bluuebunny/crossref_metadata_2025 huggingface dataset:
Intensity expression for short-range-order diffuse scattering with ordering energies in a ternary alloy system
Authors: Hashimoto S.
Published: July 2002

An X-ray partial diffuse intensity equation has been explicitly expressed as a function of ordering energies between different atomic species by referring to the description of the interatomic correlation function of de Fontaine [J. Phys. Chem. Solids (1973), 34, 1285–1304]. The expression suggests the appearance of a negative partial intensity. As an interesting example of its application, the calculation of the partial intensity for the disordered Cu2NiZn ternary alloy by means of the derived equation in terms of the ordering energies obtained theoretically by de Rooy, van Royen, Bronsveld & de Hosson [Acta Metall. (1980), 28, 1339–1347] is shown to lead to a distribution of diffuse scattering very similar to that given by experimental observations [Hashimoto, Iwasaki, Ohshima, Harada, Sakata & Terauchi (1985). J. Phys. Soc. Jpn, 54, 3796–3807].
A model-fitting procedure incorporating the double-null technique for use in protein structure refinements
Authors: Tomlin J. L.
Published: July 2002

The double-null technique in conjunction with the conjugate-gradient algorithm gives an efficient method of regularizing protein structures. The double-null technique constrains planar groups by introducing two artificial atoms which are geometrically the apices of tetrahedra from three selected atoms in the planar group. The model-fitting procedure is simply concerned with reconciling information on (x, y, z) atomic coordinates with information on bond length, bond angle and planarity constraints. This can be done without treatment of hydrogen-bond, van der Waals or electrostatic interactions and consequently the minimization function is nearly quadratic. The equations which have to be solved have many unknowns but few coefficients and an effective iterative method can be used.
Testing the method of crystallographic refinement using molecular dynamics
Authors: Fujinaga M. , Gros P. , van Gunsteren W. F.
Published: July 2002

The method of crystallographic refinement using molecular dynamics [Brünger, Kuriyan & Karplus (1987). Science, 235, 458–460] has been implemented to work with the GROMOS simulation package. It has been tested by applying it to the structure of phospholipase A2. The structure of this molecule had previously been refined at high resolution with conventional methods. The new method successfully refined the initial multi-isomorphous replacement structure, removing most of the errors, without any manual intervention. All the refinement was performed at 300 K. The use of lower-resolution data allows greater conformational transitions to occur whereas the inclusion of high-resolution data results in a more accurate structure.
Multiple small-angle neutron scattering characterization of the densification of ceramics: application to microporous silica
Authors: Long G. G. , Krueger S.
Published: July 2002

Multiple small-angle neutron scattering was used to characterize the microstructure evolution of porous silica as a function of thermal processing. This new technique offers a statistically significant determination of microstructure morphology in the 0.08–10 μm range, which was previously inaccessible without increasing the resolution of the currently available scattering spectroscopy beamlines. All of the scatterers, which in the present work are pores within ceramic bodies, are measured whether they are open or closed. Earlier mercury porosimetry and nitrogen desorption measurements of the microporous silica system indicated that there are two major populations of pores in this material, differing in pore size by approximately an order of magnitude. In this work, it was found that densification during the intermediate stages of sintering is accompanied by coarsening to radii > 0.22 μm within the population of large pores in microporous silica. In the late stages of sintering, there are no detectable pores with radii > 0.08 μm, and radii of gyration equal to 33 and 28 nm were measured. Finally, Monte Carlo simulations were carried out to complement the neutron-scattering measurements, to predict the influence on the results of the bimodal distribution, and to explore the sensitivity of the multiple-scattering method.
Crystals and composites
Authors: Newnham R. E. , Trolier-McKinstry S.
Published: July 2002

This paper is a review of the symmetry and connectivity of composite materials with particular emphasis on the effect that these have on composite properties. Analogies are drawn between composites and crystal structures to demonstrate the similarities between microscopic and macroscopic connectivity. A notation for composite transitions which can be used to describe changes in symmetry and connectivity is also presented.
Array-type universal profile function for powder pattern fitting
Authors: Toraya H.
Published: July 2002

An array-type universal profile function for powder-pattern fitting is described. It is defined as an array of unknown parameters representing the profile heights at discrete angular steps. The unknown parameters are determined during least-squares fitting together with the integrated intensity, the peak position, the peak width and background parameters. The function has been applied to profile fitting in a small 20 range, and has better R-factors than the pseudo-Voigt and Pearson VII functions. This new function has some important advantages: it can model any complex profile shape, which would be difficult to describe by a smoothly varying analytical-type function; it generally gives a better fit and thus more precise and accurate analysis than currently used analytical-type functions; and it can be applied to the data of all radiation sources including conventional X-rays, synchrotron radiation and time-of-flight and fixed-wavelength neutrons without changing the mathematical form. The optimized use of the function and the accuracy of deduced parameters are also discussed.
Structure determination of LiMoP2O7 from multiphase powder X-ray diffraction data
Authors: Wang S. L. , Wang P. C. , Nieh Y. P.
Published: July 2002

