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## Space Groups (space + groups)
Kinds of Space Groups
## Selected Abstracts## X-Cell: a novel indexing algorithm for routine tasks and difficult cases JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 2 2003Marcus A. NeumannX-Cell is a novel indexing algorithm that makes explicit use of systematic absences to search for possible indexing solutions from cells with low numbers of calculated reflections to cells with high numbers of reflections. Space groups with the same pattern of systematic absences are grouped together in powder extinction classes, and for a given peak number range an independent search is carried out in each powder extinction class. The method has the advantage that the correct cell is likely to be found before the rapid increase of possible solutions slows down the search significantly. A successive dichotomy approach is used to establish a complete list of all possible indexing solutions. The dichotomy procedure is combined with a search for the zero-point shift of the diffraction pattern, and impurity peaks can be dealt with by allowing for a user-defined portion of unindexed reflections. To rank indexing solutions with varying numbers of unindexed reflections, a new figure of merit is introduced that takes into account the highest level of agreement typically obtained for completely incorrect unit cells. The indexing of long and flat unit cells is facilitated by the possibility to search for rows or zones in reciprocal space first and then to use the lattice parameters of the dominant row or zone in the unit-cell search. The main advantages of X-Cell are robustness and completeness, as demonstrated by a validation study on a variety of compounds. The dominant phase of phase mixtures can be indexed in the presence of up to 50% of impurity peaks if high-quality synchrotron data are available. [source] ## Symmetry rules and strain/order-parameter relationships for coupling between octahedral tilting and cooperative Jahn,Teller transitions in ABX3 perovskites. ACTA CRYSTALLOGRAPHICA SECTION B, Issue 2 2009Space groups, order-parameter and strain/order-parameter coupling relationships in ABX3 perovskite structures which combine cooperative Jahn,Teller distortions and octahedral tilting have been investigated from the perspective of group theory using the computer program ISOTROPY. Two common Jahn,Teller ordering schemes are associated with the irreducible representations and of the space group . A third, less-common ordering scheme is associated with . These combine with tilting instabilities associated with and to generate a predicted suite of Jahn,Teller structure types that includes many of the known structures of manganites, vanadates, Cu and Cr halides. Order-parameter coupling and possible phase transitions are described using Landau free-energy expansions, and general expressions for the relationships between symmetry-adapted spontaneous strains and particular order-parameter components are presented. These provide a general formal framework for determining structural evolution across multi-component order-parameter space and for characterizing the influence of tilting instabilities on Jahn,Teller instabilities or of Jahn,Teller ordering on octahedral tilting. [source] ## Dicopper(II) Complexes with the Enantiomers of a Bidentate Chiral Reduced Schiff Base: Inclusion of Chlorinated Solvents and Chiral Recognition of1,2-Dichloroethane Rotamers in the Crystal Lattice EUROPEAN JOURNAL OF INORGANIC CHEMISTRY, Issue 14 2006Vamsee Krishna MuppidiAbstract Bisphenoxo-bridged dicopper(II) complexes [Cu2Ln2Cl2] {1 (n = 1) and 2 (n = 2)} with the N,O-donor reduced Schiff bases N -(2-hydroxybenzyl)-(R)-,-methylbenzylamine (HL1) and N -(2-hydroxybenzyl)-(S)-,-methylbenzylamine (HL2) have been synthesised and characterised. In both 1 and 2, the bidentate chiral ligands coordinate the metal centres through the secondary amine N atom and the bridging phenolate O atom. The chloride ion occupies the fourth coordination site and completes a slightly distorted square-planar NO2Cl environment around each copper(II) centre. Magnetic susceptibility measurements in the solid state suggest a strong antiferromagnetic interaction between the metal centres in both complexes. Both 1 and 2 readily form 1:1 host-guest compounds with chlorinated solvents such as CH2Cl2, CHCl3 and Cl(CH2)2Cl. All the host-guest compounds crystallise in noncentrosymmetric space groups. 