bluuebunny/crossref_metadata_2025 huggingface dataset:
Performance and First Results of the ELETTRA High-Flux Beamline for Small-Angle X-ray Scattering
Authors: Amenitsch H. , Bernstorff S. , Kriechbaum M. , Lombardo D. , Mio H. , Rappolt M. , Laggner P.
Published: July 2002

A new beamline for small-angle X-ray scattering (SAXS) has recently been constructed and is presently under final commissioning at the 2 GeV storage ring ELETTRA. It has been designed specifically for time-resolved studies of non-crystalline and fibrous materials and has been optimized for small-angle scattering measurements. The beamline operates with a SAXS resolution between 10 and about 1400 Å in d spacing (at 8 keV) and has been optimized with respect to high flux at the sample [of the order of 1013 photons s−1 for 8 keV photons (2 GeV, 400 mA)]. Soon it will be possible to perform simultaneously wide-angle diffraction measurements in the d-spacing range 1.2–8 Å (at 8 keV). In order to allow time-resolved (resolution ~1 ms) small-angle scattering measurements, a high-power 57-pole wiggler is used as the beamline source. From its beam, one of three discrete energies, 5.4, 8 and 16 keV, can be selected with a double-crystal monochromator, which contains three pairs of asymmetrically cut plane Si(111) crystals. Downstream, the beam is focused horizontally and vertically by a toroidal mirror. Commissioning tests of this new SAXS beamline showed that all design parameters have been realized.
Measurement and Interpretation of Curvatures of the Oil–Water Interface in Isometric Bicontinuous Microemulsions
Authors: Chen S.-H. , Choi S.-M.
Published: July 2002

A small-angle neutron scattering (SANS) study was carried out on a three-component isometric (equal volume fractions of water and oil) ionic microemulsion system, composed of AOT/brine/decane [AOT= surfactant sodium bis(ethylhexylsufo)succinate]. SANS measurements were made as a function of volume fraction of surfactant within the one-phase channel at the hydrophile–lipophile balance (HLB) salinity and at a constant temperature. We analyzed SANS data taken with oil–water contrast in terms of a modified Berk random wave model. The good agreement of the model with SANS intensity requires a proper form of spectral function. We chose a spectral function which is an inverse eighth-order polynomial in wave number k, containing three length scales 1/a, 1/b and 1/c. The spectral function has finite second and fourth moments. The model shows good agreement with the intensity data in an absolute scale. The three parameters so obtained were then used to calculate the average square mean curvature and the average Gaussian curvature of the interface. The variation of these curvatures and the underlying spectral functions as a function of the surfactant volume fraction were determined and their implications for the degree of local order of the bicontinuous structure are discussed.
The Quantification of Different Forms of Cristobalite in Devitrified Alumino-Silicate Ceramic Fibres
Authors: Butler M. A. , Dyson D. J.
Published: July 2002

When heat treated, amorphous alumino-silicate fibres will devitrify into crystalline phases which on cooling become stable at room temperature. X-ray diffraction has been used to identify and quantify the phases present in such products; mullite and two distinct forms of cristobalite have been observed. One form of cristobalite has been identified as α-cristobalite, the second form has been designated as α′-cristobalite. An internal standard approach was used to enable calibration curves to be obtained for the three crystallite phases, including the α′- cristobalite for which no commercially available standard exists. The accuracy of the methods was estimated as ± 5 wt% for all three crystalline phases present. This was achieved by quantifying the proportion of α′-cristobalite in a standard alumino-silicate fibre after heat treatment for 48 h at 1773 K and then using this material as the `standard' for α′-cristobalite. This `standard' contained 32.9 wt% α′-cristobalite, 1.6 wt% α-cristobalite and 65.5 wt% mullite. The exact nature of the α′- cristobalite phase has also been examined using high-temperature X-ray diffraction and differential scanning calorimetry. It has been shown to be more similar in nature to α-cristobalite than β-cristobalite since it undergoes an α′ → β phase transition on heating. Compared with α-cristobalite it has a different lattice size, and both the temperature and enthalpy of the α′ → β phase transition are lower than for the α → β phase transition. It has been proposed that the α′-cristobalite observed is a defect form of α-cristobalite but with a constant amount of defects/substituted cations which gives it a well defined and consistent structure.
Neutron Diffraction by the Flux Line Lattice in YBa2Cu3O7−δ Single Crystals
Authors: Brandstätter G. , Weber H. W. , Chattopadhyay T. , Cubitt R. , Fischer H. , Wylie M. , Emel'chenko G. A. , Wiedenmann A.
Published: July 2002

Small-angle neutron diffraction was used to image the mixed state in a large superconducting YBa2Cu3O7−δ single crystal. The flux line lattice was observed in fields up to 2 T at various temperatures from 2.4 to 80 K. The integrated intensity I of the (10) reflection was calculated as a function of temperature for three different fields (0.8, 1 and 2 T). From these I(T) curves, the magnetic penetration depth λ(T) was obtained on an absolute scale. This quantity is of particular interest, since it provides information on the nature of the pairing mechanism in the superconductor, i.e. the symmetry of the wavefunction of the electron pairs. The results are discussed in terms of BCS theory (s-wave pairing) and of d-wave pairing with and without impurity scattering.
A Small-Angle Neutron Scattering Investigation of the TDMAO Micelle System at High Hydrostatic Pressure
Authors: Gorski N. , Kalus J. , Kuklin A. I. , Smirnov L. S.
Published: July 2002

