One-dimensional kinematic model of preferred orientation development

The one-dimensional model to analyse the kinematics of crystallographic pre ferred 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 contra sting situations are distinguished. The first is where lattice rotations of opposing sense occur and there are orientations for which the rotation rat e is zero. In this case a continually intensifying preferred orientation at an orientation with zero rotation rate will result. The second situation i s where the rotation of the lattice is in the same sense for all orientatio ns. Initially maxima develop in the orientation of greatest negative diverg ence in the lattice rotation rate function. A steady-state preferred orient ation profile is possible which is the normalised inverse of the function d escribing lattice rotation rate vs. orientation and the maxima are at the o rientations 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 mylonit e preferred orientation which consists of a c axis maximum in the mylonitic foliation perpendicular to the stretching lineation. It is argued that the crystal lattices rotate about a stably oriented c axis and the profile thr ough the orientation distribution describing the probability of finding par ticular orientations differing by a rotation about c is inverted to give an estimate of the lattice rotation rate profile. It is found that the lattic e rotates slowest when the second-order prism direction a is aligned parall el to the foliation normal and fastest when a is aligned sub-parallel to th e stretching lineation. (C) 1999 Elsevier Science B.V. All rights reserved.