Asymmetric and symmetric Wulff constructions of island shapes on a missing-row reconstructed surface

The two-dimensional equilibrium shapes and structures of adatom or vacancy islands on the (1×2) missing-row (MR) reconstructed Au(110) surface have special characteristics. One type of island has steps parallel to the MR's on opposite sides of the island, which differ both in structure and in formation energy. Hence, the polar step free-energy plot is asymmetric with respect to the Wulff point, and one also expects an asymmetric island contour via the Wulff construction. However, the equilibrium shape of these islands does appear to be symmetric. We show that the Wulff point and the island center do not necessarily coincide and explain how a symmetric equilibrium shape can result from an asymmetric Wulff plot. A second island type has identical steps on opposite sides, which are curved into an almond shape with sharp corners. The Wulff constructions of both types of islands are calculated analytically, and the temperature dependence of the contour shapes is investigated. The results are confirmed by Monte Carlo simulations.