Physical Review B (Condensed Matter), 15 July 1995, vol.52, (no.3):2154-64
Kinetics of surface steps in the presence of impurities; patterns and
Kandel, D.; Weeks, J.D.
We consider the flow of atomic steps on a crystal surface in the
presence of impurities. A mesoscopic model of the effect is proposed and
studied by numerical simulations. In the small line tension limit complex
highly connected step patterns are formed that exhibit distinct repeating
features. To explain these features we make the ansatz that the system is
locally close to weakly unstable steady states. Using a differential
equation approach we calculate these steady-state configurations
analytically, and verify the ansatz; the analytical predictions are in
agreement with numerical simulations. We also predict that the typical
length scale of the patterns should grow with time as square root t. This
coarsening law is consistent with numerical simulations of the mesoscopic
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