Self-Assembly of Islands on Spherical Substrates by Surface Instability. 
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.  The faster growth rate of surface undulation is associated with the core/shell system of a harder substrate, larger radius, or misfit strain.  On the basis of a Ag core/SiO2 shell system, the self-assemblies of SiO2 nanoislands were explored experimentally.  The numerical and experimental studies herein could guide the fabrication of ordered quantum structures via surface instability on closed and curved substrates.