1·CH2Cl2 and 2·CH2Cl2 crystallise in the P21 space group while 1·CHCl3, 2·CHCl3, 1·Cl(CH2)2Cl and 2·Cl(CH2)2Cl crystallise in the P212121 space group. In these inclusion crystals, the C,H···Cl interactions between the guest and the host molecules are primarily responsible for enclatheration of the chloroalkane molecules. In the case of CH2Cl2, one of its Cl atoms acts as the acceptor. On the other hand, for CHCl3 and Cl(CH2)2Cl, the metal coordinated Cl atom of the host complex acts as the acceptor. The structures of 1·(P)-Cl(CH2)2Cl and 2·(M)-Cl(CH2)2Cl provide rare examples for chiral recognition of the right handed (P) and the left handed (M) gauche forms of Cl(CH2)2Cl in molecular assemblies. (© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2006) [source] ## Teaching crystallography to undergraduate physical chemistry students JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 5-2 2010Virginia B. PettTeaching goals, laboratory experiments and homework assignments are described for teaching crystallography as part of two undergraduate physical chemistry courses. A two-week teaching module is suggested for introductory physical chemistry, including six to eight classroom sessions, several laboratory experiences and a 3,h computer-based session, to acquaint undergraduate physical chemistry students with crystals, diffraction patterns, the mathematics of structure determination by X-ray diffraction, data collection, structure solution and the chemical insights available from crystal structure information. Student projects and laboratory work for three to four weeks of an advanced physical chemistry course are presented. Topics such as symmetry operators, space groups, systematic extinctions, methods of solving the phase problem, the Patterson map, anomalous scattering, synchrotron radiation, crystallographic refinement, hydrogen bonding and neutron diffraction all lead to the goal of understanding and evaluating a crystallographic journal article. Many of the ideas presented here could also be adapted for inorganic chemistry courses. [source] ## Structure of the quaternary alloy Zn0.6Mn0.4In2S4 from synchrotron powder diffraction and electron transmission microscopy JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 1 2006Asiloé J. MoraThe aim of the present work was to determine the structure of the quaternary alloy Zn0.6Mn0.4In2S4 and to locate the Mn2+. This was accomplished by means of powder synchrotron X-ray diffraction, high-resolution microscopy and convergent-beam electron diffraction (CBED). The powder X-ray diffraction pattern was indexed in a rhombohedral cell, with cell constants a = 3.875,(2), c = 37.208,(4),Å, and possible space groups Rm or R3m. Rietveld refinements using different cationic arrangements in these space groups were performed. A model in space group R3m, in which the tetrahedral and octahedral sites were occupied by different proportions of Zn, Mn and In atoms, gave the best result. The Rietveld refinement of this model led to figures of merit Rwp = 9.8%, Rp = 9.1% and ,2 = 11.1. Selected-area electron diffraction patterns and high-resolution transmission electron micrographs along [001] reveal the rhombohedral configuration. CBED patterns perpendicular to [001], showing the distinctive 3m symmetry, confirmed space group R3m and the breaking of the centrosymmetry of the parent compound, ZnIn2S4. [source] ## Bridging the gap , structure determination of the red polymorph of tetrahexylsexithiophene by Monte Carlo simulated annealing, first-principles DFT calculations and Rietveld refinement JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 3 2002Marcus A. NeumannThe crystal structure of the red polymorph of tetrahexylsexithiophene (THST) is solved from X-ray powder diffraction data by a direct-space Monte Carlo simulated-annealing approach. First-principles density functional theory (DFT) calculations are used to distinguish between three nearly identical solutions in the space groups C2/m, C2 and P and to improve the overall accuracy of the crystal structure. The correct space group is found to be C2/m. In all space groups, the thiophene backbone is planar and the hexyl side chains assume an all- trans conformation except for two terminal methyl residues, which adopt a gauche orientation. The ability of first-principles DFT calculations to provide atomic coordinates of single-crystal quality is demonstrated by lattice-energy minimization of the known crystal structure of the yellow polymorph of THST. The combination of Monte Carlo simulated annealing, first-principles DFT calculations and Rietveld refinement presented in this paper is generally applicable. It provides a powerful alternative to standard approaches in cases where the information content of the powder diffraction pattern alone is insufficient to distinguish between different structure solutions. DFT calculations can also provide invaluable guidance in Rietveld refinement. [source] ## Solving