Showing papers in "Journal of Applied Crystallography in 1994"

A correction for powder diffraction peak asymmetry due to axial divergence

Abstract: Analysis of a crystal structure using the Rietveld profile technique requires a suitable description of the shape of the peaks. In general, modern refinement codes include accurate formulations for most effects; however, the functions used for peak asymmetry are semi-empirical and take very little account of diffraction optics. The deficiencies in these methods are most obvious for high-resolution instruments. This study describes the implementation of powder diffraction peak profile formulations devised by van Laar & Yelon [J. Appl. Cryst. (1984), 17, 47–54]. This formalism, which describes the asymmetry due to axial divergence in terms of finite sample and detector sizes, does not require any free parameters and contains intrinsic corrections for the angular dependence of the peak shape. The method results in an accurate description of the observed profiles for a variety of geometries, including conventional X-ray diffractometers, synchrotron instruments with or without crystal analyzers and neutron diffractometers.

Determination of size distribution from small‐angle scattering data for systems with effective hard‐sphere interactions

Abstract: Methods for the free-form determination of size distributions for systems with hard-sphere interactions are described. An approximation, called the local monodisperse approximation, is introduced. Model calculations show that this approximation gives relatively small errors even at relatively high polydispersities and large volume fractions. The size distributions are determined by least-squares methods with smoothness and non-negativity constraints. The local monodisperse approximation leads to normal equations that are linear in the amplitude of the size distribution. This is used when solving the least-squares problem: only the two effective parameters describing the interference effects are treated as nonlinear parameters in an external optimization routine. The parameters describing the size distribution are determined by a linear least-squares method. The size distribution is also determined using the nonlinear equations from the calculation of the scattering intensity in the Percus–Yevick approximation. For this, a nonlinear least-squares routine with a smoothness constraint and a non-negativity constraint is used. Both approaches are tested by analysis of simulated examples calculated by the analytical expressions in the Percus–Yevick approximation. Finally, the methods are applied to two sets of experimental data from silica particles and from δ′ precipitates in an Al–Li alloy. For the simulated examples, good agreement is found with the input distributions. For the experimental examples, the results agree with the expected and known properties of the samples.

SnB: crystal structure determination via shake‐and‐bake

Abstract: Shake-and-bake is a direct-methods phasing algorithm for structure determination based on the minimal principle. SnB is a program based on shake-and-bake that has been used successfully to solve more than a dozen structures in a variety of space groups. The focus of this paper is on the details of this program, including its structure, system requirements, running times and the rationale for coding in a combination of C and Fortran. A summary of successful SnB applications is also provided. These include solving two previously unknown 100-atom structures and re-solving crambin (a structure containing the equivalent of approximately 400 fully occupied atomic positions) for the first time with a direct-methods technique.

Early finding of preferred orientation: a new method

Abstract: Pattern decomposition programs are able to derive, from the measured powder diffraction patterns, estimates of the square moduli of the structure factors. A method is described that, by statistical analysis of the normalized structure-factor moduli, is able to obtain information about the possible presence of preferred orientation. Cylindrical symmetry of the specimen is necessary. The method proves to be efficient and quite useful for the application of direct methods to powder data.

R values in analysis of powder diffraction data using Rietveld refinement

Abstract: Profile and Bragg R values are discussed with respect to different versions of the Rietveld program. The R values calculated from an exemplary neutron diffraction pattern are compared. Results obtained by a modified treatment of background and by a simplified method to decompose an observed pattern into Bragg intensities are presented.

