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Investigations on the EPR parameters and defect structures for Cu2+ in alkaline earth zinc borate glasses
Optik 127 (2016) 9167–9171
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Optik journal homepage: www.elsevier.de/ijleo
Original research article
Investigations on the EPR parameters and defect structures for Cu2+ in alkaline earth zinc borate glasses Yong-Qiang Xu a,b,∗ , Shao-Yi Wu a,∗ , Li-Juan Zhang a , Chang-Chun Ding a a Department of Applied Physics, School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu, 610054, China b College of Physics and Electronic Information, Gannan Normal University, Ganzhou 341000, China
a r t i c l e
i n f o
Article history: Received 3 May 2016 Accepted 29 June 2016 Keywords: Electron Paramagnetic Resonance (EPR) Defect structures Cu2+ 10RO + 30ZnO + 60B2 O3 (R = Mg, Ca and Sr)
a b s t r a c t The electron paramagnetic resonance (EPR) parameters and defect structures for Cu2+ in alkaline earth zinc borate glasses 10RO + 30ZnO + 60B2 O3 (RZB, where R = Mg, Ca and Sr) are quantitatively investigated from the consistent analysis of these parameters for a tetragonally elongated octahedral 3d9 complex. The studied [CuO6 ]10− complexes are found to undergo the relative tetragonal elongation ratios of about 5.8%, 4.5% and 8.6% in MgZB, CaZB and SrZB glasses, respectively, due to the Jahn-Teller effect. The increasing tendencies (MgZB < CaZB < SrZB) of g// is attributed to the decreasing (MgZB > CaZB > SrZB) cubic field parameter Dq and increasing orbital reduction factor k, while the increasing magnitudes of hyperfine structure constants are illustrated by the increases of the reduction factor H arising from the tetragonal elongation distortions. The defect structures and the properties of the EPR parameters are discussed. © 2016 Elsevier GmbH. All rights reserved.
1. Introduction Alkaline earth zinc borate glasses demonstrate interesting vibrational behaviors as well as linear and non-linear optical [1–3], radiation shielding [4,5] and structural properties [6] when doped with transition-metal and rare-earth impurities. These properties may strongly rely on the local structures and electronic states of the dopants. As one of the most important and effective dopants, Cu2+ in these glass systems can exhibit remarkable optical and electron paramagnetic resonance (EPR) signals conveniently recordable at room temperatures [7,8]. EPR is a powerful tool to provide local structural information of glasses with the aid of transition-metal ion (e.g., Cu2+ ) probes, and the experimental EPR spectra are usually described by the EPR parameters (g factors and hyperfine structure constants). The EPR experiments were performed for the alkaline earth zinc borate 10RO + 30ZnO·60B2 O3 (RZB, where R = Mg, Ca and Sr) glasses, with the copper d-d optical transition bands and g factors g// and g⊥ and hyperfine structure constants A// and A⊥ measured [9]. Regretfully, the above EPR experimental results have not been theoretically investigated in a uniform way, although g factors were analyzed from the simple g formulas with the adjustable molecular orbital coefficients ␣2 and 1 2 [9]. Neither has the information of defect structures around impurity Cu2+ been obtained. In essence, analysis of the EPR parameters for impurities in the RZB glasses can be useful to reveal profound microscopic mechanisms of EPR spectra and impurity behaviors, and information about defect structures for copper dopants are helpful
∗ Corresponding authors at: Department of Applied Physics, School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu, China. E-mail addresses: [email protected] (Y.-Q. Xu), [email protected] (S.-Y. Wu). http://dx.doi.org/10.1016/j.ijleo.2016.06.122 0030-4026/© 2016 Elsevier GmbH. All rights reserved.
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to understand properties of these materials. Thus, the above EPR parameters and defect structures for Cu2+ in RZB glasses are worthy to be further investigated. This article is arranged as follows. In Sect. 2, the theoretical calculations are performed for the EPR parameters of the various RZB:Cu2+ glasses. Sect. 3 is the main results and discussion of the above calculations. The last section is conclusion of this work. 2. Theoretical calculations In this section, the perturbation calculations of the EPR parameters are carried out for RZB:Cu2+ glasses in a consistent way. 2.1. Defect structures of impurity Cu2+ in RZB glasses When impurity Cu2+ (in form of CuO) is doped into RZB glasses, it may occupy certain oxygen octahedral site of the networks and construct the [CuO6 ]10− complex. Since Cu2+ (3d9 ) is a Jahn-Teller ion having the ground orbital doublet 2 Eg in ideal octahedra, the [CuO6 ]10− complex can experience the Jahn-Teller effect by means of the vibrational interactions [10–13], which associates with removal of degeneracy of ground orbital level and results in lower symmetry and energy. Consequently, the [CuO6 ]10− complex would be subject to relative elongation by stretching two copper-oxygen bonds along C4 axis, leading to a tetragonally (D4h ) elongated oxygen octahedron. For convenience, the defect structures of the studied systems can be characterized by the relative tetragonal elongation ratios . Thus, the impurity-ligand bond lengths parallel and perpendicular to the C4 axis in the [CuO6 ]10− complexes due to the Jahn-Teller effect can be expressed in terms of the reference distance R and the relative tetragonal elongation ratio as: R// ≈ R(1 + 2), R⊥ ≈ R(1 − ).
