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Space-group Symmetry (space-group + symmetry)
Selected AbstractsA systematic approach to the derivation of standard orientation-location parts of symmetry-operation symbolsACTA CRYSTALLOGRAPHICA SECTION A, Issue 6 2007Kazimierz Stró Automatically generated orientation-location parts, or coordinate triplets describing the geometric elements, differ frequently from the corresponding parts of the symmetry-operation symbols listed in International Tables for Crystallography [(1983), Vol. A, Space-Group Symmetry, edited by Th. Hahn. Dordrecht: Reidel]. An effective algorithm enabling the derivation of standard orientation-location parts from any symmetry matrix is described and illustrated. The algorithm is based on a new concept alternative to the `invariant points of reduced operation'. First, the geometric element that corresponds to a given symmetry operation is oriented and located in a nearly convention free manner. The application of the direction indices [uvw] or Miller indices (hkl) gives a unique orientation provided the convention about the positive direction is defined. The location is fixed by the specification of a unique point on the geometric element, i.e. the point closest to the origin. Next, both results are converted into the standard orientation-location form. The standardization step can be incorporated into other existing methods of derivation of the symmetry-operation symbols. A number of standardization examples are given. [source] Structures of 6H perovskites Ba3CaSb2O9 and Ba3SrSb2O9 determined by synchrotron X-ray diffraction, neutron powder diffraction and ab initio calculationsACTA CRYSTALLOGRAPHICA SECTION B, Issue 2 2008Budwy Rowda The structures of the 6H perovskites Ba3B2+Sb5+2O9, B = Ca and Sr, have been solved and refined using synchrotron X-ray and neutron powder diffraction data. Ba3CaSb2O9 and Ba3SrSb2O9 have monoclinic C2/c and triclinic space-group symmetries, respectively, while Ba3MgSb2O9 has ideal hexagonal P63/mmc space-group symmetry. The symmetry-lowering distortions are a consequence of internal `chemical pressure' owing to the increasing effective ionic radius of the alkaline-earth cation in the perovskite B site from Mg2+ (0.72,Å) to Ca2+ (1.00,Å) to Sr2+ (1.18,Å). Increasing the effective ionic radius further to Ba2+ (1.35,Å) leads to decomposition at room temperature. The driving force behind the transition from P63/mmc to C2/c is the need to alleviate underbonding of Ba2+ cations in the perovskite A site via octahedral rotations, while the transition from C2/c to is driven by the need to regularize the shape of the Sb2O9 face-sharing octahedral dimers. Ab initio geometry-optimization calculations were used to find a triclinic starting model for Ba3SrSb2O9. [source] Space-group determination from powder diffraction data: a probabilistic approachJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 6 2004Angela Altomare Experimental powder diffraction diagrams, once indexed and decomposed into single diffraction intensities, can be submitted to statistical analysis for the determination of space-group symmetry. A new algorithm is illustrated, which is able to provide, on a quantitative basis, a probability value for each extinction symbol compatible with the previously established lattice symmetry. The algorithm has been implemented in EXPO2004 [Altomare, Caliandro, Camalli, Cuocci, Giacovazzo, Moliterni & Rizzi (2004). J. Appl. Cryst.37, 1025,1028] and has been successfully tested using a large set of experimental data. [source] Diffusion-equation method for crystallographic figure of meritsACTA CRYSTALLOGRAPHICA SECTION A, Issue 5 2010Anders J. Markvardsen Global optimization methods play a significant role in crystallography, particularly in structure solution from powder diffraction data. This paper presents the mathematical foundations for a diffusion-equation-based optimization method. The diffusion equation is best known for describing how heat propagates in matter. However, it has also attracted considerable attention as the basis for global optimization of a multimodal function [Piela et al. (1989). J. Phys. Chem.93, 3339,3346]. The method relies heavily on available analytical solutions for the diffusion equation. Here it is shown that such solutions can be obtained for two important crystallographic figure-of-merit (FOM) functions that fully