Crystal structures of Sr_{3}B_{2 + x}Si_{1 − x}O_{8 − x/2} solid solutions with nominal compositions *x* = 0.28, 0.53, 0.78 in the Sr_{3}B_{2}SiO_{8}–Sr_{2}B_{2}O_{5} section of the SrO–B_{2}O_{3}–SiO_{2} system are refined using single-crystal X-ray diffraction data. Incommensurate structure modulations are mainly associated with various orientations of corner-sharing (B,Si)-polyhedra. Preference is given to the (3 + 2)-dimensional symmetry group *Pnma*(0βγ)000(0γ)000 for a single crystal compared with an alternate model of a twin formed by monoclinic components, each of them corresponding to the (3 + 1)-dimensional symmetry group *P*2_{1}/*n*(0βγ). Single-phase polycrystalline samples of solid solutions are investigated by high-temperature X-ray powder diffraction in air. Orientation preferences of the BO_{3} units lead to a strong anisotropy of thermal expansion. Negative expansion is observed along the *a* axis over the temperature range 303–753 K. Anisotropy decreases both on heating and decreasing of the boron content.

Monoclinic dicaesium copper tetraaluminate, Cs_{2}CuAl_{4}O_{8}, space group *P*2_{1}/*c*, *a* = 8.4551 (7), *b* = 10.012 (1), *c* = 17.073 (2) Å, β = 101.643 (9)°, *Z* = 6, was obtained by high-temperature crystallization from a phosphate flux. Its microporous crystal structure presents the first example of double layers built from [AlO_{4}] tetrahedra combined in 4-, 6- and 8-rings, topologically similar to those found in the *ATT*-type zeolites and isostructural minerals armstrongite, davanite and dalyite. These layers show a rare arrangement of three [AlO_{4}] tetrahedra sharing one oxygen vertex. The aluminate slabs are further linked by chains of edge-sharing [CuO_{4}] square planes to form a mixed anionic three-dimensional framework with Cs^{+} cations in channels and cavities. An unusually short Cu...Cs distance of 3.166 Å is ascribed to the strong Jahn–Teller effect of Cu^{2+}. The magnetic subsystem demonstrates properties of an alternating antiferromagnetic chain with a gap in the spectrum of magnetic excitations.

We explored the use of machine learning methods for classifying whether a particular *AB*O_{3} chemistry forms a perovskite or non-perovskite structured solid. Starting with three sets of feature pairs (the tolerance and octahedral factors, the *A* and *B* ionic radii relative to the radius of O, and the bond valence distances between the *A* and *B* ions from the O atoms), we used machine learning to create a hyper-dimensional partial dependency structure plot using all three feature pairs or any two of them. Doing so increased the accuracy of our predictions by 2–3 percentage points over using any one pair. We also included the Mendeleev numbers of the *A* and *B* atoms to this set of feature pairs. Doing this and using the capabilities of our machine learning algorithm, the gradient tree boosting classifier, enabled us to generate a new type of structure plot that has the simplicity of one based on using just the Mendeleev numbers, but with the added advantages of having a higher accuracy and providing a measure of likelihood of the predicted structure.