The crystal structure of LiMoP2O7 was determined from conventional powder X-ray diffraction at room temperature in the presence of MoP2O7, MoO2 and Mo as impurities. Pattern decomposition was employed to eliminate complex contaminants prior to the Rietveld structure refinement. LiMoP2O7 crystallizes in the space group P21 with Z = 2, a = 4.8987 (3), b = 8.3912 (4), c = 7.0306 (4) Å, β = 109.327 (4)°, V = 272.71 Å3. Final agreement indicators were Rp
= 0.0589, Rwp
= 0.0772, RF
= 0.054 and RI
= 0.080. The framework of the structure consists of corner-sharing MoO6 octahedra and P2O7 groups, which form tunnels where the Li cations are located. The results give an example of analyzing a structure from a tetraphasic mixture using pattern decomposition in conjunction with the Rietveld refinement method.
AUTOMR: an automatic processing program system for the molecular replacement method
Authors: Matsuura Y.
Published: July 2002

An automatic processing program system of the molecular replacement method AUTOMR is presented. The program solves the initial model of the target crystal structure using a homologous molecule as the search model. It processes the structure-factor calculation of the model molecule, the rotation function, the translation function and the rigid-group refinement successively in one computer job. Test calculations were performed for six protein crystals and the structures were solved in all of these cases.
Angle-sensitive X-ray topographs obtained with Kossel lines
Authors: Wittry D. B. , Sun S. , Chang W. Z.
Published: July 2002

A simple method and simple camera of small size for obtaining X-ray topographs with a microfocus X-ray source are described and initial results and their interpretation are given for an LiF crystal. The method is based on scanning a Kossel line across the recording film by simultaneously translating the crystal and film relative to the source and to a stationary mask that blocks most of the scattered and fluorescence radiation. The mask, which is located between the specimen and the film, is made by using the Kossel line recorded on a film in the mask plane as a pattern; this provides self-alignment of the system. Theoretical calculations are given that indicate the potential angular resolution of the method when applied to nearly perfect crystals. The advantages of this method over similar methods using the X-ray continuum diverging from a point source are discussed.
Indexing in single-crystal diffractometry with an obstinate list of reflections
Authors: Duisenberg A. J. M.
Published: July 2002

An indexing method for single-crystal diffractometry is described which is applicable to especially difficult cases such as twin lattices, incommensurate structures, fragmented crystals, long axes and unreliable data. Finding the reciprocal lattice from a cloud of reciprocal-lattice points (reflections) is reduced to finding elementary periods in one-dimensional rows, obtained by projecting all observed points onto the normal to the plane formed by any three of these points. Row periodicity and offending reflections are easily recognized. Each row, by its direction and (reciprocal) spacing, defines one direct axis vector, based upon all cooperating observations. From the direct vectors so obtained a primitive direct cell is chosen and refined against the fitting reflections. The result is one main lattice, or a main lattice and a set of alien reflections. The method operates semi-automatically in the program DIRAX and has been tested, without failure, on hundreds of CAD4 reflection files, among which there were many auto-indexing-resistant lists.
Planar defects in β-iron disilicide (β-FeSi2) analyzed by transmission electron microscopy and modeling
Authors: Zheng Y. , Taccoen A. , Petroff J. F.
Published: July 2002

Microplanar defects were observed in β-iron disilicide by transmission electron microscopy. They were identified as (100)[011]/2 intrinsic stacking faults by means of electron diffraction patterns and observed in high-resolution lattice images. A structural model of the faults is proposed here in setting the defect position at x = ¼ within the cell.
Phase identification of single crystals using a self-consistent indexing scheme based on the Laue method
Authors: Pan J.
Published: July 2002

The application of the Laue method is extended to phase identification of single crystals. This extension is made possible by a new method of indexing Laue patterns, which is based on computerized rotation of the reciprocal axes of the crystal and a new criterion for judging true solutions. The new method and criterion have been tested successfully for crystals with various structures, including triclinic. An example is given for the phase identification of molybdenum oxide which has six structural modifications.
Geometrical limits and improvement of the diffraction optics in Gandolfi cameras
Authors: Gregorkiewitz M.
Published: July 2002

The Gandolfi technique is used to obtain powder diffraction patterns from a single-crystal by rotating it simultaneously around two axes. In order to maximize the number of possible orientations, the angle χ between the two axes should approach 90° but, for technical reasons, it must be smaller than 90° and some reflections will be lost. For an optimization of the technique, experiments have been realized for different χ values and equations have been established that allow the calculation of the limits (expressed in terms of fraction of missing orientations, qm
, and the maximum diffraction angle, 2θG
, up to which no reflection is lost) of a given camera (characterized by χ and the ratio h/r between the height and radius of the film or detector). With χ = 70° and h/r = 16/57.3, for example, qm
= 6% and 2θG
= 46°, which compares favourably with the conventional Gandolfi camera (χ = 45°, h/r = 14/57.3; qm
= 29%, 2θG
= 19°). For practical purposes, 2θG
= 46° means that the diffraction pattern will be complete for the whole range of spacings with d ≥ 1.96 Å (Cu Kα radiation, λ = 1.5406 Å). This is sufficient for the unambiguous identification of most crystalline solids but it is worth mentioning that a simple increase of the film height to h = 48 mm extends the complete pattern up to 2θG
, = 140°, equivalent to 94% of the theoretically accessible d spacings at a given wavelength, i.e. the Gandolfi technique can be made as reliable as true powder diffraction.
EDPDB: a multifunctional tool for protein structure analysis
Authors: Zhang X.-J. , Matthews B. W.
Published: July 2002