(1)
2.2. Splittings of energy levels for a tetragonally elongated octahedral 3d9 complex For a tetragonally elongated 3d9 complex, the original cubic ground orbital doublet 2 Eg can be split into two orbital singlets 2 B1g and 2 A1g , with the former lying lowest. Meanwhile, the original cubic excited orbital triplet 2 T2g would be separated into an orbital doublet 2 Eg and an orbital singlet 2 B2g [12–15]. The above energy separations can be labeled as E1 and E2 , corresponding to the tetragonal energy differences between the excited 2 B2g and 2 Eg and the ground 2 B1g states, respectively. They can be determined from the energy matrices for a 3d9 ion under tetragonal symmetry in terms of the cubic field parameter Dq and tetragonal field parameters Ds and Dt [16]: E1 ≈ 10Dq, E2 ≈ 10Dq − 3Ds + 5Dt.
(2)
2.3. Perturbation formulas of the EPR parameters for a tetragonally elongated 3d9 complex The perturbation formulas of the EPR parameters for a tetragonally elongated octahedral 3d9 cluster can be expressed as follows [16–18]: g// = gs + 8k/E1 + k2 /E2 2 + 4k2 /E1 E2 − gs 2 [1/E1 2 − 1/(2E2 2 )] + k3 (4/E1 − 1/E2 )/E2 2 − 2k3 (2/E1 E2 − 1/E2 2 )/E1 + gs 3 [1/(E1 E2 2 ) − 1/(2E2 3 )], g⊥ = gs + 2k/E2 − 4k2 /(E1 E2 ) + k2 [2/(E1 E2 ) − 1/E2 2 ] + 2 gs 2 /E1 2 + k3 (2/E1 − 1/E2 ) × (1/E2 + 2/E1 )/2E2 − k3 (1/E1 2 − 1/E1 E2 + 1/E2 2 )/2E2 , A// = P[− − 4H/7 + (g|| − gs ) + 3(g⊥ − gs )/7], A⊥ = P[− + 2H/7 + 11(g⊥ − gs )/14].
(3)
Here gs (≈2.0023) is the spin-only value. k is the orbital reduction factor, characteristic of covalency of the studied systems. and P denote the spin-orbit coupling coefficient and the dipolar hyperfine structure parameter of the 3d9 ion in glasses, which can be expressed in terms of the corresponding free-ion values 0 and P0 and the orbital reduction factor as ≈ k 0 and P ≈ k P0 , respectively. labels the core polarization constant, reflecting the isotropic Fermi contact interactions between copper 3d and 3s (4s) orbitals. The reduction factor H originates from the anisotropic central ion 3d-3s (4s) orbital admixtures due to the local tetragonal elongation distortion and brings forward the anisotropic contributions to hyperfine structure constants [17].
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Table 1 The g factors and hyperfine structure constants (in 10−4 cm−1 ) for Cu2+ in RZB glasses. Hosts Cal.a Cal.b Expt. [9] Cal.a Cal.b Expt. [9] Cal.a Cal.b Expt. [9]
MgZB
CaZB
SrZB
g//
g⊥
A//
A⊥
2.3558 2.3561 2.356 2.3667 2.3663 2.366 2.3676 2.3672 2.367
2.0638 2.0701 2.070 2.0728 2.0759 2.076 2.0631 2.0658 2.066
– −112.1 −112 – −114.2 −114 – −115.2 −115
– 70.4 70 – 80.2 80 – 82.1 82
a Calculations of g factors based on the simple g formulas using the adjustable molecular orbital coefficients ␣2 and 1 2 as well as the fixed 2 = 1 and orbital reduction factor K = 0.77 in the previous work [9]. b Calculations of EPR parameters based on the high order perturbation formulas and the optimal relative tetragonal elongation ratios in Eq. (5) of this work.
