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At least 883 records · Page 49

Analysis of the Electronic Crosstalk Effect in Terra MODIS Long-Wave Infrared Photovoltaic Bands Using Lunar Images

The Moderate Resolution Imaging Spectroradiometer (MODIS) is one of the key sensors among the suite of remote sensing instruments on board the Earth Observing System Terra and Aqua spacecrafts. For each MODIS spectral band, the sensor degradation has been measured using a set of on-board calibrators. MODIS also uses lunar observations from nearly monthly spacecraft maneuvers, which bring the Moon into view through the space-view port, helping to characterize the scan mirror degradation at a different angles of incidence. Throughout the Terra mission, contamination of the long-wave infrared photovoltaic band (LWIR PV, bands 27-30) signals has been observed in the form of electronic crosstalk, where signal from each of the detectors among the LWIR PV bands can leak to the other detectors, producing a false signal contribution. This contamination has had a noticeable effect on the MODIS science products since 2010 for band 27, and since 2012 for bands 28 and 29. Images of the Moon have been used effectively for determining the contaminating bands, and have also been used to derive correction coefficients for the crosstalk contamination. In this paper, we introduce an updated technique for characterizing the crosstalk contamination among the LWIR PV bands using data from lunar calibration events. This approach takes into account both the in-band and out-of-band contribution to the signal contamination for each detector in bands 27-30, which is not considered in previous works. The crosstalk coefficients can be derived for each lunar calibration event, providing the time dependence of the crosstalk contamination. Application of these coefficients to Earth-view image data results in a significant reduction in image contamination and a correction of the scene radiance for bands 27- 30. Also, this correction shows a significant improvement to certain threshold tests in the MODIS Level-2 Cloud Mask. In this paper, we will detail the methodology used to identify and correct the crosstalk contamination for the LWIR PV bands in Terra MODIS. The derived time-dependent crosstalk coefficients will also be discussed. Finally, the impact of the correction on the downstream data products will be analyzed.

Wilson, Truman↗

Characterization of Shock Effects in Calcite by Raman Spectroscopy: Results of Experiments

Carbonates comprise approx. 20% by volume of present day Earth's sedimentary rocks and store most of the terrestrial CO2 inventory. Some of the oldest meta-sedimentary rocks found on Earth contain abundant carbonate from which impact-induced release of CO2 could have played a role in the formation and evolution of the atmosphere. Carbonates are also present in the target materials for approx. 30% of all terrestrial impact structures including large impacts such as Chicxulub which happened to occur at a location with extraordinarily thick platform carbonate 3-6 km deep. The impact release of CO2 from carbonates can cause global warming as a result of the well-known greenhouse effect and have subsequent effects on climate and biota. Therefore, the shock behavior of calcite is important in understanding the Cretaceous-Paleogene event and other impacts with carbonate-bearing sediments in their target(s) such as Mars and some asteroids. A comprehensive survey utilizing a variety of techniques to characterize the effects manifest in Calcite (Iceland Spar) experimentally shocked to 60.8 GPa has been completed. Results of analysis by Raman Spectroscopy are reported here.

Bell, M. S.↗

Integrated End-to-end Performance Prediction and Diagnosis for Extreme Scientific Workflows

This report details recent progress for the ASCR funded project “Integrated End-to-end Performance Prediction and Diagnosis for Extreme Scientific Workflows”. We refer to the project as IPPD/2, reflecting the 2017 renewal under expanded scope and partners In IPPD/2, we increased our research scope to include data motion. We are focusing on three major aspects: a) observe how data is generated, distributed, and used; b) analyze how data is (repeatedly) consumed with a focus both on repeated patterns and anomalies; and c) explore how to optimize data motion. This new work on data motion will augment and complement IPPD/2’s research that focused on the computational aspects of tasks. We leverage and extend our existing tools and demonstrate our work on the Belle II workflow suite as well as on workflows from NSLS-II. The highlights of our work are as follows: Provenance for Workflows: Provenance is used to provide information enabling quality control, re-run computational workflows, and reproduce results. IPPD/2 has been building a scalable provenance management system that enables the capture of provenance from the high-level workflow through all relevant system levels in one integrated environment. Leveraging this work, our recent efforts have included using provenance as an enabling technique. Workload characterization: Leveraging provenance and analysis, we characterize data movement within network, storage, and memory over a variety of workloads. This characterization enables an understanding by performance analysts and application developers of the range of behaviors that could be expected. Performance Prediction for Workflows: The goal of modeling distributed workflows is to understand performance bottlenecks and enable more intelligent task scheduling to optimize selected metrics of interest (e.g., task throughput or output data rate). IPPD/2 has utilized both analytical and AI/ML modeling methodologies for performance modeling. Advanced Scheduling and Fault Modeling for Workflows: Scheduling of large-scale scientific workflows on geographically distributed resources is a challenging problem. To improve workflow throughput, we combined novel scheduling algorithms with task predictions from performance modeling and fault modeling. Dynamically Alleviating Bottlenecks in Workflows: Exploiting our provenance, analysis, and modeling efforts, we have explored and developed several techniques for dynamically detecting and alleviating bottlenecks in data movement. In particular, we have spent considerable effort demonstrating our techniques on production-like workflow configurations.

