Showing papers in "Journal of Applied Crystallography in 1987"

Rietveld refinement of Debye–Scherrer synchrotron X‐ray data from Al2O3

Abstract: The application of the Rietveld refinement technique to synchrotron X-ray data collected from a capillary sample of Al2O3 in Debye–Scherrer geometry is described. The data were obtained at the Cornell High Energy Synchrotron Source (CHESS) with an Si(111) double-crystal monochromator and a Ge(111) crystal analyzer. Fits to a number of well resolved individual peaks demonstrate that the peak shapes are very well described by the pseudo-Voigt function, which is a simple approximation to the convolution of Gaussian and Lorentzian functions. The variation of the Gaussian and Lorentzian half widths, ΓG and ΓL, with Bragg angle can be approximated quite closely by the functions V tan θ and X/cos θ which represent the contributions from instrumental resolution and particle-size broadening respectively. Rietveld refinement based on this model yields generally satisfactory results. The refined values of V and X are consistent with the expected vertical divergence (≃0.1 mrad) and the nominal particle size (≃ 0.3μm). In particular, the use of a capillary specimen virtually eliminates preferred orientation effects, which are highly significant in flat-plate samples of this material.

STRUCTURE TIDY– a computer program to standardize crystal structure data

Abstract: A computer program has been written for the purpose of standardizing crystal structure data according to rules formulated by Parthe & Gelato [Acta Cryst. (1984). A40, 169–183]. From input consisting of space-group symbol, unit-cell parameters and positional coordinates of the atoms, a reordered and renumbered list of standardized atom coordinates is obtained. The space group is now in the standard setting and the cell is reduced if applicable. The origin and the orientation of the coordinate system have been chosen in such a way as to minimize the standardization parameter Γ. A second standardization parameter, based on the position of the centre of gravity of the atoms in the asymmetric unit, is introduced. The Wyckoff sequence, obtained from the standardized structure data, can be used to recognize structures which are isopointal. An example of the application of STRUCTURE TIDY is given.

Quantitative phase analysis from neutron powder diffraction data using the Rietveld method

Abstract: The weight of a phase in a mixture is proportional to the product of the scale factor, as derived in a multi-component Rietveld analysis of the powder diffraction pattern, with the mass and volume of the unit cell. If all phases are identified and crystalline, the weight fraction W of phase p is given by W_{p} = S_{p}(ZMV)_{p}/\sum_{i}S_{i}(ZMV)_{i},where S, Z, M and V are, respectively, the Rietveld scale factor, the number of formula units per unit cell, the mass of the formula unit and the unit-cell volume. This is the basis of a method providing accurate phase analyses without the need for standards or for laborious experimental calibration procedures. The method is demonstrated by measurements on binary mixtures of rutile, corundum, silicon and quartz.

Absolute calibration of small‐angle neutron scattering data

Abstract: Absolute calibration forms a valuable diagnostic tool in small-angle neutron scattering (SANS) experiments, and allows the parameters of a given model to be restricted to the set which reproduces the observed intensity. Discrepancies between the observed and calculated intensities may arise from potential artifacts or even new physical processes and absolute calibration methods are useful in delineating these circumstances. General methods which are available for absolute scaling are discussed along with estimates of the degree of internal consistency which may be achieved between the various standards. In order to minimize the time devoted to calibration in a given experimental program, emphasis is placed on developing a set of precalibrated strongly scattering standards which may be run in the chosen experimental geometry. Comparison of such a set developed at the National Center for Small-Angle Scattering Research (Oak Ridge) with independent determinations by SANS users indicates consistency to within ± 5%.

Scattering from fractals

Abstract: The concepts of dilation symmetry and the fractal dimension are introduced, and from these basic concepts scattering functions are computed for surface and mass fractals. It is then shown how the fractal structure of various random media has been elucidated from scattering measurements, and how these observations relate to specific models of fractal geometry. Examples include colloidal aggregates, gels, soot and the fractal porosity of rocks of various sorts.

