What does one learn from equilibrium shapes of two-dimensional islands on surfaces?

Abstract

The equilibrium shape of islands has been determined with high accuracy as a function of temperature for Cu(1 0 0), Cu(1 1 1) and Ag(1 1 1) surfaces. The equilibrium shape is analyzed using the inverse Wulff-construction, the Ising-model, and two novel methods concerning the minimum curvature and the aspect ratio of islands. From the conventional inverse Wulff-construction, the angle dependence of the step free energy is obtained. On Cu(1 1 1) and Ag(1 1 1), the energies of A- and B-type steps differ only by about 1%. The analysis of the data using the analytical form of the equilibrium shape provided by the Ising-model yields quite acceptable values for the kink energy on (1 1 1)-surfaces, but not on the (1 0 0)-surface. It is shown that the reason for the failure is due to the different ratio of kink and step energies assumed in the Ising-model for the two surfaces. By combining well-known relations on the statistical mechanics of steps and islands, a simple relation between the kink energy and the minimum curvature of the equilibrium shape is derived and the experimental data are analyzed accordingly for the kink energies on all surfaces. On the Cu(1 0 0)-surface, the kink energy compares well with an earlier independent experimental result. The temperature dependence of the free energy of the 100% kinked step in (1 0 0)- and (1 1 1)-islands is calculated theoretically using general principles. The theory is used to determine the absolute values of the step energies from the experimental data.