Revealing stacking sequences in inverse opals by microradian X-ray diffraction

We present the results of the structural analysis of inverse opal photonic crystals by microradian X-ray diffraction. Inverse opals based on different oxide materials (TiO₂, SiO₂ and Fe₂O ₃) were fabricated by templating polystyrene colloidal crystal films grown by the vertical deposition technique. Our results suggest that most inverse opal films possess dominating twinned face-centered cubic structure accompanied by some fragments of hexagonal close-packed and random hexagonal close-packed structures. The studied samples possessed individual structures with different ratios of the above fragments. By fitting the results of the angular-dependent X-ray diffraction by the Wilson model we estimate the stacking probability α in the studied samples to be ∼0.7-0.8. Microradian X-ray diffraction therefore provides detailed structural information on opal-based photonic crystals and can be applied to opaque inverse opals or the samples with a periodicity <300 nm, whose structure cannot be investigated by conventional optical methods.