Showing papers in "Journal of Applied Crystallography in 1985"
TL;DR: TREOR as discussed by the authors is an indexing program based on trial-and-error methods that contains separate routines for cubic, tetragonal, hexagonal, orthorhombic, monoclinic and triclinic symmetries.
Abstract: An indexing program, TREOR, mainly based on trial-and-error methods is described. The program contains separate routines for cubic, tetragonal, hexagonal, orthorhombic, monoclinic and triclinic symmetries. Ten years usage has been analysed to improve the original program. For monoclinic indexing a specific short-axis test has been developed. The over-all success rate of the program has been found to be better than 90%, and considerably more for orthorhombic and higher symmetries.
1,645 citations
TL;DR: A triangulated surface is a polyhedron, all of whose faces are triangles as discussed by the authors, created by subdividing the curved faces of an analytical molecular surface that has been precalculated by an earlier algorithm.
Abstract: A method is presented for triangulating the surface of a molecule. A triangulated surface is a polyhedron, all of whose faces are triangles. The triangles are created by subdividing the curved faces of an analytical molecular surface that has been precalculated by an earlier algorithm. The triangulated surface has many applications. Molecular areas and volumes may be calculated from it. Packing defects in proteins may be identified. It may be used to determine whether a particular water molecule lies in the interior of the protein or on the surface. The triangulated surface may be drawn on pen plotters, vector graphics systems and raster graphics terminals. Mathematical functions defined on the surface may be contoured. Local maxima and minima of functions may be located. While the triangulated surface is less accurate than the analytical molecular surface it is derived from, it has the advantage of being much simpler and easier to deal with. It combines the simplicity of a dot surface with the continuity of an analytical surface.
174 citations
TL;DR: A highly interactive program system for carrying out crystal structure analyses on a dedicated 32-bit computer has been developed, with emphasis on suitability for inexpensive hardware.
Abstract: A highly interactive program system for carrying out crystal structure analyses on a dedicated 32-bit computer has been developed, with emphasis on suitability for inexpensive hardware. The system includes a new SHELX-compatible version of ORTEP that can be operated from an interactive graphics terminal by a menu of easily-usable commands.
154 citations
TL;DR: STRUPL084 as discussed by the authors is a Fortran plot program for drawing crystal structures in polyhedral or skeletal representation, which can be read in free format by standard Fortran routines.
Abstract: STRUPL084 is a Fortran plot program for drawing crystal structures in polyhedral or skeletal representation. All data are read in free format by standard Fortran routines. Atomic positions are also accepted in formats compatible with the input for the programs SHELX and ORFLS. The structure can be rotated by three rotation angles applied to the orthogonal axes. Instead of giving the rotation angles a view direction can be specified. The output includes a list of direct and orthogonal coordinates and tables with interatomic distances and angles. Atoms that were found to form coordination polyhedra are listed separately. The program is `user friendly' inasmuch as an acceptable plot can be achieved with minimum input by making use of the default options. Atoms not belonging to any polyhedra can be drawn as circles with specified radii.
149 citations
TL;DR: In this article, the absolute energy of X-rays from a synchrotron source were used to determine the zinc metal K absorption edge and to measure systematic errors in the angular settings of a typical rotation table used for X-ray spectroscopy.
Abstract: A new apparatus and technique to determine the absolute energy of X-rays from a synchrotron source were used to establish the absolute energy of the zinc metal K absorption edge [9661.1(2) eV] and to measure systematic errors in the angular settings of a typical rotation table used for X-ray spectroscopy. These errors have a period of 1° associated with the worm gear of the rotation table and should provide a warning to other synchrotron radiation spectroscopists that systematic errors exist in experimental data. The technique relies on determining the orientation of a static silicon crystal with respect to the incoming beam by establishing degenerate reflections with differing Miller indices. Absolute energies can be determined for X-rays with energies greater than 6 keV. An analysis of the system shows that the technique is also useful for the accurate characterization of the monochromator resolution.
