Showing papers in "Acta Crystallographica Section A in 1993"
544 citations
TL;DR: In this paper, a method for the determination of all possible phonon modes in framework crystal structures that leave the fundamental structural units (tetrahedra and octahedra) undistorted is described.
Abstract: This paper describes a computational method for the determination of all possible phonon modes in framework crystal structures that leave the fundamental structural units (tetrahedra and octahedra) undistorted. Such rigid-unit modes (RUMs) are prime candidates as soft modes for displacive phase transitions, such as in the perovskite structure, and this computational method can be used to rationalize the phase transitions in any framework structure. The method has been programmed for general use. The RUM approach is illustrated by consideration of the perovskite, quartz and cristobalite structures.
219 citations
TL;DR: A review of the use of transmission electron diffraction for the measurement of crystal structure-factor amplitudes and phases can be found in this paper, where the mean inner potential is found to be sensitive to the bonding distribution of valence electrons and sensitively constrains accurate X-ray structure factor measurements.
Abstract: A review is given of research into the measurement of crystal structure-factor amplitudes and phases by transmission electron diffraction. Accuracies for amplitudes are commonly a fraction of a percent (after conversion to X-ray structure factors) while phases may now be measured in favorable cases using three-beam electron diffraction to an accuracy of much better than 1°. Following a brief review of theory, the main techniques are outlined. These include quantitative convergent-beam electron diffraction, the critical-voltage method, the intersecting Kikuchi- and HOLZ-Iine methods and methods based on weak high-order reflections in wide-angle patterns. Enantiomorphs and polarity are discussed. Summaries are given of measurements of the mean inner potential and of structure factors generally. A brief review of the implications of this work for studies of crystal bonding and ordering in alloys is given, and its use to test ab initio computations of charge density. The mean inner potential is found to be the quantity most sensitive to the bonding distribution of valence electrons and sensitively constrains accurate X-ray structure-factor measurements. Electron diffraction techniques are to be preferred for studies of individual microcrystals or artificially formed structures and for the very accurate measurement of structure-factor phases in acentric crystals with small unit cells.
126 citations
TL;DR: The first three-dimensional structure of a DNA methyltransferase is presented and the core of the structure is dominated by sequence motifs conserved among all DNA (cytosine-5)-methyltransferases, and these are responsible for cofactor binding and methyl transferase function.
Abstract: The first three-dimensional structure of a DNA methyltransferase is presented. The crystal structure of the DNA (cytosine-5)-methyltransferase, M.HhaI (recognition sequence: GCGC), complexed with S-adenosyl-L-methionine has been determined and refined at 2.5 A resolution. The core of the structure is dominated by sequence motifs conserved among all DNA (cytosine-5)-methyltransferases, and these are responsible for cofactor binding and methyltransferase function.
85 citations
TL;DR: In this paper, a superspace group for the analysis of composite-crystal structures has been proposed, which is analogous to that for the modulated structure in many respects, and two possible approximations and a relation between the superspace and space groups for commensurate composite crystals are discussed.
Abstract: Superspace groups introduced for usual modulated structures have recently been applied to the analysis of composite crystals. This review describes the method of composite-crystal analysis based on the superspace group. This method is efficient for the analysis of any (incommensurate or commensurate) composite crystals. The method is analogous to that for the modulated structure in many respects. The description of composite crystals in superspace, determination of their superspace groups and unified setting of the unit vectors are mentioned. Two possible approximations and a relation between the superspace and space groups for commensurate composite crystals are discussed. Space groups of chimney-ladder structures with different periods are derived from a single superspace group by the application of this relation. Possible superspace groups for known composite structures are deduced from the space groups of average substructures. Finally, the refinement method is discussed.
82 citations
TL;DR: In this article, the mean value of Nb-O distances in the regular tetrahedron of rare earth orthoniobates (RNbO4: R = La, Nd, Ho and Yb) is estimated with the normal coordinate method.
Abstract: Precise crystal structure analysis by neutron powder diffraction is performed for rare-earth orthoniobates (RNbO4: R = La, Nd, Ho and Yb) and the distortion of NbO4 tetrahedra is estimated with the normal-coordinate method. Displacement of the cubic symmetry mode is large and increases with decreasing ionic radius of VIIIR3+. This displacement produces a regular tetrahedron of NbO4. The mean value of Nb–O distances in the regular tetrahedron of RNbO4 crystals is 1.834 A. This value is nearly equal to the mean bond length for s = 5/4, \overline R = 1.828 A, estimated by the bond-valence method. Displacements of the other symmetry modes slightly decrease or are almost constant with decreasing ionic radius.
