15-18 March 2021
Europe/Berlin timezone

The application of mean field theory to single crystal diffuse scattering

15 Mar 2021, 15:05


Oral contribution Disordered Materials, complex crystal structures and aperiodic crystals, diffuse scattering and 3D-PDF Disordered Materials, complex crystal structures and aperiodic crystals, diffuse scattering and 3D-PDF


Ella Schmidt (University of Oxford)


Correlated disorder in crystalline materials gives rise to single crystal diffuse scattering. While the average structure determination via Bragg data analysis is considered a standard procedure, disorder analysis is thought of as a lengthy and complicated process. We present a mean field approximation to model single crystal diffuse scattering in molecular materials from a simple pair-interaction Hamiltonian.

Mean filed theory is a self-consistent field theory, which is widely used in statistical physics to model high-dimensional random systems. It has proven a valuable tool in the analysis of magnetic diffuse scattering data [1]. Here, the formalism is applied to describe orientationally disordered molecular crystals.

We present a computational study based on the mean field model suggested by Naya [2] and proof its applicability to strongly correlated disorder, where the local building block geometry dictates allowed and prohibited local configurations. The system that will be analysed in detail is a two-dimensional analogue the mercury diammonium halide Hg(NH$_{3}$)$_{2}$Cl$_{2}$ as depicted in the Figure [3].

We compare the results of the diffuse scattering analysis using the mean field model as introduced by Naya [2] to the results of RMC modelling and $\Delta$PDF models based on a Warren-Cowley short range order parameter refinement (see Figure). Finally, the stability of the mean field analysis on limited data availability is demonstrated: Diffraction experiments under pressure or electric field yield a limited reciprocal space coverage. Here, we demonstrate the robustness of the proposed method against incomplete data sets.

[1] Paddison, J. A., et al. (2013). Physical review letters,110(26), 267207.
[2] Naya, S. (1974). Journal of the Physical Society of Japan,37(2), 340–347
[3] Lipscomb, W. (1953). Analytical Chemistry,25(5), 737–739.

Figure Label:
(a) Disordered structure of mercury diammonium halide Hg(NH$_{3}$)$_{2}$Cl$_{2}$ [3]. Hg in black, N in blue, Cl in light green. H atoms were omitted for clarity. The Hg is disordered over the face centres of the cubic unit cell. The ammonia groups occupy the centre of the shown cell, while the Cl is placed on the corner of the unit cell.
(b) X-ray diffuse scattering for the two-dimensional model system. Due to the fourfold symmetry of the average structure, one quadrant of the hk-layer is sufficient to represent the full data. Upper left corner: data as calculated from a model structure that fulfils the local rules; upper right corner: mean field refinement; bottom right corner: RMC refinement; bottom left corner: Warren-Cowley short range order analysis.

Primary author

Ella Schmidt (University of Oxford)


Prof. Andrew L Goodwin (University of Oxford) Mr Johnathan Bulled (University of Oxford)

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