123 citations
TL;DR: In this paper, a strategy for data collection using a diffractometer equipped with a multiwire proportional counter is described, and some examples are given to illustrate how the strategy is used in some typical protein data collection problems.
Abstract: A strategy for data collection using a diffractometer equipped with a multiwire proportional counter is described. Data are collected using an electronic rotation method similar to an earlier developed `still' method. Data are collected as a set of three to 12 or more `runs'. A data collection `run' consists of a consecutive series of hundreds of electronic rotation pictures with ω advanced by a specific amount (from 0.07 to 0.20°, depending on the mosaicity of the crystal) during each picture. Every picture in a run is taken at the same: χ and ϕ setting angles and exposure time. Information on how to extract the intensity data from these electronic rotation pictures is given elsewhere. Here, the only concern is how to choose a set of ω, χ and ϕ angles for defining a set of runs in order to get a complete set of data in a minimum time. First the diffraction geometry is discussed, then the strategy is outlined; finally, some examples are given to illustrate how the strategy is used in some typical protein data collection problems.
114 citations
TL;DR: In this article, the heat radiation of a halogen lamp of adjustable intensity is focused by a parabolic mirror on the sample capillary, which is mounted on a diffractometer and cooled by a gas stream at a controlled temperature.
Abstract: To improve the growing of single crystals for structural analysis, especially those of low-melting-point materials, a new technique and the appropriate apparatus have been developed. The heat radiation of a halogen lamp of adjustable intensity is focused by a parabolic mirror on the sample capillary, which is mounted on a diffractometer and cooled by a gas stream at a controlled temperature. The focus can be moved along the length of the capillary in any direction, for horizontal or vertical miniature zone melting or Bridgman techniques. The heat source and the movable mirror are controlled by a microprocessor, which allows systematic and software-supported search and reproduction of suitable experimental growing conditions.
103 citations
TL;DR: In this paper, the Pearson VII and pseudo-Voigt peak shape functions were used to analyze high-resolution neutron powder diffraction data, which revealed a range of peak shapes from essentially Gaussian to Lorentzian and beyond.
Abstract: Analyses of high-resolution neutron powder diffraction data, using both the Pearson VII and pseudo-Voigt peak shape functions, have revealed a range of peak shapes from essentially Gaussian to Lorentzian and beyond. Moreover, the refinements show that the Lorentzian character of the peaks in each pattern increases with increasing diffraction angle. Both kinds of shape change are associated with varying relative contributions to the peak profiles of the instrumental resolution, isotropic crystallite strain and crystallite size effects. Rietveld analysis of powder data with the standard Gaussian form when the peaks have significant Lorentzian character has little effect on atomic positional parameters, but it leads to an overestimation of the thermal vibration coefficients and higher least-squares residuals.
99 citations
TL;DR: In this article, a computer program to calculate the contributions of crystal, capillary and a simple model of mother liquor to the overall absorption of X-rays has been written based on the Gaussian quadrature method of integration.
Abstract: A computer program to calculate the contributions of crystal, capillary and a simple model of mother liquor to the overall absorption of X-rays has been written. It is based on the Gaussian quadrature method of integration; the crystal is described by the polyhedral faces bounding it, the capillary by its diameter, thickness and orientation with respect to the diffractometer axes and the mother liquor by the crystal faces that trap it between crystal and inner capillary wall. The program is written in Fortran for a VAX 11/780 computer and incorporates tables of mass absorption coefficients for silver, molybdenum and copper radiations for easy calculation of linear absorption coefficients.
83 citations
TL;DR: In this article, closed formulas for the calculation of the orientation matrix and the angles for a given reflection in a ''z-axis'' diffractometer geometry are derived for the conditions where the angle of incidence of the primary beam to the surface of the crystal is specified.
