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DOE OSTI2023

Deep Learning for Multigroup Cross-Section Representation in Two-Step Core Calculations

Here we investigate using deep learning, a type of machine-learning algorithm employing multiple layers of artificial neurons, for the mathematical representation of multigroup cross sections for use in the Griffin reactor multiphysics code for two-step deterministic neutronics calculations. A three-dimensional fuel element typical of a high-temperature gas reactor as well as a two-dimensional sodium-cooled fast reactor lattice are modeled using the Serpent Monte Carlo code, and multigroup macroscopic cross sections are generated for various state parameters to produce a training data set and a separate validation data set. A fully connected, feedforward neural network is trained using the open-source PyTorch machine-learning framework, and its accuracy is compared against the standard piecewise linear interpolation model. Additionally, we provide in this work a generic technique for propagating the cross-section model errors up to the k eff using sensitivity coefficients with the first-order uncertainty propagation rule. Quantifying the eigenvalue error due to the cross-section regression errors is especially practical for appropriately selecting the mathematical representation of the cross sections. We demonstrate that the artificial neural network model produces lower errors and therefore enables better accuracy relative to the piecewise linear model when the cross sections exhibit nonlinear dependencies; especially when a coarse grid is employed, where the errors can be halved by the artificial neural network. However, for linearly dependent multigroup cross sections as found for the sodium-cooled fast reactor case, a simpler linear regression outperforms deeper networks.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Searching for Phase Transitions in Artificial Kagome Spin Ice

Artificial Kagome spin ice is a metasurface consisting of small islands of polarizable magnets. These islands can be oriented by an external magnetic field applied in the same plane as the metasurface. By subsequently applying a relatively weaker field in the opposite direction of the initial field, a portion of the magnets in the lattice can be repolarized or “flipped” the other way. These flips cause instabilities in a previously uniformly aligned lattice, causing the system to interact with itself and induce changes in the overall magnetization of the metasurface. This Summer, my goal was to use this phenomenon to discern whether or not these systems could undergo a phase transition caused only by the initial change of the external magnetic field. Based on previous datasets that indicated that such a transition was observable, my task was to find and reproduce this potential phenomena. This process was conducted by repeating measurements on the system by using an external magnet to align the spin ice and then using Magnetic Force Microscopy (MFM) to probe the surface of the material to understand the changes in the magnetization over time. This report will discuss the characteristics of artificial Kagome spin ice, the methodology used to induce phase transitions, and the image processing methods used to understand the results. Although no reproducible evidence of a phase transition was found during the Summer, we were able to successfully reproduce short-term responses in the spin ice, as well as plot a hysteresis curve of the material.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2025

AI-powered exploration of molecular vibrations, phonons, and spectroscopy

The vibrational dynamics of molecules and solids play a critical role in defining material properties, particularly their thermal behaviors. However, theoretical calculations of these dynamics are often computationally intensive, while experimental approaches can be technically complex and resource-demanding. Recent advancements in data-driven artificial intelligence (AI) methodologies have substantially enhanced the efficiency of these studies. This review explores the latest progress in AI-driven methods for investigating atomic vibrations, emphasizing their role in accelerating computations and enabling rapid predictions of lattice dynamics, phonon behaviors, molecular dynamics, and vibrational spectra. Key developments are discussed, including advancements in databases, structural representations, machine-learning interatomic potentials, graph neural networks, and other emerging approaches. Compared to traditional techniques, AI methods exhibit transformative potential, dramatically improving the efficiency and scope of research in materials science. The review concludes by highlighting the promising future of AI-driven innovations in the study of atomic vibrations.

