c

Crystal structure and Hirshfeld surface analysis of tri­chlorido­(1,10-phenanthroline-κ2N,N')phenyltin(IV)

The title compound, [Sn(C6H5)Cl3(C12H8N2)], which was obtained by the reaction between 1,10-phenanthroline and phenyl­tin trichloride in methanol, exhibits intra­molecular hydrogen-bonding inter­actions involving the chlorine and hydrogen atoms. Crystal cohesion is ensured by inter­molecular C—H⋯Cl hydrogen bonds, as well as Y—X⋯π and π-stacking inter­actions involving three different aromatic rings with centroid–centroid distances of 3.6605 (13), 3.9327 (14) and 3.6938 (12) Å]. Hirshfeld surface analysis and the associated two-dimensional fingerprint plots reveal significant contributions from H⋯H (30.7%), Cl⋯H/H⋯Cl (32.4%), and C⋯H/H⋯C (24.0%) contacts to the crystal packing while the C⋯C (6.2%), C⋯Cl/Cl⋯C (4.1%), and N⋯H/H⋯N (1.7%) inter­actions make smaller contributions.




c

Crystal structure and Hirshfeld surface analysis of {2-[bis­(pyridin-2-ylmeth­yl)amino]­ethane-1-thiol­ato}­chlorido­cadmium(II)

The title compound, [Cd(C14H16N3S)Cl] or [CdLCl] (1), where LH = 2-[bis­(pyridin-2-ylmeth­yl)amino]­ethane-1-thiol, was prepared and structurally characterized. The Cd2+ complex crystallizes in P21/c with a distorted trigonal–bipyramidal metal coordination geometry. Supra­molecular inter­actions in 1 include parallel offset face-to-face inter­actions between inversion-related pyridyl rings and potential hydrogen bonds with chlorine or sulfur as the acceptor. Additional cooperative pyrid­yl–pyridyl inter­actions with roughly 45° tilt angles and centroid–centroid distances of less than 5.5 Å likely also contribute to the overall solid-state stability. Hirshfeld surface analysis indicates that H⋯H (51.2%), Cl⋯H/H⋯Cl (13.9%), C⋯H/H⋯C (12.3%) and S⋯H/H⋯S (11.8%) inter­actions are dominant in the solid state.




c

Synthesis and crystal structure of poly[[μ-chlorido-μ-(2,3-di­methyl­pyrazine)-copper(I)] ethanol hemisolvate], which shows a new isomeric CuCl(2,3-di­methyl­pyrazine) network

Reaction of copper(I)chloride with 2,3-di­methyl­pyrazine in ethanol leads to the formation of the title compound, poly[[μ-chlorido-μ-(2,3-di­methyl­pyrazine)-copper(I)] ethanol hemisolvate], {[CuCl(C6H8N2)]·0.5C2H5OH}n or CuCl(2,3-di­methyl­pyrazine) ethanol hemisolvate. Its asymmetric unit consists of two crystallographically independent copper cations, two chloride anions and two 2,3-di­methyl­pyrazine ligands as well as one ethanol solvate mol­ecule in general positions. The ethanol mol­ecule is disordered and was refined using a split model. The methyl H atoms of the 2,3-di­methyl­pyrazine ligands are also disordered and were refined in two orientations rotated by 60° relative to each other. In the crystal structure, each copper cation is tetra­hedrally coordinated by two N atoms of two bridging 2,3-di­methyl­pyrazine ligands and two μ-1,1-bridg­ing chloride anions. Each of the two copper cations are linked by pairs of bridging chloride anions into dinuclear units that are further linked into layers via bridging 2,3-di­methyl­pyrazine coligands. These layers are stacked in such a way that channels are formed in which the disordered solvent mol­ecules are located. The topology of this network is completely different from that observed in the two polymorphic modifications of CuCl(2,3-di­methyl­pyrazine) reported in the literature [Jess & Näther (2006). Inorg. Chem. 45, 7446–7454]. Powder X-ray diffraction measurements reveal that the title compound is unstable and transforms immediately into an unknown crystalline phase.




c

Synthesis, crystal structure and Hirshfeld surface analysis of sulfamethoxazolium methyl­sulfate monohydrate

The mol­ecular salt sulfamethoxazolium {or 4-[(5-methyl-1,2-oxazol-3-yl)sulf­amo­yl]anilinium methyl sulfate monohydrate}, C10H12N3O3S+·CH3O4S−·H2O, was prepared by the reaction of sulfamethoxazole and H2SO4 in methanol and crystallized from methanol–ether–water. Protonation takes place at the nitro­gen atom of the primary amino group. In the crystal, N—H⋯O hydrogen bonds (water and methyl­sulfate anion) and inter­molecular N—H⋯N inter­actions involving the sulfonamide and isoxazole nitro­gen atoms, link the components into a tri-dimensional network, additional cohesion being provided by face-to-face π–π inter­actions between the phenyl rings of adjacent mol­ecules. A Hirshfeld surface analysis was used to verify the contributions of the different inter­molecular inter­actions, showing that the three most important contributions for the crystal packing are from H⋯O (54.1%), H⋯H (29.2%) and H⋯N (5.0%) inter­actions.




c

8-Hy­droxy­quinolinium tri­chlorido­(pyridine-2,6-di­carb­oxy­lic acid-κ3O,N,O')copper(II) dihydrate

The title compound, (C9H8NO)[CuCl3(C7H5NO4)]·2H2O, was prepared by reacting CuII acetate dihydrate, solid 8-hy­droxy­quinoline (8-HQ), and solid pyridine-2,6-di­carb­oxy­lic acid (H2pydc), in a 1:1:1 molar ratio, in an aqueous solution of dilute hydro­chloric acid. The CuII atom exhibits a distorted CuO2NCl3 octa­hedral geometry, coordinating two oxygen atoms and one nitro­gen atom from the tridentate H2pydc ligand and three chloride atoms; the nitro­gen atom and one chloride atom occupy the axial positions with Cu—N and Cu—Cl bond lengths of 2.011 (2) Å and 2.2067 (9) Å, respectively. In the equatorial plane, the oxygen and chloride atoms are arranged in a cis configuration, with Cu—O bond lengths of 2.366 (2) and 2.424 (2) Å, and Cu—Cl bond lengths of 2.4190 (10) and 2.3688 (11) Å. The asymmetric unit contains 8-HQ+ as a counter-ion and two uncoordinated water mol­ecules. The crystal structure features strong O—H⋯O and O—H⋯Cl hydrogen bonds as well as weak inter­actions including C—H⋯O, C—H⋯Cl, Cu—Cl⋯π, and π–π, which result in a three-dimensional network. A Hirshfeld surface analysis indicates that the most important contributions to the crystal packing involving the main residues are from H⋯Cl/Cl⋯H inter­actions, contributing 40.3% for the anion. Weak H⋯H contacts contribute 13.2% for the cation and 28.6% for the anion.




