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Optical absorption spectra and radiative intensities of Pr3+ in sulphate glasses
Journal of Non-Crystalline Solids 101 (1988) 75-79 North-Holland, Amsterdam
75
OPTICAL A B S O R P T I O N SPECTRA AND RADIATIVE I N T E N S I T I E S OF Pr 3+ IN S U L P H A T E GLASSES
S.V.J. L A K S H M A N and Y.C. R A T N A K A R A M Spectroscopic Laboratories, Department of Physics, S.V. University, Tirupati, 517 502 India Received 4 November 1986 Revised manuscript received 30 October 1987
Absorption spectra of Pr(Ill) in different sulphate glasses have been studied for the first time in the visible and near-infrared regions. From the observed positions, Racah (E l, E 2, E 3) and spin-orbit (~4f) parameters are evaluated by least-squares analysis. The intensity parameters (122. 124,126) were calculated by the use of Judd-Ofelt formulae. Eigenvalues and eigenvectors are evaluated by diagonalizing the fz matrices. Radiative transition probabilities (A), branching ratios (/3), integrated cross sections (Z) and radiative lifetimes (,r) are calculated for the excited 3PD 3p0, 1D 2 and 3F3 states of Pr (III).
1. Introduction Reisfeld [1] reported the optical spectra, radiative and nonradiative transitions of rare earths in different glasses. The intensity parameters and laser analysis of Pr 3+ doped in some oxide glasses have been reported by Hormadaly and Reisfeld [2]. Since the optical absorption studies have not previously been reported in the literature for Pr 3+ in sulphate glasses, the authors took up the present investigation.
oughly mixed with these chemicals in an agate mortar for half an hour. The glasses doped with the rare-earth ion were thus prepared from this melt. Spectra were recorded in the ultraviolet, visible (UV-VIS), near-infrared (NIR) and infrared (IR) regions on Perkin-Elmer 551, Carl-Zeiss Specord 61 and Pye Unicam SP3-300 spectrophotometers, respectively. The refractive indices were measured using an Abbe refractometer. The band maxima could be measured accurately to 1 A at 5000 ~, and to 2 ,~ at 16 660 ~,.
2. Experimental 3. Results and analysis Different proportions of various sulphates (BDH samples) were mixed and melted at 900 ° C in an electrical furnace. The melt was poured on a tile and pressed quickly with another tile. The percentage composition of the mixture that gave the best glass was chosen for doping the rare-earth ion. It was found that 60 mol% of ZnSO 4 + 40 mol% of Na2SO 4 formed one good glass. Similarly 30 mol% of L i S O 4 + 7 0 mol% of Na2SO 4, 10 mol% of MgSO 4 + 90 mol% of NazSO 4, 10 mol% of CdSO 4 + 90 mol% of Na2SO4, and 10 mol% of K2SO 4 + 90 mol% of Na2SO 4 formed other good glasses. Pr 3+ ions, 0.5 to 1 tool wt.%, was thor0022-3093/88/$03,50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
3.1. Electronic energy levels
The observed spectrum of Pr 3+ in zinc sodium sulphate (ZSS) glass is shown in fig. 1. The spectra and other details of Pr 3+ obtained in the other glasses are not given to save space. The identification and analysis of the bands was straightforward. The experimental and calculated energy values [3] for ZSS glass are given in table 1. The rms deviation is reasonable within experimental error. The evaluated Racah and spin-orbit parameters for all the glasses are presented in table 2.
76
S.V.J. Lakshman, Y.C. Ratnakaram / P r ~ + in sulphate glasses
1.1
@
® 0-8
3P2 in C
13 0-9
3F
~ 0,6
-
13
~
~ 0"4
1D2
0. O
3F
3
4
3
3
H
I
~ _ _ ~
7000
6000
F
6
_
0
0.2
0.8
o-[ 420
I
I
500
560
660
0 8000
Wavelength (nm)
I
5000
4000
Wavenumber (cm-I)
Fig. 1. Absorption spectrum of Pr 3+ in zinc sodium sulphate glass. (a) UV-VIS, (b) NIR. Thickness: U V - V I S = 0.212 cm, N1R = 0.092 cm.
