bluuebunny/crossref_metadata_2025 huggingface dataset:
A method for the interpretation of the Warren–Averbach mean-squared strains and its application to recovery in aluminium
Authors: Turunen M. J. , de Keijser Th. , Delhez R. , Pers N. M. van. der.
Published: July 2002

A method for the interpretation of Warren–Averbach mean-squared strain curves is presented. If a polynomial is fitted to such a mean-squared strain curve, then the coefficients of this polynomial can be expressed simply in the mean-squared local strain in the direction perpendicular to the diffracting planes and the mean-squared derivatives of this strain. The method is applied to a series of X-ray diffraction line broadening measurements of isochronally recovery-annealed aluminium. The changes in the average squared derivatives observed after different anneals are explained as changes in the dislocation arrangements in the specimen. The parameters obtained by the method are found to be sensitive to small changes in the strain fields.
A precise determination of the shape, size and distribution of size of crystallites in zinc oxide by X-ray line-broadening analysis
Authors: Louër D. , Auffrédic J. P. , Langford J. I. , Ciosmak D. , Niepce J. C.
Published: July 2002

The Fourier and variance methods are used to analyse the breadths of X-ray diffraction peaks from ZnO powder obtained from the thermal decomposition of Zn3(OH)4(NO3)2. The shape, size, distribution of size and orientation of the crystallites are determined. It is found that the form is markedly anisotropic and that on average the crystallites may be regarded as cylinders with a diameter of about 110 Å and height about 240 Å, but that they are in fact right prisms whose cross section is an irregular hexagon. There is excellent agreement between the experimental results and the predictions of line-broadening theory, with quantitative confirmation from electron micrographs of the sample.
A focusing X-ray camera for recording low-angle diffraction from small specimens
Authors: Milch J. R.
Published: July 2002

An X-ray camera is required in many low-angle diffraction experiments to focus the X-ray beam incident on the specimen. This paper describes an X-ray camera designed to record two-dimensional diffraction data from small specimens with unit cells as large as 50 nm. It matches the 200 μm focal spot of a rotating-anode X-ray generator to an electro-optical detector with a spatial resolution of 300 μm. The camera is very flexible and can accommodate a total source-to-detector distance of 2.5 m. The X-ray beam is focused by two 20 cm mirrors bent by simple two-point benders. The theory of such benders and the design of X-ray cameras incorporating them is discussed briefly. The paper also describes a fast (1 ms) X-ray shutter and simple ion chambers useful for alignment and operation.
Double hexagonal superstructure of Au–Mg alloy containing 20 at.% Mg studied by high-voltage high-resolution electron microscopy
Authors: Shindo D. , Haraga K. , Hirabayashi M. , Terasaki O. , Watanabe D.
Published: July 2002

High-resolution observations of Au–20.2 at.% Mg alloy have been carried out by using a 1 MV electron microscope. The many-beam images with the [001] axial illumination are interpreted in terms of the double hexagonal superstructure of 9a
0−4H type. With the aid of computer simulations by the multislice method, it is revealed that two kinds of interpretable image are obtained for different specimen thicknesses at the optimum defocus. The imaging conditions are discussed in comparison with the orthorhombic structure of the D023 type.
Crystal-structure refinement by profile fitting and least-squares analysis of powder diffractometer data
Authors: Will G. , Parrish W. , Huang T. C.
Published: July 2002

The refinement of crystal structures using X-ray powder data in a two-stage method is described. (1) The integrated intensities of the individual reflections are derived by a profile fitting method in which the profile shapes are accurately defined using an experimentally determined instrument function and the sum of Lorentzian curves. (2) These values are then used in a powder least-squares refinement for structure determination. The results obtained with three simple structures (silicon, quartz and corundum) gave R(Bragg) values of 0.7 to 2.5%. The necessity of correcting for preferred orientation and the importance of proper specimen preparation are also discussed.
Determination of the anomalous scattering factors for Cu, Ni and Ti using the dispersion relation
Authors: Hoyt J. J. , de Fontaine D. , Warburton W. K.
Published: July 2002

X-ray absorption spectra about the K edges of Ni, Cu and Ti have been measured at the Stanford Synchrotron Radiation Laboratory. The imaginary part of the atomic scattering factor f′′ was determined using the optical theorem and the real part f′ computed by the Kramers–Kronig dispersion relation. Methods for evaluating this integral as well as the effects on f′ of various experimental errors are investigated. The f′ results for Cu and Ni are compared to data from interferometry experiments.
A low-temperature cooler for protein crystallography
Authors: Machin K. J. , Begg G. S. , Isaacs N. W.
Published: July 2002

A compact and economical cooling system utilizing thermoelectric modules has been designed and constructed. The cooler is small and light and can be positioned close to the crystal. It is capable of cooling air at 101 min−1 to −15°C (258 K), and can maintain a set temperature to within ± 0.1°C (0.1 K) over long periods.
A segment description for the unique set of reflections in non-centrosymmetric crystal classes
Authors: Flack H. D.
Published: July 2002

The segment description of the unique set of reflections of Gabe [In Crystallographic Computing, edited by F.R. Ahmed. Copenhagen: Munksgaard (1969)] and Le Page & Gabe [J. Appl. Cryst. (1979). 12, 464–466] has been extended to the non-centrosymmetric crystal classes. To the reflections generated by the unique set of the Laue group are added the anti-reflections generated by a set of anti-segments. These anti-segments are defined by the same lattice rows as those of the corresponding Laue group but their origins are shifted to avoid generating anti-reflections in any centrosymmetric section of reciprocal space.
Determination of single-crystal elastic constants from a cubic polycrystalline aggregate
Authors: Hayakawa M. , Imai S. , Oka M.
Published: July 2002