Analysis of neutron and x-ray reflectivity data. II. Constrained least-squares methods

Abstract: Two methods for the determination of scattering length density profiles from specular reflectivity data are described. Both kinematical and dynamical theory can be used for calculating the reflectivity. In the first method, the scattering density is parameterized using cubic splines. The coefficients in the series are determined by constrained nonlinear least-squares methods, in which the smoothest solution that agrees with the data is chosen. The method is a further development of the two-step approach of Pedersen [J. Appl. Cryst. (1992), 25, 129–145]. The second approach is based on a method introduced by Singh, Tirrell & Bates [J. Appl. Cryst. (1993), 26, 650–659] for analyzing reflectivity data from periodic profiles. In this approach, the profile is expressed as a series of sine and cosine terms. Several new features have been introduced in the method, of which the most important is the inclusion of a smoothness constraint, which reduces the coefficients of the higher harmonics in the Fourier series. This makes it possible to apply the method also to aperiodic profiles. For the analysis of neutron reflectivity data, the instrumental smearing of the model reflectivity is important and a method for fast calculation of smeared reflectivity curves is described. The two methods of analyzing reflectivity data have been applied to sets of simulated data based on examples from the literature, including an amphiphilic monolayer and block copolymer thin films. The two methods work equally well in most situations and are able to recover the original profiles. In general, the method using splines as the basis functions is better suited to aperiodic than to periodic structures, whereas the sine/cosine basis is well suited to periodic and nearly periodic structures.

Interpretation of diffuse X‐ray scattering via models of disorder

Abstract: While Bragg diffraction data can only reveal average one-body information, such as atomic positions, thermal ellipsoids and site occupancies, diffuse scattering contains two-body information and is thus potentially a rich source of information on how atoms and molecules interact. The two major mathematical approaches that have been used to understand and analyse this diffuse part of the diffraction pattern are outlined and the difficulties and limitations which arise from the necessary complexity of these mathematical descriptions for any but the simplest of systems are discussed. Further, the progress that has been made in an alternative approach to understanding the local atomic and molecular arrangements in disordered materials, which overcomes some of these difficulties, is reviewed. The method consists of comparing diffraction patterns calculated from a computer model of the disordered structure with measured X-ray diffuse intensities. The advantage of the method is that it can be applied generally to all systems regardless of their complexity or size of the atomic displacements that might be present. Examples are taken from a variety of material systems and include oxygen–vacancy ordering and metal-atom displacements in yttria-stabilized cubic zirconia, disorder in the molecular crystal p-chloro-N-(p-methylbenzylidene)aniline, C14H12ClN (MeCl), and orientational disorder in crystals of 1,3-dibromo-2,5-diethyl-4,6-dimethylbenzene, C12H16Br2 (BEMB2). The computer models are generated using both real-space Monte Carlo methods, which employ near-neighbour effective interactions, and a reciprocal-space synthesis approach. Diffraction patterns are computed in three dimensions using realistic atomic form factors so direct comparison can be made with mathematical descriptions of the diffuse scattering.

ORTEX2.1 – a 1677‐atom version of ORTEP with automatic cell outline and cell packing for use on a PC

Abstract: Method of solution: The PROSZKI package consists of separate programs that can be executed independently in any order. The main program in the system, PRMAIN, serves as a shell that enables the user to set up the parameters file, interactively create an input file for other programs, read the output file summary and write automatically the most important results to the parameter file. The system contains the following groups of programs: (i) powder diffraction pattern decomposition, NEWPEAK (Sonneveld & Visser, 1975); (ii) indexing of the powder patterns, VlSSER-12 (deductive, parameter space) (Visser, 1969), DICVOL (exhaustive, parameter space) (Lou~r & Lou~r, 1972; Lou~r & Vargas, 1982), TREOR-4 (semiexhaustive, index space) (Werner, Eriksson & Westdahl, 1985), POWDER (exhaustive, index space) (Taupin, 1968); (iii) refinement of the lattice parameters, APPLEMAN (Appleman, Evans & Handwerker, 1966), LATCON (Schwarzenbach, 1975); (iv) simulation of the powder diffraction pattern, LAZYPULVERIX (Yvon, Jeitschko & Parthc ~, 1977) Different approaches to the indexing problems increase the probability of success in the indexing procedure. Also, each program for the lattice-parameter refinement contains unique features not offered by the other programs. The programs were implemented without any modifications that could affect final results and their accuracy. The format of the input data files is virtually the same as in the original programs, allowing the use of any individual program or data file independently of the rest of the system. Optionally, input files for two popular Rietveld analysis programs, DBWS-9OO6PC (Sakthivel & Young, 1992) and XRS-82 (Baerlocher, 1982), can be created.