EDPDB is a Fortran program that simplifies the analysis of protein structure and makes it easy to extract various types of geometrical and biologically relevant information for the molecule both in isolation as well as in its crystallographic context. EDPDB offers a large set of functions by which the user can evaluate, select and manipulate the coordinates of protein structures. Types of calculation available include the determination of solvent accessibility, bond lengths and torsion angles, determination of the van der Waals volume of a group of atoms, determination of the best-fit plane through a set of points, evaluation of crystal contacts between a molecule in a crystal and all symmetry-related molecules, and the determination of `hinge-bending' motion between protein domains. It is also possible to compare different structures, to perform coordinate manipulations and to edit coordinate files. The program augments the graphic analysis of protein structure by allowing the user to construct a simple set of commands that will rapidly screen an entire structure. It may also make special purpose analyses feasible without complicated programming.
Small-Angle X-ray Scattering Size Parameters and Higher Moments of the Particle-Size Distribution Function in the Asymptotic Stage of Ostwald Ripening
Authors: Möller J. , Kranold R. , Schmelzer J. , Lembke U.
Published: July 2002

Small-angle X-ray scattering (SAXS) is a powerful tool to study the kinetics of phase separation in materials. A simple procedure is presented that allows one to prove if the particle-size distribution established in a system in the late stages of phase separation corresponds to the predictions of the classical Lifshitz–Slyozov–Wagner (LSW) theory for the asymptotic stage of Ostwald ripening. The method is based on the correlations between certain SAXS size parameters and the higher moments of the LSW size distribution functions for diffusion-limited or reaction-limited ripening. It is suggested that the use of these size parameters, which can be obtained with high accuracy from the scattering curve, is frequently more advantageous than a direct comparison of the experimentally obtained size distributions with the asymptotic size-distribution functions predicted by the LSW theory. The method is applicable if the suppositions made in the LSW theory that the precipitated particles should be homogeneous spheres with volume fraction tending to zero are fulfilled. The method is applied to a photochromic glass; although the silver-halide precipitates contained in the glass develop according to the power law of diffusion-limited Ostwald ripening, their size distribution is shown not to correspond to the features of the LSW size distribution. Consequently, in this case the LSW theory cannot describe quantitatively the kinetics of ripening.
Simultaneous Position-Resolved Determination of Phase and Stress Distributions by means of an X-ray Diffractometer with a Two-Dimensional Position-Sensitive Detector
Authors: Stephan D. , Grosse G. , Wetzig K.
Published: July 2002

With an X-ray area detector and a suitable Soller-plate collimator in the scattered radiation field, it is possible to realize a versatile X-ray diffractometer. The local diffraction information of a sample can be registered simultaneously and visualized with a spatial resolution better than 0.5 mm, maintaining reasonable measuring times of a few minutes. Results of measurements applied to local phase analysis (distribution of retained austenite and carbon on a cross section of case-hardened steel), to the determination of lateral stress distributions (laser-hardened track on C45 steel) and to the analysis of crystallite orientation (coarse-grained YBa2Cu3O
δ
) are presented.
Enumeration and Classification of Anomaly/Peak Bases in Two-Dimensional Intensity Histograms. Application of Graph Theory to Crystallographic Data Imaging
Authors: Reibenspies J. H.
Published: July 2002

Bragg-event peaks, spikes, intensity streaks and other anomalies generate abnormal regions in two-dimensional intensity histograms from area-detector images. Examination of the shapes of these regions can contribute to the identification of the types of phenomena that generated them. The points that define the anomaly bases, when connected with imaginary lines, form unique graphs. Individual graphs, in turn, can be enumerated by employing graph-theoretical notation and the graph shapes classified. The number of lines in any given graph can also be determined by summing the degrees of the graph points and dividing by two. The ratio of the number of lines per point is a direct indication of the shape of the anomaly base. Long linear and curved shapes, like those associated with intensity streaks and powder rings, will have small lines-per-point ratios, while compact round, square or oval shapes, similar to those belonging to Bragg-event peaks, will have larger lines-per-point ratios. For any given number of points (Np
), for any given graph, the minimum number of lines (q) will equal Np
− 1, while the maximum number of lines (q
max, Np
) is determined from a round-shaped graph. A graph-shape parameter (GS) can thus be defined as (q − Np
− 1)/(q
max.
Np

− Np
− 1), where a value near one indicates a round graph shape and a value near zero indicates a linear graph shape. The application of graph-theoretical techniques to anomaly bases can thus provide insight into the nature of the intensities distributed throughout the two-dimensional crystallographic data image.
Reverse Monte Carlo Analysis of Powder Patterns
Authors: Montfrooij W. , McGreevy R. L. , Hadfield R. , Andersen N. H.
Published: July 2002

