qB represent unit, orientation quaternions of grain A and grain B of a grain boundary in the lab reference frame, respectively. Let
qm be the misorientation quaternion of
qB. Quaternion inversion (
qinv) and quaternion multiplication (
qmult) are discussed in Quaternions and spatial rotations. Let
mA be the boundary plane normal pointing from grain A to grain B in the sample reference frame. Let
nA be the boundary plane normal pointing outwards from grain A towards grain B in the grain A crystal reference frame. All boundary planes are represented in 3D Cartesian coordinates.
qinv(qA) = [qA(1) -qA(2:4)] qinv(qB) = [qB(1) -qB(2:4)] qmult(qA,qB) ~= qmult(qB,qA) %non-commutative
I think the misorientation quaternion is obtained by one of the following two conversions:
qm = qmult(qinv(qA),qB);
qm = qmult(qB,qinv(qA));
I think the boundary plane normal is represented by:
nA = qmult(qA,qmult([0 mA],qinv(qA))); nA = nA(2:4); %drop 1st element which is 0
While the two misorientation quaternions share the same misorientation angle, they each represent rotations around different axes, and thus (as far as I understand), a different grain boundary.
What is the appropriate conversion of (
mA) triplets to (