Applicabilities of the Warren-Averbach Analysis and an Alternative Analysis for Separation of Size and Strain Broadening

Abstract: The validities of the Warren–Averbach analysis and of an alternative analysis for separation of size and strain contributions to diffraction line broadening are investigated. The analyses are applied to simulated and experimental line profiles. The Fourier coefficients of the simulated line profiles are derived from expressions for the distortion field around specific lattice defects: misfitting inclusions and small-angle grain boundaries. Applicability tests are also performed on experimental powder diffraction line profiles taken from plastically deformed specimens: thin aluminium layers and ball-milled molybdenum powders. It is concluded that for both methods finite but different classes of specimen exist for which they give meaningful results. In practice, each time an analysis is performed the results must be tested against common (physical) sense and all information available on the specimens.

International Union of Crystallography. Commission on Powder Diffraction. Rietveld refinement round robin. II. Analysis of monoclinic ZrO2

Abstract: The Commission on Powder Diffraction of the IUCr has undertaken a round robin of Rietveld refinement with the aims of: (i) evaluating a cross section of currently used software; (ii) examining the range and effect of various strategies of refinement; (iii) assessing the precision and accuracy (spread) of the derived parameters; (iv) comparing and contrasting various instruments and methods of data collection. These aims were addressed by circulating to 51 participants upon request: (i) two constant-wavelength X-ray and neutron powder diffraction patterns collected on PbSO4 for refinement; (ii) a sample of phase-pure monoclinic ZrO2 for both data collection and refinement. In the latter case, the raw data were requested to be returned for reanalysis with a `standard' version of Rietveld software and an `optimal' refinement protocol. A total of 23 respondents provided 18 X-ray and 20 neutron refinements of the PbSO4 crystal structure from the 'standard' data sets using 12 different Rietveld analysis programs. These results constitute Part I of the round robin and have been described previously [Hill (1992). J. Appl. Cryst. 25, 589–610]. The 28 contributors to the m-ZrO2 section of the survey were based in 12 countries and collected 27 X-ray and 14 neutron data sets, using 20 different X-ray and 11 different neutron powder diffraction instruments. The conventional X-ray instruments included 13 reflection (flat-plate) and eight transmission (capillary or thin-film) machines and used three different radiations (Co, Cu and Mo). Two additional flat-plate data sets were collected with synchrotron X-rays. The neutron data were collected on 12 constant-wavelength and two time-of-flight instruments, the former utilizing wavelengths between 1.0 and 1.9 A. The data sets yielded 27 X-ray and 15 neutron refinements of the m-ZrO2 crystal structure. The conditions used for data collection varied widely for both types of radiation: wavelengths ranged from 0.7 to 1.9 A, step widths from 0.01 to 0.12°2θ, step counting times from 0.1 to 46 s for X-rays and up to 30 min for neutrons, data-collection time from 4 min to 3 d, maximum step intensities from 350 to 99000 counts, minimum d spacings from 0.53 to 1.17 A and numbers of unique reflections from 71 to 912 (not including the time-of-flight neutron data). Variations in resolution between instruments were especially marked in the case of the neutron data but were less pronounced for the X-ray machines; the two instruments situated at synchrotron X-ray sources displayed the narrowest peak widths. The peak-to-background ratios varied markedly; in descending order of peak-to-background ratio were single-wavelength X-rays (conventional and synchrotron sources, using incident-beam monochromators), two-wavelength X-rays in parafocusing (reflection) mode, two-wavelength X-rays in transmission mode and constant-wavelength neutrons. Refinement conditions were also markedly inconsistent, with the total number of refined parameters varying from 20 to 46. The major factors associated with lower accuracy of the derived crystal structure parameters were: (i) the use of insufficiently flexible peak-shape and/or background functions; (ii) omission of the high-angle data from the refinement, especially the data with d spacings below about 1 A; (iii) use of an insufficiently wide range of diffraction angles on either side of the peak (i.e. peak truncation), especially for the reflection profiles with substantial Lorentzian (or Cauchy) character; (iv) poor instrumental resolution and/or a peak-to-background ratio less than about 