Unit Cell Translation Research Articles

Second Harmonic Generation in Exfoliated Few‐Layer ReS2

AbstractThe second harmonic generation (SHG) is systematically investigated in mechanically exfoliated, few‐layer ReS2 samples. The stacking orders are identified as (AA)nA and (ABy)nA for (2n+1)‐layer samples and (AA)n and (ABy)n for 2n‐layer samples. The layer structure A stands for that of a monolayer, and the layer structure By is mirror to A followed by a one‐tenth unit cell translation along the mirror axis, that is, the b‐axis of the crystal. Only the even‐layer samples with (ABy)n stacking order are SHG active. After carefully extracting the effective bulk susceptibility for SHG, it is found that the spectra are greatly enhanced as the fundamental photon energy matches exciton levels. The polarization dependence is strongly anisotropic, and each susceptibility component shows very different wavelength dependence. The results demonstrate that few‐layer ReS2, with its unique SHG, can be considered as an ideal platform for fundamental research in anisotropic nonlinear optics.

Modulated protein crystal structure with 28 molecules in the asymmetric unit

In modulated crystals short-range translational order is lost and the atomic structure cannot be defined by the contents of a single small unit cell. The wave of disorder is described by a modulation function, which restores long-range periodicity. If the modulation period divided by the unit cell translation is a rational number, then the modulation is commensurate, and can be described in an expanded unit cell. Otherwise it is incommensurate. The diffraction pattern of a modulated structure contains strong main reflections from the basic unit cell, surrounded by weaker satellites from the modulation wave. Modulated structures are rare in protein crystallography. Stress factors induce in plants the expression of Pathogenesis-Related (PR) proteins, divided into 17 classes. PR proteins of class 10 (PR-10) are well studied structurally but their biological function is unclear with an implication in phytohormone binding. PR-10/hormone complexes are studied using fluorescent probes such as ANS (8-anilino-1-naphthalene sulfonate). We crystallized Hyp-1, a PR-10 protein from St John's wort, in complex with ANS. Solution of the apparent P4(1)22 crystal structure was impossible by standard molecular replacement because of evident tetartohedral twinning and a bizarre modulation of reflection intensities with l periodicity of 7. The structure was solved using Phaser and data expanded to P1 symmetry. Ultimately, the structure turned out to have C2 symmetry with 28 independent protein molecules, arranged in dimers around a non-crystallographic (NCS) screw along c with a pitch of ~1/7. The seven-fold repetition along c is indicative of a commensurate modulated structure: the NCS copies are similar but not identical. For instance, the consecutive Hyp-1 molecules bind a varying number (0-3) of the ligand molecules. The structure has been successfully refined to R=22.2% using conventional methods, i.e. with unit cell expanded to encompass the entire commensurate modulation period.

Substituted 4-alkoxy-7-Cl-quinolines exhibiting π–π stacking

The molecules of 4-allyloxy-7-chloroquinoline, C(12)H(10)ClNO, (I), 7-chloro-4-methoxyquinoline, C(10)H(8)ClNO, (II), and 7-chloro-4-ethoxyquinoline, C(11)H(10)ClNO, (III), are all planar. In all three structures, π-π interactions between the quinoline ring systems are generated by unit-cell translations along the a axes, irrespective of space group. These structures are the first reported for 4-alkoxyquinolines.

