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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Understanding Formation of Irradiation-Induced Defects through 4D-STEM, Electron Tomography, and WBDF-STEM

A major challenge in advancing nuclear materials for next-generation fission and proposed fusion reactors is to comprehensively understand the formation of irradiation-induced defects. Here it is essential to correlate the evolution of irradiation-induced defects and the degradation of mechanical properties, as they collectively dictate the material's lifespan and ensure nuclear safety. Scanning transmission electron microscopy (STEM) based techniques have emerged as indispensable tools for irradiation-induced defect characterization, offering high spatial resolution imaging and chemical analysis, such as electron energy loss spectroscopy (EELS) and energy dispersive X-ray spectroscopy (EDXS). These techniques have been effectively used to obtain an atomic-scale view of the defect structure. Recent advances in electron microscopy, particularly in 4D-STEM, offer detailed insight into microstructural evolution by capturing full 2D diffraction patterns at every pixel position. Using high-speed direct electron detectors, this technology generates a four-dimensional dataset, overcoming the limitations of traditional STEM imaging.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Deformation Mechanisms at Grain Boundaries in Polycrystals (Final Report)

Despite its significance in polycrystalline materials, there have been few experimental investigations of the activity of grain boundary sliding (GBS) and the relationship between GBS and slip transmission at grain boundaries. This work addressed this knowledge gap by an experimental and analytical investigation into the interactions between grain boundary sliding (GBS) and slip transmission plastic deformation mechanisms, and how these are impacted by local microstructure. Polycrystalline columnar aluminum of 99.99% purity was examined as a highly modellable system for characterizing grain boundary-local deformation mechanism interaction. High-resolution, large field-of-view strain fields and grain orientation information were captured and statistically analyzed to identify deformation activity with respect to the local microstructure, using a combination of scanning electron microscopy and digital image correlation (SEM-DIC) with electron backscatter diffraction (EBSD). Alignment between the lower-resolution electron backscatter diffraction (EBSD) data and the higher-resolution strain fields was significantly improved by clustering of strain data within an EBSD-defined boundary mantle. Although this work specifically focuses on characterizing the relationship between grain boundary sliding (GBS) and slip transmission, the developed experimental approach, multimodal data alignment process, and automated displacement discontinuity measurement process can be used to study a variety of mechanism interactions across a broad range of materials. Regarding GBS and slip transmission interaction, significant findings include that (1) grain boundaries that slide easily do not facilitate slip transmission; (2) substantial gradients in GBS magnitude could be found along the length of individual grain boundaries, and these were caused by strain discontinuities across the boundary related to deformation anisotropy between adjacent grains; (3) direct transmission and GBS were anti-compatible and facilitated by opposing boundary types (low misorientation and high energy grain boundaries respectively); (4) increased GBS activity was correlated with decreased indirect transmission behavior; (5) GBS accommodation at triple junctions was enabled by intragranular plasticity; and (6) the local intragranular plastic strain discontinuity between grains determined the magnitude of GBS gradients. The experimental strain fields were compared to that of a tangent crystal plasticity finite element (CPFE) model developed by collaborators (Mr. Ajey Venkataraman and Professor Michael Sangid, Purdue University). Implication of this work for improving CPFE models and deformation prediction are discussed. This work provides insight into the nature of these mechanisms and can be used to identify strain transfer criteria that can lead to improved GBS-sensitive crystal plasticity models.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Tensile Deformation of DED Graded IN718-René41 Superalloy at 650°C by in-situ Neutron Diffraction and Digital Image Correlation

A compositionally graded material comprised IN718 (718, γ'/γ" strengthened superalloy) and René41 (R41, a medium γ' strengthened superalloy) was fabricated using laser blown-powder directed energy deposition (DED/LB-M). Hot gas path components that require high and low temperature capabilities at different locations may benefit from such graded superalloy, potentially eliminating the use of welded or mechanically joined components and reducing cost. In the present work, microstructure and 650°C tensile behavior of 718-R41 graded superalloy in as-built and heat-treated states are investigated by Digital Image Correlation (DIC), in-situ neutron diffraction, coupled with conventional characterization techniques. The applied heat treatment generates static recrystallization and equiaxed grains in 718 rich compositions, while R41 rich compositions remain partially or un-recrystallized. Yield strengths of 718 and R41 sections in heat-treated state are comparable to wrought forms but the graded compositions show weakness. From neutron experiment, diffraction elastic constants and single crystal elastic constants are calculated, which show small difference between the as-built and heat-treated states and between the γ and γ' phases. Grain-level load transfer from the (220) grains to (200) grains is found to be composition dependent, and qualitatively agrees with DIC measured macroscopic yield strength. Within the (200) grains, the γ/γ' phases deform elastically until the γ phase yields and afterwards the γ' phase takes load from γ phase.