A Monte Carlo algorithm for the analysis of powder diffraction patterns is presented. One aim of this algorithm, which can be used as a supplement to the regular Rietveld refinement, is to provide a self-consistent determination of the thermal displacements of the atoms. This is achieved by modelling the total scattered intensity, comprising both the Bragg peak intensity and the diffuse contribution to the spectrum from the scattering density of an assembly of atoms. This assembly, which is constructed by the reverse Monte Carlo technique so as to yield a best fit with the data, is then used to calculate the average atomic thermal displacements. This allows for a refinement that, in principle, no longer requires angle-dependent background parameters, and that is well suited for dealing with highly anisotropic Debye–Waller factors and split atomic sites.
A simple method for making reproducible fibre loops for protein cryocrystallography
Authors: Sauer U. H. , Ceska T. A.
Published: July 2002

A practical, step-by-step description of the construction of loops for protein cryocrystallography using pulled-out micro-injection capillaries is described. The advantages of this method are the high reproducibility of the loops, the ease of adjustment of the loop diameter and the formation of thin films owing to the narrow base of the loop. During assembly, the loop does not make contact with either glue or cement.
Structure and Thermotropic Behaviour of Mixed Choline Phospholipid Model Membranes
Authors: Degovics G. , Latal A. , Prenner E. , Kriechbaum M. , Lohner K.
Published: July 2002

Phosphatidylcholines and sphingomyelins are among the most abundant lipids in mammalian cell membranes, being major components of platelets or erythrocytes, and of the lipid monolayer of lipoproteins. General efforts have been devoted to the elucidation of the interaction of the ubiquitous membrane component cholesterol with these choline phospholipids, but fewer studies have been reported on the interaction between the phospholipids themselves. A gel to liquid-crystalline phase transition was observed for pure sphingomyelin liposomes at physiological temperature, while palmitoyloleoyl phosphatidylcholine adopts a liquid-crystalline phase in the temperature range 273–323 K. The two phospholipids are miscible at all molar ratios in the liquid-crystalline phase, characterized by very similar lamellar repeat distances for all binary lipid mixtures. The gel phase of pure sphingolipid liposomes exhibited a markedly smaller lamellar repeat distance as compared to mixed lipid vesicles, which increased slightly with temperature for the pure sphingomyelin (66.9–69.2 Å). Concomitantly, altered hydrocarbon chain packing was observed. Similar diffractograms were obtained in the presence of 10 mol% phosphatidylcholine. However, in the composition range between 20 and 60 mol% phosphatidylcholine in the phosphatidylcholine–sphingomyelin admixture, the lamellar repeat distance in the gel phase was markedly increased and remained almost constant (around 75 Å) below the phase transition.
Influence of Aging and Dilution on the Crystallization of Silicalite-1
Authors: de Moor P. P. E. A. , Beelen T. P. M. , van Santen R. A.
Published: July 2002

The correlation between the formation of colloidal aggregates and the crystallization of silicalite-1 from a clear solution has been investigated with in situ combined small-angle X-ray scattering and wide-angle X-ray scattering, and in situ ultra-small-angle X-ray scattering using synchrotron radiation. Increasing the aging time at room temperature of the synthesis mixture prior to heating to the reaction temperature reduced the induction period and increased the crystal growth rate without affecting the formation of colloidal aggregates. Dilution of the synthesis mixtures did not influence the nucleation and crystal growth rate, and did not affect the formation of colloidal aggregates.
Structural Characterization of a Telechelic Ionomer at Various Degrees of Neutralization
Authors: Bittencourt D. R. S. , Charier P. , Jérôme R. , Williams C. E.
Published: July 2002

The morphology of sodium-neutralized carboxytelechelic ionomers has been characterized by SAXS (small-angle X-ray scattering) for varying degrees of neutralization between 20 and 100%. The good-quality data covering a broad q range have been fitted with a functional form of the intensity. It has been found that the aggregates grow as more chain ends are neutralized while the electron density is kept constant, in agreement with the multiplet model. The excess scattering at small angles was found to vary systematically with the degree of neutralization, confirming the ionic origin of this feature.
Construction of a Two-Dimensional Ultra-Small-Angle X-ray Scattering Apparatus
Authors: Konishi T. , Yamahara E. , Furuta T. , Ise N.
Published: July 2002

A two-dimensional ultra-small-angle X-ray scattering (USAXS) apparatus was constructed using a rotating-anode X-ray generator and a Bonse–Hart camera. In this camera, two sets of two channel-cut single crystals were used to collimate the X-ray beam in both the horizontal and the vertical planes. The measured intensity profile of the direct beam showed a high small-angle resolution in all directions on the detector plane. The full width at half-maximum was 17′′, indicating that the apparatus can be applied to structural analysis in the range up to 2 μm, even for directionally oriented samples. One- and two-dimensional USAXS profiles from colloidal silica powder agreed well with each other, showing that the desmearing procedure adopted in the previous one-dimensional USAXS experiments were justified.
Structure of ZrO2SiO2 Gels
Authors: Stachs O. , Petkov V. , Gerber Th.
Published: July 2002

