The microscopic origin of compact triangular islands on close-packed surfac
es is identified using kinetic Monte Carlo simulations with energy barriers
obtained from density-functional calculations. In contrast to earlier acco
unts, corner diffusion anisotropy is found to control the shape of compact
islands at intermediate temperatures. We rationalize the correlation betwee
n the orientation of dendrites grown at low temperatures and triangular isl
ands grown at higher temperatures, and explain why in some systems dendrite
s grow fat before turning compact.