Observations of lattice curvature near the interface of a deformed aluminium bicrystal

Accurate and fast localization of EBSD pattern centers for screen moving technology

The authors of this study develop an accurate and fast method for the localization of the pattern centers (PCs) in the electron backscatter diffraction (EBSD) technique by using the model of deformation of screen moving technology. The proposed algorithm is divided into two steps: (a) Approximation: We use collinear feature points to obtain the initial value of the coordinates of the PC and the zoom factor. (b) Subdivision: We then construct a deformation function containing the three parameters to be solved, select a large region for global registration, use the inverse compositional Gauss-Newton (ICGN) to optimize the objective function, and obtain the results of iteration of the PC and the zoom factor. The proposed algorithm was applied to simulated patterns, and yielded an accuracy of measurement of the PCs that was better than 4.6×10-6 of their resolution while taking only 0.2 s for computations. Moreover, the proposed algorithm has a large radius of convergence that makes it robust to the initial estimate. We also discuss the influence of factors of mechanical instability on its results of calibration during the insertion of the detector, and show that errors in measurements caused by the tilt motion of the camera are related only to the tilt angle of its motion and the detector distance, and are unrelated to the distance moved by it.

Influence of misorientation angle and local dislocation density on β-phase distribution in Al 5xxx alloys

Al–Mg alloys undergo sensitization when exposed to elevated temperatures, making them susceptible to intergranular corrosion and stress corrosion cracking. Most of the existing research on microstructure effects on sensitization is centered on the effect of intrinsic grain boundary characteristics such as misorientation angle and coincident site lattice (CSL) values. Very few studies have systematically investigated the influence of extrinsic characteristics such as dislocation density. In this paper, the influence of local microstructure characteristics on the sensitization susceptibility of AA5456 was investigated using in situ optical microscopy corrosion experiments and electron back scattering diffraction analysis. The results show a clear trend between the local geometrically necessary dislocation (GND) density and β phase precipitation, with higher GND densities correlating with higher rates sensitized boundaries. This trend held true even for low angle grain boundaries. These results demonstrate the importance of considering factors beyond grain boundary characteristics in determining susceptibility to sensitization.

Identification of Star Defects in Gallium Nitride with HREBSD and ECCI

This paper characterizes novel “star” defects in GaN films grown with metal–organic vapor phase deposition (MOVPE) on GaN substrates with electron channeling contrast imaging (ECCI) and high-resolution electron backscatter diffraction (HREBSD). These defects are hundreds of microns in size and tend to aggregate threading dislocations at their centers. They are the intersection of six nearly ideal low-angle tilt boundaries composed of $\langle a\rangle$-type pyramidal edge dislocations, each on a unique slip system.

Correlating results from high resolution EBSD with TEM- and ECCI-based dislocation microscopy: Approaching single dislocation sensitivity via noise reduction

High resolution electron backscatter diffraction (HREBSD), an SEM-based diffraction technique, may be used to measure the lattice distortion of a crystalline material and to infer the geometrically necessary dislocation content. Uncertainty in the image correlation process used to compare diffraction patterns leads to an uneven distribution of measurement noise in terms of the lattice distortion, which results in erroneous identification of dislocation type and density. This work presents a method of reducing noise in HREBSD dislocation measurements by removing the effect of the most problematic components of the measured distortion. The method is then validated by comparing with TEM analysis of dislocation pile-ups near a twin boundary in austenitic stainless steel and with ECCI analysis near a nano-indentation on a tantalum oligocrystal. The HREBSD dislocation microscopy technique is able to resolve individual dislocations visible in TEM and ECCI and correctly identify their Burgers vectors.

Study of Geometrically Necessary Dislocations of a Partially Recrystallized Aluminum Alloy Using 2D EBSD

During recrystallization, the growth of fresh grains initiated within a deformed microstructure causes dramatic changes in the dislocation structure and density of a heavily deformed matrix. In this paper, the microstructure of a cold rolled and partially recrystallized Al-Mg alloy (AA5052) was studied via electron backscattered diffraction (EBSD) analysis. The structure and density of the geometrically necessary dislocations (GNDs) were predicted using a combination of continuum mechanics and dislocation theory. Accordingly, the Nye dislocation tensor, which determines the GND structure, was estimated by calculation of the lattice curvature. To do so, five components of the Nye dislocation tensor were directly calculated from the local orientation of surface points of the specimen, which was determined by two-dimensional EBSD. The remaining components of GNDs were determined by minimizing a normalized Hamiltonian equation based on dislocation energy. The results show the elimination of low angle boundaries, lattice curvature, and GNDs in recrystallized regions and the formation of low angle boundaries with orientation discontinuities in deformed grains, which may be due to static recovery.

