Determining local geometrical features of grain boundaries from microscopy

Grain boundaries are solid-solid interfaces whose dynamics is driven by their local curvature. As they are fluctuating interfaces and have a width comparable to the lattice spacing of the surrounding grains, the determination of their local geometrical characteristics is difficult. Here we present a method to determine the local normal direction, tangent plane and curvature of grain boundaries from microscopy images using point sampled surface analysis techniques. We apply our algorithm to study the boundary of a shrinking grain in a two-dimensional colloidal polycrystalline material. Our method is easily generalized to three dimensions, which makes it applicable to the wide range of interfaces encountered in soft matter.