Doctor of Philosophy / Department of Physics / Talat S. Rahman / This dissertation is an extensive study of several issues related to post deposition morphological evolution of fcc metal surfaces. These studies were carried out by probing the energetics and the dynamics of underlying atomistic mechanisms responsible for surface diffusion. An important aspect is the determination of relative probability of competing atomistic mechanisms and their contribution to controlling shapes and step edge patterns of nano structures on surfaces. In this scenario, the descent of adatoms from Ag islands on Ag(111) surface is examined. It shows an exchange mechanism to dominate over hopping and the process to favor the formation of (100)-microfacetted steps (A-type) over the (111)-microfacetted ones (B-type). Molecular dynamics simulations support these results at low temperature while at high temperature B-type step formation dominates. This change in the trend could happen if these processes leading to the formation of the A and B type steps have different values of their diffusion prefactors. This difference is confirmed on the basis of our calculations of the diffusion coefficients. Further, to understand the macroscopic properties of a system on the basis of its atomic scale information, spatial and temporal fluctuations of step edges on vicinal Cu(1 1 13) and Cu(1 1 19) surfaces is studied using kinetic Monte Carlo (KMC) simulations. These results show excellent agreement with experimental data, highlighting the role of mass transport along step edges, and also showing the validity of tools like KMC which aims at bridging the gap in length and time scales at which a range of interesting phenomena take place. To facilitate unbiased modeling of material properties, a novel way of performing KMC simulations is presented. In this approach the lists of diffusion processes are automatically collected during the simulation using a saddle-point search method in the potential energy landscape. The speed of the simulations is thus enhanced along with a substantial gain in reliability. Using this method the diffusion and coalescence of two-dimensional Cu and Ag adatom-island on Cu(111) and Ag(111) is studied. Together with input from molecular dynamics simulations, new processes involving the concerted motion of smaller islands are revealed. A significant difference in the scaling of the effective diffusion barriers with island size is observed for the sets of smaller (less than 10 atoms) and larger islands. In particular, the presence of concerted island motion leads to an almost linear increase in the effective diffusion barrier with size, while its absence accounts for strong size-dependent oscillations and anomalous behavior for trimers and heptamers. A crossover from diffusion due to the collective motion of the smaller island to a regime in which the island diffuses through the periphery dominated mass transport (large islands, 19 to 100 atoms) is predicted. For islands containing 19 to 100 atoms the scaling exponent is found to be in good agreement with that found in previous studies.