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Discrete Tomography for Generating Grain Maps of Polycrystals

  • A. Alpers
  • L. Rodek
  • H.F. Poulsen
  • E. Knudsen
  • G.T. Herman
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

The determination of crystalline structures is a demanding and fundamental task of crystallography. Most crystalline materials, natural or artificial, are in fact polycrystals, composed of tiny crystals called grains. Every grain has an associated average orientation that determines the spatial configuration of the crystalline lattice. Typically, the structure of a polycrystal is rendered via an orientation map or a grain map, in which individual pixels/voxels are assigned a grain orientation or a grain label. We present two related approaches to reconstructing a 2D grain map of a polycrystal from X-ray diffraction patterns. The first technique makes the assumption that each grain is actually a perfect crystal, i.e., that the specimen is not deformed. The other method can be applied also when the sample has been exposed to moderate levels of deformation. In both cases, the grain map is produced by a Bayesian discrete tomographic algorithm that uses Gibbs priors. The optimization of the objective function is accomplished via the Metropolis algorithm. The efficacy of the techniques is demonstrated by simulation experiments.

Keywords

Crystal Symmetry Average Orientation White Pixel Detector Pixel Metropolis Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 2007

Authors and Affiliations

  • A. Alpers
    • 1
  • L. Rodek
    • 2
  • H.F. Poulsen
    • 3
  • E. Knudsen
    • 3
  • G.T. Herman
    • 4
  1. 1.School of Operations Research and Industrial Engineering, Cornell UniversityNYUSA
  2. 2.Dept. of Image Processing and Computer GraphicsUniversity of SzegedSzegedHungary
  3. 3.Materials Research DepartmentRisø National LaboratoryRoskildeDenmark
  4. 4.Dept. of Computer ScienceThe Graduate Center, City Univ. of New YorkNew YorkUSA

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