Nondestructive Surface Depth Profiles from Angle-Resolved X-ray Photoelectron Spectroscopy Data Using the Maximum Entropy Method. I. A New Protocol

2009 ◽  
Vol 113 (51) ◽  
pp. 21328-21337 ◽  
Author(s):  
M. Andrea Scorciapino ◽  
Gabriele Navarra ◽  
Bernhard Elsener ◽  
Antonella Rossi
Keyword(s):  
Maximum Entropy ◽  
Photoelectron Spectroscopy ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Spectroscopy Data ◽  
X Ray ◽  
Depth Profiles

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 Applications of a Bayesian Based Maximum Entropy Method to Energy Dispersive X-ray Spectra

2005 ◽  
Vol 54 (4) ◽  
pp. 238-244
Author(s):  
Takao SHINKAWA ◽  
Natuko NAKAMURA ◽  
Hiroshi KATO ◽  
Kazuyoshi SHIBUYA ◽  
Munetaka NAKATA
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Energy Dispersive ◽  
X Ray

Charge density studies utilizing powder diffraction and MEM. Exploring of high Tc superconductors, C60 superconductors and manganites

2001 ◽  
Vol 216 (2) ◽  
Author(s):  
M. Takata ◽  
E. Nishibori ◽  
M. Sakata
Keyword(s):  
Charge Density ◽  
Maximum Entropy ◽  
Powder Diffraction ◽  
Recent Progress ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
High Tc Superconductors ◽  
High Tc ◽  
X Ray

AbstractThe recent progress of the accurate charge density studies by the Maximum Entropy Method(MEM) utilizing X-ray powder diffraction is reviewed with some examples. Results for PrBCO (PrBa

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