Same same but Different - Definition and Explicit Notation of an Orientation in MTEX vs. Quasi-Standard

Abstract:

Even though the descriptive definition of orientation is the same in both settings, the explicitnotation of a crystallographic orientation as (3 3) matrix in terms of Euler angles featuredby the popular MATLAB toolbox MTEX differs by an inversion from the quasi-standard notation datedback to the early days of quantitative texture analysis championed by H.-J. Bunge. The origin of thisdiscrepancy is revealed by an enlightening view provided in algebraic terms of a change of basis.Understanding the effect of inversion is instrumental to do proper computations with crystallographicorientations and rotations, e.g. when multiplying with elements of a crystallographic symmetry group,and to compare results of texture analyses accomplished in different settings.

• Periodical: Solid State Phenomena (Volume 365)
• Pages: 151-156
• DOI: https://doi.org/10.4028/p-2tCx0i
• Online since: November 2024
• Authors: Helmut Schaeben*
• Keywords: (3x3) Matrix of SO(3), Change of Basis of Vector Space, Crystallographic Texture, Euler Angle, Orientation, Rotation

References

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DOI: 10.1201/9781003258339

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