The phase behaviour and phase transition of the tetradecyldimethylaminoxide micellar system TDMAO/ D2O have been investigated by small-angle neutron scattering (SANS) at temperatures T between 287 and 325 K, pressures up to P = 842 MPa and at TDMAO concentrations of 55 and 102 mmol l−1. A pressure-induced structural (shape) phase transition was observed for the whole pressure versus temperature range, with a slope of the transition line of dTm
/dP ≃ 0.31° MPa−1. The reversibility and reproducibility of this phase change were tested. The SANS experiments showed a pressure-induced structural phase transition from a low-pressure phase (i), where rod-like micelles with a radius of R = 1.94 ± 0.03 nm were present, to a high-pressure phase (ii). An accurate determination of the structure of phase (ii) has not been possible up to now. In phase (ii), a discrete correlation peak in the Q range 1.8–2.2 nm−1 was found.
Determination of the Anomalous Scattering Factors in the Soft-X-ray Range using Diffraction from a Multilayer
Authors: Sève L. , Tonnerre J. M. , Raoux D.
Published: July 2002

Bragg diffraction from an Ag/Ni multilayer was used to determine independently both the real and imaginary parts of the anomalous scattering factor (ASF) around the NiLIIIandLIIedges in the soft-X-ray range. Huge resonant variations were observed with f'' reaching 55\,r_o and f' decreasing to −63 r_o at the NiLIIIedge. The independent measurements of f' and f'' are tested for coherency using the Kramers–Kronig relation. The f'' values are also compared with those derived from X-ray absorption methods such as total electron yield and fluorescence yield measurements.
Investigation of particle size distribution and aggregate structure of various ferrofluids by small-angle scattering experiments
Authors: Eberbeck Dietmar , Bläsing Jürgen
Published: July 2002

The size and the size dispersion of the composite particles of ferrofluids were determined assuming a lognormal distribution of core radii. Small-angle X-ray scattering data were fitted by the theoretical scattering function of two-phase spheres. Reliable results were obtained, because the scattering share of the surface layer can be taken into account. The particles aggregate at high as well as very low concentrations. After freezing of the carrier liquid, the particles within the clusters come together tightly. The measured minimal particle distance gives information about the effective surface-layer thickness. Two types of aggregates, namely compact clusters and extended net-like aggregates, were distinct in middle length scales.
Application of the molecular replacement method to a heavy-atom problem
Authors: Arnez John G.
Published: July 2002

The molecular replacement method has been applied to the heavy-atom problem in a case for which a heavy-atom model existed for one crystal form, and both native and derivative data were available for another crystal form of the same molecule; the absolute values of difference amplitudes for the second form were used in the calculation. The key requirement for obtaining a solution is that the contents of the asymmetric unit are the same and the same heavy-atom compound is used in both cases.
Size distribution of single-crystal nanoparticles by Monte Carlo fitting of wide-angle X-ray scattering peak shape
Authors: Di Nunzio P. E. , Martelli S.
Published: July 2002

According to Bertaut's theorem [Acta Cryst.(1950),3, 14–18], the size distribution of a powder sample constituted by perfect single-crystal particles can be easily determined from the peak shape analysis. The comparison between particle size distributions determined by a Monte Carlo fitting algorithm and those determined by direct observation using transmission electron microscopy shows that, as expected, the X-ray diffraction determination cannot be confidently used for particles with maximum dimensions above about 60 nm.
Positioning a protein molecule in the asymmetric unit using very low order reflections and packing restraints
Authors: Andersson Klas M.
Published: July 2002

A method for predicting the position of protein molecules in the unit cell is presented. This prediction is based on the structure-factor amplitudes of the very low order reflections and packing considerations. With very low resolution data, the calculated electron density is very blurred, such that a protein molecule may well be approximated as a sphere. A sphere with the same volume as the unknown protein was translated in small (2–3 Å) steps in the corresponding Cheshire cell until maximum overlap between the amplitudes calculated from the sphere and the true protein structure was found. A molecular packing can be calculated to restrain the allowable regions. This makes the positioning of the protein molecule even more reliable. Structure factors of the ten or so lowest resolution reflections were calculated with a sphere at the best position. These structure factors agreed closely with those of the true protein structure. The translation algorithm has been successfully tested for 16 proteins. For 12 out of 16 proteins tested, the position of the centre of the molecule was correctly predicted to within 5 Å. A qualitative deduction of deviations from the spherical model can be gained by comparing structure factors from the spherical model and the true protein. The very low resolution phasing obtained by this method may be used as powerful starting set for phase-extension methods such as maximum entropy.
A Gaussian–Hermite polynomials function for X-ray diffraction profile fitting
Authors: Sánchez-Bajo F. , Cumbrera F. L.
Published: July 2002

In recent years, several profile-shape functions have been successfully used in X-ray powder diffraction studies. Here, a new profile function for approximating the X-ray diffraction peaks is proposed. This model, based on a Gaussian function multiplied by a correction factor in the form of a series expansion in Hermite polynomials, can be employed in the cases where there are peak asymmetries. The function has been tested by using samples of α-Al2O3and 9-YSZ (yttria-stabilized zirconia), yielding generally satisfactory results.
An improved method for protein crystal density measurements
Authors: Leung Adelaine K. W. , Park Michael M. V. , Borhani David W.
Published: July 2002

