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

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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Time at Temperature Abstract and Intern Poster

Current NRC regulations for BWR operations dictate that any occurrence reaching the point of Departure from Nucleate Boiling (DNB) disqualifies the use of the fuel rod for further reactor operation. That criteria does not account for duration of rate of the power increase, the corresponding effects on material properties or rewetting that may occur. Previous Anticipated Operational Occurrences (AOOs) show short durations power increase that may require limited amounts of heat removal. Industrial experience has shown evidence that fuel can reach dryout yet continue to safely operate in regular reactor conditions. The gap in research into such occurrences is the motivation for a series of experiments, including this current work. Time-at-Temperature experiments aim to identify and characterize the microstructural changes in Zircaloy-2 under oxygen-free high temperatures. This work uses the FlashDSC instrument to rapidly ramp up and down the temperature of a focus ion beam (FIB) prepared large area lift-out (LALO) of Zircaloy-2 at a rate of 10,000 K/s to desired values. The focus is to characterize the microstructure evolution, if any, of Zircaloy-2 that may impact its performance under typical BWR conditions. This characterization includes analyzing grain structure and size, secondary phase particle (SPPs) size, shape, composition, and location using Transmission Electron Microscopy (TEM). Further data collection and analysis is in progress including diffraction pattern indexing and 4D STEM processing. While current results focus on the testing and characterizing unirradiated material, future plans include expansion to irradiated material to explore the effects of rapid transition rates seen in DNB and dryout conditions on irradiationg damage and defect annealing.

36 - MATERIALS SCIENCE↗
DOE OSTI2026

Time at Temperature Experiments on Neutron Irradiated Zircaloy-2 using Conventional & Flash DSC

Dryout events in Boiling Water Reactors (BWRs) are currently treated by NRC regulations as automatic disqualification for continued fuel rod operation, even though this criterion does not account for the rate or duration of power increases, associated changes in material behavior, or the possibility of rewetting. Operational history from Anticipated Operational Occurrences (AOOs) shows that short, transient power excursions often demand only modest heat removal, and industry experience suggests that fuel can briefly enter dryout yet return to safe, stable operation. The lack of detailed understanding of the material response during such events motivates the present series of experiments. This study uses unique and innovative methods to investigate microstructural evolution in irradiated Zircaloy-2 exposed to high temperatures in inert environments. Differential Scanning Calorimetry (DSC) and FlashDSC are combined to build a comprehensive experimental framework capable of identifying the a–ß phase transformation in zirconium and examining defect annealing under steep thermal gradients. FlashDSC enables rapid heating and cooling of Focused Ion Beam (FIB)–prepared large-area lift-outs (LALOs) of irradiated Zircaloy-2 at rates of 1,000 K/s to peak temperatures of 600°C, 750°C, and 900°C. The goal is to determine whether these conditions produce measurable microstructural changes that could influence cladding performance in typical BWR environments. Microstructural characterization includes quantifying dislocation density and assessing secondary phase particle (SPP) size and distribution using Transmission Electron Microscopy (TEM). Ongoing analysis, such as diffraction pattern indexing and 4D STEM processing, will further refine these observations.

36 - MATERIALS SCIENCE↗
DOE OSTI2022

Laser-induced patterning for a diffraction grating using the phase change material of Ge 2 Sb 2 Te 5 (GST) as a spatial light modulator in X-ray optics: a proof of concept

The proposed X-ray spatial light modulator (SLM) concept is based on the difference of X-ray scattering from amorphous and crystalline regions of phase change materials (PCMs) such as Ge 2 Sb 2 Te 5 (GST). In our X-ray SLM design, the “ on” and “ off” states correspond to a patterned and homogeneous state of a GST thin film, respectively. The patterned state is obtained by exposing the homogeneous film to laser pulses. In this paper, we present patterning results in GST thin films characterized by microwave impedance microscopy and X-ray small-angle scattering at the Stanford Synchrotron Radiation Lightsource.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Coexistence of vitreous and crystalline phases of H 2 O at ambient temperature