2.4. Superposition model formulas of the tetragonal field parameters In the present calculations, the EPR parameters (particularly the anisotropy g = g// − g⊥ ) can be connected with the tetragonal field parameters and hence with the defect structures of Cu2+ in RZB glasses with the aid of the superposition model. The tetragonal field parameters are determined from the local geometry and the superposition model [19–21]: t2 t2 ¯ Ds ≈ (4/7) A(R)[R/R ⊥ ) − (R/R// ) ],
Dt ≈ (16/21)A¯ 4 (R)[(R/R⊥ )t4 − (R/R// )t4 ],
(4)
Here t2 ≈ 3 and t4 ≈ 5 are the power-law exponents. A¯ 2 (R) and A¯ 4 (R) are the intrinsic parameters. For 3dn ions in octahedral crystal-fields, the relationships A¯ 4 (R) ≈ (3/4) Dq and A¯ 2 (R) ≈ 10.8 A¯ 4 have been proved reliable for many systems [22–24] and are reasonably utilized in the present computations. 2.5. Calculations for the various RZB:Cu2+ glasses The measured d-d optical transition bands reveal the slightly decreasing tendency of the cubic field parameter Dq, i.e., 1275.5, 1267.4 and 1257.8 cm−1 for Cu2+ in MgZB, CaZB and SrZB glasses, respectively [9]. Meanwhile, the optical spectral measurements [12,25] demonstrate that the orbital reduction factors k are about 0.83 for Cu2+ in some oxides. In view of the overall increasing tendency (MgZB < CaZB < SrZB) of the experimental g// [9] , the slightly increasing (MgZB < CaZB < SrZB) orbital reduction factor may be expected. Thus, one can suitably apply k ≈ 0.821, 0.829 and 0.830 for Cu2+ in MgZB, CaZB and SrZB, respectively. The above values are also largely in accordance with the roughly increasing (0.830 < 0.839–0.836 [9]) average of the molecular orbital coefficients ␣2 and 1 2 for Cu2+ in MgZB, CaZB and SrZB glasses obtained by fitting the experimental g factors. For a free Cu2+ ion, the spin-orbit coupling coefficient is 0 ≈ 829 cm−1 [26]. Inserting the relevant values into the formulas for g factors and matching the calculated g factors to the experimental data, the relative tetragonal elongation ratios ≈ 5.8%, 4.5%and8.6%
(5)
are obtained for Cu2+ in MgZB, CaZB and SrZB glasses, respectively. The corresponding g factors are shown in Table 1. For comparison, the g factors based on the simple g formulas using the molecular orbital coefficients ␣2 and 1 2 as well as the
fixed 2 = 1 and orbital reduction factor K = 0.77 in the previous work [9] are also computed and collected in Table 1. As regards hyperfine structure constants, the dipolar hyperfine structure parameter is P0 ≈ 402 × 10−4 cm−1 [26] for Cu2+ . According to the moderate tetragonal elongation distortions in Eq. (5), the reduction factors H can be suitably adopted as 0.90, 0.94 and 0.96 for Cu2+ in MgZB, CaZB and SrZB glasses, respectively, in view of the moderate (4–10%) reductions of H from the ideal value of unity in the absence of tetragonal elongation distortion. Substituting these quantities into Eq. (3), and fitting the calculated hyperfine structure constants to the observed values, one can obtain the optimal core polarization constants ≈ 0.132, 0.124and0.116 Cu2+
for in MgZB, CaZB and SrZB glasses, respectively. The corresponding hyperfine structure constants (Cal. in Table 1.
(6) b)
are listed
3. Results and discussion One can find from Table 1 that the calculated EPR parameters (Cal. b ) based on the optimal local tetragonal elongation ratios in Eq. (5) and the core polarization constants in Eq. (6) are in good agreement with the measured results. Nevertheless,
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the theoretical g factors (Cal. a ) based on the simple g formulas using various adjusted molecular orbital coefficients in the previous work [9] are not so good. 1) The calculated g⊥ (Cal. a ) based on the simple g formulas and the fitted molecular orbital coefficients ␣2 and 1 2 as well
as the fixed 2 = 1 and orbital reduction factor K = 0.77 in the previous work [9] are smaller than the experimental data or those (Cal. b ) of the present calculations based on the uniform high order perturbaiton formulas and the optimal relative tetragonal elontation ratios. The observed decreasing (MgZB > CaZB > SrZB) d-d optical transition bands E1 [9] can be attributed to the weakening of Cu2+ -O2− bonding from R = Mg to Sr due to the decreases of the electrostatic Coulombic interactions and strength of alkaline − oxygen bonding with increasing the radius of alkaline ion [27]. This point is also experimentally verified by the optical measurements for Cu2+ in the similar 90R2 B4 O7 ·9PbO·CuO (R = Li, Na, K) [28] and 20R2 CO3 ·24.5BaCO3 ·55H3 BO3 ·0.5CuCO3 (R = Li, Na, K) glass systems [29]. The slightly increasing orbital reduction factor k (≈0.821 < 0.829 ≤ 0.830 for Cu2+ in MgZB, CaZB and SrZB glasses, respectively) may be ascribed to the decreases of probability of non bridge oxygen (NBO) and hence of the Cu2+ -O2– orbital admixtures with increasing ionic radius of alkaline ion from Mg to Sr. The above values are roughly consistent with the increasing (0.830 < 0.839–0.836 [9] for Cu2+ in MgZB, CaZB and SrZB glasses, respectively) average of the molecular orbital coefficients ␣2 and 1 2 obtained by fitting the experimental g factors. Similar decreasing tendency of covalency is also reported for Cu2+ in 90R2 B4 O7 ·9PbO·CuO (R = Li, Na, K) glasses with increasing radius of alkaline ion [30]. 