Hybrid density functional calculations of hyperfine coupling tensor for hole-type defects in MgAl₂O₄

Abstract

We have performed the density functional calculations (DFT) on the hole-type defects (V-centres) in magnesium aluminate spinel (MgAl₂O₄) following the results of recent paramagnetic resonance measurements (EPR) in Nucl. Inst. Methods Phys. Res. B 435 (2018) 31–37. The hybrid B3LYP functional calculations using large supercells of 448 atoms have demonstrated excellent results not only for bulk properties but also properties of the V-centres in MgAl₂O₄. Three types of V-centres have been considered and confirmed, namely V₁, V₂ and V₂₂. The DFT calculations have revealed the atomic relaxation pattern and spin density distribution around the hole-type defects that is suggested as an important complement to the experiments. Moreover, the calculated hyperfine coupling constants (HCCs) have been analyzed and compared with those from the measured EPR spectra. A good agreement between the calculated and measured HCC values is observed and discussed.

Introduction

Magnesium aluminate spinel MgAl₂O₄ exhibits a very high tolerance to irradiation with fast neutrons due to the efficient recombination of primary radiation-induced Frenkel defects - vacancies and interstitials, which makes it a promising material for optical/diagnostics windows in the environment of future fusion reactors. It is generally accepted that the accumulation of radiation-induced structural defects determines the radiation damage and strongly affects the functionality of various optical materials/components. In this connection, the investigation/understanding of the atomic and electronic structure of defects as well as their thermal annealing plays a crucial role.

Recently, it was discussed what happens with the defects formation in neutron-irradiated single crystals of MgAl₂O₄ [1]. The EPR measurements at room temperature helped to identify the intrinsic structural defects induced by the fast fission neutrons. The obtained values of g-tensor parameters allowed to conclude that the paramagnetic nature of the hole-type centers (called, for simplicity, V-centers in [1]) is supposed to be an O⁻ ion (i.e. a single hole trapped at a regular oxygen ion) located near some negatively charged structural defect. Based on the experimentally measured angular dependencies for different V-centers and their comparison with the calculated ones in the “Easy Spin” program [2], the orientation of paramagnetic centers was determined and the following microstructures of hole-containing centers were proposed [1], [3].

This study showed three different hole-type defects labeled as V₁, V₂, and V₂₂. In the case of V₁-centre a negatively charged defect is situated at the Al³⁺-site which is the Al vacancy in the formal charge state −2, i.e. V₁-centre is a complex$V_{\mathit{Al}}^{-2}$ + O⁻. Similarly, the Mg vacancy in the formal charge state −1 is associated with the V₂-centre = $V_{\mathit{Mg}}^{-1}$ + O⁻. Also, the anti-site defect, when Mg²⁺ occupies the Al³⁺ position, showed up in the EPR spectra leading to a complex V₂₂ = $M_g{|}_{\mathit{Al}}^0$ + O⁻. It can easily be understood that all the three V-centres are compensated by the formation of holes on oxygen atoms to maintain the electroneutrality condition. The charge state coincides with the supercell charge and should not be confused with the oxidation state like Al³⁺ and Mg²⁺ at regular sites.

The DFT calculations of EPR parameters for crystals is still rare in the literature [4], [5]. Previous calculations concerned mainly complex molecules in the cluster model, see, for example, [6], [7]. In the present study we rely on the implementation as suggested in the CRYSTAL17 computer code [8]. Notice that the calculation of g-tensor is not possible in CRYSTAL at the present stage but the HCCs can be calculated as demonstrated in careful study of defects in diamond [5]. Moreover, the DFT calculations could be used to deeper analyze the properties of such defects at atomistic level that is an important complement to experimental data. In previous study of Paudel et al. [9] the anti-site defects and of Jiang et al. [10] the oxygen vacancies in MgAl₂O₄ were calculated within the so-called DFT + U and G₀W₀ approach, respectively. Borges et al. [11] studied combinations of oxygen vacancy and anti-sites in different charge states by means of DFT and meta-GGA Becke-Johnson exchange potential. So, all these advanced DFT studies were focused on optical properties of defective MgAl₂O₄. Recently, the atomic and electronic structure of oxygen interstitial defects in MgAl₂O₄ was calculated by us using the hybrid DFT calculations [12], [13]. In the present study we decided to extend our hybrid DFT calculations to the V-centres and calculate, for the first time, the HCCs for a comparison with those obtained from the measured EPR spectra.