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Effect of modifier ions on fluorescence and absorption of Eu3+ in alkali and alkaline earth silicate glasses
IOURNA
ELSEVIER
L GF
Journal of Non-Crystalline Solids 169 (1994) 288-294
Effect of modifier ions on fluorescence and absorption of in alkali and alkaline earth silicate glasses
E u 3+
Y. Nageno a, H. Takebe a, K. Morinaga a,., T. Izumitani b a Department of Materials Science and Technology, Graduate School of Engineering Sciences, Kyushu University, 6-1, Kasugakouen, Kasuga-shi, Fukuoka 816, Japan b lzumitani Special Laboratory, Hoya Corporation, 3-1, Musashino 3-Chome, Akishima-shi, Tokyo 196, Japan
(Received 2 November 1992; revised manuscript received 30 August 1993)
Abstract
Fluorescence and absorption spectra of E u 3 + in silicate glasses have been measured. The fluorescence intensity ratio of 5D 0 "">7F2 to 5D 0 --->7F1 transitions of E u 3+ increases with increasing ionic radius in the order of Li < Na < K for binary alkali silicate glasses and with decreasing ionic radius in the order of Ba < Sr < Ca for binary alkaline earth silicate glasses. It was found for the first time that the intensity ratio exhibited a maximum with the addition of alkaline earth oxides in alkali alkaline earth silicate glasses. The variation of intensity ratio and the Judd-Ofelt parameter, 02, with composition depended on the structural change in the vicinity of E u 3+ ions and E u - O covalency.
I. Introduction
Chemical composition has an important effect on the fluorescence and absorption of rare earth ions in glasses. Trivalent europium ion has often been used as a probe because of the simplicity of its energy-level structure. Using europium-doped glasses, many researchers have discussed composition for glass lasers [1] and the local structure of glasses [2,3]. The 5D 0 --~7F 1 and 5D 0 --*7F2 transitions of Eu 3+ are allowed by magnetic and forced electric dipole mechanisms, respectively [4,5]. The fluorescence intensity of the 5D 0 ~ 7F 2 transition is
* Corresponding author. Tel: +81-92 573 9611. Telefax: +81-92 575 2318.
determined only by the O2(llU(2)ll) 2 term [6], where 0 2 is one of phenomenological parameters and (llU211> is one of reduced tensor operators in the J u d d - O f e l t theory [7,8], and the 5D o ~ 7F 2 transition is very sensitive to the variation of environment of Eu 3+ ions [9,10]; the 5D o ~ 7F 1 transition is independent of that. Previous researchers reported that the fluorescence intensity ratio of 5D 0 ~ 7F 2 to 5D 0 ~ 7F 1 transitions indicated the degree of asymmetry in the vicinity of europium ions and E u - O covalency [11-14]. The fluorescence intensity ratio gives us effective information on the relation of glass structure to fluorescence. Previous works have discussed the effect of network formers [9,12] and modifiers [11,13,14] on the intensity ratio. The variation of the intensity ratio by changing network formers and modifiers, however, is not well understood.
0022-3093/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0022-3093(93)E0654-Q
Y. Nageno et aL /Journal of Non-Crystalline Solids 169 (1994) 288-294 In this study, the dependence of modifier ions on the intensity ratio of 5D 0 ~ 7F 2 tO 5D 0 ~ 7F 1 transitions has been examined for binary and ternary silicate glasses containing alkali a n d / o r alkaline earth oxides. The relations of the intensity ratio and the J u d d - O f e l t parameters was also investigated.
2. E x p e r i m e n t a l
procedure
2.1. Sample preparation Raw materials used are special grade alkali carbonates, alkaline earth carbonates, magnesium oxide, and silicon dioxide and 99% rubidium carbonate and 99.99% europium oxide. The following four series of glasses were prepared: (1) 4 0 M 2 0 - 6 0 S i O 2 - E u 2 0 3 (M = Li, Na, K); (2) 4 0 M ' O - 6 0 S i O 2 - E u z O 3 (M' = Ca, Sr, Ba); (3) 20M 2 0 - 2 0 M ' O - 6 0 S i O 2 - E u 2 0 3 (M = Li, Na, K, Rb; M' = Mg, Ca, Sr, Ba); (4) (40 - x ) M 2 0 - x M g O - 6 0 S i O 2 - E u z O 3 (M = Li, Na, K; x = 0, 5, 10, 15, 20, 25, 30, 35). Mixed batches were melted in Pt crucibles at 1300-1560°C for 1.0-1.5 h. Each glass melt was poured into a graphite mold and annealed for 2 h at temperatures 15°C above the respective glass transition temperatures. Because rapid quenching was required to form glasses of 40Li20-60SiO 2 and 40M'O-60SIO 2 ( M ' = Ca, Sr, Ba), liquid samples were flowed onto a stainless steel plate and pressed down with another stainless plate. Glass samples were cut to 2 or 10 mm thickness and polished for fluorescence and absorption measurements.
289
The J u d d - O f e l t parameters ~'~2, J'~4, and J'~6 for Eu 3+ were determined using the method applied by Krupke [15]. The integrated absorbance of an electric dipole, fk(A) dA, can be related to the line strength, S: 81r3e2A
fk(a) dA = N 3 c h ( 2 J
(n 2 + 2) 2
+ 1)
9n
S,
(1)
where k(A) is the absorption coefficient at wavelength A, N is the Eu 3+ ion concentration, A is the mean wavelength of the absorption band and n is the refractive index at the mean wavelength, A. The line strength of an electric-dipole transition between initial J manifold I(S, L ) J ) and terminal manifold I(S', L')J') is expressed as
E n,l((s, L)JIIu(t)II(s ', C)J')I 2,
s=
(2)
t = 2,4,6
where the elements
~
5Do-7F2
20Rb20-20MgO-60SiO2
5DoJFI~
2.2. Fluorescence and absorption cO
Fluorescence spectra were measured with a fluorescence spectrophotometer (Hitachi 650) at an exitation of 463 nm using a Xenon lamp. Absorption spectra were obtained with a spectrophotometer (Hitachi 330) in the range of 350600 nm using undoped silicate glasses as blanks. All measurements were carried out at 298 K. The fluorescence intensity ratio of 5D 0 ~ 7F 2 to 5D0--->7F 1 transitions of Eu 3+, R, was obtained.
E
[
I
I
I
550
600
650
700
Wavelength
/ nm
Fig. 1. Fluorescencespectra of Eu 3 + -dopedsilicate glasses.
