Acta Crystallographica Section B

Volume 67, Part 3 (June 2011)

research papers

 

Modulated anharmonic ADPs are intrinsic to aperiodic crystals: a case study on incommensurate Rb₂ZnCl₄

L. Li, A. Wölfel, A. Schönleber, S. Mondal, A. M. M. Schreurs, L. M. J. Kroon-Batenburg and S. van Smaalen

Abstract: A combination of structure refinements, analysis of the superspace MEM density and interpretation of difference-Fourier maps has been used to characterize the incommensurate modulation of rubidium tetrachlorozincate, Rb₂ZnCl₄, at a temperature of T = 196 K, close to the lock-in transition at T_lock-in = 192 K. The modulation is found to consist of a combination of displacement modulation functions, modulated atomic displacement parameters (ADPs) and modulated third-order anharmonic ADPs. Up to fifth-order Fourier coefficients could be refined against diffraction data containing up to fifth-order satellite reflections. The center-of-charge of the atomic basins of the MEM density and the displacive modulation functions of the structure model provide equivalent descriptions of the displacive modulation. Modulations of the ADPs and anharmonic ADPs are visible in the MEM density, but extracting quantitative information about these modulations appears to be difficult. In the structure refinements the modulation parameters of the ADPs form a dependent set, and ad hoc restrictions had to be introduced in the refinements. It is suggested that modulated harmonic ADPs and modulated third-order anharmonic ADPs form an intrinsic part, however small, of incommensurately modulated structures in general. Refinements of alternate models with and without parameters for modulated ADPs lead to significant differences between the parameters of the displacement modulation in these two types of models, thus showing the modulation of ADPs to be important for a correct description of the displacive modulation. The resulting functions do not provide evidence for an interpretation of the modulation by a soliton model.

Keywords: aperiodic crystals; incommensurate modulated structures; MEM density; ADPs.

	Structure factor file (CIF format) (323.6 kbytes) [ doi:10.1107/S0108768111013814/bp5035Isup2.hkl ] Contains datablock I
	Structure factor file (CIF format) (323.6 kbytes) [ doi:10.1107/S0108768111013814/bp5035IIsup3.hkl ] Contains datablock II

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