Order causes secondary Bragg peaks in soft materials

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.