Ab initio study of point defects in magnesium oxide

Energetics of a variety of point defects in MgO have been considered from an ab initio perspective using density functional theory. The considered defects are isolated Schottky and Frenkel defects and interstitial pairs, along with a number of Schottky defects and di-interstitials. Comparisons were made between the density functional theory results and results obtained from empirical potential simulations and these generally showed good agreement. Both methodologies predicted the first nearest neighbor Schottky defects to be the most energetically favorable of the considered Schottky defects and that the first, second, and fifth nearest neighbor di-interstitials were of similar energy and were favored over the other di-interstitial configurations. Relaxed structures of the defects were analyzed, which showed that empirical potential simulations were accurately predicting the displacements of atoms surrounding di-interstitials, but were overestimating O atom displacement for Schottky defects. Transition barriers were computed for the defects using the nudged elastic band method. Vacancies and Schottky defects were found to have relatively high energy barriers, the majority of which were over $2\mathrm{eV}$, in agreement with conclusions reached using empirical potentials. The lowest barriers for di-interstitial transitions were found to be for migration into a first nearest neighbor configuration. Charges were calculated using a Bader analysis and this found negligible charge transfer during the defect transitions and only small changes in the charges on atoms surrounding defects, indicating why fixed charge models work as well as they do.

Figure 1

The initial configurations of atoms for the (a) first, (b) second, (c) third, (d) fourth, and (e) fifth nearest neighbor di-interstitials. The black circles represent the Mg atoms, while the white circles represent the O atoms.

Figure 2

The initial configurations of the atoms for the (a) first, (b) second, and (c) third nearest neighbor Schottky defects. The circles represent atoms, while the squares represent vacancies. Black squares are Mg vacancies and white squares are O vacancies. This notation is used in all subsequent figures.

Figure 3

(Color online) This graph shows how a clamped cubic spline is fitted to a series of calculated energies for the transition of an isolated interstitial in a 54 atom system. The black dots represent the intermediate states between the initial and final system configurations.

Figure 4

Graphs that show the convergence of the formation energies as larger supercells are utilized. The energies in (a) are for Schottky defects and in (b) are for di-interstitials.

Figure 5

Graph showing the formation energy of di-interstitials, calculated using empirical potentials, as a function of the separation between the two interstitial atoms.

Figure 6

Graph showing the formation energy of Schottky defects, calculated using empirical potentials, as a function of the separation between the two vacant lattice sites.

Figure 7

The direction of displacement of the atoms surrounding the isolated defects: (a) Mg vacancy, (b) O vacancy, (c) Mg interstitial, and (d) O interstitial. The magnitudes of the displacements of selected atoms are shown in Table .

Figure 8

The direction of displacement, during relaxation, of atoms surrounding the (a) first and (b) second nearest neighbor Schottky defects. Magnitudes of these displacements are given in Table .

Figure 9

The direction of displacement, from perfect lattice sites, of atoms surrounding the (a) first, (b) second, (c) third, and (d) fourth nearest neighbor di-interstitials. Magnitudes of these displacements are given in Table .