Atomistic calculations of charged point defects at grain boundaries in SrTiO3

Abstract

Oxygen vacancies have been identified to play an important role in accelerating grain growth in polycrystalline perovskite-oxide ceramics. In order to advance the fundamental understanding of growth mechanisms at the atomic scale, classical atomistic simulations were carried out to investigate the atomistic structures and oxygen vacancy formation energies at grain boundaries in the prototypical perovskite-oxide material SrTiO3. In this work, we focus on two symmetric tilt grain boundaries, namely 5 (310)[001] and 5 (210) [001]. A onedimensional continuum model is adapted to determine the electrostatic potential induced by charged lattice planes in atomistic structure models containing grain boundaries and point defects. By means of this model, electrostatic artifacts, which are inherent to supercell models with periodic or open boundary conditions, can be taken into account and corrected properly. We report calculated formation energies of oxygen vacancies on all the oxygen sites across boundaries between two misoriented grains, and we analyze and discuss the formation-energy values with respect to local charge densities at the vacant sites.

How space-charge behaviour at grain boundaries in electroceramic oxides is modified by two restricted equilibria

“…Space-charge layer formation in acceptor-doped SrTiO 3 is assumed 35,116,117 to be due to a difference in the oxygen vacancies' standard chemical potential between the grain-boundary core and the bulk phase (Δ μ ⊖ v < 0), an assumption supported by the results of atomistic simulations. 118–120 This driving energy leads to segregating to the grain-boundary core, and thus, to the buildup of an excess positive core charge. Defect–defect interactions are neglected in our model, and hence, Δ μ ⊖ v is assumed to be independent of the defect concentrations within the core.…”

“…Q c is calculated from formal point-defect concentrations in the core, c c .Previous studies have indicated that the structurally distorted region around the grain-boundary plane is several lattice constants wide, 11,133,134 and only some of the sites in it are energetically more favourable than the bulk sites. 118–120 In our model, we attribute a formal width, w c , to the grain-boundary core, and a formal O-site density, γ c O < γ O , such that the areal core-site density is lower than it would be in a bulk slab of the same width. 35 For convenience, we assume that the number of sites in the Ti sublattice as well as the number of electronic interface states is lowered by the same factor, γ c O / γ O .…”

Electrostatic treatment of charged interfaces in classical atomistic simulations

“…Our values V OBC (y i ) follow a linear trend and can therefore be extrapolated by a line, which is indicated by the red dotted line in figure 2. Such a linear average potential across the supercell with a non-zero slope corresponds to the presence of a surface dipole [33]. In the case of PBC, a vacuum of arbitrary size can be added to the set of atomic planes in the supercell, as sketched by the extension of the dashed blue box in figure 1 in y direction.…”

“…By applying the scenario in section 3.1 to both grains instead of the scenario in section 3.2, we obtain a charge neutral supercell. An example would be a supercell of STO containing a symmetric tilt GB [33]. Furthermore, the supercell of an interface can be constructed by combining one crystal of the scenario in section 3.1 and another one of the scenario in section 3.2.…”

“…In a recent work [33], we derived the electrostatic potential in supercells of the perovskite oxide SrTiO 3 (STO), modelled by a classical interaction potential, where the symmetric tilt grain boundaries Σ5(210)[001] and Σ5(310)[001] were present. For this purpose, we adapted the surrogate model of Freysoldt and Neugebauer [34], which describes the electrostatic potential near an interface by a properly placed effective point charge, to a system containing grain boundaries and surfaces.…”