Han, Bowen [Oak Ridge National Laboratory (ORNL), ↗

DOE OSTI2021

Application of Dislocation Theory to Minimize Defects in Artificial Solids Built with Nanocrystal Building Blocks

Conspectus. Oriented atomic attachment of colloidal inorganic nanocrystals represents a powerful synthetic method for preparing complex inorganic superstructures. Examples include fusion of nanocrystals into dimer and superlattice structures. If the attachment were perfect throughout, then the resulting materials would have single crystal-like alignment of the individual nanocrystals' atomic lattices. While individual colloidal nanocrystals typically are free of many defects, there are a multitude of pathways that can generate defects upon nanocrystal attachment. These attachment generated defects are typically undesirable, and thus developing strategies to favor defect-free attachment or heal defective interfaces are essential. There may also be some cases where attachment-derived defects are desirable. In this Account, we summarize our current understanding of how these defects arise, in order to offer guidance to those who are designing nanocrystal derived solids. The small size of inorganic nanocrystals means short diffusion lengths to the surface, which favor the formation of nanocrystal building blocks with pristine atomic structures. Upon attachment, however, there are numerous pathways that can lead to atomic scale defects, and bulk crystal dislocation theory provides an invaluable guide to understanding these phenomena. As an example, an atomic step edge can be incorporated into the interface leading to an extra half-plane of atoms, known as an edge dislocation. These dislocations can be well described by the Burgers vector description of dislocations, which geometrically identifies planes in which a dislocation can move. Our in situ measurements have verified that bulk dislocation theory predictions for 1D defects hold true at few-nanometer length scales in PbTe and CdSe nanocrystal interfaces. Ultimately, the applicability of dislocation theory to nanocrystal attachment enables the predictive design of attachment to prevent or facilitate healing of defects upon nanocrystal attachment. We applied similar logic to understand formation of planar (2D) defects such as stacking faults upon nanocrystal attachment. Again concepts from bulk crystal defect crystallography can identify attachment pathways that can prevent or deterministically form planar defects upon nanocrystal attachment. The concepts we discuss work well for identifying favorable attachment geometries for nanocrystal pairs ; however it is currently unclear how to translate these ideas to near-simultaneous multiparticle attachment. Geometric frustration, which prevents nanocrystal rotation, and yet-to-be considered defect generation pathways unique to multiparticle attachment complicate defect-free superlattice attachment. New imaging methods now allow for the direct observation of local attachment trajectories and may enable improved understanding of such multiparticle phenomena. With further refinement, a unified framework for understanding and ultimately eliminating structural defects in fused nanocrystal superstructures may well be achievable in coming years.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2026

Limitations of probing field-induced response with STM

The kagome superconductors AV 3 Sb 5 (where A = K, Cs, Rb) exhibit intertwined density waves, unconventional superconductivity and time-reversal symmetry breaking without spin magnetism, with scanning tunnelling microscopy (STM) studies reporting, albeit not universally, magnetic-field-dependent changes in the apparent chirality of the 2 × 2 charge density wave (CDW). Related to this, Xing et al. investigated the effects of magnetic and electric fields on the 2 × 2 CDW state and the lattice structure of kagome superconductor RbV3Sb5, reporting a field-induced ~1% change in the in-plane lattice constants, concomitant with the CDW intensity modification, controlled by the field direction. Here we demonstrate how the apparent magnetic field induced lattice and CDW intensity change can be explained as a consequence of two independent experimental artifacts: a reconfiguration of atoms at the STM tip apex that alters the amplitudes of CDW modulations, and piezo creep, hysteresis and thermal drift, which artificially distort STM topographs. Here, we argue that the reported piezomagnetism could be attributed to experimental artifacts rather than an intrinsic magnetic-field-induced change of the sample.

Candelora, Christopher [Boston College, Chestnut H↗

DOE OSTI2020

Machine learning and serving of discrete field theories

A method for machine learning and serving of discrete field theories in physics is developed. The learning algorithm trains a discrete field theory from a set of observational data on a spacetime lattice, and the serving algorithm uses the learned discrete field theory to predict new observations of the field for new boundary and initial conditions. The approach of learning discrete field theories overcomes the difficulties associated with learning continuous theories by artificial intelligence. The serving algorithm of discrete field theories belongs to the family of structure-preserving geometric algorithms, which have been proven to be superior to the conventional algorithms based on discretization of differential equations. The effectiveness of the method and algorithms developed is demonstrated using the examples of nonlinear oscillations and the Kepler problem. In particular, the learning algorithm learns a discrete field theory from a set of data of planetary orbits similar to what Kepler inherited from Tycho Brahe in 1601, and the serving algorithm correctly predicts other planetary orbits, including parabolic and hyperbolic escaping orbits, of the solar system without learning or knowing Newton’s laws of motion and universal gravitation. The proposed algorithms are expected to be applicable when the effects of special relativity and general relativity are important.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2006

