Resolution Electron Backscatter Diffraction Research Articles

Nanoscale speckle patterning for combined high‐resolution strain and orientation mapping of environmentally sensitive materials

AbstractScanning electron microscopy‐based high‐resolution digital image correlation (HRDIC) is now an established technique, providing full‐field strain and displacement measurement at the microscale. Techniques for generating speckle patterns for sub‐micron strain mapping can often be either substrate dependent or rely on applying aggressive conditions which may alter the microstructure of interest or damage the substrate in highly sensitive materials. We detail a modification of a methodology successfully applied in the literature to allow its use with metallic materials that are particularly sensitive to the corrosive media, such as copper‐base alloys. Nanometre‐thick silver films, applied with physical vapour deposition, are remodelled using NaBr in non‐aqueous isopropanol, replacing the aqueous solution of NaCl in the original method, forming a uniform dispersion of silver islands highly suitable for digital image correlation (DIC) measurement. The entire procedure is performed at ambient temperature. We find that the DIC pattern is suitably electron transparent to allow electron backscatter diffraction (EBSD) measurements without pattern removal, producing diffraction patterns of sufficient quality for cross‐correlation based high‐angular resolution EBSD. This property facilitates simultaneous EBSD and DIC mapping experiments, providing deeper insights into the kinematics of plastic deformation in crystalline materials. Sub‐100 nm islands are achieved through control of the sputter coating parameters, resulting in DIC cross‐correlation subwindows of 140 nm with a 50% overlap. This resolution is sufficient to capture the fine detail of strain localisation phenomena during plastic deformation, demonstrated here with a case study in CuCrZr, a precipitation‐hardened heat sink material for application in nuclear fusion components. Here, we extract full‐field displacement data with DIC and corresponding orientation information using EBSD without the need for pattern removal.

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.

HR-EBSD analysis of in situ stable crack growth at the micron scale

Understanding the local fracture resistance of microstructural features, such as brittle inclusions, coatings, and interfaces, at the microscale is critical for microstructure-informed design of materials. In this study, a novel approach has been formulated to decompose the J-integral evaluation of the elastic energy release rate to the three-dimensional stress intensity factors directly from experimental measurements of the elastic deformation gradient tensors of the crack field by in situ high (angular) resolution electron backscatter diffraction (HR-EBSD). An exemplar study is presented of a quasi-static crack, inclined to the observed surface, propagating on low index {hkl} planes in a (001) single crystal silicon wafer.

Transient Creep in Subduction Zones by Long‐Range Dislocation Interactions in Olivine

AbstractLarge earthquakes transfer stress from the shallow lithosphere to the underlying viscoelastic lower crust and upper mantle, inducing transient creep during the postseismic interval. Recent experiments on olivine have provided a new rheological model for this transient creep based on the accumulation and release of back stresses among dislocations. Here, we test whether natural rocks preserve dislocation‐induced stress heterogeneity consistent with the back‐stress hypothesis by mapping olivine from the palaeosubduction interface of the Oman‐UAE ophiolite with high‐angular resolution electron backscatter diffraction. The olivine preserves heterogeneous residual stresses that vary in magnitude by several hundred megapascals over length scales of a few micrometers. Large stresses are commonly spatially associated with elevated densities of geometrically necessary dislocations within subgrain interiors. These spatial relationships, along with characteristic probability distributions of the stresses, confirm that the stress heterogeneity is generated by the dislocations and records their long‐range elastic interactions. Images of dislocations decorated by oxidation display bands of high and low dislocation density, suggesting that dislocation interactions contributed to the organization of the substructure. These results support the applicability of the back‐stress model of transient creep to deformation in the mantle portion of plate‐boundary shear zones. The model predicts that rapid stress changes, such as those imposed by large earthquakes, can induce order‐of‐magnitude changes in viscosity that depend nonlinearly on the stress change, consistent with inferences of mantle rheology from geodetic observations.

