Merohedral Twinning Research Articles

Temperature dependence of incommensurate modulation in Ca0.28Ba0.72Nb2O6

We present an electron microscopy and diffraction study of a CaxBa1−xNb2O6 ceramic with x=0.28 (CBN28), a ferroelectric material with a partially filled tetragonal tungsten-bronze structure. The microstructure has strong similarities to that of SrxBa1−xNb2O6, with an average orthorhombic symmetry and an intimate intermixture of merohedral twin variants at a length scale of tens of nanometers. Superstructure spots in diffraction patterns are displaced by a one-dimensional incommensurate modulation, characterized by a propagation vector δδ0. Heating experiments show that δ is strongly coupled to ferroelectric polarization, decreasing as 180° ferroelectric domains become more finely spaced and needle-like as the Curie temperature TC is approached during heating and increasing once more above TC. No change in symmetry is observed at TC, consistent with a transition from ferroelectric to antiferroelectric (or ferrielectric) relaxor properties. The superstructure spots and incommensurate modulation disappear ∼250°C above TC, consistent with polar regions in the material becoming fully transient.

Symmetry-based requirement for the measurement of electrical and thermal Hall conductivity under an in-plane magnetic field

The in-plane (thermal) Hall effect is an unconventional transverse response when the applied magnetic field is in the (heat) current plane. In contrast to the normal Hall effect, the in-plane Hall effect requires the absence of certain crystal symmetries, and possibly manifests a non-trivial topology of quantum materials. An accurate estimation of the intrinsic in-plane (thermal) Hall conductivity is crucial to identify the underlying mechanisms as in the case of the Kitaev spin-liquid candidate alpha-RuCl3. Here, we give the symmetry conditions for the in-plane Hall effect and discuss the implications that may impede the experimental evaluation of the in-plane (thermal) Hall conductivity within the single-device measurement. First, the lack of symmetry in crystals can create merohedral twin domains that cancel the total Hall signal. Second, even in a twin-free crystal, the intrinsic response is potentially contaminated by the out-of-plane conduction in three-dimensional systems, which is systematically unavoidable in the in-plane Hall systems. Third, even in a quasi-two-dimensional system, the conversion of (thermal) resistivity, rho (lambda), to (thermal) conductivity, sigma (kappa) requires protocols beyond the widely-used simplified formula due to the lack of in-plane-rotational symmetry. In principle, two independent sample devices are necessary to accurately estimate the s_xy (k_xy). As a case study, we discuss the half-integer quantization of the in-plane thermal Hall effect in the spin-disordered state of alpha-RuCl3. For an accurate measurement of the thermal Hall effect, it is necessary to avoid crystals with the merohedral twins contributing oppositely to k_xy, while the out-of-plane transport may have a negligible effect. To deal with the field-induced rotational-symmetry breaking, we propose two symmetry-based protocols, improved single-device and two-device methods.

Atomically Sharp Internal Interface in a Chiral Weyl Semimetal Nanowire

Internal interfaces in Weyl semimetals (WSMs) are predicted to host distinct topological features that are different from the commonly studied external interfaces (crystal-to-vacuum boundaries). However, the lack of atomically sharp and crystallographically oriented internal interfaces in WSMs makes it difficult to experimentally investigate topological states buried inside the material. Here, we study a unique internal interface known as merohedral twin boundary in chemically synthesized single-crystal nanowires (NWs) of CoSi, a chiral WSM of space group P213 (No. 198). Scanning transmission electron microscopy reveals that this internal interface is a (001) twin plane which connects two enantiomeric counterparts at an atomically sharp interface with inversion twinning. Ab initio calculations show localized internal Fermi arcs at the (001) twin plane that can be clearly distinguished from both external Fermi arcs and bulk states. These merohedrally twinned CoSi NWs provide an ideal platform to explore topological properties associated with internal interfaces in WSMs.