Abstract: Closed formulas are given for the calculation of the orientation matrix and the angles for a given reflection in a `z-axis' diffractometer geometry. These equations are derived for the conditions where the angle of incidence of the primary beam to the surface of the crystal is specified. Comparison is made with the standard four-circle configuration and the differences between these two geometries are evaluated. Some further applications are discussed.
55 citations
TL;DR: In this article, a unified theoretical and experimental approach for analyzing multiple scattering data is developed to obtain values for particle size, volume fraction and surface area of high-purity alumina powder.
Abstract: Microstructural parameters of high-purity alumina powder are determined quantitatively throughout the bulk of the material using small-angle neutron scattering techniques. A unified theoretical and experimental approach for analyzing multiple scattering data is developed to obtain values for particle size, volume fraction and surface area. It is shown how particle size and volume fraction can be measured in a practical way from SANS data totally dominated by incoherent multiple scattering (`beam broadening'). The general phase-shift dependence of single-particle scattering is incorporated into the multiple scattering formalism, and it is also shown that the diffractive limit (small phase shift) applies even for phase shifts as large as unity (particle radii of order 1 μm). The stability of the Porod law against multiple scattering and the phase-shift scale are described, a useful empirical formula for analysis of beam broadening data is exhibited, and the applicability of the formulations to polydispersed systems is discussed.
TL;DR: In this paper, a rigid-body refinement method and program for crystallography of macromolecules is described, where orientation and translational parameters are refined by fitting the molecular Fourier transforms to the observed structure-factor amplitudes.
Abstract: A rigid-body refinement method and program for crystallography of macromolecules is described. Orientational and translational parameters are refined by fitting the molecular Fourier transforms to the observed structure-factor amplitudes. The range of convergence of the method has been tested on four examples with known crystal structure: PTI, chymotrypsinogen and two forms of α1 anti-trypsin. It was successfully applied in the structure solution of two unknown crystal structures: a third form of α1 anti-trypsin and C-phycocyanin.
TL;DR: The small-angle scattering facility at Daresbury has been constructed for diffraction studies of a wide range of naturally occurring and synthetic materials The high brightness of the SRS is combined with focusing optics, resulting in exposure times that can be two or three orders of magnitude less than those required on a conventional source as mentioned in this paper.
Abstract: The small-angle scattering facility at Daresbury has been constructed for diffraction studies of a wide range of naturally occurring and synthetic materials The high brightness of the SRS is combined with focusing optics, resulting in exposure times that can be two or three orders of magnitude less than those required on a conventional source Spacings of 2000 A in the vertical direction and 300 A in the horizontal direction can be observed, while the resolution between diffraction orders is 5000 and 600 A In addition, preliminary results have been obtained on a double-crystal diffractometer that has a resolution, in one dimension, of better than 26 000 A For high-angle fibre diffraction studies, a camera with pinhole collimation has been constructed Examples from solution scattering and fibre diffraction are used to illustrate the performance of these facilities
TL;DR: Gerber et al. as discussed by the authors developed an improved transform technique for calculating the particle size distribution for spherical particles with radii R from small-angle X-ray scattering data, which permits N(R) to be calculated from analytical expressions that were derived for point collimation and for infinitely long slit collimation.
Abstract: An improved transform technique has been developed [Gerber (1983). Thesis, Wilhelm-Pieck-University Rostock, German Democratic Republic] for calculating the particle size distribution N(R) for spherical particles with radii R from small-angle X-ray scattering data. This method permits N(R) to be calculated from analytical expressions that were derived for point collimation and for infinitely long slit collimation. A special procedure has been introduced in order to reduce termination errors. The technique described and those developed by Schmidt [Brill, Weil & Schmidt (1968). J. Colloid Interface Sci. 27, 479–492], Vonk [J. Appl. Cryst. (1976), 9, 433–440] and Glatter [J. Appl. Cryst. (1980), 13, 7–11] were used for calculating particle size distributions from theoretical scattering curves and from an experimental scattering curve of suspended SiO2 particles (Ludox). The results obtained by the different techniques were compared, and reasonable results are given by all methods employed. The accuracy of the size distributions calculated by the improved method is somewhat higher than that obtained by Schmidt's transform technique. With Glatter's procedure, the deviations from the exact distributions are comparable to those from this improved transform technique, but the use of Glatter's program requires a large computer, whereas the new method has the advantage of being suitable for a small computer. Vonk's program also requires a large computer, and the deviations obtained are larger than those produced by other methods. The experimental scattering curve of the Ludox sample was also evaluated by assuming a log-normal distribution for the particles. The parameters μ and σ of this function were determined from a set of small-angle X-ray scattering structural parameters. The resulting log-normal distribution is significantly different from the size distribution calculated by our method.
