Step Free Energy - The equilibrium shape of a hexagonal lattice

This thesis derives an expression of the step free energy for the hexagonal lattice in the armchair and zigzag direction. This solid-on-solid model with nearest neighbor interaction recaptures the exact result of Wannier in case the armchair edge is considered. The derivation of an exact expression for the edge free energy in the zigzag edge was attempted, but we did not manage to find it. The angular dependence of the step free energy is derived and with the use of the Wulff construction the equilibrium shape at different temperatures is determined.