Densely packed dots

    The following figure shows an evolution sequence of a simulation with the average concentration 0.4.  The calculation starts from a random initial condition (The average concentration is taken to be 0.4.  The initial condition is set to fluctuate randomly within 0.001 from the average).  The epilayer forms dots instead of stripes.  One can broadly identify three stages of evolution.  In the early stage, the concentration rapidly attains the two equilibrium compositions.  In the intermediate state, the dots approach to equilibrium size and form domains.  In each domain the dots order into a triangular lattice.  The dots at the domain boundary are less ordered, and have excess energy relative to those inside the domains.  In the late stage, the dots tend to rearrange themselves to form a superlattice of long range order.  However, the rearrangement takes much longer time than setting the dot sizes.  In spinodal decomposition of a bulk alloy, the late stage evolution is characterized by coarsening: large particles grow larger and small particles disappear.  In an epilayer, the late stage involves rearrangement of dots with their size invariant.