Showing papers in "Journal of Applied Crystallography in 1993"

PROCHECK: a program to check the stereochemical quality of protein structures

Abstract: The PROCHECK suite of programs provides a detailed check on the stereochemistry of a protein structure Its outputs comprise a number of plots in PostScript format and a comprehensive residue-by-residue listing These give an assessment of the overall quality of the structure as compared with well refined structures of the same resolution and also highlight regions that may need further investigation The PROCHECK programs are useful for assessing the quality not only of protein structures in the process of being solved but also of existing structures and of those being modelled on known structures

Completion and refinement of crystal structures with SIR92

Abstract: An automatic procedure for recovering a complete crystal structure after a direct phasing process is described. The procedure consists mainly of a Fourier recycling method that can be implemented in any direct-methods package. The residual R value attained at the end of the process provides an estimate of the degree of success of the structure determination. The procedure can also be applied using a small molecular fragment as prior information. The procedure has been implemented into SIR92, the successor to SIR88.

Automatic processing of rotation diffraction data from crystals of initially unknown symmetry and cell constants

Abstract: An algorithm has been developed for the automatic interpretation of a given set of observed reciprocal-lattice points. It extracts a reduced cell and assigns indices to each reflection by a graph-theoretical implementation of the local indexing method. All possible symmetries of the observed lattice compatible with the metric of the reduced cell are recognized and reported, together with the unit-cell constants and the linear index transformation relating the conventional to the reduced cell. This algorithm has been incorporated into the program XDS [Kabsch (1988). J. Appl. Cryst. 21, 916–924], which is now able to process single-crystal area-detector data without prior knowledge of the symmetry and the unit-cell constants.

Crystal handling at low temperatures

Abstract: The cooling of a crystal in combination with the use of a protecting oil facilitates the handling and transfer to a diffractometer of even very sensitive material. The method is explained and the required device is described in this work. Basic advantages of the technique are simplicity and freedom of access to the sample without the need for sophisticated glassware. Therefore, this technique, suitable for crystal manipulation in the temperature range between room temperature and 193 K, is much more efficient than those involving the use of capillaries.

X-ray powder diffraction analysis of silver behenate, a possible low-angle diffraction standard

Abstract: Silver behenate, a possible low-angle diffraction standard, was characterized using the powder diffraction technique. Diffraction patterns obtained with 1.54 A synchrotron and Cu Kα radiations showed thirteen regularly spaced (00l) peaks in the range 1.5–20.0°2θ. With the National Institute of Standards and Technology's standard reference material silicon as an internal standard, the long spacing of silver behenate was accurately determined from the profile-fitted synchrotron diffraction peaks, with d001 = 58.380 (3) A. This result was in agreement with that obtained from the Cu Kα pattern. The profile widths of the silver behenate peaks were found to be consistently larger than those of the silicon peaks, indicating significant line broadening for silver behenate. The average crystallite size along the long-spacing direction of silver behenate was estimated using the Scherrer equation, giving Davg = 900 (50) A. Because silver behenate has a large number of well defined diffraction peaks distributed evenly in the 1.5–20.0°2θ range, it is suitable for use as an angle-calibration standard for low-angle diffraction. However, care must be taken if silver behenate is to be used as a peak-profile calibration standard because of line broadening.

Application of symmetrized harmonics expansion to correction of the preferred orientation effect

Abstract: In powder diffraction measurements, the errors in integrated intensities caused by preferred orientation can be corrected by using some suitable analytical model as the representation of the orientation distribution of the crystallites. In this paper, a model based on symmetrized harmonics expansion is described in detail. The harmonic functions in different crystal symmetries are given and the influences of various diffraction geometries are examined. Applications of the method in quantitative phase analysis and particularly in the Rietveld method are described. The method is clarified using corundum as an example.

Voigt-function modeling in Fourier analysis of size- and strain-broadened X-ray diffraction peaks

Abstract: With the assumption that both size- and strain-broadened profiles of the pure-specimen function are described with a Voigt function, it is shown that the analysis of Fourier coefficients leads to the Warren–Averbach method of separation of size and strain contributions. The analysis of size coefficients shows that the `hook' effect occurs when the Cauchy content of the size-broadened profile is underestimated. The ratio of volume-weighted and surface-weighted domain sizes can change from ~1.31, for the minimum allowed Cauchy content, to 2, when the size-broadened profile is given solely by a Cauchy function. If the distortion Subscripts coefficient is approximated by a harmonic term, mean-square strains decrease linearly with increasing the averaging distance. The local strain is finite only in the case of purely Gaussian strain broadening, because strains are then independent of averaging distance.

