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Dependence of crystal field splitting of 5d levels on hosts in the halide crystals
Chemical Physics Letters 380 (2003) 245–250 www.elsevier.com/locate/cplett
Dependence of crystal field splitting of 5d levels on hosts in the halide crystals J.S. Shi, Z.J. Wu, S.H. Zhou, S.Y. Zhang
*
Key Laboratory of Rare Earth Chemistry and Physics, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, PR China Received 24 April 2003; in final form 16 July 2003 Published online: 28 September 2003
Abstract The crystal field splitting of 5d level of Eu2þ and Ce3þ in halide crystals has been studied. Our results indicate that the 10Dq splitting can be directly related to the homopolar part of average energy gap, the coordination number of central (doped) ion, the charge of neighboring anions and bond ionicity between central ion to nearest anions. A relation between the 10Dq splitting and the above mentioned factors is presented. Our calculated results are in reasonable agreement with diverse experiments. Ó 2003 Elsevier B.V. All rights reserved.
1. Introduction The 5d energy level spectra of Ce3þ and Eu2þ in VUV–UV region were extensively studied recently [1–3]. These spectral data reveal that 5d orbital is split into t2g and eg components (10Dq) for the rare earth ions in a cubic symmetry. In lower symmetry, more components (that is, t2g and eg will be split further) are expected, and in this case 10Dq are defined as the difference of mass centers of t2g and eg . The magnitudes of crystal field splitting are different when the rare earth ions are doped in different hosts. In order to explain the phenomena,
*
Corresponding author. Fax: +81-431-5698041. E-mail address: [email protected] (S.Y. Zhang).
several researches have been conducted [4,5]. According to the point charge model, the 10Dq splitting should be proportional to R5 in cubic symmetry, where R is the bond length. However, Hernadez et al. [4] gave a graph between cubic split 10Dq and bond length R for Eu2þ ions in halides and found that 10Dq / Rn with n ¼ 1:8, 2.2, 3.1, and 4.2 for the alkali fluoride, chloride, bromide, and iodide series, respectively. Therefore, the result showed that the point charge model did not work well in explaining the crystal splitting, because the bond length R is not an unique factor in determining the magnitudes of 10Dq. Dorenbos [5] collected the data of crystal field splitting and revealed that the total crystal field splitting between the highest 5d energy level and the lowest 5d level, has a relation with the form bR2 , where b is constant depending on the structure of coordination
0009-2614/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2003.09.022
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J.S. Shi et al. / Chemical Physics Letters 380 (2003) 245–250
polyhedron, and R is the average bond distance from central (doped) ion to the nearest ligands. The relation suggested that the crystal environment such as the structure and the bond length influences the magnitudes of the crystal splitting. To our knowledge, till now a quantitative study concerning the environment influence on the crystal field splitting is still rare. Motivated by this, in this Letter, a quantitative relation between the crystal split and environmental factors has been studied for Ce3þ and Eu2þ in halide crystals. It is found that the homopolar part of average energy gap, coordination number of central ion, charge of neighboring anion, and bond ionicity between the central ion to nearest neighboring anion (for detailed explanation of the above quantities, see below) are the four main factors to influence 10Dq splitting. The established trends of the crystal splitting in Eu2þ and Ce3þ may be profitable in gaining an insight into the crystal field interaction. 2. Theoretical background It is known that although the point charge model has limits in quantitatively explaining the crystal split, it is still useful in describing qualitatively the interaction in crystals. The Hamiltonian of the crystal field in this model can be written as X X Zj e2 Hcr ¼ Akq rk Cqk ; ð1Þ ri Rj ¼ i;j