2) The increasing tendency of g// is illustrated as the decreases of cubic field parameter Dq in the denominators and the incresaes of orbital reduction factor k (in the numerators k and ). On the other hand, g⊥ first increases from MgZB to CaZB and then decreases for SrZB, which can be attributed to the decrease of the relative tetragonal elongation ratio (and also the decreases of Ds and Dt in the denominator E2 of g⊥ formula) from MgZB to CaZB and the increase of for SrZB. In addition, the moderate anisotropies g (=g|| − gˆ ≈ 0.29 [9]) for Cu2+ in RZB glasses are corresponding to the moderate relative tetragonal elongation ratios (≈4.5–8.6%) of the Jahn-Teller nature for the lowest 2 B1g state of tetragonally elongated octahedral 3d9 complexes [14,15]. Interestingly, analogous moderate relative tetragonal elongation ratios (≈3% [31] and 6.8–8.9% [32]) were found for Cu2+ in xLi2 O·(30–x)·K2 O·70B2 O3 (0 ≤ x ≤ 25 mol%) and ARbB4 O7 (A = Li, Na) glasses. 3) The signs of the experimental hyperfine structure constants have not been determined in Ref. [9]. According to the present calculations and various measured values for Cu2+ in oxides [26], the signs of A// and A⊥ are negative and positive, respectively. The overall increasing tendencies of the magnitudes of hyperfine structure constants are largely ascribed to the increasing reduction factor H. The smaller core polarization constants (≈0.12–0.13) for present RZB:Cu2+ glasses than the conventional values (≈0.26 [33]) for Cu2+ in Tutton’s salts may be illustrated as the significant weakening of copper 3d-3s (4s) orbital admixtures in RZB glasses arising from the decreases of electron cloud density around Cu2+ due to mix alkali effect [34–37]. In addition, the decreasing (MgZB > CaZB > SrZB) tendency of is explained as the decreasing copper 3d-3s (4s) orbital admixtures due to the decreasing probability of NBO with increasing alkaline ion radius. It is noted that the influences of the slightly decreasing are actually overcompensated by the much larger and more significantly increasing H, and thus lead to the whole increasing tendencies of the magnitudes of hyperfine structure constants.
4. Conclusion The EPR parameters and defect structures for Cu2+ in RZB glasses are theoretically investigated from the perturbation calculations of these parameters for tetragonally elongated octahedral 3d9 complexes. The [CuO6 ]10− complexes are found to undergo the relative tetragonal elongation ratios of about 5.8%, 4.5% and 8.6% in MgZB, CaZB and SrZB glasses, respectively, due to the Jahn-Teller effect. The increasing tendencies (MgZB < CaZB < SrZB) of g// is attributed to the decreasing (MgZB > CaZB > SrZB) cubic field parameter Dq and increasing orbital reduciton factor k, while the increasing magnitudes of hyperfine structure constants are attributable to the increases of the reduction factor H. The small core polarization constants may be illustrated by the weak copper 3d-3s (4s) orbital admixtures in RZB glasses arising from the decreases of electron cloud density around Cu2+ due to mix alkali effect. Acknowledgements This work was supported by “the Sichuan Province Academic and Technical Leaders Support Fund” [Y02028023601032] and “the Fundamental Research Funds for the Central Universities” [ZYGX2014J136]. References [1] K. Nanda, R.S. Kundu, S. Sharma, D. Mohan, R. Punia, N. Kishore, Study of vibrational spectroscopy, linear and non-linear optical properties of Sm3+ ions doped BaO-ZnO-B2 O3 glasses, Solid State Sci. 45 (2015) 15–22. [2] B. Sumalatha, I. Omkaram, T.R. Rao, C.L. Raju, Coordination and ion–ion interactions of chromium centers in alkaline earth zinc borate glasses probed by electron paramagnetic resonance and optical spectroscopy, Phys. Scr. 87 (2013) 055602. [3] B. Sumalatha, I. Omkaram, T.R. Rao, C.L. Raju, The effect of V2 O5 on alkaline earth zinc borate glasses studied by EPR and optical absorption, J. Mol. Struct. 1006 (2011) 96–103.