97 MATHEMATICS AND COMPUTING↗

Absence of magnetic order in epitaxial RuO 2 revealed by x-ray linear dichroism

Recently the topic of altermagnetism has attracted tremendous attention, and RuO 2 has been demonstrated to be one of the most promising altermagnetic candidates. However, disputes still remain on the existence of magnetic order in RuO 2 . Here in this work, we employ x-ray linear dichroism (XLD), a widely utilized technique for characterizing antiferromagnets, in conjunction with photoemission electron microscopy and multiple scattering calculation to provide clear evidence of the absence of magnetic order in epitaxial RuO 2 films. The observed XLD signal is nearly invariant with temperature and independent of cooling-field direction, in stark contrast to the substantial magnetic-order-related XLD signal predicted by multiple scattering calculation. This finding strongly suggests a nonmagnetic origin for RuO 2 . Furthermore, we observed significantly distinct XLD signals at the Ru M 3 and O K edges in RuO 2 films grown on TiO 2 substrate with different surface orientations, which can be attributed to the low-symmetry crystal field. In conclusion, these results unequivocally demonstrate the absence of magnetic order in RuO 2 and establish XLD measurement as a robust technique for probing the low-symmetry magnetic materials.

Wang, Siyu [University of Science and Technology o↗

Influence of Cr and W alloying on the fiber-matrix interfacial shear strength in cast and directionally solidified sapphire NiAl composites

Sapphire-reinforced NiAl matrix composites with chromium or tungsten as alloying additions were synthesized using casting and zone directional solidification (DS) techniques and characterized by a fiber pushout test as well as by microhardness measurements. The sapphire-NiAl(Cr) specimens exhibited an interlayer of Cr rich eutectic at the fiber-matrix interface and a higher interfacial shear strength compared to unalloyed sapphire-NiAl specimens processed under identical conditions. In contrast, the sapphire-NiAl(W) specimens did not show interfacial excess of tungsten rich phases, although the interfacial shear strength was high and comparable to that of sapphire-NiAl(Cr). The postdebond sliding stress was higher in sapphire-NiAl(Cr) than in sapphire-NiAl(W) due to interface enrichment with chromium particles. The matrix microhardness progressively decreased with increasing distance from the interface in both DS NiAl and NiAl(Cr) specimens. The study highlights the potential of casting and DS techniques to improve the toughness and strength of NiAl by designing dual-phase microstructures in NiAl alloys reinforced with sapphire fibers.

Asthana, R.↗

Measurement Sets and Sites Commonly Used for Characterization

Scientists at NASA's Earth Science Applications Directorate are creating a well-characterized Verification & Validation (V&V) site at the Stennis Space Center. This site enables the in-flight characterization of remote sensing systems and the data they acquire. The data are predominantly acquired by commercial, high spatial resolution satellite systems, such as IKONOS and QuickBird 2, and airborne systems. The smaller scale of these newer high resolution remote sensing systems allows scientists to characterize the geometric, spatial, and radiometric data properties using a single V&V site. The targets and techniques used to characterize data from these newer systems can differ significantly from the techniques used to characterize data from the earlier, coarser spatial resolution systems. Scientists are also using the SSC V&V site to characterize thermal infrared systems and active LIDAR systems. SSC employs geodetic targets, edge targets, radiometric tarps, and thermal calibration ponds to characterize remote sensing data products. This paper presents a proposed set of required measurements for visible through long-wave infrared remote sensing systems and a description of the Stennis characterization. Other topics discussed include: 1) The use of ancillary atmospheric and solar measurements taken at SSC that support various characterizations; 2) Additional sites used for radiometric, geometric, and spatial characterization in the continental United States; 3) The need for a standardized technique to be adopted by CEOS and other organizations.

