Common Region between Euler Subspace and Rodrigues Fundamental Zone for a Cubic Crystal and Orthotropy Sample Symmetry

摘要

Due to crystal and sample symmetry, texture data can be presented uniquely in a smaller domain of Euler box or Rodrigues space. As these sub-domains are obtained by different criteria, a one-to-one relation does not always exist for conversion between Euler and Rodrigues coordinates. This work presents a methodology for finding the common region between the Euler sub-space and Rodrigues fundamental zone for the case of cubic crystal and orthotropy sample symmetry, and its size is found to be cos[cos~(-1)[2 2~(1/2)+1/4]]~2.