Crystallographic phase retrieval method for liquid crystal bicontinuous phases: indicator‐based method

An indicator‐based crystallographic phase retrieval method has been developed for diffraction data of bicontinuous cubic phases of lyotropic liquid crystals. Such liquid crystals have large structural disorder; the number of independent Bragg reflections that can be observed is limited. This paper p...

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Bibliographic Details
Published in:Acta crystallographica. Section A, Foundations and advances Foundations and advances, 2022-09, Vol.78 (5), p.430-436
Main Author: Oka, Toshihiko
Format: Article
Language:English
Subjects:
Crystal structure
crystallographic phase retrieval
Crystallography
Crystals
Density distribution
Electron density
Electrons
Hessian matrices
Indicators
Interfaces
Liquid crystals
lyotropic liquid crystals
Mathematical analysis
Minimal surfaces
Phase retrieval
Phases
Research Papers
triply periodic minimal surfaces
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Summary:An indicator‐based crystallographic phase retrieval method has been developed for diffraction data of bicontinuous cubic phases of lyotropic liquid crystals. Such liquid crystals have large structural disorder; the number of independent Bragg reflections that can be observed is limited. This paper proposes two indicators to identify plausible combination(s) of crystallographic phases, i.e. electron‐density distribution. The indicators are based on the characteristics of the liquid crystals: amphiphilic molecules diffuse mainly in the direction parallel to polar–nonpolar interfaces and the electron density in the direction parallel to the interfaces is averaged. One indicator is the difference between the maximum and minimum electron density, and the other is calculated from the Hessian matrix of the electron density. Using test data, the electron densities were calculated for all possible phase combinations and indicators were obtained. The results indicated that the electron densities with the minimum indicators were close to the true electron density. Therefore, this method is effective for phase retrieval. The accuracy of the phase retrieval decreased when the volume fraction of the region including the triply periodic minimal surface increased. An indicator‐based crystallographic phase retrieval method has been developed for diffraction data of bicontinuous cubic phases of lyotropic liquid crystals. The electron densities with the minimum indicators are close to the true electron density.
ISSN:2053-2733
0108-7673
2053-2733
DOI:10.1107/S2053273322006970