Interaxial Angles Research Articles

Crystallization and preliminary X-ray diffraction analysis of staphylococcal enterotoxin type C.

The Type C staphylococcal enterotoxin produced by Staphylococcus aureus strain FRI-909 has been crystallized using a combination of two precipitants, ammonium sulfate and polyethylene glycol 400, with the addition of small amounts of detergent. Two related crystal forms have been obtained, one triclinic, and one tetragonal, both with one toxin molecule per asymmetric unit. These crystals are stable for at least 75 hr in the X-ray beam and diffract to at least 2.2 and 2.6 A, respectively. The triclinic crystals have unit cell parameters a = 38.5 A, b = 43.7 A, c = 36.9 A, and interaxial angles alpha = 99.9 degrees, beta = 95.8 degrees, and gamma = 98.5 degrees. The tetragonal crystals are of space group P4(1)22 with unit cell parameters a = 43.4 A and c = 278.0 A.

The determination of unit-cell parameters from Laue diffraction patterns using their gnomonic projections

A method is described whereby the unit cell of a crystal and its orientation can be determined from a single Laue diffraction pattern (in transmission). The axial ratios and interaxial angles can be determined precisely, but the absolute scaling of the cell depends upon the accuracy with which the minimum wavelength for the experiment is known. Several examples are given.

Indexing Powder Patterns from Relative Axial Dimensions

The usefulness of an X-ray powder diffraction data base, such as the one published by the International Centre for Diffraction Data, is largely dependent on continued additions of indexed powder patterns of single-phase materials of interest to data-base users. The single-phase character of a specimen is generally established by using known values of the unit cell constants to index all its powder pattern lines.In this manuscript we describe indexing procedures based on crystal data which provide only relative values of the cell dimensions, rather than the absolute values usually considered to be essential to the indexing process. To the best of our knowledge, the use of such data for indexing powder diffraction patterns has generally been overlooked or ignored by X-ray crystallographers. We refer to the large numbers of goniometric measurements of crystals which have been published both before, and since, the discovery of X-ray diffraction. These provide useful descriptions of chemical and physical properties of crystals as well as measurements of relative dimensions of unit cell axes. The latter are presented in the form of a/b, b/b and c/b, together with the interaxial angle or angles, if the cell is nonorthogonal.

Non-parallel chains in crystalline γ-isotactic polypropylene

CRYSTALLINE synthetic polymers generally exhibit highly anisotropic arrangements of the polymer chains, which tend to lie parallel to each other. Indeed, chain-axis parallelism has become virtually an unchallenged principle of polymer crystallization, essentially for two reasons. First, it seems consistent with the requirements of the close packing of rods, which may be assumed to approximate crystallized polymer chains, and second, most polymer crystal structures have been determined from samples that are fibrous. As part of a study1–1 of crystal structures of polymer phases that do not readily form fibrous specimens, we have determined the crystal structure of the γ-form of isotactic polypropylene (γ-iPP)5-8. We show that the structure comprises layers which are two chains wide, reminiscent of the α-phase9, but with the chain-axis directions in adjacent bilayers at an angle of 80° to one another. This feature recalls the arrangement, at the same inter-helical angle, that is proposed to occur at the branching points in α-iPP crystals10-12. Similar packing at large interaxial angles between isochiral chain fragments is also often found in globular proteins13. The γ-iPP crystal structure is unusual, however, in that non-parallel chains appear in a fully ordered array. The driving force for such packing seems to be the favourable registration between helices that occurs for this tilt angle.

Identification of structural motifs from protein coordinate data: secondary structure and first-level supersecondary structure.

A computer program is described that produces a description of the secondary structure and supersecondary structure of a polypeptide chain using the list of alpha carbon coordinates as input. Restricting the term "secondary structure" to the conformation of contiguous segments of the chain, the program determines the initial and final residues in helices, extended strands, sharp turns, and omega loops. This is accomplished through the use of difference distance matrices. The distances in idealized models of the segments are compared with the actual structure, and the differences are evaluated for agreement within preset limits. The program assigns 90-95% of the residues in most proteins to at least one type of secondary element. In a second step the now-defined helices and strands are idealized as straight line segments, and the axial directions and locations are compiled from the input C alpha coordinate list. These data are used to check for moderate curvature in strands and helices, and the secondary structure list is corrected where necessary. The geometric relations between these line segments are then calculated and output as the first level of supersecondary structure. A maximum of six parameters are required for a complete description of the relations between each pair. Frequently a less complete description will suffice, for example just the interaxial separation and angle. Both the secondary structure and one aspect of the supersecondary structure can be displayed in a character matrix analogous to the distance matrix format. This allows a quite accurate two-dimensional display of the three-dimensional structure, and several examples are presented. A procedure for searching for arbitrary substructures in proteins using distance matrices is also described. A search for the DNA binding helix-turn-helix motif in the Protein Data Bank serves as an example. A further abstraction of the above data can be made in the form of a metamatrix where each diagonal element represents an entire secondary segment rather than a single atom, and the off-diagonal elements contain all the parameters describing their interrelations. Such matrices can be used in a straightforward search for higher levels of supersecondary structure or used in toto as a representation of the entire tertiary structure of the polypeptide chain.