Quality control of protein models : directional atomic contact analysis

Abstract: Branden & Jones state, in Nature: `Protein crystallography is an exacting trade, and the results may contain errors that are difficult to identify. It is the crystallographer's responsibility to make sure that incorrect protein structures do not reach the literature.' [Branden & Jones. (1990). Nature (London), 343, 687–689.] One of several available methods of checking structures for correctness is the evaluation of atomic contacts. From an initial hypothesis that atom-atom interactions are the primary determinant of protein folding, any protein model can be tested for proper packing by the calculation of a contact quality index. The index is a measure of the agreement between the distributions of atoms around each residue fragment in the model and equivalent distributions derived from the database of known structures solved at high resolution. The better the agreement, the higher the contact quality index. This empirical test, which is independent of X-ray data, is applied to a series of successively refined crystal structures. In all cases, the model known or expected to be better (the one with the lower R-factor) has a better contact quality index, indicating that this type of contact analysis can be used as an independent quality criterion during crystallographic refinement. Modelled proteins and predicted mutant structures can also be evaluated.

The FROG PC series: programs for electron-density and model investigations for proteins

Abstract: A set of computer programs, developed for IBM-compatible personal computers and aimed at crystallographic use, is described. The programs have user-friendly interfaces and allow the calculation of various Fourier syntheses, which can be vizualized and compared. The possibility of obtaining a synthesis and an atomic model together and performing the model image rotations and translations with respect to the synthesis also exists.

Modeling of line-shape asymmetry in powder diffraction

Abstract: Theoretical calculation shows that suitable approximations of the line-shape asymmetry in powder diffraction profiles should be represented by functions having limited codomains.

MEED: a program package for electron-density-distribution calculation by the maximum-entropy method

Abstract: MEED (maximum-entropy electron density) is a program package to calculate the electron-density distribution from a set of structure-factor data by the maximum-entropy method. MEED is an upgraded version of the original maximum-entropy program, MEMTARO, which was used in the first study to use the maximum-entropy method (MEM) on silicon [Sakata & Sato (1990). Acta Cryst. A46, 263–270]. MEED is applicable to any space group and can cope with both single-crystal and powder X-ray diffraction data, whereas MEMTARO can only after modification. Another upgraded feature is the speed of calculation. By employing a new algorithm, MEED is much faster than MEMTARO for the same calculation. Computing time depends on various factors, such as the number of reflection data, accuracy of data and the number of symmetry operations. It is estimated that MEED is typically 100 times faster than MEMTARO. In an extreme case like the beryllium powder-data case, MEED is 600 times faster than MEMTARO. MEED is coded in Fortran77 for both a scaler computer, FACOM M780, and a vector computer, FACOM VP2600, which are mainframe computers at the Computation Center of Nagoya University. MEED enables the electron-density distribution to be calculated for any crystalline material, with a fine pixel size, e.g. with 128 × 128 × 128 pixels to a unit cell, provided that accurate diffraction data are available. MEED can overcome, to some extent, one of the biggest drawbacks of MEM analysis, the vast computing time required.

Structure‐refinement program for disordered carbons

Abstract: An automated structure-refinement program has been developed for X-ray powder diffraction data collected on disordered carbons. The program minimizes the difference between the observed and calculated diffraction profiles in a least-squares sense by optimizing model parameters analogously to the popular Rietveld refinement method. Unlike the Rietveld method, which is designed for crystalline materials, this program allows the quantification of the finite size, strain and disorder present in disordered carbon fibers and cokes. For example, the structural model used includes the probability of a random translation parallel to adjacent carbon layers as a refinable parameter describing turbostratic disorder. Other parameters are used to describe finite size, fluctuations in the spacing between adjacent layers, average lattice constants, background and other important quantities. The structural model, combined with the refinement program, acceptably describes the diffraction patterns from disordered carbons such as pitch heated near 823 K, cokes, fibers, heat-treated cokes and synthetic graphite.