Selective increase in CO2 electroreduction activity at grain-boundary surface terminations

Altering a material's catalytic properties requires identifying structural features that give rise to active surfaces. Grain boundaries create strained regions in polycrystalline materials by stabilizing dislocations and may provide a way to create high-energy surfaces for catalysis that are kinetically trapped. Although grain-boundary density has previously been correlated with catalytic activity for some reactions, direct evidence that grain boundaries create surfaces with enhanced activity is lacking. We used a combination of bulk electrochemical measurements and scanning electrochemical cell microscopy with submicrometer resolution to show that grain-boundary surface terminations in gold electrodes are more active than grain surfaces for electrochemical carbon dioxide (CO₂) reduction to carbon monoxide (CO) but not for the competing hydrogen (H₂) evolution reaction. The catalytic footprint of the grain boundary is commensurate with its dislocation-induced strain field, providing a strategy for broader exploitation of grain-boundary effects in heterogeneous catalysis.

Evaluating Deformation-Induced Grain Orientation Change in a Polycrystal During In Situ Tensile Deformation using EBSD

Using an in situ load frame within a scanning electron microscope, a microstructural section on the surface of an annealed tantalum (Ta) polycrystalline specimen was mapped at successive tensile strain intervals, up to ~20% strain, using electron backscatter diffraction. A grain identification and correlation technique was developed for characterizing the evolving microstructure during loading. Presenting the correlated results builds on the reference orientation deviation (ROD) map concept where individual orientation measurements within a grain are compared with a reference orientation associated with that grain. In this case, individual orientation measurements in a deformed grain are measured relative to a reference orientation derived from the undeformed (initial) configuration rather than the current deformed configuration as has been done for previous ROD schemes. Using this technique helps reveal the evolution of crystallographic orientation gradients and development of deformation-induced substructure within grains. Although overall crystallographic texture evolved slowly during deformation, orientation spread within grains developed quickly. In some locations, misorientation relative to the original orientation of a grain exceeded 20° by 15% strain. The largest orientation changes often appeared near grain boundaries suggesting that these regions were preferred locations for the initial development of subgrains.

Size-dependent energy in crystal plasticity and continuum dislocation models

In the light of recent progress in coarsening the discrete dislocation mechanics, we consider two questions relevant for the development of a mesoscale, size-dependent plasticity: (i) can the phenomenological expression for size-dependent energy, as quadratic form of Nye's dislocation density tensor, be justified from the point of view of dislocation mechanics and under what conditions? (ii) how can physical or phenomenological expressions for size-dependent energy be computed from dislocation mechanics in the general case of elastically anisotropic crystal? The analysis based on material and slip system symmetries implies the negative answer to the first question. However, the coarsening method developed in response to the second question, and based on the physical interpretation of the size-dependent energy as the coarsening error in dislocation interaction energy, introduces additional symmetries. The result is that the equivalence between the phenomenological and the physical expressions is possible, but only if the multiplicity of characteristic lengths associated with different slip systems, is sacrificed. Finally, we discuss the consequences of the assumption that a single length scale governs the plasticity of a crystal, and note that the plastic dissipation at interfaces has a strong dependence on the length scale embedded in the energy expression.

