High-energy X-ray Diffraction Microscopy Research Articles

Evaluating the Taylor hardening model in polycrystalline Ti using high energy X-ray diffraction microscopy

High energy X-ray diffraction microscopy (HEDM) was employed to index nearly 1000 grains in a polycrystalline Ti specimen and characterize their deformation during an incremental tensile test. For each grain, the positions of its associated diffraction peaks were used for analyzing its evolving crystal orientation and stress tensor. The azimuthal breadth of each peak at different load steps was measured, allowing measurement of initial yielding and providing an estimate of the dislocation density evolution in each grain. The Taylor hardening model was evaluated grain by grain using the above data, indicating that it can represent hardening in most grains. The yield stress and the strain hardening coefficient for all grains were statistically analyzed with respect to grain orientation, grain size, slip systems, and the surrounding neighborhood to examine how the yield stress and hardening are correlated.

Comparative assessment of backstress models using high-energy X-ray diffraction microscopy experiments and crystal plasticity finite element simulations

Crystal plasticity (CP) models have been evolving since their inception. Advanced experimental characterization methods have contributed significantly to assess the performance and subsequent improvement of many empirical relations in CP, which were directly adopted from classical plasticity theories of solids at the macro-scale. In this research, high energy X-ray diffraction microscopy (HEDM) has been used to track the stress-state of individual grains within a polycrystalline aggregate of a Nickel-base superalloy subjected to cyclic loading. Using path-dependent, mesoscopic stress-states from the HEDM experiment, the performance of two kinematic hardening models, in the context of CP, has been assessed. One of the models is an empirical Armstrong-Frederick equation, and the other is a geometrically necessary dislocation (GND)-based phenomenological model. The results suggest that the GND-based model is capable of capturing the cyclic crystal plasticity response. The present validation efforts are expected to take CP models one step closer towards their implementation in modern engineering workflow.

Dynamic recovery observed in distinct grains within a polycrystalline nickel-based superalloy during cyclic high temperature fatigue via high energy X-ray diffraction microscopy

Elastic micromechanical fields are tracked for a nickel-based superalloy polycrystal via high energy X-ray diffraction microscopy (HEDM) and corresponding intragranular deformation metrics are determined with peak broadening analysis during cyclic high temperature loading. A low solvus, high refractory (LSHR) sample with 252 grains was subjected to uniaxial tension and held under fixed displacement while thermally cycling between 460 °C and 770 °C with intermittent HEDM characterization to study the grain average response to thermo-mechanical deformation. Elevated temperatures were found to allow for heterogeneous amounts of recovery amongst distinct grains within the sampled region, indicating complex grain interactions; the extent of recovery was greater at higher temperatures.

A complete grain-level assessment of the stress-strain evolution and associated deformation response in polycrystalline alloys

Polycrystalline alloys are used pervasively across structural applications contingent upon extensive experimental testing. A statistically representative number of tests are necessary to expose the variability in the material's performance, as a result of non-uniform microstructures and associated micromechanical fields. In a more direct means of capturing this pertinent information, multi-modal experimental techniques are presented to measure and track the complete micromechanical state, evolving during loading, of each and every grain within the regions of interest. Specifically, a combination of high-energy X-ray diffraction microscopy and digital image correlation coupled with electron backscatter diffraction are conducted on a specimen for each of the alloys, Haynes 282 and Ti7Al. The results of the multi-modal analysis definitively demonstrate that the degree of heterogeneity increases with deformation level and is used to assess the number of grains necessary for a representative volume element description of the stress state for each of these materials. Moreover, higher resolution imaging is used for identification of the slip system activity and subsequently used to study slip transmission events. An accurate knowledge of the resolved shear stress in adjacent grains (grain interactions) is demonstrated to be a key descriptor of the slip transmission events.