Ring Silicates Cs4Tm2[Si4O12](OH)2 and Cs4(Tm,Tb)2[Si4O12](OH)2 As Merohedral Twins

New ring silicates Cs4Tm2[Si4O12](OH)2 and Cs4(Tm,Tb)2[Si4O12](OH)2 have been synthesized by the hydrothermal method. A structural analogy is revealed between them and the previously studied silicates K4Sc2(OH)2(Si4O12) and K2Sc[Si2O6]F. Their crystal structures are identified as orthorhombic merohedral twins by the lost element of tetragonal symmetry. The structures of new ring silicates are related to those of fresnoite and tetragonal melilite.

The tetrameric structure of the novel haloalkane dehalogenase DpaA from Paraglaciecola agarilytica NO2.

Haloalkane dehalogenases (EC 3.8.1.5) are microbial enzymes that catalyse the hydrolytic conversion of halogenated compounds, resulting in a halide ion, a proton and an alcohol. These enzymes are used in industrial biocatalysis, bioremediation and biosensing of environmental pollutants or for molecular tagging in cell biology. The novel haloalkane dehalogenase DpaA described here was isolated from the psychrophilic and halophilic bacterium Paraglaciecola agarilytica NO2, which was found in marine sediment collected from the East Sea near Korea. Gel-filtration experiments and size-exclusion chromatography provided information about the dimeric composition of the enzyme in solution. The DpaA enzyme was crystallized using the sitting-drop vapour-diffusion method, yielding rod-like crystals that diffracted X-rays to 2.0 Å resolution. Diffraction data analysis revealed a case of merohedral twinning, and subsequent structure modelling and refinement resulted in a tetrameric model of DpaA, highlighting an uncommon multimeric nature for a protein belonging to haloalkane dehalogenase subfamily I.

Crystal structures of three copper(II)-2,2'-bi-pyridine (bpy) compounds, [Cu(bpy)2(H2O)][SiF6]·4H2O, [Cu(bpy)2(TaF6)2] and [Cu(bpy)3][TaF6]2 and a related coordination polymer, [Cu(bpy)(H2O)2SnF6] n.

We report the hydro-thermal syntheses and crystal structures of aqua-bis-(2,2'-bi-pyridine-κ2 N,N')copper(II) hexa-fluorido-silicate tetra-hydrate, [Cu(bpy)2(H2O)][SiF6]·4H2O (bpy is 2,2'-bi-pyridine, C10H8N2), (I), bis-(2,2'-bi-pyridine-3κ2 N,N')-di-μ-fluorido-1:3κ2 F:F;2:3κ2 F:F-deca-fluorido-1κ5 F,2κ5 F-ditantalum(V)copper(II), [Cu(bpy)2(TaF6)2], (II), tris-(2,2'-bi-pyridine-κ2 N,N')copper(II) bis[hexa-fluorido-tantalate(V)], [Cu(bpy)3][TaF6]2, (III), and catena-poly[[di-aqua-(2,2'-bi-pyridine-κ2 N,N')copper(II)]-μ-fluorido-tetra-fluorido-tin-μ-fluorido], [Cu(bpy)(H2O)2SnF6] n , (IV). Compounds (I), (II) and (III) contain locally chiral copper coordination complexes with C 2, D 2, and D 3 symmetry, respectively. The extended structures of (I) and (IV) are consolidated by O-H⋯F and O-H⋯O hydrogen bonds. The structure of (III) was found to be a merohedral (racemic) twin.

Polymorphism of bis-(1,3-benzo-thia-zol-2-yl) tri-thio-carbonate.