Development of local plasticity around voids during tensile deformation

Voids can limit the life of engineering components. This motivates us to understand local plasticity around voids in a nickel base superalloy combining experiments and simulations. Single crystal samples were deformed in tension with in-situ high angular resolution electron back scatter diffraction to probe the heterogeneous local stress field under load; the reference stress is informed by crystal plasticity finite element simulations. This information is used to understand the activation of plastic deformation around the void. Our investigation indicates that while the resolved shear stress would indicate slip activity on multiple slip systems, slip is reduced to specific systems due to image forces and forest hardening. This study rationalizes the observed development of plastic deformation around the void, aiding in our understanding of component failure and engineering design.

A non-local crystal plasticity constitutive model for hexagonal close-packed polycrystals

A strain gradient crystal plasticity finite element model is developed to study the evolution of internal and localized elastic strains in hexagonal close-packed polycrystals. The results of the model are firstly compared to the previously published data for a series of in-situ neutron diffraction experiments conducted on α-zirconium specimens. The development of internal lattice strains is studied first without considering the possible effects of grain morphologies and locations. This is followed by importing the “as-measured” grain maps into the model, and investigating the development of localized lattice rotation fields, geometrically necessary dislocation densities, and statistically stored dislocation densities in the vicinity of twins. The numerical results are compared to those measured for a deformed α-zirconium specimen using high angular resolution electron back scatter diffraction technique. To understand the benefits of using non-local formulation, numerical results are further compared to those from a conventional crystal plasticity model. It is shown that while the calculated lattice strains and lattice rotations from both models are in agreement with the measured ones, the non-local model provides a better estimation of localized stresses in the regions with a sharp strain gradient. This difference is more pronounced in the vicinity of twins, where the calculated stresses and geometrically necessary dislocation densities by the non-local model are in better agreement with the measurements.

On the resolution of EBSD across atomic density and accelerating voltage with a particular focus on the light metal magnesium

We measured the physical lateral resolution of the electron backscatter diffraction (EBSD) technique for the case of pure magnesium and tungsten and compared these data with other values from literature. Spatial resolution, among other parameters, depends significantly on the accelerating voltage and the atomic number of the material. For the case of lighter metals, it is supposed to be lower than in the case of heavier metals for a given accelerating voltage. In the present work, lateral resolution was measured in dependence of accelerating voltage on a straight high angle grain boundary which was positioned parallel (horizontal boundary) and perpendicular (vertical boundary) to the tilt axis of the specimen. For magnesium the best lateral resolution of 240 nm was obtained at an accelerating voltage of 5 kV. The resolution dramatically worsened to values as high as 3500 nm as the voltage was increased from 15 kV to 30 kV. The aspect ratio of horizontal and vertical lateral resolution tended to 1.0 at the accelerating voltage of 5 kV and to 2.5 at the accelerating voltage of 30 kV. These values as function of accelerating voltages were compared with those obtained on the high atomic number metal tungsten. Here resolution at 5 kV was about a quarter of that of magnesium. With increasing voltage, the value almost didn't change. For all voltages the resolution aspect ratio stayed close to 1.0.

High‐Angular Resolution Electron Backscatter Diffraction as a New Tool for Mapping Lattice Distortion in Geological Minerals

AbstractAnalysis of distortions of the crystal lattice within individual mineral grains is central to the investigation of microscale processes that control and record tectonic events. These distortions are generally combinations of lattice rotations and elastic strains, but a lack of suitable observational techniques has prevented these components being mapped simultaneously and routinely in earth science laboratories. However, the technique of high‐angular resolution electron backscatter diffraction (HR‐EBSD) provides the opportunity to simultaneously map lattice rotation and elastic strain gradients with exceptional precision, on the order of 0.01° for rotations and 10−4 in strain, using a scanning electron microscope. Importantly, these rotations and lattice strains relate to densities of geometrically necessary dislocations and residual stresses. Recent works have begun to apply and adapt HR‐EBSD to geological minerals, highlighting the potential of the technique to provide new insights into the microphysics of rock deformation. Therefore, the purpose of this review is to provide a summary of the technique, to identify caveats and targets for further development, and to suggest areas where it offers potential for major advances. In particular, HR‐EBSD is well suited to characterizing the roles of different dislocation types during crystal plastic deformation and to mapping heterogeneous internal stress fields associated with specific deformation mechanisms/microstructures or changes in temperature, confining pressure, or macroscopic deviatoric stress. These capabilities make HR‐EBSD a particularly powerful new technique for analyzing the microstructures of deformed geological materials.

