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Remarks on Texture Coefficients of Polycrystals with Improper Crystallite Symmetry

  • Chi-Sing ManEmail author
  • Ding Zhao
Research Note
  • 13 Downloads

Abstract

The orientation distribution function (ODF) in classical texture analysis is defined on the rotation group SO(3). For polycrystalline aggregates with crystallite symmetry defined by a crystallographic point group \(G_{\mathrm{cr}}\) which is not a subgroup of SO(3), the improper group \(G_{\mathrm{cr}}\) is routinely replaced by its proper peer (i.e., a subgroup of SO(3)) in the same Laue class. In this note we examine how the texture coefficients obtained from such a practice are related to their counterparts that pertain to the corresponding ODF defined on the orthogonal group O(3) as it should.

Keywords

Crystallographic texture Orthogonal group Texture coefficients Improper point groups Laue class 

Mathematics Subject Classification (2010)

74A99 74E10 74E15 74E25 60B05 

Notes

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KentuckyLexingtonUSA

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