Pseudo Symmetry Research Articles

Bestimmung der Kristallstruktur von CaSO4(H2O)0,5 mit Röntgenbeugungsmethoden und mit Potentialprofil-Rechnungen

Abstract Crystals of CaSO4(H2O)0.5 show a superstructure with high pseudo symmetry. They are pseudo-merohedrically twinned with a three-fold axis as twin element. The substructure is trigonal, space group P3121, with a = 6.937(2), c = 6.345(1) Å and Z = 3. This average structure was refined (R = 0.055) with a statistical distribution of 1.5 H2O molecules over three positions in the tunnel of an AIII-CaSO4 like matrix. With potential profile calculations a model for an ordered distribution of H2O could be derived for the superstructure (a′ = a|[unk], b′ = b, c′ = 2c, all angles 90°, Z = 12 and space group I2). This ordering is due to hydrogen bonding of H2O to the SO[unk] groups which is responsible for the relative stability of the hemihydrate. Considering other subhydrates CaSO4(H2O) x (x = 0.62; x = 0.81) topological models for the (reversible) dehydration of these tunnel structures are given.

X-ray diffraction study of Al–Mn powder obtained by rapid solidification

Al-Mn powder samples were prepared by the gas atomisation technique in search of a possible single grain icosahedral phase. The X-ray diffraction analysis revealed the existence of a τ-phase in addition to the orthorhombic phase and glassy Al-Mn. The τ-phase occurs as single grains and it is a rational approximant structure to icosahedral quasicrystal. This τ-phase shows pseudo icosahedral symmetry. The space group of the τ-phase is I23 and its cell dimension is 14 A. It transforms, kinetically along with the glassy phase, to stable crystalline form under heating.

Observation of pseudo 10-fold symmetry in the ordered iron-zinc delta phase

The δ phase is a Zn-rich intermetallic, having a composition range of ∼ 86.5 - 92.0 atomic percent Zn, and is stable up to 665°C. The stoichiometry of the δ phase has been reported as FeZn7 and FeZn10 The deviation in stoichiometry can be attributed to variations in alloy composition used by each investigator. The structure of the δ phase, as determined by powder x-ray diffraction, is hexagonal (P63mc or P63/mmc) with cell dimensions a = 1.28 nm, c = 5.76 nm, and 555±8 atoms per unit cell. Later work suggested that the layer produced by hot-dip galvanizing should be considered as two distinct phases which are characterized by their morphological differences, namely: the iron-rich region with a compact appearance (δk) and the zinc-rich region with a columnar or palisade microstructure (δp). The sub-division of the δ phase was also based on differences in diffusion behavior, and a concentration discontinuity across the δp/δk boundary. However, work utilizing Weisenberg photographs on δ single crystals reported that the variation in lattice parameters with composition was small and hence, structurally, the δk phase and the δp phase were the same and should be thought of as a single phase, δ. Bastin et al. determined the average cell dimensions to be a = 1.28 nm and c = 5.71 nm, and suggested that perhaps some kind of ordering process, which would not be observed by x-ray diffraction, may be responsible for the morphological differences within the δ phase.

ON THE RELATION BETWEEN DECAGONAL AND ICOSAHEDRAL QUASICRYSTALS

A scheme for the relation between the decagonal and the icosahedral quasiperiodic phases is proposed. It is assumed that these phases share the 6D embedding and a fivefold axis with the primitive i-phase. The decagonal phase is interpreted as a rational approximant of the i-phase with a 6D sublattice. A simple model for the decagonal phase is used to compute kinematic diffraction data which show zone axes with pseudo fivefold and pseudo threefold symmetry.

Amorphization in Intermetallic Compounds FeTi and CoTi Under 1-MeV Electron Irradiation

Electron irradiation induced amorphization of FeTi and CoTi was studied by high voltage electron microscopy (HVEM) from 10 to 160°K. The complete amorphization was observed in both compounds, with the critical dose at 10°K and the critical temperature being about 1.7 dpa and 110°K for FeTi, and about 1.3 dpa and 90°K for CoTi. The onset of amorphization occurred in both compounds after substantial chemical disordering when irradiated below Tc, while the point defect clusters formed above Tc. In addition, the pseudo ten fold symmetry (PTEFS) diffraction spots were observed in selected area diffraction (SAD) pattern of both compounds prior to complete chemical disordering and thus complete amorphization.