c

Crystal structure and Hirshfeld surface analyses, crystal voids, inter­molecular inter­action energies and energy frameworks of 3-benzyl-1-(3-bromoprop­yl)-5,5-di­phenyl­imidazolidine-2,4-dione

The title mol­ecule, C25H23BrN2O2, adopts a cup shaped conformation with the distinctly ruffled imidazolidine ring as the base. In the crystal, weak C—H⋯O hydrogen bonds and C—H⋯π(ring) inter­actions form helical chains of mol­ecules extending along the b-axis direction that are linked by additional weak C—H⋯π(ring) inter­actions across inversion centres. The Hirshfeld surface analysis of the crystal structure indicates that the most important contributions for the crystal packing are from H⋯H (51.0%), C⋯H/H⋯C (21.3%), Br⋯H/H⋯Br (12.8%) and O⋯H/H⋯O (12.4%) inter­actions. The volume of the crystal voids and the percentage of free space were calculated to be 251.24 Å3 and 11.71%, respectively, showing that there is no large cavity in the crystal packing. Evaluation of the electrostatic, dispersion and total energy frameworks indicate that the stabilization is dominated by the dispersion energy.




c

Crystal structure and supra­molecular features of a host–guest inclusion complex based on A1/A2-hetero-difunctionalized pillar[5]arene

A host–guest supra­molecular inclusion complex was obtained from the co-crystallization of A1/A2-bromo­but­oxy-hy­droxy difunctionalized pillar[5]arene (PilButBrOH) with adipo­nitrile (ADN), C47H53.18Br0.82O10·C6H8N2. The adipo­nitrile guest is stabilized within the electron-rich cavity of the pillar[5]arene host via multiple C—H⋯O and C—H⋯π inter­actions. Both functional groups on the macrocyclic rim are engaged in supra­molecular inter­actions with an adjacent inclusion complex via hydrogen-bonding (O—H⋯N or C—H⋯Br) inter­actions, resulting in the formation of a supra­molecular dimer in the crystal structure.




c

Synthesis and crystal structure of 1H-1,2,4-triazole-3,5-di­amine monohydrate

The title compound, a hydrate of 3,5-di­amino-1,2,4-triazole (DATA), C2H5N5·H2O, was synthesized in the presence of sodium perchlorate. The evaporation of H2O from its aqueous solution resulted in anhydrous DATA, suggesting that sodium perchlorate was required to precipitate the DATA hydrate. The DATA hydrate crystallizes in the P21/c space group in the form of needle-shaped crystals with one DATA and one water mol­ecule in the asymmetric unit. The water mol­ecules form a three-dimensional network in the crystal structure. Hirshfeld surface analysis revealed that 8.5% of the inter­molecular inter­actions originate from H⋯O contacts derived from the incorporation of the water mol­ecules.




c

Synthesis, crystal structure and properties of μ-tetra­thio­anti­monato-bis­[(cyclam)zinc(II)] perchlorate 0.8-hydrate

The reaction of Zn(ClO4)2·6H2O with Na3SbS4·9H2O in a water/aceto­nitrile mixture leads to the formation of the title compound, (μ-tetra­thio­anti­monato-κ2S:S')bis­[(1,4,8,11-tetra­aza­cyclo­tetra­decane-κ4N)zinc(II)] perchlorate 0.8-hydrate, [Zn2(SbS4)(C10H24N4)2]ClO4·0.8H2O or [(Zn-cyclam)2(SbS4)]+[ClO4]−·0.8H2O. The asymmetric unit consists of two crystallographically independent [SbS4]3– anions, two independent perchlorate anions and two independent water mol­ecules as well as four crystallographically independent Zn(cyclam)2+ cations that are located in general positions. Both perchlorate anions and one cyclam ligand are disordered and were refined with a split mode using restraints. The water mol­ecules are partially occupied. Two Zn(cyclam)2+ cations are linked via the [SbS4]3– anions into [Zn2(cyclam)2SbS4]+ cations that are charged-balanced by the [ClO4]− anions. The water mol­ecules of crystallization are hydrogen bonded to the [SbS4]3– anions. The cations, anions and water mol­ecules are linked by N—H⋯O, N—H⋯S and O—H⋯S hydrogen bonds into a three-dimensional network. Powder X-ray diffraction proves that a pure sample had been obtained that was additionally investigated for its spectroscopic properties.




c

Mercury(II) halide complex of cis-[(tBuNH)(Se)P(μ-NtBu)2P(Se)(NHtBu)]

The mercury(II) halide complex [1,3-di-tert-butyl-2,4-bis­(tert-butyl­amino)-1,3,2λ5,4λ5-di­aza­diphosphetidine-2,4-diselone-κ2Se,Se']di­iodido­mercury(II) N,N-di­methyl­formamide monosolvate, [HgI2(C16H38N4P2Se2)]·C3H7NO or (1)HgI2, 2, containing cis-[(tBuNH)(Se)P(μ-NtBu)2P(Se)(NHtBu)] (1) was synthesized and structurally characterized. The crystal structure of 2 confirms the chelation of chalcogen donors to HgI2 with a natural bite angle of 112.95 (2)°. The coordination geometry around mercury is distorted tetra­hedral as indicated by the τ4 geometry index parameter (τ4 = 0.90). In the mercury complex, the exocyclic tert-butyl­amido substituents are arranged in an (endo, endo) fashion, whereas in the free ligand (1), the exocyclic substituents are arranged in an (exo, endo) pattern. Compound 2 displays non-classical N—H⋯O hydrogen-bonding inter­actions with the solvent N,N-di­methyl­formamide. These inter­actions may introduce geometrical distortion and deviation from an ideal geometry. An isostructural HgBr2 analogue containing cis-[(tBuNH)(S)P(μ-NtBu)2P(S)(NHtBu)] was also synthesized and structurally characterized, CIF data for the compound being presented as supporting information.




