Rotations above 90 degree when calculating OR's misorientations

[Igor Jordao]

Hello, again

I was trying to calculate Kurdjumov-Sachs (KS) orientation relationship (OR) angles manually, because at my analysis I need to know which pair of planes of CCC and CFC generate each Kurdjumov sachs rotation. I noticed that MTEX calculates the misorientation corresponding to an OR using:

  function mori = KurdjumovSachs(csGamma,csAlpha)
    %
    % Syntax:
    %   mori = KurdjumovSachs(csGamma,csAlpha)
    %
    % Input
    %  csGamma - parent @crystalSymmetry (cubic fcc)
    %  csAlpha - child @crystalSymmetry (cubic bcc)
    %

    mori = orientation.map(Miller(1,1,1,csGamma),Miller(0,1,1,csAlpha),...
      Miller(-1,0,1,csGamma,'uvw'),Miller(-1,-1,1,csAlpha,'uvw'));
  end

To evaluate which pair CFC and CCC planes correspond to each Kurdjumov-Sachs OR variant, I written each variant of the OR and calculatated the rotation.map and orientation.map's. By this approach, I found the order of all the 24 variants that MTEX calculates in the already implemented orientation.KurdjumovSachs method. When I tried to calculate the rotations between the CFC and CCC planes, I noticed that using orientation.KurdjumovSachs MTEX does not consider antipodal symmetry between directions, because of this behavior sometimes using angle(interface.misorientation, KS.variants, 'noSymmetry')./degree, to evaluate the KS OR deviation of an interface for example, leads to probably wrong values. A example of this behavior is: when calculating the angle between two planes with an angle of 60° between them, we obtain 120°, that is the higher angle between the planes, as calculation result. I noticed that when we calculate manually KS OR rotations considering antipodal symmetry lesser angle values are obtained as result. The reported behavior would be an evidence that probably the approach angle(interface.misorientation, KS.variants, 'noSymmetry')./degree is leading to wrong results?

Best regards!