Pagnutti, Mary↗

A High-Sensitivity Broad-Band Seismic Sensor for Shallow Seismic Sounding of the Lunar Regolith

The recently undertaken Space Exploration Initiative has prompted a renewed interest in techniques for characterizing the surface and shallow subsurface (0-10s of meters depth) of the Moon. There are several reasons for this: First, there is an intrinsic scientific interest in the subsurface structure. For example the stratigraphy, depth to bedrock, density/porosity, and block size distribution all have implications for the formation of, and geological processes affecting the surface, such as sequential crater ejecta deposition, impact gardening, and seismic settling. In some permanently shadowed craters there may be ice deposits just below the surface. Second, the geotechnical properties of the lunar surface layers are of keen interest to future mission planners. Regolith thickness, strength, density, grain size and compaction will affect construction of exploration infrastructure in terms of foundation strength and stability, ease of excavation, radiation shielding effectiveness, as well as raw material handling and processing techniques for resource extraction.

Pike, W. Thomas↗

Mode I Toughness Measurements of Core/Facesheet Bonds in Honeycomb Sandwich Structures

Composite sandwich structures will be used in many future applications in aerospace, marine and offshore industries due to the fact that the strength and stiffness to mass ratios surpass any other structural type. Sandwich structure also offers advantages over traditional stiffened panels such as ease of manufacturing and repair. During the last three decades, sandwich structure has been used extensively for secondary structure in aircraft (fuselage floors, rudders and radome structure). Sandwich structure is also used as primary structure in rotorcraft, the most common example being the trailing edge of rotor blades. As with other types of composite construction, sandwich structure exhibits several types of failure mode such as facesheet wrinkling, core crushing and sandwich buckling. Facesheet/core debonding has also been observed in the marine and aerospace industry. During this failure mode, peel stresses applied to an existing facesheet/core debond or an interface low in toughness, results in the facesheet being peeled from the core material, possibly leading to a significant loss in structural integrity of the sandwich panel. In an incident during a test on a liquid hydrogen fuel tank of the X-33 prototype vehicle, the outer graphite/epoxy facesheet and honeycomb core became debonded from the inner facesheet along significant areas, leading to failure of the tank. As a consequence of the accident; significant efforts were made to characterize the toughness of the facesheet/core bond. Currently, the only standardized method available for assessing the quality of the facesheet/core interface is the climbing drum peel test (ASTM D1781). During this test a sandwich beam is removed from a panel and the lip of one of the facesheets is attached to a drum, as shown in Fig. 1. The drum is then rotated along the sandwich beam, causing the facesheet to peel from the core. This method has two major drawbacks. First, it is not possible to obtain quantitative fracture data from the test and so the results can only be used in a qualitative manner. Second, only sandwich structure with thin facesheets can be tested (to facilitate wrapping of the facesheet around the climbing drum). In recognition of the need for a more quantitative facesheet/core fracture test, several workers have devised experimental techniques for characterizing the toughness of the facesheet/core interface. In all of these cases, the tests are designed to yield a mode I-dominated fracture toughness of the facesheet/core interface in a manner similar to that used to determine mode I fracture toughness of composite laminates. In the current work, a modified double cantilever beam is used to measure the mode I-dominated fracture toughness of the interface in a sandwich consisting of glass/phenolic honeycomb core reinforced with graphite epoxy facesheets. Two specimen configurations were tested as shown in Fig 2. The first configuration consisted of reinforcing the facesheets with aluminum blocks (Fig. 2a). In the second configuration unreinforced specimens were tested (Fig. 2b). Climbing drum peel tests were also conducted to compare the fracture behavior observed between this test and the modified double cantilever beam. This paper outlines the test procedures and data reduction strategies used to compute fracture toughness values from the tests. The effect of specimen reinforcement on fracture toughness of the facesheet/core interface is discussed.

