Origin of age softening in the refractory high-entropy alloys.

Refractory high-entropy alloys (RHEAs) are emerging materials with potential for use under extreme conditions. As a newly developed material system, a comprehensive understanding of their long-term stability under potential service temperatures remains to be established. This study examined a titanium-vanadium-niobium-tantalum alloy, a promising RHEA known for its superior high-temperature strength and room-temperature ductility. Using a combination of advanced analytical microscopies, Calculation of Phase Diagrams (CALPHAD) software, and nanoindentation, we investigated the evolution of its microstructure and mechanical properties upon aging at 700°C. Trace interstitials such as oxygen and nitrogen, initially contributing to solid solution strengthening, promote phase segregation during thermal aging. As a result of the depletion of solute interstitials within the metal matrix, a progressive softening is observed in the alloy as a function of aging time. This study, therefore, underscores the need for a better control of impurities in future development and application of RHEAs.

An iterative method for reference pattern selection in high-resolution electron backscatter diffraction (HR-EBSD).

For high (angular) resolution electron backscatter diffraction (HR-EBSD), the selection of a reference diffraction pattern (EBSP0) significantly affects the precision of the calculated strain and rotation maps. This effect was demonstrated in plastically deformed body-centred cubic and face-centred cubic ductile metals (ferrite and austenite grains in duplex stainless steel) and brittle single-crystal silicon, which showed that the effect is not only limited to measurement magnitude but also spatial distribution. An empirical relationship was then identified between the cross-correlation parameter and angular error, which was used in an iterative algorithm to identify the optimal reference pattern that maximises the precision of HR-EBSD.

Dislocation interactions in olivine control postseismic creep of the upper mantle.

Changes in stress applied to mantle rocks, such as those imposed by earthquakes, commonly induce a period of transient creep, which is often modelled based on stress transfer among slip systems due to grain interactions. However, recent experiments have demonstrated that the accumulation of stresses among dislocations is the dominant cause of strain hardening in olivine at temperatures ≤600 °C, raising the question of whether the same process contributes to transient creep at higher temperatures. Here, we demonstrate that olivine samples deformed at 25 °C or 1150-1250 °C both preserve stress heterogeneities of ~1 GPa that are imparted by dislocations and have correlation lengths of ~1 µm. The similar stress distributions formed at these different temperatures indicate that accumulation of stresses among dislocations also provides a contribution to transient creep at high temperatures. The results motivate a new generation of models that capture these intragranular processes and may refine predictions of evolving mantle viscosity over the earthquake cycle.

Effect of sample thinning on strains and lattice rotations measured from Transmission Kikuchi diffraction in the SEM.

Cross correlation based high angular resolution EBSD (or HR-EBSD) has been developed for measurement of elastic strains, lattice rotations (and estimating GND density). Recent advances in Transmission Kikuchi diffraction (TKD), especially the on-axis geometry allows the possibility of acquiring patterns at higher spatial resolution. However, some controversy remains as to whether stresses/strains measured after the sample thinning process are still representative of the bulk sample. In this paper, we explore a way of applying the HR-EBSD method to study strains and lattice rotations in an initially bulk sample, that is then progressively thinned down until a similar analysis can be performed on thin (and electron transparent) samples. Thus, HR-TKD will be compared as a possible alternative to HR-EBSD, in scenarios when it is not always possible to perform EBSD on the surface of the sample. An estimate of strain relaxation in the sample as a result of sample thinning is presented.

On the depth resolution of transmission Kikuchi diffraction (TKD) analysis.

In this paper, we have analyzed the depth resolution that can be achieved by on-axis transmission Kikuchi diffraction (TKD) using a Zr-Nb alloy. The results indicate that the signals contributing to detectable Kikuchi bands originate from a depth of approximately the mean free path of thermal diffuse scattering (λTDS) from the bottom surface of a thin foil sample. This existing surface sensitivity can thus lead to the observation of different grain structures when opposite sides of a nano-crystalline foil are facing the incident electron beam. These results also provide a guideline for the ideal sample thickness for TKD analysis of ≤ 6λTDS, or 21 times the elastic scattering mean free path (λMFP) for samples of high crystal symmetry. For samples of lower symmetry, a smaller thickness ≤ 3λTDS, or ≤ 10λMFP is suggested.

