37 lines
6.6 KiB
Markdown
37 lines
6.6 KiB
Markdown
---
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title: "Electron backscatter diffraction"
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chunk: 3/7
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source: "https://en.wikipedia.org/wiki/Electron_backscatter_diffraction"
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category: "reference"
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tags: "science, encyclopedia"
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date_saved: "2026-05-05T10:04:21.164305+00:00"
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instance: "kb-cron"
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---
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If the setup geometry is well described, it is possible to relate the bands present in the diffraction pattern to the underlying crystal and crystallographic orientation of the material within the electron interaction volume. Each band can be indexed individually by the Miller indices of the diffracting plane which formed it. In most materials, only three bands/planes intersect and are required to describe a unique solution to the crystal orientation (based on their interplanar angles). Most commercial systems use look-up tables with international crystal databases to index. This crystal orientation relates the orientation of each sampled point to a reference crystal orientation.
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Indexing is often the first step in the EBSD process after pattern collection. This allows for the identification of the crystal orientation at the single volume of the sample from where the pattern was collected. With EBSD software, pattern bands are typically detected via a mathematical routine using a modified Hough transform, in which every pixel in Hough space denotes a unique line/band in the EBSP. The Hough transform enables band detection, which is difficult to locate by computer in the original EBSP. Once the band locations have been detected, it is possible to relate these locations to the underlying crystal orientation, as angles between bands represent angles between lattice planes. Thus, an orientation solution can be determined when the position/angles between three bands are known. In highly symmetric materials, more than three bands are typically used to obtain and verify the orientation measurement.
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The diffraction pattern is pre-processed to remove noise, correct for detector distortions, and normalise the intensity. Then, the pre-processed diffraction pattern is compared to a library of reference patterns for the material being studied. The reference patterns are generated based on the material's known crystal structure and the crystal lattice's orientation. The orientation of the crystal lattice that would generate the best match to the measured pattern is determined using a variety of algorithms. There are three leading methods of indexing that are performed by most commercial EBSD software: triplet voting; minimising the 'fit' between the experimental pattern and a computationally determined orientation, and or/and neighbour pattern averaging and re-indexing, NPAR). Indexing then give a unique solution to the single crystal orientation that is related to the other crystal orientations within the field-of-view.
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Triplet voting involves identifying multiple 'triplets' associated with different solutions to the crystal orientation; each crystal orientation determined from each triplet receives one vote. Should four bands identify the same crystal orientation, then four (four choose three, i.e.
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C
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(
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4
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,
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3
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)
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{\displaystyle C(4,3)}
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) votes will be cast for that particular solution. Thus the candidate orientation with the highest number of votes will be the most likely solution to the underlying crystal orientation present. The number of votes for the solution chosen compared to the total number of votes describes the confidence in the underlying solution. Care must be taken in interpreting this 'confidence index' as some pseudo-symmetric orientations may result in low confidence for one candidate solution vs another. Minimising the fit involves starting with all possible orientations for a triplet. More bands are included, which reduces the number of candidate orientations. As the number of bands increases, the number of possible orientations converges ultimately to one solution. The 'fit' between the measured orientation and the captured pattern can be determined.
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Overall, indexing diffraction patterns in EBSD involves a complex set of algorithms and calculations, but is essential for determining the crystallographic structure and orientation of materials at a high spatial resolution. The indexing process is continually evolving, with new algorithms and techniques being developed to improve the accuracy and speed of the process. Afterwards, a confidence index is calculated to determine the quality of the indexing result. The confidence index is based on the match quality between the measured and reference patterns. In addition, it considers factors such as noise level, detector resolution, and sample quality.
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While this geometric description related to the kinematic solution using the Bragg condition is very powerful and useful for orientation and texture analysis, it only describes the geometry of the crystalline lattice. It ignores many physical processes involved within the diffracting material. To adequately describe finer features within the electron beam scattering pattern (EBSP), one must use a many-beam dynamical model (e.g. the variation in band intensities in an experimental pattern does not fit the kinematic solution related to the structure factor).
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=== Pattern centre ===
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To relate the orientation of a crystal, much like in X-ray diffraction (XRD), the geometry of the system must be known. In particular, the pattern centre describes the distance of the interaction volume to the detector and the location of the nearest point between the phosphor and the sample, on the phosphor screen. Early work used a single crystal of known orientation being inserted into the SEM chamber, and a particular feature of the EBSP was known to correspond to the pattern centre. Later developments involved exploiting various geometric relationships between the generation of an EBSP and the chamber geometry (shadow casting and phosphor movement).
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Unfortunately, each of these methods is cumbersome and can be prone to some systematic errors for a general operator. Typically they cannot be easily used in modern SEMs with multiple designated uses. Thus, most commercial EBSD systems use the indexing algorithm combined with an iterative movement of crystal orientation and suggested pattern centre location. Minimising the fit between bands located within experimental patterns and those in look-up tables tends to converge on the pattern centre location to an accuracy of ~0.5–1% of the pattern width.
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The recent development of AstroEBSD and PCGlobal, open-source MATLAB codes, increased the precision of determining the pattern centre (PC) and – consequently – elastic strains by using a pattern matching approach which simulates the pattern using EMSoft.
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=== EBSD mapping === |