neighbor interactions, type–I boundaries in fact have zero energy.[@degeneracy]

We assume here that the time–evolution of our model occurs only through atom–vacancy exchange processes. In an elementary move we first randomly single out one of the vacancies and, second, we choose at random one of its nearest neighbors occupied by an atom. The standard Metropolis algorithm is then used to decide whether the atom–vacancy exchange for the chosen pair takes place or not. In one Monte Carlo step (MCS), the system completes a series of as many such elementary moves as there are lattice sites in the system, i. e. $4L^3$, so that this time unit does not depend on the actual number of vacancies.

In previous simulations [@paper1] we have chosen the interaction parameters such that they were consistent with the observed Au–segregation at the Cu$_3$Au (001)–surface. Following Ref. , we take $V_{BB} = -V_{AA} = -V_{AB} > 0 $ and assume $c^V \simeq 6.1 \cdot 10^{-6}$ as the mean density of vacancies present in the system.[@vacancy] For vacancy concentrations of that order we have verified that both static and kinetic properties are independent of the precise value of $c^V$. To simulate a sudden quench from high temperatures to 