c

Structure of 2,3,5-tri­phenyl­tetra­zol-3-ium chloride hemi­penta­hydrate

The title hydrated mol­ecular salt, C19H15N4+·Cl−·2.5H2O, has two tri­phenyl­tetra­zolium cations, two chloride anions and five water mol­ecules in the asymmetric unit. The cations differ in the conformations of the phenyl rings with respect to the heterocyclic core, most notably for the C-bonded phenyl ring, for which the N—C—C—C torsion angles differ by 36.4 (3)°. This is likely a result of one cation accepting an O—H⋯N hydrogen bond from a water mol­ecule [O⋯N = 3.1605 (15) Å], while the other cation accepts no hydrogen bonds. In the extended structure, the water mol­ecules are involved in centrosymmetric (H2O)2Cl2 rings as well as (H2O)4 chains. An unusual O—H⋯π inter­action and weak C—H⋯O and C—H⋯Cl hydrogen bonds are also observed.




c

Crystal structure and Hirshfeld surface analysis of (nitrato-κ2O,O')(1,4,7,10-tetra­aza­cyclo­dodecane-κ4N)nickel(II) nitrate

The crystal structure of the title compound, [Ni(C8H20N4)(NO3)]NO3, at room temperature, has monoclinic (P21/n) symmetry. The structure displays inter­molecular hydrogen bonding. The nickel displays a distorted bipyramidal geometry with the symmetric bidentate bonded nitrate occupying an equatorial site. The 1,4,7,10-tetra­aza­cyclo­dodecane (cyclen) backbone has the [4,8] configuration, with three nitro­gen-bound H atoms directed above the plane of the nitro­gen atoms towards the offset nickel atom with the fourth nitro­gen-bound hydrogen directed below from the plane of the nitro­gen atoms. The nitrate anion O atoms are seen to hydrogen bond to the H atoms bound to the N atoms of the ligand.




c

Synthesis, structures and Hirshfeld surface analyses of 2-hy­droxy-N'-methyl­acetohydrazide and 2-hy­droxy-N-methyl­acetohydrazide

The structures of the title compounds 2-hy­droxy-N'-methyl­acetohydrazide, 1, and 2-hy­droxy-N-methyl­acetohydrazide, 2, both C3H8N2O2, as regioisomers differ in the position of the methyl group relative to the N atoms in 2-hy­droxy-acetohydrazide. In the structure of 1, the 2-hy­droxy-acetohydrazide core [OH—C—C(=O)—NH—NH] is almost planar and the methyl group is rotated relative to this plane. As opposed to 1, in the structure of 2 all non-hydrogen atoms lie in the same plane. The hydroxyl and carbonyl groups in structures 1 and 2 are in trans and cis positions, respectively. The methyl amino group and carbonyl group are in the cis position relative to the C—N bond in structure 1, while the amino group and carbonyl group are in the trans position relative to the C—N bond in stucture 2. In the crystal, mol­ecules of 1 are linked by N—H⋯O and O—H⋯N inter­molecular hydrogen bonds, forming layers parallel to the ab crystallographic plane. A Hirshfeld surface analysis showed that the H⋯H contacts dominate the crystal packing with a contribution of 55.3%. The contribution of the H⋯O/O⋯H inter­action is somewhat smaller, amounting to 30.8%. In the crystal, as a result of the inter­molecular O—H⋯O hydrogen bonds, mol­ecules of 2 form dimers, which are linked by N—H⋯O hydrogen bonds and a three-dimensional supra­molecular network The major contributors to the Hirshfeld surface are H⋯H (58.5%) and H⋯O/O⋯H contacts (31.7%).




c

N,N'-Di­benzyl­ethyl­enedi­ammonium dichloride

The isolation and crystalline structure of N,N'-di­benzyl­ethyl­enedi­ammonium dichloride, C16H22N22+·2Cl−, is reported. This was obtained as an unintended product of an attempted Curtius rearrangement that involved benzyl­amine as one of the reagents and 1,2-di­chloro­ethane as the solvent. Part of a series of reactions of a course-based undergraduate research experience (CURE), this was not the intended reaction outcome. The goal of the course was to engage students as active participants in a laboratory experience which applies the foundational techniques of a synthetic organic laboratory, using the Curtius rearrangement as a tool for the assembly of medicinally significant scaffolds. The isolation of the title compound, N,N'-di­benzyl­ethyl­enedi­ammonium dichloride, the result of the 1,2-di­chloro­ethane solvent outcompeting the Curtius iso­cyanate inter­mediate in the reaction with the nucleophilic amine, confirms the importance of conducting research at the undergraduate level where the outcome is not predetermined. The solid-state structure of N,N'-di­benzyl­ethyl­enedi­ammonium dichloride was found to feature an all-trans methyl­ene-ammonium backbone. Strong N—H⋯Cl hydrogen bonds and C—H⋯Cl inter­actions lead to a layered structure with pseudo-translational symmetry emulating a C-centered setting. Different phenyl torsion angles at each end of the mol­ecule enable a more stable packing by allowing stronger hydrogen-bonding inter­actions, leading to a more ordered but lower symmetry and modulated structure in P21/n.




c

The crystal structures determination and Hirshfeld surface analysis of N-(4-bromo-3-meth­oxy­phen­yl)- and N-{[3-bromo-1-(phenyl­sulfon­yl)-1H-indol-2-yl]meth­yl}- derivatives of N-{[3-bromo-1-(phenylsulfon­yl)-1H-indol-

Two new phenyl­sulfonyl­indole derivatives, namely, N-{[3-bromo-1-(phenyl­sulfon­yl)-1H-indol-2-yl]meth­yl}-N-(4-bromo-3-meth­oxy­phen­yl)benzene­sulfonamide, C28H22Br2N2O5S2, (I), and N,N-bis­{[3-bromo-1-(phenyl­sulfon­yl)-1H-indol-2-yl]meth­yl}benzene­sulfonamide, C36H27Br2N3O6S3, (II), reveal the impact of intra­molecular π–π inter­actions of the indole moieties as a factor not only governing the conformation of N,N-bis­(1H-indol-2-yl)meth­yl)amines, but also significantly influencing the crystal patterns. For I, the crystal packing is dominated by C—H⋯π and π–π bonding, with a particular significance of mutual indole–indole inter­actions. In the case of II, the mol­ecules adopt short intra­molecular π–π inter­actions between two nearly parallel indole ring systems [with the centroids of their pyrrole rings separated by 3.267 (2) Å] accompanied by a set of forced Br⋯O contacts. This provides suppression of similar inter­actions between the mol­ecules, while the importance of weak C—H⋯O hydrogen bonding to the packing naturally increases. Short contacts of the latter type [C⋯O = 3.389 (6) Å] assemble pairs of mol­ecules into centrosymmetric dimers with a cyclic R22(13) ring motif. These findings are consistent with the results of a Hirshfeld surface analysis and together they suggest a tool for modulating the supra­molecular behavior of phenyl­sulfonyl­ated indoles.




