Theoretical Studies of the Spin Hamiltonian Parameters and Local Distortions for Cu²⁺ in Alkaline Earth Lead Zinc Phosphate Glasses

1 Introduction

Phosphate glasses are both scientifically and technologically important materials because of unique physical properties superior to conventional silicate and borate glasses, e.g. low glass transition and melting temperatures, high thermal expansion coefficients, good biocompatibility, high refractive indices, and low dispersion [1], [2], [3], [4]. In addition, phosphate glasses have promising applications in fast ion conductors [5], self-cleaning materials for NH₃ gas absorption [6], important amorphous biomaterials in tissue engineering [7], [8], neural repair of dental and orthopedic cement [9], controlled release of antimicrobials or drugs [10], optical amplifiers, luminescence fibers, and laser hosts [11]. Importantly, the structural versatility using distinct ion exchanges enables phosphate glasses to modify the glass formulation and broadens the range of application fields [12]. For example, the addition of PbO can remarkably improve chemical durability [13] and shielding performance against high-energy radiations [14]. The addition of widely used dopant ZnO yields zinc phosphate glasses and enhances advantageous applications over original phosphate glasses in LED light sources [15], optical waveguides [16], and photoconducting devices [17]. On the other hand, alkaline earth oxide can act as network modifiers in terms of their field strengths [18] and form alkaline earth lead zinc phosphate (RPPZ, R=Mg, Ca, Sr, and Ba) glasses. In particular, transition-metal dopants (e.g. Cu²⁺) play a crucial role in the physical properties of the glasses. As a typical system among transition-metal ions and convenient dopants in glasses, Cu²⁺ (3d⁹) has a relatively simpler energy level structure with only one ground state and one excited state in ideal octahedra [19] and usually exhibits Jahn-Teller distortions via the vibration interactions [20], [21]. Thus, divalent copper can be taken as an effective probe to demonstrate the local structural properties of the glass systems due to the typical anisotropic (axial) spectroscopic behaviors arising from the significant orbital angular momentum interactions [19]. In general, local structures of impurity Cu²⁺ (or other transition-metal ions) in glasses can be investigated using electron paramagnetic resonance (EPR), visible and ultraviolet, infrared, and Raman spectroscopies. Recently, optical and EPR measurements were performed for RPPZ glasses containing copper oxide, and the d-d transition bands and spin Hamiltonian parameters (g factors and hyperfine structure constants) were measured for the impurity Cu²⁺ [22], with anomalies of d-d transition band and g_‖ (i.e. the largest cubic field splitting and the next highest g_‖) for R=Ba. The g factors were calculated from the simple g formulas with various molecular orbital coefficients (α, α′, and β) in the previous work [22]. Nevertheless, the above treatments failed to connect with the local structures of impurity Cu²⁺, and the hyperfine structure constants have not been theoretically analyzed in a consistent way. In fact, the anomalies of EPR and optical spectra for Cu²⁺ in RPPZ (particularly R=Ba) glasses would reveal unique mechanisms dissimilar to the conventional phosphate glasses. Moreover, information of the local structures of the copper dopants may be helpful to understand the properties of these systems. Thus, further theoretical studies for the spin Hamiltonian parameters and local structures of the impurity Cu²⁺ in RPPZ glasses have scientific and practical importance. In this work, the anisotropic g factors and hyperfine structure constants are quantitatively investigated by considering the suitable tetragonal elongation distortions of the octahedral [CuO₆]¹⁰⁻ clusters because of the Jahn-Teller effect. The whole tendencies of the d-d transition band, the EPR spectra, and their anomalies for R=Ba are discussed in view of the lead addition and cross linkage.

