Local and excess vibrational free energies of stepped metal surfaces

We present a comparative study of the local and excess vibrational thermodynamic functions for the (511), (211), and (331) surfaces of Ag and Cu, in the harmonic approximation, employing interaction potentials based on the embedded atom method. Related thermodynamic functions of the corresponding (100) and (111) surfaces are also examined. For these surfaces, local contributions to the vibrational free energy for atoms in layers down to the fifth are found to deviate from that of the atoms in the bulk, as a result of complex multilayer relaxations. These contributions show a linear dependence on temperature, beyond 200 K, and a correlation with the local coordination but without a simple relationship. The vibrational contribution to the step excess free energy for vicinals of (111) is found to be significant.