A new computational strategy to calculate the edge energy of a relaxed step. Calcite (CaCO3) as a case study

Determination of the step edge energy, ρ (J/m), is a very difficult task. For this reason, very few theoretical estimates of the edge energies of crystalline materials exist. Nowadays, ρ is calculated using a method that requires the geometry optimization of many systems. In this paper we propose a new computational approach for calculating ρ, based on the construction of a 2D periodic (hkl) slab, on which a [uvw] step delimited by two relaxed ledges (acute and obtuse) is generated; the method has been designed both for empirical and quantum-mechanical calculations. At variance with previous computational method, our strategy requires the geometry optimization of only a system; then it results to be more accurate and less expensive from a computational point of view. We applied this new methodology to the study of the [-441], [4-21] and [010] steps lying on the flat (10.4) face of calcite. The structure and energy of the different [uvw] edges were determined. We calculated, as the most stable step, the acute [-441] ledge (ρ = 5.04x10-10 J/m), followed by the Ca-terminated acute-[010] (5.39x10-10 J/m) and Ca-terminated [4-21] (9.77x10-10 J/m). Finally, by using these edge energies, we draw the equilibrium shape of a relaxed 2D nucleus lying on the (10.4) face.