Showing papers in "Acta Crystallographica Section A in 2001"
TL;DR: The proposed approach is quite general and can be used for any given crystallite shape and different distribution functions; moreover, the Fourier transform formalism allows the introduction in the line-profile expression of other contributions to line broadening in a relatively easy and straightforward way.
Abstract: Diffraction patterns for polydisperse systems of crystalline grains of cubic materials were calculated considering some common grain shapes: sphere, cube, tetrahedron and octahedron Analytical expressions for the Fourier transforms and corresponding column-length distributions were calculated for the various crystal shapes considering two representative examples of size-distribution functions: lognormal and Poisson Results are illustrated by means of pattern simulations for a fcc material Line-broadening anisotropy owing to the different crystal shapes is discussed The proposed approach is quite general and can be used for any given crystallite shape and different distribution functions; moreover, the Fourier transform formalism allows the introduction in the line-profile expression of other contributions to line broadening in a relatively easy and straightforward way
202 citations
TL;DR: The wavefunction fitting method is illustrated by developing the theory for extracting a single-determinant wavefunction for a fragment of a molecular crystal, using data obtained from elastic X-ray scattering data.
Abstract: An experimental wavefunction is one that has an assumed form and that is also fitted to experimental measurements according to some well defined procedure. In this paper, the concept of extracting wavefunctions from experimental data is critically examined and past efforts are reviewed. In particular, the importance of scattering experiments for wavefunction fitting schemes is highlighted in relation to the more familiar model, the Hamiltonian paradigm. A general and systematically improvable method for fitting a wavefunction to experimental data is proposed. In this method, the parameters in a model wavefunction are determined according to the variational theorem but subject to an imposed constraint that an agreement statistic between the calculated and observed experimental data has a certain acceptable value. Advantages of the method include the fact that any amount of experimental data can be used in the fitting procedure irrespective of the number of parameters in the model wavefunction, the fact that a unique answer is obtained for a given choice of the model wavefunction, and the fact that the method can be used to model different experiments simultaneously. The wavefunction fitting method is illustrated by developing the theory for extracting a single-determinant wavefunction for a fragment of a molecular crystal, using data obtained from elastic X-ray scattering data. Effects due to thermal motion of the nuclei, secondary extinction of the X-ray scattering and different choices for the crystal fragment are treated.
165 citations
TL;DR: Relativistic wave functions for elements with Z = 37-54 have been fitted with a linear combination of Slater-type functions as defined by Bunge, Barrientos & Bunge for use in charge-density analysis and other applications.
Abstract: Relativistic wave functions for elements with Z = 37–54 [Su & Coppens (1998). Acta Cryst. A54, 646–652] have been fitted with a linear combination of Slater-type functions as defined by Bunge, Barrientos & Bunge [At. Data Nucl. Data Tables (1993), 53, 113–162], for use in charge-density analysis and other applications. In addition, numerical relativistic wave functions have been calculated for all chemically relevant ions up to Z = 54, and corresponding analytical expressions have been derived. X-ray scattering factors calculated from the numerical wave functions are parameterized [in the sin(θ)/λ ranges 0.0–2.0, 2.0–4.0 and 4.0–6.0 A−1] with six Gaussian functions, using the same method applied previously by Su & Coppens [Acta Cryst. (1997), A53, 749–762].
115 citations
TL;DR: An algorithm for the determination of the space-group symmetry of a crystal from powder diffraction data, based upon probability theory, is described, finding that only a small number of extinction symbols are relatively highly probable and a single extinction symbol is often significantly more probable than any other.
Abstract: An algorithm for the determination of the space-group symmetry of a crystal from powder diffraction data, based upon probability theory, is described. Specifically, the relative probabilities of different extinction symbols are assessed within a particular crystal system. In general, only a small number of extinction symbols are relatively highly probable and a single extinction symbol is often significantly more probable than any other. Several examples are presented to illustrate this approach.
109 citations
TL;DR: The relation between atomic charge and kappa offers the possibility of introducing a constraint in the charge-density refinement of very large molecules, for which reduction of the size of the parameter set may be essential.