Nettles, Alan T.↗

Synthesis and morphological characterization of linear and miktoarm star poly(solketal methacrylate)- block -polystyrene copolymers

The synthesis, molecular characterization, and morphological evaluation of AB n, (n = 2,3) miktoarm star block copolymers consisting of poly(glycerol monomethacrylate) (PGMA) and polystyrene (PS) with varying molecular weights and compositions is described. The system is known to demonstrate a remarkably high Flory-Huggins interaction parameter. The corresponding linear diblock copolymer analogues, were synthesized as well, and comparisons with regard to feature dimensions and morphologies are provided. Well-ordered nanostructures of various morphologies were formed with domain spacing as low as 7.2 nm. Different morphologies were attained by some of the topological isomers indicating that in miktoarm star block copolymers the phase boundaries were strongly shifted. Additionally, a triblock ABA analogue was studied to investigate the effect of triblock copolymer conformations. Noteworthy is that for copolymers with different macromolecular architecture leading to similar morphology; different domain spacings were obtained. The synthesis of all the samples was carried out by high-vacuum anionic polymerization techniques. Molecular characterization with Size Exclusion Chromatography (SEC) and Proton Nuclear Magnetic Resonance Spectroscopy ( 1 H NMR) confirmed well-defined copolymers obtained. The morphological characterization was accomplished by Small-Angle X-ray Scattering (SAXS). In conclusion, the observations from this study highlight the potential of incorporating macromolecular architecture in the self-assembly of strongly immiscible block copolymers to attain ultra-small nanofeatures with desired morphologies.

36 MATERIALS SCIENCE↗

Variation-Resilient FeFET-Based In-Memory Computing Leveraging Probabilistic Deep Learning

Reliability issues stemming from device level nonidealities of nonvolatile emerging technologies like ferroelectric field-effect transistors (FeFETs), especially at scaled dimensions, cause substantial degradation in the accuracy of in-memory crossbar-based AI systems. Here, in this work, we present a variation-aware design technique to characterize the device level variations and to mitigate their impact on hardware accuracy employing a Bayesian neural network (BNN) approach. An effective conductance variation model is derived from the experimental measurements of cycle-to-cycle (C2C) and device-to-device (D2D) variations performed on FeFET devices fabricated using 28 nm high-k metal gate technology. The variations were found to be a function of different conductance states within the given programming range, which sharply contrasts earlier efforts where a fixed variation dispersion was considered for all conductance values. Such variation characteristics formulated for three different device sizes at different read voltages were provided as prior variation information to the BNN to yield a more exact and reliable inference. Near-ideal accuracy for shallow networks (MLP5 and LeNet models) on the MNIST dataset and limited accuracy decline by ~3.8%–16.1% for deeper AlexNet models on CIFAR10 dataset under a wide range of variations corresponding to different device sizes and read voltages, demonstrates the efficacy of our proposed device-algorithm co-design technique.

97 MATHEMATICS AND COMPUTING↗

Learning heterogeneous reaction kinetics from X-ray videos pixel by pixel

Reaction rates at spatially heterogeneous, unstable interfaces are notoriously difficult to quantify, yet are essential in engineering many chemical systems, such as batteries and electrocatalysts. Experimental characterizations of such materials by operando microscopy produce rich image datasets, but data-driven methods to learn physics from these images are still lacking because of the complex coupling of reaction kinetics, surface chemistry and phase separation. Here we show that heterogeneous reaction kinetics can be learned from in situ scanning transmission X-ray microscopy (STXM) images of carbon-coated lithium iron phosphate (LFP) nanoparticles. Combining a large dataset of STXM images with a thermodynamically consistent electrochemical phase-field model, partial differential equation (PDE)-constrained optimization and uncertainty quantification, we extract the free-energy landscape and reaction kinetics and verify their consistency with theoretical models. We also simultaneously learn the spatial heterogeneity of the reaction rate, which closely matches the carbon-coating thickness profiles obtained through Auger electron microscopy (AEM). Across 180,000 image pixels, the mean discrepancy with the learned model is remarkably small (<7%) and comparable with experimental noise. Our results open the possibility of learning nonequilibrium material properties beyond the reach of traditional experimental methods and offer a new non-destructive technique for characterizing and optimizing heterogeneous reactive surfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Learning heterogeneous reaction kinetics from X-ray movies pixel-by-pixel