Structure of 3,4;3',4'-bis(ethylenedithio)-2,2',5,5'-tetrathiafulvalenium–hydrogensulfate (3/2). A (BEDT-TTF) charge-transfer salt containing a tetrahedral anion

3C10HsSs.2HSO4, M r = 1348.1, triclinic, P]-, a ----7.633 (1), b = 9.440 (1), c = 16.607 (1) A, ~t = 92.28(1), f l=94 .97(1) , y = 8 3 . 1 3 ( 1 ) °, V = 1181.8(3)A 3, Z = l , D x = l . 8 9 M g m -3, 2(MoKa) -0 .71073A, /1= 1.175mm -~, F(000)=686, T = 298K. Electrocrystallization of BEDT-TTF with [N(C4Hg)4][HSO41 in 1,1,2-trichloroethane yields a charge-transfer salt containing BEDT-TTF cations and (HSO4)anions in a 3:2 ratio. This product consists of segregated stacks of BEDT-TTF cations with (HSOa)anions located in the cavities formed by the H atoms associated with the ethylenedithiol groups of the BEDT-TTF donors. The asymmetric unit contains two crystallographically independent BEDT-TTF molecules in a lattice which is highly cross linked with multiple intermolecular S-S contacts _ O.Oa(Fo 2) and 289 variable parameters. Introduction. The use of X-ray and neutron diffraction data, in conjunction with tight-binding band calculations, has provided considerable insight into some of the factors governing the conductivity behavior of several organic charge-transfer compounds with metal-like magnetic and electrical properties. Among the most intensively studied systems are a large number containing tetrathiafulvalene or a derivative in which tetrathiaor tetraselenafulvalene forms part of the molecular framework (Williams, Wang, Emge, Geiser, Beno, Leung, Carlson, Thorn & Schultz, 1987). For one series of charge-transfer compounds containing bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF) cations and linear centrosymmetric monovalent anions, a direct correlation between anion length and the onset temperature of superconductivity has been established (Emge, Leung, Beno, Wang, Firestone, Webb, Carlson, Williams, Venturini, Azevedo & Schirber, 1986). This type of correlation not only provides a means of fine-tuning the electrical properties of the system by the * To whom correspondence should be addressed. 0108-2701/87/112201-03501.50 judicious selection of anion, but also provides a pathway for the rational development of new materials with specific conductivity properties. As part of an ongoing project aimed at exploring structure-conductivity relationships in BEDT-TTF salts, we recently prepared a new product containing the monovalent (HSO4)anion. In this paper we report the room-temperature crystal structure of the 32 charge-transfer salt (BEDT-TTF)a(HSO4) 2. Experimental. Black multifaceted crystals of approximate dimensions 0.20 x 0.24 x 0.13 mm obtained by electrocrystallization of BEDT-TTF at a constant current of 0.42 laA in 1,1,2-trichloroethane using H-cells equipped with platinum electrodes and [N(C4H9)4][HSO 4] as the supporting electrolyte. Triclinic symmetry suggested on the basis of interaxial angles and confirmed by a Delaunay reduction. Refined cell parameters obtained from the setting angles of 25 reflections with 30 < 2 0 < 35 °. 0-20-scan data collection carried out at ambient temperature using a Nicolet P3F diffractometer and graphite-monochromated M o K a radiation. Scan rate variable, 212 ° min-~; scan range 1 . 2 ° in 20 from KGq to + 1-1 ° from Ka 2. 6648 reflections (_+8, _+10, +17)measured with 4_<20_<45 ° and averaged to give 3114 unique reflections with wR,, t = 0.021. Three standards (12i, 114, 212) measured every 47 data showed no significant variation over the period of data collection. The data were corrected for absorption, Lorentz and polarization effects. Absorption corrections applied using a Gaussian quadrature procedure following careful measurement of crystal dimensions and assignment of indices to the crystal faces. Minimum and maximum transmission 0.770 and 0.861, respectively. Structure solution and refinement carried out using a locally modified version of the UCLA collection of crystallographic software (Strouse, 1986). S-atom positions from MULTAN78 (Main, Hull, Lessinger, Germain, Declercq & Woolfson, 1978); remaining non-H-atom positions from difference-Fourier maps. H atoms associated with the BEDT-TTF donors were placed in idealized positions with fixed isotropic thermal © 1987 International Union of Crystallography