c

Synthesis and crystal structure of sodium (ethane-1,2-di­yl)bis­[(3-meth­oxy­prop­yl)phosphinodi­thiol­ate] octa­hydrate

The title compound, catena-poly[[tri­aqua­sodium]-di-μ-aqua-[tri­aqua­sodium]-μ-(ethane-1,2-di­yl)bis­[(3-meth­oxy­prop­yl)phosphinodi­thiol­ato]], [Na2(C10H22O2P2S4)(H2O)8]n, crystallizes in the triclinic space group P1. The dianionic [CH3O(CH2)3P(=S)(S—)CH2CH2P(=S)(S—)(CH2)3OCH3]2− ligand fragments are joined by a dicationic [Na2(H2O)8]2+ cluster that includes the oxygen of the meth­oxy­propyl unit of the ligand to form infinite chains.




c

Triclinic polymorph of bis­[2-methyl-3-(pyridin-2-yl)imidazo[1,5-a]pyridin-2-ium] tetra­chloridocadmium(II)

The crystal structure of the title organic–inorganic hybrid salt, (C13H12N3)2[CdCl4], (I), has been reported with four mol­ecules in the asymmetric unit in a monoclinic cell [Vassilyeva et al. (2021). RSC Advances, 11, 7713–7722]. While using two different aldehydes in the oxidative cyclization–condensation involving CH3NH2·HCl to prepare a new monovalent cation with the imidazo[1,5-a]pyridinium skeleton, a new polymorph was obtained for (I) in space group P1 and a unit cell with approximately half the volume of the monoclinic form. The structural configurations of the two crystallographically non-equivalent organic cations as well as the geometry of the moderately distorted tetra­hedral CdCl42– dianion show minor changes. In the crystal, identically stacked cations and tetra­chloro­cadmate anions form separate columns parallel to the a axis. The loose packing of the anions leads to a minimal separation of approximately 9.53 Å between the metal atoms in the triclinic form versus 7.51 Å in the monoclinic one, indicating that the latter is packed slightly more densely. The two forms also differ by aromatic stacking motifs. Similar to the monoclinic polymorph, the triclinic one excited at 364 nm shows an intense unsymmetrical photoluminescent band with maximum at 403 nm and a full width at half maximum of 51 nm in the solid state.




c

Crystal structure of a hydrogen-bonded 2:1 co-crystal of 4-nitro­phenol and 4,4'-bi­pyridine

In the title compound, C10H8N2·2C6H5NO3, 4-nitro­phenol and 4,4'-bi­pyridine crystallized together in a 2:1 ratio in the space group P21/n. There is a hydrogen-bonding inter­action between the nitro­gen atoms on the 4,4'-bi­pyridine mol­ecule and the hydrogen atom on the hydroxyl group on the 4-nitro­phenol, resulting in trimolecular units. This structure is a polymorph of a previously reported structure [Nayak & Pedireddi (2016). Cryst. Growth Des. 16, 5966–5975], which differs mainly due to a twist in the 4,4'-bi­pyridine mol­ecule.




c

Synthesis, crystal structure and absolute configuration of (3aS,4R,5S,7aR)-7-(but-3-en-1-yn-1-yl)-2,2-dimethyl-3a,4,5,7a-tetra­hydro-2H-1,3-benzodioxole-4,5-diol

The absolute configuration of the title compound, C13H16O4, determined as 1S,2R,3S,4R based on the synthetic pathway, was confirmed by single-crystal X-ray diffraction. The mol­ecule is a relevant inter­mediary for the synthesis of speciosins, ep­oxy­quinoides or their analogues. The mol­ecule contains fused five- and six-membered rings with two free hydroxyl groups and two protected as an iso­propyl­idenedioxo ring. The packing is directed by hydrogen bonds that define double planes of mol­ecules laying along the ab plane and van der Waals inter­actions between aliphatic chains that point outwards of the planes.




c

Crystal structures of two different multi-component crystals consisting of 1-(3,4-di­meth­oxy­benz­yl)-6,7-di­meth­oxy­iso­quinoline and fumaric acid

Two different multi-component crystals consisting of papaverine [1-(3,4-di­meth­oxy­benz­yl)-6,7-di­meth­oxy­iso­quinoline, C20H21NO4] and fumaric acid [C4H4O4] were obtained. Single-crystal X-ray structure analysis revealed that one, C20H21NO4·1.5C4H4O4 (I), is a salt co-crystal composed of salt-forming and non-salt-forming mol­ecules, and the other, C20H21NO4·0.5C4H4O4 (II), is a salt–co-crystal inter­mediate (i.e., in an inter­mediate state between a salt and a co-crystal). In this study, one state (crystal structure at 100 K) within the salt–co-crystal continuum is defined as the ‘inter­mediate’.




c

Crystal structure of (μ2-7-{[bis­(pyridin-2-ylmeth­yl)amino-1κ3N,N',N'']meth­yl}-5-chloro­quinolin-8-olato-2κN;1:2κ2O)tri­chlorido-1κCl,2κ2Cl-dizinc(II)

The title compound, [Zn2(C22H18ClN4O)Cl3], is a dinuclear zinc(II) complex with three chlorido ligands and one penta­dentate ligand containing quinolin-8-olato and bis­(pyridin-2-ylmeth­yl)amine groups. One of the two ZnII atom adopts a tetra­hedral geometry and coordinates two chlorido ligands with chelate coord­ination of the N and O atoms of the quinolin-8-olato group in the ligand. The other ZnII atom adopts a distorted trigonal–bipyramidal geometry, and coordinates one chlorido-O atom of the quinolin-8-olato group and three N atoms of the bis­(pyridin-2-ylmeth­yl)amine unit. In the crystal, two mol­ecules are associated through a pair of inter­molecular C—H⋯Cl hydrogen bonds, forming a dimer with an R22(12) ring motif. Another inter­molecular C—H⋯Cl hydrogen bond forms a spiral C(8) chain running parallel to the [010] direction. The dimers are linked by these two inter­molecular C—H⋯Cl hydrogen bonds, generating a ribbon sheet structure in ac plane. Two other inter­molecular C—H⋯Cl hydrogen bonds form a C(7) chain along the c-axis direction and another C(7) chain generated by a d-glide plane. The mol­ecules are cross-linked through the four inter­molecular C—H⋯Cl hydrogen bonds to form a three-dimensional network.