k
k;q
where hr i is the radial integral of central atom, Akq is the crystal field parameter depending only on the host crystals, independent of the central ions. Cqk is the coordinate parameter of the electrons which can be calculated based on angle coordinate of the electrons. Obviously, the crystal split result is from two parts: one is the central (doped) ion; the other is the host crystal environment. For any crystals doped with the same rare earth ion, the crystal environment is proportional to crystal field split. For cubic crystal field, 10Dq is usually expressed as the energy difference between the centers of gravity of the high-energy band and low-energy band. Although 5d orbit will be split into more components when the rare earth ions are in a lower symmetry site, the magnitudes of 10Dq split can be
still obtained based on group theory. For example, in Ce3þ doped LiYF4 crystal, the Ce3þ ion occupy the Y3þ site, the point group symmetry is S4 . Therefore, five energy bands are obtained in the spectrum [6]. Based on the decomposition of the point group, we have: S4 D2d Td Oh , three higher bands and two lower bands can be assigned to sub-members of t2g and eg , respectively. Thus, centers of gravity of the three higher bands and two lower bands can be denoted as t2g and eg . Therefore, the magnitudes of 10Dq split can be calculated. All the magnitudes of the 10Dq split can be found either directly or indirectly (by our calculation) from experimental data in [1–3,6–11]. In our study, we found that the following four quantities: Eh , N , Q, and fi are crucial in determining the magnitudes of 10Dq split. Eh is the homopolar part of average energy gap. According to dielectric theory, the physical interpretation of Eh is that it is the origin of bond covalency and comes from the interaction of dipole moments and other multiple moments [13]. It is expressed as: Eh ¼ 39:74R2:48 [12,13], R is the bond length. N is the coordination number of central ion. The above two parameters R and N can be determined from crystallographic data [14–16]. fi is the bond ionicity of between the central ion to nearest neighbors. Q is the charge of neighboring anion, which is obtained according to the charge neutral principle of the sub-formula [13]. For example, for Ce3þ doped LiYF4 crystal, we have LiYF4 ¼ YF8=3 + LiF4=3 (concerning the method to decompose LiYF4 into the sum of binary crystals, see [16]), the charges of Y and Li are chosen to be their normal valence 3 and 1, respectively, then, in terms of charge neutral principle in each sub-formula (YF8=3 and LiF4=3 ), the charge of F ion is 3 38 ¼ 1:125 in Y–F bond (YF8=3 ) and 3 34 ¼ 0:75 in Li–F bond (LiF4=3 ). Since Ce3þ occupy the Y3þ , therefore, Q ¼ 1:125. In our study, we found that a new parameter can be introduced, which is the combination of the four parameters mentioned above Fc ¼
Eh Qfi : N
ð2Þ
We will call Fc the environmental factor throughout the Letter.
J.S. Shi et al. / Chemical Physics Letters 380 (2003) 245–250
3. Result and discussion
ABF3 perovskite crystal serises, in which the same coordination number and charge of neighboring anion, the difference of 10Dq splitting is mainly influenced by Eh and bond ionicity. As shown in the trends of 10Dq splitting in Fig. 1, crystals considered here in a series follows the relation. For Eu2þ doped SrCl2 crystal, which has cubic crystal structure and Eu2þ occupy the Sr2þ site surrounded by six chloric ions with Q ¼ 1, the calculated magnitude of 10Dq splitting (E10Dq ¼ 10 396 cm1 ) by Eq. (3) is in good agreement with the experimental magnitude (E10Dq ¼ 10 160 cm1 ) [1]. On the other hand, in ABF3 type crystals, there are two different sites, which have the cubic perovskite crystal structure (KMgF3 , RbMgF3 , KZnF3 , and KCaF3 , see Table 1). Aþ is coordinated by 12 fluoride ions with Q ¼ 0:5, B2þ is coordinated by six fluoride ions with Q ¼ 1. Obviously, the coordination number N and Q play more important role than Eh and fi for the two sites. Eu2þ may occupy Aþ or B2þ or both sites when doped in those crystals.