2 Calculations

Cu²⁺ ions (in the form of CuO dopants) of 0.1 mol% introduced into RPPZ glasses can bring forward the 20RO·59.9P₂O₅·10Pb₃O₄·10ZnO·0.1CuO (R=Mg, Ca, Sr, Ba) glass systems [22]. Impurity Cu²⁺ ions prefer to occupy suitable octahedral sites in the glass networks and form the [CuO₆]¹⁰⁻ clusters. Because Cu²⁺ (3d⁹) is a Jahn-Teller ion with the ground orbital doublet ²E_g under ideal octahedral crystal fields, the [CuO₆]¹⁰⁻ clusters are subject to the Jahn-Teller effect via the vibrational interactions of the copper-oxygen bonds [7], [23], [24], [25], [26], [27]. For example, the two Cu²⁺–O²⁻ bonds can be elongated along the fourfold axis by a relative elongation ratio ρ, which leads to the tetragonally elongated octahedral [CuO₆]¹⁰⁻ clusters (see Fig. 1). As a result, the original twofold orbital degeneracy of cubic ground state ²E_g is removed, and this level is split into two orbital singlets ²B_1g and ²A_1g, with the former lying lowest and accounting for the measured positive g anisotropies Δg (=g_‖−g_⊥) [22], [23]. Then, the original cubic excited orbital triplet ²T_2g may be separated into an orbital singlet ²B_2g and an orbital doublet ²E_g.

Figure 1:

Local structure of the [CuO₆]¹⁰⁻ clusters in the RPPZ glasses.

3 Discussion

From Table 1, one can find that the theoretical spin Hamiltonian parameters (Calc.^c) for Cu²⁺ in the RPPZ glasses based on the high-order perturbation formulas in (1) and the relative elongation ratios in (5) show good agreement with the measured results. However, the calculated g factors (Calc.^a or Calc.^b) based on the simple g formulas and the adjusted molecular orbital coefficients (α, α′, and β or α, β, and β₁) based on the formulas of Sreehari Sastry and Rupa Venkateswara Rao [22] or Ramadevudu et al. [45] are not so well. Moreover, the local distortions around impurity Cu²⁺ in the glass systems are also quantitatively obtained. There are several points that may be discussed here.

1. Except the anomalous increases for R=Ba, both the cubic field parameter Dq [23] and the orbital reduction factor k exhibit overall decreasing tendencies (Mg>Ca>Sr) with increasing alkaline earth ionic radius, consistent with those (Li>Na>K) for the same [CuO₆]¹⁰⁻ clusters in similar alkali lead tetraborate 90R₂B₄O₇·9PbO·CuO (R=Li, Na, K) glasses [23], [24]. Physically, the overall decreasing Dq may be ascribed to the weakening electrostatic coulombic interactions with increasing alkali or alkaline earth ion radius [24], [25]. The lower Dq values for RPPZ glasses than those (≈1275.1–1302.0 cm⁻¹) for alkali lead tetraborate glasses [25] are attributable to the lower stability of the network and hence weaker Cu²⁺–O²⁻ bonding in the former. On the other hand, the overall decreasing tendency (Mg>Ca>Sr) of k may be illustrated by the increasing probability of productivity of nonbridge oxygen (NBO) and hence the enhancing Cu²⁺–O²⁻ electron cloud admixtures with increasing alkali earth ionic radius under PbO addition in the network [7], [26]. Interestingly, the previously mentioned decreasing rule of k from Mg to Sr is in accordance with the whole decreasing rule of χ (=(α+β+β₁)/3) of the molecular orbital coefficients and the increasing rule of the average Γ (=(Γ_π+Γ_σ)/2) of the normalized covalency coefficients based on (6) and (7) of Ramadevudu et al. [45] (see Tab. 2). Further, both the orders of χ (Mg>Ba>Ca>Sr) and Γ (Mg<Ba<Ca<Sr) actually reveal the order of covalency (Mg<Ba<Ca<Sr) or k (Mg>Ba>Ca>Sr) of the systems. On the other hand, the rough relationship Γ_π≤Γ_σ for Cu²⁺ in the RPPZ glasses is supported by the previous studies of Sreehari Sastry and Rupa Venkateswara Rao [22] and can be regarded as suitable. Thus, the systems may be treated as dominantly ionic, with the percentage of the covalency of approximately 9%–13%. In addition, the orbital reduction factors k for the present systems are higher than those (≈0.774, 0.762, and 0.756) for the similar 90R₂B₄O₇·9PbO·CuO glasses [23], possibly because of the weaker covalency of in-plane π bonding in phosphate glasses than borate glasses [46].