A method for determining cubic stiffness constants from polcrystalline Young's modulus and X-ray elastic constants is described. The relations used among these elastic constants are those based on Kröner's quasiisotropic model. The X-ray elastic constants required [S1(hkl)] are obtained by measuring various (hkl) d spacings of a stressed specimen under symmetric θ–2θ scan mode. An application to an Fe–31Ni alloy has given the results: C
11 = 1.47, C
12 = 1.05 and C
44 = 1.24 × 1011 Pa.
On the limitations of the Borie–Sparks method to determine short-range-order coefficients from diffraction experiments
Authors: Bubeck E. , Gerold V.
Published: July 2002

In order to determine short-range order in a solid solution from diffuse X-ray or neutron diffraction experiments the separation of atomic size effects from the experimental data is a crucial problem. It is demonstrated by a model calculation that a clear improvement of the separation method proposed by Borie & Sparks is obtained if the range of measurement is extended to include the first Brillouin zone.
The effect of sample position on the determination of triaxial stress by X-ray diffraction
Authors: Fenn R. H. , Jones A. M.
Published: July 2002

The determination of the full three-dimensional stress tensor in a specimen by X-ray diffraction requires that the strain be measured with the sample tilted in both a positive and a negative sense for different rotations of the sample in its own plane. The error introduced in the measured strain as a function of the position of the specimen relative to the X-ray diffractometer axis is investigated and it is shown that the negative tilt values are more sensitive to sample position than the positive tilt values. The determination of the shear stress components uses the difference between the measured strain at equivalent positive and negative tilts and hence it is shown that displacement of the sample could lead to incorrect deductions concerning the presence and magnitude of the shear stress components.
TABLES, a program to display space-group symmetry information in three dimensions
Authors: Abad-Zapatero C. , O'Donnell T. J.
Published: July 2002

TABLES is a computer program developed to display the crystal symmetry and the spatial location of the different symmetry operators for a given space group using interactive computer graphics. It allows the three-dimensional interactive display of the space-group information contained in International Tables for Crystallography [(1983), Vol. A. Dordrecht: Reidel]. Such a program is useful as a teaching aid in crystallography and is valuable for exploring molecular packing arrangements.
Electron microscope study of superconductor YBa2Cu3O6+δ
Authors: Łukaszewicz K. , Stępién-Damm J. , Horyń R. , Bukowski Z. , Kowalski M.
Published: July 2002

Electron microscopic observations of small single-crystal grains of YBa2Cu3O6+δ confirmed the orthorhombic symmetry and revealed very fine domain structure with twin boundaries parallel to (110) crystallographic planes.
An optical transform and Monte Carlo study of the disorder in β-cristobalite SiO2
Authors: Welberry T. R. , Hua G. L. , Withers R. L.
Published: July 2002

A previously reported lattice-dynamical model of β-cristobalite [Hua, Welberry, Withers & Thompson (1988). J. Appl. Cryst.
21, 458–465], which assumed the Wyckoff C9 structure but gave a satisfactory qualitative description of observed diffuse intensity in electron diffraction patterns, is shown to give atomic displacements which are much too small to be consistent with the 147° Si—O—Si angle observed in other forms of silica. Monte Carlo simulations of a modified model in which this angle is constrained to be close to 147° have been carried out and optical diffraction patterns obtained from the resulting lattice realisations. The diffraction patterns are very similar in appearance to those calculated for the simple C9 model, but the displacements are now consistent both with the expected geometry and also with mean-square atomic displacements derived from X-ray powder studies. In this simulation the oxygen atoms are distributed uniformly around an annulus which encircles the 16(c) sites of the Fd3m
C9 structure. The hypothesis of Wright & Leadbetter [Philos. Mag. (1975). 31, 1391–1401], that the oxygen atoms preferentially occupy the six 96(h) sites which occur around this annulus, has been tested and it is concluded that if such ordering exists it is not very pronounced.
Easy and economic ways of handling air-sensitive crystals for X-ray diffraction studies
Authors: Rao Ch. P.
Published: July 2002

Easy and convenient techniques have been developed to handle air-sensitive compounds in terms of measuring their single-crystal X-ray diffraction intensities. These methods have also been fruitfully applied in collecting X-ray data of several highly air-sensitive inorganic and organometallic compounds without using a cold stream of nitrogen.
Characteristic X-ray flux from sealed Cr, Cu, Mo, Ag and W tubes
Authors: Honkimäki V. , Sleight J. , Suortti P.
Published: July 2002

The flux of characteristic Kα radiation from sealed X-ray tubes with Cr, Cu, Mo, Ag and W targets is determined on an absolute scale by measuring integrated intensities of Bragg reflections from well characterized powder samples. The values of the flux are corrected for absorption in the tube target. The tube voltage is varied, and the flux is observed to vary as (U
0−1)
p
, where U
0 is the ratio of tube voltage to the excitation voltage of characteristic Kα radiation (over-voltage). The exponent p is very close to the theoretical value of 1.67 in the cases of Cr, Cu, Mo and Ag, while in the case of W the value of p is 1.45. The absolute values of the flux are close to the theoretical estimates of Green & Cosslett [Proc. Phys. Soc. (London) (1961), 78, 1206–1214] for Cr and Cu, 10 to 20% higher for Mo and Ag, but only about 1/3 of the calculated flux of W Kα radiation. This is due to an inadequate calculation of the indirect production of characteristic X-rays. A simple formula for the flux per unit solid angle is given in terms of the atomic number of the target, the tube voltage and the K excitation voltage.
Structural study of Cd(S,Se) doped glasses. High-resolution transmission electron microscopy (HRTEM) assisted by image processing
Authors: Allais M. , Gandais M.
Published: July 2002

