Direct measurement of stacking disorder in hard-sphere colloidal crystals

At high densities, suspensions of nearly hard sphere colloidal particles show a disorder-order, or crystallization, transition. The resulting colloidal crystals are made up of a more or less randomly-stacked sequence of hexagonal layers. There are three lateral positions, A, B, C, which layers can occupy, but each individual layer has a choice of only the two sites not occupied by the layer upon which it stacks. If two adjacent layers are in sequence AB, then a third layer can be in site A or C with probability (1 - α) or α, respectively. For completely random stacking, α = 0.5. The stacking probability α has been measured previously by light scattering and by fluorescence confocal laser scanning microscopy in which the lateral positions (A, B or C) of a sequence of close-packed layers were identified one layer at a time. We show that when a random stack of close-packed planes is viewed ‘side on’, a pattern of irregular ‘kinks’ is seen, with the number of kinks per unit length bearing a simple relationship to α. Using conventional phase-contrast optical microscopy to image colloidal crystals of (non-fluorescent) sterically-stabilised polymethylmethacrylate spheres dispersed in a mixture of decalin and tetralin, we demonstrate agreement with theoretical predictions of the angles associated with the kinks and their appearance as the plane of focus is moved through the crystal. We use the number of kinks per unit length to determine α for crystals nucleating from a metastable fluid of volume fraction φ = 0.529. The result, α = 0.60 ± 0.07, compares well with previous light scattering measurements.