Angus J. Wilkinson

A crystallographic mechanism for fatigue crack propagation through grain boundaries

A crystallographic model is proposed which takes into account both crack-plane twist and tilt effects on crack retardation at grain boundaries. The twist and tilt angles of the crack-plane deflection at a grain boundary are the key factors that control the path and growth rate of a short crack. Because of crack-plane twist, the area between the traces on the grain-boundary plane of the crack planes across the boundary has to be fractured in order for the crack to propagate through the boundary. This presents significant resistance to crack growth. As the area to be fractured increases with the extent of crack growth beneath the surface of observation, the grain boundary could still resist crack growth after the crack tip has passed the grain boundary on the surface, until the crack propagates through the whole boundary below the surface. A grain boundary with a large twist component could cause a short crack to arrest or branch. Studies of short fatigue crack growth in an Al-Li 8090 alloy plate provide evidence that supports the model.

ELECTRON DIFFRACTION BASED TECHNIQUES IN SCANNING ELECTRON MICROSCOPY OF BULK MATERIALS

Abstract The three scanning electron microscope diffraction based techniques of electron channelling patterns (ECPs), electron channelling constrast imaging (ECCI), and electron backscatter diffraction (EBSD) are reviewed. The dynamical diffraction theory is used to describe the physics of electron channelling, and hence the constrast observed in ECPs (and EBSD) and ECCI images of dislocations. Models for calculating channelling contrast are described and their limitations discussed. The practicalities of the experimental methods, including detector-specimen configurations, spatial resolution and sensitivities are given. Examples are given of the use of ECCI for imaging and characterising lattice defects, both individually and in groups, in semiconductor heterostructures and fatigued metals. Applications of the EBSD technique to orientation determination, phase identification and strain measurement are given and compared with use of ECPs. It is concluded that these techniques make the SEM a powerful instrument for characterising the local crystallography of bulk materials at the mesoscopic scale.

High resolution mapping of strains and rotations using electron backscatter diffraction

Abstract 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.

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 Nyes 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.

Quantitative deformation studies using electron back scatter patterns

Abstract The diffuseness of electron back scatter patterns (EBSPs) is observed to increase with plastic strain. The application of this technique to deformation studies has been limited by the lack of a general method of measuring the pattern quality. The degradation of EBSPs by cold work was thus thoroughly investigated using the A1 6061 alloy for the purpose. Methods of enhancing the Kikuchi band contrast by removal of the background intensity variation from digital images of 〈112〉 zone axes present in the EBSP have been developed. The contrast of the Kikuchi bands was quantified using the root mean square intensity of averaged band profiles, while the sharpness of the patterns was assessed by the attenuation of high frequency components of Fourier transforms of the enhanced images and of the averaged band profiles. Tilt was found to effect contrast but not sharpness, while cold work reduced both. However, surface contamination produced effects that were very similar to those of specimen deformation. A method is presented for quantitative determination of EBSP quality, which is independent of grain orientation and is based on the first moment of power spectra (the square of the Fourier transform) of features common to all patters to be compared.

The effect of crystal orientation on the indentation response of commercially pure titanium: experiments and simulations

This study combines nanoindentation, electron backscatter diffraction (EBSD) and crystal plasticity finite element analysis to examine the anisotropy in the indentation behaviour of individual grains within an α-Ti polycrystal. Nanoindentation is utilized to mechanically probe small volumes of material within grains for which orientations are known from prior EBSD mapping. Both indentation modulus and hardness decrease significantly as the indentation axis is inclined further from the c-axis; the plastic response showing the more marked anisotropy. Recently developed high angular resolution EBSD has been utilized to examine selected indents, providing maps of elastic strain variations and lattice rotations. From such maps lower bound solutions for the density of geometrically necessary dislocations (GNDs) have been established. Crystal plasticity modelling showed promise in capturing correctly the orientation dependence of load–displacement response and in lattice rotations local to the indenter, particularly for indentation into a basal plane which generated threefold rotational symmetry about an axis parallel with the indentation direction which was also observed in experiments.

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.

Strains, planes, and EBSD in materials science

Electron back scatter diffraction (EBSD) has made an impressive impact on the characterization of materials by directly linking microstructure and crystallographic texture to provide very rich and quantitative datasets which in many instances have forced us to rethink how microstructure should be defined and analyzed. In this article we try to first give a very basic idea of how an EBSD map is obtained and what the data produced is like. We then give a brief history detailing some of the more major steps in developing the technique to what it is today. Finally, we explore two advanced and exciting technique areas of strain mapping and 3D microscopy and demonstrate how the EBSD technique continues to evolve to tackle new applications and bolster our materials characterization toolbox.

High resolution electron backscatter diffraction measurements of elastic strain variations in the presence of larger lattice rotations

In this paper we explore methods of measuring elastic strain variations in the presence of larger lattice rotations (up to -11°) using high resolution electron backscatter diffraction. We have examined the fundamental equations which relate pattern shifts to the elastic strain tensor and modified them to a finite deformation framework from the original infinitesimal deformation one. We incorporate the traction free boundary condition into the minimisation problem for the finite deformation case (i.e. large rotations and small elastic strains). Numerical experiments show that this finite deformation kinematic analysis continues to work well, while the infinitesimal analysis fails, when the misorientation between test and reference pattern is made increasingly high. However, measurements on patterns simulated using dynamical diffraction theory indicated that this formulation is not sufficient to recover elastic strains accurately because the pattern shifts are not determined accurately when large rotations are present. To overcome this issue we remap the test pattern to an orientation that is close to that of reference pattern. This remapping was defined by a finite rotation matrix, which was estimated from the infinitesimal rotation matrix measured using cross-correlation. A second cross-correlation analysis between the reference pattern and the remapped test pattern allows the elastic strains to be recovered using the much simpler infinitesimal deformation theory. We have also demonstrated that accurate recovery of elastic strains requires accurate knowledge of the pattern centre if this remapping algorithm is used.

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 Randmans 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.