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K. Ehrmann, S. Baudis, B. Stöger:
"From space group to space groupoid: the partial symmetry of low-temperature E-vanillyl oxime";
Acta Crystallographica Section B, 75 (2019), S. 733 - 741.

The phase transition of E-vanillyl oxime {1-[(E)-(hydroxyimino)methyl]-4-hydroxy-3-methoxybenzene, C₈H₉NO₃} has been analysed by single-crystal and powder X-ray diffraction. The high-temperature (HT) phase (P2₁/a, Z = 1)
transforms into the low-temperature (LT) phase (threefold superstructure, P-1, Z = 6) at ca 190 K. The point operations lost on cooling, {m[010], 2[010]}, are retained as twin operations and constitute the twin law. The screw rotations and glide reflections are retained in the LT phase as partial operations acting on a subset of Euclidean space E³. The full symmetry of the LT phase, including partial operations, is described by a disconnected space groupoid which is built of three connected components.

phase transitions; local symmetry; groupoids; partial symmetry

http://dx.doi.org/10.1107/S2052520619008461