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Symmetric Euler orientation representations for orientational averaging.

Thomas G Mayerhöfer1

  • 1Institut für Physikalische Chemie, Friedrich-Schiller-Universität Jena, Lessingstrasse 10, D-07743 Jena, Germany. thomas.mayerhoefer@uni-jena.de

Spectrochimica Acta. Part A, Molecular and Biomolecular Spectroscopy
|July 27, 2005
PubMed
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A novel symmetric Euler orientation representation (SEOR) overcomes issues with conventional methods for orientational averaging in materials science. SEOR provides accurate, representation-independent averaging without weighting factors.

Area of Science:

  • Crystallography
  • Materials Science
  • Computational Physics

Background:

  • Conventional Euler orientation representations (Euler angles) and quaternions are standard for describing crystal orientations.
  • Existing averaging schemes based on Euler angles can introduce dependencies on the specific representation and initial crystal position.

Purpose of the Study:

  • Introduce a new orientation representation: symmetric Euler orientation representation (SEOR).
  • Investigate SEOR's properties for orientational averaging.
  • Compare SEOR-based averaging with conventional Euler angle-based methods.

Main Methods:

  • Calculated reflectance of a polycrystalline material with orthorhombic symmetry using the average refractive index theory (ARIT).
  • Compared orientational averaging results using conventional Euler angles versus SEOR.

Related Experiment Videos

  • Analyzed the impact of representation choice, initial crystal position, and weighting factors on averaging accuracy.

    • Main Results:

    • Conventional Euler angle averaging shows dependence on the chosen representation and initial crystal orientation.
    • Weighting factors can partially mitigate issues for two-axes Euler representations but leave residual differences.
    • SEOR inherently avoids these representation-dependent issues and simplifies numerical averaging.

    Conclusions:

    • Symmetric Euler orientation representation (SEOR) offers a robust and accurate method for orientational averaging.
    • SEOR eliminates the need for weighting factors or specific step spacing in numerical evaluations.
    • SEOR is ideally suited for orientational averaging procedures in materials science and crystallography.