All parameters in various crystals calculated in this Letter are listed in Tables 1 and 2. The trends of 10Dq versus Fc for Eu2þ and Ce2þ ions in halide crystals are also given in Figs. 1 and 2. 3.1. Eu2þ ion in halide crystals From our calculated results (Table 1), a linear relation between 10Dq splitting and Fc has been found. The fitted equation is E10Dq ðEu2þ Þ ¼ 4:99 þ 18:77Fc :
247
ð3Þ
It is seen that the values of 10Dq splitting increase with the increasing of charge of neighboring anion, the homopolar part of average energy gap, bond ionicity, and the decreasing number of coordination anion. For Eu2þ on a similar site in a series, such as alkali halide series, alkaline-earth halide series or
Table 1 Values of 10Dq splitting and corresponding crystal factors for Eu2þ in halide crystals (energy unit: 103 cm1 ) Crystal
Sitea
) R (A
Eh
N
Q
fi
Fc
10Dqexp b
10Dqcal f
NaF KF NaCl KCl RbCl NaBr KBr RbBr NaI KI RbI CaF2 SrF2 BaF2 SrCl2 KMgF3 RbMgF3 KZnF3 KCaF3 KCaF3
Naþ Kþ Naþ Kþ Rbþ Naþ Kþ Rbþ Naþ Kþ Rbþ Ca2þ Sr2þ Ba2þ Sr2þ Kþ Rbþ Kþ Kþ Ca2þ
2.317 2.674 2.810 3.147 3.291 2.986 3.298 3.445 3.237 3.533 3.671 2.366 2.511 2.685 3.020 2.809 2.920 2.867 2.991 2.115
4.946 3.466 3.065 2.314 2.071 2.636 2.060 1.849 2.158 1.737 1.580 4.695 4.051 3.431 2.563 3.068 2.787 2.916 2.625 6.201
6 6 6 6 6 6 6 6 6 6 6 8 8 8 8 12 12 12 12 6
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.5 0.5 0.5 0.5 1
0.946 0.954 0.936 0.951 0.956 0.933 0.953 0.955 0.929 0.948 0.954 0.947 0.952 0.956 0.949 0.978 0.980 0.973 0.980 0.942
0.738 0.526 0.448 0.349 0.316 0.382 0.312 0.281 0.310 0.260 0.240 0.526 0.459 0.392 0.288 0.122 0.111 0.115 0.105 0.916
18.35 16.61 12.85 12.00 11.66 11.75 10.93 10.27 10.63 9.52 9.06 15.50 13.50 11.30 10.16 7.50c 7.30d 7.70c 6.30e 22.00e
18.84 14.86 13.40 11.54 10.92 12.16 10.85 10.26 10.81 9.87 9.49 14.84 13.61 12.35 10.40 7.28 7.07 7.15 6.96 22.18
a
Sites occupied by Eu2þ . Ref. [1] unless specified. c Ref. [7]. d Ref. [8]. e Ref. [9]. f This work. b
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J.S. Shi et al. / Chemical Physics Letters 380 (2003) 245–250
Table 2 Values of 10Dq splitting and corresponding crystal factors for Ce3þ in halide crystals (energy unit: 103 cm1 ) Crystal LiYF4 CeF3 LiLuF4 LaF3 LuF3 KMgF3 CaF2 SrF2 BaF2 YF3 BaCl2 SrCL2
Sitea 3þ
Y Ce3þ Lu3þ La3þ Lu3þ Kþ Ca2þ Sr2þ Ba2þ Y3þ Ba2þ Sr2þ
) R (A
Eh
N
Q
fi
Fc
10Dqexp b
10Dqcal f
2.270 2.565 2.237 2.586 2.297 2.809 2.366 2.511 2.685 2.321 3.178 3.020
5.068 3.844 5.396 3.765 5.051 3.068 4.695 4.051 3.431 4.924 2.259 2.563
8 11 8 11 9 12 8 8 8 9 8 8
1.125 1 1.125 1 1 0.5 1 1 1 1 1 1
0.977 0.952 0.978 0.954 0.941 0.978 0.947 0.952 0.956 0.943 0.948 0.949
0.681 0.317 0.726 0.312 0.497 0.122 0.526 0.459 0.392 0.486 0.254 0.288
13.41 6.96c 13.73 6.71 8.35 5.91 12.20d 11.20d 10.80d 8.58 6.06e 7.91e
13.04 7.81 13.68 7.74 10.39 5.02 10.81 9.85 8.89 10.24 6.91 7.40
a
Sites occupied by Ce3þ . Ref. [2] unless specified. c Ref. [6]. d Ref. [10]. e Ref. [11]. f This work. b
24 22 20
16
3
10Dq (10 cm )
18
14 12 10 8 6 0.0
0.2
0.4
0.6
0.8
1.0
F
Fig. 1. Relation between 10Dq splitting and Fc for Eu2þ in halide crystals.