crystal structures in P1: an automated procedure for finding an allowed origin in the correct space group JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 2 2000Maria Cristina BurlaCrystal structure solution in P1 may be particularly suitable for complex crystal structures crystallizing in other space groups. However, additional efforts and human intervention are often necessary to locate correctly the structural model so obtained with respect to an allowed origin of the actual space group. An automatic procedure is described which is able to perform such a task, allowing the routine passage to the correct space group and the subsequent structure refinement. Some tests are presented proving the effectiveness of the procedure. [source] ## Contribution of electron precession to the study of perovskites displaying small symmetry departures from the ideal cubic ABO3 perovskite: applications to the LaGaO3 and LSGM perovskites JOURNAL OF MICROSCOPY, Issue 1 2008J.-P. MORNIROLISummary Electron microscopy and electron diffraction are well adapted to the study of the fine-grained, faulted pure and doped LaGaO3 and LSGM perovskites in which the latter is useful for fuel cell components. Because these perovskites display small symmetry departures from an ideal cubic ABO3 perovskite, many conventional electron diffraction patterns look similar and cannot be indexed without ambiguity. Electron precession can easily overcome this difficulty mainly because the intensity of the diffracted beams on the precession patterns is integrated over a large deviation domain around the exact Bragg condition. This integrated intensity can be trusted and taken into account to identify the ,ideal' symmetry of the precession patterns (the symmetry which takes into account both the position and the intensity of the diffracted beams). In the present case of the LaGaO3 and LSGM perovskites, the determination of the ,ideal' symmetry of the precession patterns is based on the observation of weak ,superlattice' reflections typical of the symmetry departures. It allows an easy and sure identification of any zone axes as well as the correct attribution of hkl indices to each of the diffracted beams. Examples of applications of this analysis to the characterizations of twins and to the identification of the space groups are given. This contribution of electron precession can be easily extended to any other perovskites or to any crystals displaying small symmetry departures. [source] ## Effect of Oxygen Partial Pressure on the Formation of Metastable Phases from an Undercooled YbFeO3 Melt Using an Aerodynamic Levitator JOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 4 2009Malahalli S. Vijaya KumarThe Yb2O3,Fe2O3 system was studied to investigate the effect of oxygen partial pressure on the formation of metastable phases over a wide range of oxygen partial pressures from 105 to 10,1 Pa. Two kinds of metastable phases, with space groups of P63cm and P63/mmc, were found through rapid solidification of an undercooled YbFeO3 melt in an atmosphere with reduced Po2. The crystal structure of the as-solidified samples changed from orthorhombic Pbnm to hexagonal P63cm and P63/mmc with decreasing Po2. X-ray diffractometric and scanning electron microscopic results confirmed the existence of various phases in the as-solidified samples. The stabilities of each phase were studied by annealing the bulk sample in the thermogravimetric,differential thermal analysis (TG-DTA) furnace up to 1673 K, and the equilibrium phase diagram was constructed for the Yb,Fe,O system at 1473 K. TG analysis showed an increase of the sample mass during annealing and revealed that the existence of Fe2+, which has an ionic radius larger than that of Fe3+, decreases the tolerance factor and therefore destabilizes the perovskite structure. [source] ## Zinc Vanadates in Vanadium Oxide-Doped Zinc Oxide Varistors JOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 2 2001Huey-Hoon HngConvergent-beam electron diffraction has been used to determine the space groups of ,- and ,-Zn3(VO4)2 particles in vanadium oxide-doped zinc oxide varistors. The crystal structure of ,-Zn3(VO4)2 has been determined to be monoclinic with space group P21 and lattice parameters of a= 9.80 Å, b= 8.34 Å, c= 10.27 Å, and ,= 115.8°, whereas that of ,-Zn3(VO4)2 is monoclinic with space group Cm and a= 10.40 Å, b= 8.59 Å, c= 9.44 Å, and ,= 98.8°. Energy-dispersive X-ray microanalysis of these two phases shows significant deviations from their expected stoichiometry. It is apparent that the ,-phase is, in fact, the metastable Zn4V2O9 phase, whereas the ,-phase either is a new oxide that consists of zinc, vanadium, and manganese or, more likely, is a zinc