50; (v) low pattern intensity (i.e. maximum step intensity less than about 2000 counts), especially at small d spacings; (vi) an observations-to-parameters ratio of less than about five. The X-ray- and neutron-data Zr-atom coordinates are distributed over a relatively narrow and similar range of values about the weighted mean values, viz 0.014 to 0.028 A and 0.009 to 0.014 A, respectively. On the other hand, while the values of the O-atom coordinates derived from the neutron data are determined with about the same accuracy as those of the Zr-atom ones, viz 0.006 to 0.017 A about the mean, the corresponding values derived from the X-ray data are distributed over a very much wider range, viz 0.091 to 0.193 A, no doubt due to the lower scattering power of the O atom. The atomic displacement (`thermal') parameters are reasonably determined with X-rays when flat-plate reflection-geometry instruments are used but transmission geometry produces very poor parameters ranging from large negative to large positive values; the poor quality of the latter results is due to the strong correlation between displacement and absorption effects and the generally smaller number of reflections included in the data. All but the lowest-resolution neutron data support a sensible anisotropic displacement ellipsoid for the atoms. The precision and accuracy of the population of crystal structural parameters produced from the participants' refinements were almost always substantially improved by reanalysis of the data using a `standard' program and an `optimal' refinement protocol. The mean probable errors, taken as the mean deviations of the individual estimates of the parameters from the weighted mean value, show that about two-thirds of the variation in the m-ZrO2 parameters is due to differences in the instrumental and data-collection conditions. The remaining one-third of the variation is due to differences in the software and/or the refinement strategy used. On average, the mean probable errors of the Rietveld parameters are larger than their derived estimated standard deviations by a factor of around two for coordinates, about five for the displacement parameters and around 16 for unit-cell dimensions. Of the X-ray instruments, flat-plate reflection-geometry ones provided the best crystal structure parameters for the sample of m-ZrO2 distributed in this study, but the quality was degraded when the data were cut off at d spacings larger than about 1 A. The X-ray transmission geometries produced the poorest atomic parameters because of the generally poorer peak-to-background ratio and the limited range of data available (with resultant lower observations-to-parameters ratio). The results obtained with neutron data were of roughly equivalent quality to those obtained from X-rays in the case of the Zr atom, but neutrons were markedly superior for the determination of the O-atom coordinates and displacement parameters, as expected. The time-of-flight neutron and synchrotron X-ray results were not significantly different from those obtained in the conventional neutron and better-quality conventional X-ray analyses.

Analysis of neutron and X-ray reflectivity data. I: Theory

Abstract: Different methods and approximations for calculating reflectivity curves from scattering-length density profiles are carefully discussed and compared. Dynamical theory and the approximations leading to single-scattering dynamical theory, kinematical theory with an optical path-length correction and kinematical theory with refraction corrections are described. The differences are illustrated by calculations for model profiles for which dynamical effects are important.

Characterization of thin nickel electrocoatings by the low-incident-beam-angle diffraction method

Abstract: The low-incident-beam-angle diffraction technique (LIBAD) has been developed as a powerful X-ray diffraction tool for the characterization of thin crystalline coatings. The technique can be implemented to determine the residual stress state in thin coatings, their crystallographic texture, by means of the orientation distribution function, and thickness, as well as the stress profile in a coating as a function of depth. As an example, electrodeposited nickel coatings on a copper substrate have been characterized with this technique for thicknesses varying from 0.6 to 3.8 μm. Crystallographic texture and mean residual stress appear to be correlated with the coating thickness. So, for example, the residual stress of the coatings evolves from a low to a high tensile stress with increasing coating thickness. The stress in the uppermost region of the substrate is influenced by the stress state in the coating. The stress profile in the coating was found to be linearly dependent on the information depth.

