A new type of constraint in the maximum-entropy method using ambiguous phase information from anomalous-scattering powder data

1999 ◽  
Vol 55 (4) ◽  
pp. 719-728 ◽  
Author(s):  
K. Burger ◽  
W. Prandl
Keyword(s):  
Maximum Entropy ◽  
Powder Diffraction ◽  
Entropy Method ◽  
Anomalous Scattering ◽  
X Rays ◽  
Synchrotron Source ◽  
Structure Factors ◽  
New Type ◽  
Types Of Information

Anomalous scattering of X-rays at a synchrotron source can be used for the ab initio structure determination of unknown crystal structures using only powder diffraction data. For noncentrosymmetric crystals, the phases of structure factors can only be determined with a remaining ambiguity, when one chemical element is used as resonant scatterer. A corresponding additional constraint function has been built into an enhanced version of the program MEED, so that now all types of information gained from an anomalous-scattering powder diffraction experiment can be used in a maximum-entropy calculation of the electron-density distribution: phased reflections, unphased reflections, intensities of groups of overlapping reflections, and now also reflections with a remaining ambiguity in the phase. This is important for practical use, since a lot of information is already lost in the powder diagram compared with single-crystal datasets and it is essential to use all remaining information. The new constraint is demonstrated with the structure of Cu5Zn8.

scholarly journals Synchrotron and Laboratory Studies Utilizing a New Powder Diffraction Technique

1992 ◽  
Vol 36 ◽  
pp. 653-661 ◽  
Author(s):  
G. S. Knapp ◽  
M. A. Beno ◽  
G. Jennings ◽  
M. Engbretson ◽  
M. Ramanathan
Keyword(s):  
Powder Diffraction ◽  
Sample Surface ◽  
X Rays ◽  
High Count ◽  
Synchrotron Source ◽  
Bent Crystal ◽  
Capillary Sample ◽  
Order Of Magnitude ◽  
New Type ◽  
Large Improvement

AbstractWe have developed a new type of powder diffractometer. The diffractometer has the potential of both high count rates and very high resolution when used at a synchrotron source. The laboratory based instrument can achieve an order of magnitude improvement in count rate over existing methods with proper optics. The method uses a focusing diffracted beam monochromator in combination with a multichannel detector. The incident x-rays fall on a flat plate or capillary sample and are intercepted by a bent focusing monochromator which has the focus of the bend at the sample surface. The powder diffraction lines emerging from the bent crystal monochromator are detected by a linear or 2-dimensional detector. This allows us to eliminate the background from fluorescence or other scattering and to take data over a range of 3° to 4° instead of one angle at a time thereby providing a large improvement over conventional diffractometers.

Transient electron density maps from femtosecond x-ray powder diffraction

2014 ◽  
Vol 70 (a1) ◽  
pp. C100-C100
Author(s):  
Vincent Juvé ◽  
Flavio Zamponi ◽  
Marcel Holtz ◽  
Michael Woerner ◽  
Thomas Elsaesser
Keyword(s):  
Charge Transfer ◽  
Electron Density ◽  
Powder Diffraction ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
X Rays ◽  
X Ray ◽  
Density Maps ◽  
Structure Factors ◽  
Diffraction Angle

Ultrashort hard x-ray pulses are sensitive probes of structural dynamics on the picometer length and femtosecond time scales of electronic and atomic motions. Using short hard x-ray pulses as probe in a pump-probe scheme allow to do femtosecond x-ray diffraction experiments [1], which provide transient electron density maps at a femtosecond timescale with a sub-angstrom spatial resolution. In a typical femtosecond x-ray powder diffraction experiment many Debye-Scherrer rings, up to a maximum diffraction angle 2θmax, are recorded for each time delay between the optical pump and the hard x-ray probe. From the diffraction pattern, the change of the diffracted intensity of each rings are monitored. The interference of diffracted x-rays from the many unexcited cells, with known structure factors coming from steady-state measurement, and diffracted x-rays from the few excited cells allows for the detection of the transients structure factors. Problems could arise if the 3D-Fourier transform is directly used because of the abrupt end of the collected information in the reciprocal space (maximum diffraction angle 2θmax). In order to overcome this problem, the Maximum Entropy Method is apply to the data and the transient electron density maps are derived. We apply the femtosecond x-ray powder diffraction technique and the Maximum Entropy Method to study the induced transient polarization by high optical fields on ionic crystals. Such polarizations are connected to a spatial redistribution of electronic charge, which corresponds to a charge transfer between the two ionic compounds [2]. While the charge transfer originates from the anion to the cation in the LiBH and the NaBH4, the LiH exhibits a peculiar behavior: the charge transfer occurs from the cation to the anion. As result from comparison with calculations in the COHSEX framework, this behavior is due to the strong electronic correlations in the LiH [3].

scholarly journals Determination of the time origin by 
the maximum entropy method in 
time-domain terahertz emission spectroscopy

2010 ◽  
Vol 18 (15) ◽  
pp. 15853 ◽  
Author(s):  
Takeya Unuma ◽  
Yusuke Ino ◽  
Makoto Kuwata-Gonokami ◽  
Erik M. Vartiainen ◽  
Kai-Erik Peiponen ◽  
...  
Keyword(s):  
Maximum Entropy ◽  
Time Domain ◽  
Emission Spectroscopy ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Terahertz Emission ◽  
Terahertz Emission Spectroscopy ◽  
Time Origin

X-Ray Powder Diffraction (XRPD)

2016 ◽  
pp. 326-341 ◽  
Author(s):  
Robert Heimann
Keyword(s):  
Powder Diffraction ◽  
X Rays ◽  
Powder Diffraction File ◽  
Thin Beam ◽  
Archaeological Ceramics ◽  
X Ray ◽  
Analytical Technique ◽  
Cell Dimensions ◽  
Unit Cell Dimensions

