'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.     

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.     

Novel combination of orientation measurements and transmission microscopy for experimental determination of grain boundary miller indices in silicon and other semiconductors

The determination of grain boundary planes in multicrystalline material has only been restricted to transmission electron microscope investigations (Jang et al., 1992; Elgat et al., 1985) or to metallograpical investigations of the grain boundary (Randle et al., 1993). The first method is expensive, and both are complex and time consuming in grain boundary preparation. This paper proposes the determination of grain boundary planes in semiconductor wafer by a combined application of Electron Back Scatter Diffraction and Infrared Transmission Microscopy. In particular, the new method is demonstrated with directional solidificated multicrystalline silicon.     

Preparation of metallic samples for electron backscatter diffraction and its influence on measured misorientation

Preparation of specimens for electron backscatter diffraction has to be done with great care to ensure a high indexing fraction from high-quality patterns. Despite the amount of published and recommended preparation methods for different materials, detailed information about the preparation parameters are either missing, or different preparation methods are recommended for one material. The aim of this contribution is to compare the application of several preparation techniques on different metallic samples to determine a suitable preparation method for high-quality electron backscatter diffraction measurements for a variety of alloys. From the results obtained, polishing with an oxide polishing suspension is the most appropriate preparation method for the materials and preparation methods investigated. Furthermore, the influence of mechanical polishing as well as of oxide polishing suspension polishing on misorientation is found to be negligible for misorientation angles greater than 1°. In the course of this study the absolute indexing reproducibility of the EBSD-system employed was determined to be 1.18° with respect to the misorientation angle θ.     

Five-parameter grain boundary analysis of a grain boundary–engineered austenitic stainless steel

Two different grain boundary engineering processing routes for type 304 austenitic stainless steel have been compared. The processing routes involve the application of a small level of strain (5%) through either cold rolling or uni-axial tensile straining followed by high-temperature annealing. Electron backscatter diffraction and orientation mapping have been used to measure the proportions of Σ3ⁿ boundary types (in coincidence site lattice notation) and degree of random boundary break-up, in order to gain a measure of the success of the two types of grain boundary engineering treatments. The distribution of grain boundary plane crystallography has also been measured and analyzed in detail using the five-parameter stereological method. There were significant differences between the grain boundary population profiles depending on the type of deformation applied.     

Scanning electron microscopy and transmission electron microscopy in situ studies of grain boundary migration in cold-deformed aluminium bicrystals

The crystallography of recrystallization has been investigated in channel‐die deformed pure aluminium bicrystals with {100}<011>/{110}<001> orientations. The microstructural and microtextural changes during the early stages of recrystallization were followed by systematic local orientation measurements using scanning and transmission electron microscopes. In particular, orientation mapping combined with in situ sample heating was used to investigate the formation and growth of new grains at very early stages of recrystallization. Grain boundary migration and ‘consumption’ of the as‐deformed areas was always favoured along directions parallel to the traces of the {111} slip planes that had been most active during deformation.     

High-angle triple-axis specimen holder for three-dimensional diffraction contrast imaging in transmission electron microscopy

Electron tomography requires a wide angular range of specimen-tilt for a reliable three-dimensional (3D) reconstruction. Although specimen holders are commercially available for tomography, they have several limitations, including tilting capability in only one or two axes at most, e.g. tilt-rotate. For amorphous specimens, the image contrast depends on mass and thickness only and the single-tilt holder is adequate for most tomographic image acquisitions. On the other hand, for crystalline materials where image contrast is strongly dependent on diffraction conditions, current commercially available tomography holders are inadequate, because they lack tilt capability in all three orthogonal axes needed to maintain a constant diffraction condition over the whole tilt range. We have developed a high-angle triple-axis (HATA) tomography specimen holder capable of high-angle tilting for the primary horizontal axis with tilting capability in the other (orthogonal) horizontal and vertical axes. This allows the user to trim the specimen tilt to obtain the desired diffraction condition over the whole tilt range of the tomography series. To demonstrate its capabilities, we have used this triple-axis tomography holder with a dual-axis tilt series (the specimen was rotated by 90° ex-situ between series) to obtain tomographic reconstructions of dislocation arrangements in plastically deformed austenitic steel foils.     

