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

Abstract

A serious limitation of the all‐in‐vacuum diffractometer reported by Straasø, 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 Å−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.

Accurate charge densities from powder X-ray diffraction – a new version of the Aarhus vacuum imaging-plate diffractometer

“…The increase in the 100 K model is similar to what is observed in diamond (Wahlberg, Bindzus, Bjerg et al, 2016). Besides the mentioned studies on diamond and silicon, the EDD of cubic boron nitride (cBN) and copper have also been studied with AVID (Wahlberg et al, 2015;Wahlberg, Bindzus, Christensen et al, 2016). For cBN, it was possible to determine the deformation of the core EDD, even without the use of Wilson plots, which can only be rigorously used for monoatomic solids.…”

“…Recently, the first version of the AVID was reported (Straasø et al, 2013(Straasø et al, , 2014. By performing PXRD in vacuum, the external background signal can, in the absence of fluorescence, be limited to (i) scattering from the sample container, which can be measured individually and subtracted, (ii) Compton scattering from the sample, and (iii) thermal diffuse scattering, which can be minimized by carrying out data collection at low temperature (Wahlberg, Bindzus, Christensen et al, 2016). The diffractometer had a sample-todetector distance of 300 mm (Straasø et al, 2013) and used a Fuji BAS SR-2040 imaging-plate (IP) detector positioned on a cylindrical path at the given distance.…”

“…The sample cooler used in all low-temperature experiments and also implemented in the new version of AVID was discussed by Wahlberg, Bindzus, Christensen et al (2016). It works by injecting helium gas cooled by liquid nitrogen onto the sample through a thin nozzle positioned a few millimetres from the sample and beam position.…”

Spatial distribution of electrons near the Fermi level in the metallic LaB6 through accurate X-ray charge density study

“…Recently, the charge density studies from ultra-high resolution synchrotron radiation powder diffractions have been reported using an all-in-vacuum diffractometer installed at PETRA-III26. Core electron deformations of diamond26, silicon27 and cubic boron nitride28, and anharmonic thermal vibration of copper29 have been observed from powder diffraction data. Several analytical procedures such as Wilson plot26272829, and uncertainty estimation using particle statics27 were used in the studies.…”

“…Core electron deformations of diamond26, silicon27 and cubic boron nitride28, and anharmonic thermal vibration of copper29 have been observed from powder diffraction data. Several analytical procedures such as Wilson plot26272829, and uncertainty estimation using particle statics27 were used in the studies. These techniques are under development since it still depends on materials262728.…”