xZrO2(1 − x)SiO2 gels have been prepared by hydrolytic polycondensation of tetraethylorthosilicate and zirconium n-propoxide in alcohol solution (x = 0.1–0.5). The formation of the gels has been investigated in situ by conventional small-angle X-ray scattering. (SAXS) experiments. Primary particles of size 1–2 nm have been found in all hydrogels at the first stage of the gelation process. With further progress of the gelation, the primary particles have been found to aggregate into secondary clusters with fractal characteristics. It has also been observed that the higher the Zr concentration in the sol the faster the rate of aggregation of the primary particles. Anomalous small-angle X-ray scattering (ASAXS) and wide-angle X-ray scattering (WAXS) experiments have also been carried out on samples of ZrO2–SiO2 xerogels that have been dried only and samples that have been further heat-treated at various temperatures. The ASAXS experiments have shown that the xerogels obtained without manipulating the aggregation rate do not exhibit microinhomogeneities even when heated up to 800 K. Reverse Monte Carlo simulations based on the experimental wide-angle diffraction data have also been carried out. In line with the findings of the ASAXS experiments, the simulations have suggested that Zr and Si atomic species in the ZrO2–SiO2 xerogels investigated are homogeneously distributed at the atomic scale. The first traces of a phase segregation into Si- and Zr-rich phases, as demonstrated by the emergence of tetragonal ZrO2, were detected only after prolonged heat treatment at 1100 K.
In Situ Anomalous Small-Angle X-ray Scattering Investigation of Carbon-Supported Electrocatalysts
Authors: Haubold H.-G. , Wang X. H. , Goerigk G. , Schilling W.
Published: July 2002

Anomalous small-angle X-ray scattering (ASAXS) of synchrotron radiation with X-ray energies near the Pt-L
3 X-ray absorption edge was used to examine the size distribution of nanometer-sized catalyst particles in porous electrodes for electrocatalytic applications. Carbon-supported platinum electrocatalysts with 5–80 wt% Pt were studied in situ in an electrochemical cell with a 1 M sulfuric acid electrolyte. The anodic oxidation was found to shift the particle size distribution from a mean size of 1.7 nm in the reduced state to 2.1 nm for a 10 wt% Pt/C catalyst. From the size increase, one can infer the formation of oxide shells at the particle surfaces with layer thicknesses of about 1 nm.
A cell for producing xenon-derivative crystals for cryocrystallographic analysis
Authors: Djinovic-Carugo Kristina , Everitt Peter , Tucker Paul A.
Published: July 2002

A simple pressure cell is described that may be used to bind xenon to protein crystals freely suspended in thin films which may then be flash-cooled, thus immobilizing the bound xenon. As an example, the use of the cell in the structure determination of perchloric-acid-soluble protein, by the multiple isomorphous replacement method, is described.
Harmonic composition of synchrotron white-beam X-ray topographic back-reflection images of basal-cut silicon carbide single-crystal wafers
Authors: Vetter W. M. , Dudley M.
Published: July 2002

Superscrew dislocations are visible in back-reflection synchrotron white-beam X-ray topographs of basal-cut SiC wafers in striking contrast as black rings surrounding white circles, even though such topographs suffer from extensive harmonic contamination. The contributions to the synchrotron white-beam topograph of each member of its series of harmonic reflections, {\bf g}=(0006n), where n=3 to 16, were calculated. Through intensity considerations and comparison with a {\bf g}=00018 topograph taken with Cu Kα1radiation, the {\bf g}=00024 harmonic was determined to be the most important contributor. The contrast of features lying deep beneath the crystal's surface was attributed to higher harmonics with larger penetration depths.
Secondary extinction in textured films
Authors: Yamakov V. , Tomov I.
Published: July 2002

A simple solution accounting for the secondary-extinction correction of the integrated intensity of the diffracted beam in a mosaic crystal is derived for the case of symmetrical Bragg reflection from an `infinitely thick' plane parallel plate. The solution of energy-transfer equations contains a `thickness-dependent term' which enables further extension of the problem to the `thin' film case. The new formulae are derived assuming a rectangular or triangular crystalline block distribution, which leads to exact integration of the diffracted intensity. In addition, a general term for Zachariasen [Acta Cryst.(1963),16, 1139–1147] series expansion, assuming Gaussian domain distribution, is deduced. In fact, the new analytical results represent a variety of improved approximations which are simultaneously valid both for weak and for strong extinction effects usually observed in textured films. The formulae are used for computing the pole density and secondary extinction in electrodeposited nickel films having different texture sharpnesses. It may be anticipated that the precision in any X-ray diffraction characterization of films could be enhanced using the improved secondary-extinction corrections.
Automatic determination of diffuse-peak positions and the centre of a diffraction pattern
Authors: Wilkinson S. J. , Hukins D. W. L.
Published: July 2002

Correlation with a two-dimensional Gaussian function was used to locate the positions of diffuse peaks in X-ray diffraction patterns. The centre of a pattern was defined as the centroid of the image of the undeflected beam, found by convolution with a two-dimensional Gaussian function. These methods were implemented using the IDL programing language. They were tested on diffraction patterns from systems containing oriented molecules of the protein collagen: collagen tape, elastoidin spicules and annulus fibrosus of intervertebral disc. Specimens were dusted with quartz to calibrate the diffraction patterns. These patterns were recorded on film, using a semi-transparent beam stop to obtain an image of the undeflected beam, and digitized at a resolution of 105 µm. Intermolecular spacings, calculated from the distance between a peak and the centre of a pattern, were in good agreement with those determined previously.
Quantitative phase analysis of α- and β-silicon nitrides. II. Round robins
Authors: Toraya H. , Hayashi S. , Nakayasu T.
Published: July 2002

