EMcuboMK - EMsoft-org/EMsoft GitHub Wiki

Program: EMcuboMK

This utility program can be used to sample cubochoric space and determine the MacKenzie misorientation distribution for an arbitrary crystallographic symmetry. The program samples cubochoric space in concentric cubes that correspond to spheres in Rodrigues space; the ratio of the number of sampling points that fall inside the Rodrigues fundamental zone to the total number of points on the sampling cube is an estimate for the solid angle subtended by the fundamental zone at that particular misorientation value. This solid angle function is then multiplied by the standard misorientation distribution function in the absence of crystal symmetry.

The program prompts the user for the point group number and the number of sampling points to be used along the cubochoric semi-edge. This then generates an array of misorientations between 0 and pi. The output of the program is a csv file with the misorientation angle, the sampled MacKenzie distribution function, and the analytical values for the distribution, based on [A. Morawiec, J.Appl.Cryst. (1995) 28:289-293]. The user can then take the output file and produce any desired plot using Excel, Matlab or any other program that can read .csv files and display them.

The example below uses point group symmetry 27 (hexagonal) and 100 points along the semi-edge of the cubochoric cube. The .csv file starts as follows (misorientation angle in degrees):

angle, sampled, theoretical
  150,  150,  150
  0.00000000,  0.00000000,  0.00000000
  1.01656236,  0.00000350,  0.00000350
  2.03315673,  0.00001399,  0.00001399
  3.04981510,  0.00003147,  0.00003147
  4.06656952,  0.00005595,  0.00005595
  5.08345204,  0.00008741,  0.00008741
  6.10049473,  0.00012584,  0.00012584
  7.11772975,  0.00017125,  0.00017125
  8.13518926,  0.00022362,  0.00022362
  9.15290552,  0.00028295,  0.00028295
 10.17091083,  0.00034921,  0.00034921
 11.18923760,  0.00042241,  0.00042241
 12.20791830,  0.00050252,  0.00050252
 13.22698551,  0.00058953,  0.00058953
 14.24647191,  0.00068342,  0.00068342
 15.26641029,  0.00078418,  0.00078418
 16.28683359,  0.00089178,  0.00089178
 17.30777484,  0.00100621,  0.00100621
...

and the plot looks like this (solid line = theory, + symbols = determined by cubochoric sampling).