61 Algorithm for Disorientation: 1 To find the disorientation*, as just an angle, associated with a grain boundary but not identifying which symmetry
{"Image DocumentName": "Algorithm for Disorientation: 1", "Image ImageDescription": "To find the disorientation , as just an angle, associated with a grain boundary but not identifying which symmetry operator was required for each crystal: Make a list of all crystal symmetry operators; Loop over switching symmetry (2 passes), which computes both \u2206gAB and \u2206gBA ; Loop over OA (24 different operators, for cubic xtal symmetry); Calculate \u2206g = gB (OAgA)-1 or (OAgA) gB-1 and extract the angle (e.g. as arc-cosine of [trace(\u2206g)-1]/2), depending on the first loop; If (misorientation) angle is lower than the previous result then retain the result (as the current candidate for the disorientation); End of loops: the misorientation that satisfied the tests is the disorientation because it possesses the minimum rotation angle. The misorientation axis can be placed in a single standard stereographic triangle by making all the indices positive that are associated with the minimum angle, and re-ordering so as to make h\u2264k\u2264l, for example.  Disorientation:= combination of minimum angle and axis located in the fundamental zone.", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}