Reaction rates at spatially heterogeneous, unstable interfaces are notoriously difficult to quantify, yet are essential in engineering many chemical systems, such as batteries 1 and electrocatalysts 2. Experimental characterizations of such materials by operando microscopy produce rich image datasets 3–6, but data-driven methods to learn physics from these images are still lacking because of the complex coupling of reaction kinetics, surface chemistry and phase separation 7. Here we show that heterogeneous reaction kinetics can be learned from in situ scanning transmission X-ray microscopy (STXM) images of carbon-coated lithium iron phosphate (LFP) nanoparticles. Combining a large dataset of STXM images with a thermodynamically consistent electrochemical phase-field model, partial differential equation (PDE)-constrained optimization and uncertainty quantification, we extract the free-energy landscape and reaction kinetics and verify their consistency with theoretical models. We also simultaneously learn the spatial heterogeneity of the reaction rate, which closely matches the carbon-coating thickness profiles obtained through Auger electron microscopy (AEM). Across 180,000 image pixels, the mean discrepancy with the learned model is remarkably small (<7%) and comparable with experimental noise. Our results open the possibility of learning nonequilibrium material properties beyond the reach of traditional experimental methods and offer a new non-destructive technique for characterizing and optimizing heterogeneous reactive surfaces.

Chueh, William↗

Visualization of shocked material instabilities using a fast-framing camera and XFEL four-pulse train

Many questions regarding dynamic materials could be answered by using time-resolved ultra-fast imaging techniques to characterize the physical and chemical behavior of materials in extreme conditions and their evolution on the nanosecond scale. In this work, we perform multi-frame phase-contrast imaging (PCI) of micro-voids in low density polymers under laser-driven shock compression. At the Matter in Extreme Conditions (MEC) Instrument at the Linac Coherent Light Source (LCLS), we used a train of four x-ray free electron laser (XFEL) pulses to probe the evolution of the samples. To visualize the void and shock wave interaction, here, we deployed the Icarus V2 detector to record up to four XFEL pulses, separated by 1-3 nanoseconds. In this work, we image elastic waves interacting with the micro-voids at a pressure of several GPa. Monitoring how the material’s heterogeneities, like micro-voids, dictate its response to a compressive wave is important for benchmarking the performances of inertial confinement fusion energy materials. For the first time in a single sample, we have combined an ultrafast x-ray framing camera and four XFEL pulse train to create an ultrafast movie of micro-void evolution under laser-driven shock compression. Eventually, we hope this technique will resolve the material density as it evolves dynamically under laser shock compression.

fusion↗

Phased array-based nonlinear wave mixing technique: Application to lack-of-fusion porosity characterization in additively manufactured metals

The objective of this research is to demonstrate the effectiveness of a phased array-based nonlinear wave mixing technique to characterize internal, localized microscale damage in an additively manufactured (AM) component. By using phased arrays for the generation of the incident waves, it is possible to produce a nonlinear wave mixing scanning technique without the need for immersion or changing coupling conditions. The phased arrays can be configured to generate incident waves in multiple directions that meet the resonance conditions required for nonlinear wave mixing at a variety of internal locations. This allows for the scanning of a specimen without the removal and re-coupling of the source transducers, leading to greater scanning speed and repeatability. To demonstrate the accuracy of this phased array wave mixing approach, measurements of acoustic nonlinearity in an AM component are first made with a bulk wave second harmonic generation through thickness measurement. Next, nonlinear wave mixing measurements are made with single element transducers to confirm the sensitivity of the proposed nonlinear wave mixing approach to lack-of-fusion porosity in AM metals. Finally, phased arrays are used to highlight the effectiveness of the proposed nonlinear wave mixing technique in these same AM components.