A direct indirect method of small-angle scattering data treatment

Abstract: A new method of treatment of small-angle scattering data is proposed. The real-space distribution function is developed into a series of linearly independent functions in such a way that the scattering intensity is represented as a series of orthonormal Hermite polynomials. The coefficients of this series are found by the least-squares method. The scale transformation factor ensures fast convergence of the series in real and reciprocal space and the number of terms is chosen using the orthogonal properties of the Hermite polynomials and perceptual criteria. The method allows evaluation of the distribution functions for monodisperse and polydisperse systems directly from the raw experimental data without a priori information on the particle sizes.

The use of pattern decomposition to study the combined X-ray diffraction effects of crystallite size and stacking faults in ex-oxalate zinc oxide

Abstract: The microstructure of ZnO powder, obtained from thermal decomposition of the oxalate and studied previously by electron microscopy and adsorption calorimetry, was investigated by means of X-ray powder diffraction pattern decomposition. A Williamson–Hall plot revealed that some lines were broadened solely due to the effects of crystallite size, whereas other breadths included a contribution due to stacking faults. Spherical and cylindrical models are used to describe the form of the crystallites and procedures are presented for separating 'size' effects from `mistake' broadening. This leads to estimates of the mean dimensions of the crystallites and the stacking-fault probability. The analysis demonstrates that, with good-quality data for a large number of reflections, a considerable amount of detailed information can be obtained about microstructure. On the other hand, it reveals some of the limitations of current procedures for modelling diffraction line profiles.

TLSANL: TLS parameter-analysis program for segmented anisotropic refinement of macromolecular structures

Abstract: The atomic displacements of many of the atoms in a macromolecular structure can be modelled in terms of group motions described in the harmonic approximation by T, L and S tensors. Relevant groups may be planar side groups of protein chains, units of secondary structure such as α-helices or whole protein domains. For the TLS parameters to be interpreted, they must be related to the axes of inertia of the rigid groups and, in the case of the T and S tensors, must be calculated with respect to the centre of reaction of the rigid group. A program (TLSANL) is described that analyses these 21 TLS rigid-body displacement parameters and their relation with the principal axes of the rigid body, from the output of the segmented anisotropic refinement of a macromolecular structure, as produced by a program such as RESTRAIN [Haneef, Moss, Stanford & Borkakoti (1985). Acta Cryst. A41, 426–433; Driessen, Haneef, Harris, Howlin, Khan & Moss (1989). J. Appl. Cryst. 22, 510–516].

Potential of the INEL X-ray position-sensitive detector : a general study of the Debye-Scherrer setting

Abstract: The INEL diffractometer, equipped with a CPS120 curved detector and set up in a Debye-Scherrer geometry, is a unique tool for carrying out powder diffraction studies on air-sensitive and/or small-volume samples Although it has routinely been used in powder diffractometry because of its minute acquisition times, its accuracy in d-spacing and intensity measurements has not been clearly demonstrated before now Concerning the d spacings, proper linearization of the CPS120 with a cubic Na2Ca3Al2F14 standard allowed a mean δ2θ difference of 0006° Intensity accuracy was measured with different highly and poorly absorbing samples The accuracy is fairly good for the latter but poor for the former, except when special procedures such as the dilution of the sample with boron powder are used A Rietveld calculation carried out on TI4V207 showed a very good agreement between the INEL Debye-Scherrer-geometry results and those obtained with a Philips diffractometer and Bragg-Brentano geometry

A fast and portable microspectrophotometer for protein crystallography

Abstract: Spectroscopic measurements on crystals during X-ray data collection provide additional information on the composition of the crystal and can be used in the interpretation of structural data. This paper describes a portable microspectrophotometer to obtain UV–visible–near-IR spectra from single crystals during X-ray measurements. The instrument consists of a deuterium lamp, optical fibres, a pair of mirror lenses and a monochromator equipped with a photodiode array detector. Spectra can be recorded in short periods of time (a few milliseconds) from a measurement area of 0.10 mm diameter or smaller. The device can be used to monitor spectral changes in crystals during time-resolved X-ray experiments so that the X-ray camera can be triggered at the right moment as determined by the spectrum, thereby eliminating much of the present guesswork from such studies.