High-resolution transmission electron microscopy (HRTEM) was used for examining Cd(S,Se) nanocrystals grown in silicate glasses commercially available as optical filters. The lattice images of the nanocrystals were numerated and submitted to filtering through Fourier transformation in order to sweep off the background signal originating mainly from glass. Optical filters from several firms were examined. The nanocrystals have been identified with Cd(S,Se) compounds crystallized in the wurzite structure, as in bulk material. The lattice images indicate crystallites having the shape of hexagonal prisms a little elongated along the c axis. The distribution of grain size differs according to the filter: the smallest size being about 1.5 nm (threshold for detection), the largest size varies from 7 to 10 nm, the average size sa
, from 3–4 to 5–6 nm and the characteristic size sc
from 5–6 to 7–8 nm (sc
is the size of grains occupying the main part of the crystallized volume).
Electron-density distribution from X-ray powder data by use of profile fits and the maximum-entropy method
Authors: Sakata M. , Mori R. , Kumazawza S. , Takata M. , Toraya H.
Published: July 2002

Following the profile decomposition of CeO2 X-ray powder data into individual structure factors, the maximum-entropy method (MEM) has been used to obtain an electron-density-distribution map. In the profile decomposition process, it is impossible to avoid the problems of overlapping peaks which have the same magnitude of reciprocal vectors, such as d*(511) and d*(333), for a cubic crystal, or very severely overlapping reflections. The formalism to treat such overlapping reflections in the MEM analysis is to introduce combined structure factors. The maximum value of the scattering vector, 4π(sinθ)/λ, which was used in the present analysis is small (about 7.8 Å−1) but the resulting electron-density-distribution map is of a high quality and much superior to the conventional map. As a consequence, the ionic charge of Ce and O ions can be obtained with reasonable accuracy from the MEM density map. Furthermore, the map reveals the existence of electrons around the supposedly vacant site surrounded by eight O atoms, which is probably related to the high ionic conductivity of this substance.
MXD: a general least-squares program for non-standard crystallographic refinements
Authors: Wolfers P.
Published: July 2002

MXD is a new least-squares program for non-standard crystallographic refinement. It uses an original procedure of formula management that is derived from up-to-date compiler programming techniques. While still offering all the least-squares possibilities of most traditional programs, e.g. SHELX, SDP, XRAY etc., MXD has been fully designed for complex crystallographic, magnetic and/or modulated structure refinement. The user enters all the specific formulae describing his own problem into the input data file. Thus, MXD is very convenient when dealing with very complex problems including fitting of modulated structures (magnetic and/or charge density wave), twin or magnetic domain distribution and severe secondary extinction correction. Moreover, if the experimental data are accurate enough (especially from using polarized neutrons), form-factor fitting is accessible. Independently collected data, using various wavelengths, powder or/and single-crystal data, polarized and unpolarized neutron information etc., can be treated simultaneously.
The effect of temperature on the fine structural characteristics of cotton-fibre – a small-angle X-ray scattering investigation using correlation functions. Erratum
Authors: Misra T. , Bisoyi D. K. , Khan Md. N. , Patel T.
Published: July 2002

Owing to a typsetting error, the heading ER
was wrongly mis-set as Eg
in Table 1 of the paper by Misra, Bisoyi, Khan & Patel [J. Appl. Cryst. (1991), 24, 712–714]. The correct table is given.
Measurement of powder diffraction sample absorption coefficients using monochromated radiation and transmission geometry
Authors: Ross C. R.
Published: July 2002

Powder diffraction data collected in transmission mode require an accurate value of sample absorption factor (μt) if the data are to be used quantitatively, e.g. for Rietveld refinement. When a primary-beam monochromator is in use, the direct beam may not be truly monochromatic, but rather consist of a series of harmonics of the desired wavelength. The intensity of these harmonics depends on instrumental parameters, but is sample independent. The contributions of these harmonics will result in incorrect values of μt for the primary wavelength if this is measured simply by determining the absorption of the direct beam by the sample at a single value of sample angle ω. The true value of μt may be determined by measuring the absorption over a range of ω and then fitting the data to the expression I(ω) = I
0[F
1 exp (− μt/cos ω) + (1 − F
1) exp (− μt/cos ω) ], where μt and μ't are the absorption factors for the primary component and the higher harmonics, respectively, and F
1 is the proportion of the primary component in the (attenuated) direct beam. Neglect of this effect will result in serious underestimation of μt; Rietveld refinement of data using such an incorrect value of μt will result in (in particular) unrealistic values of the thermal vibration parameters.
Observations on growth of NaCl crystals out of the surface of sodalite [Na8(Al6Si6O24)Cl2]
Authors: Hassib A. M. , Annersten H.
Published: July 2002

