Modulation functions of incommensurately modulated Cr2P2O7 studied by the maximum entropy method (MEM)

2010 ◽  
Vol 66 (2) ◽  
pp. 130-140 ◽  
Author(s):  
Liang Li ◽  
Andreas Schönleber ◽  
Sander van Smaalen
Keyword(s):  
Maximum Entropy ◽  
Diffraction Data ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Chromium Atom ◽  
Structure Model ◽  
X Ray Diffraction ◽  
Acta Cryst ◽  
X Ray

The maximum entropy method (MEM) has been used to determine electron density in superspace of incommensurately modulated chromium pyrophosphate from X-ray diffraction data measured by Palatinus et al. [(2006), Acta Cryst. B62, 556–566]. Chromium pyrophosphate, Cr2P2O7, contains ordered regions (83% of the volume) and regions with disorder. Analysis of the MEM density has allowed the determination of the displacive modulation functions within ordered regions. The disordered regions can be described as the alternate occupation of two conformations of the pyrophosphate group and two positions of the chromium atom, with occupational probabilities that depend continuously on the phase of modulation t. A structure model based on the interpretation of the MEM density provides a fit to the diffraction data of the same quality as the model given by Palatinus et al. (2006). The failure to find a model that better fits the data is attributed to the intrinsic inaccuracy of ∼ 0.01 Å for positions derived from the MEM and to the difficulties in constructing an appropriate model for the anharmonic ADPs and their modulation functions from electron densities.

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.

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.

scholarly journals Application of maximum-entropy electrostatic potential in Materials Science.

2014 ◽  
Vol 70 (a1) ◽  
pp. C101-C101
Author(s):  
Eiji Nishibori
Keyword(s):  
Maximum Entropy ◽  
Electrostatic Potential ◽  
Diffraction Data ◽  
Materials Science ◽  
Structural Information ◽  
Entropy Method ◽  
Atomic Scale ◽  
X Ray Diffraction ◽  
X Ray ◽  
Adsorption Sites

Charge density (CD) studies by Maximum Entropy Method (MEM) (Sakata & Sato, 1990) from x-ray diffraction data have been widely applied to solve problems and questions in materials science during past two decades. Encapsulations of metal atoms (Takata et al, 1995), gas molecules, as well as protein molecules in the materials have been visualized as MEM CDs. The MEM CD technique is now regarded as a sophisticated technique for visualization in atomic scale. Electrostatic potential (EP) and electric field (EF) from x-ray diffraction data using MEM have been developed in 2006 (Tanaka et al, 2006). The EP & EF successfully applied to ferroelectric material PbTiO3 and a charge ordered manganite system. The method has huge potential in materials science since interaction in the non-atomic region can be visualized experimentally. One of the promising target for EP & EF analysis is host-guest systems, such as porous coordination polymers (PCPs), zeolites, clathrates as well as endohedral metallofullerenes[3]. In the case of host-guest systems, the guest atom(s) or molecule(s) are located in spatially wider sites in comparison to other type of materials. Therefore the detailed structural information in the spatially wider sites is one of the most important issues. In the present study, I present an application of MEM EP & EF analysis to host-guest related system, icosahedral B12 cluster materials and hydrogen adsorbed PCP. The EP studies clearly visualize doping sites in B12 based superconductor and adsorption sites in PCP. The EF enables us to estimate quantitative interaction from host to guest. The quantitative evaluation really bridges between experiment and theory in materials science.

scholarly journals Characterization of Local Distortions in Thermoelectric Lead Chalcogenides

2014 ◽  
Vol 70 (a1) ◽  
pp. C106-C106
Author(s):  
Niels Bindzus ◽  
Sebastian Christensen ◽  
Mogens Christensen ◽  
Bo Iversen
Keyword(s):  
Neutron Diffraction ◽  
Maximum Entropy ◽  
Diffraction Data ◽  
Thermoelectric Materials ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Neutron Diffraction Data ◽  
Lead Chalcogenides ◽  
X Ray

Thermoelectric materials are functional materials with the unique ability to interconvert heat and electricity, holding much promise for green energy solutions such as efficient 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, emerging with temperature 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 lead chalcogenides were until recently believed to adopt the ideal, undistorted rock-salt structure. In the present study, we probe the peculiar structural features in PbX (X = S, Se, Te) using multi-temperature synchrotron powder X-ray diffraction data in combination with the maximum entropy method. Distorted atoms are detected and quantified by refinement of anharmonic probability density functions. The charge density analysis is complemented by nuclear density distributions (NDDs) reconstructed from neutron diffraction data and by a novel method: 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 diffraction data. The increased atomic resolution introduced by NEXMEM proved essential for resolving atomic distortions, see figure below showing Pb in the (100) plane. Our findings outline the extent of disorder and anharmonicity in binary lead chalcogenides, promoting our fundamental understanding of this class of high-performance thermoelectric materials. The applied approach can be used in general, opening up for widespread characterization of subtle features in crystals with unusual properties.

Sign in / Sign up

Export Citation Format

Share Document