Abstract
We have derived expressions for the free energies of the densely packed [110] and 100% kinked [010] step edges of Cu(001), including both meandering and vibrational entropy terms. The meandering entropy is calculated by taking into account nearest-neighbor and next-nearest-neighbor interactions between the Cu atoms. The vibrational entropy is determined within the framework of an isotropic Einstein oscillator. By using the earlier obtained kink creation energy by Giesen, Steimer, and Ibach [Surf. Sci. 471, 80 (2001)] and taking the strength of the next-nearest-neighbor interaction as the only fitting parameter, we obtain perfect agreement between the ratio of the calculated and experimentally determined ratio of the step free energies (i.e., ${F}_{[010]}{/F}_{[110]}).$ Moreover, in contrast to the Ising model we predict that the two-dimensional equilibrium Cu(001) island shape at $T=0\mathrm{K}$ is not a perfect square.
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