Technical Note - EBSD Confidence Index Introduction In Electron Backscatter Diffraction (EBSD), indexing is the fundamental process of deriving a material’s crystallographic orientation from the diffraction pattern. The orientation, in turn, becomes the foundation for almost everything else that follows in an EBSD analysis. Figure 1 shows an example of what indexing is all about. The pattern shown has been collected, the bands detected via the Hough transform, and the crystallographic orientation determined using the Triplet Indexing method. The final orientation is displayed as a unit cell, with a (111) plane highlighted. EDAX’s patented Confidence Index (CI) is calculated as an integral part of the indexing process and does exactly what its name suggests. It tells you when you can, or can’t, reliably trust the indexing solution, providing a statistical means to measure the quality of the data. The CI is used extensively throughout TEAM™and OIM™, allowing the analyst to easily identify and, if necessary, further process ambiguous data in a scan data set. The CI is a powerful tool. The Foundation: Triplet-voting Indexing EDAX’s indexing routine takes advantage of our being able to derive a unique orientation solution from just three Kikuchi bands. As one typically uses more than three bands, OIM™ successively analyzes all possible combinations of band triplets, with the possible combinations shown in Table 1. Each time a possible orientation is found for a band triplet, the solution receives a vote. The orientation with the most votes at the end of the process is chosen as the solution. For a more detailed discussion, see the Triplet Indexing technical note. The Confidence Index The CI is the difference in votes received by the highest and second highest ranking solutions (V1and V2 respectively) divided by the number of total possible votes (VIDEAL). CI = (V1 – V2)/ VIDEAL Figure 1. Indexing determines a crystal’s orientation from information in the EBSD pattern. The CI ranges in value from 0 (good) to 1 (perfect). Low CI data can be found in areas with very poor pattern quality, such as scratches. However, a CI = 0 doesn’t always mean a solution is bad or incorrect. Consider a pattern from a grain boundary region, containing superimposed patterns from the two neighboring grains. If, for example, six bands were selected and each grain happened to contribute three, then it is likely that the respective orientations for each grain will be equally represented in the solutions. If this is the case, the confidence index would be (10 – 10)/20 = 0. Either of the two solutions could be “correct”, but we cannot confidently say which one. Conversely, the CI does not have to be 1 in order to consider the indexing to be correct. Number Bands Possible Triplet Combinations 3 1 4 4 5 10 6 20 7 35 8 56 9 84 10 120 Table 1. Possible triplet combinations for number of bands used. Technical Note - EBSD Figure 2 shows the results from an experiment done on aluminum. It was found that for a CI of 0.1, 95% of the indexing solutions were correct. By the time the CI is 0.2, indexing is virtually 100% accurate. A Simple Example In this simplified case, the orientation for an austenitic steel pattern was automatically determined, using just four bands. (In a normal scan, it is common to use seven or more bands, depending on the material.) From Table 1, we know that four bands have four possible triplet combinations. Figure 3 shows the pattern with the four bands to be used in the indexing process (a), together with the results. One orientation proved to be a viable solution for every triplet and received four votes. This orientation is shown in (b), as well as in Figure 1. Three other possible orientations, (c) to (e), were found, though only once each. The CI is easily calculated according to the previous equation: (4-1)/4 = 0.75. Looking at the three “runner up ” orientations, it is easy to see how they found their way into the process. Figure 2. Confidence Index and indexing performance. Real Life The CI provides a valuable tool for processing data. Figure 4 (a) shows an OIM™ image quality (IQ) map of damascene copper lines in silicon. The dark areas are amorphous silicon and, although data was collected in them, they have no real orientation data. Figure 4(b) shows a histogram chart of the CI distribution for the data set. Roughly 50% of the data have a CI<0.1. Points with CI<0.05 were selected in the chart and automatically updated the image, 4(c). Clearly, we do not want these data in our analysis, a point driven home by the inverse pole figure map in 4(d). The solution, simply excludes all data below a certain CI level. In this case, 0.1 was used, resulting in the map seen in 4(e). a b Figure 3. Confidence Index (circled) and indexing results: (a) pattern and bands to be indexed; (b)-(e) solutions 1 to 4 respectively, with bands colored according to families of indices (111, 200, etc.) Conclusion Obtaining the correct indexing solution is clearly important, but how does one know if the solution is correct? EDAX’s Confidence Index provides a numerical measure of indexing quality and makes it easy to find, highlight and, if necessary, remove suspect points from a data set as quickly as possible. c d e Figure 4 - Confidence Index and data analysis. (a) image quality (IQ) map; (b) confidence index distribution; (c) IQ with CI <0.05 highlighted; (d)-(e) inverse pole figure maps with and without low CI data. © EDAX Inc., 2013 November
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