When the surface of sodalite [Na8(Si6Al6O6)Cl2] crystals was treated with an etching solution, growth of NaCl crystals could be observed. The etchant used is a dilute nitric acid solution. The acid attacks the surface and breaks it down into an Si–Al gel in which the crystals grow rapidly. Optical photography and electron-microprobe images show crystals with steplike patterns and hollow depressions at the centres of crystal faces. Preferential growth and aggregation of crystallites at grain boundaries is distinctly observed.
Direct Fitting of Grazing-Incidence Neutron and X-ray Reflectivity Profiles using the Kinematic Approximation
Authors: Lee E. M. , Milnes J. E.
Published: July 2002

At present, neutron and X-ray reflection data have been analysed either by modelling, using the optimal-matrix method, or by the fitting of partial structure factors arising from application of the kinematic approximation. Here the direct and simultaneous fitting of neutron and X-ray reflection profiles measured for a series of isotopic variations of the same interface is described. The interface is described as consisting of several components, which are either groups of atoms in a molecule or a whole molecule itself. In this work, the density distributions of the components perpendicular to the interface are described as Gaussian or tanh functions. These forms are chosen because they have analytical Fourier transforms. Fitting reflectivity profiles rather than partial structure factors reduces the sensitivity of the analysis to imperfections in one or more data sets. With existing kinematic methods, it is difficult to combine X-ray and neutron measurements. The new method readily allows such a combination, which is of importance if the capacity for isotopic substitution is limited or information about the counter-ion distribution is desired. It is also demonstrated that constraints posed by the stoichiometry of the interfacial species, by volume filling and molecular geometry, or from the results of the application of other experimental techniques, may readily be incorporated into the new fitting procedure.
An easy technique for making fiber loops for cryocrystallography
Authors: Blond L. , Pares S. , Kahn R.
Published: July 2002

A versatile system for making calibrated loops for cryo-cooling has been designed. This system facilitates the easy picking up of a crystal and its rapid insertion into a cold nitrogen stream, as required by the flash-cooling technique.
POWDER CELL – a program for the representation and manipulation of crystal structures and calculation of the resulting X-ray powder patterns
Authors: Kraus W. , Nolze G.
Published: July 2002

The main component of this program is a simultaneous representation of the unit cell and the calculated powder pattern. It allows the manipulation of the crystal structure by moving selected atoms of the asymmetric unit. The resulting powder pattern can be directly compared to experimental data in order to obtain reliable starting values for further computations in refinement programs.
Freeze-Trapping Isomorphous Xenon Derivatives of Protein Crystals
Authors: Sauer O. , Schmidt A. , Kratky C.
Published: July 2002

A simple and efficient method to prepare isomorphous derivatives of protein crystals with xenon as a heavy atom is described. The method consists of exposing a crystal to xenon gas of pressures above 5 atm (~ 0.5 MPa) for several minutes and subsequently shock-freezing the crystal to immobilize the xenon dissolved in the mother liquor and bound to the protein. Diffraction data can the be collected with the established techniques of protein cryocrystallography. Two types of high-pressure device are described to expose a protein crystal to the required xenon pressure, permitting rapid freeze-quenching after xenon exposure. One of these devices can be used for gas pressures up to and exceeding 5.0 MPa, with a gas consumption of a few millilitres of uncompressed gas. The technique has been tested with monoclinic crystals of sperm-whale metmyoglobin, which has four xenon binding sites. The results of these experiments are described and discussed. Potential applications of this technique include-besides the classical multiwavelength anomalous diffraction (MAD) or single isomorphous replacement with anomalous scattering (SIRAS) experiments-the derivation of low-angle phase information by modifying the electron density of the solvent regions within the crystal.
λ/2 Contamination in charge-coupled-device area-detector data
Authors: Kirschbaum K. , Martin A. , Pinkerton A. A.
Published: July 2002

A method is proposed to estimate the amount of λ/2 contamination inherent in area-detector [charge-coupled device (CCD) or image plate] data using Mo radiation. The intensity increase due to the Mo λ/2 contribution to Ihkl has been determined by measurement of the intensity for reflections where h, k or l is half-integral, i.e. reflections where there is no contribution from λ, for three crystals using two different CCD diffractometers. This information is present in all data sets obtained with area detectors but is usually ignored. The correction thus determined has been applied to nine data sets. The improvement to the data, as measured from the least-squares refinement, is shown to be insignificant for routine data sets, even for the weak low-angle reflections. Some reduction in the number of `observed' systematic absences is noted, thus improving space-group assignments. In addition, for strongly diffracting crystals, incorrect unit cells may be obtained owing to the presence of strong λ/2 reflections at the reciprocal-lattice nodes.
Extension of three-dimensional space-group generators to the (3+1) case
Authors: Stróż Kazimierz
Published: July 2002

A method of building up the generators of 775 (3+1)-dimensional superspace groups is proposed. The generators are based on the conventional space-group generators selected by Wondratschek and applied in theInternational Tables for Crystallography(1995, Vol. A). By the method, the generation of (3+1) space groups is found to be easier, the description of symmetry operations is closer to that used for the conventional space groups, and ambiguities in the (3+1) group notation are avoided.
Diffractometric crystal centering
Authors: Dera Przemyslaw , Katrusiak Andrzej
Published: July 2002

