Preferred Orientation in a Low-Symmetry Quartz Mylonite

Abstract

An analysis is described which allows the complete orientations of grains in a crystal aggregate to be determined from a suite of pole figures obtained with the X-ray pole-figure goniometer. The orientation of a crystallite with respect to the specimen is specified by three Euler angles and the preferred orientation of the crystallites by a frequency distribution of Euler angles, termed the "orientation distribution function" (ODF). When the ODF is plotted in a Cartesian coordinate system, it has a space group symmetry that is a function of the point group symmetry of the crystal and of the specimen. To determine the ODF, the pole figures are expanded with polyhedral harmonics and the ODF with symmetrical generalized spherical harmonics; a least-squares solution is obtained for a set of linear equations relating the coefficients of the two expansions. A recrystallized quartzite specimen with a crossed girdle pattern of optic axes from the mylonite zone of the Moine thrust (northwest Scotland) is used to illustrate the analysis. The specimen has a well-developed foliation ab and lineation b. Pole figures for nine diffraction peaks were measured with an X-ray pole-figure goniometer. Grains contributing to the strong [0001] maximum at the intersection of the two girdles subparallel to the specimen a axis (Type I maximum of Sander) have a second-order prism {112̄0} preferentially oriented parallel to foliation. The girdle pattern of [0001] can be generated by rotating about two [112̄0] axes in the bc plane ±30° from b. of special significance for petrofabric studies is the ability to specify the complete orientation of the grains and in particular to determine separately pole figures for planes with the same d-value, such as r = 101̄1 and z = 011̄1 in quartz. Differences in the distribution of positive and negative forms observed in the quartzite may originate by Dauphine twinning during slight postcrystalline deformation. But it has not been possible to prove that this mechanism is the cause of the distribution of positive and negative forms in this specimen. The technique may be used to study any monomineralic aggregate and is especially well suited for the analysis of fine-grained specimens. The ODF is needed in the computation of elastic constants, the strain energy, or the chemical potential of an aggregate with preferred orientation.