MgO addimer diffusion on MgO(100): A comparison of ab initio and empirical models

Diffusion of a MgO dimer on a MgO(100) surface is investigated using both density functional theory (DFT) and empirical ionic potentials. Barriers for diffusion via hop and exchange mechanisms are calculated. A qualitative difference is found between DFT and the empirical potential for the oxide exchange barrier. DFT predicts a saddle point for the process with a barrier of $0.88\mathrm{eV}$, whereas the empirical potential of Lewis and Catlow, with a formal charge of $\pm 2.0e$, finds this structure to be a stable intermediate minimum with an energy of $0.19\mathrm{eV}$, relative to the most stable addimer structure. The empirical potential predicts that the oxide hop and exchange mechanisms are equally likely; whereas, DFT shows that the oxide adion hop mechanism has a lower energy barrier. A Bader population analysis of the DFT charge density indicates that the magnesium and oxide ions have partial charges of magnitude $\pm 1.7e$. Using an empirical potential with this partial charge, the local minimum in the oxygen exchange process becomes a saddle at $0.62\mathrm{eV}$, which is in better agreement with DFT. The standard deviation between the energy of the DFT minima and the saddle points with those of the empirical potential was reduced from $0.32\mathrm{eV}$ when using the formal charge parameters of Lewis and Catlow to $0.15\mathrm{eV}$ using partial charges. The qualitative agreement found for each diffusion barrier using the partial charge model suggests that a Bader analysis can be used to obtain suitable partial charges for constructing empirical potentials.

Figure 1

The magnesium hop process in which a magnesium adion hops from on top of a substrate oxide ion, across a hollow site, onto an adjacent oxide ion site. There is a shallow intermediate minimum of only $14\mathrm{meV}$ below the saddle energy of $0.33\mathrm{eV}$ with the magnesium adion at the hollow site. In the final state, the addimer has rotated by 90° about the oxide adion.

Figure 2

The magnesium exchange starts in the same way as the hop process, with a magnesium ion moving to an intermediate minimum on a hollow site. From this shallow minimum, the magnesium adion pushes out the surface magnesium ion from directly below the oxide adion into a hollow site. A second half hop moves the magnesium adion to an oxide site. In the final state, the addimer has rotated 180° about the oxide adion, and the magnesium adion has been exchanged with one from the surface.

Figure 3

Intermediate minima along the magnesium and oxide exchange minimum energy pathways. The magnesium exchange minimum (a) is stable with an energy of $0.24\mathrm{eV}$, whereas the oxide exchange minimum (b) is unfavorable with an energy of $0.88\mathrm{eV}$, just $1\mathrm{meV}$ below the saddle point energy. The high energy of the oxide exchange intermediate forces the oxide adion to diffuse via the lower energy hop process, whereas the magnesium hop and exchange mechanisms are equally likely.

Figure 4

Connectivity of hop and exchange diffusion processes for the magnesium ion in the MgO addimer as found with DFT. The top and bottom rows illustrate the hop process and an intermediate minimum. These intermediate minima are connected with an exchange process, in which the magnesium adion exchanges with the magnesium ion below the oxide adion. Another intermediate minimum is found along this pathway, in which the oxide ion is supported on the bridge formed by the exchanging magnesium ions. Similar diffusion mechanisms are found for the oxide ion, except in that case there is no intermediate minimum for the hop process.

Figure 5

Convergence of MgO diffusion barriers via both hop (dashed) and exchange (solid) mechanisms. The localized hop processes converge rapidly with system size, overestimating the converged barrier by only $0.03\mathrm{eV}$ with a substrate of $4\times 4$ MgO units per layer. The exchange (xch) mechanisms converge slowly with system size due to the relaxation of surrounding substrate ions. Fitting an exponentially decaying function to the exchange barriers as a function of number of MgO units in the simulation cell indicates that the barriers of 0.88 and $0.32\mathrm{eV}$ for the oxide and magnesium exchange, respectively, overestimate the converged barriers by 3–4%.

Figure 6

Histogram of the magnitude of Bader charges for ions within a 200 atom slab with an adsorbed MgO dimer on the surface. Magnesium ions have a positive charge and oxide ions have a negative charge. The distribution of charge transferred from magnesium to oxide ions is peaked about the average value of $1.73e$. The charge of the atoms in the adsorbed dimer and the nearest surface oxygen atom fall outside the range of the plot. The charge on these atoms is indicated in the inset cross section of the slab.

Figure 7

Energy barriers for the oxygen exchange mechanism. The formal $(\pm 2.0e)$ charge models of Lewis and Catlow (L-C) and Ball and Grimes (B-G) predict a low energy intermediate split oxygen structure, in qualitative disagreement with the density functional (DFT) calculations. A reduction in the ionic charge to $\pm 1.7e$ in the Ball and Grimes potential causes the oxygen split structure to become a saddle point at $0.62\mathrm{eV}$ instead of a minimum at $0.37\mathrm{eV}$, bringing the energy 50% closer to the DFT value of $0.88\mathrm{eV}$.

Figure 8

Diffusion process found during a temperature accelerated dynamics simulation. The intermediate structure (b) between a magnesium exchange intermediate (a) and the oxide exchange intermediate (c) has an energy of $0.35\mathrm{eV}$ and $0.48\mathrm{eV}$ with the B-G $\pm 2.0e$ and $\pm 1.7e$ models, respectively. The high energy of the final oxide exchange intermediate minimum makes this process unfavorable according to DFT and the reduced charge B-G $\pm 1.7e$ model.