A New Method to Determine the Optical Orientation of Biaxial Minerals: a Mathematical Approach

A mathematical approach has been developed to determine the optical orientation of biaxial minerals by combining spindle stage and X-ray-diffractometer measurements. First, a goniometer head, with crystal affixed, is screwed onto a spindle stage, and its orientation matrix for the biaxial indicatrix is determined. Next, the same goniometer head is transferred to a single-crystal Xray diffractometer, where the unit cell and, in turn, an orientation matrix for the reciprocal crystallographic axes are determined. The necessary transformations and calculations are then developed to relate these two orientation matrices mathematically. Examples for two orthorhombic minerals of known optical orientation, one monoclinic mineral of unknown optical orientation, and one triclinic mineral of known optical orientation are given. Several measurements were repeated to test the accuracy, reproducibility, and systematic errors of the method; these measurements yielded an accuracy and reproducibility of the method to within 1.0°. Once a suitable crystal has been selected and mounted on a goniometer head, all the required measurements and calculations can be performed in approximately one hour.