290
Y. Nageno et al. /Journal of Non-Crystalline Solids 169 (1994) 288-294
Table 1 The fluorescence intensity ratio of 5D 0 -o 7F2 to 5D 0 ~ 7F 1 transitions of Eu 3+, R, in various silicate glasses Composition (mol%)
R
40Li20-60SiO 2 40Na20-60SiO 2 40K20-60SIO 2
3.20 3.67 3.72
40CaO-60SiO 2 40SrO-60SiO 2 40BaO-60SiO 2
4.03 3.62 3.23
20Li20-20MgO-60SiO 2 20Li20-20CaO-60SiO 2 20Li 20-20SrO-60SiO2 20LiEO-20BaO-60SiO 2
3.72 3.50 3.23 3.56
20NaEO-20MgO-60SiO 2 20Na 20-20CaO-60SiO 2 20Na20-20SrO-60SiO 2 20NaEO-20BaO-60SiO 2
4.43 4.00 3.99 3.64
20K 2° -20MgO-60SiO 2 20K 20-20CaO-60SiO 2 20K 20-20SrO-60SiO2 20KEO-20BaO-60SiO 2
4.85 4.57 4.19 3.91
20Rb20-20MgO-60SiO 2 20Rb20-20CaO-60SiO 2 20Rb20-20SrO-60SiO 2 20RbEO-20BaO-60SiO 2
refractive index, n, were determined on experiment. Density was determined by the Archimedes displacement method using kerosene. Refractive index was measured by the minimum deviation method. A simple Cauchy dispersion equation [17] for n ( A ) = a + b / A 2 was applied to the determination of the refractive index, n, at the mean wavelength, A, of an absorption band. The Judd-Ofelt parameters 122, 124, and g26 were calculated with Eqs. (1) and (2). The spontaneous emission probability of an electric-dipole transition is given by
I:)J'; ( S, L)i] 64,n.4e 2
n ( n 2 + 2) 2
3h(ZJ' + 1)~ 3
9
E o,((s', L')/'IIu<'II(L t ) J ) m
×
5.48 4.90 4.26 3.93
.
(3) For ([[U(t)[[) values in Eq. (3), those calculated by Weber [6] were used. The spontaneous emission probability of a magnetic-dipole transition was calculated using the equation of Weber [18] and E u 3 + eigenfunctions [19].
Table 2 The fluorescence intensity ratio of 5D 0 -o 7F2 to 5D 0 --* 7F 1 transitions of Eu 3+, R in various hosts reported previously Composition (molar ratio)
R
Ref.
64SIO2-16K20-16BaO-4Eu 203 72 ~ 74.75SiO2-5BaO-15Na205ZNO-0.25 ~ 3.00Eu20 3 68GEO2-(29 - x ) K 2 0 - x N a 2 0 - 3 E u 2 0 3 (x=0,5,15,25,29) (97 - x ) G e O 2 - x K 2 0 - 3 E u 2 0 3 (x = 12.5, 16, 25, 30, 33.3, 40) (99.5 - x)B203-x L i 2 0 - 0 . 5 E u 203 (x = 10, 25, 40) (100 - x ) B 2 0 3 - x N a 2 0 - 1 E u 2 0 3 (x = 10, 15, 20, 25, 30, 35) 49P205-49MO-2Eu 203
3.42
[9]
SrTiO2:Eu 203
2
t = 2,4,6
The integrated absorbance of an electric dipole, f k ( A ) d,l, the Eu 3+ ion concentration, N, the mean wavelength of absorption band, A, and the
100M(PO3)2-2.5Eu(PO 3)3
_
4.85 3.98(x=5) 3.70(x = 40) 2.41(x = 10) 2.8(x = 10) 3.39(M = Ba) 2.08(M = Zn) 1.28
4.08 (x=25) 4.60 (x = 12.5) 3.25 (x = 45) 4.8 (x = 35) 4.10 (M = Mg) 3.88 (M-Ba)
[20] [9] [9] [9] [13] [9] [14] [21]
Y. Nageno et al. / Journal of Non-Crystalline Solids 169 (1994) 288-294
291
3. Results
Fig. 1 shows the fluorescence spectra of Eu 3+doped silicate glasses. In these samples, the minimum and maximum values for the fluorescence intensity ratio of SD0 ~ 7F2 to SD0 ~ 7F l transitions of Eu 3+, R value, were obtained. The intensity ratio, R, changed with glass composition. Table 1 shows the R value of 40M20-60SIO 2, 40M'O-60SIO 2 and 20M20-20M'O-60SiO 2 glasses. The intensity ratio, R, increases with increasing ionic radius in the order of Li < Na < K for binary alkali silicate glasses and with decreasing ionic radius in the order of Ba < Sr < Ca for binary alkaline earth silicate glasses. The R values of ternary silicate glasses containing alkali and alkaline earth oxides change by larger amounts than those of binary silicate glasses. The R value of silicate glasses measured in this study is in the range of 3.20-5.48 and the maximum value is higher than those of various hosts reported previously, shown in Table 2. Fig. 2 shows the relations between R and MgO content for ( 4 0 - x ) M 2 0 - x M g O - 6 0 S i O 2
5.0 Na/X
~2 LL
/
\
r~
£3
LL
4.0
\
~.
\ ~ \
5D4
350
tool% MgO
51_6
400
5D2 I
[
I
I
450
500
550
600
Wavelength / nm Fig. 3. Absorption spectra of ( 4 0 - x ) K z O - x M g O - 6 0 S i O 2E u 2 0 3 glasses.
(M:Li, Na, K) glasses. Because the glass of 40MgO-60SiO 2 could not be prepared, the R of this glass is the extrapolation of R as a function of MgO content. The values of R in the LiEOMgO-SiO 2 system increase monotonically with MgO content: the values of R in the N a 2 0 MgO-SiO 2 and KEO-MgO-SiO 2 systems have maxima near 25 mol% MgO. The result means that the Judd-Ofelt parameters, g22, have maxima in these systems because the value of R is determined only by the 122(11U(2)[1)2 term and (llU~2)ll) is independent of glass composition [6].
(40-X) M20-x MgO- 60Si02 rr
~f
40-X) KaO-x MgO- 60Si02
3.1. Fluorescence
~-/
u~ v m
3.2. Absorption
3.0 0
I 10
I 20
I 30
I 40
Composition , mol% MgO Fig. 2. Relations between R value and MgO content for ( 4 0 - x)M20-xMgO-60SiOz-Euz03 (M: Li, Na, K) glasses.