Radical cation salts of CLEDO‐TTF with octahedral anions

AbstractA new π‐donor, 4‐chloro‐4′,5′‐ethylenedioxytetrathiafulvalene (CLEDO‐TTF) was synthesized from 4‐methoxycarbonyl‐4′,5′‐ethylenedioxytetrathiafulvalene in the yield of 85%. In the crystal of neutral molecule, the head‐to‐head type uniform stacking column, in which the donor molecules are related by a unit cell translation, was formed. The electrocrystallization of CLEDO‐TTF with PF6 afforded two kinds of 1:1 salts of purple rods and green plates as miner species. In both 1:1 salts, the head‐to‐tail dimers with ring‐over‐ring overlapping mode were formed. Geometrically, the dimers were included in slipped stacking column in the purple rod salt, while the two‐dimensional network was formed in the green plate salt. The significant steric effect of chlorine atom along the molecular long axis was confirmed by the intermolecular arrangement in the green plate salt, in which the chlorine atom is faced to the hydrogen atom of the neighbouring donor along the long axis. The normal mode analyses were carried out for the neutral and monocationic CLEDO‐TTF, which agreed well with the observed Raman spectra. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Cadmium sulfite hexahydrate revisited

The present structural revision of the title compound, tetra­cadmium tetra­sulfite hexa­hydrate, [Cd4(SO3)4(H2O)5]·H2O, is a low-temperature upgrade (T = 100 K and R = 0.017) of the original room-temperature structure reported by Kiers & Vos [Cryst. Struct. Commun. (1978). 7, 399–403; T = 293 K and R = 0.080). The compound is a three-dimensional polymer with four independent cadmium centres, four sulfite anions and six water mol­ecules, five of them coordinated to two cadmium centres and the remaining one an unbound solvent mol­ecule which completes the asymmetric unit. There are two types of cadmium environment: CdO8 (through four chelating sulfite ligands) and CdO6 (by way of six monocoordinated ligands). The former groups form planar arrays [parallel to (001) and separated by half a unit cell translation along c], made up of chains running along [110] and [10], respectively. These chains are, in turn, inter­connected both in an intra­planar as well as in an inter­planar fashion by the latter CdO6 polyhedra into a tight three-dimensional framework. There is, in addition, an extensive network of hydrogen bonds, in which all 12 water H atoms act as donors and eight O atoms from all four sulfite groups and two water mol­ecules act as acceptors.

Cholic acid–quinoxaline (2/1)

In the title inclusion compound, 2C24H40O5·C8H6N2, the unit cell contains two mol­ecules of cholic acid (3α,7α,12α-trihydr­oxy-5β-cholan-24-oic acid) and one mol­ecule of quinoxaline which implies disorder of the quinoxaline in the space group P21. The amphiphilic mol­ecules of cholic acid assemble, in an anti­parallel arrangement, via O—H⋯O hydrogen bonds, into typical corrugated host bilayers which are lipophilic on the outside and lipophobic on the inside. The host framework belongs to the so called α-trans subtype. The quinoxaline mol­ecules are accommodated in lipophilic channels formed between neighboring bilayers with only van der Waals inter­actions between host and guest. There is a crystallographic twofold screw axis directed along an empty channel in the host framework; however, neighboring guests in any one channel are related by a unit-cell translation along the b axis. Thus, the overall structure is a 1:1 superposition of two such channels related by the crystallographic twofold screw axis.

Two 9-[(E)-nitrophenylvinyl]-9H-carbazoles

The crystal structures of 9-[(E)-(4-nitrophenyl)vinyl]-9H-carbazole and 9-[(E)-(3-nitrophenyl)vinyl]-9H-carbazole, both C20H14N2O2, are determined mainly by van der Waals forces and pi-pi interactions between the carbazole and benzene systems. However, the packing modes are different. In the 4-nitro derivative, the molecules in the weakly bound stack are related by a unit-cell translation, while in the 3-nitro derivative there are centrosymmetric pairs of molecules joined by pi-pi interactions and also pairs of molecules, related by another centre of symmetry, connected by eight relatively short C-H...O interactions.