account for space-group symmetry and allow the diffusion-equation solution to vary depending on whether atomic coordinates are fixed or not. The resulting expression is computationally efficient, taking the same order of floating-point operations to evaluate as the starting FOM function measured in terms of the number of atoms in the asymmetric unit. This opens the possibility of implementing diffusion-equation methods for crystallographic global optimization algorithms such as structure determination from powder diffraction data. [source] Form, symmetry and packing of biomacromolecules.ACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2010The differentiation of the human rhinovirus into serotypes, all having very similar structures and the same architecture, is shown to be related to the packing of the viruses in the crystal and to its space-group symmetry. The molecular crystallographic properties (here described in terms of a molecular lattice ,M instead of the form lattice ,F considered in previous publications) appear to be compatible with the crystal structure and with the packing lattice ,P, introduced in Part I [Janner (2010). Acta Cryst. A66, 301,311]. On the basis of the enclosing forms of the capsid, a sphere packing is considered, where the spheres touch at kissing points. Residues of each of the four coat proteins (VP1, VP2, VP3, VP4), having a minimal distance from the kissing points, define a set of kissing point related (KPR) residues. In this set only four different residues occur, one for each coat protein, ordered into symmetric clusters {already classified in a previous publication [Janner (2006). Acta Cryst. A62, 270,286]} and indexed by neighbouring lattice points of ,P (or equivalently of ,M). The indexed KPR residues allow a fingerprint characterization of the five rhinovirus serotypes whose structures are known (HRV16, HRV14, HRV3, HRV2 and HRV1A). In the fingerprint they occur as internal (if inside the given capsid), as external (if belonging to the neighbouring viruses) or as a contact residue (if at a kissing point position). The same fingerprint, periodically extended, permits a coarse-grained reconstruction of the essential properties of the crystal packing, invariant with respect to the space group of the serotype. [source] The symmetry of HK codes representing close-packed structures and the efficient generation of non-equivalent polytypes of a given lengthACTA CRYSTALLOGRAPHICA SECTION A, Issue 5 2008Ernesto Estevez-Rams The 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] Pressure-induced phase transitions in l -alanine, revisitedACTA CRYSTALLOGRAPHICA SECTION B, Issue 4 2010N. A. Tumanov The effect of pressure on l -alanine has been studied by X-ray powder diffraction (up to 12.3,GPa), single-crystal X-ray diffraction, Raman spectroscopy and optical microscopy (up to ,,6,GPa). No structural phase transitions have been observed. At ,,2,GPa the cell parameters a and b become accidentally equal to each other, but without a change in space-group symmetry. Neither of two transitions reported by others (to a tetragonal phase at ,,2,GPa and to a monoclinic phase at ,,9,GPa) was observed. The changes in cell parameters were continuous up to the highest measured pressures and the cells remained orthorhombic. Some important changes in the intermolecular interactions occur, which also manifest themselves in the Raman spectra. Two new orthorhombic phases could be crystallized from a MeOH/EtOH/H2O pressure-transmitting mixture in the pressure range 0.8,4.7,GPa, but only if the sample was kept at these pressures for at least 1,2,d. The new phases converted back to l -alanine on decompression. Judging from the Raman spectra and cell parameters, the new phases are most probably not l -alanine but its solvates. [source] Structures of 6H perovskites Ba3CaSb2O9 and Ba3SrSb2O9 determined by synchrotron X-ray diffraction, neutron powder diffraction and ab initio calculationsACTA CRYSTALLOGRAPHICA SECTION B, Issue 2 2008Budwy Rowda The structures of the 6H perovskites Ba3B2+Sb5+2O9, B = Ca and Sr, have been solved and refined using synchrotron X-ray and neutron powder diffraction data. Ba3CaSb2O9 and Ba3SrSb2O9 have monoclinic C2/c and triclinic space-group symmetries, respectively, while Ba3MgSb2O9 has ideal hexagonal P63/mmc space-group symmetry. The symmetry-lowering distortions are a consequence of internal `chemical