Fig. 3 shows the absorption spectra of ( 4 0 x)K20-xMgO-60SiO2-Eu20 3 glasses, in which the value of R varied. The integrated absorbance, ]k(A) dA, and the mean wavelength, A, of each electric dipole transition were determined from the absorption spectra. The Judd-
292
Y. Nageno et al. /Journal of Non-Crystalline Solids 169 (1994) 288-294
Table 3 Density, the Eu 3+-ion concentration, refractive index and Abbe number of (40 - x)K 2O-x MgO-60SiO2-Eu 203 glasses Composition Density Concentration Refractive index, Abbe number (mol%)
(g cm -3)
(10 20 cm -3)
nD
35K20-5MgO-60SiO 2 30K20-10MgO-60SiO 2 25K 20-15MgO-60SiO 2 20K 20-20MgO-60SiO 2 15K20-25MgO-60SiO 2 10K20-30MgO-60SiO 2 5K20-35MgO-60SiO 2
2.486 2.493 2.489 2.493 2.513 2.554 2.601
4.017 4.178 4.334 4.517 4.746 5.036 5.366
1.52174 1.51997 1.52081 1.52090 1.52285 1.53128 1.54487
Table 4 Judd-Ofelt parameters for Eu 3+ in (40-x)K20-xMgO60SiO2-Eu203 glasses Composition 02 •4 ~'~6 (mol%) (10 -20 (10 -20 (10 -2o 35K20-5MgO-60SiO 2 30K20-10MgO-60SiO 2 25K20-15MgO-60SiO 2 20K20-20MgO-60SiO 2 15K20-25MgO-60SiO 2 10K20-30MgO-60SiO 2 5K 20-35MgO-60SiO 2
cm 2 )
cm 2 )
cm 2 )
6.54 6.36 6.86 9.28 9.65 8.98 8.65
3.57 3.94 4.10 4.81 6.68 -
0.28 0.51 0.55 0.88 1.15 1.52 1.66
55.2 55.9 56.6 57.4 57.7 58.6 59.3
m a x i m u m at 25 m o l % M g O ; the p a r a m e t e r s ~'~4 and 126 increase, monotonically, with M g O content. W e suggest that this result shows that the p a r a m e t e r 0 2 is related to a structural change in the vicinity of E u 3+ ions; the ~'~4 and ~-~6 are i n d e p e n d e n t of this change. Table 5 shows spontaneous emission probabilities in these glasses. F r o m Tables 4 and 5, the 0 2 corresponds to the s p o n t a n e o u s emission probability of 5D 0 ~ 7F 2 transition.
4. Discussion Table 5 Spontaneous emission probabilities for Eu 3+ in (40-x)K20- xMgO-60SiO 2-Eu20 3 glasses Composition 5D0-7F1 5D0-TF2 5D0-7F4 (mol%) (S -1) (S -1) (S -1) 35K20-5MgO-60SiO 2 30K20-10MgO-60SiO 2 25K20-15MgO-60SiO 2 20KzO-20MgO-60SiO2 15K20-25MgO-60SiO 2 10K20-30MgO-60SiO 2 5K20-35MgO-60SiO 2
52.4 52.3 52.3 52.3 52.8 53.4 54.9
253.6 245.3 265.5 359.2 376.9 355.2 351.8
70.5 77.6 80.9 94.9 133.0 -
Ofelt p a r a m e t e r s 0 2, ~'~4, and 0 6 were obtained from 7F o ~ 5D 2, 7F 0 ~ 5D 4 and 7F 0 ~ 5L 6 transitions [14], respectively. For x = 30 and 35, the 0 4 was not calculated because of the low intensity of the 7F 0 ~ 5D 4 transition. Table 3 shows density, the Eu3+-ion concentration, refractive index and A b b e n u m b e r of ( 4 0 - x ) K 2 0 - x M g O - 6 0 S i O 2E u 2 0 3 glasses. Substituting these values in Eqs. (1) and (2), the J u d d - O f e l t p a r a m e t e r s were calculated and given in Table 4. T h e 122 has a
As described previously, the fluorescence intensity ratio of 5D 0 ----~TF2 to 5D 0 ----~7F1 transitions of E u 3+, R, corresponds to 0 2. O n the basis of the J u d d - O f e l t theory, the parameters 0 2, 0 4 and ~'~6 contain two terms [5]: one is the crystal field parameters, Asp, which relates to the structural change in the vicinity of E u 3+ ions, e.g., symmetry and distortion, and the other is -~(t, A) which relates to the radial integral of the wave functions between 4f and admixing levels, e.g., 5d, 5g, and the energy denominater between these two levels, i.e., the covalency between the rare earth ion and the oxygen ion for oxide glasses. T h e J u d d - O f e l t parameters are then expressed as [5] a t = ( 2 t + 1) ~ I Aso [ 2-W2(s, t ) ( 2 s + 1) - 1 , p,s
t=2,
4, 6.
(4)
Consequently, the varation of the 0 2 and R is related to the structural change in the vicinity of Eu 3+ ions a n d / o r E u - O covalency [9,10,13,14].
Y. Nageno et al. /Journal of Non-Crystalline Solids 169 (1994) 288-294
For instance, Tanabe et al. [10] showed that the variation of 0 2 with composition was related to the change in asymmetry of the ligand field of Eu 3+ ions due to the structural mixing of borate groups in alkali-metal borate glasses. Zahir et al. [13] reported that 122 and R depended on the asymmetry in the range of 10-25 mol% N a 2 0 and the asymmetry and E u - O covalency in the range of 25-35 m o l % N a 2 0 in sodium borate glasses. Fig. 4 shows the relations between R and cation field strength, Z / a 2 [22] of modifier ions for binary silicate glasses, where Z is the valency of the cation and a is the distance between the cation and the oxygen ion. The trend of R with the cation field strength, Z / a 2, for binary alkali silicate glasses is opposite to that for binary alkaline earth silicate glasses: with increasing cation field strength, Z / a 2, R decreases in binary alkali silicate glasses and increases in binary alkaline earth silicate glasses. The basicity of binary silicate glasses increases
40M20-60SiO2
4.0 -
(M: Li,Na,K)
rr
e-.
7Ca
7 3.5
3.0 0.10
I
I
0.20
0.30
Cation Field Strength , z / a
0.40 2
Fig. 4. Relations between R and c~ation field strength, Z / a 2, of modifier ions for Eua+-doped alkali or alkaline earth silicate glasses. Z is the valency of the cation and a is the distance between the cation and the oxygen ion.
