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At least 1,027 records · Page 57

Evaluation of Marine Boundary Layer Clouds Over the Northeast Pacific During the CSET Campaign in E3SM Version 2

It is still challenging to reproduce marine boundary layer (MBL) clouds well in large-scale models despite their importance to the Earth's radiation budget and hydrological cycle. This study evaluates representation of the MBL and clouds in the Energy Exascale Earth System Model (E3SM) version 2. This study compares the E3SM simulation results with remote sensing and reanalysis data during the Cloud System Evolution in the Trades (CSET) field campaign to better understand the stratocumulus-to-cumulus cloud transition (SCT) over the northeast Pacific. E3SM results are extracted along the CSET Lagrangian trajectories. The comparison shows that the E3SM simulation applying horizontal wind nudging performs well in reproducing thermodynamic variables of the MBL and evolution trends of cloud variables along the trajectories. However, substantial overestimations of aerosol and cloud drop number (N d ) are observed, which is explained as an issue with version 2 of the model. Cloud fraction (CF) does decrease from the Californian coast to Hawaii in the E3SM simulation, but most CF values indicate either an overcast or almost clear sky, which differs from satellite and reanalysis data. The effect of N d overestimation on CF evolution is assessed via prescribed-N d simulations. Those simulations with N d modifications show negligible CF changes. A comparison of estimated inversion strength (EIS) also shows that the simulated EIS values are similar to those of reanalysis data. Our study suggests that cloud macrophysics and boundary layer processes are more important in improving the simulation to capture the SCT than refining the model's thermodynamics or cloud microphysics.

Choi, Kyoung Ock [Univ. of Washington, Seattle, WA↗

Basic Research Needs for Inverse Methods for Complex Systems under Uncertainty

Inverse problems, which aim to infer unknown properties of a system using experimental and observational data, are central to addressing many of the U.S. Department of Energy’s (DOE) most critical scientific and engineering challenges. Accurate, computationally efficient, and data-efficient solutions to inverse problems are essential for advancing DOE mission-critical science drivers, including analyzing data from large-scale experimental facilities, optimizing fusion reactor performance, accelerating materials discovery, enhancing geophysical imaging, improving wildfire predictions, and enabling autonomous systems and digital twins. However, these problems are becoming increasingly complex, often involving nonlinear, highdimensional, and interconnected systems and models that span multiple physics and scales, while relying on data with varying quantity, quality, and information content. Compounding these challenges is the uncertainty inherent in DOE-relevant systems, where errors in inputs, noise in data, incompleteness of data, and discrepancies between models and reality constrain the accuracy and precision of solutions. At the same time, the convergence of recent scientific computing trends—scientific machine learning, artificial intelligence, and computing advances such as exascale computing—is creating unprecedented opportunities for tackling these challenges. The cross-cutting nature of inverse problems, combined with their growing complexity and rapidly evolving data and algorithmic demands, strongly motivates the formulation of a prioritized research agenda to maximize their capabilities and impact. In response to this need, DOE’s Advanced Scientific Computing Research (ASCR) program in the Office of Science convened the Workshop on Basic Research Needs for Inverse Problems for Complex Systems Under Uncertainty in June 2025. This workshop brought together experts across disciplines to identify grand challenges and major opportunities in the field. Through collaborative discussions, the workshop defined transformative research directions aimed at addressing the mathematical, statistical, and computational challenges posed by inverse problems under uncertainty. As a result of these efforts, four priority research directions (PRDs) were identified to guide future research and development in this area. These PRDs, summarized below, represent a roadmap for advancing the foundational science and mathematics of inverse problems, enabling robust, scalable, and uncertainty-aware solutions that are critical for DOE applications.