Long-Wavelength Infrared (LWIR) Quantum Dot Infrared Photodetector (QDIP) Focal Plane Array

We have exploited the artificial atomlike properties of epitaxially self-assembled quantum dots for the development of high operating temperature long wavelength infrared (LWIR) focal plane arrays. Quantum dots are nanometer-scale islands that form spontaneously on a semiconductor substrate due to lattice mismatch. QDIPs are expected to outperform quantum well infrared detectors (QWIPs) and are expected to offer significant advantages over II-VI material based focal plane arrays. QDIPs are fabricated using robust wide bandgap III-V materials which are well suited to the production of highly uniform LWIR arrays. We have used molecular beam epitaxy (MBE) technology to grow multi-layer LWIR quantum dot structures based on the InAs/InGaAs/GaAs material system. JPL is building on its significant QWIP experience and is basically building a Dot-in-the-Well (DWELL) device design by embedding InAs quantum dots in a QWIP structure. This hybrid quantum dot/quantum well device offers additional control in wavelength tuning via control of dot-size and/or quantum well sizes. In addition the quantum wells can trap electrons and aide in ground state refilling. Recent measurements have shown a 10 times higher photoconductive gain than the typical QWIP device, which indirectly confirms the lower relaxation rate of excited electrons (photon bottleneck) in QDPs. Subsequent material and device improvements have demonstrated an absorption quantum efficiency (QE) of approx. 3%. Dot-in-the-well (DWELL) QDIPs were also experimentally shown to absorb both 45 deg. and normally incident light. Thus we have employed a reflection grating structure to further enhance the quantum efficiency. JPL has demonstrated wavelength control by progressively growing material and fabricating devices structures that have continuously increased in LWIR response. The most recent devices exhibit peak responsivity out to 8.1 microns. Peak detectivity of the 8.1 micrometer devices has reached approx. 1 x 10(exp 10) Jones at 77 K. Furthermore, we have fabricated the first long-wavelength 640x512 pixels QDP focal plane array. This QDIP focal plane may has produced excellent infrared imagery with noise equivalent temperature difference of 40 mK at 60K operating temperature. In addition, we have managed to increase the quantum efficiency of these devices from 0.1% (according to the data published in literature) to 20% in discrete devices. This is a factor of 200 increase in quantum efficiency. With these excellent results, for the first time QDIP performance has surpassed the QWIP performance. Our goal is to operate these long-wavelength detectors at much higher operating temperature than 77K which can be passively achieved in space. This will be a huge leap in high performance infrared detectors specifically applicable to space science instruments.

infrared imaging↗

DOE OSTI2022

Geometric control of emergent antiferromagnetic order in coupled artificial spin ices

Artificial spin ices (ASIs) composed of coupled nanomagnets offer the possibility to create designer geometrical frustration and manipulate inter-nanomagnet interactions. In particular, by using a dimer motif consisting of two strongly coupled single-domain nano magnets as a building block, we can control and realize intriguing antiferromagnetic physical states in which the magnetic charge is not conserved. Here we create a dimer kagome ASI system within which the antiferromagnetic order is controlled by tuning lattice geometry. Different disordered antiferromagnetic phases and the inter-nanomagnet interactions are visualized directly in demagnetized lattices with different lattice parameters. Monte Carlo simulations establish that the collective ground state consists of disordered antiferromagnetic dimers across the lattice when the intra-dimer interaction is dominant. However, for lattices governed by intra-triad-unit interactions, the ground state exhibits a longrange spin-ordered state in which the vertex magnetic charge is uniform across all triads.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Ice rule breakdown and frustrated antiferrotoroidicity in an artificial colloidal Cairo ice