The crystal structures of two new natural Bi oxysulfates with the formula Bi_{14}O_{16}(SO_{4})_{5} [labelled *new phase I*; monoclinic, space group *C*2, *a* = 21.658 (4), *b* = 5.6648 (9), *c* = 15.092 (3) Å, β = 119.433 (11)° and *Z* = 2] and Bi_{30}O_{33}(SO_{4})_{9}(AsO_{4})_{2} [labelled *new phase II*; triclinic, space group *P*1, *a* = 5.670 (3), *b* = 13.9408 (9), *c* = 22.7908 (18) Å, α = 80.903 (5), β = 82.854 (14), γ = 78.27 (2)° and *Z* = 1] from the high-temperature fumarole deposit of the La Fossa crater at Vulcano (Aeolian Islands, Italy) are reported. The structures are built up by a combination of fluorite-related Bi—O units and isolated (SO_{4})^{2−} tetrahedra (*new phase I*) or both (SO_{4})^{2−} and (AsO_{4})^{3−} tetrahedra (*new phase II*). Owing to the effect of stereoactive lone pairs of Bi^{3+}, Bi—O units in both the structures can be suitably described in terms of oxo-centered OBi_{4} tetrahedra. The structure of Bi_{14}O_{16}(SO_{4})_{5} is based upon one-dimensional [O_{16}Bi_{14}]^{10+} ribbons formed by six chains of edge-sharing OBi_{4} tetrahedra extending along [010]. In the structure of Bi_{30}O_{33}(SO_{4})_{9}(AsO_{4})_{2} the same ribbon type coexists with another one-dimensional ribbon formed by seven chains of edge-sharing OBi_{4} tetrahedra and with the composition [O_{17}Bi_{16}]^{14+}. Ribbons of the same type are joined by (SO_{4})^{2−} and (AsO_{4})^{3−} tetrahedra along [010] – if a reduced triclinic unit-cell setting is considered – so forming two different (001) slabs which alternate to each other along [001] and are joined by additional (SO_{4})^{2−} tetrahedra. *New phase I* represents the natural analogues of synthetic Bi_{14}O_{16}(SO_{4})_{5}, but with an ordered structure model.

The systematic twinning of three 2,6-diaminopyridine-based Fe-PNP complexes is interpreted using order–disorder (OD) theory. The monoclinic [Fe^{0}(PNP^{Et}-^{i}Pr)(CO)_{2}] [*P*112_{1}/*b*, *Z*′ = 4] possesses pseudo-orthorhombic metrics and crystallizes as a reflection twin by pseudo-merohedry with the twin plane (100). The structure is made up of layers with idealized *p*2_{1}*a*(*b*) symmetry. The *a* glide planes of adjacent layers do not overlap, leading to OD polytypism. *trans*-[Fe^{II}(PNP-Et)Br_{2}(CO)] [*P*2_{1}/*n*, *Z*′ = 1] is systematically twinned *via* twofold rotation about [001]. It is made up of OD layers with idealized *p*2_{1}2_{1}(2) symmetry. OD polytypism is caused by the twofold rotation axes of adjacent layers which do not overlap. [Fe^{II}(κ^{2}*P*,*N*-PNP-^{i}Pr,TAD)Cl_{2}]·THF [*P1*, ] is systematically twinned *via* a twofold rotation about [010]. It is made up of layers with idealized *p*12_{1}(1) symmetry. OD polytypism is caused by screw rotations relating adjacent layers with an intrinsic translation along a fourth of a primitive lattice vector. In all three structures the twin individuals are a polytype with a maximum degree of order (MDO) and at the twin interface is located a fragment of the second MDO polytype.

3-Furylfulgides are photochromic compounds showing high thermal stability in their closed forms. However, their photochromic properties in the solid state should be improved further to fabricate molecular devices. Understanding how the size and the flexibility of the non-aromatic alkylidene moiety alter the crystalline state photochromic properties is also important here, as the alkylidene group is directly involved in the photochromic ring closing and opening reactions. The synthesis of four 3-furylfulgides composed of different alkylidene groups (rigid isopropyl, flexible 2-butyl, rigid cyclopentyl and flexible cyclohexyl), their crystal structures and structure–photochromic property correlation in the crystalline state are reported here. Crystallographic data along with reaction cavity volumes calculated using the program *CAVITY* [Ohashi *et al.* (1981), *J. Am. Chem. Soc.***103**, 5805–5812] disclosed that fulgides with flexible groups at the ring closing site have more free volume around the reactive area in the crystal lattice, which can provide more space for the atomic movements in the reaction and flexibility can reduce the strain built up in the closed *C*-isomers by making conformations. According to UV–vis spectroscopic data, a higher yield of *C*-isomers and a better fatigue resistance were obtained for the 3-furylfulgide with the largest and flexible cyclohexyl group showing greater photochromic properties in the crystalline state than the fulgide containing the smallest and rigid isopropyl group.

