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

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. Th e equilibrium shape is analyzed using the inverse Wulff-construction, the I sing-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%. Th e analysis of the data using the analytical form of the equilibrium shape p rovided by the Ising-model yields quite acceptable values for the kink ener gy on (1 I I)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 ener gies assumed in the Ising-model for the two surfaces. By combining well-kno wn relations on the statistical mechanics of steps and islands, a simple re lation between the kink energy and the minimum curvature of the equilibrium shape is derived and the experimental data are analyzed accordingly for th e kink energies on all surfaces. On the Cu(1 0 0)-surface, the kink energy compares well with an earlier independent experimental result. The temperat ure 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 th eory is used to determine the absolute values of the step energies from the experimental data. (C) 2001 Elsevier Science B.V. All rights reserved.