Determination of the density of protein crystals by flotation in organic solvent density gradients using simple methods for the preparation of the density gradients and the transfer of crystals into these gradients is described. The method was tested with crystals of hen egg white lysozyme. These methods are especially suitable for use with fragile, high-solvent-content protein crystals. These methods were applied to the measurement of the density of human apolipoprotein A-I crystals.
Effect of sample transparency in powder diffractometry with Bragg–Brentano geometry as a convolution
Authors: Ida T. , Kimura K.
Published: July 2002

The effect of transparency and finite thickness of the sample on the peak profile in powder diffractometry with Bragg–Brentano geometry is treated as a convolution with an asymmetric aberration function. The formula of the aberration function and a practical method for numerical calculation of the convolution are proposed. The model function for the total profile is given by triple convolution of the pseudo-Voigt function with asymmetric functions based on vertical (axial) divergence, horizontal (equatorial) divergence and sample transparency. The validity of the model profile function is examined by fitting the CuKα X-ray diffraction profile of diluted lanthanum hexaboride (LaB6) standard samples (SRM660) of 0.5 mm thickness, the transparency of which is varied by mixing with different amounts of starch; all the parameters that may affect the shape of the profile function are treated as fixed parameters. Even in the case of heavily distorted profiles of highly transparent samples with the inverse linear absorption coefficients μ−1= 0.34 and 1.19 mm, experimental profiles are fairly well reproduced by the model function, typically within several % inRfactor. It is also demonstrated that the lattice constants of the transparent samples are precisely evaluated by applying this model function.
Combined Rietveld and stereochemical restraint refinement of a protein crystal structure
Authors: Von Dreele R. B.
Published: July 2002

By combining high-resolution X-ray powder diffraction data and stereochemical restraints, Rietveld refinement of protein crystal structures has been shown to be feasible. A refinement of the 1261-atom protein metmyoglobin was achieved by combining 5338 stereochemical restraints with a 4648-step (dmin= 3.3 Å) powder diffraction pattern to give the residualsRwp= 2.32%,Rp= 1.66%,R(F2) = 3.10%. The resulting tertiary structure of the protein is essentially identical to that obtained from previous single-crystal studies.
Orientation relationship between Al6Mn precipitates and the Al matrix during continuous recrystallization in Al–1.3%Mn
Authors: Yang Ping , Engler Olaf , Klaar Hans-Joachim
Published: July 2002

Annealing of cold-rolled supersaturated Al–1.3 wt% Mn leads to heavy precipitation of fine particles on the as-deformed microstructure. Depending on the crystallographic orientation of the deformed matrix grains, particles with different morphologies, namely spherical, rhomboidal and plate-like, have been observed. This variation in morphology could be traced back to differences in local misorientation caused by different dislocation substructures in different matrix orientations. Microstructural investigations and selected-area diffraction (SAD) analysis in a transmission electron microscopy (TEM) study were employed to characterize the various particles and to determine their orientation relationship to the Al matrix. Independent of the particle morphology, most Mn precipitates were identified as Al6Mn; only occasionally was Al12Mn observed. Upon consideration of the various crystal symmetries, two different orientation relationships were discerned, which can be written as (110)m||(111)p, [001]m||[2¯11]pand (110)m||(111)p, [11¯2]m||[12¯1]p. These orientation relationships are discussed with respect to the existence of several low misfits of lattice spacings and compared to literature data.
Morphology of encapsulated iron nanoparticles obtained by co-sputtering and implantation: a GISAXS study
Authors: Babonneau D. , Naudon A. , Cabioc'h T. , Lyon O.
Published: July 2002

A grazing incidence small-angle X-ray scattering (GISAXS) study is presented on the morphology of iron nanoparticles buried in carbon matrices, obtained either by ion-beam sputtering co-deposition or by ion-implantation. It is shown that, depending on the experimental synthesis conditions, the shape of the iron nanoparticles is either spherical or elongated perpendicularly to the substrate. The possible growth mechanisms are examined in terms of volume and surface diffusion, defect density, interfacial energy and residual stress.
Program construction for macromolecule atomic model refinement based on the fast Fourier transform and fast differentiation algorithms; erratum
Authors: Lunin V. Yu. , Urzhumstev A. G.
Published: July 2002

In Lunin & Urzhumtsev [Acta Cryst. (1985), A41, 327-333] references to Lifshitz (Agarwal, 1981) on pages 327 and 329 should be amended to Lifchitz (Agarwal, 1981).
Modified multislice theory for calculating the energy-filtered inelastic images in REM and HREM
Authors: Wang Z. L.
Published: July 2002

Inelastic plasmon diffuse scattering (PDS) is treated as an effective position-dependent potential perturbing the incident electron wavelength in a solid surface, resulting in an extra phase grating term in the slice transmission function. This potential is derived for the geometry of reflection electron microscopy (REM) and high-resolution electron microscopy (HREM). The energy-filtered inelastic images can be calculated following the routine image simulation procedures by using different slice transmission functions for the elastic and inelastic waves, by considering the 'transitions' of the elastic scattered electrons to the inelastic scattered electrons. It is predicted that the inelastic scattering could modify the electron intensity distribution at a surface. It is possible to take high-resolution energy-filtered inelastic images of crystals, the resolution of which is about the same as that taken from the elastic scattered electrons.
Determination of composite crystal structures and superspace groups
Authors: Yamamoto A.
Published: July 2002