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Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Original research article
Investigations on the EPR parameters and defect structures for Cu2+ in alkaline earth zinc borate glasses Yong-Qiang Xu a,b,∗ , Shao-Yi Wu a,∗ , Li-Juan Zhang a , Chang-Chun Ding a a Department of Applied Physics, School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu, 610054, China b College of Physics and Electronic Information, Gannan Normal University, Ganzhou 341000, China
a r t i c l e
i n f o
Article history: Received 3 May 2016 Accepted 29 June 2016 Keywords: Electron Paramagnetic Resonance (EPR) Defect structures Cu2+ 10RO + 30ZnO + 60B2 O3 (R = Mg, Ca and Sr)
a b s t r a c t The electron paramagnetic resonance (EPR) parameters and defect structures for Cu2+ in alkaline earth zinc borate glasses 10RO + 30ZnO + 60B2 O3 (RZB, where R = Mg, Ca and Sr) are quantitatively investigated from the consistent analysis of these parameters for a tetragonally elongated octahedral 3d9 complex. The studied [CuO6 ]10− complexes are found to undergo the relative tetragonal elongation ratios of about 5.8%, 4.5% and 8.6% in MgZB, CaZB and SrZB glasses, respectively, due to the Jahn-Teller effect. The increasing tendencies (MgZB < CaZB < SrZB) of g// is attributed to the decreasing (MgZB > CaZB > SrZB) cubic field parameter Dq and increasing orbital reduction factor k, while the increasing magnitudes of hyperfine structure constants are illustrated by the increases of the reduction factor H arising from the tetragonal elongation distortions. The defect structures and the properties of the EPR parameters are discussed. © 2016 Elsevier GmbH. All rights reserved.
1. Introduction Alkaline earth zinc borate glasses demonstrate interesting vibrational behaviors as well as linear and non-linear optical [1–3], radiation shielding [4,5] and structural properties [6] when doped with transition-metal and rare-earth impurities. These properties may strongly rely on the local structures and electronic states of the dopants. As one of the most important and effective dopants, Cu2+ in these glass systems can exhibit remarkable optical and electron paramagnetic resonance (EPR) signals conveniently recordable at room temperatures [7,8]. EPR is a powerful tool to provide local structural information of glasses with the aid of transition-metal ion (e.g., Cu2+ ) probes, and the experimental EPR spectra are usually described by the EPR parameters (g factors and hyperfine structure constants). The EPR experiments were performed for the alkaline earth zinc borate 10RO + 30ZnO·60B2 O3 (RZB, where R = Mg, Ca and Sr) glasses, with the copper d-d optical transition bands and g factors g// and g⊥ and hyperfine structure constants A// and A⊥ measured [9]. Regretfully, the above EPR experimental results have not been theoretically investigated in a uniform way, although g factors were analyzed from the simple g formulas with the adjustable molecular orbital coefficients ␣2 and 1 2 [9]. Neither has the information of defect structures around impurity Cu2+ been obtained. In essence, analysis of the EPR parameters for impurities in the RZB glasses can be useful to reveal profound microscopic mechanisms of EPR spectra and impurity behaviors, and information about defect structures for copper dopants are helpful
∗ Corresponding authors at: Department of Applied Physics, School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu, China. E-mail addresses: [email protected] (Y.-Q. Xu), [email protected] (S.-Y. Wu). http://dx.doi.org/10.1016/j.ijleo.2016.06.122 0030-4026/© 2016 Elsevier GmbH. All rights reserved.
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to understand properties of these materials. Thus, the above EPR parameters and defect structures for Cu2+ in RZB glasses are worthy to be further investigated. This article is arranged as follows. In Sect. 2, the theoretical calculations are performed for the EPR parameters of the various RZB:Cu2+ glasses. Sect. 3 is the main results and discussion of the above calculations. The last section is conclusion of this work. 2. Theoretical calculations In this section, the perturbation calculations of the EPR parameters are carried out for RZB:Cu2+ glasses in a consistent way. 2.1. Defect structures of impurity Cu2+ in RZB glasses When impurity Cu2+ (in form of CuO) is doped into RZB glasses, it may occupy certain oxygen octahedral site of the networks and construct the [CuO6 ]10− complex. Since Cu2+ (3d9 ) is a Jahn-Teller ion having the ground orbital doublet 2 Eg in ideal octahedra, the [CuO6 ]10− complex can experience the Jahn-Teller effect by means of the vibrational interactions [10–13], which associates with removal of degeneracy of ground orbital level and results in lower symmetry and energy. Consequently, the [CuO6 ]10− complex would be subject to relative elongation by stretching two copper-oxygen bonds along C4 axis, leading to a tetragonally (D4h ) elongated oxygen octahedron. For convenience, the defect structures of the studied systems can be characterized by the relative tetragonal elongation ratios . Thus, the impurity-ligand bond lengths parallel and perpendicular to the C4 axis in the [CuO6 ]10− complexes due to the Jahn-Teller effect can be expressed in terms of the reference distance R and the relative tetragonal elongation ratio as: R// ≈ R(1 + 2), R⊥ ≈ R(1 − ).