3.2. Spectral intensities
Judd-Ofelt intensity parameters (I2x) evaluated from the formula [1]
The intensities of the bands have been interpreted using Judd-Ofelt theory. The necessary intermediate coupling matrix elements have been evaluated using the eigenvectors obtained from the diagonalization of the f2 energy matrices. These values are very close to those reported in the literature [4]. The observed and calculated oscillator strengths for ZSS glass are presented in table 3. The oscillator strengths of the bands in zinc sodium sulphate glass are higher than those found in any other glass. This indicates that the nonsymmetric component of the electric field acting on the Pr 3+ ion is very strong in this glass. The
~x(cm2) = 9.2185 × 10 -~2 ×
( 2 J + 1)T x, (n 2 + 2) 2
(1) for Pr 3+ in the five glasses, namely ZSS (zinc sodium sulphate), LSS (lithium sodium sulphate), CSS (cadmium sodium sulphate), KSS (potassium sodium sulphate) and MSS (magnesium sodium sulphate) glasses are presented in table 4. 3.3. Hypersensitive transition 3H4 ~ 3 F2 is a hypersensitive transition for the Pr 3+ ion. The oscillator strengths ( f ) of this tran-
Table 1 Experimental and calculated energy levels of Pr 3÷ in zinc sodium sulphate glass Transition from ground 3H 4
Eexv (cm - ] )
Eca~c (cm - ] )
3H 6 3F2 3F3 3F4 1D2 3Po 3P1 3P2 R M S deviation
4200 5000 6 320 6 760 17177 20 828 21453 22618
4238 4847 6 220 6 746 17176 20 848 21445 22662 + 96
Table 2 Racah ( E 1, E 2, E 3) and spin-orbit (~4f) parameters of Pr 3+ in sulphate glasses (all values in cm -1) Parameter
ZSS a)
LSS
CSS
KSS
MSS
E] E2 E3 /J4f
4771.1 22.1 461.3 739.5
4559.4 21.9 456.6 769.2
4656.0 21.6 458.6 749.5
4614.3 21.5 457.9 780.0
4662.6 21.5 460.3 751.3
") ZSS: zinc sodium sulphate glass. LSS: lithium sodium sulphate glass. CSS: c a d m i u m sodium sulphate glass. KSS: Potassium sodium sulphate glass. MSS: m a g n e s i u m sodium sulphate glass.
S. V.J. Lakshman, Y. C. Ratnakaram / P r 3 + in sulphate glasses Table 3
where
Observed and calculated oscillator strengths of Pr 3+ in zinc sodium sulphate glass
Sed = e 2
S'L'J'
fexp )< 106
foal X 106
3H 6 3F z 3F3 3F,I 1D 2 3Po 3P1 3P2 RMS deviation
1.05 + 0.21 7.61 _+0.84 15.00_+ 1.27 3.17 _+0.42 7.13 _+0.76 3.06 _+0.47 6.42 _+0.86 20.19 + 2.36
1,35 7,68 13.46 6.59 2.29 9.22 9.45 7.30 _+7.08
77
(3)
E ~"~A(~JIIU'~ [ l ~ ' J ' ) 2, h = 2,4,6
Table 5
Squared reduced matrix elements of Pr 3÷ in zinc sodium sulphate glass Transition
IIU2 II=
IIU4 II 2
[IU6 II 2
3P 1 --,3P0 1D2 1G 4 4F4 3F 3 3i=2 3H 6 3H 5 3H 4
0 0.07900 0 0 0.57143 0.27018 0 0 0
0 0 0.07622 0.27056 0.19643 0 0 0.28572 0.17107
0 0 0 0 0 0 0.12465 0.08929 0
3Po __,1D2 tG 4 3F4 3F3 3F2 3H 6 31-15
0.01544 0 0 0 0.29431 0 0
0
0 0.05231 0.11110 0 0 0 0 0.17190
0 0 0 0 0 0.07260 0 0
The total radiative transition probability is given by
1D2 ~ I G 4 3F4 3F3 3F2 -~H 6 3H 5 3H 4
0.31928 0.58256 0.03236 0.01343 0 0 0.00295
0.05108 0.00010 0.01901 0.08453 0.06972 0.00265 0.01636
0.07791 0.01881 0 0 0.00606 0.00013 0.05215
A( ~J, ~'J')
3F3 ~ 3 F 2
0.02122
0.05079 0.31822 0.34669 0.36828
0 0.84606 0 0.65428
sition in various glasses along with the ~22, 124 and ~"~6 parameters are given in table 4. As is seen from the table, 122 and 126 parameters are found to decrease with the decrease of the intensity of the hypersensitive transition in three similar composition glasses, namely cadmium sodium sulphate, magnesium sodium sulphate and potassium sodium sulphate glasses (zinc and lithium glasses have different compositions). It is also found that with the increase of the weight of the glass (or atomic number of the variable component) there is a decrease in the ~24 parameter.