The use of an imaging proportional counter in macromolecular crystallography

Abstract: A multiwire proportional chamber known as an imaging proportional counter has been used to collect X-ray intensity data for the determination of several structures by molecular replacement or difference Fourier analysis and has provided data for numerous other macromolecular crystallographic projects. Results obtained with an imaging proportional counter mounted on a rotating-anode X-ray generator indicate that the detector produces accurate intensity information and that its reliability is high.

Crystal orientation and X-ray pattern prediction routines for area-detector diffractometer systems in macromolecular crystallography

Abstract: Routines for crystal orientation and the prediction of expected reflections which are part of the data collection software package MADNES for area-detector diffractometer systems in macromolecular crystallography are described. This package is designed to be area-detector-system independent. In addition to refining crystal cell lengths and angles, crystal orientation, crystal-to-detector distance, position of the primary beam on the detector, and rotation of the detector around the primary beam, the orientation routine also refines the effective mosaic spread of the crystal, the beam inclination angle μand the detector tilt angle τ. A prealignment procedure is described for rapid rough orientation of the crystal. The routines are written in Fortran 77 in a modular way, so that they may be used independently of MADNES and each other.

Computer derivation of the symmetry elements implied in a structure description

Abstract: The space-group symmetry implied in the atomic coordinates of a structure can be reconstructed by deriving the metric symmetry elements of the lattice from the cell data, and finding the location and the glide for corresponding space-group symmetry elements with the same orientation using the list of atomic coordinates. The MISSYM computer program designed along these principles treated correctly the known examples of overlooked symmetry or quasi-symmetry that were submitted to it. As no computer program operating on refined atomic coordinates can prove the presence of extra symmetry in the crystal, the user should scrutinize the experimental evidence and report either a different space group or the existence of pseudo-symmetry whenever extra structural symmetry elements are disclosed by the program. The MISSYM program is part of the NRCVAX system of programs.

Incorporation of fast Fourier transforms to speed restrained least‐squares refinement of protein structures

Abstract: Modifications to the restrained least-squares refinement program of Hendrickson & Konnert [Biomolecular Structure, Function, Conformation, and Evolution, edited by R. Srinivasan, pp. 43–57 (1980). Oxford: Pergamon Press] are described that result in dramatic acceleration of the refinement of protein structures. Proven fast-Fourier-transform-based algorithms for computing structure factors and least-squares matrix elements are incorporated that reduce up to a hundredfold the computation time required for a single cycle. The modified program is shown to give results comparable to refinement by conventional methods and has been successfully applied to the refinement of several protein crystal structures.

The use of the Durbin–Watson d statistic in Rietveld analysis

Abstract: A weighted form of the Durbin–Watson d statistic [Durbin & Watson (1971). Biometrika, 58, 1–19] has been used to quantify the serial correlation between adjacent least-squares residuals in Rietveld refinements of step-scan powder diffraction data. Analyses of X-ray and neutron data from a range of materials have shown that the d statistic: provides a sensitive measure of the progress of a refinement and remains discriminating when other agreement indices fail, for example, when comparing results at different step widths; provides quantitative information about the significance of serial correlation present in the residuals; provides a convenient means of assessing the reliability of the estimates of the parameter variances; and provides a basis for the selection of values of step width and intensity corresponding to optimum and/or minimum use of experimental beam time.

Experiences with a new translation-function program

Abstract: The development of a new translation-function program is reported. It is one that uses a linear correlation coefficient to determine the correct position of an oriented molecule in the crystal cell. The method has been implemented in a computer program called BRUTE. The program can also refine the orientation of the model and accept a set of atoms with fixed positions. Comparison of the correlation coefficient with other translation functions indicates that it is comparable to or slightly better than the rest. The most important feature of the program is its ability to adjust the orientation of the model. This allows for errors in the orientation obtained from the rotation function to be corrected.

Rietveld analysis of powder patterns obtained by TOF neutron-diffraction using cold neutron sources

Abstract: A computer program has been developed for the Rietveld analysis of time-of-flight neutron diffraction data taken on a high-resolution powder diffractometer, HRP, at the pulsed spallation neutron source, KENS. A new profile shape function is implemented which is optimized for a solid-methane moderator at 20 K. The program has several convenient features such as single-pass operation, multiphase capability, automatic successive refinements and constrained minimization. The results of Rietveld refinements of Si and α-Al2O3 show that the profile shape function fits neutron diffraction patterns taken on the HRP very well, and that very precise crystal-structure parameters can be obtained with this program.

