Higher Symmetry Space Group Research Articles

CRYSTAL STRUCTURE DATA ON A NEW CUBIC PHASE ACTING AS ANTAGONIST IN THE SYNTHESIS OF Hg(Re)-1223 SUPERCONDUCTOR

During the attempts to improve sealed-quartz tube synthesis of Hg(Re)-1223 superconductor, a new compound was systematically identified in certain unsuccessful experimental conditions. It was characterized by a well distinct powder diffraction pattern with cubic diamond-like extinctions and lattice parameter 8.48-8.53 Å. The composition was determined as Hg 2 Re 0.5 Ba 4 Ca 1.5 O 8.5 and an univocal interpretation was found in terms of the high-symmetry space group Fm3m(225), with Z=2, (= 6.70 g/cm 3; the reliability factor was 5.0%. This phase, Cu-free and not superconductive, rather than a precursor can be considered as an unwanted accident in Hg(Re)-1223 preparation route. Its existence was confirmed by a successful synthesis starting from the above reported stoichiometry.

A new Cu-free cubic phase as competitor in the synthesis of Hg(Re)-1223 superconductor

During the attempts to improve the sealed-quartz tube synthesis of Hg(Re)-1223 superconductor, a new compound was systematically identified under certain unsuccessful experimental conditions. It was characterized by a distinct powder diffraction pattern with cubic diamond-like extinctions and lattice parameter 8.48–8.53 Å, according to thermal treatment length. A comparison with other cubic phases, uncommon in superconducting systems, and in particular Ba 4CaCu 3O 8.25, together with electron microprobe analysis, allowed us to determine a composition Hg 2Re 0.5Ba 4Ca 1.5O 8.5 and supplied a reliable model for its structure. However, the peculiarity of the observed pattern, among the apparently manifold possible answers, led to an univocal interpretation in terms of the high-symmetry space group Fm3 m(225), with Z=2, ρ=6.70 g/cm 3; the reliability factor was 5.0%. Indeed this phase, singularly Cu-free and clearly not superconductive, much more than a precursor can be considered an unwanted accident in Hg(Re)-1223 preparation route: its existence was confirmed by a successful synthesis starting from the above reported stoichiometry.

Combined molecular replacement

Current molecular-replacement methods assume that the correct rotations to be applied to a search atomic model are close to peaks in the rotation function. In addition, generally only the top peaks in the rotation function are examined by the translation function. For difficult structures and for high-symmetry space groups, this assumption may no longer hold true. The more powerful approach is to examine not only the peaks but also other angles that have reasonable values in the rotation function to look for the molecular-replacement solutions. The combined molecular-replacement protocol is therefore a limited six-dimensional search, where the sampling of the rotational degrees of freedom is restricted by the rotation function. A packing check is used to eliminate solutions that cause steric clashes of the search atomic model in the crystal. Several new structures have been determined with this protocol.

Correction to: Synthesis and structures of layered metal sulfonate salts

The crystal structure of cobalt benzenesulfonate hexahydrate, Co(C6H5SO3)2·6H2O, has been rerefined in a higher symmetry space group, resulting in much more regular bond distances and angles with smaller estimated standard deviations. The new atomic positions and isotropic thermal parameters are presented. Crystal data: monoclinic, P21/c,a = 7.017 (2), b = 6.324 (2), c = 23.966 (4) A, β = 110.68 (3)°, V = 995 (1) A3, Z = 2.

The Crystal Structure and Chemical Properties of U2Al3C4 and Structure Refinement of Al4C3

A well crystallized sample of U2Al3C4 was obtained by melting the elemental components in a carbon crucible in a high frequency furnace. The crystal structure of this compound was determined from single-crystal diffractometer data of a twinned crystal: P63mc, a = 342.2(1) pm. c = 2323.0(3) pm. Z = 2 , R = 0.030 for 537 structure factors and 18 variable parameters. The structure can also be described in the higher symmetry space group P63/mmc with one split aluminum position. It consists of close packed layers of uranium and aluminum atoms with carbon atoms at interstitial sites. The structure is closely related to that of Al4C3, which was refined from single-crystal X-ray data to a residual of R = 0.033 for 135 F-values and 11 variables. The hydrolysis of U2Al3C4 with diluted hydrochloric acid resulted in about 74 (wt-)% methane, 8% ethane and ethylene, and 18% saturated and unsaturated higher hydrocarbons.

