We introduce a chemical-thermodynamic model to explain the formation and an
nealing behavior of Ge nanocrystalline islands grown on Si(001). Assuming t
he nanocrystals are essentially large adsorbed molecules, we propose a simp
le free energy expression for islands of different shapes interacting with
each other via the substrate on which they reside. Nanocrystal growth, disa
ppearance, and shape transitions are all consonant with a near-equilibrium
system constrained by mass conservation and characterized by interisland re
pulsions. We construct an equilibrium shape diagram from experimentally det
ermined free energy differences between island shapes and use it to resolve
several anomalies that have been noted for the Ge on Si(001) system.