Symmetry of belladonna mottle virus: rotation function studies

Belladonna mottle virus, a spherical plant virus belonging to the tymovirus group, was crystallized by precipitation with polyethylene glycol 6000 in sodium citrate buffer (pH 5.6). The crystals belong to rhombohedral space group R3 (a \simeq 300 A, \alpha \simeq 60 °) with one molecule in the unit cell, and diffract X-rays to 3.5/~ resolution. Owing to the special interaxial angle of \simeq 60°, the lattice can also be described in terms of a pseudo-face-centred cubic cell. The face-centring vectors of the pseudo cell form the cell edges of the rhombohedral cell. The three-dimensional X-ray diffraction data on these crystals were collected using screenless oscillation photography to a resolution of 6 A. 37 842 independent reflections with {I/ \sigma (I) \geq 2-0} were measured on 51 filn ^pairs. The cell parameters were refined to a = 295.4A and \alpha = 59.86 ° by a postrefinement procedure. A rotation function was calculated using data between 11 and 13 A resolution. The function unambiguously reveals the particle icosahedral symmetry and orientation in the unit cell. The body diagonals of the pseudo-cubic cell are nearly tetrahedral. The icosahedral particle also has a set of tetrahedrally related threefold axes. The particle orientation is such that these two sets can be made coincident by a rotation of \simeq 180 ° about the rhombohedral [111] direction.

Electron irradiation effects in (Cs,Ba)-hollandites

High-resolution electron microscopy examination of mixed (Cs,Ba)-hollandites reveals evidence for significant short-range order in the distribution of cation vacancies in the incompletely occupied tunnels. The structure was observed to be quite unstable under 400-keV electron irradiation after only a few minutes' study at a dose rate of ca. 10 4 electrons Å −2 sec −1. Transformations to a microtwinned phase having interaxial angles of 80°/110° rather than 90°, and finally to an amorphous substance, were directly observed and recorded using video techniques. It is evident that hollandites are structurally, chemically, and mechanically unstable under intense electron irradiation. The significance of these observations to the possible effects of self-irradiation in SYNROC preparations, where radioactive 137Cs +1 transmites to 137Ba 2+ by electron decay, is discussed.

予荷重試験によるTi-Ni合金の応力誘起変態

In this study, the stress dependence of strain-and electrical resistance-temperature relations is investigated by thermal-cycling tests with tensile pre-load for Ti-Ni alloys (49.8 and 50.2 at%Ni) heat-treated at temperature between 743 K and 933 K. The resulting stress (σ)-transformation temperature (T) diagrams are, then, analyzed in detail. The results are summarized as follows.(1) The σ-T diagram in the present study shows similar aspects to that in the tensile test by Miyazaki et al. except for the low stress range in which an analysis with enough accuracy could not be made in tensile test.(2) The σ-T relation of the R→M transformation is not linear and is divided into three parts according to the stress level; (a) low-stress part with large dσ⁄dT, (b) middle-stress part with small dσ⁄dT and (c) high-stress part with relatively large dσ⁄dT. While the R-phase transformation strain increases as the stress becomes larger in the stress range of part (a), it remains constant in the stress range of parts (b) and (c). In the part (c), the R→M transformation takes place before the interaxial angle of the R-phase reaches a maximum. Furthermore, in the stress range of part (c), it is noted that stress dependence of the martensitic transformation strain becomes relatively small, that the residual strain becomes evident at Af point, and that the apparent heat of transformation evaluated from the Clausius-Clapeyron formula increases.(3) The electrical resistance at Mf point increases as stress becomes larger. As for the R→M transformation, the amount of the increase is found to be approximately twice as large as the value estimated from the elongation of the sample during transformation and the apparent increase in the specific resistance which brings residual resistance at Af point.

A computer program for the cartesian translation of crystallographic data

A computer program has been developed to enable a Cartesian description of any crystal. This program requires standard crystallographic data (system, number of forms, Miller indices, axial ratios and interaxial angles) to calculate the general equations of the faces present, a cyclic list of vertices on each face, and the volume and total surface area of the observed crystal. For verification or illustration purpose, a graphic treatment can be selected. This graphic treatment rotates, translates and scales the crystal projection according to specifications. For many purposes, crystals of low symmetry or complex crystallographic properties are more easily treated once expressed in a Cartesian manner.