vanadate phase with a Zn:V atomic ratio of 1:1 that has the ability to go into solid solution with manganese. [source] ## Magnetic semiconductors in ternary Cd,Mn,Te compounds PHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 5 2008Yong LiuAbstract Since Mn-doped CdTe in zincblende structure has been fabricated for Mn concentrations from 0 to 0.5, we use a first-principles full-potential method to study CdTe-based ternary Cd,Mn,Te compounds for possible magnetic semiconductors. The compounds are constructed by substituting Mn for some Cd atoms in zincblende CdTe. We optimize fully their geometric structures and internal atomic positions, and then study their electronic and magnetic properties. We find that the stable CdMnTe2 and Cd3MnTe4 are antiferromagnetic semiconductors with space groups 160 and 111, and the stable Cd7MnTe8 is a layered ferromagnetic semiconductor with space group 115. Their real lattice constants are a little smaller than CdTe's and an Mn atom contributes 5 Bohr magnetons to their total magnetic moments. The antiferromagnetism for the CdMnTe2 is attributed to the Te-based superexchange of Mn spins. For the other two, the MnMn spin interactions are dependent on the MnMn distance and the environment. The antiferromagnetism for the Cd3MnTe4 and the layered ferromagnetism for the Cd7MnTe8 can be attributed to two weaker indirect exchange interactions based on both Cd and Te. The Kohn,Sham gaps of the three magnetic semiconductors are 0.52 eV, 0.80 eV, and 1.23 eV, respectively. The real semiconductor gaps may be larger than 1 eV considering the fact that the Kohn,Sham gap of CdTe is 0.55 eV but the experimental semiconductor gap is 1.56 eV at 300 K. These magnetic semiconductors, compatible with semiconductors such as CdTe, could be useful in spintronics applications. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## The role of the tangent bundle for symmetry operations and modulated structures ACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2010Philippe KocianAn equivalence relation on the tangent bundle of a manifold is defined in order to extend a structure (modulated or not) onto it. This extension affords a representation of a structure in any tangent space and that in another tangent space can easily be derived. Euclidean symmetry operations associated with the tangent bundle are generalized and their usefulness for the determination of the intrinsic translation part in helicoidal axes and glide planes is illustrated. Finally, a novel representation of space groups is shown to be independent of any origin point. [source] ## Alternative type I and I, turn conformations in the ,8/,9 ,-hairpin of human acidic fibroblast growth factor PROTEIN SCIENCE, Issue 3 2002Jaewon KimAbstract Human acidic fibroblast growth factor (FGF-1) has a ,-trefoil structure, one of the fundamental protein superfolds. The X-ray crystal structures of wild-type and various mutant forms of FGF-1 have been solved in five different space groups: C2, C2221, P21 (four molecules/asu), P21 (three molecules/asu), and P212121. These structures reveal two characteristically different conformations for the ,8/,9 ,-hairpin comprising residue positions 90,94. This region in the wild-type FGF-1 structure (P21, four molecules/asu), a his-tagged His93,Gly mutant (P21, three molecules/asu) and a his-tagged Asn106,Gly mutant (P212121) adopts a 3:5 ,-hairpin known as a type I (1,4) G1 ,-bulge (containing a type I turn). However, a his-tagged form of wild-type FGF-1 (C2221) and a his-tagged Leu44,Phe mutant (C2) adopt a 3:3 ,-hairpin (containing a type I, turn) for this same region. A feature that distinguishes these two types of ,-hairpin structures is the number and location of side chain positions with eclipsed C, and main-chain carbonyl oxygen groups (, , +60°). The effects of glycine mutations upon stability, at positions within the hairpin, have been used to identify the most likely structure in solution. Type I, turns in the structural data bank are quite rare, and a survey of these turns reveals that a large percentage exhibit crystal contacts within 3.0 Å. This suggests that many of the type I, turns in X-ray structures may be adopted due to crystal packing effects. [source] ## Comments on tables of magnetic space groups ACTA CRYSTALLOGRAPHICA SECTION A, Issue 2 2009Hans GrimmerLitvin [Acta Cryst. (2008), A64, 419,424 and supplementary material] extends much of the information contained in Volume A of International Tables for Crystallography for the 230 space-group types to the 1651 types of Shubnikov space groups, using Opechowski,Guccione (OG) notation for the space groups with a black,white lattice. It is pointed out that OG notation has crucial disadvantages