digital image correlation↗
NASA NTRS1988

Applications of synchrotron radiation to materials science: Diffraction imaging (topography) and microradiography

Synchrotron radiation sources are now available throughout the world. The use of hard X-ray radiation from these sources for materials science is described with emphasis on diffraction imaging for material characterization. With the availability of synchrotron radiation, real-time in situ measurements of dynamic microstructural phenomena have been started. This is a new area where traditional application of X-rays has been superseded. Examples are chosen from limited areas and are by no means exhaustive. The new emerging information will, no doubt, have great impact on materials science and engineering.

Kuriyama, Masao↗
NASA NTRS2018

Water-Rock Interactions in Outer Solar System Bodies: Evidence from the Coordinated Analysis of Interplanetary Dust

NASA has an ongoing program of collecting interplanetary dust particles (IDPs) in the stratosphere using high altitude research aircraft. The collected IDPs are derived from asteroids and comets and here we report studies of a subset of hydrated IDPs rich in carbonaceous matter that are proposed to have a cometary origin. Our studies are aimed at understanding the evolution of oxygen reservoirs in the Solar System and their interaction with cometary minerals and organic matter. The small size (<20 μm) and fragility of these IDPs present a number of analytical challenges. We have pioneered techniques for performing chemical, mineralogical, isotopic, and spectroscopic measurements on the same sample in a carefully coordinated sequence. Coordinated analyses of nanogram-size samples is made possible by several delicate sample preparation techniques. To avoid organic contamination, we embed IDPs in elemental sulfur and use ultramicrotomy to partly section the particles (the first few micrometers). Multiple thin sections (50-70 nm thick) are placed on different substrates depending on the analysis technique. We use a JEOL 2500SE scanning, transmission electron microscope (STEM) to determine the mineralogy, microstructure, and elemental compositions of constituent minerals in the thin sections through a combination of high resolution imaging, electron diffraction, quantitative energy-dispersive x-ray mapping, and electron energy-loss spectroscopy. Following the STEM analyses, we use a NanoSIMS 50L for high spatial resolution isotopic measurements of H, C, N, and O to search for presolar grains and to understand the origin of the indigenous organic matter. The isotopic analyses are performed on the same sections analyzed in the STEM in order to correlate isotopic properties with the elemental and mineralogical data. We reserve other thin sections for non-destructive analyses utilizing synchrotron-based techniques including Fourier-transform infrared (FTIR) micro-spectroscopy and X-ray absorption near-edge structure (XANES) analyses, especially for functional group analysis of organic matter in the particles. The remainder of the IDP is extracted from the sulfur bead that was used for microtomy and is pressed into Au foil for quantitative analysis (including light elements) using a JEOL 8530F field emission electron probe microanalyzer (EPMA). After the EPMA measurements, high precision oxygen isotopic analyses are obtained using Cameca IMS1270/1290 instruments at UCLA. The hydrated IDPs in this study are dominated by saponitic clays, with minor magnetite, carbonate and abundant organic matter. The remarkable oxygen isotopic compositions, high carbon contents, and the abundance of isotopically anomalous organic matter, together suggest that the high carbon, hydrated IDPs are derived from primitive sources not yet represented in meteorite collections such as outer main belt P- and D-type asteroids or comets.