97 MATHEMATICS AND COMPUTING↗

Nondestructive Evaluation of Concrete: Elastic Property Imaging Through Full Waveform Inversion

Concrete is a major construction material worldwide and plays a crucial role in the nuclear industry. The elastic properties of concrete are prone to change and degrade while in service, as it is often subjected to extreme operational and environmental conditions. An accurate evaluation of concrete's elastic properties is thus essential to ensure structural integrity and safety. This is especially true for concrete in nuclear power plants, where irradiation effects significantly impact concrete mechanical properties. There are various methods to assess these properties, with ultrasound-based techniques showing high potential due to their nondestructive nature, cost-effectiveness, and safety. While several nondestructive evaluation methods exist, most rely on idealizations such as assuming homogeneous material and plane wavefronts. In this work, we address these issues by introducing an ultrasound-based nondestructive method aimed at reconstructing spatially varying images of concrete mechanical properties. By accurately modeling wave physics, including scattering and reflection, we overcome several of the aforementioned idealizations and aim to utilize the full waveform for imaging material properties through depth, resulting in more reliable images. Full waveform inversion (FWI) was first introduced by geophysicists to reconstruct subsurface elastic property images. The goal is to minimize the difference between simulated and recorded wavefield signals, often through gradient-based optimization algorithms. While FWI is primarily conducted using the acoustic approximation of the wave equation, few works focus on elastic FWI, where the goal is to reconstruct images of not only the pressure wave speed but also the shear wave speed and density (or their equivalents). This work explores the potential of using elastic FWI to predict concrete mechanical properties as an initial effort for a more accurate monitoring of concrete conditions in service. Reconstructing images of different elastic parameters enables more specificity and accurate condition diagnosis. This paper will detail this approach and provide examples demonstrating the effectiveness of elastic FWI in reconstructing comprehensive maps of concrete mechanical properties.

42 - ENGINEERING↗

Spitzer Phase-curve Observations and Circulation Models of the Inflated Ultrahot Jupiter WASP-76b

The large radii of many hot Jupiters can only be matched by models that have hot interior adiabats, and recent theoretical work has shown that the interior evolution of hot Jupiters has a significant impact on their atmospheric structure. Due to its inflated radius, low gravity, and ultrahot equilibrium temperature, WASP-76b is an ideal case study for the impact of internal evolution on observable properties. Hot interiors should most strongly affect the nonirradiated side of the planet, and thus full phase-curve observations are critical to ascertain the effect of the interior on the atmospheres of hot Jupiters. In this work, we present the first Spitzer phase-curve observations of WASP-76b. We find that WASP-76b has an ultrahot dayside and relatively cold nightside with brightness temperatures of 2471 ± 27 K/1518 ± 61 K at 3.6 μm and 2699 ± 32 K/1259 ± 44 K at 4.5 μm, respectively. These results provide evidence for a dayside thermal inversion. Both channels exhibit small phase offsets of 0.68 ± 0.°48 at 3.6 μm and 0.67 ± 0.°2 at 4.5 μm. We compare our observations to a suite of general circulation models (GCMs) that consider two endmembers of interior temperature along with a broad range of frictional drag strengths. Strong frictional drag is necessary to match the small phase offsets and cold nightside temperatures observed. From our suite of cloud-free GCMs, we find that only cases with a cold interior can reproduce the cold nightsides and large phase-curve amplitude at 4.5 μm, hinting that the hot interior adiabat of WASP-76b does not significantly impact its atmospheric dynamics or that clouds blanket its nightside.

79 ASTRONOMY AND ASTROPHYSICS↗

Joint physics-based and data-driven time-lapse seismic inversion: Mitigating data scarcity

In carbon capture and sequestration (CCS), developing rapid and effective imaging techniques is crucial for real-time monitoring of the spatial and temporal dynamics of CO 2 propagation during/after injection. With continuing improvements in computational power and data storage, data-driven techniques based on machine learning (ML) have been effectively applied to seismic inverse problems. In particular, ML helps alleviate the ill-posedness and high computational cost of full-waveform inversion (FWI). However, such data-driven inversion techniques require massive high-quality training data sets to ensure prediction accuracy, which hinders their application to time-lapse monitoring of CO 2 sequestration. We propose an efficient “hybrid” time-lapse workflow that combines physics-based FWI and data-driven ML inversion. The scarcity of the available training data is addressed by developing a new data-generation technique with physics constraints. The method is vali dated on a synthetic CO 2 -sequestration model based on the Kimberlina storage reservoir in California. The proposed approach is shown to synthesize a large volume of high-quality, physically realistic training data, which is critically important in accurately characterizing the CO 2 movement in the reservoir. In conclusion, the developed hybrid methodology can also simultaneously predict the variations in velocity and saturation and achieve high spatial resolution in the presence of realistic noise in the data.