Crystallization and preliminary crystallographic study of cathepsin D inhibitor from potatoes

Single crystals of the glycosylated inhibitor of cathepsin D and trypsin isolated from potato tubers were obtained using the hanging drop vapor diffusion method and ammonium nitrate as precipitant. The crystals exhibit strong F222 pseudo symmetry but belong to the orthorhombic space group C222 or C222 1 , with cell parameters a = 73.8 A ̊ , b = 119.9 A ̊ and c = 133.2 A ̊ with two molecules per asymmetric unit. The crystals diffract to a resolution of 2.4 Å.

Electronic structures of square planar coordinated transition metal ions in compounds with gillespite structure

Electronic structures of square planar coordinated transition metal ions in BaCuSi4O10 and CaCrSi4O10 are investigated using the ligand-field theory (LFT), angular overlap model (AOM) and iterative extended Huckel molecular orbital theory (IET). The electronic energy levels of the natural mineral dioptase are also investigated, in which the Cu2+ ions occupy the sites of pseudo D4h symmetry. Both LFT and AOM predict that the crystal-field levels of transition metal ions in these compounds follow such an order that E (2B1g <E(2B2g <E(2A1g )<E(2Eg ), and the frequencies of the crystal-field transitions obtained from point charge calculations are in good agreement with those observed. However, the energy-level order cannot be determined unambiguously from the IET calculation because it depends on the values of parameters chosen for the calculation.

Simulation of energy levels schemes and of some magnetic properties of divalent copper in tetragonal or pseudo tetragonal symmetries

The optical and magnetic properties of 20 complexes of divalent copper are re-analysed. The aim of the work is to simulate simultaneously the data by using a unique set of phenomenological parameters, those introduced by the crystal-ligand field theory, when the vectorial space basis is described on the |αSLJM> kets.

A novel structure of secondary alcohol derived from (+)-Δ3-carene with pseudo three-fold symmetry

The crystal structure of C12OH20 (lR-6R-4R-2 R-3,7,7-trimethyl-4-(2-hydroxyethyl) bicyclo [4.1.0] hept-2-ene) has been determined by X-ray diffraction. The compound crystallizes in space group P212121 witha = 5.893(1),b = 22.572(2), c = 26.164(3) A,V = 3480.3 A3, Z= 12. The structure was solved by modified direct methods and refined to anR value of 0.081 for 607 unique reflections. Each asymmetric unit has three molecules which are held together through intermolecular hydrogen bonds resulting in a novel spiral-type arrangement of molecules. The six-membered ring has a half-chair conformation.

Vibrational (i.r. and Raman) spectra and conformational studies of 1-formyl-3-thiosemicarbazide

The i.r. and Raman spectra (30–4000 cm −1) of 1-formyl-3-thiosemicarbazide (FTSC) and deuterated ftsc- d 4, have been studied. Most of the vibration modes reveal pairs of bands and show strong temperature dependence. A band group {ν(NNH 2)} at ∼ 1100 cm −1 exhibits well resolved doublet (1095 and 1112 cm −1) structure below 100 k. The intensity in the 11 12 cm −1 band decreases regularly (band disappears at 150 K) with the rise in temperature. Two new bands at 955 and 1070 cm −1 appear while measured above 400 K. The system eventually exists in several conformers in simultaneous equilibria. Moreover, a few bands {e.g. ν(CO), ν(CS) and ν(CH)} that show strong intensifies in i.r. exhibit weak (or zero) intensifies in the Raman and vice-versa. The features (characteristic of u and g vibration species) could be explained by a C 2 h pseudo symmetry space group proposed for the system. Both the FTSC and FTSC- d 4 represent strong molecular associations. This favours the maximum abundance in the dimer stabilized conformers.

