By generalizing the concepts of the wavevector star channel in the Brillouin zone and its symmetry group [Kim et al. (2017). Acta Cryst. A73, 403-413; Kim et al. (2021). Acta Cryst. A77, 572-592] to a reducible wavevector star containing several Lifshitz stars, new concepts of the reducible wavevector star channel and its symmetry group are defined and methods of finding them are proposed. It is shown that structural distortions, such as octahedral tilting, atomic displacement and Jahn-Teller ordering, characterized by ten reducible stars related to the Lifshitz ones Γ, M, R and X in ferroics and multiferroics belonging to 15 parent space groups of the simple cubic lattice, are described by 105 reducible star channels, allowed by symmetry, and reducible star channel groups are found. The symmetry analysis of ordered phases induced by the reducible representations of the reducible wavevector star channel groups Pm3m[k11(1)k13] and Pm3m[k11(1)k12k13] has been carried out to show that the complex ordered phases observed experimentally in many perovskite crystals, including CaTiO3, SrZrO3, KMnF3, CsPbCl3 and Pb1-xCaxTiO3, can be described by much simpler order parameter models, rather than the ones associated with reducible representations corresponding to the reducible wavevector star of the space group Pm3m.
Nanocrystals exhibit size-dependent structural behaviour because surface and interface effects become increasingly important as the characteristic domain size decreases. In this work, we investigate the size dependence of three diffraction-derived structural parameters - lattice parameter, isotropic Debye-Waller coefficient and microstrain - by combining molecular dynamics simulations of spherical Pd, Fe and Ti nanocrystals with powder diffraction analysis and comparison with representative literature data. The atomistic results show that small nanocrystals are characterized by a mean compressive state together with pronounced surface-stress inhomogeneity, while enhanced atomic displacements are concentrated in the outer coordination shells. On this basis, three simple nanoscale hypotheses are proposed. The lattice parameter is described as an ideal capillarity-driven reference trend with leading 1/D (where D is the particle diameter) behaviour, although comparison with experimental data confirms that this quantity is not universal and may be strongly modified by surface chemistry, defects, non-stoichiometry and morphology. By contrast, the Debye-Waller coefficient follows a more general 1/D decrease, consistent with a surface-shell picture of enhanced vibrational and static disorder. Microstrain arises from surface-stress gradients and, in the small-particle limit, exhibits a natural 1/D2 dependence associated with surface-stress heterogeneity; over broader size ranges, a mixed 1/D + 1/D2 form provides a more effective description. These results support a heuristic surface-driven interpretation of nanoscale structural disorder and clarify the different degrees of generality of the three scaling laws.
A small protein structure would not yield a solution via the single-atom R1 (sR1) method. A salient sign of trouble was that many atoms were dubiously accepted into the model because their introduction caused the sR1 value to increase. A plausible hypothesis is that this was very likely due to a hidden solvent diffraction effect. After accounting for this hidden solvent effect via padding additional C atoms, this small protein structure now has been successfully solved by the sR1 method. Further analysis of the protein crystal density indicated that the above successful padding of C atoms had over-accounted for the solvent content. However, empirical observations have indicated that, when an initial application of the sR1 method shows that many atoms are not welcomed into the model, padding numerous C atoms (even if over-accounting for the solvent content) benefits the sR1 calculation by making spotting plausible fragments more reliable and/or making the resulting model more complete.
This article presents a review of the landscape of Open Science development and its relevance to crystallography. As open as possible as closed as necessary is the model for Open Science as commended by the UK and China. Mainland Europe requires compulsory release after 3 years since measurement of raw data. The USA policy situation has fluctuated considerably in recent years. Altogether, this article addresses the International Union of Crystallography's (IUCr) input into these activities. It considers its participation in international scientific and societal organizations, as well as its compliance with the policy recommendations. It considers the practical landscape in which crystallographers work, including their funding agencies, governments, central facilities and universities. This article sets the wider scene before describing how crystallography benchmarks against those under development. The IUCr's Teaching Pamphlets and the Online Dictionary of Crystallography are educational resources fully open to Global South and Global North readers and authors. Crystallography provides a mature, practice-based model of responsible openness that predates and can inform contemporary Open Science policy.
This work introduces reverse EXAFS analysis (REA), a novel, ab initio framework that transforms extended X-ray absorption fine structure (EXAFS) spectroscopy from a complementary local probe into a primary tool for de novo crystal structure determination. By integrating iterative FEFF simulations with a reverse-fitting algorithm, REA directly extracts full crystallographic parameters, lattice constants, space group and atomic positions, from EXAFS oscillations, without requiring the user to supply an initial structural model from X-ray diffraction; instead, candidate models are retrieved from crystallographic databases and evaluated against EXAFS data. Validated on LiCrO2 and CuFeO2, REA uncovered unexpected phase complexities in CuFeO2, identifying secondary CuFe2O4 and CuFe5O8 phases undetected by conventional methods. This paradigm shift enables accurate structure solving in disordered, nanostructured and novel materials where diffraction fails, establishing EXAFS as a stand-alone crystallographic technique.