Acoustics↗

In-Situ Synchrotron X-Ray Diffraction of Ultrasonic Microstructural Refinement During Solidification in a Commercial Al–Si–Mg Alloy

This study reports the first use of in-situ synchrotron X-ray diffraction (SXRD) to study the effects of ultrasonic melt processing (USMP) on phase and grain size evolution during solidification in a commercial Al–Si–Mg casting alloy. USMP is a technique that, when applied to aluminum as it solidifies, can be used to refine the local microstructure of large-scale castings. Analysis of the in-situ SXRD data to estimate the average grain size of primary α-Al grains during USMP demonstrates that USMP slows the growth rate of α-Al grains and reduces grain size by 36 pct. Furthermore, there is also evidence that USMP causes the primary α-Al grains to move relative to the X-ray beam; such motion increases the probability of primary α-Al grains colliding and fragmenting. This movement becomes constrained at the onset of the Al–Si binary eutectic, suggesting that USMP ceases to effectively refine the microstructure once the Al–Si binary eutectic begins to form. Complementary laboratory-scale X-ray diffraction (XRD) data were used to correlate the lattice parameters of the α-Al and Si (D-A4) phases with temperature to estimate cooling rate during solidification. Thus, this study can guide the design of novel castings with spatially distributed fine-grained regions produced using local ultrasonic processing.

Aluminum Alloys↗

Stennis Space Center Verification & Validation Capabilities

Scientists within NASA s Applied Sciences Directorate have developed a well-characterized remote sensing Verification & Validation (V&V) site at the John C. Stennis Space Center (SSC). This site enables the in-flight characterization of satellite and airborne high spatial and moderate resolution remote sensing systems and their products. The smaller scale of the newer high resolution remote sensing systems allows scientists to characterize geometric, spatial, and radiometric data properties using a single V&V site. The targets and techniques used to characterize data from these newer systems can differ significantly from the techniques used to characterize data from the earlier, coarser spatial resolution systems. Scientists are also using the SSC V&V site to characterize thermal infrared systems and active lidar systems. SSC employs geodetic targets, edge targets, radiometric tarps, atmospheric monitoring equipment, and thermal calibration ponds to characterize remote sensing data products. The SSC Instrument Validation Lab is a key component of the V&V capability and is used to calibrate field instrumentation and to provide National Institute of Standards and Technology traceability. This poster presents a description of the SSC characterization capabilities and examples of calibration data.

Pagnutti, Mary↗

Ultraviolet Photoemission Spectroscopy and Kelvin Probe Measurements on Metal Halide Perovskites: Advantages and Pitfalls

In this essay, a case study is presented on the electronic structure of several metal halide perovskites (MHP) using Kelvin probe (KP)-based surface photovoltage (SPV) measurements and ultraviolet photoemission spectroscopy (UPS) to demonstrate the advantages, but also the pitfalls, of using these techniques to characterize the surfaces of these materials. The first part addresses the loss of halide species from perovskite surfaces upon supragap illumination in vacuum. This has the potential to cause both a long-term alteration of the sample work function and a modification of the KP tip during SPV measurements. If undetected, this leads to a misinterpretation of the MHP surface potential. The second part illustrates the difficulties in determining the valence band maximum (VBM) of MHP surfaces with UPS and stresses the importance of taking into account the low density of states at the VBM edge. Given this circumstance, specific care must be taken to eliminate measurement artifacts in order to ascertain the presence or absence of low densities of electronic gap states above the VBM. This essay also highlights issues such as film degradation, nonequilibrium situations (e.g., SPV), and satellite emissions, which occur during photoemission spectroscopy.

36 MATERIALS SCIENCE↗

Determining the twist angle of stacked MoS 2 layers using machine learning-assisted low-frequency interlayer Raman fingerprints

The investigation of twisted stacked few-layer MoS 2 has revealed novel electronic, optical, and vibrational properties over an extended period. For the successful integration of twisted stacked few-layer MoS 2 into a wide range of applications, it is crucial to employ a noninvasive, versatile technique for characterizing the layered architecture of these complex structures. Here, in this work, we introduce a machine learning-assisted low-frequency Raman spectroscopy method to characterize the twist angle of few-layer stacked MoS 2 samples. A feedforward neural network (FNN) is utilized to analyze the low-frequency breathing mode as a function of the twist angle. Moreover, using finite difference method (FDM) and density functional theory (DFT) calculations, we show that the low-frequency Raman spectra of MoS 2 are mainly influenced by the effect of the nearest and second nearest layers. A new improved linear chain model (TA-LCM) with taking the twist angle into the consideration is developed to understand the interlayer breathing modes of stacked few-layer MoS 2 . This approach can be extended to other 2D materials systems and provides an intelligent way to investigate naturally stacked and twisted interlayer interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