293
6.0 20M20-20M'O-60SiO2
u_
% 50-
t~
Rb-Ca O /
-"~ ~
K-Ca Na'MgO~
'
/~JK-Sr
OK-Mg
X~R~-Sr m
_~
4.0-
K-Ba _
Na-aad
OLi_Mg L i - B ~ , ~ Li-Ca @ Li-Sr 3.0-
0
0.5
1.0
1.5
2.0
2.5
Radius Ratio of Alkali to Alkaline Earth Ions , r M / r M'
Fig. 5. Relation between R and the radius ratio of alkali to alkaline earth ions, rM/rM,, for 20M20-20M'O-60SiO 2Eu203 (M: Li, Na, K, Rb; M': Mg, Ca, Sr, Ba) glasses.
with increasing ionic radius in the order of Li < Na < K or Ca < Sr < Ba at the same silica content [23]. Because the structure of silicate anion varies monotonically with the basicity of silicate glasses, the variation of R is related to E u - O covalency in binary alkali silicate glasses. There is the other reason for the change of R in alkaline earth silicate glasses. The cation field strengths of alkaline earth ions are larger than those of alkali ions. Therefore, the variation of distortion around Eu 3+ ions due to the addition of alkaline earth oxides probably contributes to the increase of R in silicate glasses containing alkaline earth oxides. The R of binary silicate glasses was in the range of 3.20-4.03; that of ternary silicate glasses was in the range of 3.23-5.48. Namely, larger changes in R of ternary silicate glasses were observed than in the case of binary silicate glasses. Fig. 5 shows the relation between R and the radius ratio of alkali to alkaline earth ions, rM/rM,, for 2 0 M 2 0 - 2 0 M ' O - 6 0 S i O 2 glasses. R
294
Y. Nageno et al. /Journal of Non-Crystalline Solids 169 (1994) 288-294
increases linearly with the radius ratio, rM/rM,. The marked change of R in ternary silicate glasses cannot be accounted for in terms of E u - O covalency only. Izumitani et al. [24] suggested that the change of the R in silicate glasses was not very large because the cage surrounding rare earth ions would not distort to a large degree in the rigid, three-dimensional network of silicate anions. However, the R of ternary silicate glasses changed considerably in the range of 3.23-5.48. We suggest that, in ternary silicate glasses, the interaction effect on the E u - O covalency and structural change in the vicinity of E u 3 + ions due to alkali and alkaline earth ions resulted in the marked change in R, i.e., 0 2. As shown in Table 4, ~'~4 and J"~6 for E u 3+ increased monotonically with MgO content in (40 - x)Na20-xMgO-60SiO 2 glasses. The result suggested that the parameters O 4 and ~(~6 were related to the E u - O covalency and were independent of the structural change in the vicinity of E u 3+ ions.
5. Conclusions
The fluorescence intensity ratio of 5D 0 ~ 7F2 to 5D 0 ~ 7F 1 transitions of E u 3+ increases with increasing ionic radius in the order of Li < Na < K for binary alkali silicate glasses and with decreasing ionic radius in the order of Ba < Sr < Ca for binary alkaline earth silicate glasses. The intensity ratios had maxima near 25 mol% MgO in (40 - x)Na20-xMgO-60SiO 2 and (40 - x ) K 2 0 xMgO-60SiO 2 glasses. The intensity ratio increased linearly with the radius ratio of alkali to alkaline earth ions in 20M20-20M'O-60SiO 2 (M: Li, Na, K, Rb; M': Mg, Ca, Sr, Ba) glasses. The variation of intensity ratio and ,02 with composition depended on the structural change in the
vicinity of E u 3+ ions and E u - O covalency in silicate glasses.
6. References [1] H. Toratani, T. Izumitani and H. Kuroda, J. Non-Cryst. Solids 52 (1982) 303. [2] M. Zahir, C. Parent, R. Olazcuaga, G. Le Flem and P. Hagenmuller, J. Non-Cryst. Solids 81 (1986) 53. [3] S. Tanabe, S. Todoroki, K. Hirao and N. Soga, J. NonCryst. Solids 122 (1990) 59. [4] C.K. Jorgensen and B.R. Judd, Molec. Phys. 8 (1964) 281. [5] R.D. Peacock, Struct. Bonding 22 (1975) 83. [6] M.J. Weber, in: Optical Property of Ions in Crystal, ed. H.M. Crosswhite and H.W. Mops (Interscience, New York, 1967) p. 467. [7] B.R. Judd, Phys. Rev. 127 (1962) 750. [8] G.S. Ofelt, J. Chem. Phys. 37 (1962) 511. [9] E.W.J.L. Oomen and A.M.A. van Dongen, J. Non-Cryst. Solids 111 (1989) 205. [10] S. Tanabe, T. Ohyagi, N. Soga and T. Hanada, Phys. Rev. B 46 (1992) 3305. [11] P.K. Gallagher, C.K. Kurkjian and P.M. Bridenbaugh, Phys. Chem. Glasses 6 (1965) 95. [12] R. Reisfeld, Struct. Bonding 22 (1975) 123. [13] M. Zahir, R. Olazcuaga, C. Parent, G. Le Flem and P. Hagenmuller, J. Non-Cryst. Solids 69 (1985) 221. [14] A. Capobianco, P.P. Proulx, M. Bettinelli and F. Negrisolo, Phys. Rev. B42 (1990) 5936. [15] W.F. Krupke, IEEE J. Quantum Electron. QE10 (1974) 4450. [16] W.T. Carnall, P.R. Fields and K, Rajnak, J. Chem. Phys. 49 (1968) 4450. [17] W.F. Krupke and J.B. Gruber, Phys. Rev. 139 (1965) A2008. [18] M.J. Weber, Phys. Rev. 157 (1967) 262. [19] G.S. Ofelt, J. Chem. Phys. 38 (1963) 2171. [20] R.A. Velapoldi, R. Reisfeld and L. Boehm, Phys. Chem. Glasses 14 (1973) 101. [21] M.J. Weber and R.F. Schaufele, J. Chem. Phys. 43 (1965) 1702. [22] A. Dietzel, Z. Elektrochem. 48 (1942) 9. [23] H. Ikeda, Y. Murayama, Y. Ohoka, K. Morinaga and T. Yanagase, J. Jpn. Inst. Met. 47 (1983) 1063. [24] T. Izumitani, H. Toratani and H. Kuroda, J. Non-Cryst. Solids 47 (1982) 87.
