3.1 Introduction
Calcium fluoride (CaF2) based TLDs belong to one of the various high Z
thermoluminescent phosphors and have a long and rich history of its own [1].
Essentially four varieties of TLDs based on CaF2 matrix have been extensively
studied for their various practical applications. The four varieties are: natural
fluorite of some specific origin containing suitable activities or synthetic CaF2
with either manganese (Mn), dysprosium (Dy), or Thulium (Tm) as their dopants.
The suitability of a material for being considered as a TLD is based on
various properties, one of them being the stability of the dosimetric glow peak. A
detail account this important aspect of applicability of six commonly used TLDs
that include CaF2:Dy, CaF2:Tm and CaF2:Mn has been presented by Harvey et
al[2]. As a thumb rule the dosimetric glow peak must be strong and occur in the
region[3] 200 – 250°C. The stability of a particular glow peak is dependent on the
lifetime (τ) of a glow peak i.e. the lifetime of the associated electron / hole in the
relevant trapping level. It is given by:æ E ö
÷
è kT ø
t = s -1 exp ç
(3.1)
where, τ = lifetime of charge in the trap,
E = trap-depth,
s = frequency factor,
T = storage temperature ≈ 300 K
and k = Boltzmann constant.
Equation (3.1) is strictly true for first order kinetics (b = 1) and for 1 ≤ b < 2 the
modified equation as derived by Lovedy and Gartia[4] is
æ E ö
exp ç ÷
è kT ø
τ=
s(2 - b)
(3.2)
i.e. for non-first order (b ≠ 1) glow peak, τ is significantly different depending
upon the magnitude of b; when b = 2, τ is few order of magnitude more than that
for b = 1. We note that for b = 2 we cannot evaluate τ. Assuming b ≈ 1.99, τ for
the most dominant TL peaks may be estimated to be multiple of ≈ 100 or more.
66
Here lies the importance of the parameter b a point that will be examined in the
present paper.
Thus briefly speaking the stability of electron / hole in a trapping level
relevant to dosimetry depends upon three key parameters i.e. E, s, and b.
Unfortunately in the investigation of trapping levels in most materials including
TLDs most workers have not considered the importance of E, s, and b an equal
footing. This paper will examine the following important points that will provide
the physical basis to the entire glow curve i.e. TL in CaF2 based TLDs.
These are:i)
The number of TL peaks that constitute the entire glow curve under
consideration (RT – 400°C).
ii)
Can we indiscriminately use first order kinetics (b = 1) for all the TL
peaks as done by many workers?
iii)
Finally reliability of the evaluated values of trapping parameters that
determines the suitability of the material in terms of stability of the
relevant TL peak.
iv)
Is there something unique in terms of trap-spectroscopy of CaF2 based
as TLDs?
In order to establish these points we analyze TL curves of natural fluorite
of bluish-green shade of Indian origin as well as TLD-200, TLD-300 and TLD400. The TL data of natural fluorite is measured in our own laboratory while for
those of other TLDs we have used some of the published work of some other
workers. Two glow curves of TLD-200 and TLD-400 are from the work[2] of
Harvey et al whereas those for TLD-300 are from the work of Olko[5] and
Moyers and Nelson[6].
3.2 Experimental techniques and theory
3.2.1 Experimental
The TL of natural fluorite of Indian origin (bluish-green shade) is gently
hand crushed in an agate mortar to a uniform size of 90 - 100µm. 10 mg of the
reader annealed material is used in each measurement. The TL measurement is
performed using the commercial TL/OSL reader (model no. Risø TL/OSL reader
67
TL-DA-15). The equipment is globally accepted as a standard TL reader[2]. The
samples are irradiated at room temperature with an inbuilt beta irradiation (90Sr)
source with a dose rate of (0.084 Gy s-1). The irradiated samples are read out in
flowing nitrogen atmosphere. Clean standard glass filters (combination of Schott
UG – 11 and BG – 39) are always installed in the reader between the sample and
the photomultiplier tube (EMI 9635). These filters permit the passage of light
wavelength ranging from ~ 300 to ~ 400 nm and eliminate unwanted radiations
emitted from the heater. The duration between irradiation and TL reading is
always kept constant at about 10 min. All data is presented after subtraction of
the background emission.
