Oka Toshihiko
Department of Physics, Faculty of Science, Shizuoka University, Shizuoka, 422-8529, Japan.
Acta Crystallogr A Found Adv. 2022 Sep 1;78(Pt 5):430-436. doi: 10.1107/S2053273322006970. Epub 2022 Jul 28.
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.
针对溶致液晶双连续立方相的衍射数据，开发了一种基于指标的晶体学相位恢复方法。此类液晶具有较大的结构无序性；可观测到的独立布拉格反射数量有限。本文提出了两个指标来识别晶体学相位（即电子密度分布）的合理组合。这些指标基于液晶的特性：两亲分子主要在平行于极性 - 非极性界面的方向上扩散，且平行于界面方向的电子密度是平均的。一个指标是最大电子密度与最小电子密度之差，另一个指标是根据电子密度的海森矩阵计算得出。利用测试数据，针对所有可能的相位组合计算了电子密度并获得了指标。结果表明，具有最小指标的电子密度接近真实电子密度。因此，该方法对于相位恢复是有效的。当包含三重周期极小曲面的区域的体积分数增加时，相位恢复的精度会降低。