High-Energy Coherent X-Ray Diffraction Microscopy of Polycrystal Grains: Steps Toward a Multiscale Approach

We present proof-of-concept imaging measurements of a polycrystalline material that integrate the elements of conventional high-energy X-ray diffraction microscopy with coherent diffraction imaging techniques, and that can enable in-situ strain-sensitive imaging of lattice structure in ensembles of deeply embedded crystals over five decades of length scale upon full realization. Such multi-scale imaging capabilities are critical to addressing important questions in a variety of research areas such as materials science and engineering, chemistry, and solid state physics. Towards this eventual goal, the following key aspects are demonstrated: 1) high-energy Bragg coherent diffraction imaging (HE-BCDI) of sub-micron-scale crystallites at 52 keV at current third-generation synchrotron light sources, 2) HE-BCDI performed in conjunction with far-field high-energy diffraction microscopy (ff-HEDM) on the grains of a polycrystalline sample in an smoothly integrated manner, and 3) the orientation information of an ensemble of grains obtained via ff-HEDM used to perform complementary HE-BCDI on multiple Bragg reflections of a single targeted grain. These steps lay the foundation for integration of HE-BCDI, which typically provides a spatial resolution tens of nanometers, into a broad suite of well-established HEDM methods, extending HEDM beyond the few-micrometer resolution bound and into the nanoscale, and positioning the approach to take full advantage of the orders-of-magnitude improvement of X-ray coherence expected at fourth generation light sources presently being built and commissioned worldwide.

Voxel-based strain tensors from near-field High Energy Diffraction Microscopy

High energy X-ray diffraction microscopy is one of several techniques that use spatially resolved diffraction to nondestructively map crystal unit cell orientations in three dimensions inside bulk polycrystalline samples. The near-field variant of the technique (nf-HEDM) yields grain shapes, grain boundary character information, and intra-granular orientation variations. Here, we demonstrate, through analysis of simulated and physical data sets, the extension nf-HEDM to include mapping of heterogeneous intra-granular strain states with spatial resolution on the micron scale. Sensitivity to all strain tensor components is <5×10-4. The GPU assisted implementation of an optimization algorithm is described.

Creating, probing and confirming tetragonality in bulk FeNi alloys

Effects derived from the simultaneous application of passive, uniform saturating magnetic field and tensile stress during long-time annealing utilizing a unique and simple processing tool, the MultiDriver furnace, are reported. In particular, the evolution of the crystalline structure and the magnetic domain configuration of severely deformed and subsequently annealed equiatomic FeNi alloys were revealed by high-energy synchrotron X-Ray diffraction and Magneto-Optic Kerr Microscopy. These alloys are known to undergo a first-order magnetic phase transformation to a chemically ordered tetragonal (L10) structure in astronomical timeframes. MultiDriver-annealed specimens are found to retain a tetragonal crystallographic state and texture that is similar to that of the precursor deformed state, with a smaller unit cell volume and a larger c/a ratio relative to those of control samples that were annealed under the same conditions but without magnetic field and stress drivers. Magnetic domain images echo these observations: while as-cast FeNi alloys exhibit domain patterns consistent with the presence of a stress-modified cubic magnetocrystalline anisotropy, large areas of domains with uniaxial anisotropy are present in MultiDriver-annealed samples. While no chemical order was demonstrated in these samples, a strategy is proposed for achieving the ordered state by employing a passive magnetic gradient in the MultiDriver furnace to enhance diffusion.

Understanding Micromechanical Material Behavior Using Synchrotron X-rays and In Situ Loading

With the flux of high-energy, deeply penetrating X-rays that a 3rd-generation synchrotron source can provide and the current generation of large fast area detectors, the development and use of synchrotron X-ray methods have experienced impressive growth over the past two decades. This paper describes the current state of an important subset of synchrotron methods—high-energy X-ray diffraction employing in situ loading. These methods, which are known by many acronyms such as 3D X-ray diffraction (3DXRD), diffraction contrast tomography (DCT), and high-energy X-ray diffraction microscopy (HEDM), have shifted the focus of alloy characterization to include crystal scale behaviors in addition to microstructure and have made it possible to track the evolution of a polycrystalline aggregate during loading conditions that mimic alloy processing or in-service conditions. The paper is delineated into methods for characterizing elastic behavior including measuring the stress tensor experienced by each crystal and the inelastic response including crystal plasticity, phase transformations, and the onset of damage. We discuss beam size and detector placement, resolution, and speed in the context of the spatial and temporal resolution and scope of the resulting data. Work that emphasizes material models and the interface of data with various numerical simulations and machine learning is presented.