Synthesis, Structure, and Magnetic Properties of an Antiferromagnetic Spin-Ladder Complex: Bis(2,3-dimethylpyridinium) Tetrabromocuprate

The complex (2,3-dmpyH)2CuBr4 has been synthesized and its crystal packing determined by single-crystal X-ray diffraction (2,3-dmpyH = 2,3-dimethylpyridinium). The compound crystallizes in the triclinic space group P1. The crystal packing is characterized by the formation of a ladder structure for the CuBr4 anions showing short Br...Br contacts. The rungs of the ladder are formed via a crystallographic inversion center, while the rails are formed via unit cell translations. Variable temperature magnetic susceptibility measurements agree very well with the ladder model [Jrung = -3.10 cm-1 (-4.34 K) and Jrail = -6.02 cm-1 (-8.42 K)]. The assignment as a magnetic ladder is confirmed by first principles bottom-up theoretical calculations which conclude that Jrung = -3.49 cm-1 (-4.89 K) and Jrail = -7.79 cm-1 (-10.9 K), in very good agreement with the experimental values. They also support the absence of additional significant magnetic exchange within the crystals. Thus, (2,3-dmpyH)2CuBr4 represents the second reported example of a weak-exchange limit magnetic ladder (that is, one in which the exchange along the rail is stronger than that across the rung).

N-(2-Methyl-3,6-dinitrophenyl)acetamide

The structure of the title compound, C9H9N3O5, was determined as one of a group of five related compounds in order to assess its suitability as a test material for the 2004 Cambridge Crystallographic Data Centre `Blind Structure Prediction Test'. The structure consists of hydrogen-bonded ribbons of mol­ecules stacked along the a axis with the benzene rings parallel by unit-cell translations.

1,4-Phenylenediboronic acid

In the crystal structure of the title compound, C6H8B2O4, centrosymmetric 1,4-phenyl­enediboronic acid mol­ecules are linked by characteristic hydrogen bonding of B(OH)2 groups. Primary association involves the formation of centrosymmetric cyclic dimers which leads to the formation of linear chains; these, in turn, associate by secondary hydrogen bonding, via unit-cell translations in the a axis direction, to form sheets.

Crystallization and preliminary analysis of xenobiotic reductase A and ligand complexes from Pseudomonas putida II-B.

Diffraction-quality crystals have been obtained of the xenobiotic reductase A (XenA) from Pseudomonas II-B, which was originally cultured from the contaminated soil of a World War II era munitions-manufacturing plant. Several complete X-ray diffraction data sets have been collected and analyzed. The native XenA data set includes reflections between 35 and 1.65 A. Four-wavelength MAD data sets from selenomethionine-enriched XenA and from three different ligand complexes are also reported. The XenA crystals belong to space group P2(1)2(1)2, with unit-cell parameters a = 84, b = 158, c = 57 A. Experimental phasing from analysis of the MAD data from selenomethionine-enriched XenA reveals the presence of two molecules in the asymmetric unit. They are related by a non-crystallographic 2(1) screw axis nearly parallel to the c axis, but offset by a quarter unit-cell translation. Thus, the local symmetry produces approximate systematic absences along the (00l) principal axis and complicates the space-group determination.

(1R*,2R*)-2-(Methylphenylamino)-1,2-dihydronaphthalen-1-ol–water (4/1)

The asymmetric unit of the title compound, 4C17H17NO·H2O, contains four independent naphthalenol mol­ecules and one mol­ecule of water. All of the mol­ecules in the asymmetric unit are connected into a contiguous row via O—H⋯O hydrogen bonds. This unique hydrogen-bonded row is, in turn, linked to form extended O—H⋯O hydrogen-bonded chains, through unit-cell translations in the a direction. The hydrogen-bonding motif also contains an O(water)—H⋯π(arene) weak hydrogen bond, with an H⋯Cg distance of 2.64 (4) Å (where Cg is the center of gravity of the phenyl ring).

