Investigations of the Spin-Hamiltonian Parameters and Defect Structure for the (TiO4)5− Tetrahedral Clusters in ZrSiO4: Ti3+ Crystal

The spin-Hamiltonian parameters (g factors g//, g⊥ and hyperfine structure constants 47Ai, 49Ai, where i = // or ⊥, 47Ai and 49Ai denote the values of isotopes 47Ti3+ and 49Ti3+) of Ti3+ ions at the tetragonal tetrahedral Si4+ sites in ZrSiO4 crystal are computed from the high-order perturbation formulas based on the cluster approach where the contributions due to both the d orbitals of central dn ion and p orbitals of ligand ion are considered. The calculated results are reasonably coincident with the experimental values. The defect structure of tetragonal (TiO4)5− impurity cluster which differs from the replaced host (SiO4)4− cluster in ZrSiO4 is evaluated from the calculation. The results are discussed.


Introduction
Zircon, ZrSiO 4 , is a well-known mineral for dating by means of the thermoluminescence (TL) method [1]. It can be used as the Raman or Infrared (IR) spectroscopybased pressure sensor [2,3] (because its Raman shifts and IR spectra are highly sensitive to the pressure applied) and the matrix material of ceramic pigment [4,5]. Importantly, ZrSiO 4 and materials with zircon-type structure doped with transition (d n ) and rare earth (4f n ) ions can be applied as the laser, phosphor and luminescence materials [6][7][8][9][10]. These applications are connected with defects (which can also be caused by radiation and doping) in zircon and zircon-type crystals. The electron paramagnetic resonance (EPR) technique is a powerful tool to study the defects and defect structures (including the d n and f n impurity clusters) in crystals. So, the EPR spectra of d n -and f n -doped ZrSiO 4 crystals have been widely investigated [11][12][13][14][15][16]. For example, the EPR spectra of Ti 3+ -doped ZrSiO 4 crystal were measured by some authors [14][15][16]. It is found that Ti 3+ ions can substitute for both the dodecahedral Zr 4+ site and the tetrahedral Si 4+ site in ZrSiO 4 crystal [14][15][16]. The spin-Hamiltonian parameters (g factors g i , hyperfine structure constants 47 A i , 49 A i , where i = // or ⊥, 47 A i and 49 A i denote the values of isotopes 47 Ti 3+ and 49 Ti 3+ ) of Ti 3+ ions at the tetragonal Si 4+ tetrahedral sites (note: the symmetry of host (SiO 4 ) 4− cluster is D 2d with the bond length R(Si 4+ -O 2− )≈ 1.622 Å and the angle θ between the direction of R and C 4 axis being 48.5° [17]) were given from the EPR experiment by Claridge et. al. [16]. The observed same symmetry (D 2d ) of (TiO 4 ) 5− tetrahedral cluster as that of the host (SiO 4 ) 4− cluster [16] clearly suggests that the charge compensation is far away because if a charge compensator, e.g., a M 5+ cation at the neighboring Si 4+ or Zr 4+ site, or an anion X − at the neighboring O 2− site, the symmetry of (TiO 4 ) 5− cluster should be changed from tetragonal to rhombic or lower. Until now no theoretical calculations for these spin-Hamiltonian parameters have been made. Furthermore, the defect structure of (TiO 4 ) 5− tetrahedral cluster in ZrSiO 4 crystal has not been studied. Since the spin-Hamiltonian parameters of a paramagnetic impurity center in crystals depend sensitively upon its defect structure, the theoretical analysis of spin-Hamiltonian parameters can obtain some useful information on the defect structure of the paramagnetic impurity center. In this paper, as an example, we compute the spin-Hamiltonian parameters of (TiO 4 ) 5− cluster in ZrSiO 4 : Ti 3+ crystal by means of the high-order perturbation formulas resting on the cluster approach. The defect structure of (TiO 4 ) 5− tetrahedral cluster is acquired on the basis of the calculation. The results are discussed.
The observed g // < g ⊥ indicates that the (TiO 4 ) 5− cluster in ZrSiO 4 : Ti 3+ is a tetragonally-elongated tetrahedron (which is similar to the host (SiO 4 ) 4− cluster) with the ground state 2 ). The high-order perturbation formulas of the spin-Hamiltonian parameters for d. 1 ions in a tetragonlly-elongated tetrahedral cluster are deduced as [18] where g e ≈ 2.0023 is the spin-only g value. κ is the core polarization constant. The crystal field energy levels The crystal field parameters Dq, D s and D t can be computed from the superposition model [27]. In this model, these parameters can be expressed as where the intrinsic parameter ratio A 2 (R)∕A 4 (R) ≈ 10 obtained by analyzing the crystal field parameters in optical and EPR spectra for 3d n ions in many crystals with the superposition model [18,20,[28][29][30][31][32]. θ is the angle between the direction of metal-ligand distance R and C 4 axis in the studied tetragonal tetrahedral cluster. The θ h ≈ 48.5° in the host (SiO 4 ) 4− clusters in ZrSiO 4 [17]. Analogous to the metal-ligand distance R, the angle θ in the (TiO 4 ) 5− impurity center is unlike the host angle θ h . Here we assure θ ≈ θ h + Δθ, where Δθ is the impurity-caused angular distortion.
The MO coefficients N γ and λ γ in Eq. (1) can be estimated from the normalization correlation [18,33] and the approximate relationship [33] in which f t ≈ f e ≈ f γ is a parameter describing the covalence effect, which is treated as an adjustable parameter. Thus, in the above calculated formulas, we have four parameters f γ ,A 4 (R) , Δθ and κ are not unfixed. They are taken as the adjustable parameters determined by fitting the experimental spin-Hamiltonian parameters with the above formulas. The calculations indicate that the good fit of the observed spin-Hamiltonian parameters of the (TiO 4 ) 5− cluster in ZrSiO 4 : Ti 3+ crystal requires The calculated spin-Hamiltonian parameters g // , g ⊥ , 47 A // , 47 A ⊥ , 49 A // , and 49 A ⊥ along with the experimental values are given in Table 1.
Similar to the observed 47 A i and 49 A i (i = // or ⊥), the calculated 47 A i and 49 A i are almost the same (see Table 1). The cause is that as shown above, the dipolar hyperfine structure constants P 0 for isotopes 47 Ti 3+ and 49 Ti 3+ are also almost identical. Table 1 shows that the calculated spin-Hamiltonian parameters for the tetragonal (TiO 4 ) 5− tetrahedral cluster in ZrSiO 4 : Ti 3+ are in rational accord with the experimental values. There are small divergences of calculated values from the experimental ones. The main cause may be the point: The experimental spin-Hamiltonian parameters originate from two contributions, the static contribution related to the crystal field and the dynamic contribution due to electron-phonon interaction [36][37][38]. We disregard the small dynamic contribution in the calculation. So, these calculated results can be accredited.
The impurity-caused angular distortion Δθ ≠ 0 demonstrates that the angle θ in the (TiO 4 ) 5− impurity cluster in ZrSiO4: Ti 3+ is indeed not the same as the angle θ h in the host cluster (in addition, the bond length R ≈1.792 Å in the (TiO 4 ) 5− impurity cluster is also different from R h ≈ 1.622 Å [17] in the host cluster). It appears that the information on defect structure of paramagnetic impurity center in crystals can be obtained by analyzing its EPR parameters.