60
R. Van Deun et al. / Journal of Alloys and Compounds 283 (1999) 59–65
Table 1
micrometer. Absorption spectra were recorded at room
temperature on a Shimadzu UV-3100 spectrophotometer.
In general, the absorption spectra were recorded between
2500 and 300 nm.
Judd–Ofelt intensity parameters Vl (l52, 4, 6) for the trivalent
lanthanide ions in the fluorophosphate glass 75NaPO3 –24BaF2 –1LnF3
(Ln5lanthanide ion)
Lanthanide ion
V2 (10220 cm2)
V4 (10220 cm2)
V6 (10220 cm2)
Pr31
20.0660.94
2.4160.28
2.2360.25
4.07
6.2161.04
3.2760.32
3.8260.23
5.09
5.5060.38
5.1960.25
2.1860.15
3.74
2.1260.05
1.8060.24
2.0560.12
0.8460.06
1.3060.23
Nd31
Sm31
Eu31
Tb31
Dy31
Ho31
Er31
3. Theoretical background
a
a
The transitions observed in the absorption spectra of the
trivalent lanthanide ions are intraconfigurational f–f transi-
tions. The majority of these transitions are induced electric
dipole transitions, although a few magnetic dipole transi-
tions are present. The intensities of the transitions can be
characterised by the dipole strength D:
–
–
3.9160.36
3.7860.22
2.2760.12
2.5360.80
1.7660.36
2.9760.32
0.8660.16
1.0160.61
Tm31
a The V2 and V4 parameters of Tb31 doped glass are indeterminate.
¯
A(n)
¯
n
1
served, because of a strong absorption by the glass matrix
in the spectral region of interest.
]
¯
dn
D 5
E
(1)
108.9 3 C 3 d
It has been known for a long time that the application of
the Judd–Ofelt theory to Pr31 gives no good agreement
between experimental and calculated dipole strengths. For
a general discussion of this topic, see Ref. [14,15]. If all
the transitions are used in the intensity fitting, especially
where C is the concentration of the lanthanide ion (mol
l
21), d is the optical path length (cm), A is the absorbance
(A52log(I/I0)) and n is the wavenumber (cm21). The
dipole strength is expressed in D2 (Debye2). According to
the Judd–Ofelt theory [4–6], the intensity of induced
electric dipole transitions can be described in terms of
three phenomenological intensity parameters Vl (l52, 4
and 6):
¯
3
the hypersensitive transition P2←3H4 is simulated badly.
The calculated value is less than one third of the actual
value, and this transition is one of the most intense 4f–4f
transitions of the whole lanthanide series. When using all
transitions, the resulting parameter set is V2 5
(20.1463.24)310220 cm2, V4 5(6.1363.57)310220 cm2
and V6 5(5.7661.32)310220 cm2. The RMS error value
is very high: 33431026 Debye2. As proposed by other
1036 (n2 1 2)2
2J 1 1
D 5
e
O
Vl ukJiU (l)iJ9lu2
(2)
2
]
9n
l52,4,6
The factor 1036 converts esu?cm units into Debye2. The
elementary charge e is 4.803310210 esu. The degeneracy
of the ground state is equal to 2J11. The factor (n212)2 /
9n takes into account that the lanthanide ion is not in a
vacuum, but in a dielectric medium (n is the refractive
index of the glass). Finally, the ukJiU (l)iJ9lu are the
squared reduced matrix elements and will be abbreviated
throughout the text as U (l). We used in our Judd–Ofelt
parameterisation the matrix elements reported by Carnall
and co-workers [10–13] for the trivalent lanthanide ions in
aqueous solution. We can use these matrix elements,
because the matrix elements are virtually host independent.
The Vl parameters are determined by a standard-least
squares fitting method.
3
authors [16–18], we preferred not to include the P2←3H4
transition in the fitting procedure. The new set of parame-
ters
is:
V2 5(20.0660.94)310220
cm2,
V4 5
(6.2161.04)310220 cm2 and V6 5(5.5060.38)310220
cm2. Now, the agreement between the calculated and
experimental dipole strength for the P2←3H4 transition is
3
still bad, but the overall agreement for the other transitions
is much better, resulting in better defined parameters and a
much lower RMS error value (9631026 Debye2). The
intensity calculations for the praseodymium-doped glass
are summarised in Table 2.
The absorption spectrum of 75NaPO3 –24BaF2 –1NdF3
glass is given in Fig. 1. Application of the Judd–Ofelt
theory to Nd31 poses no problems. The results of the
intensity calculations are reported in Table 3. A good
agreement is found between experimental and calculated
4. Results and discussion
dipole
strengths.
The
hypersensitive
transition
4G5 / 2, G7 / 2←4I9 / 2 at 17 200 cm21 is the most intense of
all f–f transitions observed for trivalent lanthanide ions in
the fluorophosphate glasses (but the molar absorptivity e of
this transition is still less than 6 mol21 l cm21). The
absorption spectrum of Nd31 in 75NaPO3 –24BaF2 –1NdF3
glass is very similar to those in comparable fluorophos-
phate glasses [19].
2
The Judd–Ofelt parameters, together with the errors on
these parameters, are presented in Table 1. Ce31 and Yb31
doped glasses are not considered because the 4f1 of Ce31
and the 4f13 configuration of Yb31 consists of only two
free-ion levels, so that only one f–f transition can be
observed for these ions. This makes the determination of
the three intensity parameters impossible. Pm31 is radioac-
tive and therefore cumbersome to handle. A Gd31-doped
glass was prepared, but no f–f transition could be ob-
Although assignments in the visible part of the absorp-
tion spectrum of Sm31 are very difficult because of the