58 GEOSCIENCES↗

Direct Prediction of Phonon Density of States With Euclidean Neural Networks

Abstract Machine learning has demonstrated great power in materials design, discovery, and property prediction. However, despite the success of machine learning in predicting discrete properties, challenges remain for continuous property prediction. The challenge is aggravated in crystalline solids due to crystallographic symmetry considerations and data scarcity. Here, the direct prediction of phonon density‐of‐states (DOS) is demonstrated using only atomic species and positions as input. Euclidean neural networks are applied, which by construction are equivariant to 3D rotations, translations, and inversion and thereby capture full crystal symmetry, and achieve high‐quality prediction using a small training set of examples with over 64 atom types. The predictive model reproduces key features of experimental data and even generalizes to materials with unseen elements, and is naturally suited to efficiently predict alloy systems without additional computational cost. The potential of the network is demonstrated by predicting a broad number of high phononic specific heat capacity materials. The work indicates an efficient approach to explore materials' phonon structure, and can further enable rapid screening for high‐performance thermal storage materials and phonon‐mediated superconductors.

97 MATHEMATICS AND COMPUTING↗

On the Relationship Between the Marine Cold Air Outbreak M Parameter and Low-Level Cloud Heights in the Midlatitudes

Focusing on conditions of subsidence when low clouds are present, ground-based observations in both the North Atlantic and the Southern Ocean reveal strong relationships between cloud boundary (base and top heights) and different measures of lower tropospheric instability. The difference in potential temperature between the surface and 800 hPa (a metric called M) provides a stronger relationship than measures of inversion strength such as the lower tropospheric stability and estimated inversion strength. This is because (1) inversion strength itself does not correlate well with cloud boundaries, and (2) M contains information that appears important for cloud boundaries. These include the surface forcing through the use of sea surface rather than near-surface air temperature and an upper level close to the real cloud top. These results expand upon previous work on the importance of M as a predictor of cloud morphology. However, important differences are found in low-cloud conditions for the North Atlantic as compared to the Southern Ocean (for a given value of M): stronger inversions, deeper boundary layers, and much larger sea level pressures. Therefore, the relationship between cloud boundaries and M differs between the two regions. A general circulation model provides similar relationships as observed between M and both cloud top height and temperature but tends to place clouds higher and at colder temperatures than observed for a given M. This might cause issues with the representation of precipitation, cloud cover and radiation in the Southern Ocean.

54 ENVIRONMENTAL SCIENCES↗

Quantitative imaging and automated fuel pin identification for passive gamma emission tomography

Compliance of member States to the Treaty on the Non-Proliferation of Nuclear Weapons is monitored through nuclear safeguards. The Passive Gamma Emission Tomography (PGET) system is a novel instrument developed within the framework of the International Atomic Energy Agency (IAEA) project JNT 1510, which included the European Commission, Finland, Hungary and Sweden. The PGET is used for the verification of spent nuclear fuel stored in water pools. Advanced image reconstruction techniques are crucial for obtaining high-quality cross-sectional images of the spent-fuel bundle to allow inspectors of the IAEA to monitor nuclear material and promptly identify its diversion. In this work, we have developed a software suite to accurately reconstruct the spent-fuel cross sectional image, automatically identify present fuel rods, and estimate their activity. Unique image reconstruction challenges are posed by the measurement of spent fuel, due to its high activity and the self-attenuation. While the former is mitigated by detector physical collimation, we implemented a linear forward model to model the detector responses to the fuel rods inside the PGET, to account for the latter. The image reconstruction is performed by solving a regularized linear inverse problem using the fast-iterative shrinkage-thresholding algorithm. We have also implemented the traditional filtered back projection (FBP) method based on the inverse Radon transform for comparison and applied both methods to reconstruct images of simulated mockup fuel assemblies. Higher image resolution and fewer reconstruction artifacts were obtained with the inverse-problem approach, with the mean-square-error reduced by 50%, and the structural-similarity improved by 200%. We then used a convolutional neural network (CNN) to automatically identify the bundle type and extract the pin locations from the images; the estimated activity levels finally being compared with the ground truth. The proposed computational methods accurately estimated the activity levels of the present pins, with an associated uncertainty of approximately 5%.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Semimetal–Mott insulator quantum phase transition of the Hubbard model on the honeycomb lattice