pressure' owing to the increasing effective ionic radius of the alkaline-earth cation in the perovskite B site from Mg2+ (0.72,Å) to Ca2+ (1.00,Å) to Sr2+ (1.18,Å). Increasing the effective ionic radius further to Ba2+ (1.35,Å) leads to decomposition at room temperature. The driving force behind the transition from P63/mmc to C2/c is the need to alleviate underbonding of Ba2+ cations in the perovskite A site via octahedral rotations, while the transition from C2/c to is driven by the need to regularize the shape of the Sb2O9 face-sharing octahedral dimers. Ab initio geometry-optimization calculations were used to find a triclinic starting model for Ba3SrSb2O9. [source] Capabilities and limitations of a (3,+,d)-dimensional incommensurately modulated structure as a model for the derivation of an extended family of compounds: example of the scheelite-like structuresACTA CRYSTALLOGRAPHICA SECTION B, Issue 1 2008Alla Arakcheeva The previously reported incommensurately modulated scheelite-like structure KNd(MoO4)2 has been exploited as a natural (3,+,1)-dimensional superspace model to generate the scheelite-like three-dimensional structure family. Although each member differs in its space-group symmetry, unit-cell parameters and compositions, in (3,+,1)-dimensional space, they share a common superspace group, a common number of building units in the basic unit cell occupying Wyckoff sites with specific coordinates (x, y, z) and specific basic unit-cell axial ratios (c/a, a/b, b/c) and angles. Variations of the modulation vector q, occupation functions and t0 are exploited for the derivation. Eight topologically and compositionally different known structures are compared with their models derived from the KNd(MoO4)2 structure in order to evaluate the capabilities and limitations of the incommensurately modulated structure to act as a superspace generating model. Applications of the KNd(MoO4)2 structure as a starting model for the refinement and prediction of some other modulated members of the family is also illustrated. The (3,+,1)-dimensional presentation of the scheelite-like structures reveals new structural relations, which remain hidden if only conventional three-dimensional structure descriptions are applied. [source] Temperature-dependent crystal structure refinement and 57Fe Mössbauer spectroscopy of Cu2Fe2Ge4O13ACTA CRYSTALLOGRAPHICA SECTION B, Issue 1 2007Günther J. Redhammer The germanate compound Cu2Fe2Ge4O13, dicopper diiron germanate, was synthesized by solid-state reaction at 1403,K and ambient pressure. There is no change of space-group symmetry between 10 and 900,K. Between 40,K and room temperature the a lattice parameter shows a negative thermal expansion which can be connected to a decreasing Cu,Cu interatomic distance. Above room temperature all the lattice parameters are positively correlated with temperature. Among the structural parameters several alterations with temperature occur, which are most prominent for the distorted Fe3+ octahedral site. Besides an increase of the average bond length and of the interatomic Fe,Fe distances, distortional parameters also increase with temperature, while the average Cu,O bond length remains almost constant between 100 and 900,K, as do the average Ge,O distances. 57Fe Mössbauer spectroscopy was used to detect long-range magnetic ordering in Cu2Fe2Ge4O13. While around 100,K, which is the temperature at which a broad maximum is observed in the magnetic susceptibility, no magnetic ordering was detected in the Mössbauer spectrum, below 40,K a narrow split sextet is developed which is indicative of a three-dimensional magnetic ordering of the sample. [source] Prediction of new displacive ferroelectrics through systematic pseudosymmetry search.ACTA CRYSTALLOGRAPHICA SECTION B, Issue 6 2002Pmc21 symmetry, Results for materials with Pba Polar structures with pseudosymmetry related to a hypothetical non-polar configuration are considered as good candidates for ferroelectrics. Recently, a procedure has been developed for a systematic pseudosymmetry search among structures with a given space-group symmetry. The aim of this paper is the extension of the pseudosymmetry procedure to the case of structures with polar symmetry and its application in the search for new ferroelectrics. The results obtained by the generalized pseudosymmetry search among the compounds with symmetries and listed in the Inorganic Crystal