Multipole electron densities and atomic displacement parameters in urea from accurate powder X-ray diffraction

2019 ◽  
Vol 75 (4) ◽  
pp. 600-609 ◽  
Author(s):  
Bjarke Svane ◽  
Kasper Tolborg ◽  
Lasse Rabøl Jørgensen ◽  
Martin Roelsgaard ◽  
Mads Ry Vogel Jørgensen ◽  
...  
Keyword(s):  
Electron Density ◽  
Molecular System ◽  
Atomic Displacement ◽  
High Symmetry ◽  
X Ray Diffraction ◽  
High Quality ◽  
Acta Cryst ◽  
X Ray ◽  
Density Determination ◽  
Structure Factors

Electron density determination based on structure factors obtained through powder X-ray diffraction has so far been limited to high-symmetry inorganic solids. This limit is challenged by determining high-quality structure factors for crystalline urea using a bespoke vacuum diffractometer with imaging plates. This allows the collection of data of sufficient quality to model the electron density of a molecular system using the multipole method. The structure factors, refined parameters as well as chemical bonding features are compared with results from the high-quality synchrotron single-crystal study by Birkedalet al.[Acta Cryst.(2004), A60, 371–381] demonstrating that powder X-ray diffraction potentially provides a viable alternative for electron density determination in simple molecular crystals where high-quality single crystals are not available.

Accurate charge densities from powder X-ray diffraction – a new version of the Aarhus vacuum imaging-plate diffractometer

2017 ◽  
Vol 73 (4) ◽  
pp. 521-530 ◽  
Author(s):  
Kasper Tolborg ◽  
Mads R. V. Jørgensen ◽  
Sebastian Christensen ◽  
Hidetaka Kasai ◽  
Jacob Becker ◽  
...  
Keyword(s):  
Electron Density ◽  
High Energy ◽  
Imaging Plate ◽  
High Symmetry ◽  
X Rays ◽  
X Ray Diffraction ◽  
Core Electron ◽  
X Ray ◽  
Peak Broadening ◽  
Structure Factors

In recent years powder X-ray diffraction has proven to be a valuable alternative to single-crystal X-ray diffraction for determining electron-density distributions in high-symmetry inorganic materials, including subtle deformation in the core electron density. This was made possible by performing diffraction measurements in vacuum using high-energy X-rays at a synchrotron-radiation facility. Here we present a new version of our custom-built in-vacuum powder diffractometer with the sample-to-detector distance increased by a factor of four. In practice this is found to give a reduction in instrumental peak broadening by approximately a factor of three and a large improvement in signal-to-background ratio compared to the previous instrument. Structure factors of silicon at room temperature are extracted using a combined multipole–Rietveld procedure and compared withab initiocalculations and the results from the previous diffractometer. Despite some remaining issues regarding peak asymmetry, the new diffractometer yields structure factors of comparable accuracy to the previous diffractometer at low angles and improved accuracy at high angles. The high quality of the structure factors is further assessed by modelling of core electron deformation with results in good agreement with previous investigations.

scholarly journals Crystallographic features of ammonium fluoroelpasolites: dynamic orientational disorder in crystals of (NH4)3HfF7 and (NH4)3Ti(O2)F5

2017 ◽  
Vol 73 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Anatoly A. Udovenko ◽  
Alexander A. Karabtsov ◽  
Natalia M. Laptash
Keyword(s):  
Single Crystal ◽  
Electron Density ◽  
Diffraction Data ◽  
Central Atom ◽  
X Ray Diffraction ◽  
Dynamic Nature ◽  
Orientational Disorder ◽  
High Quality ◽  
Structural Units ◽  
X Ray

A classical elpasolite-type structure is considered with respect to dynamically disordered ammonium fluoro-(oxofluoro-)metallates. Single-crystal X-ray diffraction data from high quality (NH4)3HfF7 and (NH4)3Ti(O2)F5 samples enabled the refinement of the ligand and cationic positions in the cubic Fm \bar 3 m (Z = 4) structure. Electron-density atomic profiles show that the ligand atoms are distributed in a mixed (split) position instead of 24e. One of the ammonium groups is disordered near 8c so that its central atom (N1) forms a tetrahedron with vertexes in 32f. However, a center of another group (N2) remains in the 4b site, whereas its H atoms (H2) occupy the 96k positions instead of 24e and, together with the H3 atom in the 32f position, they form eight spatial orientations of the ammonium group. It is a common feature of all ammonium fluoroelpasolites with orientational disorder of structural units of a dynamic nature.

