Number-theoretic method for practical indexing of crystal directions

I. A. Sheremetyev, S. V. Gorfman

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)223-227
Number of pages5
JournalNuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
Issue number1-2
StatePublished - 1 Sep 2001
Externally publishedYes


  • Laud method
  • Number theory
  • Stereographic method


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