Stiffness of the Crystal-Liquid Interface in a Hard-Sphere Colloidal System Measured from Capillary Fluctuations

Abstract

Face-centered cubic single crystals of \(σ=1.55 μm\) diameter hard-sphere silica colloidal particles were prepared by sedimentation onto (100) and (110) oriented templates. The crystals had a wide interface with the overlaying liquid that was parallel to the template. The location of the interface was determined by confocal microscopic location of the particles, followed by identification of the crystalline and liquid phases by a bond-orientation order parameter. Fluctuations in the height of the interface about its average position were recorded for several hundred configurations. The interfacial stiffness \(γ̃\) was determined from the slope of the inverse squared Fourier components of the height profile vs the square of the wave number, according to the continuum capillary fluctuation method. The offset of the fit from the origin could quantitatively be accounted for by gravitational damping of the fluctuations. For the (100) interface, \(γ̃ =(1.3±0.3)k_{B}T/σ^{2}\); for the (110) interface, \(γ̃ =(1.0±0.2)k_{B}T/σ^{2}\). The interfacial stiffness of both interfaces was found to be isotropic in the plane. This is surprising for the (110), where crystallography predicts twofold symmetry. Sedimentation onto a (111) template yielded a randomly stacked hexagonal crystal with isotropic \(γ̃ =0.66k_{B}T/σ^{2}\). This value, however, is less reliable than the two others due to imperfections in the crystal.