Complete Structural Determination of Mesostructural Dodecagonal Quasicrystalline Particles

Abstract

Quasicrystals have revolutionized our understanding of order in solids by demonstrating exotic structural and physicochemical properties with diverse potential applications. Despite the development of various theoretical models and experimental techniques to describe quasicrystal structures, the precise determination of local three dimensional (3D) arrangements of constituent atoms, or of secondary building units such as clusters or micelles, remains elusive. This challenge is particularly acute in self assembled soft matter quasicrystalline systems, where the complex assembly of molecular groups introduces additional defects and structural modulations. Herein, we report the first complete structural determination of self-assembled mesostructural dodecagonal quasicrystalline particles. Employing advanced electron tomography, combined with dedicated structural tracing and processing workflows, the 3D coordinates of all nodal sites were extracted. This approach reveals that the actual structure deviates from the conventionally assumed tetrahedral close packing geometry, exhibiting diverse coordination environments and displacive fluctuations. We identified and quantified rotational intergrowths arising from node exchange, as well as various defects and disorder, with these features discernible only through 3D analysis. Additionally, we propose a simplified two-layer stacking of isomorphic hexagonal model to form dodecagonal quasicrystal. This work advances our understanding of soft-matter dodecagonal quasicrystals and paves the way for detailed structural elucidation of self-assembled systems.