energy and $r_0 = 2.885$ [Å]{}.

![\[Au-substrate-potentials\]*(Color online) Au/graphite (squares) and Au/a-C substrate potentials (circles) as calculated within the DFT approach. The inset shows the corrugated surface layer of the a-C model with the locations of the calculated potentials (a)-(d) indicated by arrows. The fitted potentials used in the MC simulations are shown as solid lines for graphite (g) and the a-C model substrate. Dashed lines are guides to the eye.*](dft-fig.eps){width="47.50000%"}

For a more realistic description of the a-C substrate we have constructed a model a-C surface. To ensure that sp$^2$ bonding will be dominant[@RFG04] and to obtain a simple model consistent with the observed Au-film formation we use graphite as our starting point. We use a supercell consisting of 4x4 graphite unit cells in the x-y plane and four carbon layers in the z direction. Additional carbon atoms were added in localized regions but otherwise randomly inbetween the graphite planes so as to create voids consistent with the observed holographic phase fluctuations.[@DFTquote]

The resulting supercell of 150 carbon atoms was relaxed into a local minimum. Two main effects of the relaxation can be observed: The carbon structure expanded strongly in the z-direction and the graphite layers buckled due to 