Two round robins (RRs) of the quantitative phase analysis (QPA) of silicon nitrides (Si3N4) using the mean normalized intensity (MNI) method and the Rietveld method were conducted as one of the projects for establishing standard methods of characterizing advanced ceramic materials. Accuracy and precision of three techniques, namely the MNI method using peak-height intensity (MNI+P), the MNI method using integrated intensity (MNI+I) and the Rietveld method (R), were tested. Precision of the methods was found to follow the order R < MNI+I < MNI+P in the first RR and MNI+I < R < MNI+P in the second RR. Resulting accuracy of the methods was ranked R ≃ MNI+P < MNI+I in the first RR and MNI+P < R ≃ MNI+I in the second. The MNI+P method, which relies upon a simple and routine procedure for measuring peak-height intensities, gave the best precision in both RRs. Both the accuracy and the precision of the Rietveld method were the worst among the three techniques in the first RR. They were, however, significantly improved in the second RR. Although the precision of the MNI+I method was the worst in the second RR, it was better than that in the first, and the accuracy was the best in both the first and the second RR. The degree of improvement from the first to the second RR, in both precision and accuracy, was MNI+P < MNI+I < R, coinciding with the ease of these three techniques in reverse order. This result is largely due to (i) a new protocol for experimental and analytical parameters and (ii) improved skill of the participants in data analysis in the second RR. Magnitudes and signs of the observed errors could be interpreted through results of the theoretical studies.
SANS study of associative triblocks in microemulsion solutions
Authors: Bhatia S.R. , Russel W.B. , Lal J.
Published: July 2002

Small-angle neutron scattering was used to study the interactions between AOT/water/decane microemulsions and poly(ethylene oxide)-polyisoprene-poly(ethylene oxide) triblocks. The interdroplet spacing seems to be independent of molecular weight and polymer concentration. Scattering experiments on the polyisoprene layer yield a high q exponent of −1.6 ± 0.1, indicating that the layer is swollen by decane.
Scattering vector dependence of the small-angle scattering from mixtures of hydrogenated and deuterated organic solvents
Authors: Arleth Lise , Pedersen Jan Skov
Published: July 2002

In connection with a contrast variation small angle neutron scattering (SANS) study of water-in-oil microemulsions, mixtures of hydrogenated and deuterated n-decane and similar mixtures of iso-octane have been measured as backgrounds. For the pure deuterated and hydrogenated solvents the spectra were flat but for all the mixtures the large molecular size of the alkanes give rise to a scattering vector dependence in the small angle scattering region. An explanation of this can be given based on the scattering contributions which have been identified for mixtures of water. The intensity is proportional to x(x − 1) where x is the volume fraction of deuterated molecules. Using the analogy to scattering from polymer blends of hydrogenated and deuterated chains, the scattering spectra are analysed using the model for random gaussian coils. For the solvent mixtures investigated in the present study, the radius of gyration was determined to be 3.8 Å for decane and 2.9 Å for iso-octane, independent of the fraction of deuterated molecules.
Anomalous conformational properties of PEO in H2O and D2O by SANS, PCS and Raman scattering
Authors: Branca C. , Faraone A. , Magazù S. , Maisano G. , Migliardo P. , Triolo A. , Triolo R. , Villari V.
Published: July 2002

PEO solutions in water and heavy water have been investigated using SANS, PCS and Raman spectroscopy. The employement of these techniques allows to carry out a comparison between the diffusive properties of PEO/H2O and PEO/D2O systems, in order to study the coil conformation dependence on temperature and concentration. The data reveal the different conformational properties of PEO in the two solvents which have been attributed to a different solvent quality of H2O and D2O. These results provide evidence to the fact that the properties of macromolecules, even of simple structure, can be influenced by the isotopic composition of the solvent.
Phase behavior of blends of linear and branched polyethylenes on micron length scales via ultra-small angle neutron scattering (USANS)
Authors: Agamalian M. M. , Alamo R. G. , Londono J. D. , Mandelkern L. , Wignall G.D.
Published: July 2002

SANS experiments on blends of linear, high density (HD) and long chain branched, low density (LD) polyethylenes indicate that these systems form a one-phase mixture in the melt. However, the maximum spatial resolution of pinhole cameras is ∼103Å and it has therefore been suggested that data might also be interpreted as arising from a bi-phasic melt with large a particle size (∼1µm), because most of the scattering from the different phases would not be resolved. We have addressed this hypothesis by means of USANS experiments, which confirm that HDPE/LDPE blends are homogenous in the melt on length scales up to 20µm. We have also studied blends of HDPE and short-chain branched linear low density polyethylenes (LLDPEs), which phase separate when the branch content is sufficiently high. LLDPEs prepared with Ziegler-Natta catalysts exhibit a wide distribution of compositions, and may therefore be thought of as a "blend" of different species. When the composition distribution is broad enough, a fraction of highly branched chains may phase separate on µm-length scales, and USANS has also been used to quantify this phenomenon.
He bubble growth in a martensitic steel for fusion reactors
Authors: Coppola R. , Magnani M. , May R. , Moeslang A.
Published: July 2002