THE PSEUDO-SYMMETRY IN THE LOW SYMMETRY CRYSTAL SYSTEMS

The pseudo-symmetry often occurs in the crystal structures. The types of pseudo-symmetry may be classified into three categories, i.e. enantiomorphous, translational and those based on other symmetry elements. The present paper discussed some possible translational types in detail, and derived the elements of the pseudo-symmetry for the low symmetry crystal systems (74 space groups). A number of examples show that the pseudo-symmetry is universally exist. Finally, the compatibility between the pseu-do and inberent symmetry groups is also discussed.

Combined CBED and HREM in the electron microscope

A configuration of the JEOL 200CX electron microscope is described that allows direct switching between convergent beam electron diffraction and imaging of the same field of view at ultra high resolution. The usefulness of this configuration is illustrated by: the determination of symmetry elements such as mirror planes, mirror glides, screw axes, and pseudo symmetry in a number of ternary copper sulphides and selenides; the identification of regions within which the phase grating approximation is satisfied; the measurement of lattice parameters; and the assessment of diffuse scattering.

Atomic arrangements on the twin boundaries of crystals of calcite and aragonite

AbstractBy constructing ball-and-spoke models an attempt has been made to arrive at the atomic arrangements on the twin boundaries of four twins of calcite and one of aragonite. The Miller indices of the twins of calcite are (111), (110), (100) and (11). The twin plane in aragonite is (110). Each of the models of calcite twins has the same plane for twin plane and composition plane, and in each case it is a true mirror plane. Aragonite has a pseudo glide plane parallel to (110) gliding in the [001] direction. By making this pseudo symmetry element into a true glide plane a good model of the twin is obtained. In the (111), (110) and (100) twins of calcite all the CO3 groups in the composition plane are parallel to it. In the (11) twin the composition plane contains only CO3 groups and these are perpendicular to it.

Reactions of phenylimidotrichlorobis(triphenyl-phosphine)rhenium(V). Reaction with trimethyl-phosphine and reduction of trimethylphosphine complex to phenylamido complexes of rhenium(I, III). The X-ray crystal structures of phenylamido-(dinitrogen)tetrakis(trimethylphosphine)-rhenium(I) and phenylamido(buta-1,3-diene)-tetrakis-(trimethylphosphine)rhenium(I)

The interaction of Re(NPh)Cl 3(PPh 3) 2 with PMe 3 gives Re(NPh)Cl 3(PMe 3)(PPh 3) or Re(NPh)Cl 3(PMe 3) 2 depending on conditions. In the presence of excess PMe 3 the phenylimido compounds in tetrahydrofuran are reduced by sodium amalgam giving products whose nature depends on the atmosphere (Ar, N 2, H 2 CO, butadiene) used. The following compounds have been characterised: Re(NHPh)(N 2)(PMe 3) 4, ReH(NHPh)(η′-CH 2PMe 2)(PMe 3) 4, Re(H) 2(NHPh)(PMe 3) 4, Re(NHPh)(CO) 2(PMe 3) 3, Re(NHPh)(CO) 3(PMe 3) 2, Re(NHPh)(η 4-C 4H 6)(PMe 3) 3 and Re(NPh)Cl 2(PMe 3) 3. The structures of Re(NHPh)(N 2)(PMe 3) 4 ( 3) and Re(NHPh)(C 4H 6)(PMe 3) 3, ( 8) have been confirmed by single-crystal X-ray diffraction studies. ( 3) is monoclinic, space group P2 1/ n with a = 9.574(2), b = 19.528(3), c = 14.385(3)Å and β = 99.06(2)°; ( 8) is orthorhombic, space group Pbc2 1, with a = 12.207(2), b = 13.884(2), c = 14.242(2)Å. The structures were solved via the heavy atom method and refined by least squares to R values of 0.065 and 0.062 for 3249 and 2009 observed diffractometer data, respectively. In the dinitrogen complex the N 2 and NHPh ligands adopt a cis configuration with ReN bond lengths of 1.955(13) and 2.200(14)Å, respectively. In the butadiene complex, whose structure is not well defined due to disorder and/or pseudo symmetry correlation effects, the ReN (amido) distance is 2.13(3)Å.