Superspace groups introduced for usual modulated structures have recently been applied to the analysis of composite crystals. This review describes the method of composite-crystal analysis based on the superspace group. This method is efficient for the analysis of any (incommensurate or commensurate) composite crystals. The method is analogous to that for the modulated structure in many respects. The description of composite crystals in superspace, determination of their superspace groups and unified setting of the unit vectors are mentioned. Two possible approximations and a relation between the superspace and space groups for commensurate composite crystals are discussed. Space groups of chimney-ladder structures with different periods are derived from a single superspace group by the application of this relation. Possible superspace groups for known composite structures are deduced from the space groups of average substructures. Finally, the refinement method is discussed.
Simulations for imaging with atomic focusers
Authors: Dunin-Borkowski R. E. , Cowley J. M.
Published: July 2002

The basis has been explored for the possible application of the various schemes that have been proposed for making use of the focusing properties of single heavy atoms, or rows of atoms extending through thin crystals in axial directions, for the attainment of ultra-high resolution in electron microscopy. Calculations are reported for the form of 200 keV electron beams channeled along rows of atoms through crystals and propagated in the vacuum beyond the crystals. The conditions for forming beams less than 0.05 nm in diameter have been established. Simulations of images having resolutions of this order are reported for the case that the specimen is placed at the Fourier image position beyond the exit face of a thin crystal and the transmission of the periodic array of ultra-fine beams, translated laterally by tilting the incident beam, may be observable using a conventional transmission-electron-microscopy (TEM) instrument.
X-ray standing wave as a result of only the imaginary part of the atomic scattering factor
Authors: Negishi Riichirou , Fukamachi Tomoe , Kawamura Takaaki
Published: July 2002

The X-ray standing wave has been studied when the real part of the scattering factor is zero. In the symmetric Laue case, the phase of the standing wave advances by π when the deviation parameter W changes from −1 to 1, which is the same variation as in the usual symmetric Bragg case when only the real part of the scattering factor exists. However, the phase in the former case is different from that in the latter by \pi/2. By using the standing waves, the origins of the anomalous transmission and anomalous absorption effects reported by Fukamachi & Kawamura [Acta Cryst. (1993), A49, 384–388] have been analysed. The standing wave in the Laue case can give rise to a more accurate method of site determination of a specified impurity atom as well as a wider range of applications than a conventional standing-wave approach.
Boron nitride cones: structure determination by transmission electron microscopy
Authors: Bourgeois Laure , Bando Yoshio , Shinozaki Satoshi , Kurashima Keiji , Sato Tadao
Published: July 2002

A form of turbostratic boron nitride containing a large percentage of micrometre-size conically shaped particles was investigated by transmission electron microscopy. Electron diffraction patterns revealed the presence of correlations between adjacent boron nitride layers. The diffraction patterns were also used to determine the cone apex angle of many cone-like objects. The apex angles exhibited a broad distribution from 84 to 130° with an ill defined peak in the 92–95° region. These results could be accounted for by a structure model in which conical boron nitride layers are helically wound about a disclination axis, according to overlap angles that correspond to high densities of coincidental lattice sites between successive layers. The clustering of the apex angles near 93° was attributed to the formation of a square ring during the nucleation stage. This appears to be specific to the boron nitride system.
Experimental and theoretical characterization of structure in thin disordered films
Authors: McCulloch D. G. , McKenzie D. R. , Goringe C. M. , Cockayne D. J. H. , McBride W. , Green D. C.
Published: July 2002

The electron microscope provides an ideal environment for the structural analysis of small volumes of amorphous and polycrystalline materials by enabling the collection of scattering information as a function of energy loss and momentum transfer. The scattered intensity at zero energy loss can be readily processed to a reduced density function, providing information on nearest-neighbour distances and bond angles. A method for collecting and processing the scattered intensity, which allows for the collection of an energy-loss spectrum for a range of momentum transfers, is discussed. A detailed structural determination from a reduced density function alone is difficult and it is shown that a more detailed structural model can be obtained by combining the experimental reduced density function with model structures obtained from molecular dynamics based on first-principles quantum mechanics. This method is applied to tetrahedral amorphous carbon, as an example of a monatomic network, and to aluminium nitride, as a prototype for a binary amorphous alloy.
Three-phase structure invariants and structure factors determined with the quantitative convergent-beam electron diffraction method
Authors: Høier R. , Birkeland C. R. , Holmestad R. , Marthinsen K
Published: July 2002

Quantitative convergent-beam electron diffraction is used to determine structure factors and three-phase structure invariants. The refinements are based on centre-disc intensities only. An algorithm for parameter-sensitive pixel sampling of experimental intensities is implemented in the refinement procedure to increase sensitivity and computer speed. Typical three-beam effects are illustrated for the centrosymmetric case. The modified refinement method is applied to determine amplitudes and three-phase structure invariants in noncentrosymmetric InP. The accuracy of the results is shown to depend on the choice of the initial parameters in the refinement. Even unrealistic starting assumptions and incorrect temperature factor lead to stable results for the structure invariant. The examples show that the accuracy varies from 1 to 10° in the electron three-phase invariants determined and from 0.5 to 5% for the amplitudes. Individual phases could not be determined in the present case owing to spatial intensity correlations between phase-sensitive pixels. However, for the three-phase structure invariant, stable solutions were found.
Quantitative zone-axis convergent-beam electron diffraction (CBED) studies of metals. I. Structure-factor measurements
Authors: Saunders M. , Fox A. G. , Midgley P. A.
Published: July 2002