A general formalism for centering a single-crystal on a four-circle diffractometer, based on the setting angles of reflections, is presented. The minimum information for the determination of crystal displacement are the diffractometer setting angles of two reciprocal vectors. The method is independent of the crystallographic system and does not require prior information about the crystal lattice. The size of the radiation source, beam divergence and homogeneity are shown to be significant factors for calculating the crystal displacement from the positions of the reflections. The method is primarily designed for samples enclosed in high-pressure diamond-anvil cells and other environments obscuring visual control of the sample position; however, high accuracy of the method in most cases allows the optical centering of the crystals to be improved, particularly for irregularly shaped samples. A procedure for retrieving true lattice dimensions, by accounting for the effect of the crystal displacement from the diffractometer center, is also presented.
X-ray powder diffraction quantitative analysis performedin situat high temperature: application to the determination of NiO in ceramic pigments
Authors: Gualtieri Alessandro F. , Mazzucato Edoardo , Venturelli Paolo , Viani Alberto , Zannini Paolo , Petras Laszlo
Published: July 2002

Although nickel(II) oxide (NiO) is a potential carcinogenic agent, it is still used in the synthesis of ceramic pigments because during their preparation at high temperature, NiO is thought to combine with other compounds, crystallizing as new phases with spinel-like structures. Unfortunately, there are no widely accepted methods for the determination offreeNiO in ceramics, the main reason being experimental difficulties. In fact, quantitative phase analysis (QPA) by X-ray powder diffraction (XRPD) may fail because diffraction peaks of NiO with space groupFm3¯manda≃ 4.18 Å overlap with those of the spinel with space groupFd3¯manda≃ 8.4 Å. To overcome this problem, in this work QPA has been performedin situat high temperature to resolve the peak overlap of NiO and spinel by taking advantage of the different thermal expansion of each phase. It is believed that this is the first report of the application of this technique.
Correction of specimen absorption in X-ray diffuse scattering experiments with area-detector systems
Authors: Scheidegger Stefan , Estermann Michael Alexander , Steurer Walter
Published: July 2002

Methods for correcting specimen absorption in X-ray diffraction experiments, dedicated to two-dimensional area-detector systems and broad diffuse scattering phenomena, are implemented and tested. The respective transmission factors, in relation to the crystal or specimen shape, are applied to the intensity of every pixel of the two-dimensional detector. The pixel-wise approach allows for a fully quantitative treatment of continuous diffraction information, such as disorder diffuse scattering or scattering from amorphous materials, which is collected with a two-dimensional detector system. This is in contrast to routine data reduction, where the transmission factors are applied to the integrated Bragg intensities only. Furthermore, it is possible to assign different linear attenuation coefficients to the paths of the incident and scattered beams, as is desirable, for instance, in the case of X-ray holography with an internal resonant scatterer. Broad diffuse scattering data collected with synchrotron radiation and numerical calculations are used to study in detail the influence of experimental parameters on the accuracy of the pixel-wise absorption correction.
Nano-sized ceramics of coated alumina and zirconia analyzed with SANS
Authors: Keiderling U. , Wiedenmann A. , Srdic V. , Winterer M. , Hahn H.
Published: July 2002

The sintering behaviour of two new types of coated ceramics, made from alumina grains coated with a zirconia shell and from zirconia grains coated with an alumina shell, was analyzed with small angle neutron scattering (SANS). Measurements were performed both for the plain samples, and with contrast variation using D2 O as immersion liquid. The size distribution and the volume fraction of grains and pores were determined from the corrected scattering curves using a direct model fitting, applying two different approaches, a sphere model and a combined sphere/spherical shell model. Results are discussed in context with the macroscopic density of the samples. The sintering behaviour of the two ceramics types was found to be very different.
In-situ observation of small-angle X-ray scattering by dislocations
Authors: Long G.G. , Levine L.E. , Thomson R.
Published: July 2002

Ultra-small-angle X-ray scattering by dislocations in single-crystal aluminum has been observed in situ as a function of plastic deformation. The scattering is strongly dependent upon sample orientation, with single dislocations, dislocation dipoles, and the dislocation distribution within walls each exhibiting distinct scattering profiles. Among the microstructural features that have been observed are: the correlations between the ordered fraction of dislocations, the presence of dislocation dipoles, the increasing dislocation content with increasing strain, and the decreasing width of the interface between dislocation walls and the surrounding nearly-dislocation-free material with increasing deformation.
Reversion of precipitates in phase separated soda lime silica glass
Authors: Kranold R. , Hoell A. , Kammel M. , Lembke U. , von Krosigk G.
Published: July 2002

The glass with composition 13Na2O-11CaO-76SiO2 (mol%) undergoes subliquidus phase separation via a binodal mechanism. At temperatures below the binodal temperature, T
b = 978 K, the glass separates into two amorphous phases, silica-enriched droplets and a silica-poor matrix. Small-angle X-ray scattering was used to study the formation of the droplet phase at 923 K as well as the process of reversion where the precipitates dissolve after an increase in temperature. After a heat treatment of 48 h at 923 K the system is in the stage of coarsening. However, the equilibrium volume fraction of the droplet phase, w
e = 0.073, has not yet precipitated. The reversion of the droplets was studied at T = 983 K and T = 963 K. For T > T
b, the precipitates dissolve completely by an interdiffusion process resulting in a decrease of the silica concentration of the droplets, while the phase boundary is preserved over long times. For T < T
b, the reversion process shows two distinct stages. In the first stage, the silica concentration inside the droplets decreases and all precipitates shrink until the concentration in the matrix reaches its new equilibrium value. Afterwards, the largest droplets grow again by slow coarsening.
Exact joint distribution of E

h
, E

k
and E

h+k
, and the probability for the positive sign of the triple product in the space group P\overline{1}
Authors: Shmueli U. , Weiss G. H.
Published: July 2002