Using a two-dimensional detector for X-ray powder diffractometry

Abstract: Special software has been developed to calculate the intensity–scattering-angle dependence. Powder diffraction patterns are obtained in a diffractometer with a two-dimensional area detector. The detector used is a planar proportional chamber with fast delay lines. The optimum sample geometry for both the transmission and reflection method is considered. The application of the method for powders and for the investigation of phase transitions in liquid crystals is illustrated.

SUPERIMPOSE– a program for the unambiguous structural superposition of spatially related molecules, including macromolecules

Abstract: invariants are estimated via proper representations (Giacovazzo, 1977, 1980). Trial solutions are obtained by the magic-integer approach (Main, 1978) or by random phases (Baggio, Woolfson, Declercq & Germain, 1978). The best solution, selected by proper figures of merit (FOM's), is automatically processed through a cyclic procedure integrating structure-factor calculation, least-squares refinement and 2Fo-Fc Fourier synthesis. Owing to reflection overlap, the observations in the leastsquares routine are the total intensities of groups of reflections, while intensities of single reflections constitute single observations only when they do not overlap with any other. The final outcome is a set of refined atomic parameters (x, y, z) associated with atomic species. When neutron data are processed, parameters of atomic species with negative scattering length can also be determined. If a graphic device is available, the user can follow structure solution and refinement on the screen. In the final stage, a menudriven interface is available in order to study molecular geometry and restart refinement. Owing to the small number of observations/number-of-parameters ratio, the residual R values must be carefully considered by the user (usually final values are between 0.06 and 0.20). Software environment: The program has been written in standard Fortran77. A module written in C is supplied for interface with X-window or DECWindow terminals. Besides a C compiler, an Xlib library is also needed. Two ASCII files are associated with the program: the first contains coefficients for calculating scattering factors, the second, necessary for graphics, contains on-line help. Hardware environment: The program runs on Unix and DEC workstations, on main-frame and personal computers (at least 4 Mbytes of RAM and a VGA monitor are needed). Program specification: The source code of the program consists of 44000 Fortran lines and 2000 C lines (including

XRDA: a program for energy-dispersive X-ray diffraction analysis on a PC

Abstract: XRDA, an analysis software for energy-dispersive X-ray diffraction data obtained from samples compressed in a diamond-anvil cell using synchrotron radiation, is described. The code takes advantage of the recent availability of inexpensive fast PC's and the widespread Windows graphical environment. The program offers an efficient way to analyze the numerous diffraction patterns usually recorded as a function of pressure. In addition to X-ray data file management, peak profile fitting and diffraction intensity calculations, crystalline structure determinations can easily be performed.

Real‐time X‐ray synchrotron powder diffraction studies of the dehydration processes in scolecite and mesolite

