Determination of thermoluminescence kinetic parameters of thulium doped lithium calcium borate

Radiation Measurements 46 (2011) 1026e1032

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Determination of thermoluminescence kinetic parameters of thulium doped lithium calcium borate M.T. Jose a, *, S.R. Anishia a, b, O. Annalakshmi a, V. Ramasamy a, b a b

Radiological Safety Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, Tamil Nadu, India Department of Physics, Annamalai University, Chidambaram, Tamil Nadu, India

a r t i c l e i n f o

a b s t r a c t

Article history: Received 12 February 2011 Received in revised form 30 July 2011 Accepted 1 August 2011

For the first time kinetic parameters of thulium doped Lithium calcium borate (LCB) Thermoluminescence (TL) material are reported here. Irradiated LCB:Tm3þ powder has revealed two intense TL glow peaks one at 510 (peak 1) and the other at 660 K (peak 2). Activation energy (E), frequency factor (s) and order of kinetics (b) of these peaks were determined by various heating rate (VHR), initial rise (IR), and peak shape (PS) methods. The trap depth and frequency factor determined for peaks 1 and 2 of LCB:Tm phosphor using VHR and IR methods are in good agreement. The average activation energy of peaks 1 and 2 obtained by these methods is 1.62 and 1.91 eV respectively. The frequency factors of peaks 1 and 2 are in the range of 1013e16 and 1012e14 sec1 respectively. The E and s values estimated using the glow peak shape dependent parameters are relatively less compared to the values obtained from other methods. The large difference in these values is due to the complex nature of the glow curves. The order of the kinetics process for complex glow curve peaks could not be assigned on the basis of shape parameters alone but Tm response on absorbed dose is to be considered for final confirmation. Glow peaks 1 and 2 of LCB:Tm3þ obey first and general order kinetics respectively. Ó 2011 Elsevier Ltd. All rights reserved.

Keywords: Lithium calcium borate Thermoluminescence Kinetic parameters

1. Introduction Studies on radiation induced defects in insulating materials have been interesting over the last few decades. Thermoluminescence (TL) is one such radiation induced defect related process in crystalline materials. In TL, while heating the irradiated material, energy stored in the crystal is released with the emission of light and the intensity of the emitted light as a function of temperature, forms a glow curve. The position, shape, and intensities of the glow peaks are related to the properties of the trapping states responsible for the TL (Azorin, 1986). The main applications of these materials are in radiation dosimetry for personnel and environmental monitoring. Many sensitive synthetic materials are developed for this purpose. Borate based TL materials are synthesized and studied because of their tissue equivalent absorption coefficient, low cost, thermal stability and neutron sensitivity (Kitis et al., 2000). Improvement in the TL characteristics of borates was reported for recently developed rare earth doped mixed lithium calcium borates (LCBs) (Anishia et al., 2010; Jiang et al., 2008).

* Corresponding author. Tel.: þ91 44 27480352; fax: þ91 44 27480235. E-mail address: [email protected] (M.T. Jose). 1350-4487/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.radmeas.2011.08.001

The dosimetric properties of TL materials mainly depend on the kinetic parameters of its glow peak. Kinetic parameters give valuable information about mechanism responsible for the TL emission in material. Reliable dosimetric studies of any TL material include a good knowledge of its kinetic parameters as well. For example, TL intensity fading of irradiated material on storage depends on the position of the trapping levels within the forbidden gap. Important TL parameters are trap depth (E) or activation energy which is the thermal energy required to liberate the trapped electrons and holes, frequency factor (s) and the order of kinetics (b). Activation energy (E) and frequency factor (s) were determined by Variable Heating Rate (VHR), Initial Rise (IR), Isothermal Decay (ID), and Peak Shape (PS) methods. The order of kinetics (b) is generally calculated by PS methods from the peak shape parameters. This paper discusses the kinetic parameters of Tm-doped LiCaBO3 phosphor synthesized by the high temperature solid state diffusion technique. In irradiated LiCaBO3:Tm3þ phosphor two major dosimetric glow peaks were observed one at 510 K (peak 1) and another at 660 K (peak 2) along with some satellite peaks. TL sensitivity of these major peaks to gamma radiation is about 8 times that of TLD-100 (Anishia et al., 2010). For the first time the kinetic parameters of these peaks were calculated by different methods and the results are presented in this paper.