Structure Database are discussed. The calculations have been performed by the program PSEUDO, which forms part of the Bilbao Crystallographic Server (http://www.cryst.ehu.es). In addition, an empirical relation between the atomic displacements necessary to reach the non-polar structure and the transition temperature is proposed and compared with the Abrahams,Kurtz,Jamieson relation. [source] A monoclinic polymorph of bis(tert -butylperthiophosphonic) dianhydrideACTA CRYSTALLOGRAPHICA SECTION C, Issue 3 2000Burkhard Ziemer In comparison with the known orthorhombic polymorph oftrans -2,4-di- tert -butyl-2,4-dithioxo-1,3-dithia-2,4-diphosphetane, C8H18P2S4, (I) [Shore, Pennington, Noble & Cordes (1988). Phosphorous Sulfur, 39, 153,157], the new crystallographic modification is monoclinic and the corresponding solid density is markedly higher. In both structures, the molecules have 2/m symmetry imposed by space-group symmetry and all corresponding bond lengths and angles are equal within the limits of errors. [source] Pseudo-merohedral twinning and noncrystallographic symmetry in orthorhombic crystals of SIVmac239 Nef core domain bound to different-length TCR, fragmentsACTA CRYSTALLOGRAPHICA SECTION D, Issue 2 2010Walter M. Kim HIV/SIV Nef mediates many cellular processes through interactions with various cytoplasmic and membrane-associated host proteins, including the signalling , subunit of the T-cell receptor (TCR,). Here, the crystallization strategy, methods and refinement procedures used to solve the structures of the core domain of the SIVmac239 isolate of Nef (Nefcore) in complex with two different TCR, fragments are described. The structure of SIVmac239 Nefcore bound to the longer TCR, polypeptide (Leu51,Asp93) was determined to 3.7,Å resolution (Rwork = 28.7%) in the tetragonal space group P43212. The structure of SIVmac239 Nefcore in complex with the shorter TCR, polypeptide (Ala63,Arg80) was determined to 2.05,Å resolution (Rwork = 17.0%), but only after the detection of nearly perfect pseudo-merohedral crystal twinning and proper assignment of the orthorhombic space group P212121. The reduction in crystal space-group symmetry induced by the truncated TCR, polypeptide appears to be caused by the rearrangement of crystal-contact hydrogen-bonding networks and the substitution of crystallographic symmetry operations by similar noncrystallographic symmetry (NCS) operations. The combination of NCS rotations that were nearly parallel to the twin operation (k, h, ,l) and a and b unit-cell parameters that were nearly identical predisposed the P212121 crystal form to pseudo-merohedral twinning. [source] An alternate description of two crystal structures of phospholipase A2 from Bungarus caeruleusACTA CRYSTALLOGRAPHICA SECTION D, Issue 4 2007Isolde Le Trong Reinterpretations of the space-group symmetry are reported for two crystal structures of phospholipase A2 isoforms (PDB codes 1u4j and 1g2x). The two structures reported in space groups R3 and C2 are isomorphous with a third isoform with space group R32 (PDB code 1fe5). The original structure reports were interpreted in terms of different oligomeric forms of the isoforms, but these conclusions are not supported by the isomorphous structures. [source] Crystallization and X-ray diffraction analysis of the DNA-remodelling protein DnaD from Bacillus subtilisACTA CRYSTALLOGRAPHICA SECTION F (ELECTRONIC), Issue 2 2007Sabine Schneider The DnaD protein is an essential component of the chromosome-replication machinery of the Gram-positive bacterium Bacillus subtilis and is part of the primosomal cascade that ultimately loads the replicative ring helicase DnaC onto DNA. Moreover, DnaD is a global regulator of DNA architecture, as it forms higher order nucleoprotein structures in order to open supercoiled DNA. Here, the crystallization and preliminary X-ray diffraction analysis of the two domains of DnaD from B. subtilis are reported. Crystals of the N-terminal domain are trigonal, with either P3121 or P3221 space-group symmetry, and diffracted X-rays to 2.0,Å resolution; crystals of the C-terminal domain are hexagonal, with space group P61 or P65, and diffracted X-rays to 2.9,Å resolution in-house. Determination of the structure of the DnaD domains will provide insight into how remodelling of the nucleoid is associated with priming of replication in the model Gram-positive organism B. subtilis. [source] | ||||||||||