Angle calculations for a six‐circle surface X‐ray diffractometer

Abstract: Angle calculations are presented for a new type of diffractometer suitable for surface X-ray diffraction. The new geometry results from combining the four-circle and the z-axis geometries and involves six circles. Instruments based on this concept can be operated in different diffraction geometries. Compared to the four-circle and z-axis geometries, a larger fraction of the reciprocal space perpendicular to the sample is available to experiments when all six circles are used. This results in an improved out-of-plane resolution in any X-ray structure study. In each geometry, either the angle of incidence or the outgoing angle of the X-rays can be chosen. At the same time, the surface normal can be aligned in the horizontal diffractometer plane, providing optimum resolution and sample illumination. All equations are given in closed form. The different modes of operation are compared and operation schemes are discussed.

A Direct Method of Beam-Height Correction in Small-Angle X-ray Scattering

Abstract: A direct (i.e. noniterative) method for desmearing the beam-height effect in small-angle X-ray scattering is discussed. The method is applicable to rectangular collimation systems with arbitrary beam-height intensity profiles. The process involves the construction of an upper-triangular matrix of terms containing the resolution information. A straightforward back-substitution process can then be used to determine the ideal pinhole-collimated curve for any experimental curve obtained with the given resolution. The principal advantage of the method lies in its simplicity, which facilitates an examination of the propagation of random errors through the desmearing process. A comparison between the direct method and the iterative approach of Glatter [J. Appl. Cryst. (1974), 7, 147-153] is made to illustrate the efficiency of the technique.

The determination of unit-cell parameters from Bragg reflection data using a standard reference material but without a calibration curve

Abstract: The procedure for determining unit-cell parameters from Bragg reflection data, using a standard reference material but without a calibration curve, is described. In this procedure, the observation equations for both the sample to be measured (SMP) and a standard reference material (SRM) are solved simultaneously and the unit-cell parameters and a form of error function are determined during the least-squares calculation. The theory, which was first proposed as a linear least-squares procedure [Toraya & Kitamura (1990). J. Appl. Cryst. 23, 282–285], has been extended to create a nonlinear least-squares procedure. The procedure can be used in two different ways. In one approach, the unit-cell parameters of the SMP and the parameters in the error function are refined while the unit-cell parameters of the SRM are fixed during the least-squares calculation. This procedure requires knowledge of the wavelength but it gives a stable solution and the tangent term in the error function gives a perfect correction for the error in wavelength. In the other approach, the unit-cell parameters of both the SMP and the SRM are refined, together with the parameters in the error function. The procedure does not require knowledge of the wavelength. The solution, however, became unstable when the correlation was strong between the unit-cell parameters and the error function and careful selection of the error function was required. The first approach gave the same result as the second and is, therefore, more practical to use. Since the form of the angle-dependent error function is determined using reflection data from both the SMP and the SRM, just one or two reflections from the SRM were enough for the correction of systematic error. The procedure, coupled with high-precision reflection data, can determine accurately the unit-cell parameters in a routine analysis.

Indirect transformation in reciprocal space : desmearing of small-angle scattering data from partially ordered systems

Abstract: Indirect Fourier transformation is a widely used technique for the desmearing of instrumental broadening effects, for data smoothing and for Fourier transformation of small-angle scattering data. This technique, however, can only be applied to scattering curves with a band-limited Fourier transform, i.e. separated and noninteracting scattering centers. It can therefore not be used for scattering data from partially ordered systems. In this paper, a modified technique for partially ordered systems working in reciprocal space is presented. A peak-recognition technique allows its application to scattering functions with narrow peaks, such as the scattering functions of layered systems like lamellar stacks or strongly interacting particles. Arbitrary geometry effects and wavelength effects can be corrected. Examples of simulations show the merits and limits of this new method. One example shows its applicability to real data.