ELSEVIER
L GF
Journal of Non-Crystalline Solids 169 (1994) 288-294
Effect of modifier ions on fluorescence and absorption of in alkali and alkaline earth silicate glasses
E u 3+
Y. Nageno a, H. Takebe a, K. Morinaga a,., T. Izumitani b a Department of Materials Science and Technology, Graduate School of Engineering Sciences, Kyushu University, 6-1, Kasugakouen, Kasuga-shi, Fukuoka 816, Japan b lzumitani Special Laboratory, Hoya Corporation, 3-1, Musashino 3-Chome, Akishima-shi, Tokyo 196, Japan
(Received 2 November 1992; revised manuscript received 30 August 1993)
Abstract
Fluorescence and absorption spectra of E u 3 + in silicate glasses have been measured. The fluorescence intensity ratio of 5D 0 "">7F2 to 5D 0 --->7F1 transitions of E u 3+ increases with increasing ionic radius in the order of Li < Na < K for binary alkali silicate glasses and with decreasing ionic radius in the order of Ba < Sr < Ca for binary alkaline earth silicate glasses. It was found for the first time that the intensity ratio exhibited a maximum with the addition of alkaline earth oxides in alkali alkaline earth silicate glasses. The variation of intensity ratio and the Judd-Ofelt parameter, 02, with composition depended on the structural change in the vicinity of E u 3+ ions and E u - O covalency.
I. Introduction
Chemical composition has an important effect on the fluorescence and absorption of rare earth ions in glasses. Trivalent europium ion has often been used as a probe because of the simplicity of its energy-level structure. Using europium-doped glasses, many researchers have discussed composition for glass lasers [1] and the local structure of glasses [2,3]. The 5D 0 --~7F 1 and 5D 0 --*7F2 transitions of Eu 3+ are allowed by magnetic and forced electric dipole mechanisms, respectively [4,5]. The fluorescence intensity of the 5D 0 ~ 7F 2 transition is
* Corresponding author. Tel: +81-92 573 9611. Telefax: +81-92 575 2318.
determined only by the O2(llU(2)ll) 2 term [6], where 0 2 is one of phenomenological parameters and (llU211> is one of reduced tensor operators in the J u d d - O f e l t theory [7,8], and the 5D o ~ 7F 2 transition is very sensitive to the variation of environment of Eu 3+ ions [9,10]; the 5D o ~ 7F 1 transition is independent of that. Previous researchers reported that the fluorescence intensity ratio of 5D 0 ~ 7F 2 to 5D 0 ~ 7F 1 transitions indicated the degree of asymmetry in the vicinity of europium ions and E u - O covalency [11-14]. The fluorescence intensity ratio gives us effective information on the relation of glass structure to fluorescence. Previous works have discussed the effect of network formers [9,12] and modifiers [11,13,14] on the intensity ratio. The variation of the intensity ratio by changing network formers and modifiers, however, is not well understood.
0022-3093/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0022-3093(93)E0654-Q
Y. Nageno et aL /Journal of Non-Crystalline Solids 169 (1994) 288-294 In this study, the dependence of modifier ions on the intensity ratio of 5D 0 ~ 7F 2 tO 5D 0 ~ 7F 1 transitions has been examined for binary and ternary silicate glasses containing alkali a n d / o r alkaline earth oxides. The relations of the intensity ratio and the J u d d - O f e l t parameters was also investigated.
2. E x p e r i m e n t a l
procedure
2.1. Sample preparation Raw materials used are special grade alkali carbonates, alkaline earth carbonates, magnesium oxide, and silicon dioxide and 99% rubidium carbonate and 99.99% europium oxide. The following four series of glasses were prepared: (1) 4 0 M 2 0 - 6 0 S i O 2 - E u 2 0 3 (M = Li, Na, K); (2) 4 0 M ' O - 6 0 S i O 2 - E u z O 3 (M' = Ca, Sr, Ba); (3) 20M 2 0 - 2 0 M ' O - 6 0 S i O 2 - E u 2 0 3 (M = Li, Na, K, Rb; M' = Mg, Ca, Sr, Ba); (4) (40 - x ) M 2 0 - x M g O - 6 0 S i O 2 - E u z O 3 (M = Li, Na, K; x = 0, 5, 10, 15, 20, 25, 30, 35). Mixed batches were melted in Pt crucibles at 1300-1560°C for 1.0-1.5 h. Each glass melt was poured into a graphite mold and annealed for 2 h at temperatures 15°C above the respective glass transition temperatures. Because rapid quenching was required to form glasses of 40Li20-60SiO 2 and 40M'O-60SIO 2 ( M ' = Ca, Sr, Ba), liquid samples were flowed onto a stainless steel plate and pressed down with another stainless plate. Glass samples were cut to 2 or 10 mm thickness and polished for fluorescence and absorption measurements.
289
The J u d d - O f e l t parameters ~'~2, J'~4, and J'~6 for Eu 3+ were determined using the method applied by Krupke [15]. The integrated absorbance of an electric dipole, fk(A) dA, can be related to the line strength, S: 81r3e2A
fk(a) dA = N 3 c h ( 2 J
(n 2 + 2) 2
+ 1)
9n
S,
(1)
where k(A) is the absorption coefficient at wavelength A, N is the Eu 3+ ion concentration, A is the mean wavelength of the absorption band and n is the refractive index at the mean wavelength, A. The line strength of an electric-dipole transition between initial J manifold I(S, L ) J ) and terminal manifold I(S', L')J') is expressed as
E n,l((s, L)JIIu(t)II(s ', C)J')I 2,
s=
(2)
t = 2,4,6
where the elements
~
5Do-7F2
20Rb20-20MgO-60SiO2
5DoJFI~
2.2. Fluorescence and absorption cO
Fluorescence spectra were measured with a fluorescence spectrophotometer (Hitachi 650) at an exitation of 463 nm using a Xenon lamp. Absorption spectra were obtained with a spectrophotometer (Hitachi 330) in the range of 350600 nm using undoped silicate glasses as blanks. All measurements were carried out at 298 K. The fluorescence intensity ratio of 5D 0 ~ 7F 2 to 5D0--->7F 1 transitions of Eu 3+, R, was obtained.
E
[
I
I
I
550
600
650
700
Wavelength
/ nm
Fig. 1. Fluorescencespectra of Eu 3 + -dopedsilicate glasses.