Pattern matching analysis of electron backscatter diffraction patterns for pattern centre, crystal orientation and absolute elastic strain determination - accuracy and precision assessment.

Pattern matching between target electron backscatter patterns (EBSPs) and dynamically simulated EBSPs was used to determine the pattern centre (PC) and crystal orientation, using a global optimisation algorithm. Systematic analysis of error and precision with this approach was carried out using dynamically simulated target EBSPs with known PC positions and orientations. Results showed that the error in determining the PC and orientation was <10-5 of pattern width and <0.01° respectively for the undistorted full resolution images (956 × 956 pixels). The introduction of noise, optical distortion and image binning was shown to have some influence on the error although better angular resolution was achieved with the pattern matching than using conventional Hough transform-based analysis. The accuracy of PC determination for the experimental case was explored using the High Resolution (HR-) EBSD method but using dynamically simulated EBSP as the reference pattern. This was demonstrated through a sample rotation experiment and strain analysis around an indent in interstitial free steel.

Applications of multivariate statistical methods and simulation libraries to analysis of electron backscatter diffraction and transmission Kikuchi diffraction datasets.

Multivariate statistical methods are widely used throughout the sciences, including microscopy, however, their utilisation for analysis of electron backscatter diffraction (EBSD) data has not been adequately explored. The basic aim of most EBSD analysis is to segment the spatial domain to reveal and quantify the microstructure, and links this to knowledge of the crystallography (e.g. crystal phase, orientation) within each segmented region. Two analysis strategies have been explored; principal component analysis (PCA) and k-means clustering. The intensity at individual (binned) pixels on the detector were used as the variables defining the multidimensional space in which each pattern in the map generates a single discrete point. PCA analysis alone did not work well but rotating factors to the VARIMAX solution did. K-means clustering also successfully segmented the data but was computational more expensive. The characteristic patterns produced by either VARIMAX or k-means clustering enhance weak patterns, remove pattern overlap, and allow subtle effects from polarity to be distinguished. Combining multivariate statistical analysis (MSA) approaches with template matching to simulation libraries can significantly reduce computational demand as the number of patterns to be matched is drastically reduced. Both template matching and MSA approaches may augment existing analysis methods but will not replace them in the majority of applications.

Strong grain neighbour effects in polycrystals.

Anisotropy in single-crystal properties of polycrystals controls both the overall response of the aggregates and patterning of local stress/strain distributions, the extremes of which govern failure processes. Improving the understanding of grain-grain interactions has important consequences for in-service performance limits. Three-dimensional synchrotron X-ray diffraction was used to study the evolution of grain-resolved stresses over many contiguous grains in Zr and Ti polycrystals deformed in situ. In a significant fraction of grains, the stress along the loading axis was found to decrease during tensile plastic flow just beyond the macroscopic yield point; this is in the absence of deformation twinning and is a surprising behaviour. It is shown that this phenomenon is controlled by the crystallographic orientation of the grain and its immediate neighbours, particularly those adjacent along the loading axis.

Size effects resolve discrepancies in 40 years of work on low-temperature plasticity in olivine.

The strength of olivine at low temperatures and high stresses in Earth's lithospheric mantle exerts a critical control on many geodynamic processes, including lithospheric flexure and the formation of plate boundaries. Unfortunately, laboratory-derived values of the strength of olivine at lithospheric conditions are highly variable and significantly disagree with those inferred from geophysical observations. We demonstrate via nanoindentation that the strength of olivine depends on the length scale of deformation, with experiments on smaller volumes of material exhibiting larger yield stresses. This "size effect" resolves discrepancies among previous measurements of olivine strength using other techniques. It also corroborates the most recent flow law for olivine, which proposes a much weaker lithospheric mantle than previously estimated, thus bringing experimental measurements into closer alignment with geophysical constraints. Further implications include an increased difficulty of activating plasticity in cold, fine-grained shear zones and an impact on the evolution of fault surface roughness due to the size-dependent deformation of nanometer- to micrometer-sized asperities.