A system for collection and on-line integration of X-ray diffraction data from a multiwire area detector

Abstract: A system for collecting and measuring X-ray diffraction data from protein crystals has been developed for a multiwire area detector. Computer programs run concurrently on two microcomputers, which collect and reduce detector data to integrated intensities. The self-contained system consists of an X-ray area detector, a rotation/oscillation camera, and two microcomputers connected by a high-speed Ethernet network. One microcomputer is dedicated to operation of the detector, control of the camera, and storage of the raw data. The second microcomputer automatically integrates the data as they are collected and allows the user to monitor the quality of data as they are processed. The integration programs are written in Fortran 77 and have been designed to be portable. Additional programs for crystal alignment, detector and camera control, and graphics are written in the C programming language. A description of the system, some characteristics of the detector, and the results of data collection are presented.

Reflection electron microscopy

Abstract: Reflection electron microscopy (REM) in ultra-high vacuum (UHV) conditions is reviewed. UHV-REM can characterize surface structures of monolayer levels such as steps, domains of reconstructed surface structures and their boundaries and these capabilities are used to observe surface dynamic processes such as phase transitions of reconstructed surface structures and adsorbate structures and adsorption processes, oxidations, sublimations and ion-sputtering and annealing. The method is compared with other surface-imaging techniques.

Addition of symmetry‐related contact restraints to PROTIN and PROLSQ

Abstract: Symmetry-related van der Waals contacts and hydrogen bonds are stereochemical restraints which are often ignored in macromolecular structure refinement programs. PROTIN and PROLSQ have been modified to account for symmetry-related contacts. The derivatives calculated for an atom in its symmetry-transformed position need only be multiplied by the appropriate rotation matrix to be applied to the atom in its untransformed position. Therefore the code already present in PROLSQ for van der Waals contacts is readily adapted to account for symmetry-related contacts. The `cubing' algorithm, shown to be much faster than residue-by-residue center and radius methods for generating potential contacts, has been incorporated in PROTIN.

CRYSRULER, an integrated system of computer programs for crystal structure analysis on personal computers

Abstract: A system of programs and routines is presented that is expressly designed to be user friendly, as much as possible, and to give the real possibility of performing all the stages of crystallographic computation on a personal computer. The package has been developed in a modular way to support adapted versions of some popular crystallographic programs, such as MULTAN, SHELX, PLUTO, ORTEP and PARST. Original facilities are provided for file and system management and molecular graphics on screen display, plotter and matrix printer. The result is a powerful menu-assisted package, which represents the first example of an independent crystallographic work station running under the MS–DOS operating system. The package has been implemented on an IBM AT and can be used without modifications on any XT/AT-compatible personal computer.

Experiments with automated protein crystallization

Abstract: A liquid handling system for setting up crystallization experiments by the hanging-drop technique has been developed. The system, organized about a pipetting station and multiport rotary valve under computer control, increases the speed at which experiments can be set up and facilitates systematic studies of protein crystallization. The system is described and results of crystallization trials on 14 proteins are reported.

Structure determination by use of pattern decomposition and the Rietveld method on synchrotron X-ray and neutron powder data; the structures of Al2Y4O9and T2O4

Abstract: High-resolution synchrotron powder X-ray data have been used to solve the structures of I2O4 and Al2Y4O9 by profile decomposition into individual structure amplitudes, followed by application of standard Patterson and direct methods. The data were obtained from a series of spectra recorded with a small linear position-sensitive detector, and some of the errors arising from this approach are discussed. The final structures were obtained by Rietveld refinement, and Rp values for the profile intensities are 10.9 and 9.2% for Al2Y4O9 and I2O4 respectively. For Al2Y4O9 good agreement was found with the known isomorphous compound Al2Eu4O9, while I2O4 data were compared with high-resolution neutron powder data. This analysis, together with other recently reported studies, shows that structure determination from powder data will be feasible even for rather complicated structures.