X-ray powder diffraction (XRPD) is an important tool to determine the phase composition of archaeological ceramics. In principle, a thin beam of X-rays incident to a lattice plane of crystalline matter is scattered in specific directions and angles depending on the distances of atoms. This allows determination of characteristic unit cell dimensions and serves to unambiguously identify crystalline phases in the ceramics. In this chapter, generation of X-rays and the theory of diffraction will be briefly discussed as well as equipment, focusing conditions, and sample preparation procedures of common XRPD methods. The X-ray pattern obtained will provide an analytical fingerprint that can be matched against the Powder Diffraction File of the International Centre for Diffraction Data. Examples will be given of application of this analytical technique to archaeological clays and ceramics.

scholarly journals Improving the accuracy for Photosystem II and other XFEL structures

2014 ◽  
Vol 70 (a1) ◽  
pp. C571-C571
Author(s):  
Nicholas Sauter ◽  
Aaron Brewster ◽  
Johan Hattne ◽  
Muhamed Amin ◽  
Jan Kern ◽  
...  
Keyword(s):  
Photosystem Ii ◽  
De Novo ◽  
Anomalous Scattering ◽  
Separate Determination ◽  
Structure Factors ◽  
Detector Geometry ◽  
Small Structure ◽  
Image Pixels

Femtosecond-scale XFEL pulses can produce diffraction free from radiation damage, under functional physiological conditions where reaction dynamics can be studied for systems such as photosystem II. However, it has been extremely difficult to derive accurate structure factors from the data since every shot is a still exposure from a distinct specimen. Accuracy can be improved by software methods implemented in the program cctbx.xfel, including optimal indexing and retention of data from multiple lattices, and separate determination of the resolution cutoff for individual lattices. Various techniques can produce well-conforming descriptions of the Bragg spot shape and crystal mosaicity, enabled in part by sub-pixel characterization of the detector geometry. By carefully discriminating between image pixels known to contain diffraction signal and the surrounding pixels containing only background noise, and by extending postrefinement techniques that lead to a better crystal orientation, we derive accurate structure factors with substantially fewer crystal specimen exposures. It is hoped that these developments will make it easier to measure small structure factor differences, such as those from anomalous scattering that will enable the de novo determination of macromolecular structure.

Determination of the Cation Distribution in NiFe2(PO4)2 using Resonant X-ray and Neutron Powder Diffraction

1995 ◽  
Vol 28 (5) ◽  
pp. 494-502 ◽  
Author(s):  
J. K. Warner ◽  
A. K. Cheetham ◽  
D. E. Cox
Keyword(s):  
Powder Diffraction ◽  
National Laboratory ◽  
Time Of Flight ◽  
Brookhaven National Laboratory ◽  
Neutron Powder Diffraction ◽  
Anomalous Scattering ◽  
Edge Structure ◽  
X Ray ◽  
Scattering Correction

The distribution of divalent iron and nickel over two metal sites of differing coordination geometry in NiFe2(PO4)2, sarcopside, has been investigated by resonant X-ray and time-of-flight neutron powder diffraction. To assess the reproducibility of the X-ray technique, data have been collected from instruments X7A at Brookhaven National Laboratory and 8.3 at the Synchrotron Radiation Source, Daresbury Laboratory, England, using wavelengths λ X1 = 1.7437 (3) Å and λ X2 = 1.7434 (1) Å, respectively, close to the Fe2+ K edge determined by X-ray absorption near-edge structure. The real part of the anomalous-scattering correction for iron at each energy, f′(Fe) X1 = −7.81 (9) and f′(Fe) X2 = −10.16 (6), was determined experimentally by diffraction from Fe3(PO4)2 under identical conditions. Occupancies obtained for iron at the M(1) site were found to be M(1) X1 = 0.366 (6) and M(1) X2 = 0.376 (3), compared with M(1) N = 0.26 (15) from time-of-flight neutron powder diffraction.

Charge density study with the Maximum Entropy Method on model data of silicon. A search for non-nuclear attractors

1996 ◽  
Vol 74 (6) ◽  
pp. 1054-1058 ◽  
Author(s):  
R.Y. de Vries ◽  
W.J. Briels ◽  
D. Fell ◽  
G. te Velde ◽  
E.J. Baerends
Keyword(s):  
Charge Density ◽  
Maximum Entropy ◽  
Density Functional ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
X Ray Diffraction ◽  
Functional Theory ◽  
Structure Factors ◽  
The Density Functional Theory ◽  
Structure Calculations

In 1990 Sakata and Sato applied the maximum entropy method (MEM) to a set of structure factors measured earlier by Saka and Kato with the Pendellösung method. They found the presence of non-nuclear attractors, i.e., maxima in the density between two bonded atoms. We applied the MEM to a limited set of Fourier data calculated from a known electron density distribution (EDD) of silicon. The EDD of silicon was calculated with the program ADF-BAND. This program performs electronic structure calculations, including periodicity, based on the density functional theory of Hohenberg and Kohn. No non-nuclear attractor between two bonded silicon atoms was observed in this density. Structure factors were calculated from this density and the same set of structure factors that was measured by Saka and Kato was used in the MEM analysis. The EDD obtained with the MEM shows the same non-nuclear attractors that were later obtained by Sakata and Sato. This means that the non-nuclear attractors in silicon are really an artefact of the MEM. Key words: Maximum Entropy Method, non-nuclear attractors, charge density. X-ray diffraction.

Sign in / Sign up

Export Citation Format

Share Document