72 citations
TL;DR: In this paper, the calculated reflectivity from geometrical and resolution-function factors is compared with the measured reflectivity of a commercial silicon wafer and of a niobium film on a sapphire substrate.
Abstract: X-ray reflectivity is a powerful technique to study electron density profiles in the direction normal to the surface of a fiat sample. As usual in scattering experiments, where the phase information is lost, it is necessary to build a model that can be used to calculate the reflectivity for comparison with the measured reflectivity. In the calculations, it is necessary to correct the calculated reflectivity from geometrical and resolution-function factors, which play a major role at low angles of incidence. These factors are presented in this paper and the corrected calculated intensity is compared with the measured reflectivity of a commercial silicon wafer and of a niobium film on a sapphire substrate.
64 citations
TL;DR: In this paper, the authors analyzed molecular packing in benzene, naphthalene and anthracene crystals in terms of molecular dimer interaction using empirical (exp−6−1) potential-energy functions.
Abstract: Molecular packing in benzene, naphthalene and anthracene crystals is analyzed in terms of molecular dimer interaction. Intermolecular energies of the gas dimer molecules are calculated for various intermolecular distances and orientations using empirical (exp−6−1) potential-energy functions. The gas dimers are compared to pairs of molecules extracted from the observed crystal structures. Particular attention is given to intermolecular Coulombic interaction. Net atomic charges are obtained by the potential-derived method from 6-31G and 6-31G** level ab initio wavefunctions. In the benzene crystal there are strong edge-plane intermolecular Coulombic interactions. The edge-plane interaction becomes somewhat less important in naphthalene and anthracene and the van der Waals interaction increases in importance.
63 citations
TL;DR: In this article, the authors used Delaney symbols and the properties of the 219 isomorphism classes of crystallographic space groups to find exactly 88 equivariant types that fall into seven topological families.
Abstract: It has long been known that there exists an infinite number of types of tile-transitive periodic three-dimensional tilings Here, it is shown that, by contrast, the number of types of face-transitive periodic three-dimensional tilings is finite The method of Delaney symbols and the properties of the 219 isomorphism classes of crystallographic space groups are used to find exactly 88 equivariant types that fall into seven topological families
56 citations
TL;DR: In this paper, the authors describe a method for automatic structure determination by the application of Karle-Hauptman matrices to the phase problem, using the common-minor strategy, which combines the information contained in several KH matrices.
Abstract: This paper describes a method for automatic structure determination by the application of Karle–Hauptman matrices to the phase problem. A new method, the common-minor strategy, is used to combine the information contained in several Karle–Hauptman matrices. Sets of phases large enough to define the structure are obtained. If the matrices are linked properly, phases contained in a larger array of matrices can be adequately restricted to a common origin. The partial solutions obtained on Fourier transformation are extended to the complete structure in a fully automatic manner. A new algorithm is presented for the maximization of the determinant of a Karle–Hauptman matrix as a function of the phases.
50 citations
TL;DR: Barium ferrite Ba2Fe2O5 was solved using a combination of high-resolution electron microscopy (HREM), crystallographic image processing (CIP) and electron diffraction as discussed by the authors.
Abstract: Barium ferrite Ba2Fe2O5 is a complex perovskite-related structure. The crystal is monoclinic P21/c, with a = 6.969 (1), b = 11.724 (1), c = 23.431 (5) A, β = 98.74 (1)°. The composition of one unit cell is Ba28Fe28O70. The structure was solved using a combination of high-resolution electron microscopy (HREM), crystallographic image processing (CIP) and electron diffraction. The structure can be described as a perovskite with 14 oxygen positions unoccupied with respect to the ABO3 stoichiometry in the monoclinic unit cell. These positions can be identified from the potential map obtained by HREM and CIP. They form two linear groups. Seven of them lie on a line along [476]m (corresponding to [110]c of perovskite), while the seven other symmetry-related positions lie along [4\overline 76]m (corresponding to [101]c of perovskite).