Formation of vitreous ice during rapid compression of water at room temperature is important for biology and the study of biological systems. Here, we show that Raman spectra of rapidly compressed water at greater than 1 GPa at room temperature exhibits the signature of high-density amorphous ice, whereas the X-ray diffraction (XRD) pattern is dominated by crystalline ice VI. To resolve this apparent contradiction, we used molecular dynamics simulations to calculate full vibrational spectra and diffraction patterns of mixtures of vitreous ice and ice VI, including embedded interfaces between the two phases. We show quantitatively that Raman spectra, which probe the local polarizability with respect to atomic displacements, are dominated by the vitreous phase, whereas a small amount of the crystalline component is readily apparent by XRD. The results of our combined experimental and theoretical studies have implications for detecting vitreous phases of water, survival of biological systems under extreme conditions, and biological imaging. The results provide additional insight into the stable and metastable phases of H 2 O as a function of pressure and temperature, as well as of other materials undergoing pressure-induced amorphization and other metastable transitions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

High‐speed 4‐dimensional scanning transmission electron microscopy using compressive sensing techniques

Abstract Here we show that compressive sensing allows 4‐dimensional (4‐D) STEM data to be obtained and accurately reconstructed with both high‐speed and reduced electron fluence. The methodology needed to achieve these results compared to conventional 4‐D approaches requires only that a random subset of probe locations is acquired from the typical regular scanning grid, which immediately generates both higher speed and the lower fluence experimentally. We also consider downsampling of the detector, showing that oversampling is inherent within convergent beam electron diffraction (CBED) patterns and that detector downsampling does not reduce precision but allows faster experimental data acquisition. Analysis of an experimental atomic resolution yttrium silicide dataset shows that it is possible to recover over 25 dB peak signal‐to‐noise ratio in the recovered phase using 0.3% of the total data. Lay abstract : Four‐dimensional scanning transmission electron microscopy (4‐D STEM) is a powerful technique for characterizing complex nanoscale structures. In this method, a convergent beam electron diffraction pattern (CBED) is acquired at each probe location during the scan of the sample. This means that a 2‐dimensional signal is acquired at each 2‐D probe location, equating to a 4‐D dataset. Despite the recent development of fast direct electron detectors, some capable of 100kHz frame rates, the limiting factor for 4‐D STEM is acquisition times in the majority of cases, where cameras will typically operate on the order of 2kHz. This means that a raster scan containing 256^2 probe locations can take on the order of 30s, approximately 100‐1000 times longer than a conventional STEM imaging technique using monolithic radial detectors. As a result, 4‐D STEM acquisitions can be subject to adverse effects such as drift, beam damage, and sample contamination. Recent advances in computational imaging techniques for STEM have allowed for faster acquisition speeds by way of acquiring only a random subset of probe locations from the field of view. By doing this, the acquisition time is significantly reduced, in some cases by a factor of 10‐100 times. The acquired data is then processed to fill‐in or inpaint the missing data, taking advantage of the inherently low‐complex signals which can be linearly combined to recover the information. In this work, similar methods are demonstrated for the acquisition of 4‐D STEM data, where only a random subset of CBED patterns are acquired over the raster scan. We simulate the compressive sensing acquisition method for 4‐D STEM and present our findings for a variety of analysis techniques such as ptychography and differential phase contrast. Our results show that acquisition times can be significantly reduced on the order of 100‐300 times, therefore improving existing frame rates, as well as further reducing the electron fluence beyond just using a faster camera.

Robinson, Alex W.↗
DOE OSTI2022

Psilocybin: crystal structure solutions enable phase analysis of prior art and recently patented examples