The polymorphism of the title compound, C15H8N2S5, is reported, in which the (syn,syn) and (syn,anti) conformers simultaneously crystallized from a chloro-form solution. The complete mol-ecule of the (syn,syn) form is generated by a crystallographic twofold axis. The geometries of both conformers are compared in detail, revealing no significant differences in bond lengths, despite different bond angles because of the conformational changes. Analysis of the inter-molecular inter-actions, aided by Hirshfeld surfaces, shows distinctive S⋯S and S⋯N contacts only for the (syn,anti) conformer. Aromatic π-π-stacking inter-actions are found for both conformers, which occur for the (syn,anti) conformer between pairs of mol-ecules, but are continuous stacks in the (syn,syn) conformer. Non merohedral twinning was found for the crystal of the (syn,anti) conformer used for data collection.

Structural studies of 3-tert-butyl-8-(methylchalcogenyl)pyrazolo[5,1-c][1,2,4]triazin-4(1H)-ones

Crystal structures of novel 3-tert-butyl-8-(methylchalcogenyl)pyrazolo[5,1-c][1,2,4]triazin-4(1H)-ones, C10H14N4OE (E = S, 3; Se, 4; Te, 5), have been determined. Compound 3 crystalizes in the monoclinic crystal system (P21/c), whereas 4 provides two polymorph modifications, 4a (orthorhombic, Pbca) and 4b (tetragonal, I41/a, merohedral twin), depending on solvent media. Crystal structure of 5 (tetragonal, I41/a) is isomorphous with 4b. The studied structures of pyrazolo[5,1-c][1,2,4]triazin-4(1H)-ones exhibit a planar heterocyclic C5N4O core possessing a conjugated π-electron system, which is partly involved in the conjugation with the chalcogen atom. In general, geometric parameters found by X-ray method and ab initio calculated by density functional theory (DFT) for a single molecule (method PBE1PBE/Def2TZV, gas phase) are in good agreement. The structures form 1D infinite chains in the crystalline lattice via intermolecular NH∙∙∙O/N hydrogen bonding and demonstrate short E···E (3, 4b, 5) and E···C/N (all compounds) interactions among molecules of the neighboring chains. Such non-valence interactions do not perturb much the geometries of 3, 4b, and 5 but move the Se atom out of the C5N4O plane in 4a, compared with geometries calculated by DFT method. Photochemical studies have revealed that UV irradiation induces decomposition of telluride 5, accompanied with the Te-C8 bond cleavage, while sulfide 3 and selenide 4 remain inert under analogous conditions.

Optimizing the refinement of merohedrally twinned P61 HIV-1 protease-inhibitor cocrystal structures.

Twinning is a crystal-growth anomaly in which protein monomers exist in different orientations but are related in a specific way, causing diffraction reflections to overlap. Twinning imposes additional symmetry on the data, often leading to the assignment of a higher symmetry space group. Specifically, in merohedral twinning, reflections from each monomer overlap and require a twin law to model unique structural data from overlapping reflections. Neglecting twinning in the crystallographic analysis of quasi-rotationally symmetric homo-oligomeric protein structures can mask the degree of structural non-identity between monomers. In particular, any deviations from perfect symmetry will be lost if higher than appropriate symmetry is applied during crystallographic analysis. Such cases warrant choosing between the highest symmetry space group possible or determining whether the monomers have distinguishable structural asymmetries and thus require a lower symmetry space group and a twin law. Using hexagonal cocrystals of HIV-1 protease, a C2-symmetric homodimer whose symmetry is broken by bound ligand, it is shown that both assigning a lower symmetry space group and applying a twin law during refinement are critical to achieving a structural model that more accurately fits the electron density. By re-analyzing three recently published HIV-1 protease structures, improvements in nearly every crystallographic metric are demonstrated. Most importantly, a procedure is demonstrated where the inhibitor can be reliably modeled in a single orientation. This protocol may be applicable to many other homo-oligomers in the PDB.

Crystal structure and optical properties of fused-ring chalcone (E)-3-(anthracen-9-yl)-1-(4-nitro-phen-yl)prop-2-en-1-one.

