Pseudo-symmetry analysis to unravel the secrets of twins-A case study with four diverse examples

Four twins are interpreted by pseudo-symmetry analysis. The pincer complexes Co(PCP)X (X=Cl, Br) are order-disorder (OD) twins. The individuals are composed of one polytype with a maximum degree of order (MDO) with Pc symmetry, whereas at the composition plane is located a fragment of the second MDO polytype with Pbc2₁ symmetry. The twinning of the low-temperature (LT, 100 K) P2₁ phase of 2,3-dicyanohydroquinone dihydrate (DCHQ·H₂O) can be explained by a symmetry reduction of index 2 from the high-temperature (HT, 250 K) Pn2₁m phase. Propylammonium perchlorate (nPrNH₃ClO₄) features different kinds of twinning. On the one hand, transformation twinning is caused by a symmetry reduction of index 2 from the HT (150 K) Pbnm to the LT (100 K) P2₁/n phase. On the other hand, the crystals feature growth twinning by rotation about the [010] axis, where the nature of the twin interface remains unknown. The twinning of the Ccce Ba[H₂TeO₅] structure with pseudo-tetragonal metrics is explained by a part of the structure featuring higher P4₂/nmc symmetry. At the twin interface is probably located a fragment with the formal composition TeO₃.