M.T. Jose et al. / Radiation Measurements 46 (2011) 1026e1032

2. Experimental details

3. Results

Thulium doped LCB phosphor powder has been prepared by solid state diffusion reaction method. For the synthesis, the analytical grade lithium carbonate, calcium carbonate, magnesium oxide, boric acid, silver nitrate, and rare earth oxides were used as raw materials. Before the characterization studies the powder was ground in an agate mortar and sieved to get uniform grains of 53e150 mm sizes. TL measurements are carried out using the Riso make, TL/OSL reader (model TL/OSL-DA-20). For irradiation, a gamma chamber procured from Board of Radiation and Isotope Technology (BRIT), Mumbai, India, containing a 60Co source of strength 3.8 TBq at dose rate of 270 Gy/h was employed. All sample irradiations were carried out at room temperature. About 2 g of uniform grain size powder packed in a paper was loaded in a small 3 mm thick walled cylindrical chamber made up of Perspex to have the electronic equilibrium condition during irradiation inside the gamma chamber. For each measurement known amount of powder (about 10 mg) has been taken and spread as a uniform thin layer over the heating element for good thermal contact. Kinetic parameters of TL glow peaks have been evaluated using three different methods by the procedure explained below. (a) Variable Heating Rates (VHR) method: TL glow curves of irradiated LCB:Tm3þ samples were recorded at different linear heating rates between 0.1 and 10 K s1 (Fig. 1). Trap depth (E) and frequency factor (s) of peaks at 510 and 660 K were calculated using different sets of heating rates and their corresponding peak maximum temperature (Tm). By graphical method E and s values are calculated from the linear plot of ln(b/T2m) versus 1/Tm. From the slope of the linear graph one can obtain the activation energy. (b) Initial Rise (IR) method: This method is based on the assumption that in the initial rising part of the TL glow curve T  Tm, where Tm is the maximum peak temperature, the rate of change of trapped carrier population is negligible. TL intensity I is proportional to exp(E/kT) and the plot of ln I(T) versus 1/T gave straight line. From the slope of the straight line E/k, the activation energy E can be obtained. Irradiated LCB:Tm3þ phosphor was pre-heated at 473 and 545 K to remove the lower temperature of peaks 1 and 2 respectively. Glow curves are acquired for these samples by heating up to 773 K at linear heating rate of 5 K s1 (c) Peak Shape (PS) method: The order of kinetics, frequency factor and activation energies of the glow peaks 1 and 2 of LCB:Tm3þ are determined from the shape of the glow curves acquired for gamma irradiated sample (dose of 128 Gy) at linear heating rates from 0.1 to 10 K s1.

3.1. Kinetic parameters

b d

TL Intensity (a.u.)

400 c

b d c ef g

0 100

150

200

250

300

350

(1)

Booth and Bohun working independently have used two different heating rates b1 and b2 and solved equation (1) to evaluate the trap depth E and frequency factor s. The expression for E given in equation (2) is based on the experimental variation of Tm with the linear heating rates b.

E ¼

  b KTm1 Tm2 ln 1 ðTm2 =Tm1 Þ2 b2 Tm1  Tm2

(2)

Here Tm1 and Tm2 are temperatures corresponding to the maximum TL intensities for heating rates b1 and b2, respectively. The value of frequency factor s can be evaluated by substituting E in equation (3).

