Nanna Wahlberg

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.

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.

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.

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.

Accurate Charge Densities from Synchrotron Powder Diffraction

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 dspacing. [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 structuredependency. 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.