Preliminary X-ray diffraction data for chicken muscle glycerol 3-phosphate dehydrogenase

Single crystals of chicken muscle glycerol 3-phosphate dehydrogenase have been obtained which are suitable for a high resolution structure analysis. The crystals are triclinic with smallest cell dimensions of a=58.9 Å b=54.5 Å c=58.5 Å α=91° β=95° δ=89° but show a substantial degree of pseudo symmetry which indicates the presence of at least an approximate and possibly exact dyad axis relating the two subunits in the asymmetric unit.

Synthesis and X-Ray Structure of Triethylenetetramine-palladium(II) Complex

Abstract The triethylenetetraminepalladium(II) perchlorate and the potassium triethylenetetraminepalladium(II)tris-(hexafluorophosphate) were prepared; the X-ray structure analysis has been carried out for the latter compound. The crystal of [Pd(trien)](PF6)2·KPF6 is orthorhombic, with space group Pbca: a=21.645 (5), b=20.873 (5), c=9.541 (2) Å, and Z=8. The structure has been determined from X-ray diffractometer data and refined to R=0.091 (1166 reflections). The Pd atom has a planar coordination of 4N atoms disposed in a somewhat trapezoidal form. The complex cation has a pseudo symmetry plane which is perpendicular to the 4 N plane and bisects the H2N–Pd–NH2 angle. In the quadridentate triethylenetetramine ligand, each of the terminal H2N–CH2–CH2–NH– fragments forms a 5-membered chelate ring with the asymmetric envelope conformation, whereas the chelate ring formed by the middle –NH–CH2–CH2–NH– fragment has the symmetric envelope conformation. The electronic spectrum of [Pd(trien)]2+ is presented.

Preliminary structure analysis of canavalin from Jack Bean

The plant seed protein canavalin has been crystallized alter trypsinization by using vapor diffusion to effect isoelectric precipitation. The space groups and cell dimensions are R3 with a ̄ = 81.3 A ̊ , γ = 111 ° and having extremely high R32 pseudo symmetry, P6 3 with a ̄ = 126 A ̊ and c ̄ = 51 A ̊ , C222 1, with a ̄ = 136 A ̊ , b ̄ = 152 A ̊ , and c ̄ = 131 A ̊ . X-ray data combined with electron microscopy suggests the molecule to be composed of six identical subunits. each of 18,500 daltons, arranged in a staggered hexameric ring and related by perfect or near perfect 3 2 point group symmetry. The outside diameter of the molecule is approximately 65 Å and there appears to be a large solvent channel coincident with the molecular triad.

Molecular energy levels of azines; ab initio calculations and correlation with photoelectron spectroscopy

Non-empirical calculations using a standard gaussian atomic orbital basis (LCGO) have been carried out for known and unknown azines. The wavefunctions show pseudo D6h symmetry and have been correlated with those of benzene; this correlation has been used to interpret the combinations of ‘lone pair’ orbitals that occur. In the case of the tetrazines the splitting of the lone pair levels leads to extensive overlap with the CH region of energy so that mixing occurs and 1,2,4,5-tetrazine shows five orbitals which can be described as ‘lone pair orbitals’. The orbital energy ordering is effectively identical with that obtained from recent double ζ calculations on a few of the molecules; these energies correlate well with photoelectron spectra and obey the relationship IPobs= 0·790IPcalc. Correlations using CNDO/2, INDO, and the Extended Huckel Method (EHM) are less satisfactory both in grouping of the orbitals and absolute energies. The LCGO band assignments are generally in good agreement with those made by Lindholm et al. based upon the EHM. The thermodynamic stability of the azines with respect to fragmentation is discussed; the difference in energies between the classical alternating bond lengths and the observed ones for selected examples are in the region 6–10 kcal mol–1.