Hexagonal Indexing Research Articles

Chiral Crystallization of Helical Polymers

Crystallization of achiral or racemic helical polymers in chiral crystals is quite frequent and while in some cases it may relate to the thermodynamic stability of the chiral polymorph, in others it must be associated with kinetic factors. Analysis of the available literature data suggests that in the second instance a key role must be played by the nucleation step, i.e. specifically by the formation of precrystalline entities. Furthermore a survey of the chiral crystal structures for helical polymers evidences that they are frequently characterized by a quasi-hexagonal packing. The hexagonality index H, defined as the ratio of the largest to the smallest distance between the axis of the reference helix and its six nearest neighbors, appears to be a reliable indicator of the presence of helices of a single handedness or, respectively, of both in a given crystal structure. A detailed analysis of the general energetic and entropic factors favoring chiral crystallization of helical polymers is carried out. It is shown that a hexagonal or pseudohexagonal arrangement (i.e. the 6-fold coordination) in either the crystalline or precrystalline state, promotes chiral crystallization and is in its own turn favored by clustering of isochiral helices.

Synthesis and characterisation of [(η-C5Me5)Ru(µ,η-C5Me5)Ru(η-C5Me5)]+[A]–; [A]–= TCNE, TCNQ, C3[C(CN)2]3. Crystal structure of the one-dimensional salt [(η-C5Me5)Ru(µ,η-C5Me5)Ru(η-C5Me5)]+[TCNE]–

Charge-transfer salts [(η-Cp*)Ru(µ,η-Cp*)Ru(η-Cp*)]+[anion]– Cp*= C5Me5; anion = tetracyanoethylene (TCNE, 2), 7,7,8,8-Tetracyano-p-quinodimethane (TCNQ, 3), or C3[C(CN)2]3(4)] prepared from [(η-Cp*)Ru(µ,η-Cp*)Ru(η-Cp*)+ OTf–(1)(OTf–= trifluoromethanesulphonate) and M+[anion]–(M+= Li+, NBu4+) salts are described. Single-crystal X-ray studies show that 2 crystallises in the trigonal system, in the non-centrosymmetric space group R3m with a=b= 14.432(3)A, c= 14.432(3)A, α=β= 90°, γ= 120° with hexagonal indexing, V= 2603.3 A3, ρc= 1.41 g cm–3, Z= 3, R= 0.0634 and Rw= 0.0715. The unit cell in 2 comprises alternating cations and anions aligned parallel to the crystallographic c axis. The cation has a multidecker structure with parallel Cp* rings and Ru–Cp˙(centroid) distances of 1.826(7), 1.89(8), 1.826(7), and 1.828(9)A. The diamagnetic [(η-Cp*)Ru(µ,η-Cp*)Ru(η-Cp*)]+ cation and the S= 1/2 [TCNE]– radical anion lie on the crystallographic three-fold symmetry axis and consequently are highly disordered. The disordered anions possess local D2h symmetry with C–CN, CN distances of 1.39(3) and 1.10(3)A, respectively. For 2 and 3 the magnetic susceptibility obeys the Curie–Weiss expression χ=C/(T–θ), with µeff and θ values of 1.73 µB and 0.07° for 2 and 1.45 µB and –3.7° for 3.

Diffraction study on bainite of Cu-Al alloy

Structure of bainite in Cu-Al and Cu-Zn-Al alloys has been reported as 3R, 9R or 18R long period stacking structure (LPS) by X-ray and electron diffraction studies. In the present work, a Cu-25.5 (at)% Al alloy sample was heated at 900°C for 2 h then isothermally held at 450°C for 60 s before quenching into iced brine. FIG.1 shows a TEM bright field image of bainite plates (marked B) grown from grain boundary. The parent phase ( with DO3 structure ) has transformed to martensite (marked M ) during cooling from 450° C to 0°C. Both bainite and martensite plates have dense striations inside.Careful diffraction study on a JEOL 2000FX TEM with accelerating voltage 200 KV revealed (FIG.2) that the diffraction patterns contai_ning the same zone axis [001] ( hexagonal index ) or [111]c ( cubic index ) are from a bainite plate with obtuse V-shape. They are indexed as [010], [140], [130], [120], [230], [340] and [110] zone pattern for hexagonal system respectively.