("

s ¼

E exp k

Tm2 ln

2 Tm2

b2

 Tm1 ln

2 Tm1

#,

b1

)

ðTm1  Tm2 Þ

(3)

The trap depth and frequency factors of peaks 1 and 2, calculated using expressions (2) and (3) for different pairs of heating rates b1 and b2 (0.1e10 K s1) and their corresponding peak maximum temperatures (Tm) are given in Table 1. The calculated values of trap depth for peak 1 varied from 1.53 to 1.75 eV with the mean value at 1.63 eV. The frequency factor for peak 1 is found to be in the range of 1014e16 s1. The activation energy of peak 2 varied from 1.72 to 2.04 eV with the average value at 1.88 eV and s in the range of 1012e15 s1. Hoogenstraaten (1958) has used equation (1) and several heating rates to evaluate E graphically, based on the position of Tm with heating rate b. A linear relation is obtained between ln(T2m/b) and 1/kTm as follows:


 2 ln Tm =b ¼ lnðE=skÞ þ E=kTm

b1 (K s1)

100

50



2 bE=kTm ¼ s expðE=kTm Þ

(4)

Table 1 Experimentally calculated activation energy and frequency factor of peaks at 510 and 660 K in LCB:Tm by various heating rate methods.

f

a

200




e g

300

3.1.1. Variable heating rate method The heating rate is a fundamental experimental variable in TL measurements. Variable heating rate methods are based on the shift of the glow peak temperature to higher temperatures with heating rate. The position of the glow peak temperature Tm is obtained by means of the derivative of RandalleWilkins equation with respect to temperature T and equating it to zero (Azorin, 1986), and is given as

The plot of ln(T2m/b) versus 1/kTm should give a straight line with slope E and intercept ln(E/sk). Extrapolation to 1/kTm ¼ 0 gives ln(E/ sk) from which s can be calculated using the value of E obtained from the slope. Fig. 2a and b shows the plot of ln(T2m/b) versus 1/kTm for peaks 1 and 2 respectively. Most of the points corresponding to

a

500

1027

400

450

500

o

Temperature ( C) Fig. 1. TL glow curves of gamma irradiated LCB:Tm phosphor at various heating rates: (a) 0.1; (b) 0.3; (c) 0.6; (d) 1; (e) 3; (f) 6 and (g) 10 K s1 (Gamma dose e 128 Gy).

3 6 10 3 6 0.6 6 3 Average

b2 (K s1) 0.1 0.3 0.6 1 1 0.1 0.6 0.6

Peak 1 at 510 K

Peak 2 at 660 K

E (eV)

s (s1)

E (eV)

s (s1)

1.67 1.62 1.75 1.58 1.53 1.74 1.55 1.60

1.26Eþ16 3.41Eþ15 8.40Eþ16 1.40Eþ15 4.11Eþ14 7.37Eþ16 7.43Eþ14 2.35Eþ15

1.82 2.04 1.99 1.72 1.94 1.97 1.85 1.68

2.25Eþ13 1.54Eþ15 7.92Eþ14 3.33Eþ12 2.30Eþ14 4.83Eþ14 4.55Eþ13 1.53Eþ12

1.63  0.08

2.23Eþ16

1.88  0.13

3.90Eþ14

1028

M.T. Jose et al. / Radiation Measurements 46 (2011) 1026e1032

low and high heating rates fall on the fitted line. In our TL measurements, sample heating is performed in a controlled manner by placing it over a metallic strip. In contact heating the temperature of the emitting surface of sample differs from the heater-strip. The difference in the temperature between the sample and the heater-strip is called temperature lag. Due to slow heating temperature lag will be negligible at low linear heating rates. Temperature lag is further minimized by using fewer amounts (w10 mg) of small powder grains of 53e150 mm size for measurements. It can be inferred from Fig. 2a and b that the data points corresponding to the lowest and highest heating rates 0.1 and 10 K s1 fall on the fitting straight line, which means that the temperature lag appears to be negligible in our measurements. In the graph, slope equals to E and intercept value equals to ln(E/ sk). Trap depth and frequency factor of peak 1 (510 K) estimated from Fig. 2a are found to be at 1.69 eV and 1.86  1016 s1 respectively. By following a similar procedure E and s values are calculated for peak 2 (660 K) from Fig. 2b and are found to be 1.95 eV and 7.28  1014 s1 respectively. 3.1.2. Initial rise method Initial rise method first proposed by Garlick and Gibson (1948) is the simplest method to calculate the trap depth of the TL materials.

