Measurement of crystal parameters on backscatter kikuchi diffraction patterns

Electron backscatter Kikuchi diffraction patterns (BKDPs) recorded in the scanning electron microscope (SEM) require measurements on the plane of the photographic film or on the recording screen. The parameters that require measurements are the equivalent electron source point on the pattern, or pattern centre, specimen-to-film distance, true interzonal angles, true interplanar angles, Bragg angles, and interplanar spacing. In this paper, the geometry and the methods of calculation of these parameters on BKDPs recorded directly on film are described in detail. The methods described are suitable for practical purposes, providing speed of calculation but limited accuracy. The inherent factors that limit the accuracy of any measurements on BKDPs are the limitations of the gnomonic projection, resulting in projected distortions in Kikuchi bands and diffuseness of Kikuchi band edges originating from inelastic scattering of electrons. The methods described are applied to crystallographic analysis of BKDPs recorded from silicon and polycrystalline copper.     

Automatic high-precision measurements of the location and width of Kikuchi bands in electron backscatter diffraction patterns

The demands for reliability and precision of crystal orientation data obtained through automatic analysis of electron backscattering patterns (EBSPs) in the SEM result in similar demands on the quality of the band position data which is provided by an image analysis procedure. This paper describes a new image processing procedure which is capable of providing accurate measurements of the location and width of typically 10–15 bands in digitized EBSPs of average quality. The new procedure is based on the Hough transform (HT) for line detection, and employs a special backmapping technique for generating two simplified HTs which separately focus on bright and dark lines in the images. A coordinated search for peaks in the two HTs leads to precise estimates of both the position and the width of bands in the patterns. A visual evaluation of the data produced by the new procedure shows that it performs significantly better than the conventional procedure with regard to both reliability and precision. Additionally, the measured band width data are fairly precise and can be used for obtaining a more robust and reliable indexing of the bands. Finally, the computational costs of the new procedure are smaller than for the conventional procedure.     

Problems in determining the misorientation axes, for small angular misorientations, using electron backscatter diffraction in the SEM

The errors associated with calculating misorientation axes from electron backscatter diffraction (EBSD) data have been assessed experimentally. EBSD measurements were made on the same grains after imposed rotations of 2°, 5°, 7°, 10°, 12°, 17°, 27° and 180° around the normal to the specimen surface. The misorientation magnitudes and the misorientation axes associated with the imposed rotations have been calculated from the EBSD data. Individual measurements of misorientation axes are precise for misorientation magnitudes greater than ≈ 20°. The errors must be appreciated when assessing misorientation data at lower misorientation magnitudes and particularly at magnitudes less than 5°. Where misorientation axes can be characterized by the distribution of axes from a number of individual measurements, current EBSD techniques are satisfactory, for data sets of 30 measurements, as long as misorientation magnitudes are 10° or more. With larger data sets it may be possible to extend this approach to smaller misorientation magnitudes. For characterization of individual misorientations less than 5°, new EBSD techniques need to be developed.     

Dynamical effects of anisotropic inelastic scattering in electron backscatter diffraction

We present a model which describes the appearance of excess and deficiency features in electron backscatter diffraction (EBSD) patterns and we show how to include this effect in many-beam dynamical simulations of EBSD. The excess and deficiency features appear naturally if we take into account the anisotropy of the internal source of inelastically scattered electrons which are subsequently scattered elastically to produce the EBSD pattern. The results of simulations applying this model show very good agreement with experimental patterns. The amount of the excess-deficiency asymmetry of the Kikuchi bands depends on their relative orientation with respect to the incident beam direction. In addition, higher order Laue zone rings are also influenced by the same effect.     

Factors affecting the accuracy of high resolution electron backscatter diffraction when using simulated patterns

High resolution EBSD directly compares electron backscattering patterns (EBSPs), generated in a scanning electron microscope, to measure relative strain and rotation to a precision of ～ 10(-4) in strain and 10(-4)rad (0.006 °) in rotation. However the measurement of absolute strain and rotation requires reference EBSPs of known strain and orientation (or a far field region of known strain). Recent suggestions of using simulated EBSPs with known strain show much promise. However precise measurement of the experimental geometry (pattern centre) is required. Common uncertainties of 0.5% in pattern centre result in uncertainty of ～ 10(-3) in strain state. Aberrations in the compact lenses used for EBSP capture can also result in image shifts that correspond to strains/rotations of ± 10(-3) between experimental and simulated EBSPs. Simulated EBSPs can be generated using dynamical or kinematic models (or a combination of the two). The choice in simulation model has a significant effect on the measured shifts, particularly at zone axis and high structure factor bands, due to large intensity variations, and for simple kinematic simulations can result in the measurement of rogue shifts and thus erroneous strain measurements. Calibrant samples of known strain provide a method of measuring the experimental geometry but imprecise stage movement combined with the high depth of field in the SEM could also result in uncertainties in strain of ～ 10(-3).     

