators, an electron and a hole with the same spin bind together, and the resulting exciton is a spin singlet. Here, we report the experimental observation of a spin-triplet excitonic insulator in the ultra-quantum limit of a three-dimensional topological material HfTe 5 . We observe that the spin-polarized zeroth Landau bands dispersing along the field direction cross each other beyond a characteristic magnetic field in HfTe 5 , forming the one-dimensional Weyl mode. Transport measurements reveal the emergence of a gap of about 2⁢5⁢0 μ⁢eV when the field surpasses a critical threshold. By performing the material-specific modeling, we identify this gap as a consequence of a spin-triplet exciton formation, where electrons and holes with opposite spin form bound states, and the translational symmetry is preserved. The system reaches charge neutrality following the gap opening, as evidenced by the zero Hall conductivity over a wide magnetic field range (10–72 T). In conclusion, our finding of the spin-triplet excitonic insulator paves the way for studying novel spin transport including spin superfluidity, spin Josephson currents, and Coulomb drag of spin currents in analogy to the transport properties associated with the layer pseudospin in quantum Hall bilayers.

36 MATERIALS SCIENCE↗

DOE OSTI2021

In 2 O 3 -Ga 2 O 3 Alloys as Potential Buffer Layers in CdTe Thin-Film Solar Cells

The efficiency of state-of-the-art Cd Te solar cells remains limited by the relatively low open-circuit voltage (V OC ). Improving the front interface is key towards realizing a higher V OC after achieving the necessary bulk carrier density and lifetime. Recent efforts in identifying buffer layers beyond Cd S have focused on Mg x Zn 1-x O, which offers tunability of the band offsets, but often suffers from high interfacial defect densities. Ga 2 O 3 -based buffer layers demonstrate tremendous improvements in interfacial defect passivation in crystalline silicon and dye-sensitized solar cells, leading to record high V OC , yet remain largely unexplored in Cd Te-based devices. Here, we perform hybrid density-functional-theory calculations to investigate pure Ga 2 O 3 and InGaO 3 alloys as a window layer in Cd Te photovoltaics. We report calculated band offsets for several pairs of solid-solid interfaces comprising transparent conducting oxide (TCO) and Cd Te heterojunctions. The results support a large conduction band offset spike of 0.67 eV for the Cd Te/Ga 2 O 3 (100) interface, while the offset is reduced to 0.18 eV for the InGaO 3 alloy and matches closely with the preferred optimum value of 0.2 eV. Device-level modeling tests of Cd Te solar cells integrating our results indicate that the highest efficiency is achieved with InGaO 3 acting both as a buffer layer and TCO. Finally, our results suggest that alloys of In 2 O 3 and Ga 2 O 3 may be attractive alternatives to Mg x Zn 1-x O for tailoring optimal conduction-band offsets of the buffer and TCO layers in high-efficiency Cd Te thin-film solar cells.

14 SOLAR ENERGY↗

DOE OSTI2020

Tunneling spectroscopy of c -axis epitaxial cuprate junctions

Atomically precise epitaxial structures are unique systems for tunneling spectroscopy that minimize extrinsic effects of disorder. We present a systematic tunneling spectroscopy study, over a broad doping, temperature, and bias range, in epitaxial c-axis La 2-x Sr x CuO 4 /La 2 CuO 4 /La 2-x Sr x CuO 4 heterostructures. The behavior of these superconductor/insulator/superconductor (SIS) devices is unusual. Down to 20 mK there is complete suppression of c-axis Josephson critical current with a barrier of only 2 nm of La 2 CuO 4 , and the zero-bias conductance remains at 20–30% of the normal-state conductance, implying a substantial population of in-gap states. Tunneling spectra show greatly suppressed coherence peaks. Furthermore, as the temperature is raised, the superconducting gap fills in rather than closing at T c . For all doping levels, the spectra show an inelastic tunneling feature at ~80 meV, suppressed as T exceeds T c . These nominally simple epitaxial cuprate junctions deviate markedly from expectations based on the standard Bardeen-Cooper-Schrieffer theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Migration of Ga vacancies and interstitials in β – Ga 2 O 3

