From space group to space groupoid: the partial symmetry of low-temperature E-vanillyl oxime

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\overline{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 {\bb E}^3. The full symmetry of the LT phase, including partial operations, is described by a disconnected space groupoid which is built of three connected components.