Abstract: Structure factors based on periodic density-functional (DFT) calculations on 25 molecular crystals have been used to evaluate trends in refined values of the κ and κ′ expansion–contraction parameters of the Hansen–Coppens multipole formalism. As found previously and expected physically, the spherical-valence-shell κ parameters are closely related to the net atomic charges, negative atoms being expanded and vice versa. κ′ parameters, which scale the radial dependence of the non-spherical deformation functions, are remarkably consistent for particular bonding environments. Systematic trends are observed for both carbon and oxygen, but the values obtained for nitrogen show a larger variation. Average values for oxygen and carbon in different bonding environments are tabulated and can be used whenever refinement of experimental data is affected by lack of uniqueness of the charge-density parameter set. Values for nitrogen must be more finely tuned to the specific bonding environment. The relation between atomic charge and κ offers the possibility of introducing a constraint in the charge-density refinement of very large molecules, for which reduction of the size of the parameter set may be essential.
100 citations
TL;DR: A wavefunction has been derived for the oxalic acid dihydrate molecule using accurate low-temperature X-ray electron-density structure-factor data and is unable to fit to within the experimentally quoted error bounds without allowing an unreasonably large change in the energy of the constrained wavefunction.
Abstract: A wavefunction has been derived for the oxalic acid dihydrate molecule using accurate low-temperature X-ray electron-density structure-factor data. The electron density from this constrained theoretical wavefunction is compared to those of unconstrained theoretical wavefunctions. Fitted electron densities around hydrogen atoms show significant deviation compared to Hartree–Fock calculations. In particular, hydrogen bonding appears enhanced in the crystal over theoretical predictions, while the density usually attributed to lone-pair electrons of the oxalic acid oxygen atoms is decreased. The constrained fitting procedure improves the overall agreement of the calculated structure factors even for structure factors that were not used as input to the fitting procedure. The pictures obtained from the constrained fitting procedure are insensitive to random errors introduced into the data. Similarly, the fitting procedure is able to reproduce features that arise from more accurate theoretical calculations. However, we are unable to fit our wavefunction to within the experimentally quoted error bounds without allowing an unreasonably large change in the energy of the constrained wavefunction. Large Hartree–Fock and density functional theory (DFT) cluster calculations involving up to 86 atoms in size also do not show significantly improved agreement with the experimentally observed structure factors. Derived properties from the constrained wavefunction fragments, such as the kinetic energy, electrostatic potential and the electron localization function, are also presented. In general, there are no difficulties in extracting experimental wavefunctions and the associated derived properties from elastic X-ray scattering data for crystal fragments of the order of 20 atoms.
91 citations
TL;DR: The DZ model leads to significant improvement in the agreement with the theoretical charge density along the covalent bonds and its topological parameters, and eliminates some of the bias introduced by the limited flexibility of the radial functions when a theoretical density is projected into the conventional multipole formalism.
Abstract: A double-zeta (DZ) multipolar model has been applied to theoretical structure factors of four organic molecular crystals as a test of the ability of the multipole model to faithfully retrieve a theoretical charge density. The DZ model leads to significant improvement in the agreement with the theoretical charge density along the covalent bonds and its topological parameters, and eliminates some of the bias introduced by the limited flexibility of the radial functions when a theoretical density is projected into the conventional multipole formalism. The DZ model may be too detailed for analysis of experimental data sets of the accuracy and resolution typically achieved at present, but provides guidance for the type of algorithms to be adapted in future studies.
85 citations
TL;DR: The structure of a decagonal Al72Ni20Co8 quasicrystal with space group P10(5)/mmc has been determined on the basis of a single-crystal X-ray data set using the five-dimensional description and is compared with previously discussed model structures including cluster-based models having 20 A tenfold symmetric clusters.
Abstract: The structure of a decagonal Al_{72}Ni_{20}Co_{8} quasicrystal with space group P10_{5}/mmc has been determined on the basis of a single-crystal X-ray data set using the five-dimensional description. The best-fit model structure based on a cluster model having lower symmetry than the decagonal symmetry with 103 parameters gives wR = 0.045 and R = 0.063 for 449 reflections. The structure is well described by the hexagon, boat and star tiling with an edge length of 6.36 A and is very consistent with recent high-resolution electron-microscopy images. The refined structure is compared with previously discussed model structures including cluster-based models having 20 A tenfold symmetric clusters.