Abstract We combine experiments and numerical simulations to investigate the low energy states and the emergence of topological defects in an artificial colloidal ice in the Cairo geometry. This type of geometry is characterized by a mixed coordination ( z ), with coexistence of both z = 3 and z = 4 vertices. We realize this particle ice by confining field tunable paramagnetic colloidal particles within a lattice of topographic double wells at a one to one filling using optical tweezers. By raising the interaction strength via an applied magnetic field, we find that the ice rule breaks down, and positive monopoles with charge q = + 2 accumulate in the z = 4 vertices and are screened by negative ones ( q = − 1 ) in the z = 3. The resulting, strongly coupled state remains disordered. Further, via analysis of the mean chirality associated to each pentagonal plaquette, we find that the disordered ensemble for this geometry is massively degenerate and it corresponds to a frustrated antiferrotoroid.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Vertically Aligned Single-Crystalline CoFe 2 O 4 Nanobrush Architectures with High Magnetization and Tailored Magnetic Anisotropy

Micrometer-tall vertically aligned single-crystalline CoFe 2 O 4 nanobrush architectures with extraordinarily large aspect ratio have been achieved by the precise control of a kinetic and thermodynamic non-equilibrium pulsed laser epitaxy process. Direct observations by scanning transmission electron microscopy reveal that the nanobrush crystal is mostly defect-free by nature, and epitaxially connected to the substrate through a continuous 2D interface layer. In contrast, periodic dislocations and lattice defects such as anti-phase boundaries and twin boundaries are frequently observed in the 2D interface layer, suggesting that interface misfit strain relaxation under a non-equilibrium growth condition plays a critical role in the self-assembly of such artificial architectures. Further, magnetic property measurements have found that the nanobrushes exhibit a saturation magnetization value of 6.16 μB/f.u., which is much higher than the bulk value. The discovery not only enables insights into an effective route for fabricating unconventional high-quality nanostructures, but also demonstrates a novel magnetic architecture with potential applications in nanomagnetic devices.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Stabilized Co-Free Li-Rich Oxide Cathode Particles with An Artificial Surface Prereconstruction

Li-rich metal oxide (LXMO) cathodes have attracted intense interest for rechargeable batteries because of their high capacity above 250 mAh g –1 . However, the side effects of hybrid anion and cation redox (HACR) reactions, such as oxygen release and phase collapse that result from global oxygen migration (GOM), have prohibited the commercialization of LXMO. GOM not only destabilizes the oxygen sublattice in cycling, aggravating the well-known voltage fading, but also intensifies electrolyte decomposition and Mn dissolution, causing severe full-cell performance degradation. In this study, an artificial surface prereconstruction (ASR) for Li 1.2 Mn 0.6 Ni 0.2 O 2 particles with a molten-molybdate leaching is conducted, which creates a crystal-dense anion-redox-free LiMn 1.5 Ni 0.5 O 4 shell that completely encloses the LXMO lattice (ASR-LXMO). Differential electrochemical mass spectroscopy and soft X-ray absorption spectroscopy analyses demonstrate that GOM is shut down in cycling, which not only stabilizes HACR in ASR-LXMO, but also mitigates the electrolyte decomposition and Mn dissolution. ASR-LXMO displays greatly stabilized cycling performance as it retains 237.4 mAh g –1 with an average discharge voltage of 3.30 V after 200 cycles. More crucially, while the pristine LXMO cycling cannot survive 90 cycles in a pouch full-cell matched with a commercial graphite anode and lean (2 g A –1 h –1 ) electrolyte, ASR-LXMO shows high capacity retention of 76% after 125 cycles in full-cell cycling.

25 ENERGY STORAGE↗

DOE OSTI2024

Comparative Assessment of U-Net-Based Deep Learning Models for Segmenting Microfractures and Pore Spaces in Digital Rocks

