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Order causes secondary Bragg peaks in soft materials

Nature Materials volume 6, pages 888–893 (2007)Cite this article

Abstract

Highly ordered soft materials exhibit Bragg peaks that cannot be indexed assuming homogeneous crystal structures. Their origin has been attributed to changes in the crystal structure that are induced by the ordering process such as by application of external fields. This would restrict the use for the generation of highly ordered nano- and microstructured materials where a homogeneous crystal structure is a key requirement. Here, we demonstrate that these Bragg peaks are an inherent property of homogeneous ordered soft materials related to the finite coherence of their crystalline lattice. Their consideration allows a detailed and quantitative analysis of the diffraction patterns of seemingly unrelated materials such as lyotropic liquid-crystalline phases, mesoporous materials, colloidal dispersions, block copolymers, electrorheological fluids and photonic crystals. It further enables us to develop a concise picture of order, line density, field-induced orientation and epitaxial relations for soft-material lattices.

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Figure 1: Evolution of Debye–Scherrer rings into Bragg peaks with increasing order.
Figure 2: Ewald construction and schematic model to illustrate the origin of secondary Bragg peaks.
Figure 3: SEM images of the silica replica of the f.c.c. lattice showing characteristic grain boundaries and orientational deviations.
Figure 4: Unified scheme of order and mutual orientation of the most common soft-material structures.

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Acknowledgements

Financial support of the DFG-Graduiertenkolleg GK611 is gratefully acknowledged.

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Authors and Affiliations

  1. Institute of Physical Chemistry, University of Hamburg, Grindelallee 117, D-20146 Hamburg, Germany

    Stephan Förster, Andreas Timmann, Carsten Schellbach, Andreas Frömsdorf, Andreas Kornowski & Horst Weller

  2. HASYLAB, DESY, Notkestrasse 85, D-22603 Hamburg, Germany

    Stephan V. Roth

  3. Institut-Laue-Langevin, 6, rue Jules Horowitz, F-38042 Grenoble Cedex 9, France

    Peter Lindner

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Correspondence to Stephan Förster.

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Förster, S., Timmann, A., Schellbach, C. et al. Order causes secondary Bragg peaks in soft materials. Nature Mater 6, 888–893 (2007). https://doi.org/10.1038/nmat1995

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