Mapping structural heterogeneity in three-dimensional biophotonic gyroid networks using position-resolved small-angle X-ray scattering

Abstract The wings of select Papilionid and Lycaenid butterflies contain a three-dimensional gyroid network of a solid cuticle phase in air. In butterfly scales, gyroid networks are optically interesting, as they create the green colour observed in the wings of these butterflies. Here, we used position-resolved synchrotron small-angle X-ray scattering (SAXS) to map the spatial heterogeneity of these three-dimensional biophotonic networks. An automated analysis procedure extracted crystallographic parameters from >10 000 individual SAXS spectra, which were then mapped onto butterfly photographs. Analysis of Bragg peak positions and shapes across four butterfly species revealed spatial variation in the structural parameters of the single-gyroid network space group (I4132), within individual wings, between individuals and between species. Our approach enables a statistical comparison of lattice parameters between species and of local variations within a species. Intraspecies variation within the wings of a single individual of Callophrys rubi was identified. A larger difference in the unit cell size was identified among individuals of the species Callophrys gryneous, Parides sesostris and Callophrys rubi. Among the four species, a single specimen of Teinopalpus imperialis exhibited the greatest variability in unit cell size, largest crystalline domain size and distribution of the cubic phase within the wing. This article is part of the theme issue ‘Geometry, materials and the imagination’.