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InGaAs quantum wells embedded in GaAs nanowires can serve as compact near-infrared emitters for direct integration onto Si complementary metal oxide semiconductor technology. While the core-shell geometry in principle allows for a greater tuning of composition and emission, especially farther into the infrared, the practical limits of elastic strain accommodation in quantum wells on multifaceted nanowires have not been established. One barrier to progress is the difficulty of directly comparing the emission characteristics and the precise microstructure of a single nanowire. Here we report an approach to correlating quantum well morphology, strain, defects, and emission to understand the limits of elastic strain accommodation in nanowire quantum wells specific to their geometry. We realize full 3D Bragg coherent diffraction imaging (BCDI) of intact quantum wells on vertically oriented epitaxial nanowires, which enables direct correlation with single-nanowire photoluminescence. By growing In

We have developed and demonstrated an image super-resolution method—XR-UNLOC: X-Ray UNsupervised particle LOCalization—for hard x-rays measured with fast-frame-rate detectors that is an adaptation of the principle of photo-activated localization microscopy (PALM) and stochastic optical reconstruction microscopy (STORM), which enabled biological fluorescence imaging at sub-optical-wavelength scales. We demonstrate the approach on experimental coherent Bragg diffraction data measured with 52 keV x-rays from a nanocrystalline sample. From this sample, we resolve the fine fringe detail of a high-energy x-ray Bragg coherent diffraction pattern to an upsampling factor of 16 of the native pixel pitch of 30 μm of a charge-integrating fastCCD detector. This was accomplished by analysis of individual photon locations in a series of “nearly-dark” instances of the diffraction pattern that each contain only a handful of photons. Central to our approach was the adaptation of the UNLOC photon fitting routine for PALM/STORM to the hard x-ray regime to handle much smaller point spread functions, which required a different statistical test for photon detection and for sub-pixel localization. A comparison to a photon-localization strategy used in the x-ray community (“droplet analysis”) showed that XR-UNLOC provides significant improvement in super-resolution. We also developed a metric by which to estimate the limit of reliable upsampling with XR-UNLOC under a given set of experimental conditions in terms of the signal-to-noise ratio of a photon detection event and the size of the point spread function for guiding future x-ray experiments in many disciplines where detector pixelation limits must be overcome.

The phase retrieval problem, where one aims to recover a complex-valued image from far-field intensity measurements, is a classic problem encountered in a range of imaging applications. Modern phase retrieval approaches usually rely on gradient descent methods in a nonlinear minimization framework. Calculating closed-form gradients for use in these methods is tedious work, and formulating second order derivatives is even more laborious. Additionally, second order techniques often require the storage and inversion of large matrices of partial derivatives, with memory requirements that can be prohibitive for data-rich imaging modalities. We use a reverse-mode automatic differentiation (AD) framework to implement an efficient matrix-free version of the Levenberg-Marquardt (LM) algorithm, a longstanding method that finds popular use in nonlinear least-square minimization problems but which has seen little use in phase retrieval. Furthermore, we extend the basic LM algorithm so that it can be applied for more general constrained optimization problems (including phase retrieval problems) beyond just the least-square applications. Since we use AD, we only need to specify the physics-based forward model for a specific imaging application; the first and second-order derivative terms are calculated automatically through matrix-vector products, without explicitly forming the large Jacobian or Gauss-Newton matrices typically required for the LM method. We demonstrate that this algorithm can be used to solve both the unconstrained ptychographic object retrieval problem and the constrained “blind” ptychographic object and probe retrieval problems, under the popular Gaussian noise model as well as the Poisson noise model. We compare this algorithm to state-of-the-art first order ptychographic reconstruction methods to demonstrate empirically that this method outperforms best-in-class first-order methods: it provides excellent convergence guarantees with (in many cases) a superlinear rate of convergence, all with a computational cost comparable to, or lower than, the tested first-order algorithms.