Quantifying microscale drivers for fatigue failure via coupled synchrotron X-ray characterization and simulations

During cyclic loading, localization of intragranular deformation due to crystallographic slip acts as a precursor for crack initiation, often at coherent twin boundaries. A suite of high-resolution synchrotron X-ray characterizations, coupled with a crystal plasticity simulation, was conducted on a polycrystalline nickel-based superalloy microstructure near a parent-twin boundary in order to understand the deformation localization behavior of this critical, 3D microstructural configuration. Dark-field X-ray microscopy was spatially linked to high energy X-ray diffraction microscopy and X-ray diffraction contrast tomography in order to quantify, with cutting-edge resolution, an intragranular misorientation and high elastic strain gradients near a twin boundary. These observations quantify the extreme sub-grain scale stress gradients present in polycrystalline microstructures, which often lead to fatigue failure.

Estimation of anisotropic elastic moduli from high energy X-Ray data and finite element simulations

A suite of finite element simulations was executed to find optimal values for high-temperature single crystal elastic moduli of low solvus high refractory (LSHR) nickel super alloy from high energy x-ray diffraction microscopy (HEDM) measurements. In the experiment, a polycrystalline specimen was scanned in an unloaded state to determine a three-dimensional spatial map of lattice orientations in the gauge volume. The specimen was then heated and loaded while performing in situ X-ray measurements to determine grain-averaged elastic strain tensors at several macroscopic loads. The finite element simulations, utilizing three meshes of increasing resolution, mimicked the experimental loading. Initial simulations were conducted to find a box containing the optimal moduli, from which a finer grid of trial moduli was created. A suite of simulations was then executed using these meshes and moduli. For each simulation, an error was determined by comparing the simulated strain field to the measured one, with the resulting data set providing rich information about this fitting process. Anisotropy of the optimal moduli was studied relative to the level of mesh refinement, and a tendency for the anisotropy to decrease as the mesh refinement increases was found. Optimal values of anisotropic moduli and isotropic moduli were determined using the presented optimization methodology; the anisotropic moduli gave appreciably better results. Furthermore, we examined the sensitivity of the error to changes in the moduli; the takeaway was that size of the modulus had a primary effect on the sensitivity, with larger moduli being harder to fit.

Homoepitaxial growth of 9,10-diphenylanthracene

Organic single crystals are often shown to have significantly improved optoelectronic properties over polycrystalline thin films such as exciton diffusivity and carrier mobility. There is growing interest in incorporating such crystals in organic electronics despite a number of challenges. In this work, the homoepitaxial vapor phase growth modes for 9,10-diphenylanthracene (DPA) homoepitaxy are mapped as a function of growth rate and temperature using in situ ultra-low current reflection high energy electron diffraction (RHEED), X-ray diffraction (XRD), and atomic force microscopy (AFM). Vapor phase deposition was performed on free-standing single crystal DPA substrates, which show clear Kikuchi patterns. At room temperature, a transition from Frank-Van der Merwe layer-by-layer growth to step-flow growth is observed as the deposition rate is decreased, while at lower temperatures a Stranski-Krastanov layer-plus-island growth is observed. This is the first demonstration of true step-flow growth from room temperature vapor phase deposition for organic semiconductors and is reminiscent of traditional semiconductor growth regimes. Accordingly, these results could lead to improved control over growth and doping of organic single crystals, and lead to enhanced single crystal organic optoelectronic applications.

Epitaxial growth of SrCaTiO3 films on GaN by molecular beam epitaxy with a TiO2 buffer layer

We demonstrate the epitaxial growth of (111)-oriented Sr1 − xCaxTiO3 (SCTO) thin films on (0002) GaN using a thin (100) TiO2 buffer layer by RF-plasma-assisted oxide molecular beam epitaxy. We explore the growth window of SCTO for both x = 0 (i.e., SrTiO3) and x = 0.24 with various TiO2 buffer layer thicknesses and find that a substrate temperature of 650 °C and TiO2 thickness of 1 nm produce the highest quality films, as determined by reflection high energy electron diffraction, x-ray diffraction, and atomic force microscopy. SCTO films deposited without a buffer layer are polycrystalline, confirming the necessity of the TiO2 buffer layer to facilitate (111)-oriented epitaxial growth of SCTO on GaN. Transmission electron microscopy performed on the samples shows that the SCTO films grown with a TiO2 buffer layer are highly textured, and selected-area electron diffraction patterns indicate that some domains in the oxide exhibit cation ordering along the (111) direction. We also show that the growth mode changes from 2D to 3D as the thickness of SCTO increases past 10 nm, which leads to film relaxation and a rougher surface morphology.