The zone-axis CBED pattern-matching technique ZAPMATCH [Bird & Saunders (1992). Ultramicroscopy, 45, 241–251] has been applied to low-order structure-factor measurements in nickel and copper. Considerable disagreement exists between previously published results obtained with a variety of solid-state theories and experimental techniques. The nickel ZAPMATCH results confirm previous electron-diffraction critical-voltage measurements and are in excellent agreement with FLAPW (full-potential linearized augmented plane-wave) theory calculations. This is further proof of the accuracy achievable with ZAPMATCH analysis. For copper, however, while the results support the findings of previous experimental measurements, they are consistently higher than those given by a range of solid-state theories, perhaps demonstrating some limitation in the existing theory. Two extensions to the ZAPMATCH technique are also considered. First, rules are developed to determine the number of structure factors that can be refined accurately from a given CBED pattern. Second, the imaginary potential generally introduced to account for the effects of thermal diffuse scattering (TDS) is also refined. It is shown that, while the widely used Einstein model is a useful approximation, the refined values are consistently higher than the model predicts. In addition, the importance of a second-order (real) TDS correction arising from the Einstein model is investigated. Although its effects are limited in this instance, it may prove to be more significant at lower beam energies or for materials of higher atomic number.
Dynamical calculation of crystal truncation rods for surfaces and interfaces using a Cartesian coordinate transformation technique
Authors: Chien Hung-Chun , Gau Tsai-Sheng , Chang Shih-Lin , Stetsko Yuri P.
Published: July 2002

A dynamical calculation scheme that employs Cartesian coordinates with a z axis normal to the crystal surface to define polarization unit vectors and wavefields is applied to interpret the intensity distribution of crystal truncation rods for surfaces and interfaces. A comparison between this calculation scheme and the asymptotic iteration approach using the conventional presentation of the polarization components of the wavefields, with the σ and π components perpendicular to the wave-vectors, is presented. It is found that the use of Cartesian coordinate systems can provide correct boundary conditions in determining the wavefield amplitudes, thus leading to a rigorous and general calculation scheme for dynamical diffraction from surfaces and interfaces.
The efficient calculation of the normal matrix in least-squares refinement of macromolecular structures
Authors: Tronrud Dale E.
Published: July 2002

The optimization procedure with the greatest power of convergence is the full-matrix method. This method has not been utilized to a great extent in macromolecular refinement because of the great cost of both calculating and inverting the `normal' matrix. This paper describes an algorithm that can calculate this matrix in a relatively short amount of computer time. The procedure requires two Fourier transforms, which can be performed with the fast-Fourier transformation (FFT) algorithm, as well as a large number of simple function products.
Structure characterization and predictability by Voronoi analysis
Authors: Christensen Stefan W. , Thomas Noel W.
Published: July 2002

The unique ability of tessellation methods to characterize atomic structures is highlighted, with the Voronoi tessellation, by virtue of its freedom from constraining assumptions, emphasized as pre-eminent among these methods. It is demonstrated how to extract information from an atomic structure by constructing its Voronoi tessellation and analysing the results. In so doing, insight is gained into the coordination patterns of the atoms and how their positions are influenced by neighbours. As an example of such a procedure, typical Voronoi volumes are calculated for 72 atom types found in a set of 249 binary intermetallic and ionic compounds. Whereas the various atom types have broadly characteristic volumes, these are also sensitive to the other atom types with which they are combined in a given compound, i.e. whether the latter behaves as a metal, semimetal, semiconductor or insulator. Further, smaller variations in volume occur for different atom types within these four categories. Thus, structural information obtained from the Voronoi tessellation may possibly be correlated directly with atomic properties.
X-ray diffraction in perfect t × l crystals. Rocking curves
Authors: Thorkildsen Gunnar , Larsen Helge B.
Published: July 2002

A general formalism, based on the Takagi–Taupin equations, for calculating rocking curves in perfect t\times l crystals is presented. It includes nonsymmetrical scattering, refraction, and ordinary and anomalous absorption. t and l may be varied independently. In the limit of a semi-infinite crystal, the standard results from the fundamental theory are retrieved. For crystal dimensions less than the extinction length, the theory converges to the kinematical limit. Simulations for germanium and silicon show significant influence of crystal finiteness. When dynamical effects are prominent, the curves exhibit various degrees of asymmetry and the full width at half-maximum is generally larger than the corresponding Darwin width. This is attributed to combined Laue and Bragg contributions which are shifted with respect to each other owing to refraction.
Identification of two allotwins of mica polytypes in reciprocal space through the minimal rhombus unit
Authors: Nespolo Massimo , Ferraris Giovanni , Takeda Hiroshi
Published: July 2002

The X-ray investigation (precession method) of the Ruiz Peak oxybiotite, which is well known for the occurrence of a large number of polytypes and twins, revealed two complex diffraction patterns, which cannot be identified as long-period polytypes. These patterns are analysed in terms of the minimal rhombus, a geometrical asymmetric unit in reciprocal space which permits the decomposition of the composite reciprocal lattice of a twin or allotwin into the reciprocal lattices of the individuals. Both the recorded patterns correspond to a 1M–2M
1 allotwin: the relative rotation between the individuals is 120° in one case and 60° in the other. The geometrical criteria for evaluating the presence of twinning or allotwinning are analysed through these two natural examples.
Comparison of the structural motifs of acetoacetanilides and related azo pigments
Authors: Chisholm Greig , Kennedy Alan R. , Wilson Sharon , Teat Simon J.
Published: July 2002

