Many compounds adopting the spinel AB(2)X(4) structure are technologically important owing to their tunable physical and chemical properties enabling diverse applications in energy storage, catalysis, magnetism, and functional ceramics. Most of them are traditionally assigned to the centrosymmetric space group Fd (3) over barm. However, the physical properties of some spinels are incompatible with centrosymmetry. This discrepancy is often accounted for by reducing the symmetry to the non-centrosymmetric space group F (4) over bar 3m, allowing thus small atomic displacements from their original position in Fd (3) over barm. In this work, we demonstrate that the loss of the inversion symmetry can occur without any atomic displacements, since the centrosymmetric Fd (3) over barm and non-centrosymmetric F4(1)32 space groups are equivalent for structure determination and refinement based on X-ray diffraction data. If consistent with experiment, only the use of an anharmonic model of atomic displacements can distinguish these space groups. This study aims to clarify certain misconceptions regarding the structural symmetry and physical properties of spinel-type compounds.
Metastable allotropes of silicon recovered from high-pressure conditions exhibit a wide range of crystal structures, physical properties and transformation pathways that remain only partially understood despite decades of study. This article combines original crystallographic observations with a critical review of phase transformations, nucleation mechanisms and crystal growth processes in elemental Si and Na-Si systems synthesized under high-pressure, high-temperature conditions. Using in situ diffraction data, structural characterization and computational approaches, we analyze how symmetry breaking, lattice instabilities and kinetic constraints govern the formation of dense polymorphs (Si-II, Si-III, Si-XI) and open-framework structures, including clathrate and channel phases. Particular attention is given to the role of large-volume synthesis and chemically assisted growth routes in controlling phase selection, defect formation and recoverability. The evolution of hexagonal polytypes, including nanostructured 6H silicon, is discussed in terms of stacking modifications driven by stress release and thermal treatment. By integrating crystallographic relations, thermodynamic considerations and growth kinetics, this work identifies phase-transformation mechanisms as the key factor linking structure, synthesis conditions and functional properties of silicon allotropes. The results provide a unified framework for understanding crystal growth at high pressure and offer guidance for the controlled synthesis of advanced silicon materials.
GalC8 [L-threo-D-galacto-octitol, systematic name (2S,3R,4R,5R,6R,7S)-octane-1,2,3,4,5,6,7,8-octol] crystallizes with a pseudo-tetragonal lattice featuring a long (∼88 Å) c axis. The bulk of the structure possesses P43212 (Z' = 1) pseudo-symmetry, whereby molecules are arranged linearly with eight molecules in a translation period, thus explaining the long c axis. According to this pseudo-symmetry, adjacent molecules are alternately related by 21 screw rotations (in 〈100〉 directions) and twofold rotations (in 〈110〉 directions). Due to an asymmetrical hydrogen-bonding network, symmetry is broken in the vicinity of the twofold rotation axes, leading to an overall P21 (Z' = 4) space-group symmetry. The lost symmetry is retained as a twin operation. The structure can be classified as a `non-classical' OD polytype, in the sense that there are nonequivalent layer contacts, yet all members of the polytype family are locally equivalent. The main polytype is not of a maximum degree of order (MDO) and can be described as an alternation of fragments of the two MDO polytypes with P43 and P212121 symmetry, respectively.
The incommensurate structure of AlPO4-5 and its stability have been investigated in detail. Under ambient conditions, single-crystal X-ray diffraction measurements reveal weak satellite reflections, which become significantly enhanced upon exposure to vacuum. Temperature-dependent X-ray diffraction and Raman scattering measurements of the O-H stretching region show that the appearance of satellite reflections is due to the desorption of water molecules under vacuum, and the satellite reflections disappear above 335 (5) K, whereas their intensity increases again upon cooling to room temperature. To elucidate the origin of the modulation, single-crystal X-ray diffraction experiments were performed on a dehydrated sample. Diffraction data including satellite reflections up to second order were successfully collected, with a modulation vector of q = 0.36710 (5)c*. Analysis of systematic absences up to second-order satellites indicate that the (3+1)D superspace group is P6(00γ)h. On the basis of these data, the first-order positional modulation amplitudes were refined. The results indicate that the modulation originates from correlated rotational displacements of AlO4 and PO4 tetrahedra. This behaviour suggests that phonon-like motions, as proposed in previous studies, persist over a long modulation period and give rise to the observed satellite reflections. These findings highlight a fundamental connection between the intrinsically spatial description of atomic positional modulations in the incommensurate structure and the underlying temporal dynamics.
Crystal structures with asymmetric units comprising large numbers of molecules (Z ' > 4) remain rare. Their study provides a unique opportunity to further the understanding of the physical basis for crystal formation, supporting the advancement of crystal structure prediction, crystal engineering and the study of polymorphism. Here the crystal structures of a series of three related 2,3,9,9a-tetrahydro-1H-carbazoles are discussed, one of which exhibits an asymmetric unit comprising six crystallographically independent molecules (Z ' = 6). Careful analysis of this structure reveals approximate Fdd2 symmetry and strong evidence for this being linked to a symmetry-reducing, low-temperature phase transition. Comparison of the structures reveals that the variation in Z ' values is linked to conformational changes related to the lack of classical hydrogen bonding in the high-Z ' structure.