Growth control of ZnTe epitaxial thin films on Si (111)

Zinc telluride layers were directly grown on highly-lattice-mismatched Si (111) substrates by molecular beam epitaxy (MBE). Reflection high-energy electron diffraction (RHEED), X-ray diffraction (XRD) and atomic force microscopy (AFM) were used to study the growth mechanism and crystal quality of ZnTe on Si (111). The results show that the growth mode related with the Ⅵ/Ⅱ beam pressure ratio is one of important factors affecting the initial growing process, crystal quality and morphology of ZnTe epitaxial thin films. From in situ RHEED observations, two-dimensional (2D) growth mode was found upon increasing Ⅵ/Ⅱ beam pressure ratio to 3.3 while three-dimensional (3D) growth mode remained in Zn-rich atmosphere or at Ⅵ/Ⅱ beam pressure ratio larger than 6. Small full-width at half-maximum (~540 arcsec) showed that the growth of ZnTe on Si (111) in Te-rich atmosphere, especially in a layer-by-layer mode, was more suitable for nucleation growth.

An algorithm for resolving intragranular orientation fields using coupled far-field and near-field high energy X-ray diffraction microscopy

We present a novel algorithm for reconstructing spatial intragranular lattice orientation fields using both far-field and near-field high energy X-ray diffraction microscopy (HEDM) measurements. An established far-field indexing algorithm is modified to include lattice orientation distribution information (grain orientation envelopes) in addition to average grain orientations. The near-field data reduction algorithm utilizes this enriched far-field orientation data as a seed for reconstructing intragranular spatial maps of lattice orientation from the diffraction images. The primary benefit of the new algorithm is a significant decrease in the number of trial calculations that must be performed in the reconstruction process compared to existing methodologies while maintaining scalability. The resulting gains in efficiency facilitate the use of relatively modest computational resources and improve throughput at the point of measurement. We provide two example applications: volumetric orientation field reconstructions for a Ti-Al alloy both before and after the application of 3% uniaxial strain. The results showcase the efficiency of the new method and the ability to resolve subtle changes in microstructure, which are associated with incipient plastic deformation.

Mechanism of Saponite Crystallization from a Rapidly Formed Amorphous Intermediate

Clays are crucial mineral phases in Earth’s weathering engine, but we do not know how they form in surface environments under (near-)ambient pressures and temperatures. Most synthesis routes, attempting to give insights into the plausible mechanisms, rely on hydrothermal conditions, yet many geological studies showed that clays may actually form at moderate temperatures (<100 °C) in most terrestrial settings. Here, we combined high-energy X-ray diffraction, infrared spectroscopy, and transmission electron microscopy to derive the mechanistic pathways of the low-temperature (25–95 °C) crystallization of a synthetic Mg-clay, saponite. Our results reveal that saponite crystallizes via a two stage process: (1) a rapid (several minutes) coprecipitation where ∼20% of the available magnesium becomes incorporated into an aluminosilicate network, followed by (2) a much slower crystallization mechanism (several hours to days) where the remaining magnesium becomes gradually incorporated into the growing saponite sheet structure.

Role of template layers for heteroepitaxial growth of lanthanum oxide on GaN(0001) via atomic layer deposition

