Investigating anharmonicity and disorder in cadmium and zinc telluride

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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Nuclear-weighted X-ray maximum entropy method – NXMEM

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s2053273314024103 ◽

2015 ◽

Vol 71 (1) ◽

pp. 9-19 ◽

Cited By ~ 14

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.

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Phase determination and extension using X-ray multiple diffraction and the maximum-entropy method

Acta Crystallographica Section A Foundations of Crystallography ◽

10.1107/s0108767300018869 ◽

2001 ◽

Vol 57 (4) ◽

pp. 420-428 ◽

Cited By ~ 3

Author(s):

Chien-Mei Wang ◽

Chun-Hsiung Chao ◽

Shih-Lin Chang

Keyword(s):

Maximum Entropy ◽

Maximum Entropy Method ◽

Entropy Method ◽

Multiple Diffraction ◽

Phase Determination ◽

X Ray

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A model-independent maximum-entropy method for the inversion of small-angle X-ray diffraction patterns

Journal of Applied Crystallography ◽

10.1107/s0021889899010560 ◽

1999 ◽

Vol 32 (6) ◽

pp. 1069-1083 ◽

Cited By ~ 10

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).

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An Evaluation of Deconvolution Techniques in X-ray Profile Broadening Analysis and the Application of the Maximum Entropy Method to Alumina Data

Advances in X-ray Analysis ◽

10.1154/s0376030800018036 ◽

1994 ◽

Vol 38 ◽

pp. 387-395 ◽

Cited By ~ 1

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.

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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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Nuclear Enhanced MEM Used to Analyze Local Distortions in Lead Chalcogenides

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s2053273314098945 ◽

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.

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