Interplay of stresses, plasticity at crack tips and small sample dimensions revealed by in-situ microcantilever tests in tungsten

The evolution and distribution of stresses and geometrically necessary dislocation densities during microcantilever testing were studied in-situ in a scanning electron microscope using high-angular resolution electron back scatter diffraction. Focused ion beam milling was used to prepare the beams with dimensions of ca. 5–7µm in height and width and 20µm in length in a tungsten single crystal along a 〈100〉 axis. Un-notched cantilevers were tested to gain insight into dislocation mechanisms leading to significant strengthening during loading. Locally increased yield and flow stresses were linked to pronounced stress gradients on specific slip planes and dislocation pile-ups at regions of zero stress. The limited plastic deformation behaviour of tungsten at room temperature allowed also detailed observations of the interplay between crack initiation and the formation of a plastic zone at the crack tip. Due to the lack of dislocation sources in the crack tip vicinity, dislocations were initially emitted on {110} planes from the crack tip, which led to finite crack tip blunting. The initiated crack was stopped by compressive stresses and a significant plastic zone developed, which kept the crack from growing with ongoing loading. The combined experimental and analytical observations allow a mechanistic understanding, which helps in explaining the recently reported size-dependent plastic deformation and fracture behaviour of semi-brittle materials.

Crack nucleation using combined crystal plasticity modelling, high-resolution digital image correlation and high-resolution electron backscatter diffraction in a superalloy containing non-metallic inclusions under fatigue.

A crystal plasticity finite-element model, which explicitly and directly represents the complex microstructures of a non-metallic agglomerate inclusion within polycrystal nickel alloy, has been developed to study the mechanistic basis of fatigue crack nucleation. The methodology is to use the crystal plasticity model in conjunction with direct measurement at the microscale using high (angular) resolution-electron backscatter diffraction (HR-EBSD) and high (spatial) resolution-digital image correlation (HR-DIC) strain measurement techniques. Experimentally, this sample has been subjected to heat treatment leading to the establishment of residual (elastic) strains local to the agglomerate and subsequently loaded under conditions of low cyclic fatigue. The full thermal and mechanical loading history was reproduced within the model. HR-EBSD and HR-DIC elastic and total strain measurements demonstrate qualitative and quantitative agreement with crystal plasticity results. Crack nucleation by interfacial decohesion at the nickel matrix/agglomerate inclusion boundaries is observed experimentally, and systematic modelling studies enable the mechanistic basis of the nucleation to be established. A number of fatigue crack nucleation indicators are also assessed against the experimental results. Decohesion was found to be driven by interface tensile normal stress alone, and the interfacial strength was determined to be in the range of 1270–1480 MPa.

A wedge-mounting technique for nanoscale electron backscatter diffraction

The practical spatial resolution of electron backscatter diffraction (EBSD) is around 100 nm, which limits the length scales from which phase and orientation relationship characterization can be accomplished. This precludes collection of statistically relevant data on the crystallography of interfaces within nanomaterials where such information is essential for understanding the unique properties of these materials. In this work, we present a wedge-mounting technique that enables EBSD data to be collected for sub-100 nm thick layers of Cu-Nb bimetallic multilayers fabricated via accumulative roll bonding. We present statistics on layer thickness distributions, grain morphology, orientation distributions, twin volume fraction, and interface character for material with an averaged layer thickness of 86 and 56 nm.

