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Optical absorption spectra and EPR g factor of divalent nickel doped magnesia crystal
Optik 122 (2011) 1512–1514
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Optical absorption spectra and EPR g factor of divalent nickel doped magnesia crystal W.L. Feng a,b,c,∗ , X.M. Li a,d,∗ , W.J. Yang d , C.Y. Tao d , Y.L. Yang d a
Key Laboratory for Optoelectronic Technology and Systems, Ministry of Education; College of Optoelectronic Engineering, Chongqing University, Chongqing 400044, China Department of Applied Physics, Chongqing University of Technology, Chongqing, 400054, China International Centre for Materials Physics, Chinese Academy of Sciences, Shengyang, 110016, China d College of Chemistry and Chemical Engineering, Chongqing University, Chongqing, 400044, China b c
a r t i c l e
i n f o
Article history: Received 24 May 2010 Accepted 30 September 2010
Keywords: Optical properties Crystal- and ligand field Electron paramagnetic resonance MgO Ni2+
a b s t r a c t Based on the crystal- and ligand-field theory, the optical absorption spectra and electron paramagnetic resonance (EPR) g factor of Ni2+ ion at Mg2+ position in MgO have been investigated. The bond length (i.e. Ni2+ –O2− distance) was determined from the cubic field parameter Dq; the crystal field Hamiltonian including the spin–orbital (SO) coupling effect of the ligand was diagonalized in the complete basis of 45 wave functions. Results of calculations are in a good agreement with experimental data. © 2010 Elsevier GmbH. All rights reserved.
1. Introduction Magnesia (magnesium oxide) is extensively application in desiccant, medication, magnetic and optical film, etc. Thus, many spectroscopic studies have been made for transition-metal ions in MgO [1–6]. Among them, the experimental data of the optical absorption spectra and electron paramagnetic resonance (EPR) g factor of Ni2+ ion at Mg2+ position in MgO were measured [1,3–6]. The theoretical investigations of optical and EPR spectra of Ni2+ doped MgO based on single spin–orbital coupling have been made by Kuang and Ma et al. [2,7]. For example, the energy spectrum and g factor of MgO:Ni2+ and their pressure-induced shift were calculated [7]. However, the spin–orbit (SO) coupling effect of the ligand and local lattice relaxation due to the substitution of Ni2+ for Mg2+ is not considered in their calculation. To understand the detailed physical and chemical properties of MgO:Ni2+ crystal, further theoretical explanations for the optical absorption spectra and g factor of MgO:Ni2+ should be carried out. In the present paper, we calculate the optical absorption spectra and g factor of MgO:Ni2+ from a diagonalizing the full energy matrix method which the SO coupling effect of the ligand oxygen is included. Since the ionic radius
∗ Corresponding authors at: College of Optoelectronic Engineering, Chongqing University, Chongqing, 400044, China. E-mail addresses: [email protected] (W.L. Feng), [email protected] (X.M. Li). 0030-4026/$ – see front matter © 2010 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2010.09.034
˚ of Ni2+ is greater than that (≈0.66 A) ˚ of Mg2+ ion [8], the (≈0.69 A) local lattice relaxation for the Ni2+ center in MgO crystal due to the size mismatch is also taken into account in the present calculation. 2. Theoretical calculation MgO crystal has the cubic symmetry which has a space group Fm-3m . When Ni2+ ion replaces Mg2+ ion in MgO, the radius difference between Ni2+ and Mg2+ will lead to somewhat lattice relaxation. Because no zero-field splitting was observed by spectroscopic analysis [3–5], the symmetry of Ni2+ center is still cubic. The bond length of Ni2+ –O2− due to the local lattice relaxation of Ni2+ center in MgO can be estimated by the cubic crystal-field parameter Dq, 1 1 , Dq = − eq fr r 4 0 R5 6
(1)
i
in which e is the electronic charge, q is the charge of the oxygen ligand (i.e. q = 2e for O2− ). Ri is the impurity–ligand distance (i.e. Ni2+ –O2− distance), fr is the averagereduction factor due to the covalency, and the expectation value r 4 for the free ion is given 0 by [9]
4 r
0
= 13.4043 a.u.