compared to Belov,Neronova,Smirnova (BNS) notation. It is shown how Litvin's diagrams of symmetry elements for the orthorhombic Shubnikov space groups can be interpreted in terms of BNS symbols and how those containing e -glides can be simplified. A number of mistakes in the diagrams of Litvin are corrected. [source] ## Abelianization of space groups ACTA CRYSTALLOGRAPHICA SECTION A, Issue 1 2009John G. RatcliffeThe abelianization of a group is its commutator quotient group. In this paper, we provide tables of the abelianizations of all the n -dimensional space groups for n = 1, 2, 3. We prove that the exponent of the torsion subgroup of the abelianization of an arbitrary n -dimensional space group , divides the order of the point group of ,. [source] ## The symmetry of HK codes representing close-packed structures and the efficient generation of non-equivalent polytypes of a given length ACTA CRYSTALLOGRAPHICA SECTION A, Issue 5 2008Ernesto Estevez-RamsThe HK representation of close-packed polytypes is studied as a binary code. It is shown that the HK code can be seen as operators forming a group. The neutrality condition is then translated to HK sequences that result in the identity operator. The symmetry of an HK word can be related to the space-group symmetry of the corresponding polytype. All HK code types corresponding to all possible close-packed space groups are reported. From a coding perspective, equivalent HK codes correspond to bracelet equivalent classes. An efficient algorithm with execution time constant per generated object is modified to generate all non-equivalent polytypes of a given length. [source] ## Enantiomorphism of crystallographic groups in higher dimensions with results in dimensions up to 6 ACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2003Bernd SouvignierThis paper gives classification results for crystallographic groups in dimensions up to 6 which refine earlier enumeration results. Based on the classification data, the asymptotic growth of the number of space-group types is discussed. The classification scheme for crystallographic groups is revisited and a new classification level in between that of geometric and arithmetic crystal classes is introduced and denoted as harmonic crystal classes. Enantiomorphic pairs are determined on all classification levels from space-group types to crystal families and the enantiomorphic pairs of fixed-point-free space groups are given. A general algorithm to compute enantiomorphic pairs is described. [source] ## Distinction between space groups having principal rotation and screw axes, which are combined with twofold rotation axes, using the coherent convergent-beam electron diffraction method ACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2001Koh Saitoh23 sets of space groups remain indistinguishable by the convergent-beam electron diffraction (CBED) method. Recently, Tsuda, Saitoh, Terauchi, Tanaka & Goodman [Acta Cryst. (2000), A56, 359,369] demonstrated that the coherent CBED method can distinguish two space-group pairs (I23, I213) and (I222, I212121) by observing the relative arrangements of 2-fold-rotation and 21 -screw axes. The other ten space-group sets, which are composed of principal rotation and screw axes and other 2-fold-rotation axes such as P321 and P3121 (P3221), are shown to be distinguishable using the coherent CBED method. [source] ## The pair-functional method. ACTA CRYSTALLOGRAPHICA SECTION A, Issue 2 2001The theory of the pair-functional ensemble is developed to provide estimates of the pairing forces from experimental X-ray intensities. The statistical mechanics of the grand ensemble leads to a diagram expansion for the forces, in terms of the direct correlation function of the fluid ensemble combined with a series of small higher-order corrections. A simpler treatment, based on a biased Gaussian probability distribution, gives approximate formulae, valid for reflections of any type in all space groups. The role of symmetry is analysed. The entropy of an asymmetrical ensemble can always be increased by averaging it over equivalent positions of the atoms in the true space group, with the result that the atoms naturally tend to adopt the highest symmetry compatible with the data. In a cell with different types of atom, the atoms experience a single force function but they interact with a strength proportional to the products of their scattering factors. Numerical estimates are given for typical cases. [source] ## Ill-conditioned Shake-and-Bake: the trap of the false minimum ACTA CRYSTALLOGRAPHICA SECTION A, Issue 2 2000Hongliang XuThe alternation of phase refinement with the imposition of real-space constraints is the essence of the Shake-and-Bake