Keller, Lindsay P.↗
DOE OSTI2025

Generalizable Image Segmentation for Microstructure Characterization Through Integrated SEM and EBSD Analysis

We demonstrate generalizable semantic segmentation using minimal ground truth data. Correlated scanning electron microscopy (SEM) images and electron backscatter diffraction (EBSD) measurements of frictionstir processed 316L stainless steel plates were used to train deep learning models for grain boundary segmentation. Secondary electron (SE) imaging taken at an accelerating voltage of 10 keV correlated to EBSD-derived grain boundaries produced the best performing model. Notably, an ensemble of three models trained on a single SE image produced accurate segmentation over a series of BSE images of samples manufactured under different processing parameters, with a resultant mean absolute error in grain size of 0.34 µm. The striking generalizability of the models likely results from the similar escape depths of the SE training input and the EBSD training output and the reduced probability of dislocation artifacts appearing in the image. This finding highlights the importance of considering the physical principles behind imaging in the development of robust segmentation models for microstructure characterization.

Taufique, Mohammad Fuad Nur↗
DOE OSTI2023

Dendritic deformation modes in additive manufacturing revealed by operando x-ray diffraction

Abstract Dynamic solidification behavior during metal additive manufacturing directly influences the as-built microstructure, defects, and mechanical properties of printed parts. How the formation of these features is driven by temperature variation (e.g., thermal gradient magnitude and solidification front velocity) has been studied extensively in metal additive manufacturing, with synchrotron x-ray imaging becoming a critical tool to monitor these processes. Here, we extend these efforts to monitoring full thermomechanical deformation during solidification through the use of operando x-ray diffraction during laser melting. With operando diffraction, we analyze thermomechanical deformation modes such as torsion, bending, fragmentation, assimilation, oscillation, and interdendritic growth. Understanding such phenomena can aid the optimization of printing strategies to obtain specific microstructural features, including localized misorientations, dislocation substructure, and grain boundary character. The interpretation of operando diffraction results is supported by post-mortem electron backscatter diffraction analyses.

Dass, Adrita (ORCID:000000019100635X)↗
DOE OSTI2025

An Integrated High-Speed Microstructural Characterization Method Using Simultaneous XRD, Stereo-DIC, and PCI

High-speed characterization of the deformation mechanisms in polycrystalline metals requires the quantification of full strain fields and local microstructural evolutions simultaneously. In this paper, we present a novel experimental method to integrate phase-contrast imaging (PCI), stereographic digital image correlation (stereo-DIC), and full-ring X-ray diffraction (XRD) to allow for the simultaneous characterization of polycrystalline metals at 1MHz or higher. A Kolsky bar was integrated into the synchrotron X-ray source in Sector 32 ID-B at the Advance Photon Source (APS) at Argonne National Laboratory. When the sample is dynamically loaded, the diagnostic methods of full-ring XRD, PCI, and stereo-DIC are properly synchronized to record the deformation behavior at both continuum and microstructural scales as a function of the loading history. An advanced high-strength steel (AHSS) is used as a model material to demonstrate the capabilities of this new experimental method.

36 MATERIALS SCIENCE↗
NASA NTRSDate not supplied

Zircon (U-Th)/He Impact Crater Thermochronometry and the Effects of Shock Microstructures on Helium Diffusion Kinetics

Absolute age determination of impact cratering events remains difficult and often controversial; a challenge that has resulted in < 50% of known impact craters regarded as accurately and precisely dated. Besides conventional 40Ar/39Ar and U-Pb methods, zircon (U-Th)/He (ZHe) dating of impactites has been applied to large- to medium-sized impact structures. ZHe dates can be fully reset in minutes at 1000°C, which is commonly reached in central sections of the melt sheet, whereas resetting of ZHe at <300°C, which might be encountered near the crater margins or persist in post-impact hydrothermal systems, may take >103-6 years. There is a critical need to quantify the effects of shock-induced microstructures and impact metamorphism on helium diffusion kinetics in well-characterized, variably shocked zircon to further establish the reliability of (U-Th)/He for dating impacts. For this purpose, we investigated suevite and impact melt samples from two impact structures, the Chicxulub multi-ring basin and the Ries complex crater, which enables us to compare zircon helium diffusion kinetics from impact structures with differing sizes, ages, and hydrothermal system longevities. Shock microstructures were characterized by backscattered-electron (BSE) imaging prior to diffusion step-heating fractional release experiments using light-bulb furnace with prograde and retrograde incremental 10°C steps from 250°C to 600°C. Afterward, we characterize the diffusion domain sizes and their interconnectivity within the shocked zircon grains using electron backscatter diffraction (EBSD). We find that zircon with few shock microstructures exhibit no significant deviation from helium diffusion kinetics of undamaged zircon. In contrast, zircon grains with planar deformation features (PDFs) and granular textures classified by BSE and EBSD are characterized by a dramatic decrease in helium retentivity, similar to radiation damaged grains, due to a reduction in the effective domain size and the introduction of interconnected fast diffusion pathways created by shock microstructures. A subset of grains were dated by ZHe after the external morphology of the grains was determined by BSE imaging. The euhedral grains yielded a weighted mean age within the uncertainty of the accepted impact ages, whereas the grains with PDFs or granular textures exhibited younger ages. Thus, these diffusion experiments and ZHe dates suggest that the dramatic decrease in domain size likely renders shocked grains more susceptible to impact-induced hydrothermal resetting and subsequent overprinting. Hence, characterization of shock microstructures is critical for determining accurate impact ages using ZHe methods especially when applied to previously unconstrained craters. The thermochronometer also offers the opportunity to determine the magnitude and duration of post-impact hydrothermal circulation.