(2)
the double SO approach, the single electron function Following ϕ of the ML6 octahedral clusters has the linear expansion of
W.L. Feng et al. / Optik 122 (2011) 1512–1514 Table 1 The optical absorption spectra (in cm−1 ) and EPR g factor. ˛2S + 1 6 2
t e t5 e3
3
t5 e3 t6 e2 t5 e3
3
t5 e3 t4 e4
1
t6 e2 t5 e3 t4 e4 t4 e4 t4 e4
1
A2 3 T2 T1 E 3 T1 1
T2 3 T1 A1 T1 1 E 1 T2 1 A1 1
Ta
Calculation
Experiment
T2 E T1 T2 A2 A1 E T1 T2 E T2 E A1 T2 T1 A1 T1 E T2 A1
0 8037 8173 8522 8669 13089 13389 13528 14220 14965 21386 24216 24436 24478 24588 24847 28353 33894 34563 57067
0 8003b 8179b 8591b 8645b , 8845c 13100b 13120b 13520b 14333b 14770b 21126, 21134d
EPR g factor
2.2145
1513
where the four terms are, respectively, the electron–electron interactions, the cubic crystal-field potentials, the SO coupling interactions and the Trees correction term (˛ = 140 cm−1 here [9]). From the strong field basis functions [21], the complete energy matrix (45 × 45) related to the above Hamiltonian of the 3d8 ion in Td symmetry is constructed. Considering the equivalence between the EPR g factor and the Zeeman interaction, we have g=
3
A2 (t26 e2 ), 1, e2 k± Lj + gs Sj 3 A2 (t26 e2 ), 1, e2
(8)
in which 3 A2 (t26 e2 ), Ms is the eigenfunction of the ground state 3A 2
24552b , 24500c 25000b
with spin Ms obtained by diagonalizing the above full energy matrix. Lj (j = x, y, z) and Sj represent the operators of orbit and spin angular momentums, respectively. By diagonalizing the full energy matrix based on the two SO coupling constants, the optical absorption and EPR g factor can be calculated simultaneously. To reach the good agreement between calculation and experiment, the following fitting parameters have been obtained,
2.2145e
Ri ≈ 2.1316 Å ,
fr ≈ 0.8043
(9)
a
is the irreducible representation of Oh group; T is the one considering the double SO approach. b From Ref. [3]. c From Ref. [4]. d From Ref. [5]. e From Refs. [1,6].
d (the d orbital of 3dn ion) and p (the p orbital of ligand), i.e., [10–14]
ϕ = N1/2 d − p
(3)
where = eg or t2g are the irreducible representations, with t2g = x+ , x− , x0 and eg = u+ , u− . The normalization factors N and the orbital mixing coefficients can be related by the normalization correlation 2 1/2
N [1 + 2 Sdp () + ( ) ]
=1
(4)
and the approximate relationship [12–14] fr =
B B0
or
C C0
2 = N2 [1 − 2 Sdp () + 2 Sdp ()]
(5)
where Sdp () is the group overlap integral, which can be calculated from the Slater-type SCF functions [15,16] and the metal–ligand distance RH of the studied system. For the studied MgO:Ni2+ system, RH = 2.0975 A˚ [17], we obtain Sdp (t2g ) ≈ 0.0081235 and Sdp (eg ) ≈ 0.0279372. B and C are the Racah parameters of 3dn ions in crystals and B0 and C0 are the corresponding parameters in free state. For free Ni2+ ion, B0 ≈ 1084 cm−1 and C0 ≈ 4831 cm−1 [18]. Thus, for the studied system, we obtain B ≈ frB0 , C ≈ frC0 . Although the contribution of the SO coupling to the optical spectra is relatively small, it is important to the EPR g factor. According to the double SO coupling approach, the two SO constants , and two orbital angular momentum reduction factors k, k could be calculated by using the following formulas [12–14,19] = Nt (d0 + 2t p0 /2),