The structures of three methyl-substituted acetoacetanilides and of an azo pigment derived from one of them are presented and discussed together with a review of related known crystal structures. By considering the position of any aromatic substituents it is possible to predict whether the simple acetoacetanilides adopt planar structures with intramolecular hydrogen bonding or twisted structures featuring intermolecular hydrogen bonding. However, we find that the same crystal engineering rules cannot be applied to the related azo pigments: this is apparently due to the presence of an
sp

2 atom which facilitates the adoption of planar conformations. The thermal properties of the acetoacetanilides were measured by DSC and are discussed with reference to their crystal structures.
Synchrotron X-ray analysis of the electron density in CoF2 and ZnF2
Authors: O'Toole Nicholas J. , Streltsov Victor A.
Published: July 2002

Accurate structure factors for small crystals of the rutile-type structures CoF2, cobalt difluoride, and ZnF2, zinc difluoride, have been measured with focused λ = 0.8400 (2) Å synchrotron X-radiation at room temperature. Phenomenological structural trends across the full series of rutile-type transition metal difluorides are analysed, showing the importance of the metal atom in the degree of distortion of the metal–F6 octahedra in these structures. Multipole models reveal strong asphericities in the electron density surrounding the transition metals, which are consistent with expectations from crystal field theory and the structural trends in these compounds. Transition metal 3d-orbital populations were computed from the multipole refinement parameters, showing significant repopulation of orbitals compared with the free atom, particularly for CoF2.
Structural basis for the phase transitions of Cs2HgCl4
Authors: Bagautdinov Bagautdin , Jobst Andreas , Ludecke Jens , van Smaalen Sander
Published: July 2002

The a
0 × b
0 × 2c
0 twofold superstructure of dicaesium mercury tetrachloride, Cs2HgCl4, at T = 120 K has been determined by single-crystal X-ray diffraction using synchrotron radiation. Lattice parameters were found as a = 9.7105 (2), b = 7.4691 (1), c = 26.8992 (4) Å, and β = 90.368 (1)° with the supercell space group P21/c. Refinements on 1828 observed unique reflections converged to R = 0.053 (wR = 0.057) using anisotropic temperature factors for all atoms. This phase is the stable phase of Cs2HgCl4 below 163 K. A quantitative comparison is made of the distortions of the 2c
0 superstructure with the undistorted phase that is stable at room temperature, and with the 3c
0 and 5a
0 superstructures that are stable at temperatures between 163 K and room temperature. The principal difference between the 2c
0 superstructure and all other phases of Cs2HgCl4 is that the Cs cations are displaced away from the centers of their coordination polyhedra in the 2c
0 superstructure. The structural basis for the driving force of the series of phase transitions in this compound is found in the variations of the environments of Cs atoms and in the variations of the distortions of the HgCl4 tetrahedra.
Structure of the X-phase of 38% brominated betaine calcium chloride dihydrate
Authors: Vieira L. G. , Hernandez O. , Ribeiro J. L. , Cousson A. , Kiat J.-M. , Chaves M. R. , Almeida A. , Klöpperpieper A.
Published: July 2002

The structures of the high- and low-temperature phases of 38% brominated BCCD [betaine (trimethylammonioacetate) calcium chloride dihydrate], the latter being known as the X-phase, have been determined by single-crystal neutron diffraction at 295 and 20 K, respectively. The symmetry of the X-phase is described by the P212121 space group. The distortion with respect to the high-temperature Pnma phase is characterized by anti-symmetric displacements of the betaine molecules as well as of the Ca octahedra. On the basis of a symmetry-mode analysis, we propose an interpretation of the direct phase transition that occurs around 80 K between these two phases.
Reversible dimerization of C60 molecules in the crystal structure of the bis(arene)chromium fulleride [Cr(C7H8)]2C60
Authors: Hönnerscheid Andreas , Dinnebier Robert , Jansen Martin
Published: July 2002

Bis(toluene)chromium fulleride, [Cr(C7H8)2]C60, has been synthesized as a black microcrystalline powder from C60 and [Cr(C7H8)2] in toluene. [Cr(C7H8)2]C60 is an ionic compound in which the fullerene is negatively charged and the bis(toluene)chromium molecule positively charged. At T = 250 K a reversible first-order phase transition from a primitive cubic high-temperature phase to a triclinic low-temperature phase occurs. The high-temperature phase [Pm\overline 3m, a = 9.9840 (1) Å, T = 295 K] is composed of dynamically disordered fulleride anions and bis(toluene)chromium(I) cations in a CsCl-type arrangement. The triclinic low-temperature modification [P\overline 1, a = 13.6414 (8), b = 13.8338 (7), c = 13.8548 (7) Å, α = 91.830 (3), β = 116.776 (2), γ = 119.333 (2)°, T = 235 K] consists of ordered C60 dimers and two crystallographically distinct bis(toluene)chromium entities.
Polymorphism of maleic hydrazide. I. Erratum
Authors: Katrusiak Andrzej
Published: July 2002

