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Keywords:

  • orthogonal groups;
  • SO(3);
  • orientation space;
  • coincidence lattices;
  • crystallographic texture

Orientations deviating from an ideal orientation by angles not exceeding a given limit constitute a ball in the metric space of orientations. Such balls arise in crystallographic computations, and in some cases intersections of the balls are of interest. This paper provides an analytical formula for calculation of the volume of the intersection of two balls from their radii and the distance between their centers. The formula is used to determine the volumes of the intersections of balls corresponding to misorientations of coincident lattices.