Maximum-entropy-method analysis of neutron diffraction data

Abstract: The maximum-entropy method (MEM) is a very powerful method for deriving accurate electron-density distributions from X-ray diffraction data. The success of the method depends on the fact that the electron density is always positive. In order to analyse neutron diffraction data by the MEM, it is necessary to overcome the difficulty of negative scattering lengths for some atoms, such as Ti and Mn. In this work, three approaches to the MEM analysis of neutron powder diffraction data are examined. The data, from rutile (TiO2), have been collected previously and analysed by the Rietveld method [Howard, Sabine & Dickson (1991). Acta Cryst. B47, 462–468]. The first approach is to add an artificial large constant to the scattering-length density to maintain that density positive, then to subtract the same constant at the completion of the MEM analysis. This approach, however, proves unsuccessful since unrealistic density distributions result. In the second approach, the observed structure factors are amended so that the sign of the contribution from the Ti atoms is reversed. This method produces plausible maps of scattering-length density but suffers the disadvantage that the observations must be corrected by a model-dependent calculated factor before the MEM analysis can proceed. The third approach is based not on scattering-length densities but on nuclear densities, which are always positive. Two equations are obtained, one for atoms with nuclei of positive scattering length and the other for atoms with negative scattering length. From these two equations, the nuclear densities of Ti and O atoms can be calculated separately. This procedure, like its X-ray counterpart, requires no structural model. MEM analysis of the rutile data by this approach has been successfully completed. As expected, and in contrast to the electron-density distribution obtained by the MEM [Sakata, Uno, Takata & Mori (1992). Acta Cryst. B48, 591–598], the map shows both Ti and O nuclear densities localized in very small regions around the atomic centres. It is concluded that the MEM applied to neutron powder diffraction data is superior to conventional Fourier transformation and, in spite of the longer computation time, is very well worthwhile.

X‐ray reflection properties of elastically bent perfect crystals in Bragg geometry

Abstract: Reflection curves of bent crystals were calculated using the Takagi–Taupin theory of dependence on bending radius, wavelength, crystal thickness and Bragg angle. The reflection properties of bent crystals were measured for bending radii down to 90 mm. Usually, for the measurement of rocking curves of crystals with large bending radii, the double-crystal diffractometer was used in parallel position (n, −n). A special achromatic diffractometer consisting of a plane and a bent crystal is proposed. It is used to measure rocking curves of bent crystals with small bending radii (R < 1 m). Experimental values show close agreement with the theory. The reflection properties are important for X-ray microscopy with two-dimensionally bent crystals and for X-ray spectroscopy with bent crystals.

REPLACE, a suite of computer programs for molecular-replacement calculations

Abstract: A suite of computer programs (REPLACE) for crystal-structure determination by the molecular-replacement method has been developed. It currently includes a general (locked) rotation-function program (GLRF) and a translation-function program (TF). The rotation-function program can carry out ordinary as well as locked self- or cross-rotation-function calculations. It can also optimize non-crystallographic symmetry parameters based on the maximal electron-density overlap of the subunits related by the non-crystallographic symmetry. The translation search can be based on R-factors, correlation coefficients, Patterson correlation and electron-density-correlation criteria. The packing of the molecular structure in the unit cell can be checked as well.

Evaluation of 3D small-angle scattering from non-spherical particles in single crystals

Abstract: Three-dimensional small-angle scattering is discussed as a tool for investigation of anisometric particles in single-crystalline alloys. The measurement and evaluation methods take advantage of the well defined orientation relation between the precipitates and the matrix in alloys. The determination of shape, size and orientation of precipitates from the scattering in several planes of reciprocal space is discussed for the example of ellipsoids and plates. Shape and orientation of ellipsoids with small aspect ratio can be determined by deviations of the scattering intensity from spherical symmetry in certain planes of reciprocal space. Particle size is obtained from one-dimensional slices along certain directions. The small-angle scattering of plate-like particles with large aspect ratio is concentrated along radial streaks in reciprocal space. Slices along and across these streaks allow the determination of the plate thickness as well as size and aspect ratio of the plate surface. In addition, the evaluation of such `off-center' slices provides a resolution enhancement of almost one order of magnitude compared to the conventional Guinier method applied to spherically averaged data.

