Number-theoretic method for practical indexing of crystal directions

The paper presents new number-theoretic approaches to the solution of orientation problems in single crystal studies. A fast method for indexing any rational crystal lattice direction was developed to be a new 3D generalization of the Euclid algorithm. Based on the latter, a method for indexing directions in any crystal lattice was developed, where the practical problem is reduced to the search of the shortest primitive lattice vector within a certain angular error for the direction in analysis. A multipurpose personal computer system for testing both real and reciprocal lattices of familiar crystals is devised. The compact-in-memory software represents a principally new “bottomless” atlas of any crystal stereographic projections, where each point of the projection field is indexed within a desired accuracy.