A new calculation strategy to analyze the vibrational free energy of a slab and calculate the vibrational contribution of the surface free energy

Abstract

We developed a new calculation strategy for determining the vibrational contribution of each layer or atom forming a slab, where the latter is a two-dimensional periodic structure of given thickness, generated by separating the bulk structure along the hkl plane of interest and used to simulate the crystal surfaces. By means of this new calculation methodology, it is now possible to estimate how the surface free energy of a crystal face changes with temperature by only taking into account the entropic contribution due to the vibrational motion of atoms in the slab. Furthermore, the model is extended to the calculation of the vibrational contribution to the free energy of the interface between (i) two identical crystals in a twinning relationship and (ii) two different crystals in an epitaxial relationship. Our model uses the frequencies of the vibrational modes of a slab and it is based on the construction of a weight function taking into account how the vibrational amplitude of the atoms involved in the vibrational mode is modified by the presence of the surface. We applied the model to the following systems: (i) 28-layer (100) slab of LiF and (ii) 10-layer (10.4) slab of calcite (CaCO₃). In both cases, the vibrational energy, vibrational entropy and vibrational free energy of the optimized slab, and the contribution to these quantities of each atom and layer forming the slab were calculated.