3.4, Transitionprobabilitiesandradiativelifetimes
--64~'4v33h (2 J + 1 )
[ n(ne+2)2Sed+n3Smd 1 9
,
31-14
(2)
3H 6
0
3H 5 3Ha
0.62856 0.06556
Table 4 Judd-Ofelt intensity parameters of Pr 3+ in sulphate glasses
Parameter
ZSS a)
LSS
CSS
KSS
MSS
122 × 102° (cm 2 ) 124 x 1020 (cm2) ~6 X 1020 (cm 2 ) n h) f X 106
3.37 + 0.56 15.24 + 1.18 10.14 _ 0.83 1.562 7.61
0.14 + 0.58 12.69 5:0.59 8.95 + 0.48 1.496 4.88
2.52 + 0.31 3.08 +_0.11 3.52 + 0.32 1.634 2.64
0.92 _+0.21 3.42 + 0.22 3.10 ___0.34 1.592 1.87
1.29 + 0.29 5.66 -+ 0.39 3.57 +_0.25 1.503 2.53
a) See footnote to table 2. b) n: refractive index; f: oscillator strength of 3H 4 ~ 3F2 transition.
6 2717 11766 0 10061 8335 0 58678
542 1213 262 1236 1202 71 1972
1 37 187 1060
3H 5 3H 4
3P0 --" 1D2 1G4 3F4 3F3 3Fz 3H 6 3I-I5 3H 4
I D 2 --*IG4 3F4
3H 5 3H 4
3F3 ---~3F2 3H 6 3H 5 3H 4
0
~ 0 0.03 0.14 0.82
0.08 0.18 0.04 0.19 0.18 0.01 0.30
0 0.03 0.13 0 0.11 0.09 0 0.64
0.36 0.24
0.06
- 0 0.02 0.12 0.16 0.04
~) See footnote to table 2.
3H 6
3F2
3F3
5306
31529 21191
3H 6
0
18 1463 10820 14315 3438
1D 2 1G4 3F4 3F3 3F2
0.3 5.1 5.9 14.9
5.3 6.0 1.2 4.4 3.9 0.1 3.6
0.2 11.9 32.1 0 21.6 16.4 0 73.4
45.6 25.0
9.7
0.5 5.8 27.2 33.5 6.8
0
23 96 811
1
214 131 119 828 771 39 1459
0 2247 7634 0 363 6061 0 42152
1349 7376 6331 124 3888 22438 14990
1
0
LSS ,X(10 - a s )
A ( s -1)
fl
ZSS a)
A ( s -1)
3PI ~3po
Transition
0.02 0.10 0.87
- 0
0.06 0.04 0.03 0.23 0.21 0.01 0.41
0 0.04 0.13 0 - 0 0.10 0 0.72
0.02 0.13 0.11 - 0 0.07 0.39 0.26
- 0
0
fl
3.9 3.4 12.2
0.2
2.4 0.7 0.6 3.4 2.9 0.1 3.0
0 10.9 22.9 0 0.8 13.5 0 58.3
5.8 20.3 16.5 0.3 8.0 36.1 19.5
0
0
,~(10 -18)
11 76 355
- 1
255 922 94 295 257 13 663
6 641 2651 0 8568 3260 0 13594
374 2469 6758 2922 2081 8150 4887
18
0
A ( s -1)
CSS
0.01 0.09 0.24 0.10 0.07 0.29 0.17
0
0
-
0.02 0.17 0.80
0
0.05 0.19 0.02 0.06 0.10 - 0 0.14
- 0 0.02 0.09 0 0.30 0.11 0 0.47
-
fl
1.5 2.2 4.5
0.1
2.5 4.4 0.4 1.0 0.8 0 1.1
0.2 2.6 6.7 0 16.8 5.9 0 15.7
1.4 5.7 14.6 5.3 3.55 10.9 5.3
0
0
,~(10 - a s )
8 46 315
- 1
122 331 59 289 257 13 586
2 657 2608 0 2878 2565 0 13979
395 2482 3614 981 1647 7815 4988
7
0
A ( s -1)
KSS
-
-
0.02 0.12 0.85
0
0.07 0.20 0.03 0.17 0.15 0.01 0.35
0 0.03 0.11 0 0.13 0.11 0 0.61
0.02 0.11 0.16 0.04 0.07 0.35 0.22
0
0
fl
1.3 1.4 4.1
0.1
1.3 1.7 0.3 1.0 0.8 0 1.1
0 2.8 6.9 0 5.9 5.0 0 16.9
1.54 6.0 8.3 1.8 3.0 11.0 5.6
0.2
0
,X(10 - i s )
11 59 342
- 1
145 327 70 370 339 16 588
2 896 3785 0 2973 2559 0 19281
523 3511 4492 1013 1633 10207 6937
6
0
A(s -1)
MSS
-
0.02 0.14 0.82
0
0.08 0.17 0.04 0.19 0.18 0.01 0.31
0 0.03 0.13 0 0.10 0.08 0 0.65
0.02 0.12 0.16 0.03 0.05 0.36 0.24
0
0
fl
0.1 1.7 2.0 5.1
1.7 1.8 0.4 1.5 1.2 - 0 1.2
0 4.3 11.2 0 6.8 5.5 0 26.1
-0 0.2 2.2 9.5 11.4 2.1 3.2 16.0 8.8
X(10 -is)
Table 6 Radiative transition probabilities (A), branching ratios (fl) and integrated cross-sections (Z(cm-1)) for the excited 3po, 3p1, I D 2 and 3F3 states of Pr 3+ in sulphate glasses
%
+
t~
S. V.J. Lakshman, E C. Ratnakararn / P r 3+ in sulphate glasses
and
e2h 2
Stud=
16~rZm2c 2
(~pJIIL+ 2SII~p'J') z.