Orientation precision of electron backscatter diffraction measurements near grain boundaries

Electron backscatter diffraction (EBSD) has become a common technique for measuring crystallographic orientations at spatial resolutions on the order of tens of nanometers and at angular resolutions <0.1°. In a recent search of EBSD papers using Google Scholar™, 60% were found to address some aspect of deformation. Generally, deformation manifests itself in EBSD measurements by small local misorientations. An increase in the local misorientation is often observed near grain boundaries in deformed microstructures. This may be indicative of dislocation pile-up at the boundaries but could also be due to a loss of orientation precision in the EBSD measurements. When the electron beam is positioned at or near a grain boundary, the diffraction volume contains the crystal lattices from the two grains separated by the boundary. Thus, the resulting pattern will contain contributions from both lattices. Such mixed patterns can pose some challenge to the EBSD pattern band detection and indexing algorithms. Through analysis of experimental local misorientation data and simulated pattern mixing, this work shows that some of the rise in local misorientation is an artifact due to the mixed patterns at the boundary but that the rise due to physical phenomena is also observed.

Three-dimensional rocking curve imaging to measure the effective distortion in the neighbourhood of a defect within a crystal: an ice example

A three-dimensional Bragg diffraction imaging technique, which combines rocking curve imaging with ‘pinhole’ and ‘section’ diffraction topography in the transmission case, allows three-dimensional lattice distortion in the bulk of an ice crystal under compression to be measured.

Rocking curve imaging (RCI) is a quantitative version of monochromatic beam diffraction topography that involves using a two-dimensional detector, each pixel of which records its own ‘local’ rocking curve. From these local rocking curves one can reconstruct maps of particularly relevant quantities (e.g. integrated intensity, angular position of the centre of gravity, FWHM). Up to now RCI images have been exploited in the reflection case, giving a quantitative picture of the features present in a several-micrometre-thick subsurface layer. Recently, a three-dimensional Bragg diffraction imaging technique, which combines RCI with ‘pinhole’ and ‘section’ diffraction topography in the transmission case, was implemented. It allows three-dimensional images of defects to be obtained and measurement of three-dimensional distortions within a 50 × 50 × 50 µm elementary volume inside the crystal with angular misorientations down to 10⁻⁵–10⁻⁶ rad. In the present paper, this three-dimensional-RCI (3D-RCI) technique is used to study one of the grains of a three-grained ice polycrystal. The inception of the deformation process is followed by reconstructing virtual slices in the crystal bulk. 3D-RCI capabilities allow the effective distortion in the bulk of the crystal to be investigated, and the predictions of diffraction theories to be checked, well beyond what has been possible up to now.

Measurement of geometrically necessary dislocation density with high resolution electron backscatter diffraction: effects of detector binning and step size

Recent advances using cross-correlation analysis of full resolution high quality electron backscatter diffraction (EBSD) patterns have provided a method for quantitatively mapping the stored dislocation density at high spatial resolution. Larger areas could be mapped with image binning or coarser step sizes. We have studied the effects of image binning and step size on the recovery of GND density. Our results suggest that: (i) the measured lower bound GND density noise floor broadly agrees with Wilkinson and Randman's 2009 prediction, where a decrease in step size or an increase in misorientation uncertainty increases the noise floor; (ii) increasing the step size results in a lower GND density being recovered as some dislocations are now considered as statistically stored dislocations (SSDs); (iii) in deformed samples the average GND density stays relatively constant as the degree of pattern binning is increased up to 8×8. Pattern binning thus provides a means of increasing the data acquisition and analysis rate without unduly degrading the data quality.

Three-dimensional plastic response in polycrystalline coppervianear-field high-energy X-ray diffraction microscopy

The evolution of the crystallographic orientation field in a polycrystalline sample of copper is mapped in three dimensions as tensile strain is applied. Using forward-modeling analysis of high-energy X-ray diffraction microscopy data collected at the Advanced Photon Source, the ability to track intragranular orientation variations is demonstrated on an ∼2 µm length scale with ∼0.1° orientation precision. Lattice rotations within grains are tracked between states with ∼1° precision. Detailed analysis is presented for a sample cross section before and after ∼6% strain. The voxel-based (0.625 µm triangular mesh) reconstructed structure is used to calculate kernel-averaged misorientation maps, which exhibit complex patterns. Simulated scattering from the reconstructed orientation field is shown to reproduce complex scattering patterns generated by the defected microstructure. Spatial variation of a goodness-of-fit or confidence metric associated with the optimized orientation field indicates regions of relatively high or low orientational disorder. An alignment procedure is used to match sample cross sections in the different strain states. The data and analysis methods point toward the ability to perform detailed comparisons between polycrystal plasticity computational model predictions and experimental observations of macroscopic volumes of material.

