The structures of the six perrhenates (AReO4 A = Ag, Na, K, Rb, Cs and Tl) at RT and the phase transitions associated with change in the orientation of the ReO4− tetrahedra seen for A = Rb, Cs and Tl are described.

Crystalline solids consisting of three-dimensional networks of interconnected rigid units are ubiquitous amongst functional materials. In many cases, application-critical properties are sensitive to rigid-unit rotations at low temperature, high pressure or specific stoichiometry. The shared atoms that connect rigid units impose severe constraints on any rotational degrees of freedom, which must then be cooperative throughout the entire network. Successful efforts to identify cooperative-rotational rigid-unit modes (RUMs) in crystals have employed split-atom harmonic potentials, exhaustive testing of the rotational symmetry modes allowed by group representation theory, and even simple geometric considerations. This article presents a purely algebraic approach to RUM identification wherein the conditions of connectedness are used to construct a linear system of equations in the rotational symmetry-mode amplitudes.

The development of electrodes for ambient temperature sodium-ion batteries requires the study of new materials and the understanding of how crystal structure influences properties. In this study, we investigate where sodium locates in two Prussian blue analogues, Fe[Fe(CN)6]1-x·yH2O and FeCo(CN)6. The evolution of the sodium site occupancies, lattice and volume is shown during charge-discharge using in situ synchrotron X-ray powder diffraction data. Sodium insertion is found to occur in these electrodes during cell construction and therefore Fe[Fe(CN)6]1-x·yH2O and FeCo(CN)6 can be used as positive electrodes. NazFeFe(CN)6 electrodes feature higher reversible capacities relative to NazFeCo(CN)6 electrodes which can be associated with a combination of structural factors, for example, a major sodium-containing phase, ∼Na0.5FeFe(CN)6 with sodium locating either at the x = y = z = 0.25 or x = y = 0.25 and z = 0.227(11) sites and an electrochemically inactive sodium-free Fe[Fe(CN)6]1-x·yH2O phase. This study demonstrates that key questions about electrode performance and attributes in sodium-ion batteries can be addressed using time-resolved in situ synchrotron X-ray diffraction studies.

Possibilities for 'simple' octahedral tilting in the hexagonal and tetragonal tungsten bronzes (HTB and TTB) have been examined, making use of group theory as implemented in the computer program ISOTROPY. For HTB, there is one obvious tilting pattern, leading to a structure in space group P6₃/mmc. This differs from the space group P6₃/mcm frequently quoted from X-ray studies – these studies have in effect detected only displacements of the W cations from the centres of the WO6 octahedra. The correct space group, taking account of both W ion displacement and the octahedral tilting, is P6₃22 – structures in this space group and matching this description have been reported. A second acceptable tilting pattern has been found, leading to a structure in P6/mmm but on a larger '2 × 2 × 2' unit cell – however, no observations of this structure have been reported. For TTB, a search at the special points of the Brillouin zones revealed only one comparable tilting pattern, in a structure with space-group symmetry I4/m on a '2(1/2) × 2(1/2) by 2' unit cell. Given several literature reports of larger unit cells for TTB, we conducted a limited search along the lines of symmetry and found structures with acceptable tilt patterns in Bbmm on a '2(1/2)2 × 2(1/2) × 2' unit cell. A non-centrosymmetric version has been reported in niobates, in Bbm2 on the same unit cell.