  The surface diffusion of Cu adatoms in the presence of an adisland at FCC or
HCP sites on Cu(111) is studied using the EAM potential derived by Mishin {\it
et al.} [Phys. Rev. B {\bf 63} 224106 (2001)]. The diffusion rates along
straight (with close-packed edges) steps with (100) and (111)-type microfacets
(resp. step A and step B) are first investigated using the transition state
theory in the harmonic approximation. It is found that the classical limit
beyond which the diffusion rates follow an Arrhenius law is reached above the
Debye temperature. The Vineyard attempt frequencies and the (static) energy
barriers are reported. Then a comparison is made with the results of more
realistic classical molecular dynamic simulations which also exhibit an
Arrhenius-like behavior. It is concluded that the corresponding energy barriers
are completely consistent with the static ones within the statistical errors
and that the diffusion barrier along step B is significantly larger than along
step A. In contrast the prefactors are very different from the Vineyard
frequencies. They increase with the static energy barrier in agreement with the
Meyer-Neldel compensation rule and this increase is well approximated by the
law proposed by Boisvert {\it et al.} [Phys. Rev. Lett. {\bf 75} 469 (1995)].
As a consequence, the remaining part of this work is devoted to the
determination of static energy barriers for a large number of diffusion events
that can occur in the presence of an adisland. In particular, it is found that
the corner crossing diffusion process for triangular adislands is markedly
different for the two types of borders (A or B). From this set of results the
diffusion rates of the most important atomic displacements can be predicted and
used as input in Kinetic Monte-Carlo simulations.
