Implications of X-ray thermal diffuse scattering in integrated Bragg intensities of silicon and cubic boron nitride

Abstract

This article describes a theoretical quantification of the thermal diffuse scattering (TDS) contribution to the integrated intensities of single‐crystal diffraction from silicon and cubic boron nitride. The TDS intensity is calculated ab initio and the intensity contribution to the Bragg peak determined by integration of a volume of appropriate size. The effect of including TDS in the structure factors is assessed in a subsequent refinement, where the effect on the atomic displacement parameters and the residual Fourier maps is inspected. In both compounds changes caused solely by the TDS inclusion are observed. Particularly, adding TDS to the structure factors of silicon produces significant features in the residual Fourier maps and a change in the atomic displacement parameter. Significant effects are also present at low temperatures. Thus, it is important to address the effect of TDS when pursuing high‐accuracy charge densities or if analyzing the atomic displacement parameters.

Experimental X-ray Charge-Density Studies─A Suitable Probe for Superconductivity? A Case Study on MgB2

“…It should be noted at this point that negligence or insufficient treatment of thermal diffuse scattering (TDS) may be one source of error introducing a slight bias into the decomposition of Δρ total ( r ). That is, the resolution-dependent variation of TDS contributions to the integrated reflection intensities can artificially reduce the ADPs in the refined multipolar models, affect the scale factor and monopole populations, and produce mainly atom-centered features in the residual electron density. − However, the resulting errors should be negligible ,, in view of the small unit cell size [29.236(2) Å 3 at RT], the large bulk modulus of ∼150 GPa (compared to cubic BN: ∼420 GPa; diamond: ∼460 GPa), and the high Debye temperature of 1200 K of MgB 2 (compared to cubic BN: 1600 K; diamond: 1850 K). Also, a refinement of resolution-dependent scale factors ,, and inspection of reconstructed reciprocal-space planes did not point to a significant contamination of our XRD data sets by TDS (for further details, see the Supporting Information).…”

Quantum Crystallography: Current Developments and Future Perspectives

“…[176] This implies that even in quantum crystallographic studies in which the dynamics is of secondary interest, it is important to have an accurate model of motion in order to properly take these contributions into account. If TDS is not accounted for it will give rise to additional systematic changes in the Bragg intensities,a nd thus create artifacts in the crystallographic models, as it was recently demonstrated in am odel study on silicon and cubic boronn itride.…”

“…The TDS signal can be diminished by cooling the crystals to very low temperatures, but it can never be fully removed. If TDS is not accounted for it will give rise to additional systematic changes in the Bragg intensities, and thus create artifacts in the crystallographic models, as it was recently demonstrated in a model study on silicon and cubic boron nitride . This implies that even in quantum crystallographic studies in which the dynamics is of secondary interest, it is important to have an accurate model of motion in order to properly take these contributions into account.…”

Full Elasticity Tensor from Thermal Diffuse Scattering

“…Accurate measurements will help to improve the understanding of condition and composition of planets interior by comparison with seismic data. The quantitative treatment of TDS furthermore constrains the atomic displacement patterns 20 which is important for the crystallographic refinement of new high-pressure phases.…”