These phenomena were studied by several authors and concluded that Eu2þ ions are either in Kþ or in Rbþ sites in KMgF3 , KZnF3 , and RbMgF3 [17,18]. Our calculation suggests that when Eu2þ ion occupy the Aþ site, which has the larger coordination number and the smaller charge of neighboring anions in halide crystals, 10Dq splitting are the smallest. This is in good agreement with experiments: E10Dq ¼ 7500 cm1 in KMgF3 [7], E10Dq ¼ 7700 cm1 in KZnF3 [7], and E10Dq ¼ 7300 cm1 in
RbMgF3 [8], as shown in the left lower part of Fig. 1. On the other hand, if Eu2þ ions occupy B2þ sites, the Fc is nearly four times larger than that in Aþ . Thus, the 10Dq splitting magnitudes in both sites have similar relation in terms of Eq. (3). Dorenbos [5] analyzed the spectra of KCaF3 :Eu2þ which was reported by Garcia et al. [9], and suggested that the lowest and highest energy bands may be attributed to the t2g and eg bands of Eu2þ in Ca2þ site, the third band may come from the overlapping between t2g
J.S. Shi et al. / Chemical Physics Letters 380 (2003) 245–250
249
14
10
3
-1
10Dq (10 cm )
12
8
6
4
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
F
Fig. 2. Relation between 10Dq splitting and Fc for Ce3þ in halide crystals.
and eg bands of Eu2þ in Kþ site. This analysis is in good agreement with our calculated results obtained from Eq. (3). Our estimated E10Dq ¼ 22 000 cm1 for Eu2þ in the Ca2þ sites and E10Dq ¼ 6300 cm1 in the Kþ sites from the spectra in [9]. 3.2. Ce3þ ion in halide crystals It is seen from Fig. 2 that distribution of sites is not as good as the case of Eu2þ . This may be due to the definition of t2g and eg components of 5d level because there are more bands (at most five bands) in the spectra of Ce3þ doped halide crystals. However, the trend between the 10Dq splitting and Fc is still obtained as follows: E10Dq ðCe3þ Þ ¼ 3:27 þ 14:34Fc :
ð4Þ
It can be seen from Table 2 that 10Dq splitting in KMgF3 crystal is the smallest, while that in LiYF4 is the largest. Eqs. (3) and (4) also reveal that, suppose the environmental factor Fc are similar, 10Dq split in Eu2þ is 35% larger than that in Ce3þ . This can be qualitatively explained in terms of Eq. (1). From Eq. (1), it is seen that the 10Dq split increases with the increasing of the radial integral hrk i of central atom. Although the values of hrk i for the rare earth ion are not available, for a crude estimation we could use the ionic radius ri instead of hrk i. In
doing so, a consistent trend is observed, because the ionic radius ri ¼ 109 pm of Eu2þ is larger than ri ¼ 103 pm of Ce3þ . This may be an explanation in determining the trend of 10Dq split. In summary, a relation between the 10Dq splitting and environmental factors for Eu2þ and Ce3þ is obtained. Our results revealed that the cubic crystal field split can be described by the homopolar part of the average energy gap, the coordination number of central ion, the charge of neighboring anions, and bond ionicity between the central ion to nearest anion. Hopefully, these relations may be extended to other systems and further study is under way.
References [1] [2] [3] [4] [5] [6] [7] [8] [9]
O.J. Rubio, J. Phys. Chem. Solids 52 (1991) 101. P. Dorenbos, Phys. Rev. B 62 (2000) 15640. P. Dorenbos, Phys. Rev. B 62 (2000) 15650. J.A. Hernadez, F.J. Lopez, H.S. Murrieta, O.J. Rubio, J. Phys. Soc. Jpn. 50 (1981) 225. P. Dorenbos, J. Alloys Comp. 341 (2002) 156. L. van Pieterson, M.F. Reid, G.W. Burdick, A. Meijerink, Phys. Rev. B 65 (2002) 045114. A. Ellens, A. Meijerink, G. Blasse, J. Lumin. 59 (1994) 293. R. Alcala, D.K. Sardar, W.A. Sibley, J. Lumin. 27 (1982) 273. J.M. Garcia, W.A. Sibley, C.A. Hunt, J.M. Spaeth, J. Lumin. 42 (1988) 35.