Intensity-based domain refinement of oriented but unpositioned molecular replacement models

A program is described that performs least-squares group refinement of oriented molecular replacement models whose positions in the unit cell are unknown. The program (INTREF) is designed to produce improved models for use in a translation function by optimizing the orientations and relative translations of the model domains. The molecular contents of the asymmetric unit are refined as a small number of rigid bodies whose origins relative to each other may be unknown. More than one molecule in the asymmetric unit can be accommodated. The refinement seeks to minimize the residual error between the observed and calculated intensities that have been modified to produce the equivalent of a radial weighting in Patterson space. Calculated intensities include contributions from all symmetry-related molecules, enabling meaningful refinement in high-symmetry space groups. Derivatives of the intensities with respect to the rigid-body parameters are evaluated numerically using fast Fourier transforms and the shifts are obtained by non-linear least-squares analysis. Results with test cases show that the program is capable of adjusting the orientations and relative translations of protein domains to give models that more closely resemble the known structures. Consequently, the resulting models produce more accurate and more interpretable results in translation functions. The importance of including all crystallographically related molecules and of downweighting the contribution of the longer-radius region of the Patterson function is demonstrated.

Reinvestigation of SmCo(CN) 6 · 4H 2O and SmFe(CN) 6 · 4H 2O

The crystal structures of SmCo(CN) 6 · 4H 2O and SmFe(CN) 6 · 4H 2O have been determined by means of single crystal X-ray diffractometry. Both compounds refine equally well in orthorhombic Cmcm (No. 63) and monoclinic P2 1 m (No. 11). Since this is the case, the higher symmetry space group should be the preferred choice.

Structural resonance through harmonic and anharmonic interactions: the characterisation of local and overall chirality in TMACuCl3

The complicated structure of one of the phases of tetramethylammonium trichlorocuprate (TMACuCl3) is discussed. The observed deformations with respect to the high-symmetry space group have been decomposed into irreducible representations of this group (P63/mmc). The representations that induce the deformations are tau 5 (k=2 pi (0,0,1/5c)) and tau 6 (k=2 pi (0,0,2/5c)) (Kovalev notation). Structural resonance occurs between these two waves through anharmonic energy contributions. This resonance is such that in the resulting structure two building blocks are discernible, one block showing all characteristics of CsCuCl3 and one some of RbCuCl3. The elements of the gyration tensor have been calculated using single-crystal diffraction data. The chiral functions from which the tensor elements are calculated form fourth-order invariants when squared. This concept can be demonstrated on both the Jahn-Teller octahedra and the successive Cu and Cl layers of this compound. Furthermore, an explanation is given for the fact that some of the TMA groups are disordered, thus contributing to the free energy by an entropy term, and some are not. The superposition of the two waves is such that the E(X) in Jahn-Teller effect of the individual octahedra fits in precisely.

Patterson-oriented automatic structure determination: getting a good start

On the basis of a generalized symmetry minimum function several computer-oriented methods for interpreting Patterson functions and for locating the position of heavy-atom fragments in crystals belonging to space groups of higher symmetry than P1 have been developed. The methods utilize cross vectors for finding relationships among the peaks of the symmetry minimum function. This approach has the advantage of suppressing false peaks of the symmetry minimum function, in locating more than one atom and in revealing the correct solution with greater probability. The heavy-atom fragment can be extended by superposition or Fourier methods. The methods are valid for all space groups, are simple to apply and form the basis for fully automated structure determination. In contrast to many other Patterson methods no a priori structural information is necessary. A few selected examples demonstrate the power of the new version of the computer program XFPS.

The ambiguity problem of vector-set interpretation

An efficient method based on the utilization of crystal symmetry for the interpretation of vector sets of crystals belonging to space groups of higher symmetry than P1 is described. New equality relations between atomic position vectors which are sufficient to provide the possibility of an ambiguous solution are derived. It is proved that for many space groups of the polar kind these conditions of ambiguity are necessarily satisfied. A complete list of such space groups is given.

More space-group changes

Revised structures are reported for 19 crystalline compounds, based on space groups of higher symmetry than originally reported. In four cases the Laue symmetry is changed, one from 1 to 2/m and three from 2/m to mmm; in the remaining fifteen a center of symmetry has been added. For eight of these latter compounds we have obtained F values and carried out least-squares refinements in the centrosymmetric space groups, with more satisfactory results than originally reported.

IMPAS–A simple structure determination procedure based on intermolecular Patterson vectors

A computer method for interpreting Patterson functions of crystals belonging to space groups of higher symmetry than P1 is described. A table of all Patterson peaks in the entire cell is initially searched for vectors between symmetry-related atoms. Such 'generalized Harker vectors' are identified not only by known symmetry-fixed components, but also by statistical criteria based on a systematic search for pairs of vectors which relate additional atoms to the pair involved in the generalized Harker vector. Subsequent searches, using the same basic principle, are carried out to find additional atoms. Pairs of vectors, whose components add up to the previously established Harker vector, indicate newly found atom positions after appropriate transformations into crystal space. The correctness of these atom positions can be further tested by applying all symmetry operations of the space group in question and looking for a complete set of related vectors. In contrast to many other Patterson search methods no information about known molecular fragments is requested. Also described are four structures which were solved with the IMPAS procedure following unsuccessful attempts to solve them by direct methods.