290
Y. Nageno et al. /Journal of Non-Crystalline Solids 169 (1994) 288-294
Table 1 The fluorescence intensity ratio of 5D 0 -o 7F2 to 5D 0 ~ 7F 1 transitions of Eu 3+, R, in various silicate glasses Composition (mol%)
R
40Li20-60SiO 2 40Na20-60SiO 2 40K20-60SIO 2
3.20 3.67 3.72
40CaO-60SiO 2 40SrO-60SiO 2 40BaO-60SiO 2
4.03 3.62 3.23
20Li20-20MgO-60SiO 2 20Li20-20CaO-60SiO 2 20Li 20-20SrO-60SiO2 20LiEO-20BaO-60SiO 2
3.72 3.50 3.23 3.56
20NaEO-20MgO-60SiO 2 20Na 20-20CaO-60SiO 2 20Na20-20SrO-60SiO 2 20NaEO-20BaO-60SiO 2
4.43 4.00 3.99 3.64
20K 2° -20MgO-60SiO 2 20K 20-20CaO-60SiO 2 20K 20-20SrO-60SiO2 20KEO-20BaO-60SiO 2
4.85 4.57 4.19 3.91
20Rb20-20MgO-60SiO 2 20Rb20-20CaO-60SiO 2 20Rb20-20SrO-60SiO 2 20RbEO-20BaO-60SiO 2
refractive index, n, were determined on experiment. Density was determined by the Archimedes displacement method using kerosene. Refractive index was measured by the minimum deviation method. A simple Cauchy dispersion equation [17] for n ( A ) = a + b / A 2 was applied to the determination of the refractive index, n, at the mean wavelength, A, of an absorption band. The Judd-Ofelt parameters 122, 124, and g26 were calculated with Eqs. (1) and (2). The spontaneous emission probability of an electric-dipole transition is given by
I:)J'; ( S, L)i] 64,n.4e 2
n ( n 2 + 2) 2
3h(ZJ' + 1)~ 3
9
E o,((s', L')/'IIu<'II(L t ) J ) m
×
5.48 4.90 4.26 3.93
.
(3) For ([[U(t)[[) values in Eq. (3), those calculated by Weber [6] were used. The spontaneous emission probability of a magnetic-dipole transition was calculated using the equation of Weber [18] and E u 3 + eigenfunctions [19].
Table 2 The fluorescence intensity ratio of 5D 0 -o 7F2 to 5D 0 --* 7F 1 transitions of Eu 3+, R in various hosts reported previously Composition (molar ratio)
R
Ref.
64SIO2-16K20-16BaO-4Eu 203 72 ~ 74.75SiO2-5BaO-15Na205ZNO-0.25 ~ 3.00Eu20 3 68GEO2-(29 - x ) K 2 0 - x N a 2 0 - 3 E u 2 0 3 (x=0,5,15,25,29) (97 - x ) G e O 2 - x K 2 0 - 3 E u 2 0 3 (x = 12.5, 16, 25, 30, 33.3, 40) (99.5 - x)B203-x L i 2 0 - 0 . 5 E u 203 (x = 10, 25, 40) (100 - x ) B 2 0 3 - x N a 2 0 - 1 E u 2 0 3 (x = 10, 15, 20, 25, 30, 35) 49P205-49MO-2Eu 203
3.42
[9]
SrTiO2:Eu 203
2
t = 2,4,6
The integrated absorbance of an electric dipole, f k ( A ) d,l, the Eu 3+ ion concentration, N, the mean wavelength of absorption band, A, and the
100M(PO3)2-2.5Eu(PO 3)3
_
4.85 3.98(x=5) 3.70(x = 40) 2.41(x = 10) 2.8(x = 10) 3.39(M = Ba) 2.08(M = Zn) 1.28
4.08 (x=25) 4.60 (x = 12.5) 3.25 (x = 45) 4.8 (x = 35) 4.10 (M = Mg) 3.88 (M-Ba)
[20] [9] [9] [9] [13] [9] [14] [21]
Y. Nageno et al. / Journal of Non-Crystalline Solids 169 (1994) 288-294
291
3. Results
Fig. 1 shows the fluorescence spectra of Eu 3+doped silicate glasses. In these samples, the minimum and maximum values for the fluorescence intensity ratio of SD0 ~ 7F2 to SD0 ~ 7F l transitions of Eu 3+, R value, were obtained. The intensity ratio, R, changed with glass composition. Table 1 shows the R value of 40M20-60SIO 2, 40M'O-60SIO 2 and 20M20-20M'O-60SiO 2 glasses. The intensity ratio, R, increases with increasing ionic radius in the order of Li < Na < K for binary alkali silicate glasses and with decreasing ionic radius in the order of Ba < Sr < Ca for binary alkaline earth silicate glasses. The R values of ternary silicate glasses containing alkali and alkaline earth oxides change by larger amounts than those of binary silicate glasses. The R value of silicate glasses measured in this study is in the range of 3.20-5.48 and the maximum value is higher than those of various hosts reported previously, shown in Table 2. Fig. 2 shows the relations between R and MgO content for ( 4 0 - x ) M 2 0 - x M g O - 6 0 S i O 2
5.0 Na/X
~2 LL
/
\
r~
£3
LL
4.0
\
~.
\ ~ \
5D4
350
tool% MgO
51_6
400
5D2 I
[
I
I
450
500
550
600
Wavelength / nm Fig. 3. Absorption spectra of ( 4 0 - x ) K z O - x M g O - 6 0 S i O 2E u 2 0 3 glasses.
(M:Li, Na, K) glasses. Because the glass of 40MgO-60SiO 2 could not be prepared, the R of this glass is the extrapolation of R as a function of MgO content. The values of R in the LiEOMgO-SiO 2 system increase monotonically with MgO content: the values of R in the N a 2 0 MgO-SiO 2 and KEO-MgO-SiO 2 systems have maxima near 25 mol% MgO. The result means that the Judd-Ofelt parameters, g22, have maxima in these systems because the value of R is determined only by the 122(11U(2)[1)2 term and (llU~2)ll) is independent of glass composition [6].
(40-X) M20-x MgO- 60Si02 rr
~f
40-X) KaO-x MgO- 60Si02
3.1. Fluorescence
~-/
u~ v m
3.2. Absorption
3.0 0
I 10
I 20
I 30
I 40
Composition , mol% MgO Fig. 2. Relations between R value and MgO content for ( 4 0 - x)M20-xMgO-60SiOz-Euz03 (M: Li, Na, K) glasses.