Psilocybin {systematic name: 3-[2-(dimethylamino)ethyl]-1 H -indol-4-yl dihydrogen phosphate} is a zwitterionic tryptamine natural product found in numerous species of fungi known for their psychoactive properties. Following its structural elucidation and chemical synthesis in 1959, purified synthetic psilocybin has been evaluated in clinical trials and has shown promise in the treatment of various mental health disorders. In a recent process-scale crystallization investigation, three crystalline forms of psilocybin were repeatedly observed: Hydrate A, Polymorph A, and Polymorph B. The crystal structure for Hydrate A was solved previously by single-crystal X-ray diffraction. This article presents new crystal structure solutions for the two anhydrates, Polymorphs A and B, based on Rietveld refinement using laboratory and synchrotron X-ray diffraction data, and density functional theory (DFT) calculations. Utilizing the three solved structures, an investigation was conducted via Rietveld method (RM) based quantitative phase analysis (QPA) to estimate the contribution of the three different forms in powder X-ray diffraction (PXRD) patterns provided by different sources of bulk psilocybin produced between 1963 and 2021. Over the last 57 years, each of these samples quantitatively reflect one or more of the hydrate and anhydrate polymorphs. In addition to quantitatively evaluating the composition of each sample, this article evaluates correlations between the crystal forms present, corresponding process methods, sample age, and storage conditions. Furthermore, revision is recommended on characterizations in recently granted patents that include descriptions of crystalline psilocybin inappropriately reported as a single-phase `isostructural variant.' Rietveld refinement demonstrated that the claimed material was composed of approximately 81% Polymorph A and 19% Polymorph B, both of which have been identified in historical samples. In this article, we show conclusively that all published data can be explained in terms of three well-defined forms of psilocybin and that no additional forms are needed to explain the diffraction patterns.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

The Focus of an Ultraintense Laser Pulse

Back in 1885, von Lommel studied the diffraction of a circular opening. His study was one step further than the Airy diffraction model (describing patterns in the focal plane) because von Lommel’s model was able to describe what the light distribution before and after the focus is. Today’s extreme lasers have a flat-top profile whose diffraction pattern in the vicinity of the focus is very much reminiscent of von Lommel’s description. In the present Chapter, we will compute, based on a Huygens-Fresnel integral method, the laser field distribution around the focus. This modelling is particularly important because the intensity distribution before and after the focal plane (where the Airy disk exists) is very relevant to many contemporary experiments, and is key to the ionization of atoms and the dynamics of liberated electrons. For clarity, we are going to analyze three cases corresponding to three f-numbers: f/10, f/1.8, and f/1.1. Our computed results reveal the present-day significance of von Lommel’s pioneering results. Here, they help us understand the light distribution in the entire focal region of an ultraintense laser pulse including the full vectorial fields, not just the focal plane.

Roso, Luis [Universidad de Salamanca (Spain)]↗
DOE OSTI2024

Exploring 2D X-ray diffraction phase fraction analysis with convolutional neural networks: Insights from kinematic-diffraction simulations

Abstract Deep-learning models are effective for analyzing the complex information in 2D X-ray diffraction (XRD) patterns. Accurately collecting parameters of the material sample is crucial during model training, significantly impacting model performance. In this study, we employ a kinematic-diffraction simulator to generate simulated 2D XRD patterns for Ti–6Al–4V alloy, allowing precise control of sample parameters. These simulated patterns are used to train convolutional neural networks, predicting $$\upbeta$$ β -phase volume fractions. The training data set consists exclusively of 2D XRD patterns with pure $$\upalpha$$ α - or pure $$\upbeta$$ β -phase, while the testing set incorporates patterns with intermediate phase volume fraction. In particular, we investigate how the architectures of the model influence prediction reliability and computational performance. Experimental results reveal that, with appropriate training, the convolutional neural network accurately detects intermediate phase volume fractions even trained with only pure-phase patterns, achieving a mean square error accuracy of $$9.4 \times 10^{-4}$$ 9.4 × 10 - 4 . Graphical abstract

Yue, Weiqi↗
DOE OSTI2026

Machine learning approaches for crystallographic classification from synthetic 2D X-ray diffraction data

Crystallographic structure identification is crucial for understanding material properties; however, current methodologies often depend on labor-intensive and time-consuming analyses of 2D X-ray diffraction (XRD) patterns. To address these limitations, this study employs synthetic 2D XRD patterns combined with deep learning (DL) techniques to enable automated and high-throughput classification of the seven crystal systems and 230 space groups. We introduce the novel Auto Diffraction Pipeline, designed to generate synthetic 2D XRD spot patterns from crystallographic information files under diverse conditions, including varying zone axes, atomic substitution, atomic depletion and mechanical loading. These conditions enhance the realism of synthetic data, mitigating the scarcity of experimental datasets and enabling the creation of large representative training sets. Convolutional neural networks were trained and validated on these synthetic datasets to classify crystallographic structures across multiple scenarios. Our results demonstrate that integrating synthetic 2D XRD patterns with DL facilitates rapid, accurate and automated crystallographic classification, promoting the wider adoption of data-driven approaches in materials science.

