Mathematical Geosciences

, Volume 42, Issue 4, pp 359–375

Orientation Distribution Within a Single Hematite Crystal


DOI: 10.1007/s11004-010-9271-z

Cite this article as:
Hielscher, R., Schaeben, H. & Siemes, H. Math Geosci (2010) 42: 359. doi:10.1007/s11004-010-9271-z


While crystallography conventionally presumes that a single crystal carries a unique crystallographic orientation, modern experimental techniques reveal that a single crystal may exhibit an orientation distribution. However, this distribution is largely concentrated; it is extremely concentrated when compared with orientation distributions of polycrystalline specimen. A case study of a deformation experiment with a single hematite crystal is presented, where the experimental deformation induced twining, which in turn changed a largely concentrated unimodal “parent” orientation distribution into a multimodal orientation distribution with a major mode resembling the parent mode and three minor modes corresponding to the progressive twining. The free and open source software MTEX for texture analysis was used to compute and visualize orientations density functions from both integral orientation measurements, i.e. neutron diffraction pole intensity data, and individual orientation measurements, i.e. electron back scatter diffraction data. Thus it is exemplified that MTEX is capable of analysing orientation data from largely concentrated orientation distributions.


Texture analysisIndividual orientation measurementsElectron back scatter diffraction (EBSD)Orientation density functionKernel density estimation on SO(3)

Copyright information

© International Association for Mathematical Geosciences 2010

Authors and Affiliations

  • Ralf Hielscher
    • 1
  • Helmut Schaeben
    • 2
  • Heinrich Siemes
    • 3
  1. 1.Applied Functional AnalysisTUChemnitzGermany
  2. 2.Geoscience Mathematics and InformaticsTU BergakademieFreibergGermany
  3. 3.RWTHAachenGermany