Crystallization and preliminary X-ray studies of Escherichia coli glycerol kinase

Escherichia coli glycerol kinase, a major regulatory enzyme which catalyzes the reversible MgATP-dependent phosphorylation of glycerol has been crystallized by the hanging drop vapor diffusion method at room temperature. Three different crystal forms have been obtained in the presence of glycerol and appear to be suitable for X-ray crystallographic studies. Vapor diffusion against 55% ammonium sulfate and 1% β-octyl glucoside (pH 7.0) yields rhombohedral crystals with space group R32, a = b = 277.1 A ̊ , c = 78.7 A ̊ (hexagonal indexing) containing a dimer of M r 112,000 in the asymmetric unit ( V m = 2.64 A ̊ 3/dalton ). Vapor diffusion against sodium chloride in the presence of 10% (w/v) polyethylene glycol (pH 6.5 to 7.0) yields two different crystal forms, both with space group P2 1. The first form has a = 88.1 A ̊ , b = 99.3 A ̊ , c = 114.6 A ̊ , β = 119 ° , the second form has a = 92.5 A ̊ , b = 117.6 A ̊ , c = 108.3 A ̊ , β = 93.64 ° . Addition of ADP enhances growth of the monoclinic forms. These forms appear to contain an entire tetramer of M r 224,000 in the asymmetric unit and have V m values of 2.28 and 2.65 Å 3/dalton, respectively. All forms diffract to better than 3.0 Å resolution while the second monoclinic form diffracts to approximately 1.8 Å.

Diffraction pattern indexing in lithium niobate

SUMMARYCrucial to the interpretation of diffraction contrast experiments conducted in the transmission electron microscope is the self consistent indexing of zone‐axis patterns for the crystal under study. Because indexing the diffraction patterns of a crystal as complicated as lithium niobate is not a trivial exercise, computer simulation of diffraction patterns, extinction distance calculations, and consideration of several unit cell representations are used in order to make diffraction pattern interpretation more tractable. It was found that the zone‐axes were most easily indexed by considering the pseudo‐cubic representation of rhombohedral perovskite crystals. The pseudo‐cubic system also facilitates the indexing of Bragg reflections and the visualization of the major features of the reciprocal lattice. Ultimately, however, hexagonal indices must be used to understand a particular lattice defect, since the symmetries associated with the hexagonal lattice are real symmetries, unlike the apparent symmetries that are implied by a pseudo‐cubic crystal. For this reason, we have tabulated the matrices for transforming from the hexagonal system to the pseudo cubic system. For the sake of completeness, transformation matrices relating all four relevant lattice systems (hexagonal, pseudo‐cubic, primitive rhombohedral, and orthohexagonal), as well as the atomic positions in each system, are tabulated.

Crystallographic characterization of phthalate oxygenase reductase, an iron-sulfur flavoprotein from Pseudomonas cepacia.

Pseudomonads grown on phthalate synthesize a series of enzymes that metabolize this aromatic substrate. Among the inducible enzymes is a reductase which transfers electrons from NADH to the terminal dioxygenase that converts phthalate to the corresponding cis-1,2-dihydrodiol (Keyser, P. (1976) Ph. D. thesis, University of Miami; Ribbons, D. W., and Evans, W. C. (1960) Biochem. J. 76, 310-318). The phthalate oxygenase reductase induced in Pseudomonas cepacia is a single polypeptide chain (Mr approximately equal to 33,000) with two prosthetic groups, FMN and [2Fe-2S]. This oxidoreductase has been crystallized at pH 6.7 from polyethylene glycol 6000 in space group R3 with a = b = 113.4 A and c = 77.7 A (hexagonal indexing).

