Niels Bindzus

Maximum‐entropy‐method charge densities based on structure‐factor extraction with the commonly used Rietveld refinement programs GSAS, FullProf and Jana2006

Structure-factor extractions in commonly used Rietveld refinement programs (FullProf, Jana2006 and GSAS) were examined with respect to subsequent calculation of electron-density distributions (EDDs) using the maximum entropy method (MEM). As a test case, 90 K synchrotron powder X-ray diffraction data were collected on the potential hydrogen storage material, NaGaH(4), at SPring-8, Japan. To support the model, neutron powder diffraction data were collected on the fully deuterated sample at PSI, Switzerland. Firstly, it was established whether the programs can produce observed structure factors, F(obs), corrected for anomalous dispersion and scaled to the scattering power of one unit cell. Secondly, different models for background and peak-shape description were investigated with respect to the extracted F(obs), and the effect on the subsequent MEM EDDs was analysed within the quantum theory of atoms in molecules. Substantial differences are observed in the estimated standard deviations, σ(obs), produced by the different programs. Since σ(obs) is a vital parameter in the calculation of MEM EDDs this leads to substantial variation between the MEM EDDs obtained with different Rietveld programs even in cases with similar F(obs). A new approach for selecting an optimized MEM EDD and thereby minimizing the effect of variation in σ(obs) is suggested.

Experimental determination of core electron deformation in diamond

Synchrotron powder X-ray diffraction data are used to determine the core electron deformation of diamond. Core shell contraction inherently linked to covalent bond formation is observed in close correspondence with theoretical predictions. Accordingly, a precise and physically sound reconstruction of the electron density in diamond necessitates the use of an extended multipolar model, which abandons the assumption of an inert core. The present investigation is facilitated by negligible model bias in the extraction of structure factors, which is accomplished by simultaneous multipolar and Rietveld refinement accurately determining an atomic displacement parameter (ADP) of 0.00181 (1) Å(2). The deconvolution of thermal motion is a critical step in experimental core electron polarization studies, and for diamond it is imperative to exploit the monatomic crystal structure by implementing Wilson plots in determination of the ADP. This empowers the electron-density analysis to precisely administer both the deconvolution of thermal motion and the employment of the extended multipolar model on an experimental basis.

Contemporary X-ray electron-density studies using synchrotron radiation.

The use of synchrotron radiation for experimental electron-density determination during the last decade is reviewed. Possible future directions of this field are examined.

Nuclear-weighted X-ray maximum entropy method – NXMEM

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 Ba(8)Ga(16)Sn(30). 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, Ba(8)Ga(16)Sn(30), 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.

Synchrotron powder diffraction of silicon: high-quality structure factors and electron density.

Crystalline silicon is an ideal compound to test the current state of experimental structure factors and corresponding electron densities. High-quality structure factors have been measured on crystalline silicon with synchrotron powder X-ray diffraction. They are in excellent agreement with benchmark Pendellösung data having comparable accuracy and precision, but acquired in far less time and to a much higher resolution (sin θ/λ < 1.7 Å(-1)). The extended data range permits an experimental modelling of not only the valence electron density but also the core deformation in silicon, establishing an increase of the core density upon bond formation in crystalline silicon. Furthermore, a physically sound procedure for evaluating the standard deviation of powder-derived structure factors has been applied. Sampling statistics inherently account for contributions from photon counts as well as the limited number of diffracting particles, where especially the latter are particularly difficult to handle.

Carrier concentration dependence of structural disorder in thermoelectric Sn1−xTe

The crystal structure of SnTe is investigated from 20 to 800 K in two samples with different carrier concentrations by single-crystal and powder synchrotron X-ray diffraction, coupled with maximum entropy analysis.

Low-temperature powder X-ray diffraction measurements in vacuum: analysis of the thermal displacement of copper

A serious limitation of the all-in-vacuum diffractometer reported by Straaso, Dippel, Becker & Als-Nielsen [J. Synchrotron Rad. (2014), 21, 119–126] has so far been the inability to cool samples to near-cryogenic temperatures during measurement. The problem is solved by placing the sample in a jet of helium gas cooled by liquid nitrogen. The resulting temperature change is quantified by determining the change in unit-cell parameter and atomic displacement parameter of copper. The cooling proved successful, with a resulting temperature of ∼95 (3) K. The measured powder X-ray diffraction data are of superb quality and high resolution [up to sinθ/λ = 2.2 A−1], permitting an extensive modelling of the thermal displacement. The anharmonic displacement of copper was modelled by a Gram–Charlier expansion of the temperature factor. As expected, the corresponding probability distribution function shows an increased probability away from neighbouring atoms and a decreased probability towards them.

Nuclear Enhanced MEM Used to Analyze Local Distortions in Lead Chalcogenides

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 Pbdisplacement 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 highperformance thermoelectric materials. Furthermore we introduce NEXMEM which can be used for widespread characterization of subtle atomic features in crystals with unusual properties.

Characterization of Local Distortions in Thermoelectric Lead Chalcogenides

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 highperformance thermoelectric materials. The applied approach can be used in general, opening up for widespread characterization of subtle features in crystals with unusual properties.

Experimental core electron density of cubic boron nitride

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.