Geometrical and structural relations in the rhombohedral perovskites

The rhombohedral perovskites are of interest in lattice dynamics (e.g. LaAlO3, PrAlO3) and for their ferroelectric properties (e.g. LiNbO3, PbZr/TiO3). In this paper, data scattered through the literature are correlated, with correction of some misleading mistakes of calculation. Geometrical descriptions are put in a form allowing comparisons. The structures, classified by their space groups, are described in terms of four structural parameters, the octahedron tilt ω, octahedron distortion d, and A- and B-cation displacements s and t, together with an elongation or flattening ζ of the octahedron, deducible with the help of ω from the interaxial angle αrh. Attention is drawn to the variety of physical causes underlying these departures from ideal perovskite. In the R{\bar 3}c structures a correlation not previously noted in the literature is found between the tilt angle ω and a flattening of the octahedron, and some tentative suggestions are made as to its cause. In the R3m and R3c structures, a lack of general correlation between B-cation displacement and the other parameters is noted, in contradiction to earlier reports.

The significance of amphibole compositions in the Genesis of eclogites

Values of the interaxial angle β distinguish the three major amphiboles found in eclogites — iron-magnesium amphiboles, alkali amphiboles, and calcic amphiboles — while d(100) indicates the cation content in octahedral coordination (Y) and atoms with irregular 6- and 8-fold coordination in the X-site. Thus eclogitic amphiboles are subdivided into carinthines under amphibolite facies conditions, glaucophanes in blueschist facies rocks, hornblendes in granulite facies rocks, and kaersutites in igneous eclogites.

Magnetic Interaction of Cerium and Cobalt Ions in Double Nitrate Crystals

The space group of the double nitrate crystals ${{M}_{2}}^{\ensuremath{'}}{{M}_{3}}^{\ensuremath{'}\ensuremath{'}}{(\mathrm{N}{\mathrm{O}}_{3})}_{12}\ifmmode\cdot\else\textperiodcentered\fi{}24{\mathrm{H}}_{2}\mathrm{O}$, where ${M}^{\ensuremath{'}}$ is a trivalent cation and ${M}^{\ensuremath{'}\ensuremath{'}}$ is a divalent cation, has been determined from x-ray data to be $R\overline{3}m$. The rhombohedral unit cell has sides of 13.1 A, interaxial angles of 49\ifmmode^\circ\else\textdegree\fi{} and contains one molecule. The cerium ions have the locations \ifmmode\pm\else\textpm\fi{}(\textonequarter{},\textonequarter{},\textonequarter{}). The line shapes of the derivative with respect to magnetic field of the paramagnetic resonance absorption of small concentrations of cobaltous ions substituted in ${\mathrm{Ce}}_{2}$${\mathrm{Zn}}_{3}$${(\mathrm{N}{\mathrm{O}}_{3})}_{12}$ \ifmmode\cdot\else\textperiodcentered\fi{}24${\mathrm{H}}_{2}$O are described and used to determine the spatial relations of the cerium ions and cobalt ions, as well as to justify the assumption of a dipolar interaction between them described by the spin Hamiltonian parameters of the cerium and cobalt ions. It is concluded that the more isotropic of the two paramagnetic spectra of cobalt ions observed in this salt is due to ions in either the special sites \ifmmode\pm\else\textpm\fi{}(0.399,0.399,0.399) or, rather less likely, in the special sites \ifmmode\pm\else\textpm\fi{}(0.101,0.101,0.101) and that the highly anisotropic spectrum of cobalt ions is due to ions in the body-centered site.

An accurate determination of the cell dimensions of bultfonteinite, Ca4Si2O10H6F2

Bultfonteinite from Bultfontein mine, Kimberley, South Africa, is a hydrated fluorine-containing calcium silicate, of approximate composition Ca4Si2O10H6F2. It was first described in 1932 by Parry, Williams, and Wright,1 who gave an account of its morphology, optical properties, composition, and chemical relationships. It is triclinic but markedly pseudo-orthorhombic. The present work consists primarily of a determination of the unit-cell dimensions, involving a more accurate evaluation of the interaxial angles than the earlier one; this is followed by some tentative suggestions about the structure.

Determination of interaxial angles of a triclinic crystal from a single setting

Determination of interaxial angles of a triclinic crystal from a single setting

L. The crystal structures of the rhombohedral forms of selenium and tellurium

The structures of metallic selenium and of tellurium were determined by the powder method of X-ray crystal analysis; they may be regarded as simple rhombohedral structures with interaxial angles of...