Free energies of steps on (111) fcc surfaces

For a hexagonal two-dimensional lattice we derive, using a surprisingly simple route, exact expressions for the step free energies along the high symmetry directions, left angle bracket1–10right-pointing angle bracket and left angle bracket11–2right-pointing angle bracket. If we consider only nearest-neighbor interactions, ε, and ignore step overhangs the step free energy vanishes at a temperature View the MathML source. In a more sophisticated model that incorporates step overhangs we find a reduction of TR to about 0.87ε/kb. The obtained step free energy expressions are also valid for the free energy of walls between two regions of opposite spins of the triangular 2D Ising system.