The Determination of the Orientation of Rhombohedral and Cubic Crystals from Traces on a Single Surface

The determination of the orientation of rhombohedral and cubic crystals from the angles between traces produced on a single surface of a specimen by three crystallographically equivalent planes is considered. It is shown that the direction normal to the crystal surface may be determined directly by taking readings from simple physical models which may be readily constructed. A new algebraic formulation of the problem which leads directly to the possible orientations, is also presented. Degenerate cases which arise in this analysis are discussed and a table of results is given for the case of traces produced by {11 1 } planes in mercury crystals. A convenient method of plotting these results is described, and it is shown that the results obtained using the models are accurate to within 1½° when compared with those obtained numerically.