One-Dimensional Kinematic Model of Preferred Orientation Development

The one-dimensional model to analyse the kinematics of crystallographic preferred orientation of Ribe (1989) is presented and developed further. It is argued that this approach can be applied to rotational deformations where the predominant deformation mechanism is grain boundary sliding. Two contrasting situations are distinguished. The first is where lattice rotations of opposing sense occur and there are orientations for which the rotation rate is zero. In this case a continually intensifying preferred orientation at an orientation with zero rotation rate will result. The second situation is where the rotation of the lattice is in the same sense for all orientations. Initially maxima develop in the orientation of greatest negative divergence in the lattice rotation rate function. A steady-state preferred orientation profile is possible which is the normalised inverse of the function describing lattice rotation rate vs. orientation and the maxima are at the orientations for which the lattice rotation rate is a minimum. The intensity of the preferred orientation is a function of the ratio of the greatest to least lattice rotation rates. The results are applied to a natural mylonite preferred orientation which consists of a axis maximum in the mylonitic foliation perpendicular to the stretching lineation. It is argued that the crystal lattices rotate about a stably oriented axis and the profile through the orientation distribution describing the probability of finding particular orientations differing by a rotation about is inverted to give an estimate of the lattice rotation rate profile. It is found that the lattice rotates slowest when the second-order prism direction is aligned parallel to the foliation normal and fastest when is aligned sub-parallel to the stretching lineation