Schottky defect formation energy in MgO calculated by diffusion Monte Carlo

Abstract

The energetics of point defects in oxide materials plays a major role in determining their high-temperature properties, but experimental measurements are difficult, and calculations based on density functional theory ͑DFT͒ are not necessarily reliable. We report quantum Monte Carlo calculations of the formation energy E S of Schottky defects in MgO, which demonstrate the feasibility of using this approach to overcome the deficiencies of DFT. In order to investigate system-size errors, we also report DFT calculations of E S on repeating cells of up to ϳ1000 atoms, which indicate that QMC calculations on systems of only 54 atoms should yield high precision. The DFT calculations also provide the relaxed structures used in the variational and diffusion Monte Carlo calculations. For MgO, we find E S to be in close agreement with results from DFT and from model interaction potentials, and consistent with the scattered experimental values. The prospects for applying the same approach to transition metal oxides such as FeO are indicated.The quantum Monte Carlo ͑QMC͒ technique 1,2 is important in condensed matter science, because it is generally much more accurate than density functional theory ͑DFT͒ and allows one to make accurate predictions for problems where DFT fails. 3-7 It is usually competitive in accuracy with high-level quantum chemistry methods, but it has the advantage of being practicable for large systems containing hundreds of atoms. Recently, efforts have been made to apply QMC to oxide systems, including transition metal oxides, 8,9 for which DFT gives poor predictions for magnetic properties, phonon frequencies, and other properties. 10 We have recently reported 11 a QMC study of bulk MgO for which we find excellent agreement with experiments for the bulk lattice parameter and bulk modulus, provided appropriate corrections are made. We report here on a QMC calculation of an oxide lattice defect energy, namely the Schottky formation energy E S in MgO. Defect energies in oxide materials are technologically important for applications ranging from high-temperature superconductors to radioactive waste disposal, but are also very difficult to measure experimentally. We shall show that our results for E S in MgO are consistent with available experimental data, as well as supporting earlier DFT predictions. 12 The Schottky energy E S is the energy required to form a cation and anion vacancy pair, and governs the thermal equilibrium concentration of vacancies. 13 The calculation of E S in ionic materials has a very long history, going back to the very early work of Mott and Littleton. 14-16 DFT calculations on defect formation and migration energies in oxides first became possible in the early 1990s, and are now routinely performed. However, particularly in transition metal oxides, the reliability of DFT calculations is questionable.QMC calculations are usually performed in two stages. 1 In the first, known as variational Monte Carlo ͑VMC͒, a trial many-body wave function is constructed as a product of a Slater d...

An ab initio study of the effect of charge localization on oxygen defect formation and migration energies in magnesium oxide

“…g De Vita et al (1992). h Alfé & Gillan (2005). The lower value for the Schottky defect energy calculated here can be explained by the GGA methodology employed, which tends to predict lower cohesive energies (Perdew & Schmidt 2001), thus lower defect energies, than the LDA methodologies employed in previous publications.…”

“…Doubly charged Schottky defect energies have previously been calculated using ab initio techniques using the Hartree-Fock embedded cluster methodology (Grimes & Catlow 1990) and periodic DFT (De Vita et al 1992;Alfé & Gillan 2005;Gilbert et al 2007) using 32, 128 and 180 ion cells, respectively, with local density approximation (LDA) pseudopotentials. De Vita et al (1992) and Alfé & Gillan (2005) employed G-point sampling, while Gilbert et al (2007) used a 6 × 6 × 6 k-point mesh with a localized orbital methodology. Gilbert et al (2007).…”

Ab initiostudy of point defects in magnesium oxide

“…8 and 9͒ and with higher order methods. 10 Our basis sets contained 23 basis functions for Mg and 14 basis functions for O. The required numerical integrations were carried out on an atom centered grid consisting of 40 points in the radial direction and 35 points in the angular direction.…”

Structural stability and defect energetics of ZnO from diffusion quantum Monte Carlo

“…For instance, DMC has recently been applied to study different properties of transition-metal oxides, 10,[16][17][18] MgSiO 3 perovskite, 19 boron-nitride, 20 and point defects in MgO, 21,22 Al, 23 Si [24][25][26] and diamond. 27 Other QMC methods have also recently been applied to study transition-metal oxides.…”