(4)
The matrix elements of I[ L + 2S II are (since the selection rule is z~d = 0, ±1) as follows: d' =d:
(~s/_J II/~ + 2s II ~s/_J')
79
Table 7 Radiative lifetimes (rR) for the excited states 3p0, 3P D 1D 2 and 3F3 of Pr 3+ in sulphate glasses (values in ~s) State
ZSS ")
LSS
CSS
KSS
MSS
3P0 3P1 1D 2 3F3
11 11 154 777
17 18 280 1074
35 36 399 2252
44 45 602 2697
34 35 538 2418
a) See footnote to table 2.
= g [ J ( J + 1)(2J + 1)] '/2, where
J(J + 1) + S(S + 1 ) - L ( L + 1)
g=l+
2 ( J ) ( J + 1)
J'=J-l:
(~S/_d II t + 25 II a S t ,
J -
1)
= [ { ( S + L + J + 1)(S+ L + l - J ) × ( J + S- L)(J + L - S)}(4J}-'] '/2, (5) * J'=J+l: ( a S L J [[ t + 2S II aSt, J + 1) = [((S+ L+J+ 2)is+J+ ×(L +J+
l-L)
1 - S)(S+L-J)}
X (4(g + 1)}-'] '/2
References
Since the excited-state relaxation usually involves transition to a n u m b e r o f states, we define a total
radiative relaxation rate AT(~PJ) = E A(tpJ, ~p'J'), ~p'j"
(6)
where the sum runs over all ~ ' J ' lower in energy than ~pJ. The radiative lifetime of a state is
TR(~pj ) = [AT(~pj) ] -1
(7)
The integrated absorption cross section is given by z =
1
A
x - - .
The squared reduced matrix elements II Ux II 2 between 3Pl, 3P0, 1D2, 3F3 and all the next lower lying states were calculated in the intermediate coupling scheme using the eigenvectors of Pr 3+ for all the glasses. The results for zinc sodium sulphate glass only are presented in table 5. Radiative transition probabilities (A), branching ratios (fl) and integrated absorption cross sections (2~) are compared for all the glasses in table 6, The calculated lifetimes of these fluorescent levels are all collected in table 7. The radiative lifetimes of 3P0 and 3P1 levels are equal in each of the glasses and they are very small in comparison either with the 1 D 2 o r 3 F 3 levels.
(8)
8qT"Ctl2
* Printing errors are found in these equations published by Lakshman et al. [5-11].
[1] R. Reisfeld, Structure and Bonding 22 (1975) 123. [2] J. Hormadaly and R. Reisfeld, J. Non-Cryst. Solids 30 (1979) 337. [3] S.V.J. Lakshman and A. Suresh Kumar, J. Non-Cryst. Solids 85 (1986) 162. [4] M.J. Weber, J. Chem. Phys. 48 (1968) 4774. [5] S.V.J. Lakshman and S. Buddhudu, Proc. Indian Nat. Sci. Acad. 47 A (1981) 721. [6] S.V.J. Lakshman and S. Buddhudu, JQSRT 27 (1982) 531. [7] S.V.J. Lakshman and S. Buddhudu, J. Phys. Chem. Sol. 43 (1982) 849. [8] S.V.J. Lakshman and S. Buddhudu, Ind. J. Pure Appl. Phys. 20 (1982) 667. [9] S.VJ. Lakshman and S. Buddhudu, Acta Phys. Hungarica 54 (1983) 231. [10] S.VJ. Lakshman and S. Buddhudu, Polydedra 2 (1983) 403. [11] S.V.J. Lakshman and S. Buddhudu, Ind. J. Pure Appl. Phys. 21 (1983) 413.