Electron backscatter diffraction of grain and subgrain structures — resolution considerations

Characterization of microstructures containing small grains or low-angle grain boundaries by electron backscattered diffraction (EBSD) is limited by the spatial and angular resolution limits of the technique. It was found that the best effective spatial resolution (60 nm) for aluminium alloys in a tungsten-filament scanning electron microscope (SEM) was obtained for an intermediate probe current which provided a compromise between pattern quality and specimen interaction volume. The same specimens and EBSD equipment when used with a field-emission gun SEM showed an improvement in spatial resolution by a factor of 2–3. For characterizing low-angle boundary microstructures, the precision of determining relative orientations is a limiting factor. It was found that the orientation noise was directly related to the probe current and this was interpreted in terms of the effect of probe current on the quality of the diffraction patterns.     

Study of dynamic grain growth by electron microscopy and EBSD

The effect of hot deformation on fully recrystallized aluminium–copper alloys (Al-4wt%Cu and Al-33wt%Cu) with different volume fractions of CuAl₂ has been studied. The alloys are Zener pinned systems with different superplastic properties. Strain-induced grain growth, observed in both alloys, was quantitatively estimated by means of electron microscopy and EBSD and compared with the rate of static grain growth. Surface marker observations and in situ hot-deformation experiments combined with EBSD were aimed at clarifying the mechanisms responsible for the changes in the deformed microstructures. A sequence of secondary and backscattered electron images and EBSD maps was obtained during in situ SEM deformation with different testing conditions. Overlaying EBSD maps for the Al-4wt%Cu with channelling contrast images showed that grain boundary motion occurred during deformation, creating a layered structure and leading to an increase in size of some grains and shrinkage of others. Of a particular interest are results related to behaviour of CuAl₂ in superplastic Al-33wt%Cu during deformation, including several problems with the use of EBSD in this alloy.     

The effect of three-fold astigmatism on measurements of grain boundary volume expansion by high-resolution transmission electron microscopy

In the absence of high-order aberrations, the lattice fringe technique should allow measurement of grain boundary rigid-body displacements to accuracies about an order of magnitude better than the point-to-point resolution of the transmission electron microscope. The three-fold astigmatism, however, introduces shifts of the lattice fringe pattern that depend on the orientation of the lattice relative to the direction of the three-fold astigmatism and thus produces an apparent shift between the two grains bordering the grain boundary. By image simulation of grain boundary model structures, the present paper explores the effect of these extraneous shifts on grain boundary volume expansion measurements. It is found that the shifts depend, among others, on zone axis direction and the magnitude of the lattice parameter. For many grain boundaries of interest, three-fold astigmatism correction to better than 100 nm appears necessary to achieve the desired accuracies.     

In situ transmission electron microscopy studies and real-time digital imaging

A newly designed CCD camera has been utilized for real-time and static image acquisitions. The performance of the camera is demonstrated for heating/cooling in-situ TEM experiments performed on a commercial high strength aluminium alloy using a double tilt heating holder. The real-time digital imaging capability of the new camera should facilitate the in-situ TEM that is now re-establishing itself as a strategic tool for materials characterization.     

Distinguishing crystallographic misorientations of lanthanum zirconate epilayers on nickel substrates by electron backscatter diffraction

Electron backscatter diffraction (EBSD) was used for distinguishing crystallographic orientations and local lattice misfits of a La₂Zr₂O₇ (LZO) buffer layer epitaxially grown on a cube textured Ni-5.%W (Ni-W) substrate for a YBCO superconductor film. Orientation data were obtained from the LZO epilayer using low energy primary electrons (5 keV) and from the Ni-W substrate by increasing the voltage to 15 keV. In-plane and out-of-plane orientations of the LZO epilayer were revealed with respect to its Ni-W substrate. A strong {1 0 0} 〈0 1 1〉 rotated-cube texture in the LZO epilayer was formed on the {1 0 0} 〈0 0 1〉 cube-textured Ni-W substrates. LZO and Ni in-plane crystallographic axes are related by an expected 45° rotation. The step-misorientations and the local misfit strains between the LZO epilayer and the substrate were also analyzed.     