a

15

14

2

ln(Tm /β)

12

where C is the constant, I(T) is the TL intensity at any temperature T, when the sample is heated at a linear heating rate of b ¼ dT/dt, E is the thermal activation energy and k is Boltzmann’s constant. A plot of ln I(T) versus 1/T over the initial rise region gives a straight line and from the slope of the straight line E/k, activation energy E is calculated. The important requirement for this initial rise analysis is that the concentration of the trapped carriers remains approximately constant at any instant. But beyond the cut-off temperature this assumption becomes invalid. However, the initial rise technique can be used only when the glow peak is well defined and is clearly separated from the other peaks. To find frequency factor (s) value, use the intercept I obtained from the plot of ln I(T) versus 1/T graph for the initial rise part. The general order expression for s is given below (Rawat et al., 2009).

s ¼ antilogðI  lnðAÞÞ

10 22.5

23.0

23.5

24.0

24.5

25.0

1/kTm

b

(5)

(6)

where b is the order of kinetics, N is the total concentration of the traps, n0 is the initial concentration of trapped electrons, I is intercept of the initial rise plot and A is the area under the TL peak. It can be assumed that n0/N ¼ 1, when all traps are filled, i.e., the TL intensity has reached saturation. However for first order kinetics process, b ¼ 1, and hence the expression for s reduces to

11

Slope = 1.953 Intercept = -23.332

14

13

2

ln(Tm /β)

IðTÞ ¼ C expðE=kTÞ

s ¼ antilogðI  ln A  ðb  1Þlnðn0 =NÞÞ slope =1.685 Intercept = -27.576

13

15

The initial rise method is based on the assumptions, that in the initial rising part of the TL curve where T  Tm, the rate of change of trapped carriers’ population is negligible. This assumption is valid for temperatures up to a cut-off temperature, corresponding to an intensity which is smaller than 10e15% of the maximum intensity (McKeever, 1985). The TL intensity I is proportional to exp(E/kT), assuming the frequency factor to remain the same and there is no overlapping of glow peaks, i.e.

12

11

(7)

Thus the determination of the frequency factor value from Eq. (7) is very simple and it requires the intercept value of initial rise plot and area under the glow peak, both values can be obtained experimentally. This initial rise technique is applied only when the glow curve is well defined and for clearly separated glow peaks. It is very difficult to identify a material which has clean and clear glow peaks. So thermal cleaning has to be done to the sample before using the initial rise method. This cleaning can remove all the satellite or embedded peaks. For recording the TL, LCB:Tm samples have been irradiated near to the saturation dose of peak 2 (gamma dose ¼ 64 Gy). The low temperature peaks are cleared before recording the initial rise portion by preheating the samples at 473 and 545 K for peaks 1 and 2 respectively. The ln I(T) versus 1/ T graph for peaks 1 and 2 is given in Fig. 3a and b. The activation energy of peaks at 510 and 660 K has been calculated from the slope of the straight line graph. The frequency factor has been calculated using Eq. (7) where the antilog of the intercept value of initial rise plot and area under the peak are used. The kinetic parameter values obtained for peaks 1 and 2 are given in Table 2. The activation energies of peaks 1 and 2 are 1.53 and 1.90 eV respectively. The frequency factor s of peaks 1 and 2 is 2.90  1013 s1 and 7.07  1012 s1 respectively. E and s values of peaks 1 & 2 obtained by IR and VHR methods almost match.

10 17.5

18.0

18.5

19.0

19.5

20.0

1/kTm Fig. 2. The linear relation of ln(T2m/b) versus 1/kTm for (a) peak 1 (510 K) of LCB:Tm phosphor and (b) peak 2 (660 K) of LCB:Tm phosphor.