Heptamanganese tricarbide Mn7C3

A procedure was examined for the preparation of Mn7C3 by reaction of manganese dust with n-pentane at 850 °C and a reduced pressure. The identity of the product was confirmed by chemical and X-ray diffraction analysis; no other carbide was found to be present. The powder X-ray diffraction patterns were investigated in terms of the structure assignment either to the hexagonal P63mc or the orthorhombic Pnma symmetry. The reflection intensities fit better the latter structure, but the possibility of hexagonal indexing indicates that the octahedral structural elements do not arrange coherently during the synthesis. The composition of the products of hydrolysis is also consistent with the formula Mn7C3. The gaseous products contain hydrogen, methane, and a number of other hydrocarbons, mostly saturated, whose concentration decreases with increasing number of carbon atoms in the molecule. The concentration distribution of the hydrocarbons is discussed in terms of the radical mechanism of the hydrolysis; the data are borne out indicating that in Mn7C3 the covalent nature of the bonds is more pronounced than in salt type carbides.

An X-ray topographic study of dislocations in a LiNbO3crystal

The Burgers vectors of dislocations in a Czochralski-grown LiNbO3 crystal have been determined by using Lang X-ray diffraction topography. Dislocations with Burgers vectors of both ⅙〈2\bar 201〉 and ⅓〈\bar 1101〉 types (in hexagonal indices) are observed. The direction of the two Burgers vectors is thus identified to be along the line from one Nb (or Li) to the nearest Nb (or Li), and along the line from one Nb (or Li) to the second neighbours respectively.

Phase equilibria and structural relations in the system BaMnO 3− x

The system BaMnO 3− x (0 ⩽ x < 0.5) in air was investigated by gravimetric, quenching, single-crystal and powder-X-ray diffraction studies. Below 1150°C hexagonal, two-layer BaMnO 3 ( a = 5.699 Å, c = 4.817 Å) is stable. Above 1150°C a series of anion deficient BaMnO 3− x phases exists. With increasing temperature, these include a rhombohedral 15-layer form ( a = 5.681 Å, c = 35.377 Å; hexagonal indexing) and hexagonal 8-layer ( a = 5.699 Å, c = 18.767 Å), 6-layer ( a = 5.683 Å, c = 14.096 Å), 10-layer ( a = 5.680 Å, c = 23.373 Å) and 4-layer ( a = 5.672 Å, c = 9.319 Å) forms. The 6-layer modification is not of the hexagonal BaTiO 3-type. A simple orderly structural sequence involving a progressive increase of cubic-type layer stacking with increasing temperature characterizes the phases prepared. Influence of anion stoichiometry on phase formation is considered.

Solid reactions in Rubidium Carbonate‐Vanadium Pentoxide system

AbstractThe reactions between rubidium carbonate and vanadium pentoxide were performed at different high temperatures. Four reaction products of the compositions: I. Rb2O · V2O5; II. 2 Rb2O · V2O5; III. 3 Rb2O · V2O5; and IV. Rb2O · 4 V2O5 were obtained. According to the determination of Rb and the X‐ray powder photographs of the products the existence of rubidium metavanadate (RbVO3) and rubidium pyrovanadate (Rb4V2O7) was confirmed. On the other hand, the preparation of a pure rubidium orthovanadate (Rb3VO4) and rubidium tetravanadate (Rb2O · 4 V2O5) was not successful. The diffraction pattern of Rb2O · V2O5 obeys hexagonal indexing with lattice dimensions a = 7.347 and c = 13.608 Å.

Effect of High Pressure on the Lattice Parameters of Cr2O3 and α-Fe2O3

The effect of pressure to several hundred kilobars has been measured on Cr2O3 and α-Fe2O3. Both have the corundum structure. Results are compared with previously published data for Al2O3. Cr2O3 exhibits a compressibility which decreases markedly with increasing pressure; Al2O3 has a compressibility nearly independent of pressure; the compressibility of α-Fe2O3 actually increases with pressure in the low-pressure region. This is probably associated with the unusual behavior observed in Mössbauer studies. Based on hexagonal indexing, Al2O3 shows the smallest change in aH and the largest change in CH. Cr2O3 is at the opposite extreme with α-Fe2O3 in between. In rhombohedral indexing, Al2O3 exhibits the largest change in aR and Cr2O3 the smallest. Al2O3 shows an increase of ½ deg in α, Cr2O3 a decrease of about 1 deg, while for Fe2O3 α is nearly independent of volume.