We take advantage of recent improvements in the grand canonical hybrid Monte Carlo algorithm, to perform a precision study of the single-particle gap in the hexagonal Hubbard model, with on-site electron-electron interactions. After carefully controlled analyses of the Trotter error, the thermodynamic limit, and finite-size scaling with inverse temperature, we find a critical coupling of U c /κ = 3.834(14) and the critical exponent zν = 1.185(43). Under the assumption that this corresponds to the expected antiferromagnetic Mott transition, we are also able to provide a preliminary estimate β = 1.095(37) for the critical exponent of the order parameter. We consider our findings in view of the SU(2) Gross-Neveu, or chiral Heisenberg, universality class. Here, we also discuss the computational scaling of the hybrid Monte Carlo algorithm, and possible extensions of our work to carbon nanotubes, fullerenes, and topological insulators.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Anatomy of information scrambling and decoherence in the integrable Sachdev-Ye-Kitaev model

The growth of information scrambling, captured by out-of-time-order correlation functions (OTOCs), is a central indicator of the nature of many-body quantum dynamics. Here, we compute analytically the complete time dependence of the OTOC for an integrable Sachdev-Ye-Kitaev (SYK) model, 𝑁 Majoranas with random two-body interactions of infinite range, coupled to a Markovian bath at finite temperature. In the limit of no coupling to the bath, the time evolution of scrambling experiences different stages. For 𝑡≲√𝑁, after an initial polynomial growth, the OTOC approaches saturation in a power-law fashion with oscillations superimposed. At 𝑡∼√𝑁, the OTOC reverses trend and starts to decrease linearly in time. The reason for this linear decrease is that, despite being a subleading 1/𝑁 effect, the OTOC in this region is governed by the spectral form factor of the antisymmetric couplings of the SYK model. The linear decrease stops at 𝑡∼2⁢𝑁, the Heisenberg time, where saturation occurs. The effect of the environment is an overall exponential decay of the OTOC for times longer than the inverse of the coupling strength to the bath. Here, the oscillations at 𝑡≲√𝑁 indicate lack of thermalization—a desired feature for better performance of quantum information devices.

Open quantum systems & decoherence↗

DIAS: A Data-Informed Active Subspace Regularization Framework for Inverse Problems

This paper presents a regularization framework that aims to improve the fidelity of Tikhonov inverse solutions. At the heart of the framework is the data-informed regularization idea that only data-uninformed parameters need to be regularized, while the data-informed parameters, on which data and forward model are integrated, should remain untouched. We propose to employ the active subspace method to determine the data-informativeness of a parameter. The resulting framework is thus called a data-informed (DI) active subspace (DIAS) regularization. Four proposed DIAS variants are rigorously analyzed, shown to be robust with the regularization parameter and capable of avoiding polluting solution features informed by the data. They are thus well suited for problems with small or reasonably small noise corruptions in the data. Furthermore, the DIAS approaches can effectively reuse any Tikhonov regularization codes/libraries. Though they are readily applicable for nonlinear inverse problems, we focus on linear problems in this paper in order to gain insights into the framework. Various numerical results for linear inverse problems are presented to verify theoretical findings and to demonstrate advantages of the DIAS framework over the Tikhonov, truncated SVD, and the TSVD-based DI approaches.

Nguyen, Hai↗

Probabilistic effects of porosity and chemical kinetics on the shock initiation of an octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) based explosive

In this work, we investigate the effects of porosity and chemical reactivity on the shock initiation of an HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine)-based polymer bonded explosive due to thin flyer impact using two-dimensional mesoscale simulations. Microstructural samples are computationally generated, and the calculated shock response is compared to experiments. The sample dimensions are 0.1×1.05 mm 2 , and each sample accounts for grain scale heterogeneities, including randomized grain morphology and pore spacing. Simulations are performed using the Lawrence Livermore National Laboratory (LLNL) arbitrary Lagrangian–Eulerian multi-physics code ALE3D. Chemistry and equation of states are handled with LLNL's thermochemical code Cheetah. We employ a modified Arrhenius-based chemical kinetics model that scales the temperature exponent fitting parameter with flyer shock conditions. This new model is calibrated to the mean response of experimental shock initiation thresholds for three separate Kapton flyer thicknesses. A simplified shock initiation criterion is proposed, which classifies the macroscale initiation response based on cross-sectional temperature profiles of the shocked sample. This criterion is used to further investigate the probabilistic response of the sample to variations in the mean porosity and chemical kinetics rate, and we find an inverse correlation between the shock pressure and the confidence interval of the experimental threshold velocity. Furthermore, the methodology presented in this work for quantifying the probabilistic nature of shock initiation is material agnostic. These mesoscale studies may be used to inform continuum scale models and expedite the development of future, tailored energetic formulations.