Microstrain distribution mapping on CuInSe2 thin films by means of electron backscatter diffraction, X-ray diffraction, and Raman microspectroscopy.

The investigation of the microstructure in functional, polycrystalline thin films is an important contribution to the enhanced understanding of structure-property relationships in corresponding devices. Linear and planar defects within individual grains may affect substantially the performance of the device. These defects are closely related to strain distributions. The present work compares electron and X-ray diffraction as well as Raman microspectroscopy, which provide access to microstrain distributions within individual grains. CuInSe2 thin films for solar cells are used as a model system. High-resolution electron backscatter diffraction and X-ray microdiffraction as well as Raman microspectroscopy were applied for this comparison. Consistently, microstrain values were determined of the order of 10(-4) by these three techniques. However, only electron backscatter diffraction, X-ray microdiffraction exhibit sensitivities appropriate for mapping local strain changes at the submicrometer level within individual grains in polycrystalline materials.

Geometrically necessary dislocation densities in olivine obtained using high-angular resolution electron backscatter diffraction.

Dislocations in geological minerals are fundamental to the creep processes that control large-scale geodynamic phenomena. However, techniques to quantify their densities, distributions, and types over critical subgrain to polycrystal length scales are limited. The recent advent of high-angular resolution electron backscatter diffraction (HR-EBSD), based on diffraction pattern cross-correlation, offers a powerful new approach that has been utilised to analyse dislocation densities in the materials sciences. In particular, HR-EBSD yields significantly better angular resolution (<0.01°) than conventional EBSD (~0.5°), allowing very low dislocation densities to be analysed. We develop the application of HR-EBSD to olivine, the dominant mineral in Earth's upper mantle by testing (1) different inversion methods for estimating geometrically necessary dislocation (GND) densities, (2) the sensitivity of the method under a range of data acquisition settings, and (3) the ability of the technique to resolve a variety of olivine dislocation structures. The relatively low crystal symmetry (orthorhombic) and few slip systems in olivine result in well constrained GND density estimates. The GND density noise floor is inversely proportional to map step size, such that datasets can be optimised for analysing either short wavelength, high density structures (e.g. subgrain boundaries) or long wavelength, low amplitude orientation gradients. Comparison to conventional images of decorated dislocations demonstrates that HR-EBSD can characterise the dislocation distribution and reveal additional structure not captured by the decoration technique. HR-EBSD therefore provides a highly effective method for analysing dislocations in olivine and determining their role in accommodating macroscopic deformation.

The effect of pattern overlap on the accuracy of high resolution electron backscatter diffraction measurements.

High resolution, cross-correlation-based, electron backscatter diffraction (EBSD) measures the variation of elastic strains and lattice rotations from a reference state. Regions near grain boundaries are often of interest but overlap of patterns from the two grains could reduce accuracy of the cross-correlation analysis. To explore this concern, patterns from the interior of two grains have been mixed to simulate the interaction volume crossing a grain boundary so that the effect on the accuracy of the cross correlation results can be tested. It was found that the accuracy of HR-EBSD strain measurements performed in a FEG-SEM on zirconium remains good until the incident beam is less than 18 nm from a grain boundary. A simulated microstructure was used to measure how often pattern overlap occurs at any given EBSD step size, and a simple relation was found linking the probability of overlap with step size.

Using transmission Kikuchi diffraction to study intergranular stress corrosion cracking in type 316 stainless steels.