Shahnazari, Ayoub [Univ. of Rochester, NY (United ↗
DOE OSTI2020

General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part II

X-ray Bragg coherent diffraction imaging (BCDI) has been demonstrated as a powerful 3D microscopy approach for the investigation of sub-micrometre-scale crystalline particles. The approach is based on the measurement of a series of coherent Bragg diffraction intensity patterns that are numerically inverted to retrieve an image of the spatial distribution of the relative phase and amplitude of the Bragg structure factor of the diffracting sample. This 3D information, which is collected through an angular rotation of the sample, is necessarily obtained in a non-orthogonal frame in Fourier space that must be eventually reconciled. To deal with this, the approach currently favored by practitioners (detailed in Part I) is to perform the entire inversion in conjugate non-orthogonal real- and Fourier-space frames, and to transform the 3D sample image into an orthogonal frame as a post-processing step for result analysis. In this article, which is a direct follow-up of Part I, two different transformation strategies are demonstrated, which enable the entire inversion procedure of the measured data set to be performed in an orthogonal frame. The new approaches described here build mathematical and numerical frameworks that apply to the cases of evenly and non-evenly sampled data along the direction of sample rotation ( i.e. the rocking curve). The value of these methods is that they rely on the experimental geometry, and they incorporate significantly more information about that geometry into the design of the phase-retrieval Fourier transformation than the strategy presented in Part I. Finally, two important outcomes are (1) that the resulting sample image is correctly interpreted in a shear-free frame and (2) physically realistic constraints of BCDI phase retrieval that are difficult to implement with current methods are easily incorporated. Computing scripts are also given to aid readers in the implementation of the proposed formalisms.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Valence Electron Distributions from Sub-Angstrom Convergent Beam Electron Diffraction

Modern aberration-corrected scanning transmission electron microscopes can acquire four-dimensional data sets (“4D STEM”) by recording convergent beam electron diffraction (CBED) patterns, using precisely positioned, sub-angstrom probes. Here, we demonstrate that these patterns can probe the site symmetry, atomic displacements, and valence electron distributions at individual atomic columns. To this end, 4D STEM CBED patterns were acquired from SrTiO 3 single crystals and compared with patterns calculated using scattering potentials derived from density functional theory. Here, we show that an aspherical valence electron charge build-up at the oxygen sites causes intensity asymmetries in the low-angle scattering portion of the patterns. Using strained SrTiO 3 films containing subtle polar displacements within nanometer-sized domains, it is shown that the high-angle scattering portion in each pattern is sensitive to atomic displacements.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Microscopic piezoelectric behavior of clamped and membrane (001) PMN-30PT thin films

Bulk single-crystal relaxor-ferroelectrics, like Pb(Mg 1/3 Nb 2/3 )O- 3 -PbTiO 3 (PMN-PT), are widely known for their large piezoelectricity. This is attributed to polarization rotation, which is facilitated by the presence of various crystal symmetries for compositions near a morphotropic phase boundary. Relaxor-ferroelectric thin films, which are necessary for low-voltage applications, suffer a reduction in their piezoelectric response due to clamping by the passive substrate. To understand the microscopic behavior of this adverse phenomenon, we employ the AC electric field driven in-operando synchrotron x-ray diffraction on patterned device structures to investigate the piezoelectric domain behavior under an electric field for both a clamped (001) PMN-PT thin film on Si and a (001) PMN-PT membrane released from its substrate. In the clamped film, the substrate inhibits the field-induced rhombohedral (R) to tetragonal (T) phase transition resulting in a reversible R to Monoclinic (M) transition with a reduced longitudinal piezoelectric coefficient d 33 < 100 pm/V. Releasing the film from the substrate results in recovery of the R to T transition and results in a d 33 > 1000 pm/V. Here, using diffraction with spatial mapping, we find that lateral constraints imposed by the boundary between the active and inactive materials also inhibit the R to T transition. Phase-field calculations on both clamped and released PMN-PT thin films simulate our experimental findings. Resolving the suppression of thin film piezoelectric response is critical to their application in piezo-driven technologies.