scholarly journals Estimating the structure factors in X-ray diffraction

2018 ◽  
Vol 74 (5) ◽  
pp. 481-498 ◽  
Author(s):  
Paul F. Fewster
Keyword(s):  
Diffraction Theory ◽  
Bragg Angle ◽  
Enhancement Effect ◽  
Diffraction Effect ◽  
X Ray Diffraction ◽  
Acta Cryst ◽  
X Ray ◽  
Background Removal ◽  
Structure Factors ◽  
Path Lengths

This article takes the concepts of the `new diffraction theory' [Fewster (2014). Acta Cryst. A70, 257–282] and examines the implications for the interpretation of experimental results and the estimation of structure factors. Further experimental evidence is included to justify the conclusions in the theory, showing that the residual intensity at twice the Bragg angle is a diffraction effect and not associated with the crystal shape. This `enhancement' effect is independent of whether kinematical or dynamical theories are applied and can lead to a clearer understanding of how the dynamical effects are suppressed in imperfect crystals. By applying the idea that the higher-order peaks are due to path lengths of nλ, it is shown that `systematically absent' reflections in the conventional theory may not be absent. Because this new theory considers the intensity to be more distributed, it suggests that the entire structure factor can be difficult to capture by experiment. This article suggests some routes to achieve a good approximation of the structure factors for typical methods of data collection. Any measurement of intensity with background removal will exclude some of the distributed intensity, again leading to an underestimate of the structure factors, and therefore the missing intensity needs to be estimated.

Synchrotron X-ray Imaging of the Electron Density in RFeO3 (R = Y, Ho) Using an APD Detector

1998 ◽  
Vol 5 (5) ◽  
pp. 1309-1316 ◽  
Author(s):  
Victor A. Streltsov ◽  
Nobuo Ishizawa ◽  
Shunji Kishimoto
Keyword(s):  
Electron Density ◽  
High Speed ◽  
Magnetic Phase ◽  
Avalanche Photodiode ◽  
Magnetic Interactions ◽  
Magnetic Phase Transitions ◽  
High Symmetry ◽  
X Ray ◽  
X Ray Imaging ◽  
Structure Factors

Structure factors for small hydrothermally grown yttrium and holmium orthoferrites, RFeO3 (R = Y, Ho), were measured with focused synchrotron radiation at wavelengths of 0.70 and 0.84 Å using both scintillation and high-speed avalanche photodiode (APD) detectors. Resulting APD Δρ images showed striking correlations between aspherical electron densities around Fe and rare-earth metals. Approximate high symmetry in the Δρ images indicates that cations deform the electron density far more strongly than the O atoms. The Ho—Fe magnetic interactions appear to affect the electron density distribution of the Fe atoms and the magnetic phase transitions. Space group Pnma, orthorhombic, YFeO3 (APD): M r = 192.76, a = 5.5931 (3), b = 7.6102 (4), c = 5.2806 (3) Å, V = 224.77 (2) Å3, Z = 4, D x = 5.695 Mg m−3, μ0.84 = 15.56 mm−1, F(000) = 356, T = 293 K, R = 0.045, wR = 0.073, S = 4.83 (9) for 1282 unique reflections; HoFeO3 (APD): M r = 268.78, a = 5.5922 (3), b = 7.6157 (5), c = 5.2798 (3) Å, V = 224.86 (2) Å3, Z = 4, D x = 7.939 Mg m−3, μ0.84 = 61.98 mm−1, F(000) = 356, T = 293 K, R = 0.036, wR = 0.037, S = 3.07 (6) for 1284 unique reflections.

Li+/Na+ β-alumina: a combined single-crystal neutron and X-ray diffraction study. Erratum

1997 ◽  
Vol 53 (5) ◽  
pp. 849-849
Author(s):  
K. Edström ◽  
T. Gustafsson ◽  
J. O. Thomas ◽  
G. C. Farrington
Keyword(s):  
Single Crystal ◽  
Diffraction Study ◽  
X Ray Diffraction ◽  
International Union ◽  
Acta Cryst ◽  
X Ray ◽  
Structure Factors ◽  
Anisotropic Displacement Parameters ◽  
Atomic Coordinates

Lists of atomic coordinates, anisotropic displacement parameters and structure factors have been deposited with the IUCr (Reference: AB0365) for this article [Edström, Gustafsson, Thomas & Farrington, Acta Cryst. B53, 631–638]. Copies may be obtained through The Managing Editor, International Union of Crystallography, 5 Abbey Square, Chester CH1 2HU, England.