= (Nt Ne )1/2 (d0 − t e p0 /2)
k = Nt (1 − 2t Sdp (t2g ) + 2t /2), k = (Nt Ne )
1/2
(6)
(1 − t Sdp (t2g ) − e Sdp (eg ) − t e /2)
in which SO coefficient d0 = 636 cm−1 for free Ni2+ ion [18], p0 = 150 for free O2− ion [20]. Thus, for Ni2+ (3d8 ) ion in cubic symmetry, the Hamiltonian can be written as H = Hee (B, C) + HCF (Dq) + HSO (, ) + HTrees (˛)
(7)
The calculated optical absorption spectral bands (d–d transition) and EPR g factor together with the experiments are listed in Table 1. 3. Conclusions (1) From Table 1, one can see that the calculated optical absorption spectra and EPR g factor agree well with the experimental data. Thus, the optical absorption spectra and EPR g factor of MgO:Ni2+ can be uniformly explained by the double SO approach. (2) For MgO:Ni2+ , if we omit the ligand SO coupling and then take p0 = 0, the calculated g factor is g( d ) ≈ 2.2174. We have g-shift g = g( d ) − g = 0.0029. Thus, the influence of the SO coupling of the ligand p electron is existent for the EPR g factor. (3) The calculated result shows that Ni2+ in MgO does occupy the real Mg2+ site and expand outside about 0.0341 A˚ (R = Ri − RH ), which is comparable with the value 0.03 A˚ (r = ri (Ni2+ ) − rH (Mg2+ ) [8]) of the radius difference between the impurity and replaced host ion. Acknowledgements This work was partially supported by the Foundation of Chongqing University of Technology (Nos. 2008ZQ12, 2009ZD09) and the Term of Science and Technology of Chongqing Education Committee (No. KJ090608). References [1] J.W. Orton, P. Auzins, J.E. Wertz, Double-quantum electron spin resonance transitions of nickel in magnesium oxide, Phys. Rev. Lett. 4 (1960) 128–129. [2] X.Y. Kuang, K.W. Zhou, Study of exchange interaction of Ni2+ pairs in MgO:Ni2+ , KMgF3 :Ni2+ and KNiF3 crystals, Phys. B: Condens. Mat. 305 (2001) 169–174. [3] R. Pappalardo, D.L. Wood, R.C. Linares Jr., Optical absorption spectra of Ni-doped oxide systems. I, J. Chem. Phys. 35 (1961) 1460–1478. [4] S. Minomura, H.G. Drickamer, Effect of pressure on the spectra of transition metal ions in MgO and Al2 O3 , J. Chem. Phys. 35 (1961) 903–907. [5] S.A. Payne, Energy-level assignments for the 1 E and 3 T1a states of MgO:Ni2+ , Phys. Rev. B 41 (1990) 6109–6116. [6] P.R. Locher, S. Geschwind, Electron-nuclear double resonance of Ni61 in Al2 O3 and variation of hfs through an inhomogeneous line due to random crystal fields, Phys. Rev. Lett. 11 (1963) 333–336. [7] D.P. Ma, N. Ma, X.D. Ma, H.M. Zhang, Energy spectrum and g factor of MgO:Ni2+ and their pressure-induced shift, J. Phys. Chem. Solids 59 (1998) 1211–1217. [8] R.C. Weast, CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton, 1989. [9] M.G. Zhao, M.L. Du, G.Y. Shen, A – –˛ correlation ligand-field model for the Ni2+ –6X− cluster, J. Phys. C 20 (1987) 5557–5571.