TL;DR: Experimental high-pressure X-ray diffraction studies have been performed on ThN powder for pressures up to 47 GPa using synchrotron radiation and a diamond anvil cell as discussed by the authors.
Abstract: Experimental high-pressure X-ray diffraction studies have been performed on ThN powder for pressures up to 47 GPa using synchrotron radiation and a diamond anvil cell. The bulk modulus B0 and its pressure derivative B′0 have been determined: B0 = 175(15) GPa and B'0 = 4.0(4). No structural phase transition has been found in contrast to UN studied previously.
TL;DR: The theory of small-angle neutron or X-ray scattering from a solution consisting of rods that are uncorrelated in position and orientation and its use in determining the mass per unit length and cross-sectional radius of gyration is extended to rods of finite length and non-uniform crosssectional structure.
Abstract: The theory of small-angle neutron or X-ray scattering from a solution consisting of rods that are uncorrelated in position and orientation and its use in determining the mass per unit length and cross-sectional radius of gyration is extended to rods of finite length and non-uniform cross-sectional structure. The case of a rod made up of identical motifs spaced in a regularly repeating axial structure is considered first. Analysis of the small-angle scatter by a modified Guinier plot gives the mean mass per unit length of the motifs. The apparent squared cross-sectional radius of gyration is the weight average. These results are then generalized to the case where variable randomly distributed structural elements are present including variable spacing between the motifs making up the rod. In this way expressions are obtained that describe the scatter from rods with structural contributions from random thermal fluctuations, bound ligands and intrinsic structural heterogeneity. It is shown that, in general, systematic errors are introduced in the analysis of rods of finite length having variable structural components. However, if all the motifs have the same mass, and if the variance in their spacing is small, such errors are not important provided that the rods are of sufficient length.
TL;DR: In this article, high-pressure X-ray diffraction studies have been performed on UN powder for pressures up to 34 GPa using synchrotron radiation and a diamond anvil cell.
Abstract: High-pressure X-ray diffraction studies have been performed on UN powder for pressures up to 34 GPa using synchrotron radiation and a diamond anvil cell. For the cubic low-pressure phase the bulk modulus B0 equals 203(6) GPa and its pressure derivative B′0 equals 6.3(6) in good agreement with other data from the literature. The UN material has been found to transform to a new phase, UN III, at 29 GPa. The transformation is first order with a 3.2% decrease in volume. The UN III phase has been indexed according to a face-centred rhombohedral cell with a = 4.657(5) A and α = 85.8(2)° at 34 GPa. The influence of the 5f electrons in the transformation is discussed.
TL;DR: In this article, the stability of the lattice-parameter profiles deduced by simulating the rocking curves using the Takagi-Taupin equations is shown to be good.
Abstract: Synchrotron radiation has been used to obtain double-crystal X-ray rocking curves from inhomogeneous layers of GaInAs on InP at a range of wavelengths. The consistency of the lattice-parameter profiles deduced by simulating the rocking curves using the Takagi–Taupin equations is shown to be good. The computational method has been extended to calculate the rocking curves from relatively thick multilayer structures of GaAlAs on GaAs grown by molecular beam epitaxy. This dynamical-theory approach permits the prediction of positions, heights and widths of major and satellite peaks. Results are in excellent agreement with experimental measurements, and by comparing experimental and calculated profiles the structural parameters of the layer can be deduced. The dynamical theory is particularly suitable for calculating the complete rocking curve especially where thick confining layers are present and the computational model is directly applicable to multi-layers with varying layer thicknesses.