Group actions as applied to symmetry breaking in hexagonal crystals with space group P63/m

A procedure is outlined that allows one to predict the possible low-symmetry space groups for a commensurate phase transition associated with a broken symmetry. By considering each irreducible representation of the high-symmetry space group and using a subduction procedure involving the theory of group actions, one may determine a complete set of representative order parameters and their little groups. Each little group can be identified as a possible space group for the low-symmetry phase. The method is used to deduce all possible broken symmetries of space group P63/m that can result from a phase transition associated with one of the symmetry points in the Brillouin zone. As a specific application of the resulting tables of possible order parameters and associated low-symmetry space groups, changes in the X nuclear quadrupole resonance spectrum due to structural phase transitions in hexagonal AX3 crystals with the high-symmetry space group P63/m are considered.

Group theoretical classification of halogen nuclear quadrupole resonance spectra of distorted tetragonal antifluorite crystals

A classification of the patterns of halogen nuclear quadrupole resonance lines resulting from distortions of the tetragonal R 2MX 6 structures C 4 h 5( I4/ m) and D 4 h 6( P4/ mnc) is given. Formal methods of group thepry are used to identify low symmetry space groups with the symmetries of vectors in an irreducible representation space of the high symmetry space group. Classification charts are presented which permit the identification of those space groups and primary order parameters which are compatible with particular halogen nuclear quadrupole resonance spectra. The discussion is limited to structural phase transitions involving the points of symmetry in the Brillouin zones of the high temperature phases. The sequences of structural transitions in K 2ReCl 6 and (NH 4) 2SnBr 6 are discussed as illustrations of the use of these charts.

The crystal structure of NH 4MnFeF 6: Re-refinement in a higher symmetry space group

The crystal structure of NH 4MnFeF 6, which was originally described in space group Pb2n, can be better described in Pbcn. Refinement in Pbcn has led to an improved R of 0.018, smaller standard deviations, and a more regular structure. One of the two structurally independent ammonium groups appears to be ordered, the other disordered.

Crystal structure of a molybdenum(VI) compound with a tetradentate N2S2 ligand: re-refinement in a higher symmetry space group

Crystal structure of a molybdenum(VI) compound with a tetradentate N2S2 ligand: re-refinement in a higher symmetry space group

Group theoretical classification of halogen nuclear quadrupole resonance spectra of distorted cubic antifluorite crystals

A classification of the patterns of halogen nuclear quadropole resonance lines resulting from distortions of the cubic antifluorite structure is given. Formal methods of group theory are used to identify low-symmetry space groups with the symmetries of vectors in an irreducible representation space of the high-symmetry space group. The formal arguments predict the number of resonance lines and their intensities and give the nature of the change of the spectrum for each distorted structure and the possible secondary-order parameters. The irreducible representations considered are those corresponding to normal modes and homogeneous strains. It is assumed that the primary-order parameter involves a single wave vector. The analysis is limited to commensurate transitions involving the Γ, X, L, and W points of the Brillouin zone.

Intensity distributions in space groups of higher symmetry

Intensity distributions in space groups of higher symmetry

Effects of misplaced atoms on the residualR2in space groups of higher symmetry

In space groups of symmetry higher than P1 misplacement of a single atom implies the misplacement of all those in the same Wyckoff position, and hence the effect on the residual is larger than in P1. 'Exact' values of the residual R2 are obtained, with explicit allowance for dispersion.

The application of direct methods to the analysis of heavy-atom derivatives

Heavy atoms in isomorphous derivatives of concanavalin-A and formylmethionine transfer RNA have been found by applying the tangent formula in three dimensions to EΔ's, the normalized moduli of the differences between the scaled amplitudes of the derivative and parent structure factors. A full three-dimensional set of starting phases was computed from trial heavy-atom constellations derived from symbolic-addition analysis of the centrosymmetric axial projections. This strategy compares favorably with the analysis of two- and three-dimensional difference Patterson syntheses usually employed to find heavy atoms, and is flexible enough to incorporate other sources of structural information when available. It is preferable when circumstances, such as high-symmetry space groups, data of poor quality or low resolution, and multiple heavy-atom sites per asymmetric unit make the Patterson syntheses difficult to interpret. Problems peculiar to the application of direct methods to the solution of isomorphous heavy-atom derivatives are discussed.