Small-angle neutron scattering (SANS) has been used to study thegrowth of He bubbles in a martensitic steel for fusion reactors. The samples had been homogeneously implanted at 523 K with 400 appm He, then subjected to thermal annealing at temperatures up to 1248 K. Suitable reference samples, submitted solely to identical thermal treatments, were also measured. The He bubble volume distribution functions obtained show that a dense population of bubbles 10 Å or less in size is accompanied by a secondary distribution of bubbles one order of magnitude larger, as expected after post-implantation annealing. These results are discussed in terms of background subtraction and available Q-range.
The determination of absolute structure. III. An ambiguity table for the non-centrosymmetric crystal classes
Authors: Jones P. G.
Published: July 2002

The general term 'determination of absolute structure' is more precisely defined for each non-centrosymmetric crystal class.
Ferroelectric space groups
Authors: Litvin D. B.
Published: July 2002

The 440 ferroelectric space groups, viz the Heesch-Shubnikov (magnetic) space groups, which are symmetry groups of ferroelectric electric-dipole arrangements in crystals, are derived and tabulated. By considering automorphisms induced by the automorphisms of the discrete space-time group, we show that although ferroelectric, ferromagnetic and ferrocurrent point groups all number 31, the number of ferroelectric space groups differs from 275, which is that of both ferromagnetic and ferrocurrent space groups.
An analytical function for absorption correction
Authors: Katayama C.
Published: July 2002

A new analytical function is proposed for absorption correction. It is expressed by surface harmonics with polar angles that specify the primary and secondary beam directions. This function has an advantage over Fourier expansion because it is rotationally invariant. Two empirical, methods are used to determine the expansion coefficients. One uses the intensity deviations of equivalent reflections, and the other uses the calculated intensities at the stage of structure refinement. The utility of the analytical function is demonstrated with a model and with actual data.
X-ray diffraction profiles described by refined analytical functions
Authors: Rao S. , Houska C. R.
Published: July 2002

The line profiles from a sample containing small spherical particles, non-uniform strain and instrumental broadening can be described exactly by using error functions with complex arguments. Consequently, the development by Houska & Smith [J. Appl. Phys. (1981). 52, 748-754] has been revised in terms of these functions. This calculation has been extended, by the use of error functions with complex arguments, to include a more general distribution of particle size or column heights than that obtained from a single sphere. The latter extension is applied to profiles obtained from a partially stabilized zirconia wear debris. It is found, in this example, that a column-height variation coefficient that is greater than that from a single sphere gives a somewhat better fit of the experimental line profiles. We find that if the single-sphere model is used to fit the profiles the particle size and root-mean-square strain differ by about 12 and 5% respectively.
Crystallography, geometry and physics in higher dimensions. V. Polar and mono-incommensurate point groups in the four-dimensional space %E4
Authors: Veysseyre R. , Weigel D.
Published: July 2002

The crystallographic point groups of the four-dimensional Euclidean space {\bb E}4are a convenient means of studying some crystallized solids of physical space, for instance the groups of magnetic structures and the groups of mono-incommensurate structures, as is demonstrated by a simple example. The concept of polar crystallographic point groups defined here in {\bb E}4, and also in {\bb E}nenables the list and the WPV notation {geometric symbol of Weigel, Phan & Veysseyre [Acta Cryst.(1987), A43, 294-304]} of these special structures to be stated in a more precise way. This paper is especially concerned with the mono-incommensurate structures while a discussion on magnetic structures will be published later.
Approximate model for the crystal structure of precipitates in NaF doped with AlF3
Authors: Suzuki K.
Published: July 2002

The crystal structure of precipitates in a mixed crystal of NaF and 1 mol% AlF3 has been studied at room temperature using both stationary-crystal and rotating-crystal X-ray photographic methods. It has been found that almost all the reflections can be assigned to a face-centered-cubic (f.c.c.) lattice with unit-cell parameter 7.77 Å. The main feature of the diffraction pattern is that the 311 reflection is very strong while the 222 reflection is practically zero, in contrast to the case of high-form cryolite, i.e. cubic Na3AlF6. These features are explained by assuming an f.c.c. arrangement of AlF6 octahedra that are rotated around the 〈111〉 axes by about 47° from the highest-symmetry orientation. It has also been shown that the F ions in each octahedron make large overlaps with the Al ion at the center of the octahedron. A random distribution of rotation axes is also proposed to conform to the cubic symmetry of the lattice structure of the precipitate.
Temperature-dependent X-ray dynamical diffraction: Darwin theory simulations
Authors: Chung Jin-Seok , Durbin Stephen M.
Published: July 2002