81 citations
TL;DR: Both static deformation electron-density distribution and structure amplitudes compare well with corresponding results obtained from band-structure calculations using the linearized-augmented-plane-wave (LAPW) method and reveal bond critical point properties for the two unique Si--O bonds.
Abstract: The electron-density distribution of the high-pressure polymorph of SiO2, stishovite [a = 4.177 (1), c = 2.6655 (5) A, space group P42/mnm, Z = 2], has been redetermined by single-crystal diffractometry using synchrotron radiation of 100.42 and 30.99 keV, respectively, in order to obtain essentially absorption- and extinction-free data. Room-temperature diffraction experiments on two samples of irregular shape were carried out on two different diffractometers installed at HASYLAB/DESY, Hamburg, Germany. The structure refinement on the high-energy data converged at R(F) = 0.0047, wR(F) = 0.0038, GoF = 0.78, for a multipole model with neutral atoms and multipole expansions up to seventh order. For each atom, the radial expansion coefficients of the multipole orders (l > 0) were constrained to a common value. The absence of extinction was indicated by a refined correction parameter equalling zero within error limit. The excellent quality of the data is also illustrated by a high-order (HO) refinement (s > 0.7 A−1) yielding R(F) = 0.0060, wR(F) = 0.0048, GoF = 0.85. Both static deformation electron-density distribution and structure amplitudes compare well with corresponding results obtained from band-structure calculations using the linearized-augmented-plane-wave (LAPW) method. Ensuing topological analysis of the total model electron density distribution revealed bond critical point properties for the two unique Si—O bonds, indicating a predominantly closed-shell interaction mixed with a significant shared interaction contribution that decreases with increasing interatomic distance. Calculation of atomic basins yielded charges of +3.39 e and −1.69 e for Si and O, respectively, in good agreement with the theoretically calculated values of +3.30 e and −1.65 e. The volumina of the Si and O basins are 2.32 and 10.48 A3, corresponding to spheres with radii of 0.82 and 1.36 A, respectively. The results also conform well with correlations between bond length and bond critical point properties reported in the literature for geometry-optimized hydroxyacid molecules. Estimates of the Si cation electronegativity indicate that the change of Si coordination by oxygen from 4 to 6 is accompanied by an increase of the ionicity of the Si—O bond of about 7%.
70 citations
TL;DR: It is shown that a lonsdaleite configuration may be deformed into a cubic primitive lattice within the Wyckoff position Cmcm 8(f) m.
Abstract: A crystallographic interpretation of a possible transition mechanism from the wurtzite to the NaCl type is given. For this purpose, different atoms in the structures of both types are replaced by like ones, resulting in lonsdaleite-type configurations and in cubic primitive lattices, respectively. The atomic arrangements of both types correspond to homogeneous sphere packings. It is shown that a lonsdaleite configuration may be deformed into a cubic primitive lattice within the Wyckoff position Cmcm 8(f) m.. 0,y,z. Such a transition is displacive since no bonds have to be broken. The corresponding phase transformation from the wurtzite to the NaCl type can be described as a deformation of a heterogeneous sphere packing. The intermediate structure would have the symmetry Cmc21.
46 citations
TL;DR: Comparisons of deformation and residual densities show that the multipolar analysis works satisfactorily but also indicate some drawbacks in the refinement.
Abstract: This electron-density study on corundum (α-Al2O3) is part of the Multipole Refinement Project supported by the IUCr Commission on Charge, Spin and Momentum Densities. For this purpose, eight different data sets (two experimental and six theoretical) were chosen from which the electron density was derived by multipolar refinement (using the MOLLY program). The two experimental data sets were collected on a conventional CAD4 and at ESRF, ID11 with a CCD detector, respectively. The theoretical data sets consist of static, dynamic, static noisy and dynamic noisy moduli of structure factors calculated at the Hartree–Fock (HF) and density functional theory (DFT) levels. Comparisons of deformation and residual densities show that the multipolar analysis works satisfactorily but also indicate some drawbacks in the refinement. Some solutions and improvements during the refinements are proposed like contraction or expansion of the inner atomic shells or increasing the order of the spherical harmonic expansion.