3.2.2
Theoretical techniques used for analysis
The theoretical technique used for the analysis of the glow curves has
been given in detail in the recent paper[8]. The equation governing the TL
process for general order kinetics (1<b≤2) following Pagonis et al[9] can be
written as
T
æ E ö ¢ù
é E ù é s ¢¢(b - 1)
´
+
1
exp ç I (T ) = n0 s ¢¢ exp êê
÷dT ú
ò
ú
b
è kT ¢ ø úû
ë kT û êë
T0
æ b ö
-ç
÷
è b -1 ø
(3.3)
where E = activation energy or trap depth (eV),
k =Boltzmann’s constant (eV K-1),
T= absolute temperature (K),
T = T0 + bt where b =
dT
, heating rate.
dt
t = time (s),
T0= temperature at time t = 0 (K)
n0 = number of trapped electrons at time t = 0 (m-3)
b = kinetic order, a parameter with values typically between 1
and 2
s¢= effective pre-exponential factor for general order kinetics (m3(b-1)s-1)
and s² = s¢n0(b-1), an empirical parameter acting as an “effective frequency
factor” for general-order kinetics (in s-1).
68
It is to be noted that equation (2) is not valid for b = 1 and hence for b = 1
we compute the TL with b = 1.001. Equation (3.3) is routinely used in
Computerized Glow Curve Deconvolution (CGCD) of glow curves of dosimetric
materials[10].
In CGCD the criteria of goodness-of-fit is generally the low value (~ less
than 1%) of Figure Of Merit (FOM)[11-12], defined as
j stop
FOM = å
100 y j - y (x j )
j start
A
(3.4)
where,
jstart = the initial temperature in the fit region
jstop = the final temperature in the fit region
yj = the experimental TL intensity at temperature j
y(xj) = the value of the fit found at temperature j
A = the integral of the fitted glow curve
In addition we have used standard statistical tests like KolmogorovSmirnov (K-S)[13], Lilliefors[14], and Shapiro-Wilk (W)[15] to check the
goodness-of-fit. These tests are built-in in STATISTICA.
3.3 Results and Discussion
The deconvolution of TL curves of fluorite of bluish-green shade of
Indian origin recorded with heating rate (β) 1°s-1 and 5°s-1 are shown in Fig. 3.1
(a and b) while the relevant TL parameters are presented in table 3.1. The low
value of FOM shows that the fitting is excellent.
The deconvolution of three TL curves of TLD-300 are shown in Fig. 3.2
(a, b and c). The curves are those excited by γ (Cs-137), α (Am-241) and iron-ion
beams. The selection of these are based on the fact that TLD-300 response in
terms of ratios of the high temperature TL peak (~ 250°C) and the low
temperature peak (~ 150°C) are quite sensitive to the energy of the photon[1].
This provides us the opportunity to investigate a system that exhibits common TL
peaks i.e. trapping levels but of different intensities. This gives additional support
to the acceptability of our data analysis. The relevant TL parameters are shown in
table 3.2 which shows that there is a fairly good agreement in terms of trap-depth
69
of the so called peak 3 and peak 5. Trap-depth of peak 3 is ~ 1.20 to 1.30 eV
while that for peak 5 is ~ 1.60 to 1.90 eV.
CGCD of a glow curve of TLD-200 (where the low temperature peaks are
allowed for 28 days post-irradiation fading) reported [2] by Harvey et al is shown
in Fig. 3.3 and the relevant CGCD output is presented in table 3.3. It shows that
the complex glow curve consists of five highly overlapped glow peaks but
a
FOM = 0.63
%
Histogram: Var1
K-S d=.12770, p<.01 ; Lilliefors p<.01
Shapiro-Wilk W=.96651, p=.00016
90
80
70
80
60
No. of obs.
Intensity (Norm)
120
50
40
30
20
10
40
0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
X <= Category Boundary
0
25
125
225
325
425
Temperature (°C)
b
FOM = 0.51%
Histogram: Var1
K-S d=.10058, p<.10 ; Lilliefors p<.01
Shapiro-Wilk W=.96267, p=.00011
110
100
90
80
80
70
No. of obs.
Intensity (Norm)
120
60
50
40
30
20
10
40
0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
X <= Category Boundary
0
25
125
225
325
425
Temperature (°C)
Fig. 3.1: Deconvoluted TL curves of natural CaF2 of bluish-green shade.
a) for β = 1°s-1 and b) for β = 5°s-1.
○○○○ – experimental data;
── – best-fit component TL peaks;
70
▬▬ – sum of best-fit component TL peaks.
(The histogram of deviation is shown in inset)
a
120
FOM = 0.72%
Histogram: Var1
K-S d=.07034, p<.20 ; Lilliefors p<.01
Shapiro-Wilk W=.98177, p=.00406
90
70
60
No. of obs.
Intensity (Norm.)