36 MATERIALS SCIENCE↗
DOE OSTI2020

One–Step Fabrication of Nanocrystalline Nanonetwork SnO 2 Gas Sensors by Integrated Multilaser Processing

An integrated multilaser process is developed to fabricate nanocrystalline nanonetwork SnO 2 gas sensors in one integrated procedure, which combines electrodes fabrication, nanomaterials deposition, and postannealing. Interdigit electrodes are fabricated on an Au-coated fused silica substrate using a picosecond (ps) laser, which ablates the Au coating from the back of the substrate to pattern the electrodes. A novel transmitted Ps laser deposition (TPLD) process is designed to deposit SnO 2 nanonetwork on the interdigit electrodes with precise deposition area control under a close target-to-substrate distance. The obtained SnO 2 nanonetwork is in situ postannealed by a CO 2 laser to improve the crystallinity, while the nano morphology and grain size keep intact. To investigate the morphology and formation process of the nanonetwork, the microstructure of the laser-deposited SnO 2 layer is characterized. As a result, the crystallization control of CO 2 laser annealing is investigated through analyzing the Raman spectrum, X-ray diffraction (XRD) patterns, and lattice structures of the samples. By exposed to H 2 atmosphere, the fabricated gas sensor is demonstrated for H 2 monitoring.

08 HYDROGEN↗
DOE OSTI2020

Atomic resolution convergent beam electron diffraction analysis using convolutional neural networks

Two types of convolutional neural network (CNN) models, a discrete classification network and a continuous regression network, were trained to determine local sample thickness from convergent beam diffraction (CBED) patterns of SrTiO 3 collected in a scanning transmission electron microscope (STEM) at atomic column resolution. Acquisition of atomic resolution CBED patterns for this purpose requires careful balancing of CBED feature size in pixels, acquisition speed, and detector dynamic range. The training datasets were derived from multislice simulations, which must be convolved with incoherent source broadening. Sample thicknesses were also determined using quantitative high-angle annular dark-field (HAADF) STEM images acquired simultaneously. The regression CNN performed well on sample thinner than 35 nm, with 70% of the CNN results within 1 nm of HAADF thickness, and 1.0 nm overall root mean square error between the two measurements. The classification CNN was trained for a thicknesses up to 100 nm and yielded 66% of CNN results within one classification increment of 2 nm of HAADF thickness. Our approach depends on methods from computer vision including transfer learning and image augmentation.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Chemical Bonding Governs Complex Magnetism in MnPt 5 P

Subtle changes in chemical bonds may result in dramatic revolutions in magnetic properties in solid-state materials. MnPt 5 P, a derivative of the rare-earth-free ferromagnetic MnPt 5 As, was discovered and is presented in this work. Specifically, MnPt 5 P was synthesized, and its crystal structure and chemical composition were characterized by X-ray diffraction as well as energy-dispersive X-ray spectroscopy. Accordingly, MnPt 5 P crystallizes in the layered tetragonal structure with the space group P4/mmm (No. 123), in which the face-shared Mn@Pt 12 polyhedral layers are separated by P layers. In contrast to the ferromagnetism observed in MnPt 5 As, the magnetic properties measurements on MnPt 5 P show antiferromagnetic ordering occurs at ~188 K with a strong magnetic anisotropy in and out of the ab-plane. Moreover, a spin-flop transition appears when a high magnetic field is applied. An A-type antiferromagnetic structure was obtained from the analysis of powder neutron diffraction (PND) patterns collected at 150 and 9 K. Calculated electronic structures imply that hybridization of Mn-3d and Pt-5d orbitals is critical for both the structural stability and observed magnetic properties. Semiempirical molecular orbitals calculations on both MnPt 5 P and MnPt 5 As indicate that the lack of 4p character on the P atoms at the highest occupied molecular orbital (HOMO) in MnPt 5 P may cause the different magnetic behavior in MnPt 5 P compared to MnPt 5 As. The discovery of MnPt 5 P, along with our previously reported MnPt5As, parametrizes the end points of a tunable system to study the chemical bonding which tunes the magnetic ordering from ferromagnetism to antiferromagnetism with the strong spin–orbit coupling (SOC) effect.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Au assisted smooth ultrathin epitaxial ZnO film grown by pulsed laser deposition on sapphire(0001)