c

Crystal structure of N,N',N''-tri­cyclo­prop­ylbenzene-1,3,5-tricarboxamide

The title compound, C18H21N3O3, was prepared from 1,3,5-benzene­tricarbonyl trichloride and cyclo­propyl­amine. Its crystal structure was solved in the monoclinic space group P21/c. In the crystal, the three amide groups of the mol­ecule are inclined at angles of 26.5 (1), 36.9 (1) and 37.8 (1)° with respect to the plane of the benzene ring. The mol­ecules are linked by N—H⋯O hydrogen bonds, forming two-dimensional supra­molecular aggregates that extend parallel to the crystallographic ab plane and are further connected by C—H⋯O contacts. As a result of the supra­molecular inter­actions, a propeller-like conformation of the title mol­ecule can be observed.




c

Crystal structure of catena-poly[[di­aqua­di­imida­zole­cobalt(II)]-μ2-2,3,5,6-tetra­bromo­benzene-1,4-di­carboxyl­ato]

The asymmetric unit of the title compound, [Co(C8Br4O4)(C3H4N2)2(H2O)2]n or [Co(Br4bdc)(im)2(H2O)2]n, comprises half of CoII ion, tetra­bromo­benzene­dicarboxylate (Br4bdc2−), imidazole (im) and a water mol­ecule. The CoII ion exhibits a six-coordinated octa­hedral geometry with two oxygen atoms of the Br4bdc2− ligand, two oxygen atoms of the water mol­ecules, and two nitro­gen atoms of the im ligands. The carboxyl­ate group is nearly perpendicular to the benzene ring and shows monodentate coordination to the CoII ion. The CoII ions are bridged by the Br4bdc2− ligand, forming a one-dimensional chain. The carboxyl­ate group acts as an inter­molecular hydrogen-bond acceptor toward the im ligand and a coordinated water mol­ecule. The chains are connected by inter­chain N—H⋯O(carboxyl­ate) and O—H(water)⋯O(carboxyl­ate) hydrogen-bonding inter­actions and are not arranged in parallel but cross each other via inter­chain hydrogen bonding and π–π inter­actions, yielding a three-dimensional network.




c

Crystal structure, Hirshfeld surface analysis, and DFT and mol­ecular docking studies of 6-cyanona­phthalen-2-yl 4-(benz­yloxy)benzoate

In the title compound, C25H17NO3, the torsion angle associated with the phenyl benzoate group is −173.7 (2)° and that for the benz­yloxy group is −174.8 (2)° establishing an anti-type conformation. The dihedral angles between the ten-membered cyanona­phthalene ring and the aromatic ring of the phenyl benzoate and the benz­yloxy fragments are 40.70 (10) and 87.51 (11)°, respectively, whereas the dihedral angle between the aromatic phenyl benzoate and the benz­yloxy fragments is 72.30 (13)°. In the crystal, the mol­ecules are linked by weak C—H⋯O inter­actions forming S(4) chains propagating parallel to [010]. The packing is consolidated by three C—H⋯π inter­actions and two π–π stacking inter­actions between the aromatic rings of naphthalene and phenyl benzoate with centroid-to-centroid distances of 3.9698 (15) and 3.8568 (15) Å, respectively. Inter­molecular inter­actions were qu­anti­fied using Hirshfeld surface analysis. The mol­ecular structure was further optimized by density functional theory (DFT) at the B3LYP/6–311+ G(d,p) level, revealing that the energy gap between HOMO and LUMO is 3.17 eV. Mol­ecular docking studies were carried out for the title compound as a ligand and SARS-Covid-2(PDB ID:7QF0) protein as a receptor giving a binding affinity of −9.5 kcal mol−1.




c

Crystal structure of an aceto­nitrile solvate of 2-(3,4,5-triphen­ylphen­yl)acetic acid

Crystal growth of 2-(3,4,5-triphen­ylphen­yl)acetic acid (1) from aceto­nitrile yields a monosolvate, C26H20O2·CH3CN, of the space group P1. In the crystal, the title mol­ecule adopts a conformation in which the three phenyl rings are arranged in a paddlewheel-like fashion around the central arene ring and the carboxyl residue is oriented nearly perpendicular to the plane of this benzene ring. Inversion-symmetric dimers of O—H⋯O-bonded mol­ecules of 1 represent the basic supra­molecular entities of the crystal structure. These dimeric mol­ecular units are further linked by C—H⋯O=C bonds to form one-dimensional supra­molecular aggregates running along the crystallographic [111] direction. Weak Car­yl—H⋯N inter­actions occur between the mol­ecules of 1 and aceto­nitrile.




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Synthesis and crystal structure of 1,3,5-tris­[(1H-benzotriazol-1-yl)meth­yl]-2,4,6-tri­ethyl­benzene

In the crystal structure of the title compound, C33H33N9, the tripodal mol­ecule exists in a conformation in which the substituents attached to the central arene ring are arranged in an alternating order above and below the ring plane. The three benzotriazolyl moieties are inclined at angles of 88.3 (1), 85.7 (1) and 82.1 (1)° with respect to the mean plane of the benzene ring. In the crystal, only weak mol­ecular cross-linking involving C—H⋯N hydrogen bonds is observed.




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Crystal structure of [Ni(OH2)6]Cl2·(18-crown-6)2·2H2O

The crystal structure of the title compound, hexa­aqua­nickel(II) dichloride–1,4,7,10,13,16-hexa­oxa­cyclo­octa­deca­ne–water (1/2/2), [Ni(H2O)6]Cl2·2C12H24O6·2H2O, is reported. The asymmetric unit contains half of the Ni(OH2)6 moiety with a formula of C12H32ClNi0.50O10 at 105 K and triclinic (P1) symmetry. The [Ni(OH2)6]2+ cation has close to ideal octa­hedral geometry with O—Ni—O bond angles that are within 3° of idealized values. The supra­molecular structure includes hydrogen bonding between the water ligands, 18-crown-6 mol­ecules, Cl− anions, and co-crystallized water solvent. Two crown ether mol­ecules flank the [Ni(OH2)6]2+ mol­ecule at the axial positions in a sandwich-like structure. The relatively symmetric hydrogen-bonding network is enabled by small Cl− counter-ions and likely influences the more idealized octa­hedral geometry of [Ni(OH2)6]2+.