Abstract: The high intensity of an X-ray synchrotron source in combination with a curved position-sensitive detector covering 120° (CPS120 by INEL) has been used to collect complete powder diffraction patterns, suitable for Rietveld analyses, within minutes. From consecutive patterns (ΔT ≃ 5 K), detailed information was obtained on water expulsion and phase transitions induced by dehydration of the natural zeolites scolecite and mesolite. Scolecite, Ca8Al16Si24O80.24H2O, shows an initial gradual loss of half O(2W). At ~480 K, scolecite goes through a phase transition already described by Rinne [Neues Jahrb. Mineral. Beil. (1923). 48, 240–249]. The crystal symmetry changes from F1d1 to Fd11 when half the Ca ions move by ~1/2c and the remaining O(2W) is expelled. Metascolecite: Ca8Al16Si24O80.16H2O, Fd11, Z = 1, T = 489 K, a = 18.1465 (7), b = 18.8604 (7), c = 6.5396 (3) A, α = 88.986 (2)°, Rp = 5.42%, RB = 2.51% from 3620 observations, 802 Bragg reflections and 79 refined parameters. Continued heating to 615 K did not further reduce the water content. The dehydration process in mesolite starts with a loss of half the same Ca-coordinated water as in scolecite. The initial water loss is followed by an order/disorder transition, where the Na and Ca ions become randomly distributed over the cation sites. Consequently, the b axis of metamesolite is reduced to 1/3 of bmes and the k ≠ 3n reflections disappear. Metamesolite is very similar to natrolite, with equal numbers of Na atoms, Ca atoms and vacancies in the natrolite Na-atom site and with n(H2O) varying between 16 and 10.67. Metamesolite: Ca5.33Na5.33Al16Si24O80.n(H2O), Fdd2, Z = 1, n(H2O) = 10.6 (2), T = 582 K, a = 18.1039 (6), b = 18.5763 (6), c = 6.5589 (2) A, Rp = 4.85%, RB = 2.01% from 3620 observations, 424 Bragg reflections and 54 refined parameters. Both scolecite and mesolite have one AlO4 tetrahedron with only one O atom coordinated by a cation. The initially expelled waters are in both cases hydrogen bonded to an O atom in those AlO4 tetrahedra. The initial water expulsions thus worsen the underbonding and trigger the cation rearrangements. The resulting cation distributions in metascolecite and metamesolite are the most even with respect to the AlO4 tetrahedra and are considered the driving force of both phase transitions. The cation rearrangement in mesolite requires cross-channel diffusion and is considerably slower than the in-channel rearrangement taking place in scolecite. In both zeolites, the lower limit in the calcium coordination number was found to be six. The ICDD Powder Diffraction File Nos. are: 45-1489 for Ca8Al16Si24O80.16H2O; 45-1490 for Ca8Al16Si24O80.18.9H2O; 45-1491 for Ca5.33Na5.33Al16Si24O80.12.8H2O; 45-1492 for Ca5.33Na5.33Al16Si24O80.16.7H2O.

A simple method for determining orientation and misorientation of the cubic crystal specimen

Abstract: With the aid of a double-tilt holder, a simple method for determining orientation and misorientation of a cubic crystal specimen in a transmission electron microscope is developed. To use this method, a recognizable zone axis from one grain needs to be aligned along the beam direction, the corresponding tilt positions (α0, β0) of the two rotation axes must be obtained from the meter reading of the holder and the rotation position of the Kikuchi pattern around the beam direction must be measured on the fluorescent screen with the aid of apparatus for the direct measurement of a diffraction-pattern position on screen. After the input of (α0, β0) and the rotation positions, the orientation of the grain can be calculated using a computer program. The misorientation matrix R, rotation angle Θm, axis Im and sense can then be calculated for any selected set of two grains. The accuracy of determination of the orientation of any particular grain is about 1° and, in the case of the determination of misorientation angles between two grains within a sample, the precision is within 0.1°. This method is considered to be much simpler and more rapid than previous methods because no photographs of Kikuchi patterns need to be taken and only one zone-axis orientation needs to be adjusted along the beam direction.

Energy-Dispersive Phase Plate for Magnetic Circular Dichroism Experiments in the X-ray Range

Abstract: A 220 diamond phase plate was combined with an energy-dispersive absorption spectrometer to convert linearly polarized X-rays into circularly polarized photons and to detect circular magnetic X-ray dichroism (CMXD) from ferromagnetic samples. In these experiments, carried out at LURE, the energy-dispersive spectrometer was equipped with a bent Si (311) polychromator and vertically collimating slits accepting essentially a linearly polarized incident beam. The quarter-wave plate was operated in the Bragg geometry but well outside the range of quasi total reflection, with the consequence that the forward-diffracted beam was circularly polarized with a polarization rate approaching 80% over the whole energy bandpass of the polychromator. CMXD spectra of GdFe2 and GdCo2 intermetallic compounds were recorded at ca 7.2 keV near the Gd LIII absorption edge: they are essentially identical to the spectra commonly recorded with elliptically polarized X-ray photons collected out of the orbit plane of the storage ring. It is suggested that the energy-dispersive phase plate will be very useful to detect CMXD spectra with energy-dispersive spectrometers exploiting the well collimated linearly polarized emission of standard undulators installed on the storage rings of the third generation.