Crystallographic analysis of facets using electron backscatter diffraction

Applications of electron backscatter diffraction (EBSD), also known as backscatter Kikuchi diffraction in the scanning electron microscope (SEM) are first and foremost microtexture and grain boundary misorientation analysis on a single polished section in the specimen. A more subtle and revealing approach to analysis of these data is to use EBSD to probe the orientations of planar surfaces, i.e. facets, which bound crystals. These surfaces include: • grain or phase boundaries • fractures • cracks It is of great interest to know the crystallography of such facets since it provides a key to understanding the physical properties of them.
As far as investigation methodology is concerned, surfaces or facets associated with polycrystals are of two types: exposed or unexposed. Exposed facets, such as a fracture surface, can be viewed directly in the SEM, whereas unexposed facets, such as a grain boundary, are usually revealed as an etched trace on a polished surface. Photogrammetric methods can be used to obtain the positional orientation of an exposed facet, and the crystallographic orientation is obtained either directly from the surface or by indirect sectioning. Calibrated sectioning is required to obtain the equivalent parameters for an internal surface. The present paper compares the methods for obtaining and interpreting the crystallography of facets, with illustrations from several materials.     

Characterization of nitride thin films by electron backscatter diffraction

Thin films incorporating GaN, InGaN and AlGaN are presently arousing considerable excitement because of their suitability for UV and visible light‐emitting diodes and laser diodes. However, because of the lattice mismatch between presently used substrates and epitaxial nitride thin films, the films are of variable quality. In this paper we describe our preliminary studies of nitride thin films using electron backscattered diffraction (EBSD). We show that the EBSD technique may be used to reveal the relative orientation of an epitaxial thin film with respect to its substrate (a 90° rotation between a GaN epitaxial thin film and its sapphire substrate is observed) and to determine its tilt (a GaN thin film was found to be tilted by 13 ± 1° towards [101 0]_GaN), where the tilt is due to the inclination of the sapphire substrate (cut off‐axis by 10° from (0001)_sapphire towards (101 0)_sapphire). We compare EBSD patterns obtained from As‐doped GaN films grown by plasma‐assisted molecular beam epitaxy (PA‐MBE) with low and high As₄ flux, respectively. Higher As₄ flux results in sharper, better defined patterns, this observation is consistent with the improved surface morphology observed in AFM studies. Finally, we show that more detail can be discerned in EBSD patterns from GaN thin films when samples are cooled.     

Application of electron backscatter diffraction to the study of phase transformations: present and possible future

This paper first underlines the main advantages, use and limitations of the electron backscatter diffraction technique from the viewpoint of phase transformations. To get a deeper understanding of physical mechanisms involved in phase transformations, several evolutions are now in progress to get an insight into both three-dimensional and real-time information. Two of them, in particular, improvement of data collection versus improvement of data processing are discussed in the second part of this paper.     

Progressive steps in the development of electron backscatter diffraction and orientation imaging microscopy

Ten years ago electron backscatter diffraction (EBSD) became available to a wider group active in materials research. This paper highlights some of the more significant developments in camera technology and software developments that have arisen since then. The use of slow‐scan charge couple device cameras for phase identification and rapid determination of orientation image micrographs is reviewed. The current limiting spatial resolution of the technique is shown to be less than 10 nm. A procedure for improving lattice spacing measurement by utilizing the full resolution of the camera is described with experimental measurements on silicon and nickel showing relative errors of plus/minus 3%. An investigation of partially recrystallized aluminium shows how the recrystallized fraction can be extracted with confidence but that the mapping of substructure in the highly deformed regions is questionable. Phase identification is described for complex cases in which the phase data tabulated in standard databases do not correspond to what is observed in the EBSD patterns. Phase mapping in a complex mineral in which chemical data and EBSD data are collected simultaneously is shown to be improved by recording both the chemical and the EBSD data into computer memory and proceeding with the phase discrimination and orientation measurement in off‐line analysis.     