TL;DR: The analysis has shown that the diffuse lines, which feature so prominently in the observed diffraction patterns, are due to strong longitudinal displacement correlations.
Abstract: A recently developed method for fitting a Monte Carlo computer-simulation model to observed single-crystal diffuse X-ray scattering has been used to study the diffuse scattering in benzil, diphenylethanedione, C6H5—CO—CO—C6H5. A model involving 13 parameters consisting of 11 intermolecular force constants, a single intramolecular torsional force constant and a local Debye–Waller factor was refined to give an agreement factor, R = [\textstyle \sum \omega(\Delta I){}^2/\textstyle \sum \omega I_{\rm obs}^2]{}^{1/2}, of 14.5% for 101324 data points. The model was purely thermal in nature. The analysis has shown that the diffuse lines, which feature so prominently in the observed diffraction patterns, are due to strong longitudinal displacement correlations. These are transmitted from molecule to molecule via a network of contacts involving hydrogen bonding of an O atom on one molecule and the para H atom of the phenyl ring of a neighbouring molecule. The analysis also allowed the determination of a torsional force constant for rotations about the single bonds in the molecule. This is the first diffuse scattering study in which measurement of such internal molecular torsion forces has been attempted.
TL;DR: Six packings of symmetry-related cylinders, with cylinder axes in invariant positions (coordinates completely determined by symmetry), are described and it is shown that there can be no cubic cylinder packing with axes along <110>.
Abstract: Six packings of symmetry-related cylinders, with cylinder axes in invariant positions (coordinates completely determined by symmetry), are described. Two have axes along 〈100〉 and four have axes along 〈111〉. It is shown that there can be no cubic cylinder packing with axes along 〈110〉. Earlier errors concerning the numbers of such packings and their symmetries are corrected.
TL;DR: A detailed analysis is made of the statistics and diffraction by a general, finite, two-dimensional ideal paracrystal and characteristics of diffraction patterns are discussed in terms of the different parameters of the model for square and hexagonal idealParacrystals.
Abstract: A detailed analysis is made of the statistics and diffraction by a general, finite, two-dimensional ideal paracrystal. The statistics of the diagonal chain through the ideal paracrystal are derived, and the special cases of square and hexagonal ideal paracrystals are considered. Expressions for the diffraction are derived and characteristics of diffraction patterns are discussed in terms of the different parameters of the model for square and hexagonal ideal paracrystals. The variation of peak widths with scattering angle along different directions in reciprocal space is examined.
TL;DR: It is shown how the coincidence site lattice theory can be applied to more complex ensembles of crystallites with the cubic crystal structure, including quadruple points, multiple junctions of grains and other multicrystal assemblies.
Abstract: It is shown how the coincidence site lattice theory, developed originally for grain boundaries and extended recently to triple junctions, can be applied to more complex ensembles of crystallites with the cubic crystal structure. These include quadruple points, multiple junctions of grains and other multicrystal assemblies. Application of the theory is demonstrated on hypothetical examples, which may help elucidate some practically important problems.
TL;DR: This study provides an insight into the nature of metastable modifications of crystal structures and the ways in which they are formed and indicates the existence of a critical bonding distance, above which interatomic interactions cannot be considered as bonding.
Abstract: Using theoretical simulations based on density functional theory within the generalized gradient approximation, a series of metastable phase transitions occurring in low-pressure Al2SiO5 polymorphs (andalusite and sillimanite) are predicted; similar results were obtained using semiclassical interatomic potentials within the ionic shell model. Soft lattice modes as well as related structural changes are analysed. For sillimanite, an isosymmetric phase transition at ca 35 GPa is predicted; an incommensurately modulated form of sillimanite can also be obtained at low temperatures and high pressures. The high-pressure isosymmetric phase contains five-coordinate Si and Al atoms. The origin of the fivefold coordination is discussed in detail. Andalusite was found to transform directly into an amorphous phase at ca 50 GPa. This study provides an insight into the nature of metastable modifications of crystal structures and the ways in which they are formed. Present results indicate the existence of a critical bonding distance, above which interatomic interactions cannot be considered as bonding. The critical distance for the Si—O bond is 2.25 A.
TL;DR: A review is presented of the symmetry groups of the single-wall nano- and microtubes considered in literature: BN, GaN, MS2, C, BC3, BC2N.