(1)
2.2. Splittings of energy levels for a tetragonally elongated octahedral 3d9 complex For a tetragonally elongated 3d9 complex, the original cubic ground orbital doublet 2 Eg can be split into two orbital singlets 2 B1g and 2 A1g , with the former lying lowest. Meanwhile, the original cubic excited orbital triplet 2 T2g would be separated into an orbital doublet 2 Eg and an orbital singlet 2 B2g [12–15]. The above energy separations can be labeled as E1 and E2 , corresponding to the tetragonal energy differences between the excited 2 B2g and 2 Eg and the ground 2 B1g states, respectively. They can be determined from the energy matrices for a 3d9 ion under tetragonal symmetry in terms of the cubic field parameter Dq and tetragonal field parameters Ds and Dt [16]: E1 ≈ 10Dq, E2 ≈ 10Dq − 3Ds + 5Dt.
(2)
2.3. Perturbation formulas of the EPR parameters for a tetragonally elongated 3d9 complex The perturbation formulas of the EPR parameters for a tetragonally elongated octahedral 3d9 cluster can be expressed as follows [16–18]: g// = gs + 8k/E1 + k2 /E2 2 + 4k2 /E1 E2 − gs 2 [1/E1 2 − 1/(2E2 2 )] + k3 (4/E1 − 1/E2 )/E2 2 − 2k3 (2/E1 E2 − 1/E2 2 )/E1 + gs 3 [1/(E1 E2 2 ) − 1/(2E2 3 )], g⊥ = gs + 2k/E2 − 4k2 /(E1 E2 ) + k2 [2/(E1 E2 ) − 1/E2 2 ] + 2 gs 2 /E1 2 + k3 (2/E1 − 1/E2 ) × (1/E2 + 2/E1 )/2E2 − k3 (1/E1 2 − 1/E1 E2 + 1/E2 2 )/2E2 , A// = P[− − 4H/7 + (g|| − gs ) + 3(g⊥ − gs )/7], A⊥ = P[− + 2H/7 + 11(g⊥ − gs )/14].
(3)
Here gs (≈2.0023) is the spin-only value. k is the orbital reduction factor, characteristic of covalency of the studied systems. and P denote the spin-orbit coupling coefficient and the dipolar hyperfine structure parameter of the 3d9 ion in glasses, which can be expressed in terms of the corresponding free-ion values 0 and P0 and the orbital reduction factor as ≈ k 0 and P ≈ k P0 , respectively. labels the core polarization constant, reflecting the isotropic Fermi contact interactions between copper 3d and 3s (4s) orbitals. The reduction factor H originates from the anisotropic central ion 3d-3s (4s) orbital admixtures due to the local tetragonal elongation distortion and brings forward the anisotropic contributions to hyperfine structure constants [17].
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Table 1 The g factors and hyperfine structure constants (in 10−4 cm−1 ) for Cu2+ in RZB glasses. Hosts Cal.a Cal.b Expt. [9] Cal.a Cal.b Expt. [9] Cal.a Cal.b Expt. [9]
MgZB
CaZB
SrZB
g//
g⊥
A//
A⊥
2.3558 2.3561 2.356 2.3667 2.3663 2.366 2.3676 2.3672 2.367
2.0638 2.0701 2.070 2.0728 2.0759 2.076 2.0631 2.0658 2.066
– −112.1 −112 – −114.2 −114 – −115.2 −115
– 70.4 70 – 80.2 80 – 82.1 82
a Calculations of g factors based on the simple g formulas using the adjustable molecular orbital coefficients ␣2 and 1 2 as well as the fixed 2 = 1 and orbital reduction factor K = 0.77 in the previous work [9]. b Calculations of EPR parameters based on the high order perturbation formulas and the optimal relative tetragonal elongation ratios in Eq. (5) of this work.
