Thermal roughening of an SOS-model with elastic interaction

We analyze the effects of a long-ranged step-step interaction on thermal roughening within the framework of a solid-on-solid model of a crystal surface by means of Monte Carlo simulation. A repulsive step-step interaction is modeled by elastic dipoles located on sites adjacent to the steps. In order to reduce the computational effort involved in calculating interaction energy based on long-ranged potentials, we employ a multi-grid scheme. As a result of the long-range character of the step interaction, the roughening temperature increases drastically compared to a system with short-range cutoff as a consequence of anti-correlations between surface defects

Novel Method for the Experimental Determination of Step Energies

We describe a novel method for the determination of the absolute step energies using the temperature dependence of the equilibrium shape of adatom or vacancy islands. The method is demonstrated with islands on the Cu(111) surface. PACS numbers: 68.35.Md, 05.50. + q, 68.10.Cr, 68.35.Bs The free energy of steps of monatomic height is one of the most important energetic parameters in the physics of crystalline solids. It controls the size of facets in the equilibrium shape of crystals and the curvature of rough surfaces In this Letter we describe a novel method to determine the absolute value of step energies from experimental data on the equilibrium shape of 2D islands as a function of temperature. The method is based on the fact that the leading term in the temperature dependence of the free energy of a step oriented at midangle between the two densely packed directions (i.e., a 100% kinked step) is controlled by a zero point entropy term for which an analytical expression is easily derived. The contour lines for such a step are plotted in Figs. 1(a) and 1(b) as solid lines for the square and the hexagonal lattice, respectively. The step contour changes direction after each length unit, equivalent to an atom diameter a. For the moment we assume that the energies associated with the various paths depicted as dashed lines in Figs. 1(a) and 1(b) are sufficiently close to each other so that the leading term in the configurational partition function for the step is the entropy associated with microscopic realizations of the steps shown as dotted lines i