75
OPTICAL A B S O R P T I O N SPECTRA AND RADIATIVE I N T E N S I T I E S OF Pr 3+ IN S U L P H A T E GLASSES
S.V.J. L A K S H M A N and Y.C. R A T N A K A R A M Spectroscopic Laboratories, Department of Physics, S.V. University, Tirupati, 517 502 India Received 4 November 1986 Revised manuscript received 30 October 1987
Absorption spectra of Pr(Ill) in different sulphate glasses have been studied for the first time in the visible and near-infrared regions. From the observed positions, Racah (E l, E 2, E 3) and spin-orbit (~4f) parameters are evaluated by least-squares analysis. The intensity parameters (122. 124,126) were calculated by the use of Judd-Ofelt formulae. Eigenvalues and eigenvectors are evaluated by diagonalizing the fz matrices. Radiative transition probabilities (A), branching ratios (/3), integrated cross sections (Z) and radiative lifetimes (,r) are calculated for the excited 3PD 3p0, 1D 2 and 3F3 states of Pr (III).
1. Introduction Reisfeld [1] reported the optical spectra, radiative and nonradiative transitions of rare earths in different glasses. The intensity parameters and laser analysis of Pr 3+ doped in some oxide glasses have been reported by Hormadaly and Reisfeld [2]. Since the optical absorption studies have not previously been reported in the literature for Pr 3+ in sulphate glasses, the authors took up the present investigation.
oughly mixed with these chemicals in an agate mortar for half an hour. The glasses doped with the rare-earth ion were thus prepared from this melt. Spectra were recorded in the ultraviolet, visible (UV-VIS), near-infrared (NIR) and infrared (IR) regions on Perkin-Elmer 551, Carl-Zeiss Specord 61 and Pye Unicam SP3-300 spectrophotometers, respectively. The refractive indices were measured using an Abbe refractometer. The band maxima could be measured accurately to 1 A at 5000 ~, and to 2 ,~ at 16 660 ~,.
2. Experimental 3. Results and analysis Different proportions of various sulphates (BDH samples) were mixed and melted at 900 ° C in an electrical furnace. The melt was poured on a tile and pressed quickly with another tile. The percentage composition of the mixture that gave the best glass was chosen for doping the rare-earth ion. It was found that 60 mol% of ZnSO 4 + 40 mol% of Na2SO 4 formed one good glass. Similarly 30 mol% of L i S O 4 + 7 0 mol% of Na2SO 4, 10 mol% of MgSO 4 + 90 mol% of NazSO 4, 10 mol% of CdSO 4 + 90 mol% of Na2SO4, and 10 mol% of K2SO 4 + 90 mol% of Na2SO 4 formed other good glasses. Pr 3+ ions, 0.5 to 1 tool wt.%, was thor0022-3093/88/$03,50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
3.1. Electronic energy levels
The observed spectrum of Pr 3+ in zinc sodium sulphate (ZSS) glass is shown in fig. 1. The spectra and other details of Pr 3+ obtained in the other glasses are not given to save space. The identification and analysis of the bands was straightforward. The experimental and calculated energy values [3] for ZSS glass are given in table 1. The rms deviation is reasonable within experimental error. The evaluated Racah and spin-orbit parameters for all the glasses are presented in table 2.
76
S.V.J. Lakshman, Y.C. Ratnakaram / P r ~ + in sulphate glasses
1.1
@
® 0-8
3P2 in C
13 0-9
3F
~ 0,6
-
13
~
~ 0"4
1D2
0. O
3F
3
4
3
3
H
I
~ _ _ ~
7000
6000
F
6
_
0
0.2
0.8
o-[ 420
I
I
500
560
660
0 8000
Wavelength (nm)
I
5000
4000
Wavenumber (cm-I)
Fig. 1. Absorption spectrum of Pr 3+ in zinc sodium sulphate glass. (a) UV-VIS, (b) NIR. Thickness: U V - V I S = 0.212 cm, N1R = 0.092 cm.
