Structure determination from powder data using anomalous scattering: difference and partial, Patterson densities, and phases of structure factors

1997 ◽  
Vol 212 (7) ◽  
Author(s):  
K. Burger ◽  
W. Prandl ◽  
S. Doyle
Keyword(s):  
Structure Determination ◽  
Maximum Entropy Method ◽  
Algebraic Theory ◽  
Resonant Scattering ◽  
Entropy Method ◽  
Anomalous Scattering ◽  
Atom Type ◽  
X Ray ◽  
Structure Factors ◽  
Iron Garnet

AbstractFor structure determination from X-ray powder data, anomalous (resonant) scattering can be used to obtain difference Patterson and partial Patterson densities as well as phases of structure factors. Usually tuneable synchrotron radiation is used, and two or more powder patterns near and far the absorption edge of an atom type contained in the crystal are recorded.The algebraic theory together with some novel and efficient approximations is given in detail. Also symmetry restrictions, experimental and scaling procedures, and the use of the Maximum-Entropy method (MEM) are discussed. The application to the structure of an iron garnet FeFrom an MEM calculation of the electron-density, using the signed structure factors

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].

Electron-density distribution from X-ray powder data by use of profile fits and the maximum-entropy method

1990 ◽  
Vol 23 (6) ◽  
pp. 526-534 ◽  
Author(s):  
M. Sakata ◽  
R. Mori ◽  
S. Kumazawza ◽  
M. Takata ◽  
H. Toraya
Keyword(s):  
Density Distribution ◽  
Maximum Entropy ◽  
Electron Density ◽  
Electron Density Distribution ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Distribution Map ◽  
X Ray ◽  
Profile Decomposition ◽  
Structure Factors

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

scholarly journals Investigating anharmonicity and disorder in cadmium and zinc telluride

2014 ◽  
Vol 70 (a1) ◽  
pp. C1773-C1773
Author(s):  
Mattia Sist ◽  
Niels Bindzus ◽  
Espen Eikeland ◽  
Bo Iversen
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Gamma Ray ◽  
Lead Telluride ◽  
High Energy ◽  
Structural Features ◽  
Entropy Method ◽  
Anomalous Scattering ◽  
X Ray ◽  
Photoelectric Properties

CdTe and ZnTe are often referred to as II-VI semiconductors. Due to the structural and photoelectric properties and low-cost manufacturability, CdTe and ZnTe based thin films are used in the photovoltaic technology and in variety of electronic devices such as infrared, X-ray and gamma ray detectors (Eisen at al., 1998). The structure of another telluride, PbTe, has recently been reviewed and the emerging atomic disorder with temperature seems to have an indissoluble liaison with the high thermoelectric figure of merit of such promising material (Bozin et al., 2010). Deviations of the cation from its position in the ideal rock-salt structure have been probed by means of Maximum Entropy Method (MEM) calculations on Synchrotron powder X-ray diffraction data (SPXRD) (Kastbjerg et al., 2013). Motivated by the peculiar structural features in lead telluride, we investigate anharmonicity and disorder of the cations in both the zincblende structures, CdTe and ZnTe. High resolution SPXRD data at 100 K have been collected for both compounds. High energy radiation and minute capillaries have been used with the aim to minimize systematic errors on the data such as absorption and anomalous scattering. Accurate Rietveld refinements have been carried out in order to extract the best dataset of structure factors. Maximum Entropy Method calculations have hence been computed, providing the least-biased information deduction from experimental data. The disorder, anharmonicity and chemical bonding within the crystalline CdTe and ZnTe have been deeply investigated through the MEM densities and comparisons with the cation displacement in the structure of lead telluride have been established.

High Resolution X-Ray Powder Diffraction by the Combination of Synchrotron Radiation and Imaging Plate to Observe Electron Distribution by the Maximum Entropy Method

1991 ◽  
Vol 35 (A) ◽  
pp. 85-90 ◽  
Author(s):  
Masaki Takata ◽  
Manabu Yamada ◽  
Yoshiki Kubota ◽  
Makoto Sakata
Keyword(s):  
Maximum Entropy ◽  
Electron Distribution ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Imaging Plate ◽  
Ionic Crystals ◽  
X Ray ◽  
Structure Factors ◽  
Self Consistent ◽  
Voigt Function

AbstractA Debye-Scherrer camera (radius 572 mm) was designed for the use at the Photon Factory BL-6A2. It uses 4 pieces of the Imaging Plate to cover 0° ∼ 160° in 2θ. The profiles measured by the camera had 0.083° full width at half maximum (FWHM) and were rather symmetric compared with conventional X-ray source. The observed profiles were well represented by either the split Pearson VII or pseudo-Voigt function. In order to examine the performance of the new camera, the whole powder data of LiF was analyzed by the Maximum Entropy Method(MEM). The MEM analysis of LiF was successfully accomplished using 20 measured structure factors and gave R(Bragg) 0.25%. The density distribution obtained represented a characteristic feature of ionic crystals and was consistent with the theoretical result of the self-consistent LCAO method.

A model-independent maximum-entropy method for the inversion of small-angle X-ray diffraction patterns

1999 ◽  
Vol 32 (6) ◽  
pp. 1069-1083 ◽  
Author(s):  
J. A. Elliott ◽  
S. Hanna
Keyword(s):  
Maximum Entropy ◽  
Small Angle ◽  
Disordered Systems ◽  
Maximum Entropy Method ◽  
Structural Model ◽  
Entropy Method ◽  
X Ray Diffraction ◽  
X Ray ◽  
Model Independent ◽  
Diffraction Patterns

A model-independent maximum-entropy method is presented which will produce a structural model from small-angle X-ray diffraction data of disordered systems using no other prior information. In this respect, it differs from conventional maximum-entropy methods which assume the form of scattering entitiesa priori. The method is demonstrated using a number of different simulated diffraction patterns, and applied to real data obtained from perfluorinated ionomer membranes, in particular Nafion™, and a liquid crystalline copolymer of 1,4-oxybenzoate and 2,6-oxynaphthoate (B–N).