80
50
40
30
80
20
10
0
-5
-4
-3
-2
-1
0
1
2
3
X <= Category Boundary
40
0
100
150
200
250
300
350
Temperature (°C)
b
FOM = 0.58%
Histogram: Var1
K-S d=.07474, p> .20; Lilliefors p<.05
Shapiro-Wilk W=.98251, p=.02227
100
90
80
80
70
No. of obs.
Intensity (Norm)
120
60
50
40
30
20
10
0
-3
-2
-1
0
1
2
3
X <= Category Boundary
40
0
100
200
Temperature (°C)
71
300
120
c
FOM = 0.52%
Histogram: Var1
K-S d=.08262, p> .20; Lilliefors p> .20
Shapiro-Wilk W=.97128, p=.10770
16
14
12
No. of obs.
Intensity (Norm)
18
80
10
8
6
4
2
0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
X <= Category Boundary
40
0
100
150
200
250
300
350
Temperature (°C)
Fig. 3.2: Deconvoluted TL curves of TLD-300.
a) γ (Cs-137) – irradiated Fig. 1 of Olko (1998), b) α (Am-241) –
irradiated Fig. 1 of Olko (1998) and c) iron-ion beams irradiated Fig.
6 of Moyers and Nelson (2009).
○○○○ – digitized experimental data;
── - best-fit component TL peaks;
▬▬ - sum of best-fit component TL peaks.
(The histogram of deviation is shown in inset)
72
Histogram: Var1
K-S d=.09739, p> .20; Lilliefors p> .20
Shapiro-Wilk W=.96685, p=.29910
16
FOM = 0.24%
14
12
10
No. of obs.
Intensity (Norm)
120
8
6
4
2
0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
X <= Category Boundary
80
40
0
100
150
200
250
300
Temperature (°C)
Fig. 3.3: Deconvoluted TL curves of TLD-200.
γ (Cs-137) – irradiated 28 days faded Fig. 6b of Harvey et al. (2010).
○○○○ – digitized experimental data;
── - best-fit component TL peaks;
▬▬ - sum of best-fit component TL peaks.
(The histogram of deviation is shown in inset)
120
FOM = 0.20%
Histogram: Var1
K-S d=.04543, p> .20; Lilliefors p> .20
Shapiro-Wilk W=.98177, p=.01414
100
90
70
No. of obs.
Intensity (Norm)
80
60
50
40
30
80
20
10
0
-1.5
-1.0
-0.5
0.0
0.5
1.0
X <= Category Boundary
40
0
200
250
300
350
400
Temperature (°C)
Fig.3.4:Deconvoluted TL curves of TLD-400.
γ (Cs-137) – irradiated 1 day faded Fig. 12b of Harvey et al. (2010).
○○○○ – digitized experimental data;
── - best-fit component TL peaks;
▬▬ - sum of best-fit component TL peaks.
(The histogram of deviation is shown in inset)
73
*
1.31
0.79
13.61
19.90
100.00
4.19
11.52
110.50
140.00
190.00
248.00
304.00
332.00
410.00
1.90
1.90
1.90
1.50
1.30
1.19
1.19
0.99
(eV)
E
1.08
1.00
1.00
2.60 × 1015
4.05 × 1014
4.95 × 1012
1.00
2.00
1.00
1.31
2.00
12
13
14
13
b
1.97 × 1013
9.97 × 10
2.55 × 10
4.09 × 10
1.02 × 10
(s )
-1
s
For b = 2, we have approximated b = 1.99.
12.04
(relative)
(°C)
82.00
Im
Tm
Heating rate, β = 1°Cs-1
74
5.32 × 1011 y
6.50 × 1009 y
1.10 × 1009 y
2.55 × 1006 y
2.20 × 10 y
01
1.22 × 10 y
01
2.78 d
1.70 h
(b = b*)
τ300K
434.00
350.00
326.00
270.00
208.50
148.00
118.00
100.00
(K)
Tm
6.88
9.21
100.00
19.58
13.23
0.69
2.12
12.17
(Relative)
Im
1.90
1.90
1.90
1.50
1.30
1.19
1.19
0.99
(eV)
E
13
13
14
12
7.73 × 1012
6.67 × 1014
2.98 × 1015
2.41 × 1013
1.32 × 10
6.50 × 10
9.73 × 10
9.75 × 10
(s )
-1
s
Heating rate, β = 5°Cs-1
Table 3.1: TL parameters of Natural fluorite (bluish-green shade)
1.00
1.00
1.00
1.40
1.00
2.00
1.25
1.14
b
3.41 × 1011 y
3.95 × 1009 y
8.85 × 1008 y
3.47 × 1004 y
1.66 × 1001 y
4.79 y
1.56 d
1.42 h
(b = b*)
τ300K
Fig. 2c
Fig. 2b
Fig. 2a
300 (CaF2:Tm)
Glow curves of
TLD-
*
24.07
72.82
35.03
29.52
32.63
100.00
20.87
76.82
16.56
100.00
43.05
212.50
261.00
293.50
170.50
215.60
257.85
290.00
159.50
198.00
244.70
277.00
1.90
1.90
1.50
1.30
1.90
1.89
1.20
1.20
1.90
1.60
1.60
1.30
(eV)
E
1.60
1.25
5.04 × 1017
3.71 × 1016
75
1.50
1.10
2.26 × 1014
1.72 × 10
1.13
1.41 × 1016
15
1.55
2.00
1.34 × 1017
2.62 × 10
1.74
5.89 × 1012
11
1.13
1.09 × 1016
2.00
1.30
1.20
15
13
b
1.63 × 1014
6.12 × 10
9.33 × 10
(s )
-1
s
For b = 2, we have approximated b = 1.99.
