A method for determining void arrangements in inverse opals

The periodic arrangement of voids in ceramic materials templated by colloidal crystal arrays (inverse opals) has been analysed by transmission electron microscopy. Individual particles consisting of an approximately spherical array of at least 100 voids were tilted through 90° along a single axis within the transmission electron microscope. The bright-field images of these particles at high-symmetry points, their diffractograms calculated by fast Fourier transforms, and the transmission electron microscope goniometer angles were compared with model face-centred cubic, body-centred cubic, hexagonal close-packed, and simple cubic lattices in real and reciprocal space. The spatial periodicities were calculated for two-dimensional projections. The systematic absences in these diffractograms differed from those found in diffraction patterns from three-dimensional objects. The experimental data matched only the model face-centred cubic lattice, so it was concluded that the packing of the voids (and, thus, the polymer spheres that composed the original colloidal crystals) was face-centred cubic. In face-centred cubic structures, the stacking-fault displacement vector is a/6〈211〉. No stacking faults were observed when viewing the inverse opal structure along the orthogonal 〈110〉-type directions, eliminating the possibility of a random hexagonally close-packed structure for the particles observed. This technique complements synchrotron X-ray scattering work on colloidal crystals by allowing both real-space and reciprocal-space analysis to be carried out on a smaller cross-sectional area.