TL;DR: In this article, a new phase-refinement function based on the maximization of ZR(Φ) = ΣH(EH − 〈EH〉) GH(ϵ) as a function of the collectivity Φ of phases of the reflections with large E values is presented, where EH − ϵ and GH are the Fourier coefficients of two Patterson-type functions, the first with the origin peak removed and the second taking into account the atomicity condition.
Abstract: Most Patterson-search methods are based on functions measuring the coincidence of the observed Patterson function with the model Patterson function calculated as a function of some variables, e.g. the rotation angles in the case of the rotation function. In parallel with such methods, a new phase-refinement function based on the maximization of ZR(Φ) = ΣH(EH − 〈EH〉) GH(Φ) as a function of the collectivity Φ of phases of the reflections with large E values is presented, where EH − 〈EH〉 and GH(Φ) are the Fourier coefficients of two Patterson-type functions, the first with the origin peak removed and the second taking into account the atomicity condition. It will be shown how ZR(Φ) can be maximized by a new tangent formula actively using the small E values and not possessing any weighting factor. The utility of this formula is illustrated on the basis of two representative test examples.
TL;DR: Maalouf et al. as mentioned in this paper derived an unknown part of the electron density in the unit cell of a crystal when part of its structure of contents is already known, based on the similarity of the X-ray diffraction pattern to a hologram.
Abstract: Equations are derived for finding an unknown part of the electron density in the unit cell of a crystal when part of the structure of its contents is already known. These equations are based on the similarity of the X-ray diffraction pattern to a hologram. The X-ray field scattered by the known part of the structure is identified as the holographic reference beam. It interferes with the waves scattered from the unknown part of the structure. The interference pattern contains phase information that can be exploited to recover fully the unknown part of the structure. This paper discusses mathematical properties of the resulting equations and some methods for their solution. A strong similarity to inverse problems of image processing is pointed out and connections to other known methods of X-ray crystallography are established. In paper III [Maalouf, Hoch, Stem, Szoke & Szoke (1993). Acta Cryst. A49, 866–871], some modest numerical simulations are presented.
TL;DR: In this paper, an improved algorithm for automated structure factor refinement using convergent-beam electron diffraction patterns is described. But this algorithm does not include beam-direction refinement, the inclusion of weak-beam effects using the Bethe potential, and the addition of finite-sized detector effects.
Abstract: An improved algorithm is described for automated structure-factor refinement using convergent-beam electron diffraction patterns. In addition to refinement of structure factors, absorption coefficients and sample thickness, the new algorithm includes beam-direction refinement, the inclusion of weak-beam effects using the Bethe potential and the inclusion of finite-sized detector effects. The use of these new features is illustrated through the refinement of the MgO 200 systematic reflections.
TL;DR: The structure of foot-and-mouth disease virus (FMDV) strain O1 BFS 1860 has been determined to 2.9 A resolution using the molecular-replacement method and the ambiguity in particle orientation was resolved using a self-rotation function.
Abstract: The structure of foot-and-mouth disease virus (FMDV) strain O1 BFS 1860 has been determined to 2.9 A resolution using the molecular-replacement method [Acharya, Fry, Stuart, Fox, Rowlands & Brown (1989). Nature (London), 337, 709–716]. Crystals of the virus with average dimensions 0.12 × 0.06 × 0.12 mm belong to space group I23, a = 345 A with 1/12 of the icosahedral particle per asymmetric unit giving fivefold noncrystallographic redundancy. Oscillation diffraction photographs were collected at the SERC Synchrotron Radiation Source at Daresbury in accordance with strict disease security regulations. The ambiguity in particle orientation was resolved using a self-rotation function and starting estimates of the phases to 8 A were derived from the known structures of two picornaviruses similarly oriented in the I23 unit cell. The phases were refined and extended using iterative averaging and solvent flattening with the implementation of a simple automatic envelope-determination procedure to increase the phasing power available.
TL;DR: In this paper, the relative frequency of the space groups of molecular organic compounds is determined by ease of packing, and the observed frequencies are analysed in the light of the degree of symmorphism and molecular symmetry.
Abstract: To a close approximation, the relative frequency of the space groups of molecular organic compounds is determined by ease of packing. When the molecules are in general Wyckoff positions, the relative frequency anticorrelates with the degree of symmorphism. Somewhat different considerations apply if the molecule possesses and uses some inherent symmetry (\overline 1, 2, m, 2/m, 222, mm, ...) [Kitaigorodskii (1955); Kitaigorodskii (1961). Organic Chemical Crystallography. New York: Consultants Bureau]. The observed frequencies are analysed in the light of the degree of symmorphism and molecular symmetry.