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[10] E. Loh, Phys. Rev. 154 (1967) 270. [11] Wei-Min Li, Markku Leskela, Mater. Lett. 28 (1996) 491. [12] J.A. Van Vechten, Phys. Rev. 182 (1969) 891; Phys. Rev. 187 (1969) 1007. [13] Z.J. Wu, S.Y. Zhang, J. Phys. Chem. A 103 (1999) 4270. [14] R.W.G. Wyckoff, in: Crystal Structure, vols. 1 and 2, Interscience, New York, 1964. [15] Clyde A. Morrison, Richard P. Leavitt, in: K.A. Gschneidner Jr., L. Eyring (Eds.), Handbook on the Physics and
Chemistry of Rare Earths, vol. 46, North-Holland Publishing Company, Amsterdam, 1982, p. 461. [16] G.A. Viabowa, V.T. Verelnaya, Zh. Neorg. Khim. 147 (1969) 1746. [17] S.N. Bodrug, E.C. Valyashko, V.N. Mednikova, D.T. Sviridov, R.K. Sviridov, Opt. Spectrosc. 34 (1973) 176. [18] N.S. Altshuler, E.Kh. Ivoilova, A.L. Stolov, Sov. Phys. Solid State 15 (1974) 1602.
Dependence of crystal field splitting of 5d levels on hosts in the halide crystals J.S. Shi, Z.J. Wu, S.H. Zhou, S.Y. Zhang
*
Key Laboratory of Rare Earth Chemistry and Physics, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, PR China Received 24 April 2003; in final form 16 July 2003 Published online: 28 September 2003
Abstract The crystal field splitting of 5d level of Eu2þ and Ce3þ in halide crystals has been studied. Our results indicate that the 10Dq splitting can be directly related to the homopolar part of average energy gap, the coordination number of central (doped) ion, the charge of neighboring anions and bond ionicity between central ion to nearest anions. A relation between the 10Dq splitting and the above mentioned factors is presented. Our calculated results are in reasonable agreement with diverse experiments. Ó 2003 Elsevier B.V. All rights reserved.
1. Introduction The 5d energy level spectra of Ce3þ and Eu2þ in VUV–UV region were extensively studied recently [1–3]. These spectral data reveal that 5d orbital is split into t2g and eg components (10Dq) for the rare earth ions in a cubic symmetry. In lower symmetry, more components (that is, t2g and eg will be split further) are expected, and in this case 10Dq are defined as the difference of mass centers of t2g and eg . The magnitudes of crystal field splitting are different when the rare earth ions are doped in different hosts. In order to explain the phenomena,
*
Corresponding author. Fax: +81-431-5698041. E-mail address: [email protected] (S.Y. Zhang).
several researches have been conducted [4,5]. According to the point charge model, the 10Dq splitting should be proportional to R5 in cubic symmetry, where R is the bond length. However, Hernadez et al. [4] gave a graph between cubic split 10Dq and bond length R for Eu2þ ions in halides and found that 10Dq / Rn with n ¼ 1:8, 2.2, 3.1, and 4.2 for the alkali fluoride, chloride, bromide, and iodide series, respectively. Therefore, the result showed that the point charge model did not work well in explaining the crystal splitting, because the bond length R is not an unique factor in determining the magnitudes of 10Dq. Dorenbos [5] collected the data of crystal field splitting and revealed that the total crystal field splitting between the highest 5d energy level and the lowest 5d level, has a relation with the form bR2 , where b is constant depending on the structure of coordination
0009-2614/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2003.09.022
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J.S. Shi et al. / Chemical Physics Letters 380 (2003) 245–250
polyhedron, and R is the average bond distance from central (doped) ion to the nearest ligands. The relation suggested that the crystal environment such as the structure and the bond length influences the magnitudes of the crystal splitting. To our knowledge, till now a quantitative study concerning the environment influence on the crystal field splitting is still rare. Motivated by this, in this Letter, a quantitative relation between the crystal split and environmental factors has been studied for Ce3þ and Eu2þ in halide crystals. It is found that the homopolar part of average energy gap, coordination number of central ion, charge of neighboring anion, and bond ionicity between the central ion to nearest neighboring anion (for detailed explanation of the above quantities, see below) are the four main factors to influence 10Dq splitting. The established trends of the crystal splitting in Eu2þ and Ce3þ may be profitable in gaining an insight into the crystal field interaction. 2. Theoretical background It is known that although the point charge model has limits in quantitatively explaining the crystal split, it is still useful in describing qualitatively the interaction in crystals. The Hamiltonian of the crystal field in this model can be written as X X Zj e2 Hcr ¼ Akq rk Cqk ; ð1Þ ri Rj ¼ i;j