On the Preparation and X-Ray Data-Collection of Isomorphous Xenon Derivatives

Abstract: A simple method for the preparation of isomorphous xenon derivatives is presented. A device has been designed that allows diffraction studies on protein crystals under xenon gas pressures up to 50 × 105 Pa. Crystal mounting and X-ray data collection do not significantly differ from standard techniques. Tests carried out on crystals of the protein porcine pancreatic elastase reveal a single xenon binding site with high occupancy at a pressure of 8 × 105 Pa. Xenon binding to several other crystallized proteins has also been investigated and results indicate that the method is generally applicable. Time-resolved studies show that, at 297 K, xenon binding is essentially completed within a few minutes. At pressures above 106 Pa, successful data collection is hampered by X-ray absorption and by the formation of xenon hydrate. Absorption can be reduced by using short-wavelength radiation and by mounting crystals in small capillaries. To circumvent xenon hydrate formation, higher working temperatures and the use of cryoprotective mother liquors are advocated.

Collection and analysis of powder diffraction data with near-constant counting statistics

Abstract: The concept of a variable-counting-time (VCT) strategy for use in Rietveld analysis of X-ray powder diffraction data was introduced by Madsen & Hill [Adv. X-ray Anal. (1992), 35, 39–47]. This strategy is based on a function that increases the counting time used at each step in the scan in a manner that is inversely proportional to the decline in reflection intensity that inevitably results from the combined effects of Lp factor, scattering factor and thermal vibration. The present work extends the VCT function to include the effects of reflection multiplicity, cylindrical-sample (capillary) absorption and monochromator polarization. The new algorithm has been incorporated into a PC computer program and applied to the collection of data from samples of LaB6, tourmaline, forsterite and boehmite. Subsequent analysis of the data using the Rietveld method has shown that VCT data can produce more accurate atomic coordinates and site occupancies, lower residual 'noise' in difference Fourier maps and more stable refinement of `light' atoms.

Flash freezing of protein crystals: investigation of mosaic spread and diffraction limit with variation of cryoprotectant concentration

Abstract: The effect of a cryoprotectant (glycerol) upon the mosaicity of flash-frozen T-state glycogen phosphorylase b crystals has been investigated. Glycerol concentration in a buffered solution was varied between 0 and 70% v/v. The results show that there is a well defined optimum in glycerol concentration giving lowest mosaicity, maximum resolution and no ice formation. The results also demonstrate how flash-freezing conditions can be systematically determined in-house using a minimum number of crystals and before using synchrotron time.

Small-angle X-ray scattering in carbon fibers

Abstract: Small-angle X-ray scattering (SAXS) has been used as an analytical tool to study microporosity in polyacrylonitrile- (PAN-) and pitch-based carbon fibers. Microporosity in carbon fibers consists primarily of needle-shaped voids whose long axes are oriented preferentially along the fiber axis. This preferred orientation is seen to be independent of the nature of the fiber precursor and is the major deciding factor in controlling the modulus of carbon fibers. As the modulus increases, the general trend for both PAN- and pitch-based fibers is to move from a system consisting of many small pores to one with few larger pores. At very small angles, the steep rise in scattered intensity is due to reflection effects for PAN-based fibers and multiple scattering effects from voids for pitch-based fibers.

