EPR $g$-tensor of paramagnetic centers in yttria-stabilized zirconia from first-principles calculations

In order to assign the defect responsible for the experimental electron paramagnetic resonance (EPR) signal with trigonal symmetry ($T$ center), we have studied the properties of different paramagnetic centers in yttria-stabilized cubic zirconia by computing the EPR $g$-tensor from density functional perturbation theory. We have considered reduced vacancy-zirconium complexes and reduced Ti impurities. These first-principles calculations allow us to discard the experimental assignment of the $T$ center to an extrinsic ${\mathrm{Ti}}^{3+}$ ion nearest neighbor to a single vacancy. Instead, the calculated EPR $g$ tensors of both a ${\mathrm{Zr}}^{3+}$ or a ${\mathrm{Ti}}^{3+}$ ion at the center of a divacancy aligned along the $⟨111⟩$ directions are compatible with the experimental EPR signal. However, since the EPR signal of the $T$ center is correlated experimentally with an optical absorption band at $370\mathrm{nm}$, calculated optical excitations allow us to decide in favor of the ${\mathrm{Ti}}^{3+}$ divacancy complex.

Figure 1

(Color online) Structural model of the $T$ center: a reduced Zr ion $\left({\mathrm{Zr}}^{3+}\right)$ at the center of a divacancy complex oriented along the $⟨111⟩$ directions $(◻{\mathrm{Zr}}^{3+}◻)$.

Figure 2

(Color online) Relaxation pattern of the divacancy complex in different configurations. The displacement of oxygen atoms with respect to the ideal cubic fluorite structure is mainly toward the nearest vacancy, its amplitude toward $⟨100⟩$ directions is given in angstroms (for the PBE functional). Arrows are twice longer than the real displacements, for clarity. Minor displacements along the other directions are given in Table . (a) Neutral configuration B1; (b) charged configuration B1; (c) neutral configuration C3; (d) charged configuration C3 (see text).

Figure 3

(Color online) Electronic density isosurfaces of the unpaired electron in four different paramagnetic centers: (a) ${\mathrm{Ti}}^{3+}$ eightfold coordinated (C1 configuration); (b) ${\mathrm{Ti}}^{3+}◻$ (C2 configuration); (c) $◻{\mathrm{Ti}}^{3+}◻$ (C3 configuration); (d) $◻{\mathrm{Zr}}^{3+}◻$ (B1 configuration). The isosurface encloses 70% of the total probability to find the electron for configurations C1, C2, and C3, 40% for B1. Kohn–Sham orbitals refer to B3LYP calculations on geometries optimized at the PBE level. PBE orbitals are qualitatively very similar to those reported here. The cube represents the ideal oxygen sublattice.

Figure 4

Spin-resolved electronic density of states (DOS) obtained from all-electron B3LYP calculations with a basis set of Gaussian type functions (GTFs) for (a) eightfold coordinated ${\mathrm{Ti}}^{3+}$ (configuration C1), (b) ${\mathrm{Ti}}^{3+}$ vacancy complex (${\mathrm{Ti}}^{3+}◻$, configuration C2), (c) ${\mathrm{Ti}}^{3+}$ divacancy complex ($◻{\mathrm{Ti}}^{3+}◻$, configuration C3), and (d) ${\mathrm{Zr}}^{3+}$ divacancy complex ($◻{\mathrm{Zr}}^{3+}◻$, configuration B1). The zero of energy is the (aligned) top of the valence band. The plot reports the total DOS (thin black line), the DOS projected on the GTFs of the defect atom (thick black line) and the DOS projected on the GTFs of all the other metal atoms (shaded gray) for both spins $(\alpha$ and $\beta )$. Each energy level is broadened with a Gaussian of width $0.03\mathrm{eV}$. The differences in the host band gap are due to variations in the distribution of vacancies and Y ions.

Figure 5

Calculated B3LYP position in energy (eV) with respect to the valence band maximum of the unpaired electron in different paramagnetic centers. For $◻{\mathrm{Zr}}^{3+}◻$ the configuration B1 is considered. The position of the empty state of $◻{\mathrm{Zr}}^{4+}◻$ in configuration B1 is reported as well. The energies of the PBE levels are reported in parenthesis. The host band gap is also reported (see text and Fig. 4).