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Synthesis and structure of trans-2,5-di­methyl­piperazine-1,4-diium di­hydrogen diphosphate

In the title salt, C6H16N22+ ·H2P2O72−, the complete dication is generated by a crystallographic centre of symmetry with the methyl groups in equatorial orientations. The complete dianion is generated by a crystallographic twofold axis with the central O atom lying on the axis: the P—O—P bond angle is 135.50 (12)°. In the crystal, the di­hydrogen diphosphate anions are linked by O—H⋯O hydrogen bonds, generating (001) layers. The organic cations bond to the inorganic layers by way of N—H⋯O and C—H⋯O hydrogen bonds. A Hirshfeld surface analysis shows that the most important contributions for the crystal packing are from O⋯H/H⋯O (60.5%) and H⋯H (39.4%) contacts.




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Structural multiplicity in a solvated hydrate of the anti­retroviral protease inhibitor Lopinavir

Lopinavir is a potent protease inhibitor that is used as a first-line pharmaceutical drug for the treatment of HIV. The multi-component solvated Lopinavir crystal, systematic name (2S)-N-[(2S,4S,5S)-5-[2-(2,6-di­methyl­phen­oxy)acetamido]-4-hy­droxy-1,6-di­phenyl­hexan-2-yl]-3-methyl-2-(2-oxo-1,3-diazinan-1-yl)butanamide–ethane-1,2-diol–water (8/3/7) 8C37H48N4O5·3C2H6O2·7H2O, was prepared using evaporative methods. The crystalline material obtained from this experimental synthesis was characterized and elucidated by single-crystal X-ray diffraction (SC-XRD). The crystal structure is unusual in that the unit cell contains 18 mol­ecules. The stoichiometric ratio of this crystal is eight Lopinavir mol­ecules [8(C37H48N4O5)], three ethane-1,2-diol mol­ecules [3(C2H6O2)] and seven water mol­ecules [7(H2O)]. The crystal packing features both bi- and trifurcated hydrogen bonds between atoms.




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Synthesis, crystal structure and Hirshfeld surface analysis of 2-{4-[(2-chloro­phen­yl)meth­yl]-3-methyl-6-oxopyridazin-1-yl}-N-phenyl­acetamide

In the title mol­ecule, C20H18ClN3O2, the 2-chloro­phenyl group is disordered to a small extent [occupancies 0.875 (2)/0.125 (2)]. The phenyl­acetamide moiety is nearly planar due to a weak, intra­molecular C—H⋯O hydrogen bond. In the crystal, N—H⋯O hydrogen bonds and π-stacking inter­actions between pyridazine and phenyl rings form helical chains of mol­ecules in the b-axis direction, which are linked by C—H⋯O hydrogen bonds and C—H⋯π(ring) inter­actions. A Hirshfeld surface analysis was performed, which showed that H⋯H, C⋯H/H⋯C and O⋯H/H⋯O inter­actions to dominate the inter­molecular contacts in the crystal.




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Crystal structures and photophysical properties of mono- and dinuclear ZnII complexes flanked by tri­ethyl­ammonium

Two new zinc(II) complexes, tri­ethyl­ammonium di­chlorido­[2-(4-nitro­phen­yl)-4-phenyl­quinolin-8-olato]zinc(II), (C6H16N){Zn(C21H13N2O3)Cl2] (ZnOQ), and bis­(tri­ethyl­ammonium) {2,2'-[1,4-phenyl­enebis(nitrilo­methyl­idyne)]diphenolato}bis­[di­chlorido­zinc(II)], (C6H16N)2[Zn2(C20H14N2O2)Cl4] (ZnBS), were synthesized and their structures were determined using ESI–MS spectrometry, 1H NMR spectroscopy, and single-crystal X-ray diffraction. The results showed that the ligands 2-(4-nitro­phen­yl)-4-phenyl­quinolin-8-ol (HOQ) and N,N'-bis­(2-hy­droxy­benzyl­idene)benzene-1,4-di­amine (H2BS) were deprotonated by tri­ethyl-amine, forming the counter-ion Et3NH+, which inter­acts via an N—H⋯O hydrogen bond with the ligand. The ZnII atoms have a distorted trigonal–pyramidal (ZnOQ) and distorted tetra­hedral (ZnBS) geometries with a coord­ination number of four, coordinating with the ligands via N and O atoms. The N atoms coordinating with ZnII correspond to the heterocyclic nitro­gen for the HOQ ligand, while for the H2BS ligand, it is the nitro­gen of the imine (CH=N). The crystal packing of ZnOQ is characterized by C—H⋯π inter­actions, while that of ZnBS by C—H⋯Cl inter­actions. The emission spectra showed that ZnBS complex exhibits green fluorescence in the solid state with a small band-gap energy, and the ZnOQ complex does exhibit non-fluorescence.




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Crystal structure and Hirshfeld surface analysis of the salt 2-iodo­ethyl­ammonium iodide – a possible side product upon synthesis of hybrid perovskites

The title organic–inorganic hybrid salt, C2H7IN+·I−, is isotypic with its bromine analog, C2H7BrN+·Br− [Semenikhin et al. (2024). Acta Cryst. E80, 738–741]. Its asymmetric unit consists of one 2-iodo­ethyl­ammonium cation and one iodide anion. The NH3+ group of the organic cation forms weak hydrogen bonds with four neighboring iodide anions, leading to the formation of supra­molecular layers propagating parallel to the bc plane. Hirshfeld surface analysis reveals that the most important contribution to the crystal packing is from N—H⋯I inter­actions (63.8%). The crystal under investigation was twinned by a 180° rotation around [001].




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Crystal structure of bis­{5-(4-chloro­phen­yl)-3-[6-(1H-pyrazol-1-yl)pyridin-2-yl]-1H-1,2,4-triazol-1-ido}nickel(II) methanol disolvate

The unit cell of the title compound, [Ni(C16H10ClN6)2]·2CH3OH, consists of a neutral complex and two methanol mol­ecules. In the complex, the two tridentate 2-(3-(4-chloro­phen­yl)-1H-1,2,4-triazol-5-yl)-6-(1H-pyrazol-1-yl)pyridine ligands coordinate to the central NiII ion through the N atoms of the pyrazole, pyridine and triazole groups, forming a pseudo­octa­hedral coordination sphere. Neighbouring tapered mol­ecules are linked through weak C—H(pz)⋯π(ph) inter­actions into monoperiodic chains, which are further linked through weak C—H⋯N/C inter­actions into diperiodic layers. The inter­molecular contacts were qu­anti­fied using Hirshfeld surface analysis and two-dimensional fingerprint plots, revealing the relative contributions of the contacts to the crystal packing to be H⋯H 32.8%, C⋯H/H⋯C 27.5%, N⋯H/H⋯N 15.1%, and Cl⋯H/H⋯Cl 14.0%. The average Ni—N bond distance is 2.095 Å. Energy framework analysis at the HF/3–21 G theory level was performed to qu­antify the inter­action energies in the crystal structure.




