Electrostatic treatment of charged interfaces in classical atomistic simulations

Abstract

Artificial electrostatic potentials can be present in supercells constructed for atomistic simulations of surfaces and interfaces in ionic crystals. Treating the ions as point charges, we systematically derive an electrostatic formalism for model systems of increasing complexity, both neutral and charged, and with either open or periodic boundary conditions. This allows to correctly interpret results of classical atomistic simulations which are directly affected by the appearance of these potentials. We demonstrate our approach at the example of a strontium titanite (SrTiO3) supercell containing an asymmetric tilt grain boundary. The formation energies of charged oxygen vacancies and the relaxed interface structure are calculated based on an interatomic rigid-ion potential, and the results are analyzed in consideration of the electrostatic effects.

Formation Energy Profiles of Oxygen Vacancies at Grain Boundaries in Perovskite‐Type Electroceramics

“…Here, E denotes the total energy of a supercell containing an oxygen vacancy, and is a correction energy to compensate artifacts of the finite size simulation model. As we described in detail in our previous articles, [ 39,40 ] lattice planes consisting of charged ions can lead to strong electric fields in the supercells, depending on the stoichiometry of the planes, on the charges of the ions, and on the relative shifts of the lattice planes with respect to each other during the structural relaxation. Such electric fields must be considered as artifacts of the simulation model because they are not present in realistic systems, where the electric fields can be compensated by stoichiometric changes and an adjustment of the electronic charge density to avoid the “polar catastrophe” of diverging electric fields in macroscopically sized systems.…”

“…The interaction energy of the charged point defect with the artificial field must be corrected, and we followed the procedure described in ref. [40] to obtain in Equation () for the different GB cells considered in this work. The method is based on analytic functions for the electrostatic potentials and the subtraction of the corresponding energies from the outcome of the energy calculations of the cells containing the charged oxygen vacancies.…”

“…The interaction energy of the charged point defect with the artificial field must be corrected, and we followed the procedure described in ref. [40] to obtain E corr in In the ATGB cell, the grains were initially separated by 0.5a 0 and the atoms in the gray shaded parts of the cell were fixed during the relaxation. The violet double arrows on top of each cell, together with the dash-dotted vertical lines at their ends, indicate regions of length 30 Å, with 15 Å left and right of the centers of the GBs, corresponding to the extensions of the oxygen vacancy formation energy profiles depicted in Figure 4 and 5.…”