procedure. Typically, these constraints prevent trial structures from falling into local minima. Nevertheless, structures appear to migrate to false minima with significant frequency. These false minima are characterized by the presence of a large `uranium' peak on the corresponding Fourier map. Fortunately, they can be recognized and avoided by considering the values of the minimal function both before and after the application of constraints. However, it appears that finding solutions for large structures is likely also to require parameter-shift conditions different from those that have been found to work well in other space groups. In fact, these conditions often yield an unusually high percentage of solutions. [source] ## Experimental and predicted crystal structures of Pigment Red 168 and other dihalogenated anthanthrones ACTA CRYSTALLOGRAPHICA SECTION B, Issue 5 2010Martin U. SchmidtThe crystal structures of 4,10-dibromo-anthanthrone (Pigment Red 168; 4,10-dibromo-dibenzo[def,mno]chrysene-6,12-dione), 4,10-dichloro- and 4,10-diiodo-anthanthrone have been determined by single-crystal X-ray analyses. The dibromo and diiodo derivatives crystallize in P21/c, Z = 2, the dichloro derivative in , Z = 1. The molecular structures are almost identical and the unit-cell parameters show some similarities for all three compounds, but the crystal structures are neither isotypic to another nor to the unsubstituted anthanthrone, which crystallizes in P21/c, Z = 8. In order to explain why the four anthanthrone derivatives have four different crystal structures, lattice-energy minimizations were performed using anisotropic atom,atom model potentials as well as using the semi-classical density sums (SCDS-Pixel) approach. The calculations showed the crystal structures of the dichloro and the diiodo derivatives to be the most stable ones for the corresponding compound; whereas for dibromo-anthanthrone the calculations suggest that the dichloro and diiodo structure types should be more stable than the experimentally observed structure. An experimental search for new polymorphs of dibromo-anthanthrone was carried out, but the experiments were hampered by the remarkable insolubility of the compound. A metastable nanocrystalline second polymorph of the dibromo derivative does exist, but it is not isostructural to the dichloro or diiodo compound. In order to determine the crystal structure of this phase, crystal structure predictions were performed in various space groups, using anisotropic atom,atom potentials. For all low-energy structures, X-ray powder patterns were calculated and compared with the experimental diagram, which consisted of a few broad lines only. It turned out that the crystallinity of this phase was not sufficient to determine which of the calculated structures corresponds to the actual structure of this nanocrystalline polymorph. [source] ## Symmetry analysis of extinction rules in diffuse-scattering experiments ACTA CRYSTALLOGRAPHICA SECTION B, Issue 3 2010R. L. WithersStructured diffuse-scattering intensities, whether of compositional or of pure displacive origin, static or dynamic, contain important information about the symmetry of the individual compositional and/or displacive modes responsible for the observed intensities. However, the interpretation of the experimental data is very often impeded by the lack of a symmetry-based approach to the analysis of the structured diffuse-scattering distributions. Recently, we have demonstrated the existence of systematic phonon selection rules for diffuse scattering that depend on the symmetries of the mode and the scattering vector, and not on the specific structure. Here, we show that such symmetry analysis can be successfully extended and also applied to structure-dependent diffuse scattering associated with `disordered' materials: the combination of theoretically determined, diffuse-scattering extinction conditions with the concept of non-characteristic orbits proves to be very useful in the interpretation of the observed diffuse-scattering extinctions. The utility of this approach is illustrated by the analysis of diffuse-scattering data from ThAsSe, FeOF and FeF2. The essential part of the associated calculations are performed by the computer programs NEUTRON (systematic phonon extinction rules in inelastic scattering) and NONCHAR (non-characteristic orbits of space groups) that are available on the Bilbao crystallographic server (http://www.cryst.ehu.es). [source] ## A complicated quasicrystal approximant ,16 predicted by the strong-reflections approach ACTA CRYSTALLOGRAPHICA SECTION B, Issue 1 2010Mingrun LiThe structure of a complicated quasicrystal approximant ,16 was predicted from a known and related