2.4. Superposition model formulas of the tetragonal field parameters In the present calculations, the EPR parameters (particularly the anisotropy g = g// − g⊥ ) can be connected with the tetragonal field parameters and hence with the defect structures of Cu2+ in RZB glasses with the aid of the superposition model. The tetragonal field parameters are determined from the local geometry and the superposition model [19–21]: t2 t2 ¯ Ds ≈ (4/7) A(R)[R/R ⊥ ) − (R/R// ) ],
Dt ≈ (16/21)A¯ 4 (R)[(R/R⊥ )t4 − (R/R// )t4 ],
(4)
Here t2 ≈ 3 and t4 ≈ 5 are the power-law exponents. A¯ 2 (R) and A¯ 4 (R) are the intrinsic parameters. For 3dn ions in octahedral crystal-fields, the relationships A¯ 4 (R) ≈ (3/4) Dq and A¯ 2 (R) ≈ 10.8 A¯ 4 have been proved reliable for many systems [22–24] and are reasonably utilized in the present computations. 2.5. Calculations for the various RZB:Cu2+ glasses The measured d-d optical transition bands reveal the slightly decreasing tendency of the cubic field parameter Dq, i.e., 1275.5, 1267.4 and 1257.8 cm−1 for Cu2+ in MgZB, CaZB and SrZB glasses, respectively [9]. Meanwhile, the optical spectral measurements [12,25] demonstrate that the orbital reduction factors k are about 0.83 for Cu2+ in some oxides. In view of the overall increasing tendency (MgZB < CaZB < SrZB) of the experimental g// [9] , the slightly increasing (MgZB < CaZB < SrZB) orbital reduction factor may be expected. Thus, one can suitably apply k ≈ 0.821, 0.829 and 0.830 for Cu2+ in MgZB, CaZB and SrZB, respectively. The above values are also largely in accordance with the roughly increasing (0.830 < 0.839–0.836 [9]) average of the molecular orbital coefficients ␣2 and 1 2 for Cu2+ in MgZB, CaZB and SrZB glasses obtained by fitting the experimental g factors. For a free Cu2+ ion, the spin-orbit coupling coefficient is 0 ≈ 829 cm−1 [26]. Inserting the relevant values into the formulas for g factors and matching the calculated g factors to the experimental data, the relative tetragonal elongation ratios ≈ 5.8%, 4.5%and8.6%
(5)
are obtained for Cu2+ in MgZB, CaZB and SrZB glasses, respectively. The corresponding g factors are shown in Table 1. For comparison, the g factors based on the simple g formulas using the molecular orbital coefficients ␣2 and 1 2 as well as the
fixed 2 = 1 and orbital reduction factor K = 0.77 in the previous work [9] are also computed and collected in Table 1. As regards hyperfine structure constants, the dipolar hyperfine structure parameter is P0 ≈ 402 × 10−4 cm−1 [26] for Cu2+ . According to the moderate tetragonal elongation distortions in Eq. (5), the reduction factors H can be suitably adopted as 0.90, 0.94 and 0.96 for Cu2+ in MgZB, CaZB and SrZB glasses, respectively, in view of the moderate (4–10%) reductions of H from the ideal value of unity in the absence of tetragonal elongation distortion. Substituting these quantities into Eq. (3), and fitting the calculated hyperfine structure constants to the observed values, one can obtain the optimal core polarization constants ≈ 0.132, 0.124and0.116 Cu2+
for in MgZB, CaZB and SrZB glasses, respectively. The corresponding hyperfine structure constants (Cal. in Table 1.
(6) b)
are listed
3. Results and discussion One can find from Table 1 that the calculated EPR parameters (Cal. b ) based on the optimal local tetragonal elongation ratios in Eq. (5) and the core polarization constants in Eq. (6) are in good agreement with the measured results. Nevertheless,
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the theoretical g factors (Cal. a ) based on the simple g formulas using various adjusted molecular orbital coefficients in the previous work [9] are not so good. 1) The calculated g⊥ (Cal. a ) based on the simple g formulas and the fitted molecular orbital coefficients ␣2 and 1 2 as well
as the fixed 2 = 1 and orbital reduction factor K = 0.77 in the previous work [9] are smaller than the experimental data or those (Cal. b ) of the present calculations based on the uniform high order perturbaiton formulas and the optimal relative tetragonal elontation ratios. The observed decreasing (MgZB > CaZB > SrZB) d-d optical transition bands E1 [9] can be attributed to the weakening of Cu2+ -O2− bonding from R = Mg to Sr due to the decreases of the electrostatic Coulombic interactions and strength of alkaline − oxygen bonding with increasing the radius of alkaline ion [27]. This point is also experimentally verified by the optical measurements for Cu2+ in the similar 90R2 B4 O7 ·9PbO·CuO (R = Li, Na, K) [28] and 20R2 CO3 ·24.5BaCO3 ·55H3 BO3 ·0.5CuCO3 (R = Li, Na, K) glass systems [29]. The slightly increasing orbital reduction factor k (≈0.821 < 0.829 ≤ 0.830 for Cu2+ in MgZB, CaZB and SrZB glasses, respectively) may be ascribed to the decreases of probability of non bridge oxygen (NBO) and hence of the Cu2+ -O2– orbital admixtures with increasing ionic radius of alkaline ion from Mg to Sr. The above values are roughly consistent with the increasing (0.830 < 0.839–0.836 [9] for Cu2+ in MgZB, CaZB and SrZB glasses, respectively) average of the molecular orbital coefficients ␣2 and 1 2 obtained by fitting the experimental g factors. Similar decreasing tendency of covalency is also reported for Cu2+ in 90R2 B4 O7 ·9PbO·CuO (R = Li, Na, K) glasses with increasing radius of alkaline ion [30]. 