Effective local concentration
of Tb3+ in sol-gel silicate
glasses
Carlos P. Ortiz and Dan M. Boye
Physics Department
Davidson College
Supported by
•NSF through MRI program
•ACS through PRF
Energy Levels in Terbium
30
28
5D
3
26
22
5D
4
20
620nm
590nm
490nm
545nm
14
436nm
460nm
16
414nm
18
378nm
Energy (1000cm-1)
24
12
10
8
6
4
2
0
7F
0
1
2
3
4
5
7F
6
Fluorescence (arb. units)
Emission Spectrum from 240nm
Excitation
5D 7F
4
J
5D  7F
3
J
542nm
437nm
Wavelength (nm)
Cross-Relaxation
5D
3
• Mechanism: multipolar E-field
coupling causes the crossrelaxation process.
5D
4
• In rare earths, dipole-dipole
interactions dominate the process.
Energy
(1000cm-1)
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
7F
• Thus, the cross-relaxation rate
depends strongly on the average
distance between Tb ions, which
motivates investigating the local
ion concentration in our material.
0
7F
1
2
3
4
5
6
Tb3+ ion #1
nearby Tb3+ ion #2
Why sol-gel glasses?




Versatility
Large doping with good sample quality
Low temperature production
Porous character of sol-gels allows for mobility
of the network modifying dopants and the
development of ion clusters—thus allowing us
to study cross-relaxation.
Experimental Setup
Detector
Laser System
oscilloscope
ch1 ch2
Pulsed
Nd:YAG
Mirror
Frequency
doubled
with K*DP
BS
PMT
Pin-hole
Filter
DCM dye
laser
1064nm
Spectrometer
4” lens
586nm
532nm
1068nm
K*DP
summing
crystal
Sample
12” lens
378nm
~3” lens
Filter (blocks 378nm)
Mirror
Sample Data
0.2%Tb 4.0%Al 0.0%Gd
Ln(intensity) (arb units)
1
0.1
Excite at 378nm
Detect at 437nm
0.01
0.E+00
1.E-04
2.E-04
3.E-04
4.E-04
5.E-04
time (sec)
6.E-04
7.E-04
8.E-04
9.E-04
1.E-03
Inokuti-Hirayama Model
Assumptions

The cross-relaxation energy transfer occurs via multipole-multipole
interactions between the ions.
where:
R0 

WCR  

R


n
•WCR is the rate of cross relaxation,
•R0 is the distance at which cross relaxation rate
equals the radiative rate, and
•n is determined by the dominant multipolar
interaction

Rare earth ions randomly substitute for cations in the crystal lattice.
Inokuti-Hirayama Model
I (t )  e
 t a

t ceff

c0
Where,  = fluorescence lifetime in absence of
cross-relaxation (single ions),
ceff = the effective local concentration of the ions,
from the perspective of the emitting ions,
c0 = the concentration at which the rate of cross-
relaxation equals the rate of radiative emission,
a = integration constant.
Theoretical Effect of Varying ELC.
Ln Intensity
a.u.
sec
IH model at various ELC, with
Ln(Intensity) (a.u.)
0.01
0.02
1.45ms
0.03
0.04
time sec (sec)
time
Ceff=0.0%
Ceff=0.25%
Ceff=0. 5%
Ceff=0.75%
Ceff=1.00%
Ceff=1.25%
Ceff=1.50%
Exp Decay
1.01ms
IH model
Ceff
0.83mol%
1.51ms
Single Fit


0.2%Tb 4.0%Al 0.0%Gd
Ln(intensity) (arb units)
1
0.1
Excite at 378nm
Detect at 437nm
0.01
0.E+00
1.E-04
2.E-04
3.E-04
4.E-04
5.E-04
6.E-04
7.E-04
time (sec)
data
exp decay
IH model
8.E-04
9.E-04
1.E-03
Applying the IH model to sol gel
glasses
Complication: Unlike crystals, glasses are amorphous materials. This
amorphous character leads to inhomogeneous broadening of the dopant
energy levels.
 Assume the energy levels of ions throughout the material are essentially
constant (in other words assume this effect is small compared to crossrelaxation).
Complication: Clustering in pores produces nonrandom ion distributions,
as opposed to random substitution for host ions in the crystal lattice.
 Addressing this issue requires significant modification of the IH model.



The effective local concentration is different for different clusters.
The total fluorescence can be expressed as a sum of contributions from
individual clusters each following the IH model, instead of a sum of
exponential decays.
Finding the distribution of concentrations involves Laplace Transform analysis.
Effective Tb Local Concentration
(mol%)
Effective Local Concentrations
0.5
0.4
0.3
0.2
0% Al
0.1
slope = 1
0
0
0.5
1
1.5
2
Starting Tb concentration (mol%)
2.5
Effective Local
Concentrations
Effective Tb Local Concentration
(mol%)
0.5
0.4
0.3
0.2
0% Al
0.1
slope = 1
0
0
0.5
1
1.5
2
Starting Tb concentration (mol%)
Low Tb conc.
No co-dopants.
High Tb conc.
No co-dopants.
2.5
Effective Tb Local Concentration (mol%)
Effect of Aluminum co-doping
0.5
0.4
0.3
0.2
0% Al
4% Al
0.1
slope = 1
0
0
0.2
0.4
0.6
0.8
Starting Tb concentration (mol%)
1
Effective Tb Local Concentration (mol%)
Effect of
Aluminum
co-doping
0.5
0.4
0.3
0.2
0% Al
4% Al
0.1
slope = 1
0
0
0.2
0.4
0.6
0.8
Starting Tb concentration (mol%)
Low Tb conc.
No co-dopants.
Low Tb conc.
High Al conc.
1
Effective Tb Local Concentration (mol%)
Effect of
Aluminum
co-doping
0.5
0.4
0.3
0.2
0% Al
4% Al
0.1
slope = 1
0
0
0.2
0.4
0.6
0.8
Starting Tb concentration (mol%)
High Tb conc.
No co-dopants.
High Tb conc.
High Al co-doping.
1
Energy Levels in Terbium
6P
7/2
32
30
28
5D
3
26
24
5D
4
20
620nm
590nm
490nm
545nm
14
436nm
460nm
16
414nm
18
378nm
Energy (1000cm-1)
22
Exciting
nowhere near
lowest level
in Gd
12
10
8
6
4
2
0
7F
0
1
2
3
4
5
7F
6
8S
Effective Tb Local Concentration (mol%)
Effect of Gd co-doping
0.50
0.40
0.30
0.20
0% Al
% Gd = 0.4% - % Tb
slope = 1
0.10
0.00
0
0.1
0.2
0.3
Starting Tb concentration (mol%)
0.4
Effective Tb Local Concentration (mol%)
Effect of
Gadolinium
co-doping
0.50
0.40
0.30
0.20
0% Al
% Gd = 0.4% - % Tb
slope = 1
0.10
0.00
0
0.1
0.2
0.3
Starting Tb concentration (mol%)
High Tb conc.
No co-dopants.
Low Gd co-doping.
High Gd co-doping.
0.4
Conclusions
 The distribution of Tb ions in sol-gel glasses is
nonrandom.
 Aluminum co-doping increases the ELC by dispersing
tightly bound clusters.
 Gadolinium co-doping dilutes Tb clusters, which
promotes emission from concentrated clusters.
 There remain inadequacies in applying the IH model to
sol-gel glasses which we are in the process of
addressing.