from the surface than chemisorption. The transition from physisorbed to chemisorbed states are governed by the effective energy barrier . Crystal surfaces have specific bonding sites with larger values that would preferentially be populated by vapor molecules to reduce the overall free energy. These stable sites are often found on step edges, vacancies and screw dislocations. After the most stable sites become filled, the adatom-adatom (vapor molecule) interaction becomes important. Nucleation models Nucleation kinetics can be modeled considering only adsorption and desorption. First consider case where there are no mutual adatom interactions, no clustering or interaction with step edges. The rate of change of adatom surface density , where is the net flux, is the mean surface lifetime prior to desorption and is the sticking coefficient: Adsorption can also be modeled by different isotherms such as Langmuir model and BET model. The Langmuir model derives an equilibrium constant based on the adsorption reaction of vapor adatom with vacancy on the substrate surface. The BET model expands further and allows adatoms deposition on previously adsorbed adatoms without interaction between adjacent piles of atoms. The resulting derived surface coverage is in terms of the equilibrium vapor pressure and applied pressure. Langmuir model where is the vapor pressure of adsorbed adatoms: BET model where is the equilibrium vapor pressure of adsorbed adatoms and is the applied vapor pressure of adsorbed adatoms: As an important note, surface crystallography and differ from the bulk to minimize the overall free electronic and bond energies due to the broken bonds at the surface. This can result in a new equilibrium position known as “selvedge”, where the parallel bulk lattice symmetry is preserved. This phenomenon can cause deviations from theoretical calculations of nucleation. Surface diffusion Surface diffusion describes the lateral motion of adsorbed atoms moving between energy minima on the substrate surface. Diffusion most readily occurs between positions with lowest intervening potential barriers. Surface diffusion can be measured using glancing-angle ion scattering. The average time between events can be describes by: In addition to adatom migration, clusters of adatom can coalesce or deplete. Cluster coalescence through processes, such as Ostwald ripening and sintering, occur in response to reduce the total surface energy of the system. Ostwald repining describes the process in which islands of adatoms with various sizes grow into larger ones at the expense of smaller ones. Sintering is the coalescence mechanism when the islands contact and