Imaging of high-angle annular dark-field scanning transmission electron microscopy and observations of GaN-based violet laser diodes

The first part of this paper is devoted to physics, to explain high‐angle annular dark‐field scanning transmission electron microscopy (HAADF‐STEM) imaging and to interpret why HAADF‐STEM imaging is incoherent, instructing a strict definition of interference and coherence of electron waves. Next, we present our recent investigations of InGaN/GaN multiple quantum wells and AlGaN/GaN strained‐layer superlattice claddings in GaN‐based violet laser diodes, which have been performed by HAADF‐STEM and high‐resolution field‐emission gun scanning electron microscopy.     

Local crystal structure analysis with several picometer precision using scanning transmission electron microscopy

We report a local crystal structure analysis with a high precision of several picometers on the basis of scanning transmission electron microscopy (STEM). Advanced annular dark-field (ADF) imaging has been demonstrated using software-based experimental and data-processing techniques, such as the improvement of signal-to-noise ratio, the reduction of image distortion, the quantification of experimental parameters (e.g., thickness and defocus) and the resolution enhancement by maximum-entropy deconvolution. The accuracy in the atom position measurement depends on the validity of the incoherent imaging approximation, in which an ADF image is described as the convolution between the incident probe profile and scattering objects. Although the qualitative interpretation of ADF image contrast is possible for a wide range of specimen thicknesses, the direct observation of a crystal structure with deep-sub-angstrom accuracy requires a thin specimen (e.g., 10 nm), as well as observation of the structure image by conventional high-resolution transmission electron microscopy.     

The weighted Burgers vector: a new quantity for constraining dislocation densities and types using electron backscatter diffraction on 2D sections through crystalline materials

The Weighted Burgers Vector (WBV) is defined here as the sum, over all types of dislocations, of [(density of intersections of dislocation lines with a map) × (Burgers vector)]. Here we show that it can be calculated, for any crystal system, solely from orientation gradients in a map view, unlike the full dislocation density tensor, which requires gradients in the third dimension. No assumption is made about gradients in the third dimension and they may be non-zero. The only assumption involved is that elastic strains are small so the lattice distortion is entirely due to dislocations. Orientation gradients can be estimated from gridded orientation measurements obtained by EBSD mapping, so the WBV can be calculated as a vector field on an EBSD map. The magnitude of the WBV gives a lower bound on the magnitude of the dislocation density tensor when that magnitude is defined in a coordinate invariant way. The direction of the WBV can constrain the types of Burgers vectors of geometrically necessary dislocations present in the microstructure, most clearly when it is broken down in terms of lattice vectors. The WBV has three advantages over other measures of local lattice distortion: it is a vector and hence carries more information than a scalar quantity, it has an explicit mathematical link to the individual Burgers vectors of dislocations and, since it is derived via tensor calculus, it is not dependent on the map coordinate system. If a sub-grain wall is included in the WBV calculation, the magnitude of the WBV becomes dependent on the step size but its direction still carries information on the Burgers vectors in the wall. The net Burgers vector content of dislocations intersecting an area of a map can be simply calculated by an integration round the edge of that area, a method which is fast and complements point-by-point WBV calculations.     