A recently formulated method of deriving exact Fourier-series representations of joint probability density functions (p.d.f.'s) of several normalized structure factors is applied to the derivation of an exact expression for the conditional probability that the sign of the triple product E

h

E

k

E

h
+
k

is positive. The relevant joint and conditional probabilities are derived for the space group P\bar 1. The Fourier coefficients of the p.d.f. are given by rapidly convergent series of Bessel functions, and the convergence properties of the Fourier summations are also found to be favourable. The exact conditional probability is compared with the currently employed approximate one, well known as the hyperbolic tangent formula, for several hypothetical structures. The examples illustrate the effects of the number of atoms in the unit cell, the magnitude of the E values and the atomic composition on the exact and approximate probabilities. It is found, in agreement with previous studies, that the hyperbolic tangent formula may indeed significantly underestimate the probability when the number of equal atoms is small and the E values are only moderately large, and when the structure contains outstandingly heavy atoms. The opposite behaviour, i.e. the approximate probability overestimating the exact one, was not observed in the present calculations. For large values of the triple product in equal-atom and heterogeneous models, the agreement between the approximate and exact probabilities is usually good.
The maximum entropy distribution consistent with observed structure amplitudes
Authors: Prince E.
Published: July 2002

It is shown that an electron density distribution of the formρk= exp [Σfj(rk)xj] has maximum entropy under the constraint that the expected values of a set of functions,fj(r), are constant. For a Fourier map the functionsfj(r) are the magnitudes of the structure factors for a set of reflectionshjincludingF(000). The values of the parametersxjfor which [(exp (2πihj. r))] = [Fobs(hj)[ for an arbitrarily large set of reflections may be found by an iterative algorithm in whichxi+ 1=xi+Hi-1Δi, where the matrixHis positive definite. Because the distributionρ(r) is everywhere positive, if non-negativity of electron density is sufficient information to determine a unique structure by direct methods, it follows that the maximum entropy procedure must lead to the same unique structure. Maximum entropy is thus an efficient way of expressing the phase implications of a large set of structure amplitudes.
Bond-valence parameters for ammonium–anion interactions
Authors: García-Rodríguez Lourdes , Rute-Pérez Ángeles , Piñero José Ramón , González-Silgo Cristina
Published: July 2002

Bond-valence parameters r
0 and b, relating bond valence and bond length, are calculated for interactions between the ammonium ion and anions X = O, F, Cl. Searches in the Cambridge Structural Database (CSD) and in the Inorganic Crystal Structural Database (ICSD) were performed to obtain the lengths of NH4
+...X contacts for ammonium ion environments in different structures. The procedure, which represents an extension of previous methods, allows certain environments to be rejected and enables the calculation of r
0 and b from a reasonable range of interaction distances. Results are in very good agreement with the expected values on the basis of the assumed bond-valence model and their overall applicability to ammonium ion interactions is discussed.
Structure of C
n
C
n+2C
n
-type (n = even) β′-triacylglycerols
Authors: Van Langevelde Arjen , Van Malssen Kees , Driessen René , Goubitz Kees , Hollander Frank , Peschar René , Zwart Peter , Schenk Henk
Published: July 2002

The crystal structures of the β′ phase of CLC (1,3-didecanoyl-2-dodecanoylglycerol) and MPM (1,3-ditetradecanoyl-2-hexadecanoylglycerol) have been determined from single-crystal X-ray diffraction and high-resolution X-ray powder diffraction data, respectively. Both these crystals are orthorhombic with space group Iba2 and Z = 8. The unit-cell parameters of β′-CLC are a = 57.368 (6), b = 22.783 (2) and c = 5.6945 (6) Å and the final R value is 0.175. The unit-cell parameters of β′-MPM are a = 76.21 (4), b = 22.63 (1) and c = 5.673 (2) Å and the final Rp
value is 0.057. Both the β′-CLC and β′-MPM molecules are crystallized in a chair conformation, having a bend at the glycerol moiety. The zigzag planes of the acyl chains are orthogonally packed, as is typical for a β′ phase. Furthermore, unit-cell parameters of some other members of the C
n
C
n+2C
n
-type triacylglycerol series have been refined on their high-resolution X-ray powder diffraction pattern. Finally, the crystal structures are compared with the currently known structures and models of triacylglycerols.
Structures and phase transitions of the A
7PSe6 (A = Ag, Cu) argyrodite-type ionic conductors. III. α-Cu7PSe6
Authors: Gaudin E. , Petricek V. , Boucher F. , Taulelle F. , Evain M.
Published: July 2002

The crystal structure of the third polymorph of the Cu7PSe6 argyrodite compound, α-Cu7PSe6, heptacopper phosphorus hexaselenide, is determined by means of single-crystal diffraction from twinned crystals and X-ray powder diffraction, with the help of extensive NMR measurements. In the low-temperature form, i.e. below the last phase transition, α-Cu7PSe6 crystallizes in orthorhombic symmetry, space group Pna21, with a = 14.3179 (4), b = 7.1112 (2), c = 10.1023 (3) Å, V = 1028.590 (9) Å3 (deduced from powder data, T = 173 K) and Z  = 4. Taking into account a twinning by reticular merohedry, the refinement of the α-Cu7PSe6 structure leads to the residual factors R = 0.0466 and wR = 0.0486 for 127 parameters and 3714 observed, independent reflections (single-crystal data, T = 173 K). A full localization of the Cu+
d
10 element is reached with one twofold-, one threefold- and five fourfold-coordinated Cu atoms. The observation of two phase transitions for Cu7PSe6, to be compared with only one for Ag7PSe6, is attributed to the d
10 element stability in a low coordination environment, copper being less prone to lower coordination sites than silver, especially at low temperature.
Synchrotron X-ray study of Er3Al5O12 and Yb3Al5O12 garnets
Authors: Etschmann Barbara , Streltsov Victor , Ishizawa Nobuo , Maslen E. N.
Published: July 2002