Transmission Kikuchi diffraction (TKD), also known as transmission-electron backscatter diffraction (t-EBSD) is a novel method for orientation mapping of electron transparent transmission electron microscopy specimen in the scanning electron microscope and has been utilized for stress corrosion cracking characterization of type 316 stainless steels. The main advantage of TKD is a significantly higher spatial resolution compared to the conventional EBSD due to the smaller interaction volume of the incident beam with the specimen. Two 316 stainless steel specimen, tested for stress corrosion cracking in hydrogenated and oxygenated pressurized water reactor chemistry, were characterized via TKD. The results include inverse pole figure (IPFZ) maps, image quality maps and misorientation maps, all acquired in very short time (<60 min) and with remarkable spatial resolution (up to 5 nm step size possible). They have been used in order to determine the location of the open crack with respect to the grain boundary, deformation bands, twinning and slip. Furthermore, TKD has been used to measure the grain boundary misorientation and establish a gauge for quantifying plastic deformation at the crack tip and other regions in the surrounding matrix. Both grain boundary migration and slip transfer have been detected as well.

Direct detection of electron backscatter diffraction patterns.

We report the first use of direct detection for recording electron backscatter diffraction patterns. We demonstrate the following advantages of direct detection: the resolution in the patterns is such that higher order features are visible; patterns can be recorded at beam energies below those at which conventional detectors usefully operate; high precision in cross-correlation based pattern shift measurements needed for high resolution electron backscatter diffraction strain mapping can be obtained. We also show that the physics underlying direct detection is sufficiently well understood at low primary electron energies such that simulated patterns can be generated to verify our experimental data.

Controlling the orientation, edge geometry, and thickness of chemical vapor deposition graphene.

We report that the shape, orientation, edge geometry, and thickness of chemical vapor deposition graphene domains can be controlled by the crystallographic orientations of Cu substrates. Under low-pressure conditions, single-layer graphene domains align with zigzag edges parallel to a single <101> direction on Cu(111) and Cu(101), while bilayer domains align to two directions on Cu(001). Under atmospheric pressure conditions, hexagonal domains also preferentially align. This discovery can be exploited to generate high-quality, tailored graphene with controlled domain thickness, orientations, edge geometries, and grain boundaries.

Elastic strain tensor measurement using electron backscatter diffraction in the SEM.

The established electron backscatter diffraction (EBSD) technique for obtaining crystallographic information in the SEM has been adapted to permit elastic strain measurement. Basically, the displacement of crystallographic features in an EBSD pattern, such as zone axes, which result from strain in a crystal, is determined by comparing those same features as they appear in a pattern from an unstrained region of the crystal. The comparison is made by cross-correlation of selected regions in the two patterns. Tests show that the sensitivity to displacement measurement is 1 part in 10 000, which translates to a strain sensitivity of 2 parts in 10 000. Eight components of the strain tensor are determined directly and the ninth is calculated using the fact that the free surface of the sample is traction-free. Examples discussed are taken from studies of a lenticular fracture in germanium, the strain distribution surrounding a carbide precipitate in a nickel base alloy and grain boundary studies in another nickel base alloy.

High-resolution elastic strain measurement from electron backscatter diffraction patterns: new levels of sensitivity.

In this paper, we demonstrate that the shift between similar features in two electron backscatter diffraction (EBSD) patterns can be measured using cross-correlation based methods to +/- 0.05 pixels. For a scintillator screen positioned to capture the usual large solid angle employed in EBSD orientation mapping this shift corresponds to only approximately 8.5 x 10(-5)rad at the pattern centre. For wide-angled EBSD patterns, the variation in the entire strain and rotation tensor can be determined from single patterns. Repeated measurements of small rotations applied to a single-crystal sample, determined using the shifts at four widely separated parts of the EBSD patterns, showed a standard deviation of 1.3 x 10(-4) averaged over components of the displacement gradient tensor. Variations in strains and rotations were measured across the interface in a cross-sectioned Si1-x Gex epilayer on a Si substrate. Expansion of the epilayer close to the section surface is accommodated by tensile strains and lattice curvature that extend a considerable distance into the substrate. Smaller and more localised shear strains are observed close to the substrate-layer interface. EBSD provides an impressive and unique combination of high strain sensitivity, high spatial resolution and ease of use.