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Figure 2
(a) Stereographic projection showing the Matthies–Euler convention relationship between the sample (XsYsZs), crystal coordinates (XcYcZc) and coordinates at a given orientation (XgYgZg). (b) Illustration of crystal coordinate axes XcYcZc in quartz shown aligned with the axes of the sample coordinate system XsYsZs following the rotations in (a) to give the final orientation (XgYgZg). Note that, to describe the trigonal crystal unit-cell axes (red) with the orthogonal crystal coordinate system, one crystal axis is a reciprocal axis. Orientations here are defined by Matthies–Euler rotations α, β and γ around Zc, [{\bf Y}_{\rm c}^{\prime}] and [{\bf Z}_{\rm c}^{\prime\prime}], respectively (prime, double- and triple-prime superscripts indicate the rotated axes), to arrive at the final crystal orientation in (XgYgZg).

Journal logoJOURNAL OF
APPLIED
CRYSTALLOGRAPHY
ISSN: 1600-5767
Volume 56| Part 6| December 2023| Pages 1764-1775
https://doi.org/10.1107/S1600576723009275
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