TL;DR: In this article, small-angle neutron scattering techniques were used to obtain microstructural parameters of high-purity alumina powder, including particle size, volume fraction and surface area, and compared to data from laser light scattering, X-ray sedigraph and scanning electron microscopy.
Abstract: Small-angle neutron scattering techniques developed in the preceding paper [Berk & Hardman-Rhyne (1985). J. Appl. Cryst. 18, 467-472] are used to obtain microstructural parameters of high-purity alumina powder. The values of the particle size, volume fraction and surface area have been obtained and are compared to data from techniques such as laser light scattering, X-ray sedigraph and scanning electron microscopy. The particles exhibit a log-normal distribution and are spherical in shape with a mean particle size of 342 nm determined from SANS analyses of both beam broadening and Porod regions.
TL;DR: In this paper, an integrated device for the structural study of liquid or amorphous compounds is described, where the X-ray scattering pattern produced by the sample is quickly recorded by a micro-computer-controlled goniometer with position-sensitive detection.
Abstract: A new integrated device for the structural study of liquid or amorphous compounds is described. The X-ray scattering pattern produced by the sample is quickly recorded by a micro-computer-controlled goniometer with position-sensitive detection. Interactive software allows both experimental data processing and simulation from structural models.
TL;DR: In this article, the merits of neutron scattering and anomalous X-ray scattering were compared, and the possibility of performing more than three anomalous experiments may improve the results and a new analysis of data was proposed.
Abstract: Solute partitioning during decomposition of a ternary alloy may be evaluated through the inversion of a system of linear equations, obtained by performing at least three independent small-angle scattering experiments. The merits of neutron scattering (with isotopic contrast) and of anomalous X-ray scattering (near the absorption edges) are compared. It appears that neutron scattering, although having good contrast, is not suited to these studies since slight structural differences between the three samples may lead to erroneous results. On the other hand, the use of the same sample in anomalous scattering avoids this problem, but with the drawback of a more ill-conditioned system. Nevertheless, the possibility of performing more than three anomalous experiments may improve the results and a new analysis of data is proposed.
TL;DR: In this article, the anomalous small-angle scattering (ASAXS) spectra from Al-Zn and Al−Zn-Ag alloys have been recorded at the Stanford Synchrotron Radiation Laboratory (SSRL).
Abstract: Anomalous small-angle scattering (ASAXS) spectra from Al–Zn and Al–Zn–Ag alloys have been recorded at the Stanford Synchrotron Radiation Laboratory (SSRL). The data were obtained at different energies close to the Zn absorption edge. For the binary alloy, the ASAXS intensities follow quantitatively the variation in the atomic scattering factor of zinc. For the ternary alloys, the anomalous effect decreases when the Zn content decreases. Although only weighted sums of the partial structure functions could be determined, it is shown that the results are consistent with the `two-phase' unmixing model and the direction of tie lines of the metastable miscibility gap has been determined. A new method for analyzing ASAXS data for two absorption edges is proposed.
TL;DR: In this article, a modified function for the peak full width at half maximum has been evaluated for polycrystalline Ni(OD)2, which resulted in significantly better agreement between observed and calculated profiles (the weighted residual Rw.p decreased from 14.1 to 8.5%).
Abstract: In order to accommodate anisotropic crystallite-size broadening effects in the Rietveld refinement of constant-wavelength powder neutron diffraction data, a modified function for the peak full width at half maximum has been evaluated for polycrystalline Ni(OD)2. The function resulted in significantly better agreement between observed and calculated profiles (the weighted residual Rw.p decreased from 14.1 to 8.5%), and structural standard deviations were reduced by an average of 43%.