IEEE journal of photovoltaics 9(6), 1790-1799 (2019). doi:10.1109/JPHOTOV.2019.2942487, Strain within grains and at grain boundaries (GBs) in polycrystalline thin-film absorber layers limits the overall performance because of higher defect concentrations and band fluctuations. However, the nanoscale strain distribution in operational devices is not easily accessible using standard methods. X-ray nanodiffraction offers the unique possibility to evaluate the strain or lattice spacing at nanoscale resolution. Furthermore, the combination of nanodiffraction with additional techniques in the framework of multimodal scanning X-ray microscopy enables the direct correlation of the strain with material and device parameters such as the elemental distribution or local performance. This approach is applied for the investigation of the strain distribution in CdTe grains in fully operational photovoltaic solar cells. It is found that the lattice spacing in the (111) direction remains fairly constant in the grain cores but systematically decreases at the GBs. The lower strain at GBs is accompanied by an increase of the total tilt. These observations are both compatible with the inhomogeneous incorporation of smaller atoms into the lattice, and local stress induced by neighboring grains., Published by IEEE, New York, NY

The goals of this work were to develop tools to visualize and characterize materials information, to explore new alloy compositions and/or processing, to better predict tensile strength and other mechanical properties. The 9–12 wt% Cr (9Cr) steel test data were compiled from several sources. About 3000 records with 30 predictor variables represent 82 unique steel alloy compositions, variations of thermo-mechanical processing steps and temperatures (homogenization, normalization and tempering cycles), test conditions and outcomes. Detailed data processing steps such as visualization and exploratory analysis, including univariate and bivariate analysis, different clustering techniques used to segment the data, statistical post-hoc analysis to verify significance of the findings, feature engineering to identify predictors of importance, and predictive modeling with cross-validation were performed. The outcome of analysis at each step was reviewed in the context of the domain knowledge of this class of steel, to see if there were underlying physical mechanisms that explain statistical relationships. Data analytics techniques and their parameters were fine-tuned to facilitate interpretation of the results as aligned with the insights from domain experts. The ensemble predictive modeling using Random Forest regressor and post-hoc means comparison corroborated domain knowledge on the role of Co which is known to increase strength of steel alloys through solid-solution strengthening and to affect diffusion of alloying elements and precipitates. Alloys with Co content of 0.7–8 wt% had significantly higher mean strength than the ones without (while having Cr locked within 10–11 wt% range in either group and keeping other compositional element ratios fixed). End products of the computational techniques exploration are presented as the tools that can be used in iterative workflow of materials development and testing.

Bragg coherent diffraction imaging has the potential to provide significant insight into the structure-properties relationship for crystalline materials by imaging, with nanoscale resolution, three-dimensional strain fields within individual grains and nanoparticles. The capability of present-day synchrotrons to locate and measure a multiplicity of Bragg reflections from a single grain makes it possible to recover the full strain tensor with nanometer resolution. Recent methods for coupling reconstructions from several peaks to determine the strain tensor have been developed and applied to synthetic data, but have not been applied to experimental data. Here, using a coupled genetic reconstruction algorithm, we reconstruct an experimental data set and demonstrate improvements in the ability to resolve vector-valued displacement fields internal to the particle as compared to what is achieved with a noncoupled approach. The coupled approach developed in this work was also validated on simulated data sets. In both simulated and experimental data, reconstructions from our coupled Bragg peak algorithm show improvements over the noncoupled independent reconstruction method of $5%$ in terms of accuracy and $53%$ in terms of consistency.

How materials evolve at thermal equilibrium and under external excitations at small length and time scales is crucial to the understanding and control of material properties. X-ray photon correlation spectroscopy (XPCS) at X-ray free electron laser (XFEL) facilities can in principle capture dynamics of materials that are substantially faster than a millisecond. However, the analysis and interpretation of XPCS data is hindered by the strongly fluctuating X-ray intensity from XFELs. Here we examine the impact of pulse-to-pulse intensity fluctuations on sequential XPCS analysis. We show that the conventional XPCS analysis can still faithfully capture the characteristic time scales, but with substantial decrease in the signal-to-noise ratio of the g2 function and increase in the uncertainties of the extracted time constants. We also demonstrate protocols for improving the signal-to-noise ratio and reducing the uncertainties.

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. 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.

Bragg coherent diffraction imaging (BCDI) is a powerful technique to explore the local strain state and morphology of microscale crystals. The method can potentially reach nanometer-scale spatial resolution thanks to the advances in synchrotron design that dramatically increase coherent flux. However, there are experimental bottlenecks that may limit the image reconstruction quality from future high signal-to-noise ratio measurements. In this work we show that angular uncertainty of the sample orientation with respect to a fixed incoming beam is one example of such a factor, and we present a method to mitigate the resulting artifacts. On the basis of an alternative formulation of the forward problem, we design a phase retrieval algorithm which enables the simultaneous reconstruction of the object and determination of the exact angular position corresponding to each diffraction pattern in the data set. We have tested the algorithm performance on simulated data for different degrees of angular uncertainty and signal-to-noise ratio.