Birefringence dispersion in Šolc-type anisotropic periodic bandgap structures

Forbidden gaps in Solc folded-type anisotropic periodic structures are analyzed. The azimuth angle in the first quadrant and unequal thicknesses of alternating uniaxial layers are considered. Unit-cell translation matrices are explicitly given at oblique and normal incidences. Implicit dispersion relations are obtained. Birefringence and normal group velocities are determined. Numerical examples make the distinction between the gaps determined by one root and those determined by two roots of the eigenvalue equation. When layers have unequal thicknesses, the gap determined by one root is much wider, but inside the gap the reflectivity is lower than unity, breaks appear, and an increased birefringence results.

Omnidirectional reflection from Šolc-type anisotropic periodic dielectric structures

Recently it was shown theoretically [Opt. Commun. 174, 43 (2000)] that a Solc folded-type anisotropic dielectric structure under certain conditions exhibits omnidirectional reflection at any polarization over a wide spectral range. Here, omnidirectional reflection from Solc folded-type dielectric periodic structures is further analyzed. Transfer-matrix methodology is applied. Simple expressions are obtained for transfer matrices at interfaces and the unit cell translation matrix. Dispersion relations are determined. Numerical examples are shown comparatively for isotropic and Solc-type anisotropic periodic structures. The Solc-type structure has a wider band of omnidirectional reflection. The results demonstrate that anisotropic materials should be useful in photonic bandgap structures.

Forbidden gaps in periodic anisotropic layered media

The general case of obliquely incident plane-wave propagation in periodic anisotropic layered media is presented. Arbitrary permittivity tensors of the two alternating anisotropic layers are considered. An immersion model is used with the assumption that each layer is embedded between two isotropic regions that have the same index of refraction as the isotropic medium of incidence and a thickness that is set equal to zero. Then explicit relations are presented for normally incident plane waves in periodic structures that consist of alternating biaxial layers of arbitrary principal-axis orientation. Specific cases of alternating isotropic and biaxial layers are also considered. Unit cell translation matrices are presented for both traveling directions, from the left to the right and vice versa. Dispersion relations that contain information regarding the propagation bands and the forbidden gaps in periodic anisotropic structures are presented.

High-Field Magnetization Studies of Two-Dimensional Copper Antiferromagnets

The magnetic susceptibilities and high-field magnetization data for members of two families of S = 1/2, two-dimensional, square antiferromagnetic lattices are reported. The known compounds bis-2-amino-5-methylpyridinium tetrabromocuprate, 1, and bis-2-amino-5-chloropy-ridinium tetrabromocuprate, 2, crystallize in the space group C2/c with the tetrabromocuprate ions related by the C-centering and unit cell translations, leading to a square magnetic lattice. Similarly bispyrazinecopper(II) perchlorate, 3, and bispyrazinenitratocopper(II) hex-afluoro-phosphate, 4, crystallize in the space groups C2/m and I4/mcm respectively and also generate square magnetic lattices. High-field magnetization studies, up to 60 Tesla, have determined their saturation fields to be 21 T (1), 27 T (2), 53 T (3) and 32 T (4). All show upward curvature in plots of magnetization as a function of field and fall on a universal curve in good agreement with recent theoretical predictions.

Synthesis and structural investigation of a new ternary transition metal nitride, Co3W3N

A new ternary transition metal nitride, Co3W3N, has been synthesized by the ammonolysis of a chemically derived metalloorganic precursor. The compound crystallizes in the η-carbide structure which is cubic in the space group Fd3̄m (227) with Z=16, as determined from powder X-ray diffraction and Rietveld refinement of the resulting diffraction pattern. The refinement converged with Rwp=0.1198, Rp=0.0725, RI=0.0400, and S=1.63. The unit cell of Co3W3N has a lattice parameter of a=11.0995(2) Å. The compound is isostructural with Co3W3C, the ideal structure consisting of eight regular octahedra of tungsten atoms centred on a diamond cubic lattice and eight regular tetrahedra of cobalt atoms centred on a second diamond cubic lattice that interpenetrates the first through a 12, 12, 12 unit cell translation. Sixteen additional cobalt atoms are tetrahedrally coordinated around the cobalt tetrahedra and sixteen nitrogen atoms surround the tungsten octahedra in tetrahedral coordination.