Thermal vibrations destroy the perfect crystalline periodicity generally assumed by dynamical diffraction theories. This can lead to some difficulty in deriving the temperature dependence of X-ray reflectivity from otherwise perfect crystals. This difficulty is overcome here in numerical simulations based on the extended Darwin theory, which does not require periodicity. Using Si and Ge as model materials, it is shown how to map the lattice vibrations derived from measured phonon dispersion curves onto a suitable Darwin model. Good agreement is observed with the usual Debye–Waller behavior predicted by standard theories, except at high temperatures for high-order reflections. These deviations are discussed in terms of a possible breakdown of the ergodic hypothesis for X-ray diffraction.
Dynamic inversion by the method of generalized projections
Authors: Spence J. C. H. , Calef B. , Zuo J. M.
Published: July 2002

A new approach to the inversion problem of dynamical transmission electron diffraction is described, based on the method of generalized projections in set theory. An algorithm is described that projects between two sets of constrained scattering matrices. This iterative process can be shown to converge, giving the required structure factors (for some choice of origin) if the sets are convex. For the dynamical inversion problem, the set topology is that of an N
2 torus, the sets are not convex, and traps are therefore sometimes encountered. These can be distinguished from solutions, allowing the algorithm to be restarted until a solution is found. Examples of successful inversion from simulated multiple-scattering data are given, which therefore solve the phase problem of electron diffraction for centrosymmetric or noncentrosymmetric crystal structures. The method may also be useful for the three-beam X-ray diffraction problem.
Elastic scattering of partially coherent beams of fast electrons by a crystal with a defect
Authors: Borgardt N. I.
Published: July 2002

Scattering of a quasi-monochromatic electron beam by a crystal with a defect is described with the use of the mutual coherency function and the formalism of quasi-Bloch waves. An expression correlating the mutual intensity on the exit and entrance surfaces of the crystal in terms of the scattering matrix has been found. The matrix elements are determined by a system of integro-differential equations, which have been obtained without using the column approximation. It has been shown that calculations of the matrix elements can be significantly simplified when the approximation of the small-angle scattering of quasi-Bloch waves by the defect displacement field is satisfied. Such an approximation can be applied in many cases, e.g. to a crystal with a dislocation. The mutual intensity on the crystal entrance surface has been found for the general case of defocused illumination. As an example of applying the new approach, expressions for the intensity in convergent-beam electron diffraction (CBED) and large-angle CBED (LACBED) patterns have been obtained. The LACBED patterns of a crystal with a dislocation have been simulated. It has been shown that the developed approach allows a more exact simulation of the LACBED than do the conventional approaches using the column approximation and the approximation of independent plane waves filling the illumination cone.
Decoherence in electron backscattering by kinked dislocations
Authors: Dudarev S. L. , Ahmed J. , Hirsch P. B. , Wilkinson A. J.
Published: July 2002

A model is proposed that explains the origin of the bright contrast of dislocation walls consisting of edge dislocation dipoles in electron channelling contrast images (ECCI) of fatigued crystals, when the incident beam is parallel to the edge dislocations. The model is based on the assumption that the contrast arises from the dislocation segments terminating the dipoles. These are modelled as screw-type kinks which scatter electrons. Scattering by randomly distributed kinks leads to the randomization of phase of transmitted and diffracted beams and suppresses the anomalous transmission of electrons. The predicted behaviour of electron-channeling contrast images agrees well with experimental observations.
Polysomatic series in the structures of complex cuprates
Authors: Leonyuk L. , Babonas G.-J. , Maltsev V. , Rybakov V.
Published: July 2002

The modular approach was applied to analyse the structure of complex cuprates. The modular series of various types were distinguished in the family of layered cuprates making use of the classification scheme in a fragment approximation developed earlier. The polysomatic series were revealed in the groups of cuprates which were expected to possess the properties of both salt and oxide. The structure of the ladder-type cuprates was analysed in more detail. The present study has shown that the polysomatic model can be efficiently applied to the structural analysis of complex cuprates.
A simple view of the spherical wave in dynamical theory
Authors: Guigay J. P.
Published: July 2002

The results of the Kato spherical-wave approach to the dynamical theory for perfect crystals are obtained by a simple and straightforward method based on the multiple-scattering expansion.
Chirality and general aspects of symmetry
Authors: Smirnov Boris B. , Lebedev Oleg V. , Evtushenko Alexey V.
Published: July 2002

The phenomenon of chirality is described in terms of symmetry and via symmetry operators.
Quantitative phase determination for macromolecular crystals using stereoscopic multibeam imaging
Authors: Chang Shih-Lin , Chao Chun-Hsiung , Huang Yi-Shan , Jean Yuch-Cheng , Sheu Hwo-Shuenn , Liang Fuu-Jye , Chien Hung-Chun , Chen Chun-Kuang , Yuan Hanna S.
Published: July 2002

Without invoking anomalous dispersion and heavy-atom derivatives, it is demonstrated that it is possible to directly determine the phases of a large number of reflections collected in a short time from macromolecular crystals using a stereoscopic oscillation-crystal imaging technique, in a multibeam diffraction geometry, where two crystallographic axes in opposite directions are employed as the rotation axes. The intensity profiles (distributions) of the diffraction spots versus the varying tilt Bragg angle of the rotation axis in the two stereoscopically related images yield quantitative phase information. Many multiple diffraction profiles of tetragonal lysozyme and an unknown protein structure are obtained at the rate of 100 profiles per 30 min of X-ray exposure.