Determination of elastic strain fields and geometrically necessary dislocation distributions near nanoindents using electron back scatter diffraction

The deformation around a 500-nm deep Berkovich indent in a large grained Fe sample has been studied using high resolution electron back scatter diffraction (EBSD). EBSD patterns were obtained in a two-dimensional map around the indent on the free surface. A cross-correlation-based analysis of small shifts in many sub-regions of the EBSD patterns was used to determine the variation of elastic strain and lattice rotations across the map at a sensitivity of ∼±10−4. Elastic strains were smaller than lattice rotations, with radial strains found to be compressive and hoop strains tensile as expected. Several analyses based on Nye's dislocation tensor were used to estimate the distribution of geometrically necessary dislocations (GNDs) around the indent. The results obtained using different assumed dislocation geometries, optimisation routines and different contributions from the measured lattice rotation and strain fields are compared. Our favoured approach is to seek a combination of GND types which support the six measurable (of a possible nine) gradients of the lattice rotations after correction for the 10 measurable elastic strain gradients, and minimise the total GND line energy using an L1 optimisation method. A lower bound estimate for the noise on the GND density determination is ∼±1012 m−2 for a 200-nm step size, and near the indent densities as high as 1015 m−2 were measured. For comparison, a Hough-based analysis of the EBSD patterns has a much higher noise level of ∼±1014m−2 for the GND density.

Use of an energy filter to improve the spatial resolution of electron backscatter diffraction

The electron backscatter diffraction (EBSD) analytical technique is invaluable for determining the crystallography of bulk alloys, thin films, and nanoparticles. However, our physical understanding of EBSD pattern generation is incomplete, which hinders our ability to push the limits of EBSD analysis. Here, by using an energy filter with better than 10 eV resolution, an improvement in the spatial resolution of the EBSD pattern was experimentally demonstrated. A signal depth of less than 15 nm for an aluminum film was achieved by controlling the cutoff energy of the energy filter. Additionally, a two-fold improvement in the spatial resolution across a grain boundary was observed using the energy filter.

Pyramidal indentation into fcc single crystals and quasi‐isotropic polycrystals: similar phenomena, different driving mechanisms

AbstractPyramidal microindentation into the (001) surface of an fcc single crystal made of the Ni–base superalloy CMSX‐4 has shown indent shapes which strongly depend on the azimuthal orientation of the pyramid. This observation is experimentally elucidated by digital surface models obtained from high resolution electron back–scatter diffraction (EBSD) technique along with digital image processing. Predictions of crystal plasticity finite element simulations agree with the experimental observations; the observed surface deformation patterns are due to pile–up formation, which is invariantly maximum in <110> directions thus being independent of the azimuthal orientation of the pyramid. The material pile–up is locally accommodated to the indenter faces leading to a convex, a concave contact rim at the faces of the indenter depending on the orientation. The result of maximum pile–up in <110> directions suggests that the driving mechanism for pile–up is purely crystallographic in that the influence of stress concentrations due to different indenter orientations and indenter shapes is negligible. The present findings for fcc single crystals are contrasted to well known observations for quasi–isotropic polycrystals. The different driving mechanisms resulting in phenomenologically similar material response are identified for both materials. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Cover Picture: Texture Evolution During Bending of a Single Crystal Copper Nanowire Studied by EBSD and Crystal Plasticity Finite Element Simulations (Adv. Eng. Mater. 8/2008)

The cover shows a bending test on a Cu single crystal nanowire. The distribution of the geometrically necessry dislocations in the bent wire was determined using high resolution electron back scatter diffraction and predicted using a crystal plasticity finite element method which uses a dislocation based constitutive law. More details can be found in the article of F. Weber, I. Schestakow, F. Roters, D. Raabe on page 737.

Severe Deformation of a Carbon Steel within the Ferritic Region

The influence of severe warm deformation on the microstructural evolution and flow behavior of a plain carbon steel has been investigated through torsion testing. The specimens were severe deformed within the ferritic region up to strain of 70 with constant strain rate of 0.1 s 1 − . Microstructural evolutions have been investigated using high resolution electron backscatter diffraction (EBSD). True stress-true strain curves exhibit a single and smooth maximum, followed by a slow but significant softening stage. A steady state is observed at very large strains. This finding suggests that the relative balance between comparable work hardening and dynamic work softening results in the occurrence of warm ductility during large deformation. The initial grain structure was equiaxed, but at low strains the grains become elongated in the torsion direction. However, at large strains the grain aspect ratio decreases and finally, further straining leads to the formation of new fine grains with high-angle boundaries, which become more equiaxed than the previous fragmented structure. The flow stress, as well as all the average microstructural parameters, then remains independent of strain. The mechanisms operating during such warm flow behavior and structure changes are discussed in detail.

