Automated Lattice Orientation Determination From ElectronBackscatter Kikuchi Diffraction Patterns

The ability to measure individual orientations from crystallites enables a more 
complete characterization of the microstructure. A primary obstacle to the use of 
single orientation measurements is the large investment of direct operator time 
necessary to obtain a statistically reliable data set. The most viable technique for 
obtaining individual orientation measurements is electron backscatter Kikuchi 
diffraction (BKD). Current technology requires an operator to identify a zone axis 
pair in a BKD pattern. This paper describes research in progress to automate the 
identification of lattice orientation from BKD patterns by identifying the planes 
associated with the bands that appear in the patterns. This work considered FCC crystal 
symmetry.


ORIENTATION IDENTIFICATION
Lattice orientation can be fully determined given the direction of two non-colinear lattice vectors. The information required is knowledge of the family of planes associated with two distinct bands and their interplanar angle. The proposed method for obtaining this information is to detect three bands in a BKD pattern and to identify the family of planes associated with each of the bands from the angles they make with one another. Once this information is available the following procedure can be used to calculate the lattice orientation. See figure 1 for a definition of the parameters used in the procedure.
(1) Calculate unit plane normal vectors, and n, in the specimen frame ei OPxOQ ORxOS lop x odl x osl (2) Determine the interplanar angle between these two planes: hh" + kk" + ll" h 2 + k 2 +124h "2 + k "2 +l "2 SCREEN SPECIMEN Figure 1. Schematic of the configuration of the BKD system. (5) Construct a new orthonormal frame, defined relative to the sample frame: Relative to the crystal frame ei the new frame is defined by: ,_ (hkl) ,,,= (hkl)x (h'k'l') ,,,^, e [(hkl)l' e2 I(hkl)x (h'k"l')l' e3 =e x e2 (6) Determine two sets of direction cosines according to: =el ej =el ej (7) The direction cosines which specify lattice orientation are defined by: The challenging part of this procedure is to detect three bands and to associate each of them with the correct family of planes.

IMAGE ENHANCEMENT
Several techniques have been explored for improving the quality of the images. These techniques seek to increase the contrast between the bands and the background and to reduce the noise. Both subtraction and division of a background pattern from a BKD pattern have been found to dramatically improve the visibility of bands in experimental patterns. A background image can be created by capturing a diffraction image generated from an uncolumnated electron beam. This is essentially equivalent to the average BKD pattern produced from many grains.

EDGE DETECTION
The primary difficulty in "teaching" the computer to recognize the bands is that of detecting the edges of the bands. The Burns 3 edge detection scheme has been found to KIKUCHI DIFFRACTION PATTERNS 275 lead to good results. As in most edge detections schemes, the Bums algorithm first estimates the gradient of the image by discrete convolution. Pixels with local gradient magnitudes greater than some threshold value are then grouped into regions according to the orientation of their local gradient vectors. This is done by dividing the 360 range of gradient directions into a set of regular intervals. In order to avoid artificial segmentation at the interval boundaries a second overlapping segmentation is created. Each pixel is given two labels, one for each segmentation, according to the intervals into which its gradient vector falls. Adjacent pixels are grouped into regions with the same orientation labels. Every pixel "votes" for one of the two regions to which it belongs according to the number of pixels contained within the regions. Each region is then given a "support" value according to the number of its pixels that voted for it.
Regions having support greater than 50% are selected. A line is constructed for each of these regions using a least squares fit of the (x,y) coordinates associated with each pixel in the region. Results from this procedure are shown in figure 2.

LINE DETECTION
Once the edges have been detected, they need to be linked into lines. A useful tool for performing this linking is the Hough transform. The edges can be parametedzed by p and 0 as shown in figure 3. Each edge detected will fall in a particular bucket of dimension A0xAp in p-0 space. Buckets containing many edges will correspond to lines. This technique is especially suited to this problem since the lines in the BKD patterns extend across the entire image. The Hough transform of the edges in figure 2 is shown in figure 4 along with the edges corresponding to a peak value in p-0 space. Onc thre lines hav been fixed by th lin detection algorithm th angles between these lines can b found (accounting for the projection). Th thre angles, 0i, can used as a criterion for a search for possibl band triplets. For each 0i a search is mad through the tabl of interplanar angles and a band pair is considered if it falls within +A0 of the experimental angles. Onc all possibl band pairs hav been collected for each of th experimental angles, a check is mad to se which sets of band pairs are physically possible. The results of this procedure for several A0 is shown figur 5. A0 is directly related to the precision to which the system can 1 calibrated. "THICK-THIN" BANDWIDTH ANALYSIS AS demonstrated in the previous section an ambiguity often remains in the choice of a correct band triplet. However, it is clear that some bands in the BKD patterns are thicker than others. If the change in bandwidth as a function of location and orientation in the patterns due to the projection is neglected, the bandwidth is simply inversely proportional to the interplanar spacing. Theoretical results for the four plane families discussed previously are summarized in the following table. Also shown in the table isa label distinguishing "thick" bands from "thin" bands. If the bandwidths are used to categorize the plane families into two groups, the ambiguity in the solution set associated with a band triplet is decreased as shown in figure 5.   figure 6 from the aforementioned 50 BKD patterns are summarized in table 2. The results indicate the feasibility of the proposed "thick/thin" analysis.  Figure 6. Sample band profiles and proposed bandwidth measurement.

CONCLUSIONS
The results of this and other research indicate that automated identification of lattice orientation from BKD patterns is feasible. However, several problems must be solved.. A method of calibrating the system to reduce A0 to less than 3 is required. Jensen and Schmidt 4 used a sample holder that enables a calibration sample to be placed next to and in the same plane as the sample of interest. Their results indicate that a A0 of 1 can be obtained using this configuration.
The Burns algorithm used was a commercial one designed for generic use. A customized version running on an Apple Mac Ilci takes 16.3 s. Implemented on a 25 MIP workstation it takes about 1.1 s. Recent advances in technology for obtaining BKD patterns suggest that higher quality patterns are obtainable (e.g., using fiber optics). This can only serve to heighten the capabilities of the edge extraction.
Despite the difficulties mentioned, we are confident that automated BKD pattern analysis will be a viable tool for the characterization of microstructure in polycrystalline materials.