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

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.

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Accurate charge density of the tripeptide Ala-Pro-Ala with the maximum entropy method (MEM): influence of data resolution

Acta Crystallographica Section B Structural Science ◽

10.1107/s0108768107029655 ◽

2007 ◽

Vol 63 (4) ◽

pp. 633-643 ◽

Cited By ~ 8

Author(s):

Andreas Hofmann ◽

Roman Kalinowski ◽

Peter Luger ◽

Sander van Smaalen

Keyword(s):

Charge Density ◽

Maximum Entropy ◽

Electron Density ◽

Maximum Entropy Method ◽

Atomic Displacement ◽

Accurate Estimate ◽

Entropy Method ◽

Atomic Charges ◽

Acta Cryst ◽

Reflection Data

The accurate electron density of Ala-Pro-Ala is determined by the maximum entropy method (MEM), employing the same reflection data measured at 100 K which was used for a multipole refinement by Kalinowski et al. [(2007), Acta Cryst. Accepted for publication]. Properties of the electron density are compared with the corresponding properties of the static electron density from the multipole model and to the dynamic MEM electron density of trialanine at 20 K. It is thus shown that the increased thermal smearing at 100 K leads to lower electron densities in the bond critical points and atomic charges closer to zero for Ala-Pro-Ala than has been obtained for trialanine at 20 K. The influence of the resolution of the data is investigated by a series of MEM calculations. Atomic charges and atomic volumes are found not to depend on the resolution, but the charge density in the BCPs decreases with decreasing resolution of the dataset. The origin of this dependence is found to lie mostly in the more accurate estimate of the atomic displacement parameters (ADPs) for the higher-resolution datasets. If these effects are taken into account, meaningful information on chemical bonding can be obtained with data at a resolution better than d min = 0.63 Å. Alternatively, low-resolution X-ray diffraction data can be used in accurate electron-density studies by the MEM, if another source of accurate values of the ADPs is available, e.g. from refinements with multipole parameters from a database of transferable multipole parameters.

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Experimental evidence for the existence of non-nuclear maxima in the electron-density distribution of metallic beryllium. A comparative study of the maximum entropy method and the multipole refinement method

Acta Crystallographica Section B Structural Science ◽

10.1107/s0108768194010360 ◽

1995 ◽

Vol 51 (4) ◽

pp. 580-591 ◽

Cited By ~ 69

Author(s):

B. B. Iversen ◽

F. K. Larsen ◽

M. Souhassou ◽

M. Takata

Keyword(s):

Comparative Study ◽

Density Distribution ◽

Experimental Evidence ◽

Maximum Entropy ◽

Electron Density ◽

Electron Density Distribution ◽

Maximum Entropy Method ◽

Entropy Method ◽

Refinement Method ◽

Multipole Refinement

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

Physical Review Letters ◽

10.1103/physrevlett.77.1719 ◽

1996 ◽

Vol 77 (9) ◽

pp. 1719-1722 ◽

Cited By ~ 50

Author(s):

R. Y. de Vries ◽

W. J. Briels ◽

D. Feil

Keyword(s):

Maximum Entropy ◽

Electron Density ◽

Critical Analysis ◽

Maximum Entropy Method ◽

Entropy Method

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Structural determination of Li1−yNi0.5Mn0.5O2(y = 0.5) using a combination of Rietveld analysis and the maximum entropy method

Journal of Materials Chemistry ◽

10.1039/b311827d ◽

2004 ◽

Vol 14 (1) ◽

pp. 40-42 ◽

Cited By ~ 27

Author(s):

Hironori Kobayashi ◽

Yoshinori Arachi ◽

Hiroyuki Kageyama ◽

Kuniaki Tatsumi

Keyword(s):

Maximum Entropy ◽

Maximum Entropy Method ◽

Rietveld Analysis ◽

Entropy Method ◽

Structural Determination

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

Advances in X-ray Analysis ◽

10.1154/s0376030800008697 ◽

1991 ◽

Vol 35 (A) ◽

pp. 77-83 ◽

Cited By ~ 1

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.

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