Comparison of radiation-induced decay and structure refinement from X-ray data collected from lysozyme crystals at low and ambient temperatures

Abstract: Two crystals of monoclinic hen egg-white lysozyme were irradiated in a monochromatic synchrotron X-ray beam (λ = 1.488 A), the first as a rapidly frozen crystal mounted at the end of a glass fiber at low temperature (120 K) and the second mounted in a capillary tube at ambient temperature (298 K). Comparison of oscillation photographs, extending in resolution to 1.85 A, and taken from both crystals at zero time and again after a period of exposure in the synchrotron beam (60 min exposure at 120 K; 8 min at 298 K), reveals that radiation-induced decay is not observed at 120 K but is observed, particularly at high resolution, at 298 K. In a separate set of experiments, data sets to 1.9 A resolution at 100 and 298 K were collected from two monoclinic and two tetragonal hen egg-white lysozyme crystals using a rotating-anode source (λ = 1.5418 A). Before inclusion of solvent molecules, the monoclinic and tetragonal structures at low temperature, where data were collected from rapidly frozen crystals, refined to R = 27.5 and 25.2%, respectively. The structures at ambient temperature, however, where crystals were mounted in capillary tubes, refined to significantly lower values of R = 20.9 and 20.6%. After inclusion of solvent, the R values at convergence were 20.3 and 17.6% for the monoclinic and tetragonal low-temperature structures and 17.9 and 16.2% for the room-temperature structures. Approximately twice the number of water molecules were included in the low-temperature structures at convergence (406 and 237) than could be assigned in the room-temperature structures (191 and 100). These results suggest that data sets from rapidly frozen crystals might generally be expected to yield higher initial R factors, compared to similar room-temperature structures, but that this difference should diminish appreciably as ordered solvent is included in the model. Apart from the general reduction in atomic temperature factors, the enhancement in resolution observed in diffraction patterns obtained from rapidly frozen crystals is probably due, to some significant degree, to the increase in the ordered-solvent content of the low-temperature structures.

Improved calibtration curve for the Sm2+:BaFCl pressure sensor

Abstract: The pressure sensor proposed by Shen, Gregorian & Holzapfel [High Press. Res. (1991), 7, 73–75], based on the pressure-dependent shift of the luminescence line due to the 5D0−7F0 electronic transition of Sm2+ in a matrix of BaFCl, has been tested in a diamond-anvil cell and calibrated against the R1−R2 doublet shift of ruby and the known NaCl equation of state, in the pressure range between 0.0001 and 4.3 GPa. The parabolic dependence of the shift from the pressure can be approximated by the equation Δ(nm) = 1.46P − 0.047P2, where the shift, Δ, is in nm and the pressure, P, in GPa. The estimated error in the pressure measurements is 5%. The Sm2+: BaFCl luminescence sensor can be advantageously used in the low to moderate pressure range (0.0001–5 GPa or more).

A new technique for the observation of X-ray CTR scattering by using an imaging plate detector

Abstract: A new technique, using an Imaging Plate (IP) detector, was developed for the observation of X-ray crystal truncation rod (CTR) scattering. The use of an IP detector in conjunction with a synchrotron-radiation (SR) source is very effective for the observation of CTR scattering. The advantages and disadvantages of this technique are indicated by examples of the observation of CTR scattering from various samples: a naturally oxidized surface of an Si(111) wafer; MBE-grown GaAs/AlAs/GaAs on GaAs(001) substrate; Al-capped GaAs on an Si(111) substrate; and a cleavage NaCl(001) surface. It is also shown that it is possible to convert the observed intensity of the CTR scattering to an absolute scale if a stationary photograph is taken.

Improved treatment of severely or exactly overlapping Bragg reflections for the application of direct methods to powder data

Abstract: A new method has been developed for the improved intensity assignment of severely or exactly overlapping Bragg reflections in a powder diffraction pattern. This fast iterative Patterson squaring (FIPS) method addresses, in particular, the systematic lack of small and large normalized intensities (|E| values) in severely overlapping powder data, which causes (a) the intensity statistics to be strongly acentric (even when the structure itself is centrosymmetric) and (b) the under-estimation of strong structure-invariant relationships. Direct methods for structure determination are more likely to succeed with FIPS-improved data than with conventionally used equipartitioned data (ratio of |E| values for overlapping reflections set to 1.0). In the case of the molecular sieve AFR (in which 65% of the reflections severely overlap), the ab initio structure solution was only possible after a redistribution of the intensities by the FIPS method.