Interaction of 1-(1*H*-pyrazol-5-yl)ethanone oxime (H_{2}PzOx) with copper(II) chloride in the presence of pyridine afforded a binuclear discrete [Cu_{2}(HPzOx)_{2}Cl_{2}py_{2}] complex, which was characterized by Fourier transform–IR and electron paramagnetic resonance (EPR) spectra, magnetochemistry and high-resolution X-ray diffraction experiments. Multipole refinement of X-ray diffraction data and density-functional theory (DFT) calculations of an isolated molecule allowed charge and spin distributions to be obtained for this compound. Magnetochemistry data, EPR spectra and DFT calculations of an isolated molecule show antiferromagnetic coupling between copper(II) ions. The spin distribution suggests an exchange pathway *via* the bridging pyrazole ring in the equatorial plane of the CuN_{4}Cl coordination polyhedron, thus providing support for the classical superexchange mechanism; the calculated value of the magnetic coupling constant −2*J* is equal to 220 cm^{−1}, which compares well with the experimental value of 203 ± 2 cm^{−1}. Chemical connectivity was derived by Bader's `quantum theory of atoms in molecules' and compared with Voronoi tessellation and Hirshfeld surface representations of crystal space. All methodologies gave a similar qualitative and semi-quantitative description of intra- and intermolecular connectivity.

A natural single crystal of the ferrimagnetic oxide FeCrO_{3}, which was found in an opencast mine situated in the San Luis Potosí State in Mexico, has been characterized in order to elucidate some outstanding issues about the actual structure of this material. The single-crystal X-ray analysis unambiguously shows that transition metal cations are segregated in alternating layers normal to the threefold crystallographic axis, affording a structure isomorphous to that of ilmenite (FeTiO_{3}), in the space group . The possible occurrence of cation antisite and vacancy defects is below the limit of detection available from X-ray data. Structural and magnetic results are in agreement with the coherent slow intergrowth of magnetic phases provided by the two antiferromagnetic corundum-type parent oxides Fe_{2}O_{3} (hematite) and Cr_{2}O_{3} (eskolaite). Our results are consistent with the most recent density functional theory (DFT) studies carried out on digital FeCrO_{3} [Sadat Nabi & Pentcheva (2011). *Phys. Rev. B*, **83**, 214424], and suggest that synthetic samples of FeCrO_{3} might present a cation distribution different to that of the ilmenite structural type.

Published two-body bond-valence parameters for cation–oxygen bonds have been evaluated *via* the root mean-square deviation (RMSD) from the valence-sum rule for 128 cations, using 180 194 filtered bond lengths from 31 489 coordination polyhedra. Values of the RMSD range from 0.033–2.451 v.u. (1.1–40.9% per unit of charge) with a weighted mean of 0.174 v.u. (7.34% per unit of charge). The set of best published parameters has been determined for 128 ions and used as a benchmark for the determination of new bond-valence parameters in this paper. Two common methods for the derivation of bond-valence parameters have been evaluated: (1) fixing *B* and solving for *R*_{o}; (2) the graphical method. On a subset of 90 ions observed in more than one coordination, fixing *B* at 0.37 Å leads to a mean weighted-RMSD of 0.139 v.u. (6.7% per unit of charge), while graphical derivation gives 0.161 v.u. (8.0% per unit of charge). The advantages and disadvantages of these (and other) methods of derivation have been considered, leading to the conclusion that current methods of derivation of bond-valence parameters are not satisfactory. A new method of derivation is introduced, the GRG (generalized reduced gradient) method, which leads to a mean weighted-RMSD of 0.128 v.u. (6.1% per unit of charge) over the same sample of 90 multiple-coordination ions. The evaluation of 19 two-parameter equations and 7 three-parameter equations to model the bond-valence–bond-length relation indicates that: (1) many equations can adequately describe the relation; (2) a plateau has been reached in the fit for two-parameter equations; (3) the equation of Brown & Altermatt (1985) is sufficiently good that use of any of the other equations tested is not warranted. Improved bond-valence parameters have been derived for 135 ions for the equation of Brown & Altermatt (1985) in terms of both the cation and anion bond-valence sums using the GRG method and our complete data set.