Aberration-compensated large-angle rocking-beam electron diffraction

The application of convergent beam electron diffraction (CBED) to determine symmetry, refine structure factors, and measure specimen thickness requires rather thick specimen and is very difficult or even impossible in the case of large unit cell materials. The large-angle rocking-beam electron diffraction (LARBED) technique introduced in this paper gives access to the kind of experimental data contained in CBED patterns but over a much larger angular range. In addition to symmetry determination and thickness measurement even for thin samples this technique also allows, in principle, very accurate measurements of structure factors. Similar to precession electron diffraction (PED), LARBED uses the illumination tilt coils to sequentially change the angle of incidence of the electron beam over a very large range. I will present results obtained by a recently developed self-calibrating acquisition software which compensates for aberration-induced probe shifts during the acquisition of LARBED patterns and keeps the probe within a few nm, while covering a tilt range from 0 to 100 mrad. This paper is dedicated to Prof. John C. H. Spence on the occasion of his 65th birthday.     

The relative precision of crystal orientations measured from electron backscattering patterns

Recently developed statistical methods for analysing orientation data are presented and applied here in a study of the precision by which crystal orientations can be measured from electron backscattering patterns. The use of these methods allows a direct comparison to be made between the precision obtained with manually and automatically localized bands, which is important owing to a more and more widespread use of fully automatic analysis of electron backscattering patterns. Curves which show how the precision depends on the pattern quality and on the number of bands used for the orientation measurements are presented for both manually and automatically localized bands. Typical values for the relative precision of crystal orientations measured from electron backscattering patterns are shown to be of the order of 0.5° for manually localized bands and 0.75° for automatically localized bands, when about 10 bands are used for the measurements. In a more realistic situation where a careful operator is willing to localize four to five bands in each pattern, the precision of the measured crystal orientations is similar to that obtained for automatically localized bands.     

Measurement of residual elastic strain and lattice rotations with high resolution electron backscatter diffraction

A set of dynamically simulated electron backscatter patterns (EBSPs) for α-Ti crystals progressively rotated by 1° steps were analysed using cross-correlation to determine image shifts from which strains and rotations were calculated. At larger rotations the cross-correlation fails in certain regions of the EBSP where large shifts are generated. These incorrect shifts prevent standard least square error procedures from obtaining a valid solution for the strain and rotation, where the applied rotation exceeds ∼8°. Using a robust iterative fitting routine reliable strains and rotations can be obtained for applied rotations of up to and including ∼11° even though some image shifts are measured incorrectly. Finally, high resolution electron backscatter diffraction has been used to analyse the residual elastic strain, lattice rotations and density of stored geometrically necessary dislocations in a sample of copper deformed to 10% total strain. The robust iterative fitting analysis allows reliable analysis of a larger proportion of the map, the difference being most obviously beneficial in regions where significant lattice rotations have been generated.     

Electron backscatter diffraction on pearlite structures in steel

Electron backscatter diffraction measurements were performed on a set of pearlitic steel samples after different heat treatments. The strengths and limitations of the technique with respect to the pearlite issue are presented. Interpretation of the obtained results confirmed that more than one pearlite colony may exist inside one ferrite nodule of nearly the same crystallographic orientation. It was also found that, in most cases, a misorientation of the order of several degrees exists between pearlite colonies within one ferrite nodule. Moreover, the ferrite matrix exhibits changes of crystallographic orientation inside colonies often accompanied by a network of low angle boundaries. The mean size of the ferrite nodule in the matrix was determined by means of electron backscatter diffraction. However, determination of the mean pearlite colony size was difficult and often impossible by means of both metallographic methods and electron backscatter diffraction measurements.     