A multimodal in situ nanofocused X-ray microscopy approach is demonstrated and applied to a working polycrystalline thin film solar cell that revealed chemical, structural and electronic heterogeneity from a single measurement., The factors limiting the performance of alternative polycrystalline solar cells as compared with their single-crystal counterparts are not fully understood, but are thought to originate from structural and chemical heterogeneities at various length scales. Here, it is demonstrated that multimodal focused nanobeam X-ray microscopy can be used to reveal multiple aspects of the problem in a single measurement by mapping chemical makeup, lattice structure and charge collection efficiency simultaneously in a working solar cell. This approach was applied to micrometre-sized individual grains in a Cu(In,Ga)Se2 polycrystalline film packaged in a working device. It was found that, near grain boundaries, collection efficiency is increased, and that in these regions the lattice parameter of the material is expanded. These observations are discussed in terms of possible physical models and future experiments.

This paper addresses the three-dimensional signal distortion and image reconstruction issues in X-ray Bragg coherent diffraction imaging (BCDI) in the event of a general non-orthogonal orientation of the area detector with respect to the diffracted beam. Growing interest in novel BCDI adaptations at fourth-generation synchrotron light sources has necessitated improvisations in the experimental configuration and the subsequent data analysis. One such possibly unavoidable improvisation that is envisioned in this paper is a photon-counting area detector whose face is tilted away from the perpendicular to the Bragg-diffracted beam during the acquisition of the coherent diffraction signal. We describe a likely circumstance in which one would require such a detector configuration, along with the experimental precedent at third-generation synchrotrons. Using physically accurate diffraction simulations from synthetic scatterers in the presence of such tilted detectors, we analyze the general nature of the observed signal distortion qualitatively and quantitatively and provide a prescription to correct for it during image reconstruction. Our simulations and reconstructions are based on an adaptation of the known theory of BCDI sampling geometry, as well as the recently developed projection-based methods of wavefield propagation. Such configurational modifications and their numerical remedies are potentially valuable in realizing unconventional coherent diffraction measurement geometries, eventually paving the way for the integration of BCDI into new material characterization experiments at next-generation light sources.

Coherent X-ray beams with energies $\geq 50$ keV can potentially enable three-dimensional imaging of atomic lattice distortion fields within individual crystallites in bulk polycrystalline materials through Bragg coherent diffraction imaging (BCDI). However, the undersampling of the diffraction signal due to Fourier space compression at high X-ray energies renders conventional phase retrieval algorithms unsuitable for three-dimensional reconstruction. To address this problem we utilize a phase retrieval method with a Fourier constraint specifically tailored for undersampled diffraction data measured with coarse-pitched detector pixels that bin the underlying signal. With our approach, we show that it is possible to reconstruct three-dimensional strained crystallites from an undersampled Bragg diffraction data set subject to pixel-area integration without having to physically upsample the diffraction signal. Using simulations and experimental results, we demonstrate that explicit modeling of Fourier space compression during phase retrieval provides a viable means by which to invert high-energy BCDI data, which is otherwise intractable., 10 pages, 8 figures

The crystalline strain properties of nanoparticles have broad implications in a number of emerging fields, including quantum and biological sensing in which heterogeneous internal strain fields are detrimental to performance. Here we used synchrotron-based Bragg coherent x-ray diffraction imaging (BCDI) to measure three-dimensional lattice strain fields within individual 3C-SiC nanoparticles, a candidate host material for quantum sensing, as a function of temperature during and after annealing up to ${900}^{\phantom{\rule{0.16em}{0ex}}\ensuremath{\circ}}\mathrm{C}$. We observed pronounced homogenization of the initial strain field at temperatures above ${500}^{\phantom{\rule{0.16em}{0ex}}\ensuremath{\circ}}\mathrm{C}$, and we find that the surface layers and central volumes of the nanoparticles reduce strain at similar rates, suggesting a uniform healing mechanism. Thus, we attribute the observed strain homogenization to activation of mobile point defects that annihilate and improve the overall quality of the crystal lattice. This work also establishes the feasibility of performing BCDI at high temperatures (up to ${900}^{\phantom{\rule{0.16em}{0ex}}\ensuremath{\circ}}\mathrm{C}$) to map structural hystereses relevant to the processing of quantum nanomaterials.