TL;DR: In this paper, powder X-ray diffraction data for corundum were collected by a variety of methods and reduced to structure amplitudes by two profile-fitting techniques and merged with three different single-crystal data sets to assess the improvements possible over least-squares modelling of extinction for accurate electron density analysis of minerals.
Abstract: Powder X-ray diffraction data for corundum were collected by a variety of methods and reduced to structure amplitudes by two profile-fitting techniques. The resulting averaged powder-data set was merged with three different single-crystal data sets to assess the improvements possible over least-squares modelling of extinction for accurate electron density analysis of minerals. With reference to the deformation electron density derived from multipole refinements, it is concluded that this strategy offers advantages over the post facto modelling of severe extinction effects commonly observed in such systems. The deformation electron density is found to be in quantitative agreement with the results of recent ab initio calculations on clusters and the bulk.
TL;DR: In this paper, a method for the refinement of modulated structures from a combined set of single-crystal and powder diffraction data or from powder data only is described, which is especially useful when information on light atoms is to be obtained and no single crystals of suitable size for neutron diffraction are available.
Abstract: A method is described for the refinement of modulated structures from a combined set of single-crystal and powder diffraction data or from powder data only. The method is especially useful when information on light atoms is to be obtained and no single crystals of suitable size for neutron diffraction are available. The program in which the method is encoded allows for differences in composition between the single-crystal and powder samples. Application to the incommensurately modulated superconductor Bi2Sr2CaCu2O8+y (2212) using powder neutron and single-crystal X-ray data confirms that the oxygen modulation in the Bi–O layer is saw-tooth-like, as observed in the preceding study based solely on X-ray data [Petricek, Gao, Lee & Coppens (1990). Phys. Rev. B, 42, 387–392], but with improved accuracy in the resulting parameters. The extra oxygen content is explicitly related to the modulation model and corresponds to 0.14–(4) per formula unit. With the refined site occupancies for the heavy atoms and the results of an anomalous-scattering study on the bismuth distribution [Coppens, Lee, Gao & Sheu (1991). J. Phys. Chem. Solids, 52, 1267–1272], a copper valency of 2.31 is obtained for the single-crystal sample. The powder value of 2.40 is somewhat less reliable as no anomalous-scattering data are available for the powder sample.
TL;DR: The refinement involving HMT provides a worst-case example of a general deficiency in the application of the multipole model to noncentrosymmetric structures.
Abstract: New refinements of the crystal structure of hexamethylenetetramine (HMT, C6H12N4) have been carried out using previously reported neutron and X-ray diffraction data collected at 298 K. A new feature in the structure model is the inclusion of third-order Gram–Charlier coefficients for the description of the anharmonic C–H bond stretching, which is found to be significant. The charge-density distribution is analyzed in terms of the pseudoatom model of Stewart [Acta Cryst. (1976). A32, 565–574]. Our experimental determination of the molecular octapole moment gives 〈xyz〉 = + 1.0 (3) |e| A3. The refinement involving HMT provides a worst-case example of a general deficiency in the application of the multipole model to noncentrosymmetric structures. Strong least-squares correlations occur involving the electron population parameters of all atoms for certain of the multipole terms, namely those odd-order terms that are invariant under the symmetry operations of the space group.
TL;DR: The molecular dynamics method is able to find local minima that resemble the true structure sufficiently to allow improved phasing and thus lead to interpretable difference maps for model rebuilding.
Abstract: The molecular dynamics (MD) method has been adapted for refinement of the structures of helical macromolecular aggregates against X-ray fiber diffraction data To test the effectiveness of the method, refinements of the tobacco mosaic virus structure were carried out against a set of simulated fiber diffraction intensities using the MD method as well as the conventional restrained least-squares (RLS) method The MD refinement converged to a very low R factor and produced a structure with generally statisfactory stereochemistry, while the RLS refinement was trapped at a local energy minimum with a larger R factor Results suggest that the effective experimental radius of convergence of the MD method is significantly greater than that of the RLS method Even when the initial structure is too far from the true structure to allow direct refinement, the MD method is able to find local minima that resemble the true structure sufficiently to allow improved phasing and thus lead to interpretable difference maps for model rebuilding
TL;DR: The maximum entropy method (MEM) was applied to accurate γ-ray diffraction data from MnF2 and NiF2 to explore details of the charge density distribution as discussed by the authors.