Refinement of simple crystal structures from synchrotron radiation powder diffraction data

Abstract: X-ray powder diffractometry with storage-ring radiation was used to test various aspects of a method for refining simple crystal structures (Si, CeO2 and Co3O4). Excellent powder patterns were obtained with 0.17° resolution parallel slits and 1 A X-rays. The intensities were determined with a double-Gaussian profile-fitting function and used in the powder least-squares refinement program POWLS. Except for Si, the peaks were broadened because of small particle sizes. The R(Bragg) values were in the range 0.4–1.7%.

Lorentz–polarization factor for correction of diffraction-line profiles

Abstract: The Lorentz–polarization factor (1 + cos22 θ)/sin2 θ cos θ for the integrated intensity of a diffraction line is different from the Lorentz–polarization factor (1 + cos2 2θ)/sin2 θ for a diffraction-line profile; nevertheless, in most of the literature it is being used to correct diffraction-line profiles. The errors introduced in the peak shape and position by use of the Lorentz–polarization factor (1 + cos2 2θ)/sin2 θ cos θ are discussed.

The probabilistic determination of intensities of completely overlapping reflections in powder diffraction patterns

Abstract: Two techniques are presented for the extraction of the individual intensities of completely overlapping reflections in a powder diffraction pattern. The first is analogous to Sayre's [Acta Cryst. (1952). 5, 60–65] squaring method while the second is based upon maximizing the entropy of the Patterson function subject to the constraints imposed by the observed intensities of single and overlapping groups of reflections. Although both methods are superior to a simple equipartition of intensities amongst overlapping reflections, the maximum-entropy (ME) technique is the more robust and scientifically justifiable. The ME Patterson map extracts the maximum amount of information from the available observed intensities and is thus optimal for Patterson-technique structure determination from powder diffraction patterns. The agreement between true |F|2 values of overlapping reflections and the values obtained by maximum entropy is, in most simulated cases, excellent.

Optics of Curved-Crystal Neutron Spectrometers. I. Three-Axis Spectrometers

Abstract: The optics of curved-crystal three-axis neutron spectrometers is investigated analytically. A program for computing resolution and intensity characteristics, which includes finding conditions for intensity–resolution optimization, is presented. Ways of improving spectrometer performances are discussed. The program's predictions are supported by experimental results obtained on a spectrometer with pneumatically curved perfect Si crystals.

Determination of the neutron absorption cross section for hydrogen as a function of wavelength with a pulsed neutron source

Abstract: The wavelength dependence of the neutron absorption cross section of hydrogen in [ReH3(C2H4)2{P(i-Pr)2Ph}2] was investigated by recording the decrease in Bragg peak intensity from a standard NaC1 crystal caused by attenuation of the incident beam by the Re sample. Data were collected on the Single Crystal Diffractometer (SCD) at the Intense Pulsed Neutron Source (IPNS, Argonne National Laboratory) which enabled concurrent measurements at a selection of wavelengths using the time-of-flight technique.

Sensitivity of X‐ray diffractometry for strain depth profiling in III–V heterostructures

Abstract: The use of the fine structure of X-ray rocking curves for the characterization of the abruptness of heterointerfaces is presented for the particular example of Ga1−xAlxAs/GaAs heterojunctions. The sensitivity of the method is discussed in detail for the 400 reflection with two different wavelengths (1.2378 and 1.5410 A). It is shown that the conclusions can be extended to other reflections and wavelengths provided that the ratio χhi/χhr depending on both the absorption and the strength of the reflection is kept below 10−1.