quasicrystal approximant ,6 by the strong-reflections approach. Electron-diffraction studies show that in reciprocal space, the positions of the strongest reflections and their intensity distributions are similar for both approximants. By applying the strong-reflections approach, the structure factors of ,16 were deduced from those of the known ,6 structure. Owing to the different space groups of the two structures, a shift of the phase origin had to be applied in order to obtain the phases of ,16. An electron-density map of ,16 was calculated by inverse Fourier transformation of the structure factors of the 256 strongest reflections. Similar to that of ,6, the predicted structure of ,16 contains eight layers in each unit cell, stacked along the b axis. Along the b axis, ,16 is built by banana-shaped tiles and pentagonal tiles; this structure is confirmed by high-resolution transmission electron microscopy (HRTEM). The simulated precession electron-diffraction (PED) patterns from the structure model are in good agreement with the experimental ones. ,16 with 153 unique atoms in the unit cell is the most complicated approximant structure ever solved or predicted. [source] ## A list of organic kryptoracemates ACTA CRYSTALLOGRAPHICA SECTION B, Issue 1 2010László FábiánA list of 181 organic kryptoracemates has been compiled. This class of crystallographic oddities is made up of racemic compounds (i.e. pairs of resolvable enantiomers) that happen to crystallize in Sohnke space groups (i.e. groups that include only proper symmetry operations). Most (151) of the 181 structures could have crystallized as ordered structures in non-Sohnke groups. The remaining 30 structures do not fully meet this criterion but would have been classified as kryptoracemates by previous authors. Examples were found and checked with the aid of available software for searching the Cambridge Structural Database, for generating and comparing InChI strings, and for validating crystal structures. The pairs of enantiomers in the true kryptoracemates usually have very similar conformations; often the match is near-perfect. There is a pseudosymmetric relationship of the enantiomers in about 60% of the kryptoracemate structures, but the deviations from inversion or glide symmetry are usually quite easy to spot. Kryptoracemates were found to account for 0.1% of all organic structures containing either a racemic compound, a meso molecule, or some other achiral molecule. The centroid of a pair of enantiomers is more likely (99.9% versus 99% probability) to be located on an inversion center than is the centroid of a potentially centrosymmetric molecule. [source] ## Eu3Si15,,,xAl1,+,xOxN23,,,x (x, 5/3) as a commensurate composite crystal ACTA CRYSTALLOGRAPHICA SECTION B, Issue 5 2009Yuichi MichiueA new Eu-SiAlON crystal, Eu3Si15,,,xAl1,+,xOxN23,,,x (x, 5/3), was found and the structure was determined by an X-ray diffraction technique using a twinned sample. The structure consists of a host framework, which is constructed by the connection of MX4 tetrahedra (M: Si or Al; X: O or N), and Eu ions as the guest ions. The structure is considered to be a commensurate composite crystal. The basic vectors are a1 = a/3, b and c for the first substructure, and a2 = a/5, b and c for the second substructure. The first substructure consists of part of the host framework and the Eu ions, while the remainder of the host structure is taken as the second substructure. Possible phases belonging to the series are proposed using the composite crystal model in (3,+,1)-dimensional superspace. Chemical composition, possible space groups, cell parameters, and the basic model for those phases are presented. [source] ## Electron diffraction of ABX3 perovskites with both layered ordering of A cations and tilting of BX6 octahedra ACTA CRYSTALLOGRAPHICA SECTION B, Issue 4 2009Kyosuke KishidaIt is shown that 21 ABX3 perovskites with tilted BX6 octahedra and layered ordering of A cations can be generated on the basis of group,subgroup relations. These structures (with 16 different space groups) are classified into ten diffraction types in terms of the conditions for superstructure reflections caused by the ordering of A cations, tilting of BX6 octahedra and structural absences. SAED (selected-area electron diffraction) allows the distinction of seven of the 21 different perovskites, while additional symmetry analysis by CBED (convergent-beam electron diffraction) is needed for the remaining 14 structures. The space groups of lithium lanthanum titanate pseudomorphs (with discrete chemical compositions) are successfully deduced by electron diffraction experiments. [source] ## Absolute structure determination as a reference for the enantiomeric