k
k;q
where hr i is the radial integral of central atom, Akq is the crystal field parameter depending only on the host crystals, independent of the central ions. Cqk is the coordinate parameter of the electrons which can be calculated based on angle coordinate of the electrons. Obviously, the crystal split result is from two parts: one is the central (doped) ion; the other is the host crystal environment. For any crystals doped with the same rare earth ion, the crystal environment is proportional to crystal field split. For cubic crystal field, 10Dq is usually expressed as the energy difference between the centers of gravity of the high-energy band and low-energy band. Although 5d orbit will be split into more components when the rare earth ions are in a lower symmetry site, the magnitudes of 10Dq split can be
still obtained based on group theory. For example, in Ce3þ doped LiYF4 crystal, the Ce3þ ion occupy the Y3þ site, the point group symmetry is S4 . Therefore, five energy bands are obtained in the spectrum [6]. Based on the decomposition of the point group, we have: S4 D2d Td Oh , three higher bands and two lower bands can be assigned to sub-members of t2g and eg , respectively. Thus, centers of gravity of the three higher bands and two lower bands can be denoted as t2g and eg . Therefore, the magnitudes of 10Dq split can be calculated. All the magnitudes of the 10Dq split can be found either directly or indirectly (by our calculation) from experimental data in [1–3,6–11]. In our study, we found that the following four quantities: Eh , N , Q, and fi are crucial in determining the magnitudes of 10Dq split. Eh is the homopolar part of average energy gap. According to dielectric theory, the physical interpretation of Eh is that it is the origin of bond covalency and comes from the interaction of dipole moments and other multiple moments [13]. It is expressed as: Eh ¼ 39:74R2:48 [12,13], R is the bond length. N is the coordination number of central ion. The above two parameters R and N can be determined from crystallographic data [14–16]. fi is the bond ionicity of between the central ion to nearest neighbors. Q is the charge of neighboring anion, which is obtained according to the charge neutral principle of the sub-formula [13]. For example, for Ce3þ doped LiYF4 crystal, we have LiYF4 ¼ YF8=3 + LiF4=3 (concerning the method to decompose LiYF4 into the sum of binary crystals, see [16]), the charges of Y and Li are chosen to be their normal valence 3 and 1, respectively, then, in terms of charge neutral principle in each sub-formula (YF8=3 and LiF4=3 ), the charge of F ion is 3 38 ¼ 1:125 in Y–F bond (YF8=3 ) and 3 34 ¼ 0:75 in Li–F bond (LiF4=3 ). Since Ce3þ occupy the Y3þ , therefore, Q ¼ 1:125. In our study, we found that a new parameter can be introduced, which is the combination of the four parameters mentioned above Fc ¼
Eh Qfi : N
ð2Þ
We will call Fc the environmental factor throughout the Letter.
J.S. Shi et al. / Chemical Physics Letters 380 (2003) 245–250
3. Result and discussion
ABF3 perovskite crystal serises, in which the same coordination number and charge of neighboring anion, the difference of 10Dq splitting is mainly influenced by Eh and bond ionicity. As shown in the trends of 10Dq splitting in Fig. 1, crystals considered here in a series follows the relation. For Eu2þ doped SrCl2 crystal, which has cubic crystal structure and Eu2þ occupy the Sr2þ site surrounded by six chloric ions with Q ¼ 1, the calculated magnitude of 10Dq splitting (E10Dq ¼ 10 396 cm1 ) by Eq. (3) is in good agreement with the experimental magnitude (E10Dq ¼ 10 160 cm1 ) [1]. On the other hand, in ABF3 type crystals, there are two different sites, which have the cubic perovskite crystal structure (KMgF3 , RbMgF3 , KZnF3 , and KCaF3 , see Table 1). Aþ is coordinated by 12 fluoride ions with Q ¼ 0:5, B2þ is coordinated by six fluoride ions with Q ¼ 1. Obviously, the coordination number N and Q play more important role than Eh and fi for the two sites. Eu2þ may occupy Aþ or B2þ or both sites when doped in those crystals.
