Techniques for Electron Backscatter Diffraction (EBSD) Indexing

Conventionally, all automated EBSD indexing approaches have relied on image analysis algorithms that can detect linear features in a relatively noisy image (such as the Kikuchi bands in an EBSD pattern). Since the early work of Krieger Lassen (e.g. Krieger Lassen et al. (1992), “Image processing procedures for analysis of electron back scattering patterns”. Scanning Microsc. 6, 115-121), the Hough transform has been the favoured approach, and this is explained in more detail here.

The Hough transform generates a list of detected band positions, but from this point there are several commonly used approaches to determine the best fit solution to the EBSD pattern. In all cases a theoretical list of the reflectors and their expected intensities needs to be created: this is usually done using kinematical structure factor calculations. The kinematical approach correctly reproduces the geometry of the EBSD patterns, even though it does not enable the creation of realistic pattern simulations. However, for regular Hough-based indexing this is sufficient, and the structure factor calculations (explained in the “Band Intensity” section on the EBSD Pattern Formation page here), are simply used to rank the expected reflectors in terms of their predicted intensities.

From the list of reflectors (with the highest intensities), the software will create a look up table of the angles between the reflector-plane normals, and this is what is then compared to the measured orientations of the Kikuchi bands that have been generated using the Hough transform.

Once the band detection and generation of the reflector look-up table have been created, there are several commonly used approaches to indexing, which are described below.

Full band set indexing

This approach looks at all the detected Kikuchi bands and compares their interplanar angles with the reflector look-up table. If a coherent match between the two lists of angles is found (within a pre-determined error margin), then that solution has been defined to a reflector group level (i.e. each detected Kikuchi band has been assigned to a particular group of reflectors, such as {111} or {200}). The software will then need to formulate the crystal orientation with respect to the EBSD detector, and store that orientation in a relevant format (such as an orientation matrix or Euler angles).

In general this approach requires fewer detected bands, working well with only 5-8 bands, hence giving good results from structures that give relatively poor patterns. The biggest drawback of the approach is when Kikuchi bands are poorly detected or when the measured EBSD pattern is actually a superposition of 2 overlapping patterns, such as is common at grain and phase boundaries.

This is shown in the below example: a typical high-speed EBSP has been collected at a phase boundary between a ferrite (Body Centred Cubic – BCC – Fe) grain and an austenite (Face Centred Cubic – FCC – Fe) grain. The EBSP contains Kikuchi bands from both of the grains on either side of the boundary, with approximately equal contributions. The full band set indexing approach would almost always detect bands from both structures, most likely resulting in no matching solution.

Illustration of the contribution of 2 orientations / phases to a single EBSP. The upper row shows the bands and solution associated with the Fe-BCC grain, the lower row shows the bands and solution associated with the Fe-FCC grain.

The robustness of indexing for EBSPs with overlapping contributions from 2 orientations or phases can be improved by iteratively removing 1 or 2 of the detected bands from the calculations. This improves the likelihood of finding a single solution that fully matches one of the 2 contributing orientations, but would still be unlikely to give a solution in cases where the 2 orientations contribute equally to the final pattern, as shown in the image.

For this reason most commercial EBSD systems break the detected band set down into subsets of 3 or 4 bands, as described below.

Triplet/Quadruplet indexing

Instead of evaluating all of the detected bands from an EBSD pattern as a coherent unit, an alternative approach is to break the list of bands into sets of 3 or 4 (i.e. “triplets” or “quadruplets”). Each of these band subsets can then be used to index the Kikuchi bands down to the reflector group, and then a voting scheme is then used to determine the most likely final solution.

The advantages of this approach over the full band set indexing method described above are numerous:

• More Kikuchi bands can be used in the indexing process, improving the final reliability and precision of the solution
• The indexing is less affected by poorly-detected Kikuchi bands, enabling robust indexing even if the pattern quality is poor
• Reliable indexing is still possible when 2 or more orientations contribute to a single EBSD pattern, improving indexing at grain and phase boundaries

The main difference between the use of 3 or 4 band groups during the indexing process is the number of combinations of bands that can be utilised for any one EBSD pattern. This is simply a matter of maths, and the table below shows that, if 8 or more Kikuchi bands are detected in the EBSP, then there will be more quadruplets than triplets and hence indexing is likely to be more robust. For EBSD patterns with fewer detectable Kikuchi bands, then triplet indexing is more likely to produce a solution. A more detailed description of the quadruplet approach used in the Oxford Instruments AZtec software (“class indexing”) is provided here.

Comparison between the number of groups of 3 or 4 bands (triplets and quadruplets) that can be extracted from a set of n detected bands