3.2. Spectral intensities
Judd-Ofelt intensity parameters (I2x) evaluated from the formula [1]
The intensities of the bands have been interpreted using Judd-Ofelt theory. The necessary intermediate coupling matrix elements have been evaluated using the eigenvectors obtained from the diagonalization of the f2 energy matrices. These values are very close to those reported in the literature [4]. The observed and calculated oscillator strengths for ZSS glass are presented in table 3. The oscillator strengths of the bands in zinc sodium sulphate glass are higher than those found in any other glass. This indicates that the nonsymmetric component of the electric field acting on the Pr 3+ ion is very strong in this glass. The
~x(cm2) = 9.2185 × 10 -~2 ×
( 2 J + 1)T x, (n 2 + 2) 2
(1) for Pr 3+ in the five glasses, namely ZSS (zinc sodium sulphate), LSS (lithium sodium sulphate), CSS (cadmium sodium sulphate), KSS (potassium sodium sulphate) and MSS (magnesium sodium sulphate) glasses are presented in table 4. 3.3. Hypersensitive transition 3H4 ~ 3 F2 is a hypersensitive transition for the Pr 3+ ion. The oscillator strengths ( f ) of this tran-
Table 1 Experimental and calculated energy levels of Pr 3÷ in zinc sodium sulphate glass Transition from ground 3H 4
Eexv (cm - ] )
Eca~c (cm - ] )
3H 6 3F2 3F3 3F4 1D2 3Po 3P1 3P2 R M S deviation
4200 5000 6 320 6 760 17177 20 828 21453 22618
4238 4847 6 220 6 746 17176 20 848 21445 22662 + 96
Table 2 Racah ( E 1, E 2, E 3) and spin-orbit (~4f) parameters of Pr 3+ in sulphate glasses (all values in cm -1) Parameter
ZSS a)
LSS
CSS
KSS
MSS
E] E2 E3 /J4f
4771.1 22.1 461.3 739.5
4559.4 21.9 456.6 769.2
4656.0 21.6 458.6 749.5
4614.3 21.5 457.9 780.0
4662.6 21.5 460.3 751.3
") ZSS: zinc sodium sulphate glass. LSS: lithium sodium sulphate glass. CSS: c a d m i u m sodium sulphate glass. KSS: Potassium sodium sulphate glass. MSS: m a g n e s i u m sodium sulphate glass.
S. V.J. Lakshman, Y. C. Ratnakaram / P r 3 + in sulphate glasses Table 3
where
Observed and calculated oscillator strengths of Pr 3+ in zinc sodium sulphate glass
Sed = e 2
S'L'J'
fexp )< 106
foal X 106
3H 6 3F z 3F3 3F,I 1D 2 3Po 3P1 3P2 RMS deviation
1.05 + 0.21 7.61 _+0.84 15.00_+ 1.27 3.17 _+0.42 7.13 _+0.76 3.06 _+0.47 6.42 _+0.86 20.19 + 2.36
1,35 7,68 13.46 6.59 2.29 9.22 9.45 7.30 _+7.08
77
(3)
E ~"~A(~JIIU'~ [ l ~ ' J ' ) 2, h = 2,4,6
Table 5
Squared reduced matrix elements of Pr 3÷ in zinc sodium sulphate glass Transition
IIU2 II=
IIU4 II 2
[IU6 II 2
3P 1 --,3P0 1D2 1G 4 4F4 3F 3 3i=2 3H 6 3H 5 3H 4
0 0.07900 0 0 0.57143 0.27018 0 0 0
0 0 0.07622 0.27056 0.19643 0 0 0.28572 0.17107
0 0 0 0 0 0 0.12465 0.08929 0
3Po __,1D2 tG 4 3F4 3F3 3F2 3H 6 31-15
0.01544 0 0 0 0.29431 0 0
0
0 0.05231 0.11110 0 0 0 0 0.17190
0 0 0 0 0 0.07260 0 0
The total radiative transition probability is given by
1D2 ~ I G 4 3F4 3F3 3F2 -~H 6 3H 5 3H 4
0.31928 0.58256 0.03236 0.01343 0 0 0.00295
0.05108 0.00010 0.01901 0.08453 0.06972 0.00265 0.01636
0.07791 0.01881 0 0 0.00606 0.00013 0.05215
A( ~J, ~'J')
3F3 ~ 3 F 2
0.02122
0.05079 0.31822 0.34669 0.36828
0 0.84606 0 0.65428
sition in various glasses along with the ~22, 124 and ~"~6 parameters are given in table 4. As is seen from the table, 122 and 126 parameters are found to decrease with the decrease of the intensity of the hypersensitive transition in three similar composition glasses, namely cadmium sodium sulphate, magnesium sodium sulphate and potassium sodium sulphate glasses (zinc and lithium glasses have different compositions). It is also found that with the increase of the weight of the glass (or atomic number of the variable component) there is a decrease in the ~24 parameter.