resolution of racemic mixtures of cyclophosphazenes via chiral high-performance liquid chromatography ACTA CRYSTALLOGRAPHICA SECTION B, Issue 3 2009Simon ColesReversed-phase chiral high-performance liquid chromatography (HPLC) is a potentially powerful technique for the enantiomeric resolution of racemic mixtures, although the elution order of enantiomers is only relative and it is necessary to fully characterize reference systems for this method to provide absolute configurational information. The enantiomeric resolution of a series of racemic di-spiro cyclotriphosphazene derivatives, N3P3X2[O(CH2)3NH]2 (X = Cl, Ph, SPh, NHPh, OPh) [(1),(5), respectively] was carried out by reversed-phase chiral HPLC on a commercially available Pirkle-type chiral stationary phase (R,R)-Whelk-01 using 85:15 (v/v) hexane,thf as the mobile phase. The absolute configurations of the resulting enantiomers of compounds (3) (X = SPh) and (5) (X = OPh) were determined unambiguously by X-ray crystallography. For both (3) and (5) it was found that the SS enantiomer eluted before the RR enantiomer, indicating a convenient method to determine the absolute configurations of enantiomers of this series of cyclophosphazene derivatives and providing the first set of enantiomeric reference compounds for cyclophosphazene derivatives. These structures demonstrate an interesting anomaly in that the pair of enantiomers of (3) crystallize in enantiomorphically paired space groups whilst, under the same conditions, the solid-state forms of the enantiomers of (5) form structures in Sohncke space groups that are not enantiomorphous. [source] ## Chiral carboxylic acids and their effects on melting-point behaviour in co-crystals with isonicotinamide ACTA CRYSTALLOGRAPHICA SECTION B, Issue 6 2008Andreas LemmererThe crystal structures of co-crystals of two systems of chiral carboxylic acids, optically active and racemic 2-phenylpropionic acid and 2-phenylbutyric acid, with isonicotinamide are reported to investigate the effects of the chirality of the chiral carboxylic acids on the melting point of the co-crystal complexes. It was found that the racemic co-crystal has a higher melting point than the optically active co-crystal, which correlates with the denser packing arrangement inherent in centrosymmetric space groups. [source] ## Revision of pyrrhotite structures within a common superspace model ACTA CRYSTALLOGRAPHICA SECTION B, Issue 5 2007Zunbeltz IzaolaThe structure of pyrrhotite (Fe1,,,xS with 0.05 ,x, 0.125) has been reinvestigated in the framework of the superspace formalism. A common model with a centrosymmetric superspace group is proposed for the whole family. The atomic domains in the internal space representing the Fe atoms are parametrized as crenel functions that fulfil the closeness condition. The proposed model explains the x -dependent space groups observed and the basic features of the structures reported up to now. Our model yields for any x value a well defined ordered distribution of Fe vacancies in contrast to some of the structural models proposed in the literature. A new (3,+,1)-dimensional refinement of Fe0.91S using the deposited dataset [Yamamoto & Nakazawa (1982). Acta Cryst. A38, 79,86] has been performed as a benchmark of the model. The consistency of the proposed superspace symmetry and its validity for other compositions has been further checked by means of ab initio calculations of both atomic forces and equilibrium atomic positions in non-relaxed and relaxed structures, respectively. [source] ## The commensurate composite ,-structure of ,-tantalum ACTA CRYSTALLOGRAPHICA SECTION B, Issue 3 2003Alla ArakcheevaThe single-crystal investigation of the self-hosting ,-structure of ,-tantalum (,-Ta) at 120,K (low-temperature, LT, structure) and at 293,K (RT-I before cooling and RT-II after cooling and rewarming; RT represents room temperature) shows that this structure is indeed a specific two-component composite where the components have the same (or an integer multiple) lattice constants but different space groups. The space groups of both host (H) and guest (G) components cause systematic absences, which result from their intersection. The highest symmetry of a ,-structure can be described as [H: P42/mnm; G: P4/mbm (cG = 0.5cH); composite: P42/mnm]. A complete analysis of possible symmetries is presented in the Appendix. In ,-Ta, two components modify their symmetry during the thermal process 293,K (RT-I) , 120,K (LT) , 293,K (RT-II): [H: P21m; G: P21m; composite: P21m] , [H: P, G: P4/mbm (cG = 0.5cH), composite: P] , [H: P21m, G: P4/mbm (cG = 0.5cH), composite: P21m]. Thus, the phase transition is reversible with respect to H and irreversible with respect to G. [source] |