An Analysis of Strain Path Effects on Static Recrystallisation in Hot Worked Aluminium Alloy AA5052 Using Forward and Reverse Torsion

The effects of strain path reversal, using forward and reverse torsion, on the microstructure evolution in the aluminium alloy AA5052 have been studied using high resolution electron backscatter diffraction. Deformation was carried using two equal steps of forward/forward or forward/reverse torsion at a temperature of 300°C and strain rate of 1s-1 to a total equivalent tensile strain of 0.5. Sections of the as-deformed gauge lengths of both test specimens were then annealed at 400°C for 1 hour in a salt bath in order to investigate their subsequent recrystallisation response. In both strain path histories the deformation substructure in the grains analysed consisted of microband arrays within an equiaxed dislocation cell structure. The material subjected to forward/forward deformation did, however, have a slightly greater number of low angle boundaries, i.e. boundaries < 15° misorientation, whilst the forward/reverse material had some grains containing little evidence of substructure. On annealing both materials had significantly reduced levels of low angle boundaries but only the forward/forward material had an increased number of high angle boundaries and a reduced grain size, indicating recrystallisation had only occurred in this material. This would suggest that the deformation microstructure within the forward/forward condition was sufficient to initiate and maintain recrystallisation whilst the microstructure produced by the forward/reverse test contained insufficient nuclei or internal energy to produce a recrystallised material within 1 hour. Further work is now required at different annealing times in order to determine if the major effect of strain path is on retarding nucleation, growth or both.

TEM Sample Preparation and FIB-Induced Damage

AbstractOne of the most important applications of a focused ion beam (FIB) workstation is preparing samples for transmission electron microscope (TEM) investigation. Samples must be uniformly thin to enable the analyzing beam of electrons to penetrate. The FIB enables not only the preparation of large, uniformly thick, sitespecific samples, but also the fabrication of lamellae used for TEM samples from composite samples consisting of inorganic and organic materials with very different properties. This article gives an overview of the variety of techniques that have been developed to prepare the final TEM specimen. The strengths of these methods as well as the problems, such as FIB-induced damage and Ga contamination, are illustrated with examples. Most recently, FIB-thinned lamellae were used to improve the spatial resolution of electron backscatter diffraction and energy-dispersive x-ray mapping. Examples are presented to illustrate the capabilities, difficulties, and future potential of FIB.

High resolution mapping of strains and rotations using electron backscatter diffraction

The angular resolution of electron backscatter diffraction (EBSD) measurements can be significantly improved using an analysis based on determination of small shifts in features from one pattern to the next using cross-correlation functions. Using pattern shift measurements at many regions of the pattern, errors in the best fit strain and rotation tensors can be reduced. The authors show that elements of the strain tensor and small misorientations can be measured to ± 10−4 and ±0·006° for rotations. We apply the technique to two quite different materials systems. First, we determine the elastic strain distribution near the interface in a cross-sectioned SiGe epilayer, Si substrate semiconductor heterostructure. The plane stress boundary conditions at the sample surface are used to separate every term in the strain tensor. Second, the applicability to structural materials is illustrated by determining the lattice curvature caused by dislocations within the plastic zone associated with the wake and tip of a fatigue crack in a Ni based superalloy. The lattice curvatures are used to calculate the geometrically necessary dislocation content in the plastic zone.

Thermal Stability of Electrodeposited Ni and Ni-Co Layers; an EBSD-Study

The influence of heat treatment on the microstructure and the microtexture of electrodeposited Ni and Ni-Co layers was investigated with Electron Backscatter Diffraction (EBSD) with high resolution. Samples were annealed for 1 hour at 523 K and 673 K, the temperature region wherein recrystallisation occurs. The results are discussed in relation to the resolution of EBSD for the very fine grained electrodeposits and previous X-ray diffraction investigations.