2. Despite the previously mentioned overall decreasing tendencies of Dq and k from Mg to Sr, the anomalies are found for R=Ba, i.e. both quantities show the abrupt increases related to SrPPZ, yielding the largest Dq (Ba>Mg>Ca>Sr) and the next highest k (Mg>Ba>Ca>Sr) among the systems. The anomalies can be attributed to the cross linkage of Ba²⁺ in the network because of its large ionic radius [22]. Ba²⁺ at 20 mol% may tend to coordinate with more oxygen ions and form dominantly ionic bonding owing to the high ionicity. Thus, the electron cloud admixture (or covalency) can considerably decrease and induce the increases of ionicity and effective charge Q_eff of the oxygen ions bonding to both Ba²⁺ and impurity Cu²⁺. As a result, the covalency of [CuO₆]¹⁰⁻ clusters in BaPPZ exhibits a significant decrease and yields the next highest k among the systems, consistent with the next largest χ and the next smallest Γ (see Tab. 2). As for the cubic field parameter, the relationship Dq∝Q_effk based on the point charge model is approximately held for an octahedral cluster [19]. For R=Mg, Ca, and Sr, the effective charge Q_eff of ligand oxygen may largely remain unchanged, and thus the decreasing k brings forward the decreasing order (Mg>Ca>Sr) of Dq for the three systems. As regards BaPPZ, however, the increases of both k and Q_eff arising from the cross linkage can yield a remarkable increase of Dq and lead to the resultant order Ba>Mg>Ca>Sr of Dq. Finally, the overall increasing order (Mg≤Ba<Ca<Sr) of the relative tetragonal elongation ratio ρ suitably reflects the increasing Jahn-Teller tetragonal elongations via the vibration interactions because of the decreasing crystal-field strength Dq (or force constant of the Cu²⁺–O²⁻ bonds).

3. In light of (1), the high k (≈0.9–1) and hence the large ζ as well as the moderate Dq (i.e. the denominator E₁) may account for the relatively large magnitudes (averages) of g factors. The moderate local relative elongation ratios ρ (≈3%–5%) for Cu²⁺ in RPPZ glasses can be illustrated by the measured EPR spectra characterized by the moderate positive anisotropies Δg (≈0.34 [22]). In addition, the moderate ρ due to the Jahn-Teller effect can induce moderate negative Ds and Dt and hence the moderate denominator E₂, leading to the relatively larger g_⊥ (≈2.09 [22]) for the present RPPZ glasses than those (g_⊥≈2.04 [23]) with much larger relative elongation ratios (≈18%–30% [23]) for the alkali lead tetraborate glasses. Similar moderate relative tetragonal elongations (≈6.8% and 8.9% [47]) are found for Cu²⁺ in LiRbB₄O₇ and NaRbB₄O₇ glasses. On the other hand, normally merely absolute values were experimentally determined for hyperfine structure constants in EPR measurements [22]. The present calculations and various observed hyperfine structure constants [43] for Cu²⁺ in oxides reveal that the signs of A_‖ and A_⊥ are negative and positive, respectively. This may be ascribed to the larger negative isotropic terms related to κ than the positive anisotropic ones related to the g-shifts and H [see (1)]. Further, the increasing orders (Mg<Ca<Sr<Ba) of κ and H are suitably responsible for those of the average (=|A_‖+2A_⊥|/3) and anisotropy (=|A_‖|−|A_⊥|) of the hyperfine structure constants and can be regarded as reasonable in physics.

4 Summary

The spin Hamiltonian parameters and local structures are theoretically investigated for Cu²⁺ in RPPZ glasses. The relative tetragonal elongation ratios ρ are found to be approximately 3.2%, 4.4%, 4.6%, and 3.3% for R=Mg, Ca, Sr, and Ba, respectively, because of the Jahn-Teller effect. The whole decreasing crystal-field strength Dq and orbital reduction factor k from Mg to Sr can be ascribed to the weakening electrostatic coulombic interactions and the increasing probability of productivity of NBO (the enhancing Cu²⁺–O²⁻ electron cloud admixtures), respectively, under PbO addition with increasing alkali earth ionic radius. The anomalies (i.e. the largest Dq and the next highest k among all the systems) for R=Ba with the abrupt increases related to R=Sr are attributed to the cross linkage of Ba²⁺ in the network because of its large ionic radius. The overall increasing order (Mg≤Ba<Ca<Sr) of ρ is illustrated by the decreasing crystal-field strength Dq (force constant of the Cu²⁺–O²⁻ bonds). The present studies would be helpful to understand local structures and the relationships with properties of RPPZ glasses containing copper dopants.