Microstructural and microtextural characterization of oxide scale on steel using electron backscatter diffraction

High‐temperature oxidation of steel has been extensively studied. The microstructure of iron oxides is, however, not well understood because of the difficulty in imaging it using conventional methods, such as optical or electron microscopy. A knowledge of the oxide microstructure and texture is critical in understanding how the oxide film behaves during high‐temperature deformation of steels and more importantly how it can be removed following processing. Recently, electron back‐scatter diffraction (EBSD) has proved to be a powerful technique for distinguishing the different phases in scales. This technique gives valuable information both on the microstructure and on the orientation relationships between the steel and the scale layers. In the current study EBSD has been used to investigate the microstructure and microtexture of iron oxide layers grown on interstitial free steel at different times and temperatures. Heat treatments have been carried out under normal oxidation conditions in order to relate the results to real steel manufacturing in industry. The composition, morphologies, microstructure and microtexture of selected conditions have been studied using EBSD.     

Determining the orientations of ice crystals using electron backscatter patterns

Knowing the orientations of the ice crystals in a polycrystalline aggregate is essential for understanding and modeling the flow of naturally occurring ice. Here we show, for the first time, that the orientation of crystals in polycrystalline ice can be determined with a higher angular and spatial resolution and more rapidly than any currently used method by using electron backscatter patterns (EBSPs) in a cold-stage equipped scanning electron microscope. We also present an orientation image map constructed from EBSPs, and discuss possible applications of the technique for ice. The results indicate that obtaining EBSPs and orientation images from other frozen water-containing materials, such as clathrate hydrates, may also be possible.     

'Five-parameter' analysis of grain boundary networks by electron backscatter diffraction

This paper describes state‐of‐the‐art analysis of grain boundary populations by EBSD, with particular emphasis on advanced, nonstandard analysis. Data processing based both on misorientation alone and customised additions which include the boundary planes are reviewed. Although commercial EBSD packages offer comprehensive data processing options for interfaces, it is clear that there is a wealth of more in‐depth data that can be gleaned from further analysis. In particular, determination of all five degrees of freedom of the boundary population provides an exciting opportunity to study grain boundaries by EBSD in a depth that was hitherto impossible. In this presentation we show ‘five‐parameter’ data from 50 000 boundary segments in grain boundary engineered brass. This is the first time that the distribution of boundary planes has been revealed in a grain boundary engineered material.     

Multivariate statistical approach to electron backscattered diffraction

This paper assesses the potential of multivariate statistical analysis (MSA) applied to electron backscattered diffraction (EBSD) data. Instead of directly indexing EBSD patterns on an individual basis, this multivariate approach reduces a large (thousands) set of individual EBSD patterns into a core set of statistically derived component EBSD patterns which can be subsequently indexed. The following hypotheses are considered in this paper: (1) experimental EBSD patterns from a microstructure can be analytically treated as linear combinations of spatially simple components, (2) MSA has an angular resolution on par with standard EBSD, (3) MSA can discriminate between similar and dissimilar phases, and (4) the MSA approach can improve the effective spatial resolution of automated EBSD.     

3D visualization and quantification of rat cortical bone porosity using a desktop micro-CT system: a case study in the tibia

Although micro-computed tomography (micro-CT) has become the gold standard for assessing the 3D structure of trabecular bone, its extension to cortical bone microstructure has been relatively limited. Desktop micro-CT has been employed to assess cortical bone porosity of humans, whereas that of smaller animals, such as mice and rats, has thus far only been imaged using synchrotron-based micro-CT. The goal of this study was to determine if it is possible to visualize and quantify rat cortical porosity using desktop micro-CT. Tibiae (n = 10) from 30-week-old female Sprague-Dawley rats were imaged with micro-CT (3 μm nominal resolution) and sequential ground sections were then prepared. Bland-Altman plots were constructed to compare per cent porosity and mean canal diameter from micro-CT (3D) versus histology (2D). The mean difference or bias (histology-micro-CT; ±95% confidence interval) for per cent porosity was found to be -0.15% (±2.57%), which was not significantly different from zero (P= 0.720). Canal diameter had a bias (±95% confidence interval) of -5.73 μm (±4.02 μm) which was found to be significantly different from zero (P < 0.001). The results indicated that cortical porosity in rat bone can indeed be visualized by desktop micro-CT. Quantitative assessment of per cent porosity provided unbiased results, whereas direct analysis of mean canal diameter was overestimated by micro-CT. Thus, although higher resolution, such as that available from synchrotron micro-CT, may ultimately be required for precise geometric measurements, desktop micro-CT--which is far more accessible--is capable of yielding comparable measures of porosity and holds great promise for assessment of the 3D arrangement of cortical porosity in the rat.