The title compound, C23H15NO3, adopts an s-cis conformation with respect to the ethyl-ene C=C and carbonyl C=O double bonds in the enone unit. The mol-ecule is significantly twisted with a dihedral angle of 48.63 (14)° between the anthracene ring system and the benzene ring. In the crystal, mol-ecules are linked into inversion dimers with an R 2 2(10) graph-set motif via pairs of C-H⋯O hydrogen bonds. The inter-molecular inter-actions were analysed and qu-anti-fied by Hirshfeld surface analysis. The mol-ecular structure was optimized and a small HOMO-LUMO energy gap of 2.55 eV was obtained using the DFT method at the B3LYP/6-311 G++(d,p) level of theory. This value is in close agreement with the experimental value of 2.52 eV obtained from the UV-vis analysis. The crystal used was a two-component merohedral twin with a refined ratio of 0.1996 (16):0.8004 (16).

Density functional theory calculations of merohedric twinning in KLiSO4

Abstract Density functional theory (DFT) calculations have been performed on five models of periodic, polysynthetic twin interfaces in the ambient-temperature phase of KLiSO4, which has space group P63. The models represent the three merohedric twin laws (m||z, 2⊥z and 1̅) with boundary plane (1 0 1̅ 0), also with boundary plane (0 0 0 1) in case of m, and with boundary plane (1 2̅ 1 0) in case of 1̅. The models satisfy stoichiometry at the boundary plane and maintain the fourfold coordination of the Li and S atoms and the twofold coordination of the oxygen atoms. Relaxed lattice parameters and atomic positions were determined by DFT, using the DMol3 code with functional PBEsol. The energy difference between polysynthetic twin and single crystal per primitive cell of the twin is 0.0009 eV for m(0 0 0 1), 0.09 eV for 1̅(1 0 1̅ 0), 0.58 eV for m(1 0 1̅ 0) and 0.55 eV for 2(1 0 1̅ 0). In KLiSO4 crystals grown from aqueous solutions the first twin was frequently observed, similarly also the second twin in Cr-doped crystals, whereas the third twin appeared only rarely and the fourth was not observed. Not only for KLiSO4 but also for quartz, the energy of twins and the frequency of their occurrence are closely connected for crystals grown from aqueous solutions, whereas for the formation of transformation twins the availability of twin nuclei plays a major role.

Perfect merohedral twinning combined with noncrystallographic symmetry potentially causes the failure of molecular replacement with low-homology search models for the flavin-dependent halogenase HalX from Xanthomonas campestris.

Flavin-dependent halogenases can be used as biocatalysts because they regioselectively halogenate their substrates under mild reaction conditions. New halogenases with novel substrate specificities will add to the toolbox of enzymes available to organic chemists. HalX, the product of the xcc-b100_4193 gene, is a putative flavin-dependent halogenase from Xanthomonas campestris. The enzyme was recombinantly expressed and crystallized in order to aid in identifying its hitherto unknown substrate. Native data collected to a resolution of 2.5 Å showed indications of merohedral twinning in a hexagonal lattice. Attempts to solve the phase problem by molecular replacement failed. Here, a detailed analysis of the suspected twinning is presented. It is most likely that the crystals are trigonal (point group 3) and exhibit perfect hemihedral twinning so that they appear to be hexagonal (point group 6). As there are several molecules in the asymmetric unit, noncrystallographic symmetry may complicate twinning analysis and structure determination.

Defect Structures of La1 – ySr y F3 – y, La1 – yBa y F3 – y, and Nd1 – yCa y F3 – y (y = 0.05, 0.10) Nonstoichiometric Tysonite Phases