Abstract: Nanotubes have become attractive subjects in solid-state physics owing to their potential applications in nanotechnology. Their symmetry is one of the important tools in theoretical investigations. Here a review is presented of the symmetry groups of the single-wall nano- and microtubes considered in literature: BN, GaN, MS2, C, BC3, BC2N.
TL;DR: A theory is developed as a set of theorems establishing the relationships between the geometrical parameters of the grain-boundary and triple-junction CSLs and it is shown how the theory can be extended to an arbitrary crystal lattice.
Abstract: When three grain boundaries having misorientations generating coincidence site lattices (CSLs) meet at a triple junction, a common (triple-junction) CSL is formed. A theory is developed as a set of theorems establishing the relationships between the geometrical parameters of the grain-boundary and triple-junction CSLs. Application of the theory is demonstrated in detail for the case of the cubic crystal system. It is also shown how the theory can be extended to an arbitrary crystal lattice.
TL;DR: In fact, it is shown how ideal quasiperiodic long-range order and inflation symmetry allow for the existence of inclined net planes with small corrugation and reinforce the relation with the periodic average structures.
Abstract: It is generally assumed that decagonal quasicrystals show periodically arranged atomic layers only on net planes perpendicular to the tenfold axis and quasiperiodically arranged ones parallel to it. However, there also do exist only slightly puckered atomic layers that are periodically arranged and inclined to the tenfold axis. They coincide with the net planes of the periodic average structures of the decagonal phase and are related to the strongest Bragg reflections. Since they link quasiperiodic and periodic directions, inclined net planes may play a crucial role for growth and stabilization of decagonal quasicrystals. In fact, it is shown how ideal quasiperiodic long-range order and inflation symmetry allow for the existence of inclined net planes with small corrugation and reinforce the relation with the periodic average structures.
TL;DR: A closed-form analytical solution for the inversion of the integral equation relating small-angle scattering intensity distributions of two-phase systems to chord-length distributions is presented and offers an elegant way to investigate the impact of certain features, e.g. singularities, in the chord- length distribution or its higher-order derivatives on the scattering curve.
Abstract: A closed-form analytical solution for the inversion of the integral equation relating small-angle scattering intensity distributions of two-phase systems to chord-length distributions is presented. The result is generalized to arbitrary derivatives of higher order of the autocorrelation function and to arbitrary projections of the scattering intensity (including slit collimation). This inverse transformation offers an elegant way to investigate the impact of certain features, e.g. singularities, in the chord-length distribution or its higher-order derivatives on the scattering curve, e.g. oscillatory components in the asymptotic behavior at a large scattering vector. Several examples are discussed.
TL;DR: The atomic positions of the silicon carbide (SiC) polytypes 6H and 4H differ slightly from an ideal tetrahedron, so an unambiguous calculation of the refinement parameters from the absolute values of the structure factors of the 'quasiforbidden' reflections is not possible.
Abstract: The atomic positions of the silicon carbide (SiC) polytypes 6H and 4H differ slightly from an ideal tetrahedron. These small deviations can be investigated by X-ray diffraction of so-called `quasiforbidden' reflections, which are very sensitive with respect to the extremely small variations in the structure. Nevertheless, an unambiguous calculation of the refinement parameters from the absolute values of the structure factors of the `quasiforbidden' reflections is not possible. In the case of SiC-4H, there are two and, in the case of SiC-6H, six different structure models, which yield the same absolute values of the structure factors. In order to distinguish between these models, additional phase information about the measured reflections is needed. To achieve this, Renninger-scan (\psi-scan) profiles in the vicinity of three-beam cases are used. These experimentally measured \psi-scans are compared with theoretical calculated profiles for each model. Another method to distinguish the different models is to compare the bond lengths between atoms of the two polytypes, which have equivalent vicinities. For both SiC-4H and SiC-6H, an unambiguous determination of the structure refinement parameters was possible.
TL;DR: A list is provided here of Opechowski-Guccione symbols for the 1651 magnetic space-group types with their original definitions given independent of International Tables.