1514
W.L. Feng et al. / Optik 122 (2011) 1512–1514
[10] M.L. Du, M.G. Zhao, Gyromagnetic factor and spin–orbit coupling of ligands in CsVX3 (X = Cl, Br, I), Phys. Status Solidi B 153 (1989) 249– 255. [11] W.L. Feng, Theoretical studies of EPR g-factors and microstructure of the two tetragonal palladium centers in silver chloride, Phys. Status Solidi B 246 (2009) 1945–1947. [12] W.C. Zheng, X.X. Wu, Y.J. Fan, Gyromagnetic factor of Cr4+ ions in forsterite, Spectrochim. Acta A 61 (2005) 1905–1908. [13] M.L. Du, Theoretical investigation of the g factor in RX:V2+ (R = Na, K, Rb; X = Cl, Br), Phys. Rev. B 46 (1992) 5274–5279. [14] W.L. Feng, W.C. Zheng, Studies of the optical spectral bands and spinHamiltonian parameters for Ni2+ ions in a CdCl2 crystal, Radiat. Eff. Def. Solids 163 (2008) 857–861. [15] E. Clementi, D.L. Raimondi, Atomic screening constants from SCF functions, J. Chem. Phys. 38 (1963) 2686–2689.
[16] E. Clementi, D.L. Raimondi, W.P. Reinhardt, Atomic screening constants from SCF functions. II. Atoms with 37 to 86 electrons, J. Chem. Phys. 47 (1967) 1300–1307. [17] M.I. McCarthy, N.M. Harrison, Ab initio determination of the bulk properties of MgO, Phys. Rev. B 49 (1994) 8574–8582. [18] J.S. Griffith, The Theory of Transition Metal Ions, Cambridge University Press, London, 1961. [19] X.X. Wu, W.L. Feng, Q. Zhou, W.C. Zheng, Theoretical explanation of the EPR parameters of tetragonal Ti3+ centers in ZnSe and CdS0.75 Se0.25 semiconductors, Z. Naturforsch. A 61 (2006) 505–508. [20] M.L. Du, C. Rudowicz, Gyromagnetic factors and zero-field splitting of t2 3 terms of Cr3+ clusters with trigonal symmetry: Al2 O3 , CsMgCl3 , and CsMgBr3 , Phys. Rev. B 46 (1992) 8974–8977. [21] S. Sugano, Y. Tanabe, H. Kamimura, Multiplets of Transition Metal Ions in Crystals, Academic Press, New York, 1970.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Optical absorption spectra and EPR g factor of divalent nickel doped magnesia crystal W.L. Feng a,b,c,∗ , X.M. Li a,d,∗ , W.J. Yang d , C.Y. Tao d , Y.L. Yang d a
Key Laboratory for Optoelectronic Technology and Systems, Ministry of Education; College of Optoelectronic Engineering, Chongqing University, Chongqing 400044, China Department of Applied Physics, Chongqing University of Technology, Chongqing, 400054, China International Centre for Materials Physics, Chinese Academy of Sciences, Shengyang, 110016, China d College of Chemistry and Chemical Engineering, Chongqing University, Chongqing, 400044, China b c
a r t i c l e
i n f o
Article history: Received 24 May 2010 Accepted 30 September 2010
Keywords: Optical properties Crystal- and ligand field Electron paramagnetic resonance MgO Ni2+
a b s t r a c t Based on the crystal- and ligand-field theory, the optical absorption spectra and electron paramagnetic resonance (EPR) g factor of Ni2+ ion at Mg2+ position in MgO have been investigated. The bond length (i.e. Ni2+ –O2− distance) was determined from the cubic field parameter Dq; the crystal field Hamiltonian including the spin–orbital (SO) coupling effect of the ligand was diagonalized in the complete basis of 45 wave functions. Results of calculations are in a good agreement with experimental data. © 2010 Elsevier GmbH. All rights reserved.