Structure factors for Er3Al5O12 and Yb3Al5O12 garnets were measured using focused synchrotron X-radiation, with λ = 0.7500 (2) and 0.7000 (2) Å, respectively. The difference electron density maps for Er3Al5O12 and Yb3Al5O12 were similar, as expected. This was attributed to the 4f electrons being shielded, which reduces their effectiveness in chemical bonding and the relative position of the rare-earth atoms in the periodic table. The symmetry of the difference electron density around the rare-earth atoms was found to reflect that of the cation geometry, emphasizing the importance of second nearest-neighbor interactions. This is consistent with the view that oxide-type structures may be regarded as a packed array of cations with anions in the interstices.
Relationship between bond valence and bond softness of alkali halides and chalcogenides
Authors: Adams Stefan
Published: July 2002

Established bond-valence parameter tables rely on the assumption that the bond-valence sum of a central atom is fully determined by interactions to atoms in its first coordination shell. In this work the influence of higher coordination shells is tested in detail for bonds between lithium and oxygen. It is demonstrated that the sum of the weak interactions with atoms of the second coordination shells significantly contributes to the valence sum and should therefore not be neglected. Since the independent refinement of the two parameters R
0 and b is hardly possible from the limited range of bond lengths occurring in the first coordination shell, the restriction of bond-valence sums to contributions from nearest neighbours implicated another far-reaching simplification: the postulation of a universally fixed value of the bond-valence parameter b which characterizes the shape of the bond-valence pseudopotential for the respective atom pair. However, recent more sophisticated applications of the bond-valence concept, e.g. to model ion-transport pathways in solid electrolytes, demand sensible estimates of the bond-valence sums for mobile ions not only at their equilibrium sites but also at interstitial sites and bottle-necks of transport pathways. Calculations of bond valences at these non-equilibrium sites require the knowledge of the actual shape of the bond-valence pseudopotential. A systematic route to a more realistic estimate of b for alkali halides and chalcogenides is developed in this work from an empirical correlation between b and the absolute softnesses of the interacting particles.
Crystal engineering in the gem-alkynol family: the key role of water in the structure of 2,3,5,6-tetrabromo-trans-1,4-diethynyl-cyclohexa-2,5-diene-1,4-diol dihydrate determined by X-ray and neutron diffraction at 150 K
Authors: Bilton Clair , Howard Judith A. K. , Madhavi N. N. L. , Desiraju Gautam R. , Allen Frank H. , Wilson Chick C.
Published: July 2002

The structure of the title compound has been determined using low-temperature (150 K) single-crystal X-ray and neutron diffraction data. Crystals adopt the uncommon space group P42/ncm and display a complex set of intermolecular interactions in which the water molecules play the crucial role: the water O-atom [O2(w)] accepts two hydrogen bonds and both water H atoms act as bifurcated donors. A set of O—H...O hydrogen bonds is formed around the 42 axis comprising (a) a cyclic tetrameric synthon involving four donor-H from two water molecules and two O(hydroxy) acceptors from two parent molecules, and (b) short discrete O(hydroxy)—H...O2(w) hydrogen bonds which link these tetramers along the c axis. Four Br...Br interactions [3.708 (1) Å] form cyclic Br4 tetramers around the \bar 4 axis and are linked to the O—H...O system via O2(w)—H...Br bonds with H...Br = 2.995 (2) Å. Finally, the O—H...O system is further linked to the parent molecules via C≡C...H...O2(w) bonds of 2.354 (3) Å. The supramolecular structure of the title hydrate is compared with that of the non-hydrated parent molecule, which also forms cyclic O—H...O bonded tetrameric synthons, and with its (non-hydrated) tetrachloro analogue, which forms cyclic tetrameric Cl4 synthons [Madhavi, Desiraju et al. (2000b). Acta Cryst. B56, 1063–1070].
Solid-state structures of group 1 and group 2 metal 1,5-naphthalenedisulfonates: systematic investigation of lamellar three-dimensional networks constructed by metal arenedisulfonate
Authors: Cai Jiwen , Chen Cai-Hong , Liao Cheng-Zhu , Feng Xiao-Long , Chen Xiao-Ming
Published: July 2002