Pathways and energy barriers for the migration of Ga vacancies (V Ga ) and Ga interstitials (Ga i ) in β–Ga 2 O 3 are explored using hybrid functional calculations and the nudged elastic band method. Considering β–Ga 2 O 3 as primarily being an n-type semiconductor, we focus on defect charge states relevant under such conditions: $V^{3 –}_{Ga}$, Ga$^{3+}_{i}$, and Ga$^{+}_{i}$. Notably, we describe a mechanism by which V Ga can transform between its different split configurations. In all cases, the intermediate state consists of a vacancy split between three Ga sites—a three-split vacancy—which enables passage over a significantly lower energy barrier. This is because it avoids the unfavorable simple vacancy at the tetrahedral Ga site. The proposed mechanism lowers the overall barrier for $V^{3–}_{Ga}$ diffusion along the [001] crystal direction from 1.73 to 0.97 eV, whereas the 2.08 eV barrier for the [100] and [010] directions is unaffected. For Ga$^{3+}_{i}$, we obtain similar overall migration barriers of 0.72, 0.80, and 1.02 eV for the [010], [001], and [100] directions, respectively. Ga$^{+}_{i}$ exhibits a strong preference for diffusion within the large eight-sided channel; the overall migration barrier is 0.92 eV for the [010] direction, and 2.16 eV for the [001] and [100] directions. The limiting step for the two latter directions involves ionization of Ga$^{+}_{i}$ followed by a jump to an adjacent large eight-sided channel as Ga$^{3+}_{i}$. Finally, our results are discussed in light of experimental observations of thermally activated recovery processes in irradiated material.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Plasmons in Z 2 topological insulators

Here, we study plasmonic excitations in the Kane-Mele model, a two-dimensional Z 2 topological insulator on the honeycomb lattice, using the random phase approximation (RPA). In the topologically nontrivial phase, the model has conducting edge states that traverse the bulk energy gap and display spin-momentum locking. Such a state of matter is called the quantum spin hall (QSH) phase, which is robust against time-reversal (TR) invariant perturbations. We find that in the QSH phase, gapless spin-polarized plasmons can be excited on the edges of the system. The propagation of these plasmons is chiral for each individual spin component and shows spin-momentum locking for both spin components on the same edge. Moreover, we study the effect of external magnetic fields on the gapless edge plasmons. Specifically, out-of-plane magnetic fields delocalize edge plasmons propagating in one direction without affecting the other one, while an in-plane magnetic field can be applied to selectively excite a specific spin-plasmon branch with proper doping or gating to the system. Our findings may have potential applications in novel plasmonic and spintronic devices. We also investigate plasmons in the Kane-Mele model on a finite-sized diamond-shaped nanoflake and observe low-energy plasmons circulating the boundary of the material.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Dynamics of dust particles confined in imposed potential structures in strongly magnetized, low-temperature plasmas

A new phenomenon called imposed ordered structures has been of particular interest to the dusty plasma community within the past several years. These structures are a new type of pattern formation within a dusty plasma in which the dust particles become fixed to a background confining potential whose spatial structure is determined by some conducting element present in the plasma. In previous works, this element has typically been a conducting wire mesh. One of the unanswered questions is whether the dust particles become trapped beneath the conducting surface of the mesh or in the gaps (holes) between the wires. This work makes use of a new electrode whose shape is designed to mimic that of wire mesh, but with much larger dimensions to facilitate in situ diagnostic measurements. Observations of the dust show that particles become confined to the regions beneath the holes of this new electrode. Measurements of the dust particle velocities allow for a determination of the kinetic energy within the dust cloud which show that the particles are in an energetic steady state. Further, comparisons of spatial profiles of the particle velocities also show that the dust particles typically reside in areas of increased plasma glow, possibly being trapped by plasma filaments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Unraveling the transformation pathway of the 𝛽 to 𝛾 phase transition in Ga 2 ⁢O 3 from atomistic simulations

Defect spinel 𝛾−Ga 2 ⁢O 3 is the least stable polymorph of Ga 2 ⁢O 3 , so its frequent appearance as a structural defect within or on the surface of monoclinic 𝛽−Ga 2 ⁢O 3 remains a mystery. Through first-principles calculations, we explore potential pathways for the phase transition from 𝛽−Ga 2⁢ O 3 to 𝛾−Ga 2 ⁢O 3 , and examine two key driving forces: tensile strain and Ga deficiency. When configurational entropy contributions to phase energies are included, the 𝛾 phase becomes energetically competitive with the 𝛽 phase, with the free energy difference between these phases diminishing even further under Ga-deficient conditions. Notably, a stability crossover occurs at room temperature at high vacancy concentrations ([V$^{3−}_{Ga}$]>3%) . A simple model 𝛽 → 𝛾 transformation pathway is identified, comprising two primary reactions, that enables the formation of the 𝛾 phase via simultaneous migration of Ga atoms from tetrahedral lattice sites to octahedral interstitial positions. The transformation barriers are prohibitively large in pristine Ga 2 ⁢O 3 , but can be substantially reduced by: (1) the presence of Ga vacancies, (2) elongational strains along the crystallographic 𝑎-axis, and (3) when volumetric relaxations are possible during transformation. These results elucidate prior experimental observations, where 𝛾−Ga 2⁢ O 3 is seen on damaged surfaces or in highly 𝑛-type 𝛽−Ga 2⁢ O 3 environments, which support Ga deficiency and mechanical strain. The insights into the driving forces and mechanisms of 𝛾−Ga 2⁢ O 3 formation enhance understanding of how localized strain and nonequilibrium defect concentrations may facilitate its formation from the 𝛽 phase.