Synthesis of a New Ternary Nitride, Fe4W2N, with a Uniqueη-Carbide Structure

The structure of a new ternary nitride, Fe4W2N, prepared using a metal-organic precursor synthesis route, has been determined by Rietveld refinement of the monochromatic X-ray powder diffraction data. The compound crystallizes in a cubic,η-carbide structure, space groupFd3m(227), withZ=16 and a lattice parameter ofa=11.0810(9) Å. The refinement converged withRwp=0.1273,Rp=0.0709,RI=0.0478, andS=1.72. The compound is isostructural with Fe4W2C, the ideal structure consisting of eight octahedra of metal atoms, a random mixture of which one-third are iron and two-thirds are tungsten, centered on a diamond cubic lattice and eight regular tetrahedra of iron atoms centered on a second diamond cubic lattice that interpenetrates the first through a 12,12,12 unit cell translation. Sixteen additional iron atoms are tetrahedrally coordinated around the iron tetrahedra and sixteen nitrogen atoms surround the metal octahedra in tetrahedral coordination.

Alkali-metal stoichiometry and structure ofK4C60andRb4C60

Alkali-metal fulleride samples ${\mathrm{K}}_{\mathrm{x}}$${\mathrm{C}}_{60}$ and ${\mathrm{Rb}}_{\mathrm{x}}$${\mathrm{C}}_{60}$ with stoichiometries close to x=4 were examined with x-ray powder-diffraction measurements at room temperature. We have shown through Rietveld refinements that ${\mathrm{A}}_{4}$${\mathrm{C}}_{60}$ is a line phase with charge per lattice site that is closer to integer than in any other fulleride. The ${\mathrm{C}}_{60}$ molecules are disordered between two possible orientations within the body-centered-tetragonal lattice with the three orthogonal twofold rotation axes aligned with the unit-cell translation vectors in space group I4/mmm. The x-ray diffraction results exclude any quadrupole distortion of the fullerene molecule beyond about 0.04 \AA{}. These results suggest that ${\mathrm{K}}_{4}$${\mathrm{C}}_{60}$ and ${\mathrm{Rb}}_{4}$${\mathrm{C}}_{60}$ may be Mott insulators.

Interchain interactions and three-dimensional magnetic ordering in Mn(II)Cu(II) chain compounds; crystal structure and metamagnetic properties of MnCu(pbaOH)(H 2O) 3·2H 2O, with pbaOH = 2-hydroxo-1,3-propylenebis (oxamato)

Single crystals of the novel phase MnCu(pbaOH)(H 2O) 3·2H 2O ( A) have been obtained; pbaOH stands for 2-hydroxy-1,3-propylenebis(oxamato). A crystallizes in the monoclinic system, space group P2 1/ c,with a = 21.212(4) , b = 5.033(1), c = 14.246(2) A ̊ , β = 100.72(2)° and Z = 4. The structure consits of oxamato-bridged Mn(II)Cu(II) bimetallic chains running along the a-axis direction. The shortest metal-metal separations between adjacent chains related by, respectively, the unit cell translation along the b-axis direction and the glide translation along the c-axis direction involve metal ions of the same type, in contrast with what was found in the previously described phase MnCu(pbaOH)(H 2O) 3 ( B). According to our interpretation of the three-dimensional (3-D) magnetic effects in bimetallic chain compounds, the topology of the spin carriers in A should favor a 3-D antiferromagnetic ordering, while B exhibits a 3-D ferromagnetic ordering. The study of the temperature dependence of the magnetic susceptibility as well as the temperature and field dependences of the magnetization have confirmed this prediction. The antiferromagnetic ordering occurs at 2.4 K. A magnetic field of 0.9 kOe is sufficient to overcome the weak interchain interactions, so that the compound may be described as a metamagnet built from ferrimagnetic chains.