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Based on benchmark synchrotron powder X-ray diffraction data, the subtleties in the electron density of diamond are explored. A contraction of the core density inherently linked to covalent bond formation is experimentally observed.

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Acta Cryst. (2014). A70, C105
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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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Acta Cryst. (2014). A70, C106
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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.

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Acta Cryst. (2014). A70, C283
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The resent progress in powder diffraction provides data of quality beyond multipolar modeling of the valence density. As was recently shown in a benchmark study of diamond by Bindzus et al.[1] The next step is to investigate more complicated chemical bonding motives, to determine the effect of bonding on the core density. Cubic boron nitride lends itself as a perfect candidate because of its many similarities with diamond: bonding pattern in the extended network structure, hardness, and the quality of the crystallites.[2] However, some degree ionic interaction is a part of the bonding in boron nitride, which is not present in diamond. By investigating the core density in boron nitride we may obtain a deeper understanding of the effect of bonding on the total density. We report here a thorough investigation of the charge density of cubic boron nitride with a detailed modelling of the inner atom charge density. By combining high resolution powder X-ray diffraction data and an extended multipolar model an experimental modeling of the core density is possible.[3] The thermal motion is a problem since it is strongly correlated to the changes of the core density, but by combining the average displacement from a Wilson plot and a constrained refinement, a reasonable result has been obtained. The displacement parameters reported here are significantly lower than those previously reported, stressing the importance of an adequate description of the core density. The charge transfer from boron to nitrogen clearly affects the inner electron density, which is evident from theoretical as well as experimental result. The redistribution of electron density will, if not accounted for, result in increased thermal parameters. It is estimated that 1.7-2 electrons is transferred from boron to nitrogen.

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Acta Cryst. (2014). A70, C1341
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Advancements within the field of synchrotron powder X-ray diffraction (SPXRD) have rendered it a viable approach for probing subtle electronic features. It is especially powerful for highly crystalline inorganic extended materials, resolving severe extinction issues conventionally encountered with single-crystal diffraction. Furthermore, SPXRD data exhibit markedly reduced absorption and may be collected in a single exposure. The latter prevents systematic errors from merging a multitude of detector frames, each possessing a slightly different scale factor. These experimental advantages are counterbalanced by a more complicated data analysis, where the key problems are the inherent challenges of overlapping reflections and background subtraction. To evaluate the performance of SPXRD and to test the methodologies for estimating charge densities (CDs), we use benchmark data on diamond collected to low d-spacing. [1] The critical step is the recovery of observed structure factors from the powder pattern. This is the focal point of the present study, scrutinizing several traditional and novel approaches that deviate strongly in terms of model complexity and structure-dependency. All recovered sets of structure factors are evaluated with respect to their capability to determine the true atomic displacement parameter and to estimate the CD by both multipolar modelling and maximum entropy reconstruction. The data are of such exceptional quality that they even reveal how the innermost electron density responds to the formation of covalent bonding (figure below). Supporting their huge success over the last decades, only the Rietveld-based approaches are capable of quantifying this fine feature. The study of core polarization has emerged as a new frontier in chemical bonding studies, and the relevant experimental information may be reliably accessed by SPRXD for highly crystalline materials.

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Acta Cryst. (2014). A70, C1773
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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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