1. Introduction Magnesia (magnesium oxide) is extensively application in desiccant, medication, magnetic and optical film, etc. Thus, many spectroscopic studies have been made for transition-metal ions in MgO [1–6]. Among them, the experimental data of the optical absorption spectra and electron paramagnetic resonance (EPR) g factor of Ni2+ ion at Mg2+ position in MgO were measured [1,3–6]. The theoretical investigations of optical and EPR spectra of Ni2+ doped MgO based on single spin–orbital coupling have been made by Kuang and Ma et al. [2,7]. For example, the energy spectrum and g factor of MgO:Ni2+ and their pressure-induced shift were calculated [7]. However, the spin–orbit (SO) coupling effect of the ligand and local lattice relaxation due to the substitution of Ni2+ for Mg2+ is not considered in their calculation. To understand the detailed physical and chemical properties of MgO:Ni2+ crystal, further theoretical explanations for the optical absorption spectra and g factor of MgO:Ni2+ should be carried out. In the present paper, we calculate the optical absorption spectra and g factor of MgO:Ni2+ from a diagonalizing the full energy matrix method which the SO coupling effect of the ligand oxygen is included. Since the ionic radius
∗ Corresponding authors at: College of Optoelectronic Engineering, Chongqing University, Chongqing, 400044, China. E-mail addresses: [email protected] (W.L. Feng), [email protected] (X.M. Li). 0030-4026/$ – see front matter © 2010 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2010.09.034
˚ of Ni2+ is greater than that (≈0.66 A) ˚ of Mg2+ ion [8], the (≈0.69 A) local lattice relaxation for the Ni2+ center in MgO crystal due to the size mismatch is also taken into account in the present calculation. 2. Theoretical calculation MgO crystal has the cubic symmetry which has a space group Fm-3m . When Ni2+ ion replaces Mg2+ ion in MgO, the radius difference between Ni2+ and Mg2+ will lead to somewhat lattice relaxation. Because no zero-field splitting was observed by spectroscopic analysis [3–5], the symmetry of Ni2+ center is still cubic. The bond length of Ni2+ –O2− due to the local lattice relaxation of Ni2+ center in MgO can be estimated by the cubic crystal-field parameter Dq, 1 1 , Dq = − eq fr r 4 0 R5 6
(1)
i
in which e is the electronic charge, q is the charge of the oxygen ligand (i.e. q = 2e for O2− ). Ri is the impurity–ligand distance (i.e. Ni2+ –O2− distance), fr is the averagereduction factor due to the covalency, and the expectation value r 4 for the free ion is given 0 by [9]
4 r
0
= 13.4043 a.u.
(2)
the double SO approach, the single electron function Following ϕ of the ML6 octahedral clusters has the linear expansion of
W.L. Feng et al. / Optik 122 (2011) 1512–1514 Table 1 The optical absorption spectra (in cm−1 ) and EPR g factor. ˛2S + 1 6 2
t e t5 e3
3
t5 e3 t6 e2 t5 e3
3
t5 e3 t4 e4
1
t6 e2 t5 e3 t4 e4 t4 e4 t4 e4
1
A2 3 T2 T1 E 3 T1 1
T2 3 T1 A1 T1 1 E 1 T2 1 A1 1
Ta
Calculation
Experiment
T2 E T1 T2 A2 A1 E T1 T2 E T2 E A1 T2 T1 A1 T1 E T2 A1
0 8037 8173 8522 8669 13089 13389 13528 14220 14965 21386 24216 24436 24478 24588 24847 28353 33894 34563 57067
0 8003b 8179b 8591b 8645b , 8845c 13100b 13120b 13520b 14333b 14770b 21126, 21134d
EPR g factor
2.2145
1513
where the four terms are, respectively, the electron–electron interactions, the cubic crystal-field potentials, the SO coupling interactions and the Trees correction term (˛ = 140 cm−1 here [9]). From the strong field basis functions [21], the complete energy matrix (45 × 45) related to the above Hamiltonian of the 3d8 ion in Td symmetry is constructed. Considering the equivalence between the EPR g factor and the Zeeman interaction, we have g=
3
A2 (t26 e2 ), 1, e2 k± Lj + gs Sj 3 A2 (t26 e2 ), 1, e2
(8)
in which 3 A2 (t26 e2 ), Ms is the eigenfunction of the ground state 3A 2
24552b , 24500c 25000b
with spin Ms obtained by diagonalizing the above full energy matrix. Lj (j = x, y, z) and Sj represent the operators of orbit and spin angular momentums, respectively. By diagonalizing the full energy matrix based on the two SO coupling constants, the optical absorption and EPR g factor can be calculated simultaneously. To reach the good agreement between calculation and experiment, the following fitting parameters have been obtained,
2.2145e
Ri ≈ 2.1316 Å ,
fr ≈ 0.8043
(9)
a
is the irreducible representation of Oh group; T is the one considering the double SO approach. b From Ref. [3]. c From Ref. [4]. d From Ref. [5]. e From Refs. [1,6].