c

The cadmium oxidotellurates(IV) Cd5(TeO3)4(NO3)2 and Cd4Te5O14

Monoclinic single crystals of Cd5(TeO3)4(NO3)2 (space group P21/c), penta­cadmium tetra­kis­[oxidotellurate(IV)] dinitrate, and of Cd4Te5O14 (space group C2/c), tetra­cadmium penta­oxidotellurate(IV), were obtained under the same hydro­thermal conditions. Whereas the crystal structure of Cd5(TeO3)4(NO3)2 is distinctively layered, that of Cd4Te5O14 exhibits a tri-periodic framework. In Cd5(TeO3)4(NO3)2, the three CdII atoms have coordination numbers (CN) of 7, 6 and 6. The two types of [CdO6] and the [CdO7] polyhedra [bond lengths range from 2.179 (3) to 2.658 (2) Å] share corners and edges, resulting in layers extending parallel to (100). Both TeIV atoms are coordinated by three oxygen atoms in a trigonal–pyramidal shape. The oxygen atoms of the isolated [TeO3] groups [bond lengths range from 1.847 (3) to 1.886 (3) Å] all are part of the cadmium–oxygen layer. The electron lone pairs ψ of the TeIV atoms are directed away from the layer on both sides. The available inter­layer space is co-occupied by the nitrate group, which is directly connected with two of its O atoms to the layer whereas the third O atom is solely bonded to the N atom and points towards the adjacent layer. In Cd4Te5O14, all three unique CdII atoms are coordinated by six oxygen atoms, considering Cd—O distances from 2.235 (2) to 2.539 (2) Å. By edge- and corner-sharing, the distorted [CdO6] polyhedra form an open framework that is partially filled with three different stereochemically active TeIV atoms. All of them exhibit a CN of 4, with Te—O bonds in a range from 1.859 (2) to 2.476 (2) Å. The corresponding [TeO4] units are linked to each other by corner- and edge-sharing, forming infinite helical 1∞[Te10O28] chains extending parallel to [203]. The connectivity in the chains can be described as (⋯–⋄–⋄=⋄–⋄–⋄–⋄–⋄=⋄–⋄–⋄–⋯)n where ‘⋄’ denotes a [TeO4] unit, ‘–’ a linkage via corners and ‘=’ a linkage via edges. Such a structural motif is unprecedented in the crystal chemistry of oxidotellurate(IV) compounds.




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Crystal structure and Hirshfeld surface analysis of bis­(benzoyl­acetonato)(ethanol)dioxidouranium(VI)

A new uranium metal–organic complex salt, [U(C10H9O2)2O2(C2H6O)], with benzoyl acetone, namely, bis­(benzoyl­acetonato)(ethanol)dioxidouranium(VI), was synthesized. The compound has monoclinic P21/n symmetry. The geometry of the seven-coordinate U atom is penta­gonal bipyramidal, with the uranyl oxygen atoms in apical positions. In the complex, the ligands bind to the metal through oxygen atoms. Additional weak O—H⋯O contacts between the cations and anions consolidate the three-dimensional arrangement of the structure. On the Hirshfeld surface, the largest contributions come from the short contacts such as van der Waals forces, including H⋯H, O⋯H and C⋯H. Inter­actions including C⋯C and O⋯C contacts were also observed; however, their contribution to the overall cohesion of the crystal structure is minor. A packing analysis was performed to check the strength of the crystal packing.




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Synthesis and structure of penta­kis­(2-aminopyridinium) nona­vanado(V)tellurate(VI)

In the title compound, (C5H7N2)5[TeV9O28], the tellurium and vanadium atoms are statistically disordered over two of the ten metal-atom sites in the [TeV9O28]5– heteropolyanion. The anions stack along [100] and are extended into a three-dimensional supra­molecular network through N—H⋯O and weak C—H⋯O hydrogen bonds involving the self-assembled 2-amino­pyridinium penta­mers, which are linked by C—H⋯π and π–π stacking inter­actions. The most important contributions to the Hirshfeld surface arise from O⋯H/H⋯O (54.8%), H⋯H (17.8%) and C⋯H/H⋯C (13.4%) contacts.




c

Multi-segment cooling design of a reflection mirror based on the finite-element method

Through numerical optimization of cooling lengths and cooling groove positions for the first reflection mirror of a free-electron laser [OK?], the root mean square of the height error of the mirror's thermal deformation was minimized. The optimized mirror design effectively mitigated stray light and enhanced the peak intensity of the focus spot at the sample, thereby enhancing the optical performance of the high-heat-load mirror under high repetition rates at beamline FEL-II of the SHINE facility.




c

Hard X-ray single-shot spectrometer of PAL-XFEL

A hard X-ray single-shot spectrometer comprising thin, bent Si crystals has been developed for the Pohang Accelerator Laboratory X-ray Free-Electron Laser (XFEL), for detailed analysis of ultrafast 4.5–17 keV XFEL pulses with a high spectral resolution. This instrument facilitates shot-to-shot spectral structure monitoring and optimization of the operating conditions of the XFEL owing to its ability to provide comprehensive data on the spectral properties and fluctuations of self-amplified spontaneous emission, monochromatic and seeded XFEL modes.




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Reducing heat load density with asymmetric and inclined double-crystal monochromators: principles and requirements revisited

The major principles and requirements of asymmetric and inclined double-crystal monochromators are re-examined and presented to guide their design and development for significantly reducing heat load density and gradient on the monochromators of fourth-generation synchrotron light sources and X-ray free-electron lasers.




c

Development of MHz X-ray phase contrast imaging at the European XFEL

The development of instrumentation as well as applications for megahertz X-ray phase contrast imaging at the Single Particles, Clusters, and Biomolecules and Serial Femtosecond Crystallography instrument of the European XFEL are introduced here.




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Review and experimental comparison of speckle-tracking algorithms for X-ray phase contrast imaging

This review focuses on low-dose near-field X-ray speckle phase imaging in the differential mode introducing the existing algorithms with their specifications and comparing their performances under various experimental conditions.




c

The use of ethanol as contrast enhancer in Synchrotron X-ray phase-contrast imaging leads to heterogeneous myocardial tissue shrinkage: a case report

In this work, we showed that the use of ethanol to increase image contrast when imaging cardiac tissue with synchrotron X-ray phase-contrast imaging (X-PCI) leads to heterogeneous tissue shrinkage, which has an impact on the 3D organization of the myocardium.




c

Development and testing of a dual-frequency, real-time hardware feedback system for the hard X-ray nanoprobe beamline of the SSRF

we introduce a novel approach for a real-time dual-frequency feedback system, which has been firstly used at the hard X-ray nanoprobe beamline of SSRF. The BiBEST can then efficiently stabilize X-ray beam position and stability in parallel, making use of different optical systems in the beamline.




