Analytical determination of the Landau-Ginzburg parameters of (100)metal homoepitaxial systems

In the initial stages of homoepitaxial growth on the (100) surface of metals such as Ag, Fe, Cu, Ni, and Pd, where the clean surface does not reconstruct, two-dimensional islands with compact, near-square shapes are formed. In order to determine the phenomenological material parameters of the nonlinear and nonlocal Landau-Ginzburg theory, which describes the metal homoepitaxial systems mentioned above, an atomistic model for these systems is developed. Based on this model, we derive analytical relationships between the Landau-Ginzburg parameters A, B, C, and D, and the parameters of the homoepitaxial system (such as coverage, first-neighbour interaction energy, etc.). We find that the Landau-Ginzburg parameters of the system depend on the specific material as well as on the coverage of the surface. We then apply the method to the Ag/Ag(100) system.