36 MATERIALS SCIENCE↗

Intruder configurations in 29 Ne at the transition into the island of inversion: Detailed structure study of 28 Ne

Detailed γ-ray spectroscopy of the exotic neon isotope 28 Ne has been performed for the first time using the one-neutron removal reaction from 29 Ne on a liquid hydrogen target at 240 MeV/nucleon. Based on an analysis of parallel momentum distributions, a level scheme with spin-parity assignments has been constructed for 28 Ne and the negative-parity states are identified for the first time. The measured partial cross sections and momentum distributions reveal a significant intruder p-wave strength providing evidence of the breakdown of the N=20 and N=28 shell gaps. Only a weak, possible f-wave strength was observed to bound final states. Large-scale shell-model calculations with different effective interactions do not reproduce the large p-wave and small f-wave strength observed experimentally, indicating an ongoing challenge for a complete theoretical description of the transition into the island of inversion along the Ne isotopic chain.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Seasonal trends in leaf-level photosynthetic capacity and water use efficiency in a North American Eastern deciduous forest and their impact on canopy-scale gas exchange

Vegetative transpiration (E) and photosynthetic carbon assimilation (A) are known to be seasonally dynamic, with changes in their ratio determining the marginal water use efficiency (WUE). Despite an understanding that stomata play a mechanistic role in regulating WUE, it is still unclear how stomatal and nonstomatal processes influence change in WUE over the course of the growing season. As a result, limited understanding of the primary physiological drivers of seasonal dynamics of canopy WUE remains one of the largest uncertainties in earth system model projections of carbon and water exchange in temperate deciduous forest ecosystems. Here, we investigated seasonal patterns in leaf-level physiological, hydraulic, and anatomical properties, including the seasonal progress of the stomatal slope parameter (g 1 ; inversely proportional to WUE) and the maximum carboxylation rate (V cmax ). V cmax and g 1 were seasonally variable; however, their patterns were not temporally synchronized. g 1 generally showed an increasing trend until late in the season, while V cmax peaked during the midsummer months. Seasonal progression of V cmax was primarily driven by changes in leaf structural, and anatomical characteristics, while seasonal changes in g 1 were most strongly related to changes in V cmax and leaf hydraulics. Using a seasonally variable V cmax and g 1 to parameterize a canopy-scale gas exchange model increased seasonally aggregated A and E by 3% and 16%, respectively.

54 ENVIRONMENTAL SCIENCES↗

Inversion of downhole electrical measurements for proppant mapping using very fast simulated annealing

Proppant mapping is critical for optimizing fracture treatment design and improving wells’ productivity. An electrode-based resistivity tool concept was developed earlier for proppant mapping in cased-hole wells. An array of insulating gaps is installed and cemented in place as a permanent part of the casing string. The electrical measurements are performed by imposing a voltage across each insulating gap, one at a time, before and after hydraulic fracture operations. The voltages across other insulating gaps near the transmitter gap are recorded. The method relies on direct excitation of the casing, which is expected to overcome the severe limitations of induction tools in cased-hole wells. A forward model based on a finite volume method has been developed to simulate the tool’s response to one or multiple fractures. To enable the implementation of such a practical system in multistage fractured horizontal wells, a fast and robust inversion approach is required. To that end, we have developed a divide-and-conquer approach based on a global optimization algorithm very fast simulated annealing (VFSA). Specifically, the original inverse problem is divided into subproblems and each subproblem can be solved separately using VFSA. The results indicate that our approach can invert the data and output widths and radii of multiple fractures without requiring a large number of forward simulations. The robustness of the inverse solver is also tested by adding Gaussian noise to the synthetic data. We tested example cases that demonstrate that when up to 5% noise is introduced, VFSA still provides very accurate inversion results with moderate uncertainties. Inversion results with some more realistic conditions, e.g., tilted fractures, complex fractures, and so on, are also presented.

