Orientation Distribution Within a Single Hematite Crystal
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Orientation Distribution Within a Single Hematite Crystal Ralf Hielscher · Helmut Schaeben · Heinrich Siemes
Received: 6 February 2009 / Accepted: 14 February 2010 / Published online: 14 April 2010 © International Association for Mathematical Geosciences 2010
Abstract 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. Keywords Texture analysis · Individual orientation measurements · Electron back scatter diffraction (EBSD) · Orientation density function · Kernel density estimation on SO(3)
R. Hielscher Applied Functional Analysis, TU, 09126 Chemnitz, Germany H. Schaeben () Geoscience Mathematics and Informatics, TU Bergakademie, 09596 Freiberg, Germany e-mail: [email protected] H. Siemes RWTH, 52056 Aachen, Germany
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Math Geosci (2010) 42: 359–375
1 Introduction 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. Here a single hematite crystal is experimentally deformed by 3.4% in compression perpendicular to c(0001) at 600◦ Celsius, a strain rate of 10−5 /s, and 300 MPa confining pressure. Then its texture is measured by neutron diffraction and by electron back scatter diffraction (Siemes et al. 2008). To analyse and visualize these measurements we use the free and open source Matlab® software toolbox MTEX for texture analysis (Hielscher 2007; Hielscher and Schaeben 2008a, 2008b; Schaeben et al. 2007). A unique feature of the MTEX toolbox is that it provides a unifying approach to texture analysis with integral (“pole figure”) or individual (“EBSD”) orientation measurements. Therefore, it is particularly well suited to compare patterns of preferred orientation based on data of such different origin. Moreover, it is exemplified that the mathematical method and its numerical realisation encoded in the MTEX toolbox applies to
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