Fig. 3 shows the absorption spectra of ( 4 0 x)K20-xMgO-60SiO2-Eu20 3 glasses, in which the value of R varied. The integrated absorbance, ]k(A) dA, and the mean wavelength, A, of each electric dipole transition were determined from the absorption spectra. The Judd-
292
Y. Nageno et al. /Journal of Non-Crystalline Solids 169 (1994) 288-294
Table 3 Density, the Eu 3+-ion concentration, refractive index and Abbe number of (40 - x)K 2O-x MgO-60SiO2-Eu 203 glasses Composition Density Concentration Refractive index, Abbe number (mol%)
(g cm -3)
(10 20 cm -3)
nD
35K20-5MgO-60SiO 2 30K20-10MgO-60SiO 2 25K 20-15MgO-60SiO 2 20K 20-20MgO-60SiO 2 15K20-25MgO-60SiO 2 10K20-30MgO-60SiO 2 5K20-35MgO-60SiO 2
2.486 2.493 2.489 2.493 2.513 2.554 2.601
4.017 4.178 4.334 4.517 4.746 5.036 5.366
1.52174 1.51997 1.52081 1.52090 1.52285 1.53128 1.54487
Table 4 Judd-Ofelt parameters for Eu 3+ in (40-x)K20-xMgO60SiO2-Eu203 glasses Composition 02 •4 ~'~6 (mol%) (10 -20 (10 -20 (10 -2o 35K20-5MgO-60SiO 2 30K20-10MgO-60SiO 2 25K20-15MgO-60SiO 2 20K20-20MgO-60SiO 2 15K20-25MgO-60SiO 2 10K20-30MgO-60SiO 2 5K 20-35MgO-60SiO 2
cm 2 )
cm 2 )
cm 2 )
6.54 6.36 6.86 9.28 9.65 8.98 8.65
3.57 3.94 4.10 4.81 6.68 -
0.28 0.51 0.55 0.88 1.15 1.52 1.66
55.2 55.9 56.6 57.4 57.7 58.6 59.3
m a x i m u m at 25 m o l % M g O ; the p a r a m e t e r s ~'~4 and 126 increase, monotonically, with M g O content. W e suggest that this result shows that the p a r a m e t e r 0 2 is related to a structural change in the vicinity of E u 3+ ions; the ~'~4 and ~-~6 are i n d e p e n d e n t of this change. Table 5 shows spontaneous emission probabilities in these glasses. F r o m Tables 4 and 5, the 0 2 corresponds to the s p o n t a n e o u s emission probability of 5D 0 ~ 7F 2 transition.
4. Discussion Table 5 Spontaneous emission probabilities for Eu 3+ in (40-x)K20- xMgO-60SiO 2-Eu20 3 glasses Composition 5D0-7F1 5D0-TF2 5D0-7F4 (mol%) (S -1) (S -1) (S -1) 35K20-5MgO-60SiO 2 30K20-10MgO-60SiO 2 25K20-15MgO-60SiO 2 20KzO-20MgO-60SiO2 15K20-25MgO-60SiO 2 10K20-30MgO-60SiO 2 5K20-35MgO-60SiO 2
52.4 52.3 52.3 52.3 52.8 53.4 54.9
253.6 245.3 265.5 359.2 376.9 355.2 351.8
70.5 77.6 80.9 94.9 133.0 -
Ofelt p a r a m e t e r s 0 2, ~'~4, and 0 6 were obtained from 7F o ~ 5D 2, 7F 0 ~ 5D 4 and 7F 0 ~ 5L 6 transitions [14], respectively. For x = 30 and 35, the 0 4 was not calculated because of the low intensity of the 7F 0 ~ 5D 4 transition. Table 3 shows density, the Eu3+-ion concentration, refractive index and A b b e n u m b e r of ( 4 0 - x ) K 2 0 - x M g O - 6 0 S i O 2E u 2 0 3 glasses. Substituting these values in Eqs. (1) and (2), the J u d d - O f e l t p a r a m e t e r s were calculated and given in Table 4. T h e 122 has a
As described previously, the fluorescence intensity ratio of 5D 0 ----~TF2 to 5D 0 ----~7F1 transitions of E u 3+, R, corresponds to 0 2. O n the basis of the J u d d - O f e l t theory, the parameters 0 2, 0 4 and ~'~6 contain two terms [5]: one is the crystal field parameters, Asp, which relates to the structural change in the vicinity of E u 3+ ions, e.g., symmetry and distortion, and the other is -~(t, A) which relates to the radial integral of the wave functions between 4f and admixing levels, e.g., 5d, 5g, and the energy denominater between these two levels, i.e., the covalency between the rare earth ion and the oxygen ion for oxide glasses. T h e J u d d - O f e l t parameters are then expressed as [5] a t = ( 2 t + 1) ~ I Aso [ 2-W2(s, t ) ( 2 s + 1) - 1 , p,s
t=2,
4, 6.
(4)
Consequently, the varation of the 0 2 and R is related to the structural change in the vicinity of Eu 3+ ions a n d / o r E u - O covalency [9,10,13,14].
Y. Nageno et al. /Journal of Non-Crystalline Solids 169 (1994) 288-294
For instance, Tanabe et al. [10] showed that the variation of 0 2 with composition was related to the change in asymmetry of the ligand field of Eu 3+ ions due to the structural mixing of borate groups in alkali-metal borate glasses. Zahir et al. [13] reported that 122 and R depended on the asymmetry in the range of 10-25 mol% N a 2 0 and the asymmetry and E u - O covalency in the range of 25-35 m o l % N a 2 0 in sodium borate glasses. Fig. 4 shows the relations between R and cation field strength, Z / a 2 [22] of modifier ions for binary silicate glasses, where Z is the valency of the cation and a is the distance between the cation and the oxygen ion. The trend of R with the cation field strength, Z / a 2, for binary alkali silicate glasses is opposite to that for binary alkaline earth silicate glasses: with increasing cation field strength, Z / a 2, R decreases in binary alkali silicate glasses and increases in binary alkaline earth silicate glasses. The basicity of binary silicate glasses increases
40M20-60SiO2
4.0 -
(M: Li,Na,K)
rr
e-.
7Ca
7 3.5
3.0 0.10
I
I
0.20
0.30
Cation Field Strength , z / a
0.40 2
Fig. 4. Relations between R and c~ation field strength, Z / a 2, of modifier ions for Eua+-doped alkali or alkaline earth silicate glasses. Z is the valency of the cation and a is the distance between the cation and the oxygen ion.