2) The increasing tendency of g// is illustrated as the decreases of cubic field parameter Dq in the denominators and the incresaes of orbital reduction factor k (in the numerators k and ). On the other hand, g⊥ first increases from MgZB to CaZB and then decreases for SrZB, which can be attributed to the decrease of the relative tetragonal elongation ratio (and also the decreases of Ds and Dt in the denominator E2 of g⊥ formula) from MgZB to CaZB and the increase of for SrZB. In addition, the moderate anisotropies g (=g|| − gˆ ≈ 0.29 [9]) for Cu2+ in RZB glasses are corresponding to the moderate relative tetragonal elongation ratios (≈4.5–8.6%) of the Jahn-Teller nature for the lowest 2 B1g state of tetragonally elongated octahedral 3d9 complexes [14,15]. Interestingly, analogous moderate relative tetragonal elongation ratios (≈3% [31] and 6.8–8.9% [32]) were found for Cu2+ in xLi2 O·(30–x)·K2 O·70B2 O3 (0 ≤ x ≤ 25 mol%) and ARbB4 O7 (A = Li, Na) glasses. 3) The signs of the experimental hyperfine structure constants have not been determined in Ref. [9]. According to the present calculations and various measured values for Cu2+ in oxides [26], the signs of A// and A⊥ are negative and positive, respectively. The overall increasing tendencies of the magnitudes of hyperfine structure constants are largely ascribed to the increasing reduction factor H. The smaller core polarization constants (≈0.12–0.13) for present RZB:Cu2+ glasses than the conventional values (≈0.26 [33]) for Cu2+ in Tutton’s salts may be illustrated as the significant weakening of copper 3d-3s (4s) orbital admixtures in RZB glasses arising from the decreases of electron cloud density around Cu2+ due to mix alkali effect [34–37]. In addition, the decreasing (MgZB > CaZB > SrZB) tendency of is explained as the decreasing copper 3d-3s (4s) orbital admixtures due to the decreasing probability of NBO with increasing alkaline ion radius. It is noted that the influences of the slightly decreasing are actually overcompensated by the much larger and more significantly increasing H, and thus lead to the whole increasing tendencies of the magnitudes of hyperfine structure constants.
4. Conclusion The EPR parameters and defect structures for Cu2+ in RZB glasses are theoretically investigated from the perturbation calculations of these parameters for tetragonally elongated octahedral 3d9 complexes. The [CuO6 ]10− complexes are found to undergo the relative tetragonal elongation ratios of about 5.8%, 4.5% and 8.6% in MgZB, CaZB and SrZB glasses, respectively, due to the Jahn-Teller effect. The increasing tendencies (MgZB < CaZB < SrZB) of g// is attributed to the decreasing (MgZB > CaZB > SrZB) cubic field parameter Dq and increasing orbital reduciton factor k, while the increasing magnitudes of hyperfine structure constants are attributable to the increases of the reduction factor H. The small core polarization constants may be illustrated by the weak copper 3d-3s (4s) orbital admixtures in RZB glasses arising from the decreases of electron cloud density around Cu2+ due to mix alkali effect. Acknowledgements This work was supported by “the Sichuan Province Academic and Technical Leaders Support Fund” [Y02028023601032] and “the Fundamental Research Funds for the Central Universities” [ZYGX2014J136]. References [1] K. Nanda, R.S. Kundu, S. Sharma, D. Mohan, R. Punia, N. Kishore, Study of vibrational spectroscopy, linear and non-linear optical properties of Sm3+ ions doped BaO-ZnO-B2 O3 glasses, Solid State Sci. 45 (2015) 15–22. [2] B. Sumalatha, I. Omkaram, T.R. Rao, C.L. Raju, Coordination and ion–ion interactions of chromium centers in alkaline earth zinc borate glasses probed by electron paramagnetic resonance and optical spectroscopy, Phys. Scr. 87 (2013) 055602. [3] B. Sumalatha, I. Omkaram, T.R. Rao, C.L. Raju, The effect of V2 O5 on alkaline earth zinc borate glasses studied by EPR and optical absorption, J. Mol. Struct. 1006 (2011) 96–103.
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