Defects↗

DOE OSTI2023

Transmission Optimization with Grid Enhancing Technologies Fact Sheet

The Transmission Optimization with Grid Enhancing Technologies (TOGETs) project is funded by the Department of Energy (DOE) Office of Electricity (OE) and Wind Energy Technologies Office (WETO). Idaho National Laboratory’s TOGET Task force consists of regulatory, utility, system operator, vendor, academic, and other industry participants, who will guide a two-pronged approach to fill in gaps on publicly available knowledge of GETs and conduct a full scale, multi-faceted field exercise. Ultimately the project aims to test, verify, and validate deployed GETs in a transmission system.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Phase Stability, Band Gap Tuning, and Rashba Splitting in Selenium-Alloyed Bournonite: CuPbSb(S 1– x Se x ) 3

Recently, bournonite (CuPbSbS 3 ) has been identified as a potential ferroelectric photovoltaic (PV) material with a 1.3 eV band gap, which falls in an appropriate range for single junction PV devices. Progress in applying bournonite has yielded several studies reporting successful thin-film processing, the most recent of which demonstrated a 2.65% power conversion efficiency for a bournonite-based PV device. In an effort to explore bournonite band gap engineering for PV and other prospective applications (e.g., thermoelectric, spintronic), we here consider the solid-state synthesis of selenium-alloyed bournonite, CuPbSb(S 1-x Se x ) 3 , across the full range of x (0.0 ≤ x ≤ 1.0), and report phase purity for 0.0 ≤ x ≤ 0.5. We characterize the crystal structure and band gap of the samples using X-ray diffraction and diffuse reflectance spectroscopy, determining a band gap decrease for single-phase samples from 1.25 eV at x = 0.0 to 1.06 eV at x = 0.5. Formation energies determined using dispersion corrected hybrid density functional theory (DFT) support experimental findings and are consistent with the stability (instability) of the x = 0.5 (x = 1.0) structure relative to starting materials. The computed band structures show a decreasing trend in the band gap with increasing x, again consistent with experiment, with the states at the conduction (valence) band minima (maxima) being principally derived from Pb (S/Se) states. Spin texture analysis and detailed comparison of spin splitting parameters show that Se-alloying modifies the band gap while maintaining Rashba spin splitting character within the electronic structure. Rashba splitting is most pronounced for the conduction band minimum along the Γ-X path in the Brillouin zone. Energy separation between spin states is maintained at ΔE~0.2 eV for the various Se contents, with σz as the spin direction. Furthermore, a smaller spin splitting occurs along Γ-Z (decreasing value with increasing x), with σ x as the spin direction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Statistical Analysis of Intertube Tunneling Contacts in the Macroscopic Electrical Conductivity of Carbon Nanotube Fibers

Here, this study investigates the influence of tunneling contact resistances between carbon nanotubes (CNTs) on electron transport and electrical conductivity of macroscopic carbon nanofibers (CNFs), which profoundly impacts the performance of CNT thin film electronics, CNF electron emitters and cathodes, and energy conversion and storage devices. Utilizing a self-consistent electrical contact model coupling a transmission line model with tunneling current, we calculate the contact resistances of a plethora of CNT-CNT contacts within a CNF fiber, which consists of aligned, densely packed CNTs. A statistical analysis is conducted, using Gaussian distributions to account for variations in contact lengths, tunneling gap distances, and single CNT aspect ratios, to calculate the CNT-CNT contact resistance and the overall resistance of CNT fiber. By scaling our model to a macroscopic level, our results are in good agreement with experimental measurements. Our calculation suggests that while increasing the contact overlap length diminishes individual CNT-CNT contact resistance, it could paradoxically increase macroscopic CNT fiber resistance for a given constant CNF mass density, which is due to that fact that a larger overlap length allows more CNTs to pack along an electrical conduction path per unit length, leading to more tunneling contact junctions connected in series and thus less number of parallel conduction paths within the fiber cross section. Increasing tunneling gap distance increases both individual contact and overall fiber resistance. This research provides a simple design tool for tailoring CNT fiber electrical properties to promote real-world applications using CNTs or similar low-dimensional materials.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Emergent mystery in the Kondo insulator samarium hexaboride