293
6.0 20M20-20M'O-60SiO2
u_
% 50-
t~
Rb-Ca O /
-"~ ~
K-Ca Na'MgO~
'
/~JK-Sr
OK-Mg
X~R~-Sr m
_~
4.0-
K-Ba _
Na-aad
OLi_Mg L i - B ~ , ~ Li-Ca @ Li-Sr 3.0-
0
0.5
1.0
1.5
2.0
2.5
Radius Ratio of Alkali to Alkaline Earth Ions , r M / r M'
Fig. 5. Relation between R and the radius ratio of alkali to alkaline earth ions, rM/rM,, for 20M20-20M'O-60SiO 2Eu203 (M: Li, Na, K, Rb; M': Mg, Ca, Sr, Ba) glasses.
with increasing ionic radius in the order of Li < Na < K or Ca < Sr < Ba at the same silica content [23]. Because the structure of silicate anion varies monotonically with the basicity of silicate glasses, the variation of R is related to E u - O covalency in binary alkali silicate glasses. There is the other reason for the change of R in alkaline earth silicate glasses. The cation field strengths of alkaline earth ions are larger than those of alkali ions. Therefore, the variation of distortion around Eu 3+ ions due to the addition of alkaline earth oxides probably contributes to the increase of R in silicate glasses containing alkaline earth oxides. The R of binary silicate glasses was in the range of 3.20-4.03; that of ternary silicate glasses was in the range of 3.23-5.48. Namely, larger changes in R of ternary silicate glasses were observed than in the case of binary silicate glasses. Fig. 5 shows the relation between R and the radius ratio of alkali to alkaline earth ions, rM/rM,, for 2 0 M 2 0 - 2 0 M ' O - 6 0 S i O 2 glasses. R
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Y. Nageno et al. /Journal of Non-Crystalline Solids 169 (1994) 288-294
increases linearly with the radius ratio, rM/rM,. The marked change of R in ternary silicate glasses cannot be accounted for in terms of E u - O covalency only. Izumitani et al. [24] suggested that the change of the R in silicate glasses was not very large because the cage surrounding rare earth ions would not distort to a large degree in the rigid, three-dimensional network of silicate anions. However, the R of ternary silicate glasses changed considerably in the range of 3.23-5.48. We suggest that, in ternary silicate glasses, the interaction effect on the E u - O covalency and structural change in the vicinity of E u 3 + ions due to alkali and alkaline earth ions resulted in the marked change in R, i.e., 0 2. As shown in Table 4, ~'~4 and J"~6 for E u 3+ increased monotonically with MgO content in (40 - x)Na20-xMgO-60SiO 2 glasses. The result suggested that the parameters O 4 and ~(~6 were related to the E u - O covalency and were independent of the structural change in the vicinity of E u 3+ ions.
5. Conclusions
The fluorescence intensity ratio of 5D 0 ~ 7F2 to 5D 0 ~ 7F 1 transitions of E u 3+ increases with increasing ionic radius in the order of Li < Na < K for binary alkali silicate glasses and with decreasing ionic radius in the order of Ba < Sr < Ca for binary alkaline earth silicate glasses. The intensity ratios had maxima near 25 mol% MgO in (40 - x)Na20-xMgO-60SiO 2 and (40 - x ) K 2 0 xMgO-60SiO 2 glasses. The intensity ratio increased linearly with the radius ratio of alkali to alkaline earth ions in 20M20-20M'O-60SiO 2 (M: Li, Na, K, Rb; M': Mg, Ca, Sr, Ba) glasses. The variation of intensity ratio and ,02 with composition depended on the structural change in the
vicinity of E u 3+ ions and E u - O covalency in silicate glasses.
6. References [1] H. Toratani, T. Izumitani and H. Kuroda, J. Non-Cryst. Solids 52 (1982) 303. [2] M. Zahir, C. Parent, R. Olazcuaga, G. Le Flem and P. Hagenmuller, J. Non-Cryst. Solids 81 (1986) 53. [3] S. Tanabe, S. Todoroki, K. Hirao and N. Soga, J. NonCryst. Solids 122 (1990) 59. [4] C.K. Jorgensen and B.R. Judd, Molec. Phys. 8 (1964) 281. [5] R.D. Peacock, Struct. Bonding 22 (1975) 83. [6] M.J. Weber, in: Optical Property of Ions in Crystal, ed. H.M. Crosswhite and H.W. Mops (Interscience, New York, 1967) p. 467. [7] B.R. Judd, Phys. Rev. 127 (1962) 750. [8] G.S. Ofelt, J. Chem. Phys. 37 (1962) 511. [9] E.W.J.L. Oomen and A.M.A. van Dongen, J. Non-Cryst. Solids 111 (1989) 205. [10] S. Tanabe, T. Ohyagi, N. Soga and T. Hanada, Phys. Rev. B 46 (1992) 3305. [11] P.K. Gallagher, C.K. Kurkjian and P.M. Bridenbaugh, Phys. Chem. Glasses 6 (1965) 95. [12] R. Reisfeld, Struct. Bonding 22 (1975) 123. [13] M. Zahir, R. Olazcuaga, C. Parent, G. Le Flem and P. Hagenmuller, J. Non-Cryst. Solids 69 (1985) 221. [14] A. Capobianco, P.P. Proulx, M. Bettinelli and F. Negrisolo, Phys. Rev. B42 (1990) 5936. [15] W.F. Krupke, IEEE J. Quantum Electron. QE10 (1974) 4450. [16] W.T. Carnall, P.R. Fields and K, Rajnak, J. Chem. Phys. 49 (1968) 4450. [17] W.F. Krupke and J.B. Gruber, Phys. Rev. 139 (1965) A2008. [18] M.J. Weber, Phys. Rev. 157 (1967) 262. [19] G.S. Ofelt, J. Chem. Phys. 38 (1963) 2171. [20] R.A. Velapoldi, R. Reisfeld and L. Boehm, Phys. Chem. Glasses 14 (1973) 101. [21] M.J. Weber and R.F. Schaufele, J. Chem. Phys. 43 (1965) 1702. [22] A. Dietzel, Z. Elektrochem. 48 (1942) 9. [23] H. Ikeda, Y. Murayama, Y. Ohoka, K. Morinaga and T. Yanagase, J. Jpn. Inst. Met. 47 (1983) 1063. [24] T. Izumitani, H. Toratani and H. Kuroda, J. Non-Cryst. Solids 47 (1982) 87.