Seven Group 1 and Group 2 1,5-naphthalenedisulfonates (1,5-nds) have been synthesized and structurally characterized by single-crystal X-ray diffraction, IR spectroscopy and thermal gravimetric analysis. For Group 1 metal complexes, with M = Li+ (1), Na+ (2) and K+ (3), all crystallize in the same space group (P21/c) with the same composition, [M
2(1,5-nds)(H2O)2]. They adopt similar three-dimensional packing arrangements with the metal–sulfonate inorganic layers pillared by naphthalene rings. However, the coordination behavior of three metal cations toward the SO_3^- group and water molecule are different, resulting in different architectures for the inorganic portion. For Group 2 complexes with M = Mg2+ (4), Ca2+ (5), Sr2+ (6) and Ba2+ (7), Mg2+ shows no direct coordination by the SO_3^- group while Ca2+ is coordinated by four SO_3^- groups and a two-dimensional network is formed. Complexes (6) and (7) are isostructural, adopting the same three-dimensional, inorganic–organic pillared framework as seen for (1)–(3). The coordination behavior of the metal cations in these structures neatly illustrates the increase in coordination strength with decreasing charge/radius ratio for Group 1 and Group 2 metal cations with large organic anions.
Experimental electron density in the triclinic phase of Co2(CO)6(μ-CO)(μ-C4O2H2) at 120 K
Authors: Bianchi Riccardo , Gervasio Giuliana , Marabello Domenica
Published: July 2002

The experimental electron density (ED) of the triclinic phase of Co2(CO)6(μ-CO)(μ-C4O2H2), μ-carbonyl-μ-5-oxo-2,5-dihydrofuran-2-ylbis(tricarbonylcobalt), has been determined through X-ray diffraction at 120 K. The presence of a `closed shell' Co—Co bond in the title compound, found in an experimental ED study of its orthorhombic form, is confirmed by the Quantum Theory of Atoms in Molecules. However, the two phases show a significant Co—Co bond length difference [triclinic: 2.4402 (2) Å; orthorhombic: 2.4222 (3) Å]. The flat distribution of the experimental ED along the Co—Co bond path and on the two Co2C rings allows for variations of the Co—Co bond length which may be easily induced by the different packing arrangements of the two forms.
Determination of the structure of 2(benzene-1,3,5-tricarboxylic acid)·1.5(pyrene)·2(methanol) and comparison with that of 2(benzene-1,3,5-tricarboxylic acid)·pyrene·2(ethanol)
Authors: Herbstein Frank H. , Kapon Moshe , Shteiman Vitaly
Published: July 2002

The structure of the title methanol complex (P\bar 1, Z = 2) has been determined and compared with that of the title ethanol complex (C2/c, Z = 8) using published data. Both complexes have layer structures, the (essentially planar) layers being constructed from rings of six TMA molecules, hydrogen bonded through four `carboxyl dimers' and two `interrupted dimers', where methanol (ethanol) is included in the R^4_4(12) (graph set) ring. The packing of the layers differs in the two complexes, leading to different three-dimensional structures. In the methanol complex, one pyrene molecule is located within the layer and the other, at a centre of symmetry, between the layers in one type of interlayer space, while the methyls of methanol protrude into the other type of interlayer space. In the ethanol complex, the superpositioning of the layers is such that two types of stack are formed; one of these is mixed, containing pyrene and one of the independent TMA molecules in alternating sequence, while the other stack contains only the second type of TMA. Spectroscopic study is needed to establish whether the partial mixed stack arrangement in the crystalline ethanol complex implies donor–acceptor interaction.
First sphere coordination of divalent metal cations by cyclodextrin: structure of the β-cyclodextrin–calcium chloride–water (1/2/11.25) compound
Authors: Nicolis I. , Coleman A. W. , Charpin P. , Rango C. de
Published: July 2002

The structure of the title compound provides the first illustration of direct coordination of a polyvalent cation, as well as an inorganic anion, by β-cyclodextrin (β-CD). Crystal data: P212121, Z = 4, a = 15.875 (1), b = 17.583 (1), c = 24.270 (2) Å, V = 6775 (1) Å3, R = 0.059 for 4744 unique observed reflections with I > 3σ(I). There are two CaCl2 per β-CD, with no direct contacts between the ions. None of the ions are included within the cyclodextrin cavity. The cations are in direct interaction simultaneously with two or three β-CD molecules and an eightfold coordination occurs for both. No disorder was found except for the two water molecules situated inside the cavity. The crystalline form is a novel monomer-type structure. The β-CD molecules are stacked as monomer entities inclined at ~50° along a twofold screw axis, such that they are arranged in a new herringbone-like scheme. The overall packing is stabilized by intermolecular interactions between cyclodextrin monomers and by direct coordination to the ions. Moreover, the cohesion is reinforced by hydrogen bonds involving water molecules arranged in infinite chain motifs traversing the whole structure.
Incommensurately modulated structure of TaGe0.354Te2: application of crenel functions
Authors: Boucher F. , Evain M. , Petříček V.
Published: July 2002

The incommensurately modulated structure of tantalum germanium telluride, TaGe0.354Te2, was determined by single-crystal X-ray diffraction. The dimensions of the basic orthorhombic cell are a = 6.4394 (5), b = 14.025 (2), c = 3.8456 (5) Å, V = 347.3 (1) Å3 and Z = 4. The (3 + 1)-dimensional superspace group is Pnma(00γ)s00, γ = 0.3544 (3). Refinements on 1641 reflections with I ≥ 3σ(I) converged to R = 0.065 and 0.044 for 526 main reflections and R = 0.061, 0.12, 0.28 and 0.32 for 782 first-order, 237 second-order, 37 third-order and 59 fourth-order satellites, respectively. Since the structure exhibits a strong occupational modulation of both Ta and Ge atoms, along with important displacive modulation waves, crenel functions were used in the refinement in combination with an orthogonalization procedure. Such an approach is shown to be the most convenient and to give reliable coordinations and distances. A detailed analysis of some Te...Te distances is performed, in connection with already known commensurately and incommensurately modulated MAx
Te2 structures.