3.4, Transitionprobabilitiesandradiativelifetimes
--64~'4v33h (2 J + 1 )
[ n(ne+2)2Sed+n3Smd 1 9
,
31-14
(2)
3H 6
0
3H 5 3Ha
0.62856 0.06556
Table 4 Judd-Ofelt intensity parameters of Pr 3+ in sulphate glasses
Parameter
ZSS a)
LSS
CSS
KSS
MSS
122 × 102° (cm 2 ) 124 x 1020 (cm2) ~6 X 1020 (cm 2 ) n h) f X 106
3.37 + 0.56 15.24 + 1.18 10.14 _ 0.83 1.562 7.61
0.14 + 0.58 12.69 5:0.59 8.95 + 0.48 1.496 4.88
2.52 + 0.31 3.08 +_0.11 3.52 + 0.32 1.634 2.64
0.92 _+0.21 3.42 + 0.22 3.10 ___0.34 1.592 1.87
1.29 + 0.29 5.66 -+ 0.39 3.57 +_0.25 1.503 2.53
a) See footnote to table 2. b) n: refractive index; f: oscillator strength of 3H 4 ~ 3F2 transition.
6 2717 11766 0 10061 8335 0 58678
542 1213 262 1236 1202 71 1972
1 37 187 1060
3H 5 3H 4
3P0 --" 1D2 1G4 3F4 3F3 3Fz 3H 6 3I-I5 3H 4
I D 2 --*IG4 3F4
3H 5 3H 4
3F3 ---~3F2 3H 6 3H 5 3H 4
0
~ 0 0.03 0.14 0.82
0.08 0.18 0.04 0.19 0.18 0.01 0.30
0 0.03 0.13 0 0.11 0.09 0 0.64
0.36 0.24
0.06
- 0 0.02 0.12 0.16 0.04
~) See footnote to table 2.
3H 6
3F2
3F3
5306
31529 21191
3H 6
0
18 1463 10820 14315 3438
1D 2 1G4 3F4 3F3 3F2
0.3 5.1 5.9 14.9
5.3 6.0 1.2 4.4 3.9 0.1 3.6
0.2 11.9 32.1 0 21.6 16.4 0 73.4
45.6 25.0
9.7
0.5 5.8 27.2 33.5 6.8
0
23 96 811
1
214 131 119 828 771 39 1459
0 2247 7634 0 363 6061 0 42152
1349 7376 6331 124 3888 22438 14990
1
0
LSS ,X(10 - a s )
A ( s -1)
fl
ZSS a)
A ( s -1)
3PI ~3po
Transition
0.02 0.10 0.87
- 0
0.06 0.04 0.03 0.23 0.21 0.01 0.41
0 0.04 0.13 0 - 0 0.10 0 0.72
0.02 0.13 0.11 - 0 0.07 0.39 0.26
- 0
0
fl
3.9 3.4 12.2
0.2
2.4 0.7 0.6 3.4 2.9 0.1 3.0
0 10.9 22.9 0 0.8 13.5 0 58.3
5.8 20.3 16.5 0.3 8.0 36.1 19.5
0
0
,~(10 -18)
11 76 355
- 1
255 922 94 295 257 13 663
6 641 2651 0 8568 3260 0 13594
374 2469 6758 2922 2081 8150 4887
18
0
A ( s -1)
CSS
0.01 0.09 0.24 0.10 0.07 0.29 0.17
0
0
-
0.02 0.17 0.80
0
0.05 0.19 0.02 0.06 0.10 - 0 0.14
- 0 0.02 0.09 0 0.30 0.11 0 0.47
-
fl
1.5 2.2 4.5
0.1
2.5 4.4 0.4 1.0 0.8 0 1.1
0.2 2.6 6.7 0 16.8 5.9 0 15.7
1.4 5.7 14.6 5.3 3.55 10.9 5.3
0
0
,~(10 - a s )
8 46 315
- 1
122 331 59 289 257 13 586
2 657 2608 0 2878 2565 0 13979
395 2482 3614 981 1647 7815 4988
7
0
A ( s -1)
KSS
-
-
0.02 0.12 0.85
0
0.07 0.20 0.03 0.17 0.15 0.01 0.35
0 0.03 0.11 0 0.13 0.11 0 0.61
0.02 0.11 0.16 0.04 0.07 0.35 0.22
0
0
fl
1.3 1.4 4.1
0.1
1.3 1.7 0.3 1.0 0.8 0 1.1
0 2.8 6.9 0 5.9 5.0 0 16.9
1.54 6.0 8.3 1.8 3.0 11.0 5.6
0.2
0
,X(10 - i s )
11 59 342
- 1
145 327 70 370 339 16 588
2 896 3785 0 2973 2559 0 19281
523 3511 4492 1013 1633 10207 6937
6
0
A(s -1)
MSS
-
0.02 0.14 0.82
0
0.08 0.17 0.04 0.19 0.18 0.01 0.31
0 0.03 0.13 0 0.10 0.08 0 0.65
0.02 0.12 0.16 0.03 0.05 0.36 0.24
0
0
fl
0.1 1.7 2.0 5.1
1.7 1.8 0.4 1.5 1.2 - 0 1.2
0 4.3 11.2 0 6.8 5.5 0 26.1
-0 0.2 2.2 9.5 11.4 2.1 3.2 16.0 8.8
X(10 -is)
Table 6 Radiative transition probabilities (A), branching ratios (fl) and integrated cross-sections (Z(cm-1)) for the excited 3po, 3p1, I D 2 and 3F3 states of Pr 3+ in sulphate glasses
%
+
t~
S. V.J. Lakshman, E C. Ratnakararn / P r 3+ in sulphate glasses
and
e2h 2
Stud=
16~rZm2c 2
(~pJIIL+ 2SII~p'J') z.
