Nuclear and charge density distributions in ferroelectric PbTiO3: maximum entropy method analysis of neutron and X-ray diffraction data

2013 ◽  
Vol 28 (4) ◽  
pp. 276-280 ◽  
Author(s):  
Jinlong Zhu ◽  
Wei Han ◽  
Jianzhong Zhang ◽  
Hongwu Xu ◽  
Sven C. Vogel ◽  
...  
Keyword(s):  
Charge Density ◽  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Rietveld Analysis ◽  
Entropy Method ◽  
X Ray Diffraction ◽  
X Ray ◽  
Density Distributions ◽  
Increasing Temperature ◽  
Ionic States

We conducted in-situ high-temperature neutron and X-ray diffraction studies on tetragonal PbTiO3. Using a combination of Rietveld analysis and Maximum Entropy Method, the nuclear and charge density distributions were determined as a function of temperature up to 460 °C. The ionic states obtained from charge density distributions reveal that the covalency of Pb–O2 bonds gradually weakens with increasing temperature. The spontaneous polarizations calculated from the contributions of ionic state, ionic displacement, and nuclear polarization, are in good agreement with the experimental measurements. This method provides an effective approach to determine spontaneous polarizations in multiferroics with high-current leakage and low resistance.

Maximum Entropy Method Charge Density Distributions of Novel Thermoelectric Clathrates

1999 ◽  
Vol 590 ◽  
Author(s):  
B. Iversen ◽  
A. Bentien ◽  
A. Palmqvist ◽  
D. Bryan ◽  
S. Latturner ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Charge Density ◽  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Mixed Valence ◽  
Entropy Method ◽  
X Ray Diffraction ◽  
X Ray ◽  
Density Distributions ◽  
Positively Charged

ABSTRACTRecently materials with promising thermoelectric properties were discovered among the clathrates. Transport data has indicated that these materials have some of the characteristics of a good thermoelectric, namely a low thermal conductivity and a high electrical conductivity. Based on synchrotron powder and conventional single crystal x-ray diffraction data we have determined the charge density distribution in Sr8Ga16Ge3O using the Maximum Entropy Method. The MEM density shows clear evidence of guest atom rattling, and this contributes to the reduction of the thermal conductivity. Analysis of the charge distribution reveals that Sr8Ga16Ge30 contains mixed valence alkaline earth guest atoms. The Sr atoms in the small cavities are, as expected, doubly positively charged, whereas the Sr atoms in the large cavities appear negatively charged. The MEM density furthermore suggests that the Ga and Ge atoms may not be randomly disordered on the framework sites as found in the conventional leastsquares refinements.

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.

Charge density study with the Maximum Entropy Method on model data of silicon. A search for non-nuclear attractors

1996 ◽  
Vol 74 (6) ◽  
pp. 1054-1058 ◽  
Author(s):  
R.Y. de Vries ◽  
W.J. Briels ◽  
D. Fell ◽  
G. te Velde ◽  
E.J. Baerends
Keyword(s):  
Charge Density ◽  
Maximum Entropy ◽  
Density Functional ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
X Ray Diffraction ◽  
Functional Theory ◽  
Structure Factors ◽  
The Density Functional Theory ◽  
Structure Calculations

In 1990 Sakata and Sato applied the maximum entropy method (MEM) to a set of structure factors measured earlier by Saka and Kato with the Pendellösung method. They found the presence of non-nuclear attractors, i.e., maxima in the density between two bonded atoms. We applied the MEM to a limited set of Fourier data calculated from a known electron density distribution (EDD) of silicon. The EDD of silicon was calculated with the program ADF-BAND. This program performs electronic structure calculations, including periodicity, based on the density functional theory of Hohenberg and Kohn. No non-nuclear attractor between two bonded silicon atoms was observed in this density. Structure factors were calculated from this density and the same set of structure factors that was measured by Saka and Kato was used in the MEM analysis. The EDD obtained with the MEM shows the same non-nuclear attractors that were later obtained by Sakata and Sato. This means that the non-nuclear attractors in silicon are really an artefact of the MEM. Key words: Maximum Entropy Method, non-nuclear attractors, charge density. X-ray diffraction.

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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