Abstract: The maximum-entropy method (MEM) was applied to accurate γ-ray diffraction data from MnF2 and NiF2 to explore details of the charge-density distribution. For a fair judgement of the results, Si Pendellōsung data [Saka & Kato (1986). Acta Cryst. A42, 469–478] were also treated. It is shown that conclusions drawn from MEM maps must be accepted with some reserve, particularly in the regions of interest in charge-density studies.
TL;DR: In this paper, the experimental electrostatic potential obtained from X − X spherical electron density was used to derive point charges centred on the atoms for a pseudopeptide, N-acetyl-α, β-dehydrophenylalanine methylamide.
Abstract: Observations of the experimental electrostatic potential obtained from X − X spherical electron density can be used to derive point charges centred on the atoms. This is applied to a pseudopeptide, N-acetyl-α, β-dehydrophenylalanine methylamide. The experimentally determined charges are consistent whatever the sampling points and `follow' the atomic site when the conformation of the molecule changes. However, introduction of multipolar moments is necessary as soon as the aspherical part of the electron density is added.
TL;DR: The regulatory domain of scallop myosin has been crystallized and the structure solved to 2.8 A resolution in this article, where side-chain interactions link two light chains in tandem to adjacent segments of the heavy chain bearing the IQ-sequence motif.
Abstract: The regulatory domain of scallop myosin is a three-chain protein complex that switches on this motor in response to Ca2+ binding. This domain has been crystallized and the structure solved to 2.8 A resolution. Side-chain interactions link the two light chains in tandem to adjacent segments of the heavy chain bearing the IQ-sequence motif. The Ca2+-binding site is a novel EF-hand motif on the essential light chain and is stabilized by linkages involving the heavy chain and both light chains, accounting for the requirement of all three chains for Ca2+ binding and regulation in the intact myosin molecule.
TL;DR: In this paper, the electronic structures of crystalline lithium oxide and lithium sulfide have been theoretically investigated within the Hartree-Fock approximation, and X-ray static structure factors are calculated and scattering factors of O 2- and S 2- ions are deduced following the theoretical model that uses standard scattering curves for the Li + ion.
Abstract: The electronic structures of crystalline lithium oxide and lithium sulfide have been theoretically investigated within the Hartree-Fock approximation. X-ray static structure factors are calculated and scattering factors of O 2- and S 2- ions are deduced following the theoretical model that uses standard scattering curves for the Li + ion
TL;DR: In this article, the form of the tensors describing electric and thermal conductivity, the thermoelectric Seebeck and Peltier effects and the Hall, Righi-Leduc, Nernst & Ettingshausen effect are given explicitly for all the 122 crystallographic and 21 limiting point groups.
Abstract: In a previous paper [Grimmer (1991). Acta Cryst. A47, 226–232], general connections were given between the forms of tensors describing equilibrium properties in materials with point-group symmetry described by any of the 122 crystallographic Shubnikov point groups. In the present paper, it is shown how the results must be modified to include transport properties also. At least six different prescriptions for the treatment of transport properties in magnetically ordered crystals have been proposed in the literature. It is shown that the one due to Shtrikman & Thomas [Solid State Commun. (1965), 3, 147–150; erratum (1965), 3, civ] leads to a straightforward generalization of the results for equilibrium properties that seems to agree with experiment. Tensors describing transport properties generally consist of two contributions, T = Ti+ Ts. The tensor Ti is invariant under time reversal 1', whereas Ts changes sign under 1′ and therefore vanishes for dia- and paramagnetic crystals, which are invariant under 1′. The form of the tensors describing electric and thermal conductivity, the thermoelectric Seebeck and Peltier effects and the Hall, Righi–Leduc, Nernst & Ettingshausen effect are given explicitly for all the 122 crystallographic and 21 limiting point groups.
TL;DR: In this paper, up to 100 point charges have been distributed on the surface of a sphere such that the configurations display T and O symmetry as well as being a minimum, global or local, with respect to the Coulombic potential.
Abstract: Up to 100 point charges have been distributed on the surface of a sphere such that the configurations display T and O symmetry as well as being a minimum, global or local, with respect to the Coulombic potential.