Scientific blog
June 
Thursday, 4 July, 2013, 14:29
Posted by Piotr Drzymala
Samples were examined by electron microscopy SEM, recording the success of EBSD map of the sample surface. The map was exported to a text file and loaded into the program Mathematica. Unfortunately, the map was created in a hexagonal grid (arrangement of pixels) and not orthogonal, hence the need to jog every other row of one element, but the difficulty was easily overcomed. Each pixel was colored by transforming the three Euler angles describing the orientation (φ1, Φ, φ2) in the rotation matrix, which is used to rotate the vector N = {0,0,1} crystallite in the system, which then discharges stereographic full inverse pole figure and the position of the RGB color line calculated in manner = {1-r (1-theta / (pi / 6)) * y (theta / (pi / 6)) * y}, bringing the advance angle theta to the base area. Digression: the pole figure on the reverse orientations are operating on the system, expressed in crystallite S-> C, and not in the sample circuit C-> S, as is the case with the convention rotation matrix. However, for our purposes, we use this time active matrix rotation (rotate vectors) rather than as simply passive (when the system is rotated). Therefore, if the passive rotation matrix in the system the sample is g, this passive rotation matrix in the system of the crystallites to g ^ T, and the active matrix circuit circulation of the crystallites is g = g ^ TT
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