The Systematic Determination of Crystallographic Orientations from Three Octahedral Traces on a Plane Surface

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Abstract
The problem of determining the orientation of a crystal from the directions of three nonparallel traces formed by the intersection of three octahedral planes with the surface of a suitably prepared specimen has been solved completely for the first time. A full analytical treatment is presented, and it is shown that there are either four or eight orientations. For practical purposes three procedures to calculate the orientation are suggested: a graphical method, an analytical method and an electronic computer method. These are described in sufficient detail to permit direct application to specific cases.The salient feature of our analytical approach is the introduction of the locus of a certain point C. This locus has a number of double points, whose positions depend on the primary variables. The exact locations of these double points have been determined and can be used to make a rapid plot of the locus.