All parameters in various crystals calculated in this Letter are listed in Tables 1 and 2. The trends of 10Dq versus Fc for Eu2þ and Ce2þ ions in halide crystals are also given in Figs. 1 and 2. 3.1. Eu2þ ion in halide crystals From our calculated results (Table 1), a linear relation between 10Dq splitting and Fc has been found. The fitted equation is E10Dq ðEu2þ Þ ¼ 4:99 þ 18:77Fc :
247
ð3Þ
It is seen that the values of 10Dq splitting increase with the increasing of charge of neighboring anion, the homopolar part of average energy gap, bond ionicity, and the decreasing number of coordination anion. For Eu2þ on a similar site in a series, such as alkali halide series, alkaline-earth halide series or
Table 1 Values of 10Dq splitting and corresponding crystal factors for Eu2þ in halide crystals (energy unit: 103 cm1 ) Crystal
Sitea
) R (A
Eh
N
Q
fi
Fc
10Dqexp b
10Dqcal f
NaF KF NaCl KCl RbCl NaBr KBr RbBr NaI KI RbI CaF2 SrF2 BaF2 SrCl2 KMgF3 RbMgF3 KZnF3 KCaF3 KCaF3
Naþ Kþ Naþ Kþ Rbþ Naþ Kþ Rbþ Naþ Kþ Rbþ Ca2þ Sr2þ Ba2þ Sr2þ Kþ Rbþ Kþ Kþ Ca2þ
2.317 2.674 2.810 3.147 3.291 2.986 3.298 3.445 3.237 3.533 3.671 2.366 2.511 2.685 3.020 2.809 2.920 2.867 2.991 2.115
4.946 3.466 3.065 2.314 2.071 2.636 2.060 1.849 2.158 1.737 1.580 4.695 4.051 3.431 2.563 3.068 2.787 2.916 2.625 6.201
6 6 6 6 6 6 6 6 6 6 6 8 8 8 8 12 12 12 12 6
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.5 0.5 0.5 0.5 1
0.946 0.954 0.936 0.951 0.956 0.933 0.953 0.955 0.929 0.948 0.954 0.947 0.952 0.956 0.949 0.978 0.980 0.973 0.980 0.942
0.738 0.526 0.448 0.349 0.316 0.382 0.312 0.281 0.310 0.260 0.240 0.526 0.459 0.392 0.288 0.122 0.111 0.115 0.105 0.916
18.35 16.61 12.85 12.00 11.66 11.75 10.93 10.27 10.63 9.52 9.06 15.50 13.50 11.30 10.16 7.50c 7.30d 7.70c 6.30e 22.00e
18.84 14.86 13.40 11.54 10.92 12.16 10.85 10.26 10.81 9.87 9.49 14.84 13.61 12.35 10.40 7.28 7.07 7.15 6.96 22.18
a
Sites occupied by Eu2þ . Ref. [1] unless specified. c Ref. [7]. d Ref. [8]. e Ref. [9]. f This work. b
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Table 2 Values of 10Dq splitting and corresponding crystal factors for Ce3þ in halide crystals (energy unit: 103 cm1 ) Crystal LiYF4 CeF3 LiLuF4 LaF3 LuF3 KMgF3 CaF2 SrF2 BaF2 YF3 BaCl2 SrCL2
Sitea 3þ
Y Ce3þ Lu3þ La3þ Lu3þ Kþ Ca2þ Sr2þ Ba2þ Y3þ Ba2þ Sr2þ
) R (A
Eh
N
Q
fi
Fc
10Dqexp b
10Dqcal f
2.270 2.565 2.237 2.586 2.297 2.809 2.366 2.511 2.685 2.321 3.178 3.020
5.068 3.844 5.396 3.765 5.051 3.068 4.695 4.051 3.431 4.924 2.259 2.563
8 11 8 11 9 12 8 8 8 9 8 8
1.125 1 1.125 1 1 0.5 1 1 1 1 1 1
0.977 0.952 0.978 0.954 0.941 0.978 0.947 0.952 0.956 0.943 0.948 0.949
0.681 0.317 0.726 0.312 0.497 0.122 0.526 0.459 0.392 0.486 0.254 0.288
13.41 6.96c 13.73 6.71 8.35 5.91 12.20d 11.20d 10.80d 8.58 6.06e 7.91e
13.04 7.81 13.68 7.74 10.39 5.02 10.81 9.85 8.89 10.24 6.91 7.40
a
Sites occupied by Ce3þ . Ref. [2] unless specified. c Ref. [6]. d Ref. [10]. e Ref. [11]. f This work. b
24 22 20
16
3
10Dq (10 cm )
18
14 12 10 8 6 0.0
0.2
0.4
0.6
0.8
1.0
F
Fig. 1. Relation between 10Dq splitting and Fc for Eu2þ in halide crystals.