TL;DR: In this article, the basic structure of (Cr, Fe)7C3 carbides and polytypes can be considered as a stacking of layers parallel to the {110} planes in the basic cell.
Abstract: A number of polytypes have been found in (Cr, Fe)7C3 carbides. The basic structure of these carbides and polytypes can be considered as a stacking of layers parallel to the {110} planes in the basic cell. The symmetry of all possible polytypes of M7C3 carbides can be described by four space groups: Pb, P21/b, Pca21 and Pbca (Pca21 in two settings). A procedure for structure determination based on the analysis of electron diffraction patterns is proposed and applied to the polytypes: 2O, 3M, 4O, 4M, 5M1, 5M2, 5M3, 6O, 6M1, 6M2 and 8O (in Ramsdell notation).
TL;DR: A method for estimating and removing a general global background in cases when poorly oriented less-crystalline specimens give diffraction patterns with little uncontaminated background is described and illustrated with an example.
Abstract: Background can be a major source of error in measurement of diffracted intensities in fiber diffraction patterns. Errors can be large when poorly oriented less-crystalline specimens give diffraction patterns with little uncontaminated background. A method for estimating and removing a general global background in such cases is described and illustrated with an example.
TL;DR: In this article, the case of circularly symmetric scattering measured on an instrument collimated by circular apertures is treated in detail, and the effect of various contributions to smearing is described.
Abstract: Instrumental smearing effects can result in a significant deviation of measured small-angle scattering data from the ideal cross section. The effect of various contributions to smearing is described. The case of circularly symmetric scattering measured on an instrument collimated by circular apertures is treated in detail. For such measurements, it is shown how known scattering functions can be smeared to allow estimation of parameters by a fit to the observed data, and also how the indirect Fourier transformation method can be used to desmear the observed scattered intensity.
TL;DR: Tanner and Bowen as mentioned in this paper described a method for aligning a double-crystal diffractometer based on the design of Hart, and the theoretical intensity profiles were derived for variations in crystal tilt and rotation.
Abstract: A rapid method is described for aligning a double-crystal diffractometer based on the design of Hart (Characterization of Crystal Growth Defects by X-ray Methods, edited by Tanner & Bowen, pp. 483–485. Plenum Press, London, 1980). The theoretical intensity profiles are derived for variations in crystal tilt and rotation, and a method is described that uses these profiles to align any double-crystal diffractometer in a systematic way, suitable for computer automation. The alignment requirements for simple mismatch measurements are also given.
TL;DR: In this paper, a simple approach has been used to determine the D-induced static displacement modulation δ of V along the a axis (monoclinic indexing) in the β phase of V2D.
Abstract: With a highly convergent electron beam entering a small crystal area, the Bragg condition may be fulfilled simultaneously for many diffraction orders along a reciprocal-lattice direction, and reflections with (sin θ)/λ > 2 A−1 are accessible. Considerations based on the dynamical theory of electron diffraction suggest that for Bragg reflections with (sin θ)/λ > 1 A−1, 100 keV electrons can be treated quasi-kinematically when the crystal thickness is less than 1000 A, and this is supported by experiments. This simple approach has been used to determine the D-induced static displacement modulation δ of V along the a axis (monoclinic indexing) in the β phase of V2D. From visual inspection of the Bragg intensities for large diffraction orders, up to (sin θ)/λ = 2.35 A−1, it is concluded that δ = 0.070 (5) A.
TL;DR: In this article, the crystal lattice parameters of mixtures of the normal alkanes n-C23H48 and N-C25H52 have been determined by X-ray powder diffractometry.
Abstract: Crystal lattice parameters of mixtures of the normal alkanes n-C23H48 and n-C25H52 have been determined by X-ray powder diffractometry. The c-axis length increases nearly monotonically with increasing C25H52 content, a and b are larger for the mixtures than for the pure substances with maximum values at 15% n-C25H52. The small but significant increases in a of 0.6% and b of 0.9% have not been previously reported.