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Enhancing the Efficiency of a Wavelength-Dispersive Spectrometer based upon a Slit-less Design Using a Single-Bounce Monocapillary

A slit-less wavelength-dispersive spectrometer design using a single-bounce monocapillary that aligns the sample on the Rowland circle, enhancing photon throughput and maintaining resolution. The compact design supports flexibility and reconfiguration in facilities without complex beamline infrastructure, significantly improving detection efficiency.




c

Form factor of helical structures and twisted fibres

A general formalism is presented for the isotropically averaged single-chain scattering function (form factor) of single, double, triple and higher-order helices, as well as twisted fibres consisting of concentric layers of strands. Form factors for double and triple helices with differently sized grooves have also been derived. The formulas include the longitudinal and transverse interference over the pitch and radius of the helices, respectively. The results may be useful for the analysis of small-angle scattering data of (bio)macromolecules or molecular assemblies exhibiting a helical arrangement.




c

(U)SAXS characterization of porous microstructure of chert: insights into organic matter preservation

This study characterizes the microstructure and mineralogy of 132 (ODP sample), 1000 and 1880 million-year-old chert samples. By using ultra-small-angle X-ray scattering (USAXS), wide-angle X-ray scattering and other techniques, the preservation of organic matter (OM) in these samples is studied. The scarce microstructural data reported on chert contrast with many studies addressing porosity evolution in other sedimentary rocks. The aim of this work is to solve the distribution of OM and silica in chert by characterizing samples before and after combustion to pinpoint the OM distribution inside the porous silica matrix. The samples are predominantly composed of alpha quartz and show increasing crystallite sizes up to 33 ± 5 nm (1σ standard deviation or SD). In older samples, low water abundances (∼0.03%) suggest progressive dehydration. (U)SAXS data reveal a porous matrix that evolves over geological time, including, from younger to older samples, (1) a decreasing pore volume down to 1%, (2) greater pore sizes hosting OM, (3) decreasing specific surface area values from younger (9.3 ± 0.1 m2 g−1) to older samples (0.63 ± 0.07 m2 g−1, 1σ SD) and (4) a lower background intensity correlated to decreasing hydrogen abundances. The pore-volume distributions (PVDs) show that pores ranging from 4 to 100 nm accumulate the greater volume fraction of OM. Raman data show aromatic organic clusters up to 20 nm in older samples. Raman and PVD data suggest that OM is located mostly in mesopores. Observed structural changes, silica–OM interactions and the hydro­phobicity of the OM could explain the OM preservation in chert.




c

Time-resolved high-energy X-ray diffraction studies of ultrathin Ni ferrite films on MgO(001)

Time-resolved high-energy X-ray diffraction was used during growth of ultrathin NixFe3−xO4 films with varying Ni content (0 ≤ x ≤ 1.5) deposited on MgO(001) substrates by reactive molecular beam epitaxy, providing an insight into the growth dynamics of these films. In order to obtain structural information, reciprocal-space maps were recorded and the temporal evolution of the Bragg peaks specific to the octahedral and tetrahedral lattice sites of the inverse spinel structure of NixFe3−xO4 was observed during growth of the films. A time delay, corresponding to a coverage of 1.2–1.8 nm, between the appearance of the Bragg reflections originating from octahedral sites and reflections originating exclusively from tetrahedral sites indicates that the ferrite films grow in two stages. In the initial growth phase, a rock salt interface layer is formed. Afterwards, a structural transition occurs and the films grow in an inverse spinel structure. The thickness of the initial rock salt phase was found to increase with Ni content and to be responsible for atypical strain in the thin films. Films with Ni contents x > 1 do not show a structural transition. These films remain in a (deficient) rock salt structure consisting of a mixed Ni–Fe oxide and do not form a spinel structure at all. They show an increased number of NiO clusters as detected by X-ray photoelectron spectroscopy of the valence band, accompanied by a significant roughening of the films.




c

Texture measurements on quartz single crystals to validate coordinate systems for neutron time-of-flight texture analysis

In crystallographic texture analysis, ensuring that sample directions are preserved from experiment to the resulting orientation distribution is crucial to obtain physical meaning from diffraction data. This work details a procedure to ensure instrument and sample coordinates are consistent when analyzing diffraction data with a Rietveld refinement using the texture analysis software MAUD. A quartz crystal is measured on the HIPPO diffractometer at Los Alamos National Laboratory for this purpose. The methods described here can be applied to any diffraction instrument measuring orientation distributions in polycrystalline materials.




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An electropneumatic cleaning device for piezo-actuator-driven picolitre-droplet dispensers

Recently, we introduced the liquid application method for time-resolved analyses (LAMA). The time-consuming cleaning cycles required for the substrate solution exchange and storage of the sensitive droplet-dispenser nozzles present practical challenges. In this work, a dispenser cleaning system for the semi-automated cleaning of the piezo-actuator-driven picolitre-droplet dispensers required for LAMA is introduced to streamline typical workflows.




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Van Vleck analysis of angularly distorted octahedra using VanVleckCalculator

Van Vleck modes describe all possible displacements of octahedrally coordinated ligands about a core atom. They are a useful analytical tool for analysing the distortion of octahedra, particularly for first-order Jahn–Teller distortions, but determination of the Van Vleck modes of an octahedron is complicated by the presence of angular distortion of the octahedron. This problem is most commonly resolved by calculating the bond distortion modes (Q2, Q3) along the bond axes of the octahedron, disregarding the angular distortion and losing information on the octahedral shear modes (Q4, Q5 and Q6) in the process. In this paper, the validity of assuming bond lengths to be orthogonal in order to calculate the Van Vleck modes is discussed, and a method is described for calculating Van Vleck modes without disregarding the angular distortion. A Python package for doing this, VanVleckCalculator, is introduced and some examples of its use are given. Finally, it is shown that octahedral shear and angular distortion are often, but not always, correlated, and a parameter η is proposed as the shear fraction. It is demonstrated that η can be used to predict whether the values will be correlated when varying a tuning parameter such as temperature or pressure.