An Evaluation of Deconvolution Techniques in X-ray Profile Broadening Analysis and the Application of the Maximum Entropy Method to Alumina Data

1994 ◽  
Vol 38 ◽  
pp. 387-395 ◽  
Author(s):  
Walter Kalceff ◽  
Nicholas Armstrong ◽  
James P. Cline
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Profile Analysis ◽  
Domain Size ◽  
Entropy Method ◽  
X Ray Diffraction ◽  
Profile Function ◽  
Diffraction Profile ◽  
X Ray ◽  
Deconvolution Techniques

Abstract This paper reviews several procedures for the removal of instrumental contributions from measured x-ray diffraction profiles, including: direct convolution, unconstrained and constrained deconvolution, an iterative technique, and a maximum entropy method (MEM) which we have adapted to x-ray diffraction profile analysis. Decorevolutions using the maximum entropy approach were found to be the most robust with simulated profiles which included Poisson-distributed noise and uncertainties in the instrument profile function (IPF). The MEM procedure is illustrated by application to the analysis for domain size and microstrain carried out on the four calcined α-alumina candidate materials for Standard Reference Material (SRM) 676 (a quantitative analysis standard for I/Ic determinations), along with the certified material. Williamson-Hall plots of these data were problematic with respect to interpretation of the microstrain, indicating that the line profile standard, SRM 660 (LaB6), exhibits a small amount of strain broadening, particularly at high 2θ angle. The domain sizes for all but one of the test materials were much smaller than the crystallite (particle) size; indicating the presence of low angle grain boundaries.

Electron Density Distribution Obtained from X-Ray Powder Data by the Maximum Entropy Method

1991 ◽  
Vol 35 (A) ◽  
pp. 77-83 ◽  
Author(s):  
Makoto Sakata ◽  
Masaki Takata ◽  
Yoshiki Kubota ◽  
Tatsuya Uno ◽  
Shintaro Kuhazawa ◽  
...  
Keyword(s):  
Density Distribution ◽  
Maximum Entropy ◽  
Electron Density ◽  
Diffraction Data ◽  
Electron Density Distribution ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Nuclear Density ◽  
X Ray ◽  
Distribution Maps

AbstractThe electron density distribution maps for CaF2 and TiO2 (rutile) were obtained from profile fitting of powder diffraction data by a Maximum Entropy Method (MEM) analysis. The resultant electron density maps show clearly the nature of the chemical bonding. In order to interpret the results, the nuclear density distribution was also obtained for rutile from powder neutron diffraction data. In the electron density map for rutile obtained by HEM analysis from the X-ray data, both apical and equatorial bonding can be seen. On the other hand, the nuclear density of rutile Is very simple and shows the thermal vibration of nuclei.

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.

scholarly journals Nuclear Enhanced MEM Used to Analyze Local Distortions in Lead Chalcogenides

2014 ◽  
Vol 70 (a1) ◽  
pp. C105-C105
Author(s):  
Sebastian Christensen ◽  
Niels Bindzus ◽  
Mogens Christensen ◽  
Bo Brummerstedt Iversen
Keyword(s):  
Maximum Entropy ◽  
Diffraction Data ◽  
Thermoelectric Materials ◽  
Maximum Entropy Method ◽  
Functional Materials ◽  
Entropy Method ◽  
Green Energy ◽  
Lead Chalcogenides ◽  
X Ray ◽  
Local Distortions

We introduce a novel method for reconstructing nuclear density distributions (NDDs): Nuclear Enhanced X-ray Maximum Entropy Method (NEXMEM). NEXMEM offers an alternative route to experimental NDDs, exploiting the superior quality of synchrotron X-ray data compared to neutron data. The method was conceived to analyse local distortions in the thermoelectric lead chalcogenides, PbX (X = S, Se, Te). Thermoelectric materials are functional materials with the unique ability to interconvert heat and electricity, holding much promise for green energy solutions such as waste heat recovery. The extraordinary thermoelectric performance of binary lead chalcogenides has caused huge research activity, but the mechanisms governing their unexpected low thermal conductivity still remain a controversial topic. It has been proposed to result from giant anharmonic phonon scattering or from local fluctuating dipoles on the Pb site.[1,2] No macroscopic symmetry change are associated with these effects, rendering them invisible to conventional crystallographic techniques. For this reason PbX was until recently believed to adopt the ideal, undistorted rock-salt structure. In the present study, we investigate PbX using multi-temperature synchrotron powder X-ray diffraction data in combination with the maximum entropy method (MEM) and NEXMEM. In addition NEXMEM has been validated by testing against simulated powder diffraction data of PbTe with known displacements of Pb. The increased resolution of NEXMEM proved essential for resolving Pb-displacement of 0.2 Å in simulated data. The figure below shows Pb in the (100) plane for MEM, NEXMEM and the actual NDD of the test structure. Our findings outline the extent of disorder in lead chalcogenides, promoting our understanding of this class of high-performance thermoelectric materials. Furthermore we introduce NEXMEM which can be used for widespread characterization of subtle atomic features in crystals with unusual properties.

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