In the recently published article by Katrusiak (2001) the crystal data of two polymorphs of maleic hydrazide have been printed with errors or omissions in Tables 1 and 2. It was the author's intention that the measurements of the unit-cell dimensions were possibly accurate, as the comparison of densities and unit-cell volumes of polymorphs are of particular importance. Therefore, these measurements were carried out at varied temperatures to eliminate possible differences owing to the thermal expansion of the crystals, and two different diffractometers, one with a point detector and another one with a CCD, were used to eliminate systematic errors. From these data the unit-cell dimensions at normal conditions were estimated and listed in Table 1, while the crystal data of the diffractometric experiments were duly related in Table 2. It was hoped that this procedure would provide the reader with reliable crystal data. Overestimated precision of routinely reported unit-cell dimensions has been extensively discussed by other authors (e.g. see Herbstein, 2000). The ambiguity resulting from different equipment, data collecting techniques, wavelengths etc. is further aggravated by the vague definition of the so-called room temperature. This temperature is assumed as 293 K and indeed this is the default value if not specified otherwise in programs writing CIF files, even though diffractometers are usually enclosed in safety boxes, where slowly circulating air is heated up by step motors, electronics, cables etc. or even by the X-ray tube if its heat is not totally balanced by the cooling system. Therefore, the temperature in the safety box is higher than outside: when the temperature in our laboratory is air-conditioned to 293 K, the difference in temperatures outside and inside the safety box is 3.5°. Additionally, the temperature of the measurement, even when measured with high relative precision, may considerably differ from the absolute scale. Meanwhile, the crystal data in Tables 1 and 2 were treated as redundant and after acceptance of the manuscript the crystal data were removed from Table 2 in the proof. The author's request to include these missing data resulted in the multiple errors (Katrusiak, 2001). The correct tables, as originally submitted, are reproduced below.
Conformational analysis of acetylcholine and related choline esters
Authors: Frydenvang K. , Jensen B.
Published: July 2002

The crystal structures of carbamoylcholine [2-(carbamoyloxy)-N,N,N-trimethylethanaminium] chloride, bromide and iodide, methoxycarbonylcholine [2-(methoxycarbonyloxy)-N,N,N-trimethylethanaminium] iodide, acetylcholine [2-(acetyloxy)-N,N,N-trimethylethanaminium] chloride and succinylcholine { 2,2′-[(1,4-dioxo-1,4-butanediyl)bis(oxy)]bis(N,N,N-trimethylethanaminium)} iodide have been redetermined at 105 K in order to obtain detailed and accurate information on the geometry of choline esters and to elucidate the conformationally dependent changes of geometry. The conformational flexibility and the preferred conformations are elucidated based on results obtained from X-ray crystallographic studies and molecular mechanics (MM2) calculations. The usefulness of molecular mechanics calculations for quaternary ammonium ions is discussed.
Structure of ferroelectric Pb5Al3F19 at 160 K, polarization reversal and relationship to ferroelectric Pb5Cr3F19 at 295 K
Authors: Sarraute S. , Ravez J. , Von der Mühll R. , Bravic G. , Feigelson R. S. , Abrahams S. C.
Published: July 2002

Pb5Al3F19 at 160 K is ferroelectric, crystallizing in the tetragonal system. With Mr
= 1477.9, the space group is I4cm and a = 14.07 (2), c = 7.30 (1) Å, V = 1445 (3) Å3, Z = 4, Dx
= 6.793 Mg m−3. For λ(Mo Kα) = 0.71073 Å, μ = 56.36 mm−1. F(000) = 2480 Pb5Al3F19 undergoes a first-order phase transition on cooling at 120 K and on heating at 270 K. The structure was determined from 656 independent F(hkl) with I> 3σ(I) and refined by least squares to R = 0.0527, wR = 0.0480, S = 1.065. No atom is further than 0.83 Å, from the hypothetical I4/mcm atomic positions, hence the crystal is structurally ferroelectric. The mean atomic polar displacement of the two independent Al atoms from the zero spontaneous-polarization location, allowing for the F atoms, is 0.207 (28) Å, which leads to a predicted Tc
= 860 (230) K. Several additional phase transitions are known to form before the hypothetical phase is attained. Each independent Al atom occupies a fluorine octahedron with average Al—F distance either 1.818 (5) or 1.824 (1) Å. One Pb atom is nine coordinated, occupying a distorted tricapped trigonal prism with average Pb—F = 2.66 (22) Å. The other is ten coordinated, forming a distorted bicapped cuboid, with average Pb—F = 2.61 (28) Å. Pyroelectric pulses are readily detectable in crystals cooled below 120 K, or subsequently on heating to 270 K. Similarly, numerous piezoelectric resonances are observed in the same thermal ranges; the compression mode at ~1197 kHz has been identified by its characteristic admittance circle. The mechanical quality factor Qm
for ferroelectric Pb5Al3F19, determined from the admittance-circle-derived equivalent circuit, is ~423.
Rietveld structure refinements of calcium hydroxylapatite containing magnesium
Authors: Bigi A. , Falini G. , Foresti E. , Gazzano M. , Ripmonti A. , Roveri N.
Published: July 2002

