Atomic shadowing during kinetically limited physical vapor deposition causes a chaotic instability in the layer morphology that leads to nanorod growth. Glancing angle deposition (GLAD) experiments indicate that the rod morphology, in turn, exhibits a chaotic instability with increasing surface diffusion. The measured rod width versus growth temperature converges onto a single curve for all metals when normalized by the melting point Tm. A model based on mean field nucleation theory reveals a transition from a two- to three-dimensional growth regime at (0.20±0.03) × Tm and an activation energy for diffusion on curved surfaces of (2.46±0.02) ×k Tm. The consistency in the GLAD data suggests that the effective mass transport on a curved surface is described by a single normalized activation energy that is applicable to all elemental metals. © 2009 American Institute of Physics.