Segmentation of high-resolution X-ray microcomputed tomography (µCT) images is crucial in digital rock physics (DRP), affecting the characterization and analysis of microscale phenomena in the porous media. The complexity of geological structures and nonideal scanning conditions pose significant challenges to conventional image segmentation approaches. Motivated by the recent increasing popularity of deep learning (DL) techniques in image processing, this work undertakes a comparative study of DL models, specifically U-Net and its variants, for segmenting multiple targets with distinguished features in digital rocks, including discrete fracture networks (DFNs), pore spaces, and solid rock. Particularly, DFNs have a smaller volumetric fraction over others, bringing in a substantial challenge of imbalanced segmentation. The primary focus is to evaluate the architecture and feature enhancement strategies of various DL models, including U-Net, attention U-Net, residual U-Net, U-Net++, and residual U-Net++. The models were designed as 2.5D, utilizing a central 2D image and its two adjacent upper and lower 2D images as input to provide a pseudo-3D context. In addition, because the ground truth of segmentation was unknown for real-world digital rocks, we created a benchmark data set following the inverse operations of segmentation. The data synthesis started from the label images (i.e., solid rock, pore spaces, and DFNs), followed by simulating partial volume blurring, adding random background noise, and introducing ring artifacts to mimic real raw X-ray µCT images. The data set, which included various rock types (i.e., sandstone and artificial data), scanning resolution, and magnitudes of noise and artifacts, was divided into training and testing data sets with a 90% and 10% ratio, respectively. Moreover, in addition to the conventional pixel-wise evaluation metrics, the physics-based metric of the lattice-Boltzmann method (LBM) simulated permeability provided more comprehensive assessments. The results demonstrated that the residual connections, nested architectures, and redesigned skip connections contribute to the model performance and give the residual U-Net++ the highest accuracy. The improvements were mainly on the boundaries and small targets, especially the DFNs, which dominate the interconnectivity and therefore affect the permeability greatly. This study also rigorously evaluated the efficiency and generalization of each model, demonstrating that the sophisticated architectures achieved excellent practicability and maintained robust performance on completely unseen data, ensuring their suitability for diverse and challenging DRP applications.

58 GEOSCIENCES↗

DOE OSTI2021

Emergent Collective Phenomena in Artificial Spin Ice (Final Technical Report)

This program encompassed studies of lithographically fabricated “artificial spin ice” arrays of nanometer-scale single-domain ferromagnetic islands in which the array geometry results in frustration of the magnetostatic interactions between the islands. Artificial spin ice offers a wide range of opportunities for studying the mechanism by which nature accommodates frustration and accesses physics associated with frustration in ferromagnetic nanostructures. Since the arrays are created lithographically, we can easily vary the array characteristics, including the geometry of the lattice and the level and type of lattice disorder. We can probe both the local properties of the arrays by imaging individual moments, and we can also probe thousands of moments simultaneously, allowing us to gain insight into the collective properties of the system. The research funded by this program included studies of unusual frustrated lattices, studies of magnetotransport in these systems, studies of perpendicular anisotropy moments, and a range of other related experimental measurements.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Deep residual networks for crystallography trained on synthetic data

The use of artificial intelligence to process diffraction images is challenged by the need to assemble large and precisely designed training data sets. To address this, a codebase called Resonet was developed for synthesizing diffraction data and training residual neural networks on these data. Here, two per-pattern capabilities of Resonet are demonstrated: (i) interpretation of crystal resolution and (ii) identification of overlapping lattices. Resonet was tested across a compilation of diffraction images from synchrotron experiments and X-ray free-electron laser experiments. Crucially, these models readily execute on graphics processing units and can thus significantly outperform conventional algorithms. While Resonet is currently utilized to provide real-time feedback for macromolecular crystallography users at the Stanford Synchrotron Radiation Lightsource, its simple Python-based interface makes it easy to embed in other processing frameworks. This work highlights the utility of physics-based simulation for training deep neural networks and lays the groundwork for the development of additional models to enhance diffraction collection and analysis.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Quantum simulation of an exotic quantum critical point in a two-site charge Kondo circuit

