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 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.

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
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