UNISOFT– a program package for lattice-dynamical calculations

Abstract: The program package UNISOFT has been developed for lattice-dynamical calculations. Phonon dispersion curves can be calculated for any crystal structure with up to 20 atoms per primitive cell. The interaction between each individual pair of atoms can be modelled by one or more interaction types such as longitudinal and transverse springs (Born–von Karman model), Born–Mayer potential, Lennard-Jones potential, van der Waals potential, Coulomb potential, shell model. In addition to the model calculation part, UNISOFT contains several auxiliary programs dealing with group-theoretical analysis, neighbourhood analysis, plot of the phonon dispersion, calculation of partial derivatives, check of rotational invariance, calculation of local electrical fields and gradients, calculation of phonon intensities. In combination with a spectrometer for inelastic neutron scattering, UNISOFT provides a tool for the optimization of experiments as well as for a first interpretation of the results.

Angle calculations for a five-circle diffractometer used for surface X-ray diffraction

Abstract: The basic equations are derived for the calculation of the angle settings of a five-circle diffractometer used for surface X-ray diffraction. This is done for a specified angle of incidence. An additional constraint that may be imposed is the horizontal alignment of the diffraction rods to match the divergence of the synchrotron X-ray source or the horizontal setting of the physical surface normal. Alignment procedures and the derivation of the orientation matrix are discussed.

A standardless X-ray diffraction method for the quantitative analysis of multiphase mixtures

Abstract: An X-ray diffraction method is described that determines calibration constants using only diffracted intensities and calculated phase absorption coefficients through a least-squares procedure. The conditions necessary for the application of this method are that the qualitative analysis be complete, that sufficient samples with essential differences in the quantitative phase composition be available and that the chemical compositions of the phases be known approximately. It does not require the use of pure phases or the measuring of the sample absorption coefficients. It allows the easy introduction of known calibration constants, thus reducing the number of samples needed and increasing the versatility of the method.

X-ray scattering from a Troponin C solution and its interpretation with a dumbbell-shaped-molecule model

Abstract: Small-to-moderate-angle X-ray scattering studies were performed on a troponin C solution prepared from rabbit skeletal muscle The main feature of the scattering profile is the existence of two regions in the Guinier plot, in which data points lie on a straight line The scattering profile was analyzed by way of a structural model with 'dumbbell' shape, based on the structure given by X-ray crystallography on troponin C The dumbbell model shows a `quasi-' straight-line region at higher scattering angles in the Guinier plot, in addition to the intrinsic straight-line region at very small scattering angles A ln[I(S)/S] versus S2 plot of the scattering profile at higher scattering angles gives information as to the average radius of gyration of the N-terminal and C-terminal domains of troponin C The molecular parameters determined from small-angle X-ray scattering data of troponin C (10 mg ml−1), in the absence of Ca2+ ions, are as follows: the radius of gyration of the whole troponin C molecule is 204 A and the average radius of gyration of the N- and C-terminal domains is 156 A From these radii of gyration, the center-to-center distance between the two domains is estimated to be about 26 A

Equi-Lattice-Spacing Mapping X-ray Topography

Abstract: A new X-ray topographic method is described which images with similar contrast those parts which have the same lattice spacings in an inhomogeneous single-crystal irrespective of the lattice inclination. This method was applied to GaAs, in which a variation of Δd/d ≲ 10−5 was topographically resolved.

Synchrotron‐radiation study of phase transitions in phosphorus at high pressures and temperatures

Abstract: Results are reported of an investigation using synchrotron radiation into the effects of temperatures up to 1173 K on pressure-induced phase transitions in phosphorus. A cubic type multi-anvil press was employed and a diffraction pattern in an energy-dispersive mode was taken for a period of time, typically 200 s, without suffering from a deterioration of the sample material. The pressure of the first transition, orthorhombic–rhombohedral (As-type), decreases with increasing temperature at a rate of 2.3 MPa K−1 and the As-type structure is stable at a pressure as low as 2.6 GPa at a temperature of 1073 K. The volume discontinuity at the transition, ΔV, is 10% at room temperature and remains almost unchanged with increasing temperature. The axial ratio c/a, when the rhombohedral structure is referred to the hexagonal system, changes mostly with pressure but only slightly with temperature, approaching √6 = 2.45 on going to the second transition, rhombohedral–simple cubic. The pressure of this transition, in contrast to the first one, is independent of temperature but ΔV at this transition, 3.7%, continuously decreases with increasing temperature.