A new computational strategy to calculate the surface energy of a dipolar crystal surface

Abstract

Determination of the surface energy, γ_(hkl) (J m⁻²), of crystal polar faces is a very difficult task, due to the presence of a dipole moment perpendicular to these surfaces that prevents the use of the slab model to perform empirical, semi-empirical or quantum-mechanical simulations. In the past, in order to overcome this drawback and compensate for the intrinsic dipole moment of the crystal, several computational tricks or complicated system geometries were adopted. In this work, we propose an alternative calculation strategy based on the construction of a twinned slab delimited by two equivalent surfaces: the two portions forming the twinned slab are related by a mirror plane or inversion center, to cancel out the dipole moment, allowing the calculation of the surface energy. Finally, we applied this new methodology to the study of the polar (10.4) and (00.1) (oxygen terminated) surfaces of disordered dolomite, (CaMg)(CO₃)₂ (S.G. R3), and zincite, ZnO (S.G. P6₃mc), respectively. To test the general validity of the proposed strategy, the calculations were performed at the empirical and quantum-mechanical (DFT) levels for dolomite and zincite, respectively. The surface energy of the two faces was determined: 0.526 and 1.789 J m⁻² for the (10.4) and (00.1) surfaces, respectively.