La2O3 has been reported as a good gate dielectric for GaN-based high electron mobility transistor and metal-oxide-semiconductor field effect transistor applications. In this study, atomic layer deposition (ALD) was selected as the deposition technique, and the growth behavior and structure of La2O3 films on GaN(0001) were investigated. Unlike La2O3 deposited by molecular beam epitaxy (MBE) at 450 °C that can form a two-dimensional film directly on GaN(0001), island growth mode was observed when a La2O3 film was deposited directly on GaN(0001) at 250 °C by ALD using tris(N,N′-diisopropylformamidinato)-lanthanum as the precursor and H2O as the coreactant. Only with the use of a template layer, a 2 nm-thick hexagonal La2O3 film deposited by MBE or a 3 nm-thick cubic Er2O3 film deposited by ALD, can a two-dimensional crystalline ALD-La2O3 thin film be formed on GaN(0001). Reflection high-energy electron diffraction, x-ray diffraction, and scanning transmission electron microscopy were conducted to verify the films’ crystalline nature and structure. The ALD-La2O3 film retains a cubic structure on ALD-Er2O3 templated-GaN(0001), while it transforms from the cubic phase to a mix of cubic and hexagonal phases on MBE-La2O3 templated-GaN(0001) when the film is thicker than 15 nm. The stabilization of a thin cubic La2O3 phase could be related to a difference in the surface energy and the ALD growth temperature.

Formation of omega phase induced by laser shock peening in Ti-17 alloy

Synchrotron-based high-energy X-ray diffraction and transmission electron microscopy were used to study the in-depth compressive residual strains and microstructure evolution in Ti-17 alloy subjected to two-sided laser shock peening (LSP). A noticeable difference was observed in the lattice strains and extents of peak broadening on the two sides of the sample. The compressive residual strain was smaller and the peak broadening was more pronounced on the bottom surface in comparison to the top surface. This is due to the β → ω phase transformation induced by LSP on the bottom surface. It was determined that the ω phase with fine particle morphology and incommensurate structure is located mainly in the 15 μm-thick layer under the bottom surface. The formation of the LSP-induced ω phase on the bottom surface can be attributed to the adiabatic increase in temperature due to the higher shock peak pressure on the bottom surface, and can result in the relaxation of the accumulated residual compressive strain in the original phases.

ICME Approach to Determining Critical Pore Size of IN718 Produced by Selective Laser Melting

A degree of porosity is expected in additively manufactured (AM) materials. To aid in the qualification of AM materials, the smallest pore size that results in a debit in the fatigue performance is quantified. In the work presented herein, crystal plasticity simulations are used to identify the stress concentration around pores of various sizes, revealing that a single 20-μm pore or two 10-μm pores (with centers spaced 15 μm apart) localize stress at the pore, as opposed to elsewhere in the microstructure. In situ microtomography and far-field high-energy x-ray diffraction microscopy were used to identify crack formation and the evolution of the grain-level micromechanical fields during cyclic loading. Eighteen cracks were observed (15 at pores, 3 at the surface) at highly stressed grains in a sample, although most did not propagate. The dominant crack was seen to originate from the free surface, which is rationalized by fracture mechanics.

Heterogeneous Internal Strain Evolution in Commercial Purity Titanium Due to Anisotropic Coefficients of Thermal Expansion

Heterogeneous internal elastic strain in polycrystalline hexagonal close-packed materials is found to originate from the intrinsic anisotropy in thermal expansivity. As most noncubic metals have anisotropic thermal expansivity, cooling from elevated temperature leads to internal stresses. To simulate the internal stresses present in a polycrystal prior to plastic deformation, the anisotropic coefficients of thermal expansion over a wide range of temperatures need to be known. One sample of strongly textured commercial purity titanium was probed using high-energy x-ray diffraction microscopy during in situ heating. From averages of the directional lattice strain as a function of temperature, the directional expansion of the material showed a crossover where the incremental $$ c $$-axis expansion exceeded the $$ a $$-axis expansion between 700°C and 800°C. Applying a three-dimensional crystal thermoelasticity model using a realistic microstructure based upon the experimental data, the anisotropic coefficients of thermal expansion were extracted by fitting to the average strain evolution identified from experiments.

Automated Grain Yield Behavior Classification

A method for classifying grain stress evolution behaviors using unsupervised learning techniques is presented. The method is applied to analyze grain stress histories measured in situ using high-energy x-ray diffraction microscopy from the aluminum–lithium alloy Al-Li 2099 at the elastic–plastic transition (yield). The unsupervised learning process automatically classified the grain stress histories into four groups: major softening, no work-hardening or -softening, moderate work-hardening, and major work-hardening. The orientation and spatial dependence of these four groups are discussed. In addition, the generality of the classification process to other samples is explored.