100.00
(Relative)
Im
170.00
(°C)
Tm
9.47 × 1007 y
1.31 × 1007 y
5.84 × 1002 y
1.08 y
2.15 × 1008 y
2.98 × 1007 y
1.75 × 1003 y
2.94 y
2.75 × 1008 y
1.85 × 1005 y
3.93 × 1005 y
3.36 y
(b = b*)
τ300K
Table 3.2: Thermoluminescence parameters of glow curves of TLD-300 (CaF2:Tm)
TLD-
*
70.83
16.67
238.50
281.00
1.90
1.50
1.50
1.30
1.30
(eV)
E
1.90
1.00
5.73 × 1014
2.08 × 1017
2.00
1.10
1.00
14
15
b
4.13 × 1015
4.16 × 10
3.71 × 10
(s )
-1
s
For b = 2, we have approximated b = 1.99.
13.54
100.00
176.00
212.50
23.44
(Relative)
Im
150.50
(°C)
Tm
1.27 × 1007 y
8.76 × 1003 y
1.22 × 1002 y
5.27 × 1001 y
23.96 d
(b = b*)
τ300K
Fig. 4
Glow
curves
of
TLD-400 (CaF2:Mn)
*
Im
(Relative)
37.96
84.67
100.00
E
(eV)
1.40
1.90
1.90
s
(s-1)
5.03 × 1012
5.12 × 1016
5.36 × 1015
76
For b = 2, we have approximated b = 1.99.
Tm
(°C)
287.00
307.00
341.50
1.39
1.73
1.86
b
τ300K
(b = b*)
3.42 × 1003 y
1.91 × 1008 y
3.52 × 1009 y
Table3.4: Thermoluminescence parameters of glow curves of TLD-400 (CaF2:Mn)
Fig. 3
200 (CaF2:Dy)
Glow curves of
Table 3.3: Thermoluminescence parameters of glow curves of TLD-200 (CaF2:Dy)
Table 3.5: Output of statistical Tests
Glow curves of KolmogorovLilliefors
Figure Numbers
Smirnov
(K-S) test
test
Shapiro-Wilk
test
Fig. 1a
d=0.12770, p<0.01
P<0.01
Fig. 1b
d=0.10058, p<0.10
P<0.01
Fig. 2a
d=0.07034, p<0.20
P<0.01
Fig. 2b
d=0.07474, p>0.20
P<0.05
Fig. 2c
d=0.08262, p>0.20
P>0.20
Fig. 3
d=0.09739, p>0.20
P>0.20
Fig. 4
d=0.04543, p>0.20
P>0.20
W=0.96651,
p=0.00016
W=0.96267,
p=0.00011
W=0.98177,
p=0.00406
W=0.98251,
p=0.02227
W=0.97128,
p=0.10770
W=0.96685,
p=0.29910
W=0.98177,
p=0.01414
77
(W)
100
50
TLD-400 (Cs-137 γ-rays irradiated)
0
0.5
1
1.5
2
2.5
100
50
TLD-300 (Cs-137 γ-rays irradiated)
0
0.5
1
1.5
2
2.5
100
50
TLD-300 (Am-241 α-particles irradiated)
0
0.5
1
1.5
2
2.5
D (E) (Relative)
100
50
TLD-300 (Iron ion beam irradiated)
0
0.
12..