High quality ZnO has applications in photonics and electronics. Literature has shown that continuous, but rough ZnO film can be grown on sapphire substrate by pulsed laser deposition (PLD). In this work, ZnO and Au were co-deposited by PLD on sapphire(0001) substrates from a single ZnO target overlaid with an Au strip that serves as a catalyst. The reflection high-energy electron diffraction (RHEED) patterns show paired double stripes from sample of ZnO-Au where the difference of in-plane lattice parameters between ZnO and Au is 11.4 %. The two-dimensional (2D) reciprocal space maps constructed from azimuthal RHEED (ARHEED) patterns reveal parallel epitaxial relationship between ZnO and Au in the continuous ZnO-Au film on sapphire substrate. Transmission electron microscopy (TEM) cross section images and energy dispersive spectroscopy maps show a minute amount of Au nanocrystals distributed in the entire ultrathin ZnO film. Atomic force microscopy shows the root-mean-square roughness of the surface of ultrathin ZnO film with Au is in the sub-nm range. The ARHEED and TEM results show that a couple of atomic percentages of Au co-deposited with ZnO catalyzes the growth of smooth ultrathin epitaxial ZnO film.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Stable perovskite-fluorite dual-phase composites synthesized by one-pot solid-state reactive sintering for protonic ceramic fuel cells

We report that this work synthesized a series of oxide composites with nominal compositions of BaCe 05 Zr 0.4 Y 0.1 O 3-δ (BCZY)-Ce 0.5 Y 0.5 O 2-δ (YDC) based on the BCZY/YDC molar ratios of 0.5:1, 1:1, 2:1, and 4:1 (BCZY-YDC-0.5–1, BCZY-YDC-1-1, BCZY-YDC-2-1, and BCZY-YDC-4-1) using a one-pot solid state reactive sintering (SSRS) method. The X-ray diffraction (XRD) patterns and refinement proved that the one-pot SSRS at 1450 °C for 12 h could achieve the perovskite-fluorite dual-phase composites (DPCs) with the desired structure compositions. The scanning electron microscopy (SEM) images showed that the two DPCs of BCZY-YDC-1-1 and BCZY-YDC-2-1 formed excellent percolation for perovskite and fluorite phases. The conductivity measurement by electrochemical impedance spectroscopy (EIS) and the transference number measurement by the electromotive force (EMF) test proved that changing the BCZY/YDC molar ratio and operating condition could adjust the DPC's conduction property to make them suitable for electrolytes and electrode scaffolds for protonic ceramic fuel cells (PCFCs). The long-term conductivity testing and the crystal structure analysis after EMF testing under versatile conditions indicated that the DPCs of BCZY-YDC-2-1 and BCZY-YDC-1-1 were durable PCFC component materials. The PCFC button cells with the as-discovered BCZY-YDC-2-1 and BCZY-YDC-1-1 as an electrolyte and an anode scaffold, respectively, and the reported Ba–Ce–Fe–Co–O perovskite-perovskite composite as a cathode showed promising performance under H 2 /air gradient.

08 HYDROGEN↗
DOE OSTI2021

An efficient computational framework for charge density estimation in twisted bilayer graphene

Electronic properties such as band structure and Fermi velocity in low-angle twisted bilayer graphene (TBG) are intrinsically dependent on the atomic structure. Rigid rotation between individual graphene layers provides an approximate description of the bilayer symmetry. Upon relaxation, in-plane displacement of the atoms in low angle TBG causes a change in the symmetry through the enlargement of the AB stacking regions and the reduction in size of AA and SP stacking regions. However, the effect of this in-plane relaxation on the charge density remains unexplored, because the necessary electronic structure calculations of such large supercells of low twist angle TBG are computationally infeasible. Therefore, we develop a computationally efficient framework that enables the exploration of the charge density symmetry of the low twist angle TBG. This framework is based on the Fourier representation of the charge density which presents high intensity Bragg peaks. Here we find that with the decrease of twist angle, low intensity satellite peaks also become apparent. Our framework incorporates these satellite peaks which reveals transformation of symmetry in the charge density distribution from high to low twist angle TBG. One striking outcome is the demonstration of the electron localization in the AA region of low twist angle TBG. Our framework helps to explain the effect of the atomistic relaxation on the charge density distribution and thus, it provides information about exotic electronic properties of low twist angle TBG at a low computational expense.

36 MATERIALS SCIENCE↗