d (the d orbital of 3dn ion) and p (the p orbital of ligand), i.e., [10–14]
ϕ = N1/2 d − p
(3)
where = eg or t2g are the irreducible representations, with t2g = x+ , x− , x0 and eg = u+ , u− . The normalization factors N and the orbital mixing coefficients can be related by the normalization correlation 2 1/2
N [1 + 2 Sdp () + ( ) ]
=1
(4)
and the approximate relationship [12–14] fr =
B B0
or
C C0
2 = N2 [1 − 2 Sdp () + 2 Sdp ()]
(5)
where Sdp () is the group overlap integral, which can be calculated from the Slater-type SCF functions [15,16] and the metal–ligand distance RH of the studied system. For the studied MgO:Ni2+ system, RH = 2.0975 A˚ [17], we obtain Sdp (t2g ) ≈ 0.0081235 and Sdp (eg ) ≈ 0.0279372. B and C are the Racah parameters of 3dn ions in crystals and B0 and C0 are the corresponding parameters in free state. For free Ni2+ ion, B0 ≈ 1084 cm−1 and C0 ≈ 4831 cm−1 [18]. Thus, for the studied system, we obtain B ≈ frB0 , C ≈ frC0 . Although the contribution of the SO coupling to the optical spectra is relatively small, it is important to the EPR g factor. According to the double SO coupling approach, the two SO constants , and two orbital angular momentum reduction factors k, k could be calculated by using the following formulas [12–14,19] = Nt (d0 + 2t p0 /2),
= (Nt Ne )1/2 (d0 − t e p0 /2)
k = Nt (1 − 2t Sdp (t2g ) + 2t /2), k = (Nt Ne )
1/2
(6)
(1 − t Sdp (t2g ) − e Sdp (eg ) − t e /2)
in which SO coefficient d0 = 636 cm−1 for free Ni2+ ion [18], p0 = 150 for free O2− ion [20]. Thus, for Ni2+ (3d8 ) ion in cubic symmetry, the Hamiltonian can be written as H = Hee (B, C) + HCF (Dq) + HSO (, ) + HTrees (˛)
(7)
The calculated optical absorption spectral bands (d–d transition) and EPR g factor together with the experiments are listed in Table 1. 3. Conclusions (1) From Table 1, one can see that the calculated optical absorption spectra and EPR g factor agree well with the experimental data. Thus, the optical absorption spectra and EPR g factor of MgO:Ni2+ can be uniformly explained by the double SO approach. (2) For MgO:Ni2+ , if we omit the ligand SO coupling and then take p0 = 0, the calculated g factor is g( d ) ≈ 2.2174. We have g-shift g = g( d ) − g = 0.0029. Thus, the influence of the SO coupling of the ligand p electron is existent for the EPR g factor. (3) The calculated result shows that Ni2+ in MgO does occupy the real Mg2+ site and expand outside about 0.0341 A˚ (R = Ri − RH ), which is comparable with the value 0.03 A˚ (r = ri (Ni2+ ) − rH (Mg2+ ) [8]) of the radius difference between the impurity and replaced host ion. Acknowledgements This work was partially supported by the Foundation of Chongqing University of Technology (Nos. 2008ZQ12, 2009ZD09) and the Term of Science and Technology of Chongqing Education Committee (No. KJ090608). References [1] J.W. Orton, P. Auzins, J.E. Wertz, Double-quantum electron spin resonance transitions of nickel in magnesium oxide, Phys. Rev. Lett. 4 (1960) 