Nuclear-weighted X-ray maximum entropy method – NXMEM

2015 ◽  
Vol 71 (1) ◽  
pp. 9-19 ◽  
Author(s):  
Sebastian Christensen ◽  
Niels Bindzus ◽  
Mogens Christensen ◽  
Bo Brummerstedt Iversen
Keyword(s):  
Single Crystal ◽  
Maximum Entropy ◽  
Diffraction Data ◽  
Maximum Entropy Method ◽  
Functional Materials ◽  
Structural Features ◽  
Entropy Method ◽  
Nuclear Density ◽  
Single Crystal Diffraction ◽  
X Ray

Subtle structural features such as disorder and anharmonic motion may be accurately characterized from nuclear density distributions (NDDs). As a viable alternative to neutron diffraction, this paper introduces a new approach named the nuclear-weighted X-ray maximum entropy method (NXMEM) for reconstructing pseudo NDDs. It calculates an electron-weighted nuclear density distribution (eNDD), exploiting that X-ray diffraction delivers data of superior quality, requires smaller sample volumes and has higher availability. NXMEM is tested on two widely different systems: PbTe and Ba8Ga16Sn30. The first compound, PbTe, possesses a deceptively simple crystal structure on the macroscopic level that is unable to account for its excellent thermoelectric properties. The key mechanism involves local distortions, and the capability of NXMEM to probe this intriguing feature is established with simulated powder diffraction data. In the second compound, Ba8Ga16Sn30, disorder among the Ba guest atoms is analysed with both experimental and simulated single-crystal diffraction data. In all cases, NXMEM outperforms the maximum entropy method by substantially enhancing the nuclear resolution. The induced improvements correlate with the amount of available data, rendering NXMEM especially powerful for powder and low-resolution single-crystal diffraction. The NXMEM procedure can be implemented in existing software and facilitates widespread characterization of disorder in functional materials.

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 Characterization of Local Distortions in Thermoelectric Lead Chalcogenides

2014 ◽  
Vol 70 (a1) ◽  
pp. C106-C106
Author(s):  
Niels Bindzus ◽  
Sebastian Christensen ◽  
Mogens Christensen ◽  
Bo Iversen
Keyword(s):  
Neutron Diffraction ◽  
Maximum Entropy ◽  
Diffraction Data ◽  
Thermoelectric Materials ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Neutron Diffraction Data ◽  
Lead Chalcogenides ◽  
X Ray

Thermoelectric materials are functional materials with the unique ability to interconvert heat and electricity, holding much promise for green energy solutions such as efficient 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, emerging with temperature 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 lead chalcogenides were until recently believed to adopt the ideal, undistorted rock-salt structure. In the present study, we probe the peculiar structural features in PbX (X = S, Se, Te) using multi-temperature synchrotron powder X-ray diffraction data in combination with the maximum entropy method. Distorted atoms are detected and quantified by refinement of anharmonic probability density functions. The charge density analysis is complemented by nuclear density distributions (NDDs) reconstructed from neutron diffraction data and by a novel method: 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 diffraction data. The increased atomic resolution introduced by NEXMEM proved essential for resolving atomic distortions, see figure below showing Pb in the (100) plane. Our findings outline the extent of disorder and anharmonicity in binary lead chalcogenides, promoting our fundamental understanding of this class of high-performance thermoelectric materials. The applied approach can be used in general, opening up for widespread characterization of subtle features in crystals with unusual properties.

scholarly journals Investigating anharmonicity and disorder in cadmium and zinc telluride

2014 ◽  
Vol 70 (a1) ◽  
pp. C1773-C1773
Author(s):  
Mattia Sist ◽  
Niels Bindzus ◽  
Espen Eikeland ◽  
Bo Iversen
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Gamma Ray ◽  
Lead Telluride ◽  
High Energy ◽  
Structural Features ◽  
Entropy Method ◽  
Anomalous Scattering ◽  
X Ray ◽  
Photoelectric Properties

CdTe and ZnTe are often referred to as II-VI semiconductors. Due to the structural and photoelectric properties and low-cost manufacturability, CdTe and ZnTe based thin films are used in the photovoltaic technology and in variety of electronic devices such as infrared, X-ray and gamma ray detectors (Eisen at al., 1998). The structure of another telluride, PbTe, has recently been reviewed and the emerging atomic disorder with temperature seems to have an indissoluble liaison with the high thermoelectric figure of merit of such promising material (Bozin et al., 2010). Deviations of the cation from its position in the ideal rock-salt structure have been probed by means of Maximum Entropy Method (MEM) calculations on Synchrotron powder X-ray diffraction data (SPXRD) (Kastbjerg et al., 2013). Motivated by the peculiar structural features in lead telluride, we investigate anharmonicity and disorder of the cations in both the zincblende structures, CdTe and ZnTe. High resolution SPXRD data at 100 K have been collected for both compounds. High energy radiation and minute capillaries have been used with the aim to minimize systematic errors on the data such as absorption and anomalous scattering. Accurate Rietveld refinements have been carried out in order to extract the best dataset of structure factors. Maximum Entropy Method calculations have hence been computed, providing the least-biased information deduction from experimental data. The disorder, anharmonicity and chemical bonding within the crystalline CdTe and ZnTe have been deeply investigated through the MEM densities and comparisons with the cation displacement in the structure of lead telluride have been established.

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