Characteristic features of defect structures of La1 – ySr y F3 – y, La1 – yBa y F3 – y, and Nd1 – yCa y F3 – y (y = 0.05, 0.10) nonstoichiometric phases of different compositions are determined from X-ray diffraction data. Interest in subtle details of their structure is determined by the possibility of ion transport over fluorine vacancies and by a strong compositional dependence of the ionic conductivity. The La0.95Sr0.05F2.95, La0.95Ba0.05F2.95, and Nd0.95Ca0.05F2.95 phases, as well as the La0.9Ba0.1F2.9 phase, crystallize as β-LaF3 (sp. gr. P3c1, Z = 6). The La0.9Sr0.1F2.9 and Nd0.9Ca0.1F2.9 phases lose their superstructure and are described by a cell whose volume is three times smaller (sp. gr. P63/mmc, Z = 2). Defects of crystal structure R1 – yM y F3 – y are not exhausted by vacancies in fluorine positions. All crystals with a “large” cell are twinned according to the merohedral twin law. The majority of atomic positions in models with a “small” cell are split by group symmetry elements and are occupied statistically.

Poly[bis(trimethylammonium) [hexa-μ-cyanido-cadmium(II)dicopper(I)

The title compound, {(C3H10N)2[CdCu2(CN)6]}n, has been synthesized as an alternative to the high-emitting complexes containing more expensive metals. The CN−ligands make linkages between the CuIand CdIIions to form the coordination polymer, [CdCu2(CN)6]n2−, which is a three-dimensional framework classified as pyrite net (pyr). The net has a void space for accommodating a trimethylammonium ion located on a threefold rotation axis. The CdIIion lies on a special position with site symmetry -3 and is octahedrally coordinated by six N atoms. The CuIion is located on a threefold rotation axis and has a trigonal-planar coordination geometry formed by three C atoms. In the three-dimensional net, two CuIions are arranged closely [Cu...Cu = 3.9095 (5) Å], but the distance is not short enough to suggest a CuI–CuIinteraction. The crystal studied was a merohedral twin (twin operation 2[101]), the refined component ratio being 0.9202 (7):0.0798 (7). A powder of the title compound shows strong luminescence with an emission maximum at 509 nm and a quantum yield of 98% at room temperature.

Cation tautomerism, twinning and disorder in the triclinic and monoclinic forms of 4-amino-5-chloro-2,6-dimethylpyrimidinium 5-chloro-2-hydroxybenzoate and a new disordered refinement of 2-amino-4,6-dimethoxypyrimidin-1-ium thiophene-2-carboxylate

Pyrimidines are important compounds in biology and medicine, and the aminopyrimidine fragment can be identified in three of the four bases in DNA. The targeted drug action of pharmaceuticals containing this functionality is likely to depend heavily on molecular recognition processes involving hydrogen bonding. Crystallization of an equimolar mixture of 4-amino-5-chloro-2,6-dimethylpyrimidine and 5-chloro-2-hydroxybenzoic acid yielded two forms of the 1:1 salt, C6H9ClN3+·C7H4ClO3-, each containing a different tautomeric form of the cation. 6-Amino-5-chloro-2,4-dimethylpyrimidin-1-ium 5-chloro-2-hydroxybenzoate, (I), crystallizes in the space group P-1, with Z' = 2, and all of the component ions are fully ordered. 4-Amino-5-chloro-2,6-dimethylpyrimidin-1-ium 5-chloro-2-hydroxybenzoate, (II), also crystallizes with Z' = 2, but in the space group P21/c and as a merohedral twin which closely mimics an orthorhombic unit cell. In (II), one of the cations and one of the anions is disordered, each over two sets of atomic sites having occupancies of 0.836 (2) and 0.164 (2), and 0.834 (2) and 0.166 (2). The bond lengths in the cations of (I) and (II) provide evidence for o-quinonoid and p-quinonoid bond fixation, respectively. A combination of six N-H...O hydrogen bonds links the component ions of (I) into two independent four-ion aggregates, but the ions in (II) are linked by a combination of four N-H...O and two N-H...N hydrogen bonds to form a three-dimensional framework structure. The recently reported structure of 2-amino-4,6-dimethoxypyrimidin-1-ium thiophene-2-carboxylate, C6H10N3O2+·C5H3O2S-, (III), has been rerefined, using the original data set, to show that the anion is disordered over two sets of atomic sites, approximately related by a 180° rotation about the exocyclic C-C bond, and having occupancies of 0.8687 (19) and 0.1313 (19).

