Study of cation vacancies with localized hole states in MgAl₂O₄ crystals

Highlights

• The DFT+U method was used to evaluate the electronic structures and optical spectra of MgAl₂O₄ crystals with cation vacancies.

• The color center models ${\text{V}}_{\text{Mg}}^{2-}-{\left[{\text{O}}_2^{3-}\right]}_2^{+}$ and ${\text{V}}_{\text{Al}}^{3-}-{\left[{\text{O}}_2^{3-}\right]}_3^{+}$ are proposed for a magnesium vacancy and an aluminum vacancy with localized hole states.

• Cation vacancies with localized hole states are predicted to act as a source of blue luminescence.

Abstract

The density functional theory with the Hubbard U parameter method was used to evaluate the lattice structure, electronic structures, and optical spectra of MgAl₂O₄ crystals with cation vacancies. We analyzed the electronic structures of oxygen atoms around the cation vacancies. The holes prefers to distribute themselves on all the nearest oxygen atoms around the vacancy rather than to localize on a single oxygen atom. We propose the color center models ${\text{V}}_{\text{Mg}}^{2-}-{\left[{\text{O}}_2^{3-}\right]}_2^{+}$ and ${\text{V}}_{\text{Al}}^{3-}-{\left[{\text{O}}_2^{3-}\right]}_3^{+}$ for the magnesium vacancy and the aluminum vacancy with localized hole states. Taking into account electron-phonon coupling, we obtained the optical spectra of the cation vacancies with localized hole states. The calculated absorption peaks of the cation vacancies with localized hole states are consistent with the experimental results. The emission peaks of the magnesium vacancy and the aluminum vacancy with localized hole states are at 2.63 eV and 2.62 eV, close to that of the F center at 2.69 eV. We predict that cation vacancies with localized hole states will act as a source of blue luminescence.

Introduction

Wide-band-gap MgAl₂O₄ crystals have high tolerance of cation disorder even with high doses of neutron radiation, so they are the preferred material for future fusion reactor devices. Spinel single crystals and transparent ceramics can be used as inert matrices for nuclear fuel [[1], [2], [3]]. The transparency of MgAl₂O₄ crystals, their high chemical stability, and their high thermal conductivity mean they are an effective host lattice for many doping elements, such as Ce, Cr, and Mn, which have been widely applied in solid-state lighting [4,5], near-IR light-emitting diodes [6], and wide-color-gamut backlight display devices [7]. To improve the photoluminescence performance of the MgAl₂O₄ host materials, Eu³⁺, Tb³⁺, Dy³⁺, etc. are added to MgAl₂O₄ transparent ceramics for the fabrication of solid-state lasers [8,9]. In addition, spinel as a catalyst carrier [10,11] promotes the recycling of the catalyst and increases the reaction efficiency during the photocatalytic process. It has also been considered as an attractive candidate material for temperature and humidity sensors [12,13].

Radiation-induced structural defects have a great influence on the optical properties of the MgAl₂O₄ crystal. Therefore, the mechanisms for irradiation-induced defects play a key role in regulating and controlling the function of optical components. It has generally been accepted that MgAl₂O₄ contains various intrinsic defects, such as oxygen vacancy (V_O) and magnesium vacancy (V_Mg). Sawai and Uchino [14] reported that the emission peak at 2.7 eV in the blue region is attributed to an F⁺ center (V_O with one electron). MgAl₂O₄ with excess Al₂O₃ nonstoichiometry can produce a large number of positively charged oxygen vacancies (F⁺ centers) when it is heated in a vacuum at 1900 °C. Therefore, the spinel obtained exhibits a bluish white photoluminescence with a photoluminescence quantum yield of 20%, which is attributed to excitation and recombination processes involving the F⁺ center. Ibarra et al. [15] used optical absorption and electron paramagnetic resonance methods to study the complex absorption spectrum of the cation vacancy (also called V centers) in single-crystal and polycrystalline MgAl₂O₄ samples. They speculated that the optical absorption band peaking at 3.4 eV is related to the hole localized on tetrahedral and octahedral cation vacancies. Sato et al. [16] found that the emission peaks at 1.72 and 2.75 eV disappear or the intensities are greatly reduced when MgAl₂O₄ crystals grow in Mg-rich conditions. According to the of electron paramagnetic resonance spectrum, they speculated that a single hole is trapped at an oxygen ion around the V_Mg. Lushchik et al. [17] detected several defects arising from fast neutron irradiation in MgAl₂O₄ crystals. They gave the absorption spectra of irradiated samples at room temperature over a wide spectral range of 1.5–7.8 eV and proposed four models for hole-type paramagnetic centers.

There have been many theoretical studies of anion vacancies in MgAl₂O₄ [[18], [19], [20], [21], [22], [23], [24], [25], [26], [27]]. However, few studies have investigated cation vacancies with localized hole states in MgAl₂O₄ single crystals. Therefore, the theoretical models for the structural defects induced by neutron irradiation in MgAl₂O₄ are still awaited. Moriwake et al. [28] calculated electronic structures and chemical bonding of MgCr₂O₄ and MgAl₂O₄ with chromium vacancy (V_Cr) and V_Mg. After analyzing the contour map of the square of the wave functions, they concluded that three holes are confined in the vicinity of the aluminum vacancy (V_Al). Varley et al. [29] calculated the optical properties of various wide-band-gap oxides with localized hole states using the screened hybrid functional of Heyd, Scuseria, and Ernzerhof (HSE), which allowed them to interpret the emission peaks that had been observed in experiments.

Nolan and Watson [30] used the density functional theory with the Hubbard U parameter (DFT + U) approach to calculate the localized hole states in doped and defective oxides. They revealed that DFT + U with U = 7 eV is sufficient to calculate the O 2p hole states in oxide materials, even though experimental data are lacking. More importantly, the on-site Coulomb interaction U_p-p for O 2p holes was verified by the experimental data [31]. DFT + U with U = 8 eV and the HSE functional were used to investigate the formation of self-trapped holes in three prototypical perovskites (SrTiO₃, BaTiO₃, PbTiO₃) [32], and the results revealed that the dependence of U on the configuration and the state is small in the perovskite oxides. Wang et al. [33] demonstrated the dependence of U on the different projection radii when they compared the DFT + U and HSE functional methods for the calculation of polaronic properties in rutile TiO₂, Fe₂O₃, FePO₄, LiFePO₄, and spinel MnO₂. Geneste et al. [34] considered a simple change in the calculation of the density matrix, and they proposed a slightly modified DFT + U scheme to obtain a more physical value of U, the electron number, and the band gap.

In this work, we used the DFT + U method to calculate the electronic structures of cation vacancies with localized hole states in MgAl₂O₄ crystals. We evaluated the value of U from 1 to 16 eV for the effect on the localized hole states. When U > 7 eV, the unoccupied state is well separated from the valence band. Therefore, we used U = 7.5 eV to calculate the electronic structures of cation vacancies with localized hole states. To obtain reliable defect formation energies, we used the finite-size correction to eliminate the periodic images of the charged defect states. The advanced hybrid functional method was used to align the credible charge transition level. Finally, taking into account the electron-phonon coupling, we investigated the optical spectra for cation vacancies with localized hole states in MgAl₂O₄.