zircon↗
DOE OSTI2024

Voltage and temperature effects on low cobalt lithium-ion battery cathode degradation

Degradation of low cobalt lithium-ion cathodes was tested using a full factorial combination of upper cut-off voltage (4.0 V and 4.3 V vs. Li/Li + ) and operating temperature (25 °C and 60 °C). Half-cell batteries were analyzed with electrochemical and microstructural characterization methods. Electrochemical performance was assessed with galvanostatic cycling, cyclic voltammetry (CV), and electrochemical impedance spectroscopy (EIS) supported by distribution of relaxation times (DRT) analysis. Electrode microstructure was characterized with scanning electron microscopy (SEM), X-ray diffraction (XRD), and X-ray absorption near edge structure (XANES) imaging. Higher cut-off voltage cycling shows presence of NiO x formation, a low diffusivity rock-salt phase, in both CV and XRD data. XRD patterns confirmed that the rock-salt phase was beginning to form at the low cut-off voltage at high temperature, but in much lower intensity than at the high cut-off voltage. Higher temperature accelerates degradation processes at both voltages. Degradation factors at high temperature include NiO x formation, cathode material dissolution, and electrolyte decomposition. SEM analysis suggests that supporting phases may isolate and disconnect active material particles reducing capacity retention and battery life cycle. DRT analysis and XANES imaging show that both high temperature samples revealed a NiO x phase based on an increased diffusive impedance and a visible shift in the XANES spectra. The low cut-off voltage, high temperature sample showed a split peak and shift to lower energies indicating early formation of the NiO x phase. The diffusive impedance, which hinders intercalation and deintercalation, is driven by the formation of the NiO x phase. While primarily driven by cut-off voltage, elevated temperature also contributes to this degradation mechanism.

electrochemical impedance spectroscopy↗
DOE OSTI2025

Correlating energy density induced residual stress, porosity, and mechanical property variations in directed energy deposition using neutron diffraction and imaging techniques

In a directed energy deposition (DED) process, the energy density deposited into the materials drives the structure and properties. The energy density is influenced by several printing parameters, such as laser power, hatch spacing, scanning speed, etc. In this study, 316L stainless steels samples were fabricated with varying hatch spacing aiming to induce variations in sample microstructure and properties. A combination of techniques including engineering neutron diffraction, neutron computed tomography, and tensile testing, were employed to correlate the structure and macroscopic properties. Porosity was predominantly observed at the bottom of the deposited materials and was effectively reduced by decreased hatch spacing. Correlatively, compressive residual stress was observed at the bottom of the specimens, while internal stress is largely determined by the hatch spacing. The residual stress in general decreases as the hatch spacing decreases. The maximum ultimate tensile strength (UTS) was found to increase from 517.4 to 528.6 MPa with a strain increased from 0.847 to 0.897 as the hatch spacing decreased from 0.45 to 0.42 mm. However, further increase in energy density by reducing the hatch spacing resulted in a significant decrease in UTS (as low as 452 MPa). This work provides new insights from bulk non-destructive techniques into correlating energy density induced residual stress, porosity, and mechanical property variations in directed energy deposition.