The crystal structures of four hydroxylapatite (HA) samples prepared from solutions in the presence of 10, 15, 25 and 30 Mg-atom-% have been investigated by X-ray powder pattern fitting. The total magnesium content of the solid samples, as determined by chemical analysis, was 4.9, 14.1, 20.4 and 30.6 Mg-atom-%, respectively. Rietveld analysis was performed using the computer program PREFIN implemented with routines which allow the refinements of the average crystallite sizes. Different refinement procedures were carried out in order to evaluate the effect of the amorphous and background profiles on the occupancy factor data. For comparison, magnesium-free hydroxylapatite was refined with the same strategies. The results of the different approaches indicate that the degree of magnesium substitution for calcium in the HA structure can be at most ~ 10 atom-%. Magnesium substitutes calcium preferentially at the 6(h) site. The broadening of the diffraction peaks increases on increasing the total magnesium content in the solid phase, which is always significantly higher than the amount incorporated into the HA structure. The excess is probably located in the amorphous phase and/or on the crystallite surface.
X-ray structure refinement of (3 + 1)-dimensional incommensurate composite (1-x)Ta2O5.xWO3, x = 0.1
Authors: Schmid S. , Fütterer K. , Thompson J. G.
Published: July 2002

The structure refinement of tantalum tungstate, (1−x) Ta2O5.xWO3, x = 0.1, as a (3 + 1)-dimensional incommensurately modulated composite structure was carried out using X-ray single-crystal diffraction data measured with Mo Kα radiation. The composite structure consists of two component substructures referred to as the metal-substructure (M), aM
= 6.188 (1), bM
= 3.665 (1), cM
= 3.886 (1) Å, and the oxygen-substructure (O), aO
= aM
, bO
= 2.251 Å = bM
/1.628, cO
= cM
, respectively. The primary modulation wavevector of the M substructure is chosen to be
q
M
=
b
O

*

= 1.628
b
M

*

. The overall superspace-group symmetry is C′mmm(0β0)s00. The structure was refined to an overall wR = 0.0561. The structures of the compounds x = 0.267 (Ta22W4O67) and x = 0.14 (Ta74W6O203), also members of the (1 − x) Ta2O5.xWO3, 0 ≤ x ≤ 0.267, solid solution, were rerefined as incommensurately modulated structures using intensity data reported previously. The displacive modulation wave amplitudes obtained from these refinements are in remarkable agreement with each other. Beyond the similarity of the atomic modulation functions across the solid solution, the structures show subtle but significant differences as a function of composition in the following ways: displacement of atom OM
along the b direction and both bond-valence sum and thermal parameter mean-square displacement along c of the metal atom.
A tribenzylidenemethane–tantalum compound: some experiences with `inversion twinning'
Authors: Schaefer W. P. , Marsh R. E. , Rodriguez G. , Bazan G. C.
Published: July 2002

The six-electron-donating ligand tribenzylidenemethandiide has been used to form a tantalum (group 5) mimic, (η
5-cyclopentadienyl)(η
4-tribenzylidenemethandiide)dimethyltantalum, of a group 4 bent metallocene. The material crystallizes with two molecules in the asymmetric unit with quite different packing arrangements, although the overall structures of the two are similar. The Cp and methyl ligands are disordered about a threefold axis. Crystal data: [Ta{(C7H6)3C}(C5H5)(CH3), trigonal P31c, with a = 12.681 (3), c = 16.124 (5) Å, V = 2245.5 (7) Å3, T = 293 K, Z = 4, Mr
= 558.47, Dx
= 1.65 g cm−3, F(000) = 1104, Mo Kα, λ = 0.71073 Å, μ = 4.91 mm−1, R = 0.020 for 1319 reflections with Fo
> 4σ(F
o); S = 2.18. Because of crystal decay, three separate crystals were needed for a full data set. These polar (but achiral) crystals showed apparently differing amounts of inversion twinning, leading to problems in accurately merging the three data sets and refining the structure. These problems are discussed briefly.
Anomalous dispersion analyses of the Ni-atom site in an aluminophosphate test crystal including the use of tuned synchrotron radiation
Authors: Helliwell M. , Helliwell J. R. , Cassetta A. , Hanson J. C. , Ericsson T. , Krick A. , Kaučič V. , Frampton C.
Published: July 2002

Data were collected close to the Ni K edge, using synchrotron radiation at the National Synchrotron Light Source, and using a Mo Kα rotating anode, from a crystal of a nickel-containing aluminophosphate, NiAl3P4O18C4H21N4 (NiAPO). These data sets, along with an existing Cu Kα rotating anode data set, allowed the calculation of several f′ difference-Fourier maps exploiting the difference in f′ for Ni between the various wavelengths. These differences are expected to be 7.8, 4.5 and 3.3 e for Mo Kα data to SR (synchrotron radiation), Cu Kα to SR and Mo Kα to Cu Kα, respectively. The phases were calculated either excluding the Ni atom or with Al at the Ni-atom site. The f′ difference-Fourier maps revealed peaks at the Ni-atom site, whose height and distance from the refined Ni-atom position depended on the f' difference and the phase set used. The largest peak was located at a distance of only 0.025 Å from the refined Ni-atom site and was obtained from the f′ difference map calculated with the coefficients |F
Mo Kα − F
SR| , using phases calculated with Al at the Ni-atom site. In all cases, it was found that these phases gave optimal results without introducing bias into the maps. The results confirm and expand upon earlier results [Helliwell, Gallois, Kariuki, Kaučič & Helliwell (1993), Acta Cryst. B49, 420–428]. The techniques described are generally applicable to other systems containing anomalous scatterers in chemical crystallography.