Electron density study of urea using TDS-corrected X-ray diffraction data: quantitative comparison of experimental and theoretical results

1999 ◽  
Vol 55 (1) ◽  
pp. 45-54 ◽  
Author(s):  
Valery Zavodnik ◽  
Adam Stash ◽  
Vladimir Tsirelson ◽  
Roelof de Vries ◽  
Dirk Feil
Keyword(s):  
Density Functional Theory ◽  
Electron Density ◽  
Density Functional ◽  
X Ray Diffraction ◽  
Functional Theory ◽  
X Ray ◽  
Hartree Fock ◽  
Deformation Density ◽  
Structure Factors ◽  
Theoretical Results

The electron-density distribution in urea, CO(NH2)2, was studied by high-precision single-crystal X-ray diffraction analysis at 148 (1) K. An experimental correction for TDS was applied to the X-ray intensities. R merge(F 2) = 0.015. The displacement parameters agree quite well with results from neutron diffraction. The deformation density was obtained by refinement of 145 unique low-order reflections with the Hansen & Coppens [Acta Cryst. (1978), A34, 909–921] multipole model, resulting in R = 0.008, wR = 0.011 and S = 1.09. Orbital calculations were carried out applying different potentials to account for correlation and exchange: Hartree–Fock (HF), density-functional theory/local density approximation (DFT/LDA) and density-functional theory/generalized gradient approximation (DFT/GGA). Extensive comparisons of the deformation densities and structure factors were made between the results of the various calculations and the outcome of the refinement. The agreement between the experimental and theoretical results is excellent, judged by the deformation density and the structure factors [wR(HF) = 0.023, wR(DFT) = 0.019] and fair with respect to the results of a topological analysis. Density-functional calculations seem to yield slightly better results than Hartree–Fock calculations.

A synchrotron X-ray study of the electron density in SmFeO3

1996 ◽  
Vol 52 (3) ◽  
pp. 406-413 ◽  
Author(s):  
E. N. Maslen ◽  
V. A. Streltsov ◽  
N. Ishizawa
Keyword(s):  
Synchrotron Radiation ◽  
Electron Density ◽  
Magnetic Ordering ◽  
High Symmetry ◽  
Obvious Effect ◽  
Spin Configuration ◽  
Space Group ◽  
X Ray ◽  
Structure Factors ◽  
Low Symmetry

Structure factors for small, hydrothermally grown samarium orthoferrite, SmFeO3, were measured with focused λ = 0.7 Å synchrotron radiation. Approximate high symmetry in the Δρ images indicates that cations deform the electron density far more strongly than the O atoms. The most obvious effect is on distribution of the Fe atoms. The influence of the nearest low-symmetry (Cs ) O coordination on the electron density of the Sm cation is weak by comparison with that of the Sm–Fe interactions, as is illustrated by the high symmetry of the Δρ map near the Sm atom. The Sm–Fe interactions appear to affect the magnetic ordering and spin configuration of the Fe atoms. Space group Pnma, orthorhombic, Mr = 254.20, a = 5.6001 (3), b = 7.7060 (7), c = 5.3995 (6) Å, V = 233.01 (4) Å3, Z = 4, Dx = 7.246 Mg m−3, μ 0.7 = 28.5 mm−1, F(000) = 448, T = 293 K, R = 0.017, wR = 0.021, S = 3.83 (8) for 1329 unique reflections.

Electron density and electrostatic potential of KNiF3: multipole, orbital and topological analyses of vacuum-camera-imaging plate and four-circle diffractometer data

1999 ◽  
Vol 55 (6) ◽  
pp. 923-930 ◽  
Author(s):  
Yury Ivanov ◽  
Elizabeth A. Zhurova ◽  
Vladimir V. Zhurov ◽  
Kiyoaki Tanaka ◽  
Vladimir Tsirelson
Keyword(s):  
Electron Density ◽  
Electrostatic Potential ◽  
Atomic Displacement ◽  
Imaging Plate ◽  
X Ray Diffraction ◽  
X Ray ◽  
Camera Imaging ◽  
Model Treatment ◽  
Atomic Displacement Parameters ◽  
Good Agreement