316L stainless steel↗
DOE OSTI2023

Microstructure-Property Relationships in Epitaxial Cu(In, Ga)Se2 Solar-Cell Absorbers

Epitaxially grown Cu(In,Ga)Se 2 (CIGS) absorber layers were analyzed by various techniques in scanning electron microscopy in order to reveal microstructure-property relationships in these thin films. Owing to their epitaxial nature, these CIGS absorber layers do not contain any grain boundaries, but only anti-phase domains (APDs) and dislocations. By combining electron channeling-contrast imaging, electron backscatter diffraction, and cathodoluminescence (CL), in some cases on identical specimen positions of polished cross-sections of CIGS/Mo/glass stacks, it was possible to correlate the presence and orientations of APDs and dislocations with the lateral distributions of the CL intensity and emission-peak energy. We studied CIGS layers with three different [Ga]/([Ga]+[In]) ratios as well as with and without NaF/KF treatments. Considerable differences between the CIGS layer properties in the microstructure-property relationships were found, depending on the growth parameters. Dislocations in the epitaxial CIGS layers do not tend to exhibit strong CL intensity decreases, which contrasts with the situation in numerous other semiconductor materials.

anti-phase domains↗
DOE OSTI2026

LaueMatching: an approach for rapid and robust indexing of Laue diffraction patterns

Traditional Laue diffraction pattern indexing often struggles with noisy data, weak signals, peak overlap and missing reflections, particularly from complex or deformed microstructures. Here, we introduce LaueMatching, a high-throughput indexing algorithm designed to overcome these limitations. LaueMatching utilizes a fundamentally different approach based on direct pattern correlation: experimentally pre-processed images are compared against a comprehensive pre-computed library of simulated diffraction patterns corresponding to a dense grid of possible orientations. This approach bypasses the need for explicit peak identification and fitting, steps that are often a failure point for traditional methods. The algorithm rapidly and robustly indexes multiple crystallographic orientations and crystal systems simultaneously, even from challenging patterns. LaueMatching's effectiveness and accuracy have been rigorously tested and validated on diverse experimental (Ni, Al, EuAl 2 O 4 ) and simulated diffraction patterns, demonstrating high-fidelity orientation refinement. Code to implement this approach on both CPU and GPU resources can be downloaded from https://github.com/AdvancedPhotonSource/LaueMatching.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Imaging and Segmenting Grains and Subgrains Using Backscattered Electron Techniques

We present two new methods of processing data from backscattered electron signals in a scanning electron microscope to image grains and subgrains. The first combines data from multiple backscattered electron images acquired at different specimen geometries to (1) better reveal grain boundaries in recrystallized microstructures and (2) distinguish between recrystallized and unrecrystallized regions in partially recrystallized microstructures. The second utilizes spherical harmonic transform indexing of electron backscatter diffraction patterns to produce high angular resolution orientation data that enable the characterization of subgrains. Subgrains are produced during high-temperature plastic deformation and have boundary misorientation angles ranging from a few degrees down to a few hundredths of a degree. Here, we also present an algorithm to automatically segment grains from combined backscattered electron image data or grains and subgrains from high angular resolution electron backscatter diffraction data. Together, these new techniques enable rapid measurements of individual grains and subgrains from large populations.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Microstructure Clones

Background: A material’s microstructure drives its material performance. Contemporary crystal plasticity experiments compare full-field strain measurements of polycrystal specimens to models. Because each specimen is unique, it is impossible to know which features of the observed deformation are deterministic vs statistical; thus, differences between model and experiment may or may not be significant. Objective: This paper introduces the invention of microstructure clones. Microstructure clones are 2D oligocrystal specimens that have nearly identical microstructures to remedy the aforementioned experimental limitations. Having specimens with nearly identical microstructures will allow for multiple destructive tests of a microstructure (either as repeats or intentionally different experiments), an ability to “see the future” by providing insight into how a specimen will deform, variability quantification, and experimental investigations of response to small microstructural changes. Methods: This work introduces microstructure clones. Repeatability of these clones is demonstrated in tensile bars of pure nickel. Local strain measurements from digital image correlation are compared between clone specimens and compared to results from a crystal plasticity finite element model. Results: Two sets of microstructure clones were tested in this study and displayed very consistent deformation responses within each clone set. Small observed differences in deformation invite investigation into microstructure stochasticity and the effect of small microstructural and loading differences. Conclusions: Microstructure clones represent a significant shift in understanding structure–property relationships. This work reshapes experimental crystal plasticity to allow for experiments that control for specific variables, quantification of microstructural stochasticity (and other sources of stochasticity), and opportunities for replicating experiments.

