Three-dimensional texture visualization approaches: Applications to nickel and titanium alloys

Patrick G. Callahan, McLean P. Echlin, Jean Charles Stinville, Tresa M. Pollock, Saransh Singh, Farangis Ram, Marc De Graef

Research output: Contribution to journalArticlepeer-review


This paper applies the three-dimensional visualization techniques explored theoretically by Callahan, Echlin, Pollock, Singh & De Graef [J. Appl. Cryst. (2017), 50, 430-440] to a series of experimentally acquired texture data sets, namely a sharp cube texture in a single-crystal Ni-based superalloy, a sharp Goss texture in single-crystal Nb, a random texture in a powder metallurgy polycrystalline René 88-DT alloy and a rolled plate texture in Ti-6Al-4V. Three-dimensional visualizations are shown (and made available as movies as supplementary material) using the Rodrigues, Euler and three-dimensional stereographic projection representations. In addition, it is shown that the true symmetry of Euler space, as derived from a mapping onto quaternion space, is described by the monoclinic color space group Pcc in the Opechowski and Guccione nomenclature. This paper applies three-dimensional visualization techniques to synthetic and experimentally acquired material textures (random, cube and Goss texture components) and illustrates how three-dimensional visualization can be used to gain insight about orientation distribution functions and orientation relations. The intrinsic symmetry of the Euler orientation representations is considered in detail and it is shown that a monoclinic magnetic space group properly describes the symmetry of Euler space.

Original languageEnglish (US)
Pages (from-to)1267-1279
Number of pages13
JournalJournal of Applied Crystallography
Issue number5
StatePublished - Oct 2017
Externally publishedYes


  • fundamental zones
  • Rodrigues vectors
  • texture representation
  • three-dimensional visualization

ASJC Scopus subject areas

  • Biochemistry, Genetics and Molecular Biology(all)


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