Coherent X-ray photons with energies higher than 50 keV offer new possibilities for imaging nanoscale lattice distortions in bulk crystalline materials using Bragg peak phase retrieval methods. However, the compression of reciprocal space at high energies typically results in poorly resolved fringes on an area detector, rendering the diffraction data unsuitable for the three-dimensional reconstruction of compact crystals. To address this problem, we propose a method by which to recover fine fringe detail in the scattered intensity. This recovery is achieved in two steps: multiple undersampled measurements are made by in-plane sub-pixel motion of the area detector, then this data set is passed to a sparsity-based numerical solver that recovers fringe detail suitable for standard Bragg coherent diffraction imaging (BCDI) reconstruction methods of compact single crystals. The key insight of this paper is that sparsity in a BCDI data set can be enforced by recognising that the signal in the detector, though poorly resolved, is band-limited. This requires fewer in-plane detector translations for complete signal recovery, while adhering to information theory limits. We use simulated BCDI data sets to demonstrate the approach, outline our sparse recovery strategy, and comment on future opportunities., 11 pages, 7 figures (submitted)

The main focus of this paper is a nonparametric filtering technique for the estimation of interface geometry in bulk materials obtainable from modern imaging measurements. The filtering methodology relies on an assumed hierarchy of topological features present in a typical interface network, such as foam interfaces and grain boundary networks in polycrystalline materials. Each type of topological feature is treated in order of rank in the hierarchy, with the lower-level feature being filtered subject to the positional constraints imposed by the higher-level features. Such a scheme is an alternative to existing surface smoothing/estimation techniques in microstructural materials science, in which the explicit treatment of different elements of the network topology is absent, or at best arbitrarily parameterized. We describe the ramifications of this technique in the usual microstructural applications in which the computation of important physical quantities is predicated on the precise estimation of the interface features. As an additional application, we describe a novel front-tracking algorithm for quantifying the transport of such interfaces., Accepted for publication in Computational Materials Science (33 pages, 13 figures)

Migration of grain boundaries in an idealized, well-ordered polycrystalline sample is an often-studied phenomenon in microstructural materials science. It is the subject of many imaging experiments in two dimensions and simulations in two and three dimensions, the collective knowledge of which has given us many insights into behavior of specific materials. This thesis describes the characterization of the grain boundaries in a specially prepared polycrystalline aggregate of high-purity iron with a bodycentered cubic lattice whose microstructure was imaged non-destructively in three dimensions with near-field high-energy diffraction microscopy (nf-HEDM) which uses synchrotron X-rays as a probe. The sample was imaged using nf-HEDM before and after a cycle of annealing in order to activate boundary migration for a short interval of time. Also described are the development of computational techniques for denoising grain boundary images in three dimensions as well as a scheme to solve the inverse problem of computing the dynamical parameters influencing boundary migration from the observed boundary geometries and transport. The two snapshots of the full three-dimensional grain boundary network were used to quantify the geometry and transport of individual grains and track their progress through the annealing. A study of the influence of grain boundary curvature on boundary velocity revealed a weak correlation for a large fraction of the boundaries.

The grain structure of a slightly deformed Al–0.3 wt%Mn alloy was reconstructed using diffraction contrast tomography (DCT) and high-energy diffraction microscopy (HEDM). The direct comparison shows that DCT can detect subgrain boundaries with disorientations as low as 1° and that HEDM and DCT grain boundaries are on average 4 µm apart from each other., The grain structure of an Al–0.3 wt%Mn alloy deformed to 1% strain was reconstructed using diffraction contrast tomography (DCT) and high-energy diffraction microscopy (HEDM). 14 equally spaced HEDM layers were acquired and their exact location within the DCT volume was determined using a generic algorithm minimizing a function of the local disorientations between the two data sets. The microstructures were then compared in terms of the mean crystal orientations and shapes of the grains. The comparison shows that DCT can detect subgrain boundaries with disorientations as low as 1° and that HEDM and DCT grain boundaries are on average 4 µm apart from each other. The results are important for studies targeting the determination of grain volume. For the case of a polycrystal with an average grain size of about 100 µm, a relative deviation of about ≤10% was found between the two techniques.

We report on the synthesis, stability, and local structure of In2O3 thin films grown via rf-magnetron sputtering and characterized by in-situ x-ray scattering and focused x-ray nanodiffraction. We find that In2O3 deposited onto (0 0 1)-oriented single crystal yttria-stabilized zirconia substrates adopts a Stranski–Krastanov growth mode at a temperature of 850 °C, resulting in epitaxial, truncated square pyramids with (1 1 1) side walls. We find that at this temperature, the pyramids evaporate unless they are stabilized by a low flux of In2O3 from the magnetron source. We also find that the internal lattice structure of one such pyramid is made up of differently strained volumes, revealing local structural heterogeneity that may impact the properties of In2O3 nanostructures and films.