Geochemistry & Geophysics↗

Inferring Stochastic Rates from Heterogeneous Snapshots of Particle Positions

Many imaging techniques for biological systems—like fixation of cells coupled with fluorescence microscopy—provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics they intend to capture. In this study, these snapshot observations contain no information about individual trajectories, but still encode information about movement and demographic dynamics, especially when combined with a well-motivated biophysical model. The relationship between spatially evolving populations and single-moment representations of their collective locations is well-established with partial differential equations (PDEs) and their inverse problems. However, experimental data is commonly a set of locations whose number is insufficient to approximate a continuous-in-space PDE solution. Here, motivated by popular subcellular imaging data of gene expression, we embrace the stochastic nature of the data and investigate the mathematical foundations of parametrically inferring demographic rates from snapshots of particles undergoing birth, diffusion, and death in a nuclear or cellular domain. Toward inference, we rigorously derive a connection between individual particle paths and their presentation as a Poisson spatial process. Using this framework, we investigate the properties of the resulting inverse problem and study factors that affect quality of inference. One pervasive feature of this experimental regime is the presence of cell-to-cell heterogeneity. Rather than being a hindrance, we show that cell-to-cell geometric heterogeneity can increase the quality of inference on dynamics for certain parameter regimes. Altogether, the results serve as a basis for more detailed investigations of subcellular spatial patterns of RNA molecules and other stochastically evolving populations that can only be observed for single instants in their time evolution.

59 BASIC BIOLOGICAL SCIENCES↗

Symmetric-asymmetric collision comparison: Disentangling nuclear structure and subnucleonic structure effects for small system flow

Previous flow measurements in small collision systems were mostly based on highly asymmetric collisions (p+Pb, p+Au, d+Au, 3 He+Au), where both nuclear structure and subnucleonic fluctuations are important. Comparing these asymmetric systems with the newly available symmetric 16 O+ 16 O collisions at RHIC and LHC provides a unique opportunity to disentangle these two contributions. Using Glauber models incorporating both nucleon and quark-level substructure, we analyze multiplicity distributions and initial-state estimators: eccentricities ε n for anisotropic flow ν n and inverse transverse size d ⟂ for radial flow. We find that subnucleonic fluctuations impact O+O collisions differently from asymmetric systems, creating specific patterns in flow observables that enable disentangling the competing contributions. Such experimental comparisons will reduce uncertainties in the initial conditions and improve our understanding of the properties of the QGP-like medium produced in small systems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Orientation-Controlled Large-Area Epitaxial PbI 2 Thin Films with Tunable Optical Properties

Lead iodide (PbI 2 ) as a layered material has emerged as an excellent candidate for optoelectronics in the visible and ultraviolet regime. Micrometer-sized flakes synthesized by mechanical exfoliation from bulk crystals or by physical vapor deposition have shown a plethora of applications from low-threshold lasing at room temperature to high-performance photodetectors with large responsivity and faster response. However, large-area centimeter-sized growth of epitaxial thin films of PbI 2 with well-controlled orientation has been challenging. Additionally, the nature of grain boundaries in epitaxial thin films of PbI 2 remains elusive. Here, we use mica as a model substrate to unravel the growth mechanism of large-area epitaxial PbI 2 thin films. The partial growth leading to uncoalesced domains reveals the existence of inversion domain boundaries in epitaxial PbI 2 thin films on mica. Combining the experimental results with first-principles calculations, we also develop an understanding of the thermodynamic and kinetic factors that govern the growth mechanism, which paves the way for the synthesis of high-quality large-area PbI 2 on other substrates and heterostructures of PbI 2 on single-crystalline graphene. Here, the ability to reproducibly synthesize high-quality large-area thin films with precise control over orientation and tunable optical properties could open up unique and hitherto unavailable opportunities for the use of PbI 2 and its heterostructures in optoelectronics, twistronics, substrate engineering, and strain engineering.

2D materials↗