These phenomena were studied by several authors and concluded that Eu2þ ions are either in Kþ or in Rbþ sites in KMgF3 , KZnF3 , and RbMgF3 [17,18]. Our calculation suggests that when Eu2þ ion occupy the Aþ site, which has the larger coordination number and the smaller charge of neighboring anions in halide crystals, 10Dq splitting are the smallest. This is in good agreement with experiments: E10Dq ¼ 7500 cm1 in KMgF3 [7], E10Dq ¼ 7700 cm1 in KZnF3 [7], and E10Dq ¼ 7300 cm1 in
RbMgF3 [8], as shown in the left lower part of Fig. 1. On the other hand, if Eu2þ ions occupy B2þ sites, the Fc is nearly four times larger than that in Aþ . Thus, the 10Dq splitting magnitudes in both sites have similar relation in terms of Eq. (3). Dorenbos [5] analyzed the spectra of KCaF3 :Eu2þ which was reported by Garcia et al. [9], and suggested that the lowest and highest energy bands may be attributed to the t2g and eg bands of Eu2þ in Ca2þ site, the third band may come from the overlapping between t2g
J.S. Shi et al. / Chemical Physics Letters 380 (2003) 245–250
249
14
10
3
-1
10Dq (10 cm )
12
8
6
4
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
F
Fig. 2. Relation between 10Dq splitting and Fc for Ce3þ in halide crystals.
and eg bands of Eu2þ in Kþ site. This analysis is in good agreement with our calculated results obtained from Eq. (3). Our estimated E10Dq ¼ 22 000 cm1 for Eu2þ in the Ca2þ sites and E10Dq ¼ 6300 cm1 in the Kþ sites from the spectra in [9]. 3.2. Ce3þ ion in halide crystals It is seen from Fig. 2 that distribution of sites is not as good as the case of Eu2þ . This may be due to the definition of t2g and eg components of 5d level because there are more bands (at most five bands) in the spectra of Ce3þ doped halide crystals. However, the trend between the 10Dq splitting and Fc is still obtained as follows: E10Dq ðCe3þ Þ ¼ 3:27 þ 14:34Fc :
ð4Þ
It can be seen from Table 2 that 10Dq splitting in KMgF3 crystal is the smallest, while that in LiYF4 is the largest. Eqs. (3) and (4) also reveal that, suppose the environmental factor Fc are similar, 10Dq split in Eu2þ is 35% larger than that in Ce3þ . This can be qualitatively explained in terms of Eq. (1). From Eq. (1), it is seen that the 10Dq split increases with the increasing of the radial integral hrk i of central atom. Although the values of hrk i for the rare earth ion are not available, for a crude estimation we could use the ionic radius ri instead of hrk i. In
doing so, a consistent trend is observed, because the ionic radius ri ¼ 109 pm of Eu2þ is larger than ri ¼ 103 pm of Ce3þ . This may be an explanation in determining the trend of 10Dq split. In summary, a relation between the 10Dq splitting and environmental factors for Eu2þ and Ce3þ is obtained. Our results revealed that the cubic crystal field split can be described by the homopolar part of the average energy gap, the coordination number of central ion, the charge of neighboring anions, and bond ionicity between the central ion to nearest anion. Hopefully, these relations may be extended to other systems and further study is under way.
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O.J. Rubio, J. Phys. Chem. Solids 52 (1991) 101. P. Dorenbos, Phys. Rev. B 62 (2000) 15640. P. Dorenbos, Phys. Rev. B 62 (2000) 15650. J.A. Hernadez, F.J. Lopez, H.S. Murrieta, O.J. Rubio, J. Phys. Soc. Jpn. 50 (1981) 225. P. Dorenbos, J. Alloys Comp. 341 (2002) 156. L. van Pieterson, M.F. Reid, G.W. Burdick, A. Meijerink, Phys. Rev. B 65 (2002) 045114. A. Ellens, A. Meijerink, G. Blasse, J. Lumin. 59 (1994) 293. R. Alcala, D.K. Sardar, W.A. Sibley, J. Lumin. 27 (1982) 273. J.M. Garcia, W.A. Sibley, C.A. Hunt, J.M. Spaeth, J. Lumin. 42 (1988) 35.
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