Surface energetics from the transition from step-flow growth to two-dimensional nucleation in metal homoepitaxy

Expressions for the critical temperature for transition from step-flow growth to growth by two-dimensional nucleation are derived for the cases of low and high barriers for step-down diffusion. The comparison of the equations with experimental data from diffraction studies of metal homoepitaxy makes possible the evaluation of either the energy to break first-neighbor bonds or the activation energy for step-down diffusion. The expressions are used to evaluate the bend energies and the Ehrlich-Schwoebel barrier for step-down diffusion in the systems Ag/Ag(001), Cu/Cu(001), Pd/Pd(001), Fe/Fe(001), Ag/Ag(111), Cu/Cu(111), and Pt/Pt(111).