Abstract: The interpretation of Opechowski–Guccione symbols for magnetic space-group types is based on coordinate triplets given in the now superceded International Tables for X-ray Crystallography [(1952), Vol. 1, edited by N. F. M. Henry & K. Lonsdale. Birmingham: Kynoch Press]. Changes to coordinate triplets in International Tables for Crystallography [(1983), Vol. A, edited by Th. Hahn. Dordrecht: Kluwer Academic Publishers] lead to misinterpretations of these symbols. A list is provided here of Opechowski–Guccione symbols for the 1651 magnetic space-group types with their original definitions given independent of International Tables.
TL;DR: It is shown in this paper that a feature that has been observed in the diffuse scattering patterns of a wide variety of different materials - a diffuse 'ring' or 'doughnut'-shaped region of scattering - can be understood in terms of a simple model that is borrowed from the field of sol-gel science.
Abstract: It is shown in this paper that a feature that has been observed in the diffuse scattering patterns of a wide variety of different materials – a diffuse `ring' or `doughnut'-shaped region of scattering – can be understood in terms of a simple model that has been borrowed from the field of sol–gel science. In this, it is supposed that there is a balance between the local attractive forces that are trying to make a particular structure and a rather longer range repulsive force. In the present context, it is believed that this latter force has its origin in the strain that builds as the preferred local structure tries to fit into the average crystal lattice. Simple Monte Carlo (MC) computer simulations are described that demonstrate this principle for three example materials: cubic stabilized zirconia, the p-didecylbenzene/urea inclusion compound and the pure molecular compound 1,3-dibromo-2,5-diethyl-4,6-dimethylbenzene, C12H16Br2 (BEMB2).
TL;DR: Results are applied to several families of well known polytypic materials, those represented by the compounds SiC, CdI(2) and GaSe, and also the micas and kaolins, finding that there is a finite probability for the ground state to be degenerate and disordered.
Abstract: Recent work on discrete classical problems in one-dimensional statistical mechanics has shown that, given certain elementary symmetries, such problems may not have a periodic (crystalline) ground state, even in the absence of fine tuning of the couplings. Here these results are applied to several families of well known polytypic materials. The families studied are those represented by the compounds SiC, CdI2 and GaSe, and also the micas and kaolins. For all families but SiC, it is found that there is a finite probability for the ground state to be degenerate and disordered.
TL;DR: It is shown that additional Bragg reflections can appear exclusively owing to the local chirality associated with the left-right asymmetric environment of scattering atoms in non-magnetic crystals, and this mechanism works even for centrosymmetric crystals.
Abstract: It is shown that additional Bragg reflections can appear exclusively owing to the local chirality associated with the left-right asymmetric environment of scattering atoms in non-magnetic crystals. The structure amplitude of these reflections depends on the antisymmetric part of a third-rank tensor describing the spatial dispersion effects. It enhances for resonant near-edge scattering through a mixed multipole transition, which includes a dipole-quadrupole contribution. It is shown that this mechanism works even for centrosymmetric crystals, and some realistic examples are considered in detail (alpha-Fe2O3, LiNbO3 etc.). For instance, the interference between the dipole-quadrupole and quadrupole-quadrupole terms may be responsible for the threefold symmetry of the azimuthal dependence of the hhh, h = 2n + 1, reflections observed recently in hematite.
TL;DR: In this paper, the crystal structure of the metal-rich compound Ti45Se16 was determined from selected-area electron diffraction film data using a data set of quantified h0l electron microscopy intensities.
Abstract: The crystal structure of the metal-rich compound Ti45Se16 was redetermined from selected-area electron diffraction film data. The structure was solved by quasi-automatic direct methods using a data set of quantified h0l electron diffraction intensities. Improved atomic coordinates were obtained from a subsequent least-squares refinement on the basis of the kinematical approximation. The compound crystallizes in the monoclinic space group C2/m with lattice parameters a = 36.534, b = 3.453, c = 16.984 A, β = 91.73°. The structure contains 23 titanium and 8 selenium atoms per asymmetric part of the unit cell. The refined atomic coordinates agree on average within 0.18 A with the previously determined structure from high-resolution electron-microscopy images. The precision of the determined atomic coordinates obtained in this study is better than 0.05 A. The structure of Ti45Se16 is the eighth metal-rich structure that has been solved by direct methods from two-dimensional selected-area electron diffraction data using the quasi-kinematical approximation. The present investigation proves again that direct methods with electron diffraction data work extremely reliably provided that the structure in question is composed of elements of nearly equal scattering power and that data covering the most significant parts of the unit-cell transform up to atomic resolution are available. Moreover, a method was developed that allows the estimation of the average crystal thickness from the effective atomic potential in the refined structure.