Crystal Plasticity↗
DOE OSTI2023

A Comparison of Solidification Structures and Submicroscale Cellular Segregation in Rapidly Solidified Stainless Steels Produced via Two-Piston Splat Quenching and Laser Powder Bed Fusion

Fusion-based additive manufacturing techniques leverage rapid solidification (RS) conditions to create parts with complex geometries, unique microscale/nanoscale morphological features, and elemental segregation. Three custom composition stainless steel alloys with varying chromium equivalence to nickel equivalence ratio (Cr eq /Ni eq ) between 1.53 and 1.95 were processed using laser powder bed fusion (LPBF) and/or two-piston splat quenching (SQ) to produce solidification rates estimated between 0.4 and 0.8 m/s. Both scanning electron microscopy (SEM) and transmission electron microscopy (TEM) were utilized to collect high-resolution images, electron backscatter diffraction (EBSD) phase identification, and measure cellular segregation. Similar features were observed in both LPBF and SQ samples including phase and microstructure, nanoscale oxide particles, cell size, and segregation behavior. However, dislocation pileup was observed along the cell boundaries only in the LPBF austenite solidified microstructure. Targeted adjustment of the SQ feedstock Cr and Ni concentrations, within the ASTM A240 specification for 316L resulted in no observable impact on the cell size, oxide particle size, or magnitude of segregation. Also, the amount of Ni segregation in the ferrite solidified microstructures did not significantly differ, regardless of Cr/Ni eq or processing technique. Here, SQ is demonstrated as capable of simulating RS rates and microstructures similar to LPBF for use as an alternative screening tool for new RS alloy compositions.

42 ENGINEERING↗
DOE OSTI2021

Development of High-Performance Ni-base Alloys for Gas Turbine Wheels Using a Coprecipitation Approach (Final Technical Report)

In this project, a synergistic approach involving experiments informed by modelling was used to develop γ'/γ'' coprecipitation-strengthened Ni-base superalloys for land-based gas turbine wheels. In thick sections of such turbine wheels, the slow cooling rate normally observed, as well as variations in cooling rate could potentially result in drastically inhomogeneous and coarsened microstructure. Thus, ten alloy compositions were selected based on coprecipitation and sluggish γ’ growth and coarsening during three iterations of alloy development, assisted by extensive CALPHAD modeling. Phase equilibrium calculations, informed by the characterization of early alloys, were successful in predicting suitable aging treatments to obtain bimodal coprecipitate distribution in several alloys. These aging treatments were applied to the subsequent round of alloys and the resulting microstructures were characterized in detail. Two different cooling rates were used during each of these heat treatments to simulate the range of cooling rates observed in a thick section forging. The microstructures were used to calibrate a multi-phase field model (MPF), which was used to study the formation mechanisms of various coprecipitate morphologies observed in the experiments. Following this, the most promising alloys in each round were selected and studied using high temperature tensile and creep tests. Considering that a slower cooling rate would lead to a strength debit, while a faster cooling rate might lead to a decline in creep rupture life of a full-scale wheel, tensile tests were carried out for slower cooled samples, while creep tests were carried out for faster cooled samples. The deformation microstructures were then characterized using advanced characterization techniques such as Diffraction Contrast-Scanning Transmission Electron Microscopy (DC-STEM) and Electron Channeling Contrast Imaging (ECCI). Further, a mean-field creep model was developed and calibrated using these experimental findings to predict long-term creep behavior of these coprecipitation-strengthened alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Extending the Takagi-Taupin equations for x-ray nanobeam Bragg coherent diffraction

We present an approach for simulating x-ray nanobeam Bragg coherent diffraction patterns based on the Takagi-Taupin equations. Compared to conventional methods, the current approach can be universally applied to any weakly strained system including semi-infinite crystals that diffract dynamically. It addresses issues such as the curved wave front and redivergence of the focused incident beam. In conclusion, we show excellent agreement with experimental data for a strained La 0.7 ⁢Sr 0.3⁢ MnO 3 thin film on a SrTiO 3 substrate and a path to extracting physical information using automatic differentiation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