Samarium hexaboride (SmB 6 ) is an example of a Kondo insulator, in which strong electron correlations cause a band gap to open. SmB 6 hosts both a bulk insulating state and a conductive surface state. Within a Fermi-liquid framework, the strongly correlated ground-state electronic structure can be mapped to a simple state resembling a topological insulator. Although uncertainties remain, many experiments provide compelling evidence that the conductive surface states have a topological origin. However, the bulk behavior is less well understood and some experiments indicate bulk in-gap states. This has inspired the development of many theories that predict the emergence of new bulk quantum phases beyond Landau’s Fermi-liquid model. We review the current progress on understanding both the surface and the bulk states, especially the experimental evidence for each. A mystery centres on the existence of the bulk in-gap states and why they appear in some experiments but not others. Adding to the mystery is why quantum oscillations in SmB6 appear only in magnetization but not in resistivity. Here, we conclude by elaborating on three questions: why SmB 6 is worth studying, what can be done to move forwards and what other correlated insulators could give additional insight.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Gas-Gap Calorimeter Sizing and Rating Tools for Heat Pipe Experimentation

Effective gas-gap calorimeter sizing and rating tools are required to design calorimeters that enable well-defined operating conditions, high cooling powers, and accurate calorimetry. The present report describes two tools utilizing Microsoft Excel and MathWorks MATLAB that enable the sizing and rating of gas-gap calorimeters with a He-Ar binary gas mixture in the gap. The Excel tools are two easy-to-use spreadsheets for calculating heat pipe operating temperature or He-Ar mole fractions given the required inputs. The MATLAB tool includes similar models with more robust solution algorithms along with sub-options for full-vacuum, static gas-gap, and forced circulation in the gas-gap. The accuracy of the developed tools were demonstrated by comparing with existing work in literature. The MATLAB tool was used for a parametric study to determine the gas-gap thickness, coolant gap thickness, coolant flow rate, and coolant inlet temperatures for the testing of a 3/4 in outer diameter heat pipe up to powers of 10 kW and temperatures of 1,000°C. The effects of heat pipe and calorimeter inner shell surface emissivities were investigated, considering the inability to control or accurately measure surface emissivities in most applications. It was found that controlling the He-Ar mole fractions provides a wide operating range for gas-gap thicknesses around ~ 0.042--0.090 in (~ 1.07--2.29 mm) for a surface emissivity range of 0.4--0.8, since conduction heat transfer is a significant fraction of the heat transfer across the gas-gap. In addition, it was found that turbulent flow in the coolant gap is needed at high input powers to prevent shell temperatures from approaching the boiling temperature of the water coolant. The parametric study resulted in choosing stainless steel tubes with an outer diameter and thickness of 1 x 0.065 in as the inner shell, and a 1-1/2 x 0.156 in as the outer shell of the calorimeter. Overall, this report presents the necessary information for the sizing and rating of gas-gap calorimeters with He-Ar mixtures for the testing of high-temperature heat pipes (~ 500--1,000°C).

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Predicting band gaps and band-edge positions of oxide perovskites using density functional theory and machine learning

Density functional theory (DFT) within the local or semilocal density approximations, i.e., the local density approximation (LDA) or generalized gradient approximation (GGA), has become a workhorse in the electronic structure theory of solids, being extremely fast and reliable for energetics and structural properties, yet remaining highly inaccurate for predicting band gaps of semiconductors and insulators. The accurate prediction of band gaps using first-principles methods is time consuming, requiring hybrid functionals, quasiparticle GW, or quantum Monte Carlo methods. Efficiently correcting DFT-LDA/GGA band gaps and unveiling the main chemical and structural factors involved in this correction is desirable for discovering novel materials in high-throughput calculations. In this direction, we, in this study, use DFT and machine learning techniques to correct band gaps and band-edge positions of a representative subset of ABO 3 perovskite oxides. Relying on the results of HSE06 hybrid functional calculations as target values of band gaps, we find a systematic band-gap correction of ~1.5 eV for this class of materials, where ~1 eV comes from downward shifting the valence band and ~0.5 eV from uplifting the conduction band. The main chemical and structural factors determining the band-gap correction are determined through a feature selection procedure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