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.