scholarly journals Critical Analysis of Non-Nuclear Electron-Density Maxima and the Maximum Entropy Method

1996 ◽  
Vol 77 (9) ◽  
pp. 1719-1722 ◽  
Author(s):  
R. Y. de Vries ◽  
W. J. Briels ◽  
D. Feil
Keyword(s):  
Maximum Entropy ◽  
Electron Density ◽  
Critical Analysis ◽  
Maximum Entropy Method ◽  
Entropy Method

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.

Electron density distribution in the pyroborateMn2B2O5studied by the maximum-entropy method

2005 ◽  
Vol 71 (22) ◽  
Author(s):  
F. S. Sarrat ◽  
R. B. Guimarães ◽  
M. A. Continentino ◽  
J. C. Fernandes ◽  
A. C. Doriguetto ◽  
...  
Keyword(s):  
Density Distribution ◽  
Maximum Entropy ◽  
Electron Density ◽  
Electron Density Distribution ◽  
Maximum Entropy Method ◽  
Entropy Method

Observation of orientational disorder in the hexagonal stuffed tridymite Sr0.864Eu0.136Al2O4by the maximum-entropy method

2004 ◽  
Vol 37 (5) ◽  
pp. 698-702 ◽  
Author(s):  
H. Yamada ◽  
W. S. Shi ◽  
C. N. Xu
Keyword(s):  
Maximum Entropy ◽  
Electron Density ◽  
Maximum Entropy Method ◽  
Rietveld Method ◽  
Rietveld Analysis ◽  
Atomic Displacement ◽  
Entropy Method ◽  
Apical Oxygen ◽  
Threefold Axis ◽  
Density Image

The crystal structure of a strontium europium aluminate, Sr0.864Eu0.136Al2O4, with a novel hexagonal form was investigated by a combination of Rietveld analysis and the maximum-entropy method (MEM) with synchrotron X-ray powder diffraction data. The electron density image calculated by the MEM/Rietveld method revealed that the apical oxygen ion in the AlO4tetrahedron has a broad distribution corresponding to an extraordinarily large atomic displacement parameter. This structure could be expressed by a split-atom model, with which the Rietveld refinement gaveRwp= 2.99% andRB= 4.16%. Subsequently, MEM-based pattern fitting (MPF) decreased theRfactors toRwp= 2.81% andRB= 2.34% and the electron density image clearly showed that the apical oxygen ions of the AlO4tetrahedra are split over three sites around a threefold axis involving an elongated distribution of the residual O ions along thecaxis. These results suggest that AlO4tetrahedra in Sr0.864Eu0.136Al2O4are orientationally disordered.

About the reliability of the Maximum Entropy Method in reconstructing electron density: the case of MgO

2006 ◽  
Vol 221 (9) ◽  
Author(s):  
Marcello Merli ◽  
Alessandro Pavese
Keyword(s):  
Quantum Mechanic ◽  
Maximum Entropy ◽  
Electron Density ◽  
Finite Temperature ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Thermal Motion ◽  
Temperature Electron

AbstractThe reliability of the Maximum Entropy Method (MEM) to reconstruct finite temperature electron density (ED) is here discussed, investigating the case of periclase (MgO). A theoretical electron density has been generated by quantum mechanic calculations and folded with a function simulating atomic thermal motion, in order to produce a reference errorless ED [ρ(

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