555 100
0.5
1
1.5
2
50
2.5
TLD-200 (Cs-137 γ-rays irradiated)
0
0.5
1.0
1.5
2.0
2.5
100
50
-1
Natural CaF2 (β = 5°s )
0
0.5
1
1.5
2
2.5
100
50
-1
Natural CaF2 (β = 1°s )
0
D
(E)
(Rel
ativ
e)
0.5
1
0.5
1.5
1
E 1.5
(eV)
2
2
2.5
2.5
Fig. 3.5: Plot of relative trap-density of different trapping levels in the seven
glow curves of CaF2 based TLDs.
78
100
50
EIR TLD-200 (β-rays irradiated)
0
D (E)
0.5
1
1.5
2
2.5
100
50
EVHR TLD-200 (β-rays irradiated)
0.
12..
0
555
0.5
1
1.5
2
2.5
100
50
TLD-200 (Cs-137 γ-rays irradiated)
D
(E)
(Rel
ativ
e)
0
0.5
0.5
1.0
1
1.5
2.0
E 1.5
(eV)
2.5
2
2.5
Fig. 3.6
Fig. 3.6: Trap spectroscopic comparison of TLD-200
characterized by only three trapping levels of depth 1.30, 1.50 and 1.90 eV. That
more than one TL peaks can have the same activated energy was argued by
Gartia [16] and substantiated in subsequent works [17-18]. This concept of more
than one TL peak having same trap-depth is true for natural fluorite as well as
TLD-200 and TLD-300 as well as TLD-400 (Fig. 3.4 and table 3.4). The
statistical outputs of the best-fit analysis of the present work are presented in
table 3.5.
The spectroscopy of traps (plot of density of trapping levels in energy
scale) as obtained by our analysis of seven glow curves of CaF2 based TLDs is
shown in Fig. 3.5. The data clearly shows the uniqueness of the common feature
of the system.
For the sake of demonstration of the validity of our analysis we shall
discuss briefly a specific case of TLD-200 that has been critically examined by
Yazici et al [19]. Their analysis has not led to any definite answer to the values of
79
trap depths except that for a so called TL peak no. 4. The values of trap-depths
obtained by initial rise (IR), various heating rates (VHR), peak shape (PS) and
computerized glow curve deconvolution (CGCD) for other TL peaks could not be
linked. Such failure is often encountered by various workers leading to
pessimistic view on TL data analysis. The typical recent one is that viewed by
Aitsalo et al [20], who opined that deconvolution is not a scientifically sound
method of interpretation and analysis of TL curves. Our analysis clearly
demonstrates this. Even under the extreme pessimistic view as observed in table
3.3 of Yazici et al [19], experienced workers can use the table for meaningful
interpretation. The table shows the existence of as many as nine peaks with trapdepths of 1.08, 1.08, 1.12, 1.16, 1.31, 1.32, 1.44, 1.73 and 1.50 eV respectively as
revealed by IR. These traps are very much present in TLD-200 as per our analysis
(Table 3.3). We show the trap spectroscopy of TLD-200 based on our present
result and that reported by Yazici et al [19] where we compare EIR, EVHR of
Yazici et al19 and our analysis. The comparison is shown in Fig.3.6. The
abnormal value of ECGCD obtained by Yazici et al19 is probably because of
misjudgment in accepting goodness-of-fit. This aspect we have already discussed.
Based on the entire data we would conclude the followings:i)
TL is a unique tool capable of establishing the spectroscopy of traps
relevant to TLDs. These trapping levels have trap-depths 1.20, 1.30,
1.50 and 1.90 eV in case of CaF2 based TLD. The only difference
being that the relative densities of traps occupancy for natural
fluorite, TLD-200, TLD-300 and TLD-400 are different. Sometimes
a particular trap may totally be missing.
ii)
In TLD-200 (CaF2: Dy), traps relevant to dosimetry as per our
evaluation have depths 1.30, 1.50 and 1.90 eV that give rise to five
TL peaks.
iii)
TLD-400 (CaF2: Mn) is characterized by two traps of depths 1.40
and 1.90 eV but manifested in the form of three TL peaks.
iv)
In all certainly we conclude that indiscriminate use of first order TL
peaks for all the peaks is not correct.
80
v)
The last but not the least conclusion is that this study provides a
solid physical basis for use of TLD-300 in mixed-field dosimetry; an
area of high-end use of TLDs.
81
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[2]
Harvey J A, Haverl N P & Kearfott K J, Characterization of the glowpeak fading properties of six common Thermoluminescent materials, Appl
Radiat Isotop 68, 1988-2000, (2010).
[3]
S.W.S.McKeever , Thermoluminescence of Solids (Cambridge University
Press, New York), (1985).
[4]
L.S.Lovedy, & R.K. Gartia, A new method of determination of trapping
parameters of glow peaks relevant to dosimetry and dating from their
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