KINETICS OF SURFACE STEPS IN THE PRESENCE OF IMPURITIES - PATTERNS AND INSTABILITIES

We consider the flow of atomic steps on a crystal surface in the prese nce of impurities. A mesoscopic model of the effect is proposed and st udied by numerical simulations. In the small line tension limit comple x highly connected step patterns are formed that exhibit distinct repe ating features. To explain these features we make the ansatz that the system is locally close to weakly unstable steady states. Using a diff erential equation approach we calculate these steady-state configurati ons analytically, and verify the ansatz; the analytical predictions ar e in agreement with numerical simulations. We also predict that the ty pical length scale of the patterns should grow with time as root t. Th is coarsening law is consistent with numerical simulations of the meso scopic model.