Reliability of atom column positions in a ternary system determined by quantitative high-resolution transmission electron microscopy

Employing an iterative structure refinement procedure, we have determined the atomistic structure of the Σ3 (111) grain boundary in strontium titanate (SrTiO₃) from high-resolution transmission electron microscopy (HRTEM) images. This grain boundary serves as a model system to study the effect of column occupancies on the reliability of the column positions. In this paper we introduce a method to derive confidence regions for the positions of individual atom columns at crystal defects. Based on a statistical approach we first determine the reliabilities of different types of atom columns in regions of unfaulted crystal. Next we extrapolate these reliabilities to obtain the reliabilities of individual atom columns at the grain boundary. The method accounts correctly for random errors and promises to be generally applicable provided that repetitive units of unfaulted crystal structure are contained in the HRTEM image. Under the conditions of the present study, the reliability of a column position correlates with the projected electrostatic potential of the column. Accordingly, the reliabilities of the column positions at the boundary vary with the column type: 0.008 nm for Sr–O columns, 0.014 nm for Ti columns, and 0.018 nm for O–O columns.     

Scanning electron microscopy and transmission electron microscopy study of hot-deformed γ-TiAl-based alloy microstructure

The aim of this work was to assess the changes in the microstructure of hot‐deformed specimens made of alloys containing 46–50 at.% Al, 2 at.% Cr and 2 at.% Nb (and alloying additions such as carbon and boron) with the aid of scanning electron microscopy and transmission electron microscopy techniques. After homogenization and heat treatment performed in order to make diverse lamellae thickness, the specimens were compressed at 1000 °C. Transmission electron microscopy examinations of specimens after the compression test revealed the presence of heavily deformed areas with a high density of dislocation. Deformation twins were also observed. Dynamically recrystallized grains were revealed. For alloys no. 2 and no. 3, the recovery and recrystallization processes were more extensive than for alloy no. 1.     

A comparison of grain imaging and measurement using horizontal orientation and colour orientation contrast imaging, electron backscatter pattern and optical methods

The problems associated with the definition of a grain, grain size measurement, and the issues associated with making one- and two-dimensional measurements on a three-dimensional structure are discussed. The relatively new scanning electron microscope (SEM)-based techniques of colour orientation contrast imaging (COCI) and automated electron backscatter pattern (EBSP) are explained and examples given. Comparisons with conventional (horizontal) orientation contrast imaging (HOCI) in the SEM are made. A direct comparison is made between conventional metallographic methods and these new techniques on precisely the same region of an interstitial free iron specimen. Both optical imaging and HOCI were found to miss a large number of grain boundaries (7 and 12%, respectively), and to create boundaries (≈ 2%). COCI was found to be reliable, with only 3% of boundaries missed. EBSP was taken to be the standard against which the others were compared, as it unambiguously measured changes in crystallographic orientation. Errors in the number of grain boundaries that are detected have a considerable effect on grain size measurements, e.g. mean linear intercept, and a follow-on effect on the modelling of mechanical properties. New methods for increasing the acquisition speed of orientation maps are discussed, along with examples. The combination of COCI (for grain location) and EBSP (for orientation measurement) is promising, but requires improvements in either imaging or image analysis to be totally reliable.     

Combined application of electron backscatter diffraction and stereo-photogrammetry in fractography studies

The main aim of this paper is to report on recent experimental developments that have succeeded in combining electron back-scatter diffraction (EBSD) with stereo-photogrammetry, compared with two other methods for study of fracture surfaces, namely visual fractography analysis in the scanning electron microscope (SEM) and EBSD directly from facets. These approaches will be illustrated with data relating to the cleavage plane orientation analysis in a ferritic and C-Mn steel. It is demonstrated that the combined use of EBSD and stereo-photogrammetry represents a significant advance in the methodology for facet crystallography analysis. The results of point counting from fractograph characterization determined that the proportions of intergranular fracture in C-Mn and ferritic steels were 10.4% and 9.4%, respectively. The crystallographic orientation was determined directly from the fracture surface of a ferritic steel sample and produced an orientation distribution with a clear trend towards the {001} plane. A stereo-photogrammetry technique was validated using the known geometry of a Vickers hardness indent. The technique was then successfully employed to measure the macroscopic orientation of individual cleavage facets in the same reference frame as the EBSD measurements. Correlating the results of these measurements indicated that the actual crystallographic orientation of every cleavage facet identified in the steel specimens is {001}.