Robust background modelling in DIALS.

A method for estimating the background under each reflection during integration that is robust in the presence of pixel outliers is presented. The method uses a generalized linear model approach that is more appropriate for use with Poisson distributed data than traditional approaches to pixel outlier handling in integration programs. The algorithm is most applicable to data with a very low background level where assumptions of a normal distribution are no longer valid as an approximation to the Poisson distribution. It is shown that traditional methods can result in the systematic underestimation of background values. This then results in the reflection intensities being overestimated and gives rise to a change in the overall distribution of reflection intensities in a dataset such that too few weak reflections appear to be recorded. Statistical tests performed during data reduction may mistakenly attribute this to merohedral twinning in the crystal. Application of the robust generalized linear model algorithm is shown to correct for this bias.

Twinning in chemical crystallography – a practical guide

Abstract A non-negliglible percentage of crystal structures in chemical crystallography are derived from twinned crystals. The treatment of these data is dependent on the type of twinning. Twins by strict, pseudo or reticular merohedry may hamper space group determination and structure solution, while non-merohedral twins mainly hinder the data integration process. One structure determination of each type is described in detail. CsCp*Py (1) crystallizes in space group P65, mimicking 6/mmm symmetry by merohedral twinning. The data of IPr · AlI3 (2) (IPr=1,3-bis(2,6-diisopropylphenyl)imidazol-2-ylidene) simulate mmm symmetry although the true space group is P21/n. The crystals of K[Au(CN)2] (3) are obverse/reverse twins. [Cu3(dppaO2)2((OSiMe2)2O)2(thf)2] (4) (ddpaO2=bis(diphenylphosphoryl)amine) crystallizes in space group P21/n and is an example of a non-merohedral twin.

Recovery of data from perfectly twinned virus crystals revisited.

Perfect merohedral twinning of crystals is not uncommon and complicates structural analysis. An iterative method for the deconvolution of data from perfectly merohedrally twinned crystals in the presence of noncrystallographic symmetry (NCS) has been reimplemented. It is shown that the method recovers the data effectively using test data, and an independent metric of success, based on special classes of reflections that are unaffected by the twin operator, is now provided. The method was applied to a real problem with fivefold NCS and rather poor-quality diffraction data, and it was found that even in these circumstances the method appears to recover most of the information. The software has been made available in a form that can be applied to other crystal systems.

Merohedral twins revisited: quinary twins and beyond.

A twin is defined as being an external operation between two identical crystals that share a fraction of the atomic structure with no discontinuity from one crystal to the other. This includes merohedral twins, twins by reticular merohedry as well as coherent twins by contact where only the habit plane is shared by the two adjacent crystals (epitaxy). Interesting and original cases appear when the invariant substructure is built with positions belonging to the same {\bb Z}-module as, for example, the quinary twin structure first drawn by Albrecht Dürer [(1525). The Painter's Manual: a Manual of Measurement of Lines, Areas and Solids by Means of Compass and Ruler. Facsimile Edition (1977), translated with commentary by W. L. Strauss. New York: Abaris Books]. This paper will show that the Dürer twins, once defined in five-dimensional space, are simple merohedral twins, in the sense of Georges Friedel, leaving the five-dimensional lattice invariant. This analysis will be generalized to some other higher-order {\bb Z}-modules.

A row of (XeF5+)M2+(SbF6)3(M= Mg, Ni, Mn, Co, Cu, Zn) compounds: peculiarities of crystal structure, limit of isomorphic substitution, merohedral twinning

A row of (XeF⁵⁺)<i>M</i>²⁺(SbF₆)₃(<i>M</i>= Mg, Ni, Mn, Co, Cu, Zn) compounds: peculiarities of crystal structure, limit of isomorphic substitution, merohedral twinning