Tuning a material to the cusp between two distinct ground states can produce physical properties that are unlike those in either of the neighbouring phases. Advances in the fabrication and control of quantum systems have raised the tantalizing prospect of artificial quantum simulators that can capture such behaviour. A tunable array of coupled qubits should have an appropriately rich phase diagram, but realizing such a system with either tunnel-coupled semiconductor quantum dots or metal nanostructures has proven difficult. The challenge for scaling up to clusters or lattices is to ensure that each element behaves essentially identically and that the coupling between elements is uniform, while also maintaining tunability of the interactions. Here we study a nanoelectronic circuit comprising two coupled hybrid metal–semiconductor islands, combining the strengths of both materials to form a potentially scalable platform. The semiconductor component allows for controllable inter-site couplings at quantum point contacts, while the metal component’s effective continuum of states means that different sites can be made equivalent by tuning local potentials. The couplings afforded by this architecture can realize an unusual quantum critical point resulting from frustrated Kondo interactions. In this study, the observed critical behaviour matches theoretical predictions, verifying the success of our experimental quantum simulation.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Honeycomb-Lattice Mott Insulator on Tantalum Disulphide

Effects of electron many-body interactions amplify in an electronic system with a narrow bandwidth opening a way to exotic physics. A narrow band in a two-dimensional (2D) honeycomb lattice is particularly intriguing as combined with Dirac bands and topological properties but the material realization of a strongly interacting honeycomb lattice described by the Kane-Mele-Hubbard model has not been identified. Here we report a novel approach to realize a 2D honeycomb-lattice narrow-band system with strongly interacting 5$\textit{d}$ electrons. Iin this work, we engineer a well-known triangular lattice 2D Mott insulator 1$\textit{T}$ – TaS 2 into a honeycomb lattice utilizing an adsorbate superstructure. Potassium (K) adatoms at an optimum coverage deplete one-third of the unpaired $\textit{d}$ electrons and the remaining electrons form a honeycomb lattice with a very small hopping. Ab initio calculations show extremely narrow $Z_2$ topological bands mimicking the Kane-Mele model. Electron spectroscopy detects an order of magnitude bigger charge gap confirming the substantial electron correlation as confirmed by dynamical mean field theory. It could be the first artificial Mott insulator with a finite spin Chern number.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Atomically precise engineering of spin–orbit polarons in a kagome magnetic Weyl semimetal

Atomically precise defect engineering is essential to manipulate the properties of emerging topological quantum materials for practical quantum applications. However, this remains challenging due to the obstacles in modifying the typically complex crystal lattice with atomic precision. Here, we report the atomically precise engineering of the vacancy-localized spin–orbit polarons in a kagome magnetic Weyl semimetal Co 3 Sn 2 S 2 , using scanning tunneling microscope. We achieve the step-by-step repair of the selected vacancies, leading to the formation of artificial sulfur vacancies with elaborate geometry. We find that that the bound states localized around these vacancies undergo a symmetry dependent energy shift towards Fermi level with increasing vacancy size. As the vacancy size increases, the localized magnetic moments of spin–orbit polarons become tunable and eventually become itinerantly negative due to spin–orbit coupling in the kagome flat band. These findings provide a platform for engineering atomic quantum states in topological quantum materials at the atomic scale.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Quantum Time Dynamics Mediated by the Yang–Baxter Equation and Artificial Neural Networks

Quantum computing shows great potential, but errors pose a significant challenge. This study explores new strategies for mitigating quantum errors using artificial neural networks (ANNs) and the Yang–Baxter equation (YBE). Unlike traditional error mitigation methods, which are computationally intensive, we investigate artificial error mitigation. We developed a novel method that combines ANNs for noise mitigation combined with the YBE to generate noisy data. This approach effectively reduces noise in quantum simulations, enhancing the accuracy of the results. The YBE rigorously preserves quantum correlations and symmetries in spin chain simulations in certain classes of integrable lattice models, enabling effective compression of quantum circuits while retaining linear scalability with the number of qubits. This compression facilitates both full and partial implementations, allowing the generation of noisy quantum data on hardware alongside noiseless simulations using classical platforms. By introducing controlled noise through the YBE, we enhance the data set for error mitigation. We train an ANN model on partial data from quantum simulations, demonstrating its effectiveness in mitigating errors in time-evolving quantum states, providing a scalable framework to enhance quantum computation fidelity, particularly in noisy intermediate-scale quantum (NISQ) systems. We demonstrate the efficacy of this approach by performing quantum time dynamics simulations using the Heisenberg XY Hamiltonian on real quantum devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