128–129. [2] X.Y. Kuang, K.W. Zhou, Study of exchange interaction of Ni2+ pairs in MgO:Ni2+ , KMgF3 :Ni2+ and KNiF3 crystals, Phys. B: Condens. Mat. 305 (2001) 169–174. [3] R. Pappalardo, D.L. Wood, R.C. Linares Jr., Optical absorption spectra of Ni-doped oxide systems. I, J. Chem. Phys. 35 (1961) 1460–1478. [4] S. Minomura, H.G. Drickamer, Effect of pressure on the spectra of transition metal ions in MgO and Al2 O3 , J. Chem. Phys. 35 (1961) 903–907. [5] S.A. Payne, Energy-level assignments for the 1 E and 3 T1a states of MgO:Ni2+ , Phys. Rev. B 41 (1990) 6109–6116. [6] P.R. Locher, S. Geschwind, Electron-nuclear double resonance of Ni61 in Al2 O3 and variation of hfs through an inhomogeneous line due to random crystal fields, Phys. Rev. Lett. 11 (1963) 333–336. [7] D.P. Ma, N. Ma, X.D. Ma, H.M. Zhang, Energy spectrum and g factor of MgO:Ni2+ and their pressure-induced shift, J. Phys. Chem. Solids 59 (1998) 1211–1217. [8] R.C. Weast, CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton, 1989. [9] M.G. Zhao, M.L. Du, G.Y. Shen, A – –˛ correlation ligand-field model for the Ni2+ –6X− cluster, J. Phys. C 20 (1987) 5557–5571.
1514
W.L. Feng et al. / Optik 122 (2011) 1512–1514
[10] M.L. Du, M.G. Zhao, Gyromagnetic factor and spin–orbit coupling of ligands in CsVX3 (X = Cl, Br, I), Phys. Status Solidi B 153 (1989) 249– 255. [11] W.L. Feng, Theoretical studies of EPR g-factors and microstructure of the two tetragonal palladium centers in silver chloride, Phys. Status Solidi B 246 (2009) 1945–1947. [12] W.C. Zheng, X.X. Wu, Y.J. Fan, Gyromagnetic factor of Cr4+ ions in forsterite, Spectrochim. Acta A 61 (2005) 1905–1908. [13] M.L. Du, Theoretical investigation of the g factor in RX:V2+ (R = Na, K, Rb; X = Cl, Br), Phys. Rev. B 46 (1992) 5274–5279. [14] W.L. Feng, W.C. Zheng, Studies of the optical spectral bands and spinHamiltonian parameters for Ni2+ ions in a CdCl2 crystal, Radiat. Eff. Def. Solids 163 (2008) 857–861. [15] E. Clementi, D.L. Raimondi, Atomic screening constants from SCF functions, J. Chem. Phys. 38 (1963) 2686–2689.
[16] E. Clementi, D.L. Raimondi, W.P. Reinhardt, Atomic screening constants from SCF functions. II. Atoms with 37 to 86 electrons, J. Chem. Phys. 47 (1967) 1300–1307. [17] M.I. McCarthy, N.M. Harrison, Ab initio determination of the bulk properties of MgO, Phys. Rev. B 49 (1994) 8574–8582. [18] J.S. Griffith, The Theory of Transition Metal Ions, Cambridge University Press, London, 1961. [19] X.X. Wu, W.L. Feng, Q. Zhou, W.C. Zheng, Theoretical explanation of the EPR parameters of tetragonal Ti3+ centers in ZnSe and CdS0.75 Se0.25 semiconductors, Z. Naturforsch. A 61 (2006) 505–508. [20] M.L. Du, C. Rudowicz, Gyromagnetic factors and zero-field splitting of t2 3 terms of Cr3+ clusters with trigonal symmetry: Al2 O3 , CsMgCl3 , and CsMgBr3 , Phys. Rev. B 46 (1992) 8974–8977. [21] S. Sugano, Y. Tanabe, H. Kamimura, Multiplets of Transition Metal Ions in Crystals, Academic Press, New York, 1970.