Surface Instability on Closed and Curved Substrate

Through strain-induced morphological instability, protruding patterns of roughly commensurate nanostructures are self-assembled on the surface of spherical core/shell systems. A three-dimensional (3D) phase field model is established for a closed substrate. We investigate both numerically and analytically the kinetics of the morphological evolution, from grooves to separated islands, which are sensitive to substrate curvature, misfit strain, and modulus ratio between the core and shell.