Multipole electron densities and structural parameters from synchrotron powder X-ray diffraction data obtained with a MYTHEN detector system (OHGI)

Electron density and thermal motion of diamond at elevated temperatures

The electron density and thermal motion of diamond are determined at nine temperatures between 100 K and 1000 K via synchrotron powder X-ray diffraction (PXRD) data collected on a high-accuracy detector system. Decoupling of the thermal motion from the thermally smeared electron density is performed via an iterative Wilson-Hansen-Coppens-Rietveld procedure using theoretical static structure factors from density functional theory (DFT) calculations. The thermal motion is found to be harmonic and isotropic in the explored temperature range, and excellent agreement is observed between experimental atomic displacement parameters (ADPs) and those obtained via theoretical harmonic phonon calculations (HPC), even at 1000 K. The Debye temperature of diamond is determined experimentally to be Θ_D = 1883 (35) K. A topological analysis of the electron density explores the temperature dependency of the electron density at the bond critical point. The properties are found to be constant throughout the temperature range. The robustness of the electron density confirms the validity of the crystallographic convolution approximation for diamond in the explored temperature range.

High-Precision X-ray Total Scattering Measurements Using a High-Accuracy Detector System

The total scattering method, which is based on measurements of both Bragg and diffuse scattering on an equal basis, has been still challenging even by means of synchrotron X-rays. This is because such measurements require a wide coverage in scattering vector Q, high Q resolution, and a wide dynamic range for X-ray detectors. There is a trade-off relationship between the coverage and resolution in Q, whereas the dynamic range is defined by differences in X-ray response between detector channels (X-ray response non-uniformity: XRNU). XRNU is one of the systematic errors for individual channels, while it appears to be a random error for different channels. In the present study, taking advantage of the randomness, the true sensitivity for each channel has been statistically estimated. Results indicate that the dynamic range of microstrip modules (MYTHEN, Dectris, Baden-Daettwil, Switzerland), which have been assembled for a total scattering measurement system (OHGI), has been successfully restored from 104 to 106. Furthermore, the correction algorithm has been optimized to increase time efficiencies. As a result, the correcting time has been reduced from half a day to half an hour, which enables on-demand correction for XRNU according to experimental settings. High-precision X-ray total scattering measurements, which has been achieved by a high-accuracy detector system, have demonstrated valence density studies from powder and PDF studies for atomic displacement parameters.

The Effects of Chemical Bonding at Subatomic Resolution: A Case Study on α-Boron

Similar to classical asphericity shifts, aspherical deformations of the electron density in the atomic core region can result in core asphericity shifts in refinements using a Hansen-Coppens multipolar model (HCM), especially when highly precise experimental datasets with resolutions far beyond sin(θ)/λ ≤ 1.0 Å⁻¹ are employed. These shifts are about two orders of magnitude smaller than their counterparts caused by valence shell deformations, and their underlying deformations are mainly of dipolar character for 1st row atoms. Here, we analyze the resolution dependence of core asphericity shifts in α-boron. Based on theoretical structure factors, an appropriate Extended HCM (EHCM) is developed, which is tested against experimental high-resolution (sin(θ)/λ ≤ 1.6 Å⁻¹) single-crystal diffraction data. Bond length deviations due to core asphericity shifts of α-boron in the order of 4–6·10⁻⁴ Å are small but significant at this resolution and can be effectively compensated by an EHCM, although the correlation of the additional model parameters with positional parameters prevented a free refinement of all core model parameters. For high quality, high resolution data, a proper treatment with an EHCM or other equivalent methods is therefore highly recommended.

Synchrotron total-scattering data applicable to dual-space structural analysis

Synchrotron powder X-ray diffraction (PXRD) is a well established technique for investigating the atomic arrangement of crystalline materials. At modern beamlines, X-ray scattering data can be collected in a total-scattering setting, which additionally opens up the opportunity for direct-space structural analysis through the atomic pair distribution function (PDF). Modelling of PXRD and PDF data is typically carried out separately, but employing a concurrent structural model to both direct- and reciprocal-space data has the possibility to enhance total-scattering data analysis. However, total-scattering measurements applicable to such dual-space analyses are technically demanding. Recently, the technical demands have been fulfilled by a MYTHEN microstrip detector system (OHGI), which meets the stringent requirements for both techniques with respect to Q range, Q resolution and dynamic range. In the present study, we evaluate the quality of total-scattering data obtained with OHGI by separate direct- and reciprocal-space analysis of Si. Excellent agreement between structural parameters in both spaces is found, demonstrating that the total-scattering data from OHGI can be utilized in dual-space structural analysis e.g. for in situ and operando measurements.