Modelling diffuse scattering of the disordered crystal structure of Na₂SiF₆

Many crystalline materials are not perfectly ordered, but are disordered to a smaller or larger extent. The properties of such materials are often related to the nature of the disorder. In diffraction experiments, disorder is observable as diffuse scattering. In routine X-ray structure determinations, only Bragg reflections are considered, leading to average crystal structure models. Methods to derive the average structure from the Bragg reflections are very well established, whereas diffuse scattering is rarely accounted for and mostly ignored. Our attempts at modelling the disordered structure of crystalline sodium fluorosilicate will be presented. Although the average crystal structure is known [1], there is some uncertainty about the true space group [2]. Na₂SiF₆ assumes a crystalline morphology that resembles that of ice and is therefore known as an ice-analog material [3]. In the average crystal structure (in space group P321), the asymmetric unit contains two ordered sodium cations (both sitting on a two-fold axis) and two disordered SiF₆^2- anions (one sitting on a 3-fold axis and the other on a 32 site). Each anion can occupy two alternative sites in the unit cell, related by a non-crystallographic mirror plane at z = ¼. The occupation is mutually exclusive for both anions. Diffuse scattering can be observed as planes perpendicular to l in the hnl and nkl precession images where these diffuse planes can be found at integer l. For l odd, the diffuse scattering is more intense. Also there are diffuse clouds of intensity around certain Bragg peaks. In the hkn planes, diffuse streaks are visible parallel to a*, b*, and a* - b*, while some Bragg peaks have diffuse clouds of intensity around them. The pattern of streaks and clouds evolves when going to higher order planes. In the figure below, the hk1 precession image is illustrated. The observed diffuse scattering features will be interpreted in terms of structural models obtained by Monte Carlo simulations.

Studying structure disorder in DL-Norvaline by single crystal diffuse scattering

Diffraction methods are the most important methods to study the three-dimensional arrangement of matter at the atomic level. Real materials are often not perfectly ordered and the resulting diffraction pattern may contain a weak continuous or structured background known as diffuse scattering, in addition to sharp Bragg peaks. Our motivation is to analyse diffuse scattering in order to learn about the Short Range Order (SRO) of disordered crystals and improve the tools to model disorder phenomena. We are now investigating the SRO in DL-Norvaline which crystallizes in three known temperature-dependent phases. At least two of them (beta-phase space group C2/c above -70⁰C, alpha-phase P21/c around -90⁰C) show disordered average structures in which the alkyl side chain adopts several conformations [1]. The scattering data were collected using synchrotron radiation and a noise-free Pilatus pixel detector at the ESRF BM01A station. The diffraction pattern of the β-phase shows diffuse streaks parallel to a reciprocal lattice axis and diffuse clouds around low angle reflections [2] (Fig. 1). These features result from static and dynamic disorder. The diffuse streaks indicate disorder amongst stacks of layers of molecules, while the diffuse clouds arise from thermal motion. The modelling of the disorder involves the use of the Monte Carlo and differential evolution algorithms embedded in ZODS [3]. Our progress with model development will be presented.