(4)
The matrix elements of I[ L + 2S II are (since the selection rule is z~d = 0, ±1) as follows: d' =d:
(~s/_J II/~ + 2s II ~s/_J')
79
Table 7 Radiative lifetimes (rR) for the excited states 3p0, 3P D 1D 2 and 3F3 of Pr 3+ in sulphate glasses (values in ~s) State
ZSS ")
LSS
CSS
KSS
MSS
3P0 3P1 1D 2 3F3
11 11 154 777
17 18 280 1074
35 36 399 2252
44 45 602 2697
34 35 538 2418
a) See footnote to table 2.
= g [ J ( J + 1)(2J + 1)] '/2, where
J(J + 1) + S(S + 1 ) - L ( L + 1)
g=l+
2 ( J ) ( J + 1)
J'=J-l:
(~S/_d II t + 25 II a S t ,
J -
1)
= [ { ( S + L + J + 1)(S+ L + l - J ) × ( J + S- L)(J + L - S)}(4J}-'] '/2, (5) * J'=J+l: ( a S L J [[ t + 2S II aSt, J + 1) = [((S+ L+J+ 2)is+J+ ×(L +J+
l-L)
1 - S)(S+L-J)}
X (4(g + 1)}-'] '/2
References
Since the excited-state relaxation usually involves transition to a n u m b e r o f states, we define a total
radiative relaxation rate AT(~PJ) = E A(tpJ, ~p'J'), ~p'j"
(6)
where the sum runs over all ~ ' J ' lower in energy than ~pJ. The radiative lifetime of a state is
TR(~pj ) = [AT(~pj) ] -1
(7)
The integrated absorption cross section is given by z =
1
A
x - - .
The squared reduced matrix elements II Ux II 2 between 3Pl, 3P0, 1D2, 3F3 and all the next lower lying states were calculated in the intermediate coupling scheme using the eigenvectors of Pr 3+ for all the glasses. The results for zinc sodium sulphate glass only are presented in table 5. Radiative transition probabilities (A), branching ratios (fl) and integrated absorption cross sections (2~) are compared for all the glasses in table 6, The calculated lifetimes of these fluorescent levels are all collected in table 7. The radiative lifetimes of 3P0 and 3P1 levels are equal in each of the glasses and they are very small in comparison either with the 1 D 2 o r 3 F 3 levels.
(8)
8qT"Ctl2
* Printing errors are found in these equations published by Lakshman et al. [5-11].
[1] R. Reisfeld, Structure and Bonding 22 (1975) 123. [2] J. Hormadaly and R. Reisfeld, J. Non-Cryst. Solids 30 (1979) 337. [3] S.V.J. Lakshman and A. Suresh Kumar, J. Non-Cryst. Solids 85 (1986) 162. [4] M.J. Weber, J. Chem. Phys. 48 (1968) 4774. [5] S.V.J. Lakshman and S. Buddhudu, Proc. Indian Nat. Sci. Acad. 47 A (1981) 721. [6] S.V.J. Lakshman and S. Buddhudu, JQSRT 27 (1982) 531. [7] S.V.J. Lakshman and S. Buddhudu, J. Phys. Chem. Sol. 43 (1982) 849. [8] S.V.J. Lakshman and S. Buddhudu, Ind. J. Pure Appl. Phys. 20 (1982) 667. [9] S.VJ. Lakshman and S. Buddhudu, Acta Phys. Hungarica 54 (1983) 231. [10] S.VJ. Lakshman and S. Buddhudu, Polydedra 2 (1983) 403. [11] S.V.J. Lakshman and S. Buddhudu, Ind. J. Pure Appl. Phys. 21 (1983) 413.