TL;DR: The successful application of the newly developed image-plate neutron Laue diffractometer (LADI) at the Institut Laue-Langevin (ILL), Grenoble, France, for rapid hydrogen-bonding characterization is reported, illustrating that LADI is eminently suitable for rapid characterization of hydrogen- bonded structures by neutron diffraction.
Abstract: The successful application of the newly developed image-plate neutron Laue diffractometer (LADI) at the Institut Laue–Langevin (ILL), Grenoble, France, for rapid hydrogen-bonding characterization is reported. The case study concerns the promising non-linear optical material zinc (tris)thiourea sulfate (ZTS), which contains 30 atoms in the asymmetric unit and crystallizes in the orthorhombic space group, Pca21, a = 11.0616 (9), b = 7.7264 (6), c = 15.558 (1) A [T = 100.0 (1) K]. The results from a 12 h data collection from ZTS on LADI are compared with those obtained over 135 h using the monochromatic four-circle diffractometer D9 at the same reactor source with a crystal 13 times larger in volume. Both studies reveal the extensive hydrogen bonding and other close non-bonded contacts within the material. As expected, the results from D9 are more precise than those obtained from LADI; however, the bond geometry determined from the two experiments is the same within the larger estimated standard deviations. Furthermore, the conclusions drawn from the two studies separately regarding the nature of all supramolecular features are identical. This illustrates that LADI is eminently suitable for rapid characterization of hydrogen-bonded structures by neutron diffraction, with the gain in speed compared with traditional instrumentation being several orders of magnitude.
TL;DR: Atomic scattering factors for K-shell electron energy-loss spectroscopy (EELS) have been calculated for elements in the range Z = 6 (carbon) to Z = 50 (tin) and are presented in parameterized form so that accurate values of the scattering factors can be obtained.
Abstract: Atomic scattering factors for K-shell electron energy-loss spectroscopy (EELS) have been calculated for elements in the range Z = 6 (carbon) to Z = 50 (tin). The calculations are based on relativistic Hartree–Fock wave functions for the atomic bound states and Hartree–Slater wave functions for the continuum states. The results are presented in parameterized form so that accurate values of the scattering factors can be obtained for incident electron energies between 50 and 400 keV, collection semi-angles between 10 and 40 mrad, and energy windows between 25 and 100 eV. The parameterizations are for scattering vectors with magnitude s = \sin \theta / \lambda up to 2.5 A−1 (2\theta is the scattering angle and \lambda is the wavelength of the incident electrons).
TL;DR: In this article, the linear polarization of synchrotron radiation is explored as a tuning key for the strength of simultaneously diffracted X-ray waves in crystals, where the relative strength of the waves has been defined by the reflectivities of the Bragg reflections involved in each multiple diffraction case and it has limited the applicability of the multiple-diffraction phenomenon.
Abstract: In this work, the linear polarization of synchrotron radiation is explored as a tuning key for the strength of the simultaneously diffracted X-ray waves in crystals. The relative strength of the waves has been defined by the reflectivities of the Bragg reflections involved in each multiple-diffraction case and it has limited the applicability of the multiple-diffraction phenomenon. With a proper choice of the wavelength and the polarization direction of the incident synchrotron radiation, it is demonstrated how the intensity ratios of the simultaneously diffracted beams can be drastically changed.
TL;DR: In this paper, the Debye-Waller factors associated with the two principal directions are equal within the limits of experimental errors, and the energy of formation of vacancies (Ef) has been estimated from a semi-empirical relation between Ef and θ.
Abstract: Debye–Waller factors of five h.c.p. elements (Ti, Zr, Ru, Tm, Hf) have been determined from X-ray diffraction intensities. Within the limits of experimental errors, the Debye–Waller factors associated with the two principal directions are equal. The Debye temperatures (θM) have been evaluated. The energy of formation of vacancies (Ef) has been estimated from a semi-empirical relation between Ef and θ.