Measurement of the static disorder contribution to the temperature factor in cubic stabilized ZrO2

Abstract: Neutron powder diffraction has been used to measure the temperature factors of both the cation and the anion atoms in 10mol% Y2O3–ZrO2 over the temperature range 15 to 1323 K. The Housley–Hess approach has been used to determine the static disorder term of the temperature factors for both the Zr/Y and O atoms. The static contribution was determined to be 1.04 (6) A2 for Zr/Y and 2.2 (1) A2 for O. From these results, a Debye temperature of 527 (20) K was calculated for this sample.

Simultaneous monitoring of amorphous and crystalline phases in silicalite precursor gels. An in situ hydrothermal and time-resolved small- and wide-angle x-ray scattering study

Abstract: The gel transformations and subsequent crystallization that occur in the precursor reaction mixture of silicalite were investigated using simultaneous small- and wide-angle X-ray scattering (SAXS–WAXS). The SAXS–WAXS measurements, together with the use of a high flux of synchrotron radiation and a newly developed high-pressure reaction cell, provide the possibility of in situ hydrothermal and time-resolved monitoring of amorphous gel transformations and crystallization.

Fitting of rocking curves from ion‐implanted semiconductors

Abstract: A simple fitting procedure is presented for the analysis of the strain profile in semiconductors; it has been applied to samples of ion-implanted silicon. The calculated strain profiles for some experimental rocking curves are compared with the simulated dopant-concentration profiles and the energy profiles. A two-sided Gaussian has been shown to produce an adequate fit to the strain profile in ion-implanted semiconductors. This procedure reduces the number of refinable parameters to only four and is favoured over changing the strain distribution as a function of depth in a rapid uncorrelated way. The error between the measured and calculated rocking curves has been analysed as a function of the Gaussian parameters. Besides one sharp global minimum, many local minima exist. It is shown that smoothing of the rocking curves with a triangular shape results in a reduction of the number of local minima.

Synthesizing and fitting linear position-sensitive detector step-scanned line profiles

Abstract: An X-ray powder diffractometer has been modified by the addition of a narrow-bandpass germanium pre-monochromator and a linear position-sensitive detector (LPSD) with its centre set at the normal θ–2θ focusing condition. Diffraction data are recorded using a step-scan procedure in which the patterns recorded at each step are summed to form the final pattern over a wide angular range. In this way, diffraction patterns covering 120 2θ can be recorded 100 times more rapidly than with conventional receiving-slit diffractometers for the same level of counting statistics. In this paper, an analysis has been carried out of the contribution of the instrumental parameters to the shapes of the X-ray diffraction lines obtained with either a stationary or a step-scanned LPSD. This is done by calculating theoretical profiles for defocusing, parallax error, thermal-noise broadening and LPSD pixel size and convoluting them with the Cu Kα emission spectrum and aberration profiles associated with a standard focusing powder diffractometer. Theoretical profiles for fitting to experimental step-scan data are synthesized by summing convoluted profiles across the detector window. The validity of this procedure is tested by fitting to experimental step-scan data from well characterized reference specimens of MgO and Y3Al5O12 (YAG). The extra broadening associated with the inclusion of a LPSD is refined in terms of the depth of the detector, the angular window of the LPSD and the angle of divergence of the incident beam. Good fits have been obtained to the reference profiles and the physical parameters of the diffractometer determined in this way agree well with directly measured values.

MINIMAGE: a program for plotting electron‐density maps

Abstract: MINIMAGE is a program that enables the molecular structure plotting programs MAXIMAGE (© M. Rould) and MOLSCRIPT (© P. Kraulis) to draw electron-density maps. Thus, electron-density drawings can be combined with different renderings of molecular-structure models. The user specifies electron-density contouring, coordinate transformation and selection parameters. The program produces an input file for subsequent programs that contains plotting instructions and electron-density contouring information, and two files in the Brookhaven Protein Data Bank format, one containing selected atomic coordinates and the other containing electron-density vertices. MINIMAGE is designed to work on both VAX/VMS and Unix-based operation systems.