High-energy transmission Laue micro-beam X-ray diffraction: a probe for intra-granular lattice orientation and elastic strain in thicker samples

An understanding of the mechanical response of modern engineering alloys to complex loading conditions is essential for the design of load-bearing components in high-performance safety-critical aerospace applications. A detailed knowledge of how material behaviour is modified by fatigue and the ability to predict failure reliably are vital for enhanced component performance. Unlike macroscopic bulk properties (e.g. stiffness, yield stress, etc.) that depend on the average behaviour of many grains, material failure is governed by `weakest link'-type mechanisms. It is strongly dependent on the anisotropic single-crystal elastic-plastic behaviour, local morphology and microstructure, and grain-to-grain interactions. For the development and validation of models that capture these complex phenomena, the ability to probe deformation behaviour at the micro-scale is key. The diffraction of highly penetrating synchrotron X-rays is well suited to this purpose and micro-beam Laue diffraction is a particularly powerful tool that has emerged in recent years. Typically it uses photon energies of 5-25 keV, limiting penetration into the material, so that only thin samples or near-surface regions can be studied. In this paper the development of high-energy transmission Laue (HETL) micro-beam X-ray diffraction is described, extending the micro-beam Laue technique to significantly higher photon energies (50-150 keV). It allows the probing of thicker sample sections, with the potential for grain-level characterization of real engineering components. The new HETL technique is used to study the deformation behaviour of individual grains in a large-grained polycrystalline nickel sample during in situ tensile loading. Refinement of the Laue diffraction patterns yields lattice orientations and qualitative information about elastic strains. After deformation, bands of high lattice misorientation can be identified in the sample. Orientation spread within individual scattering volumes is studied using a pattern-matching approach. The results highlight the inability of a simple Schmid-factor model to capture the behaviour of individual grains and illustrate the need for complementary mechanical modelling.

A review of strain analysis using electron backscatter diffraction

Since the automation of the electron backscatter diffraction (EBSD) technique, EBSD systems have become commonplace in microscopy facilities within materials science and geology research laboratories around the world. The acceptance of the technique is primarily due to the capability of EBSD to aid the research scientist in understanding the crystallographic aspects of microstructure. There has been considerable interest in using EBSD to quantify strain at the submicron scale. To apply EBSD to the characterization of strain, it is important to understand what is practically possible and the underlying assumptions and limitations. This work reviews the current state of technology in terms of strain analysis using EBSD. First, the effects of both elastic and plastic strain on individual EBSD patterns will be considered. Second, the use of EBSD maps for characterizing plastic strain will be explored. Both the potential of the technique and its limitations will be discussed along with the sensitivity of various calculation and mapping parameters.

A simple algorithm to eliminate ambiguities in EBSD orientation map visualization and analyses: application to fatigue crack-tips/wakes in aluminum alloys

A simple algorithm is developed and implemented to eliminate ambiguities, in both statistical analyses of orientation data (e.g., orientation averaging) and electron backscattered diffraction (EBSD) orientation map visualization, caused by symmetrically equivalent orientations and the wrap-around or umklapp effect. Using crystal symmetry operators and the lowest Euclidian-distance criterion, the orientation of each pixel within a grain is redefined. An advantage of this approach is demonstrated for direct determination of the representative orientation of a grain within an EBSD map by mean, median, or quaternion-based averaging methods that can be further used within analyses or visualization of misorientation or geometrically necessary dislocation (GND) density. If one also considers the lattice curvature tensor, five components of the dislocation density tensor-corresponding to a part of the GND content-may be inferred. The methodology developed is illustrated using EBSD orientation data obtained from the fatigue crack-tips/wakes in aerospace aluminum alloys 2024-T351 and 7050-T7451.

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.

EBSD characterization of a hot worked 304 austenitic stainless steel under strain reversal

Monotonic and strain reversal hot torsion tests were performed on a 304 austenitic stainless steel, this led to changes in microstructures depending on the strain path. electron backscatter diffraction was used as the tool for characterizing the microstructures. It was possible to find some intragranular microstructural changes due to the reversal of the strain by means of several local and global misorientation-related parameters. Sigma3 boundaries also showed sensitivity to strain reversal.