The electron density and electrostatic potential of KNiF3, nickel potassium trifluoride, were studied using multipole and orbital model treatment of the precision X-ray diffraction data measured by vacuum-camera-imaging plate and four-circle diffractometer methods. Different experimental methods lead to similar multipole and atomic displacement parameters and to qualitatively the same electron densities. Good agreement was also achieved for the Laplacians of the electron density and the electrostatic potentials. Some pitfalls of the vacuum-camera-imaging plate method that could be improved are discussed.

scholarly journals Single Particle Study by X-Ray Diffraction: Crystallographic Approach

2019 ◽  
Vol 14 (2) ◽  
pp. 500-516 ◽  
Author(s):  
V.Y. Lunin ◽  
N.L. Lunina ◽  
T.E. Petrova
Keyword(s):  
Density Distribution ◽  
Diffraction Pattern ◽  
Electron Density ◽  
Single Particle ◽  
Electron Density Distribution ◽  
Crystal Form ◽  
X Ray Diffraction ◽  
X Ray ◽  
Standard Problem ◽  
Structure Factors

An increase in the power of X-ray sources, in particular, the commissioning of X-ray free electron lasers, opens up the possibility of recording the diffraction by single macromolecular biological particles. These opportunities open the way to weakening, and, ideally, removal, of the main limitation of X-ray structure analysis, namely, the need to prepare the sample in the single-crystal form. However, the possibility of the practical recording of diffraction by a single particle is currently limited to a very low-resolution zone, what is one of the main obstacles in the development of this approach. This paper discusses the similarities and differences in the study of crystal samples and single particles. It is shown that the problem of the determination of the structure of a single particle can be formulated as a standard problem of biological crystallography, namely, as the problem of retrieval the electron density distribution in some unit cell from the magnitudes of its Fourier coefficients. This makes it possible to apply the entire range of the methods of biological crystallography to the study of isolated particles. At the same time, the possibility of recording continuous diffraction pattern for a single particle (as opposed to a discrete set of Bragg reflections in the case of a crystal) significantly increases the amount of information derived from the experiment. The analytical properties of the continuous diffraction pattern create a potential opportunity both to restore the structure factors phases (lost in the diffraction experiment), and to extrapolate the experimentally observed pattern onto a wider area, which allows to increase the resolution of Fourier syntheses for the electron density distribution.

scholarly journals Redetermination of the crystal structure of R 5Si4 (R = Pr, Nd) from single-crystal X-ray diffraction data

2020 ◽  
Vol 76 (4) ◽  
pp. 510-513
Author(s):  
Kaori Yokota ◽  
Ryuta Watanuki ◽  
Miki Nakashima ◽  
Masatomo Uehara ◽  
Jun Gouchi ◽  
...  
Keyword(s):  
Single Crystal ◽  
Diffraction Data ◽  
Three Dimensional ◽  
Atomic Displacement ◽  
Crystal Data ◽  
X Ray Diffraction ◽  
Acta Cryst ◽  
X Ray ◽  
Atomic Displacement Parameters ◽  
First Time

The crystal structures of praseodymium silicide (5/4), Pr5Si4, and neodymium silicide (5/4), Nd5Si4, were redetermined using high-quality single-crystal X-ray diffraction data. The previous structure reports of Pr5Si4 were only based on powder X-ray diffraction data [Smith et al. (1967). Acta Cryst. 22 940–943; Yang et al. (2002b). J. Alloys Compd. 339, 189–194; Yang et al., (2003). J. Alloys Compd. 263, 146–153]. On the other hand, the structure of Nd5Si4 has been determined from powder data [neutron; Cadogan et al., (2002). J. Phys. Condens. Matter, 14, 7191–7200] and X-ray [Smith et al. (1967). Acta Cryst. 22 940–943; Yang et al. (2002b). J. Alloys Compd. 339, 189–194; Yang et al., (2003). J. Alloys Compd. 263, 146–153] and single-crystal data with isotropic atomic displacement parameters [Roger et al., (2006). J. Alloys Compd. 415, 73–84]. In addition, the anisotropic atomic displacement parameters for all atomic sites have been determined for the first time. These compounds are confirmed to have the tetragonal Zr5Si4-type structure (space group: P41212), as reported previously (Smith et al., 1967). The structure is built up by distorted body-centered cubes consisting of Pr(Nd) atoms, which are linked to each other by edge-sharing to form a three-dimensional framework. This framework delimits zigzag channels in which the silicon dimers are situated.

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