3.1.3. Peak shape method The Peak Shape (PS) method is generally called as Chen’s (1969) method, which is used to determine the kinetic parameters of the glow peak of the TL materials. This method is mainly based on the temperatures Tm, T1 and T2, where Tm is the peak temperature,

M.T. Jose et al. / Radiation Measurements 46 (2011) 1026e1032

a

process, according to the value of the geometric factor (mg). Another parameter proposed by Balarin gives the kinetic order as a function of the parameter

Slope = -17622 Intercept = 46.437

10.6 10.4

g ¼ d=s ¼

10.2

ln(I)

10.0 9.8 9.6 9.4 9.2 9.0 0.00202

0.00204

0.00206

0.00208

0.00210

0.00212

1/T (K)

b

10.2 Slope = -21560 Intercept = 45.87

10.0 9.8 9.6

ln(I)

9.4 9.2 9.0 8.8 8.6 8.4 8.2 0.00166

0.00168

0.00170

0.00172

0.00174

0.00176

1/T (K) Fig. 3. Initial rise plot of ln(I) versus 1/T for (a) 510 K peak in LCB:Tm and (b) 660 K peak in LCB:Tm.

while T1 and T2 are temperatures at half the intensity on the ascending and descending parts of the glow peak respectively. To determine the kinetic parameters the following shape parameters are to be determined: the total half intensity width u ¼ T2  T1, the high temperature half width d ¼ T2  Tm and the low temperature half width s ¼ Tm  T1 (Garlick and Gibson, 1948). The peak shape method is mainly used to calculate the order of kinetics. Order of kinetics can be evaluated from the symmetry factor (mg) of the glow peak. mg is calculated using Eq. (8) from the known peak shape parameters d and u.

mg ¼ d=u ¼

T2  Tm T2  T1

(8)

Order of the kinetics depends on the glow peak shape. The value of mg for first and second order kinetics is 0.42 and 0.52 respectively. Chen has provided a plot which gives order of kinetics of the TL

Table 2 Activation energy and frequency factor evaluated for peaks 1& 2 of LCB:Tm phosphor by different methods. Methods

VHR (Graph) VHR (calculation) IR

Peak 1 (510 K)

1029

Peak 2 (660 K)

E (eV)

s (s1)

E (eV)

s (s1)

1.69 1.63 1.53

1.86  1016 2.23  1016 2.90  1013

1.95 1.88 1.9

7.28  1014 3.90  1014 7.07  1012

T2  Tm Tm  T1

(9)

For the first order kinetics the Balarin parameter (g) ranges from 0.7 to 0.8 and for the second order kinetics g varies from 1.05 to 1.20 (Balarin, 1975). Generally in the first order, the process of retrapping is negligible and the trap should be situated very close to the luminescent centre. The characteristics of the second order peak are wider and it is more symmetric than the first order peak. For a fixed heating rate, in first order kinetics both peak temperature and shape are independent of the initial trapped electron concentration but in second order the peak temperature and shape are strongly dependent on initial trapped charge concentration. The order of kinetics for peak 1 and peak 2 in LCB:Tm3þ phosphor has been determined by using the peak shape method. As a first step, glow curves at different heating rates are recorded for the gamma irradiated samples (dose ¼ 128 Gy). The peak shape parameters s, d, and u at each heating rate were determined from the temperatures T1, T2 and Tm. The symmetric factor (mg) and Balarin parameter (g) calculated for peaks 1 and 2 in LCB:Tm phosphor at different heating rates are listed in Table 3. The mean value of mg and g for peak 1 was 0.54  0.02 and 1.19  0.10 respectively and these parameters predicate a second order kinetic property. For peak 2, the mean value of mg and g was 0.43  0.01 and 0.76  0.04 respectively and it predicates a first order kinetics. TL glow curves of LCB:Tm3þ powder exposed to different gamma doses are shown in Fig. 4. TL intensities are not in same scale for comparison and these glow curves are given to illustrate the changes in shape and peak temperature as a function of dose. In the case of peak 1, no significant shift in the peak temperature is observed which means that peak 1 obeys near first order kinetics which contradicts the second order kinetics predicted from the peak shape parameters mg and g. Similarly mg and g predict first order kinetics for peak 2 (660 K) but its glow curve showed significant shift in peak temperature with gamma dose (ref. Fig. 4) which means that its order of kinetics is not one. The reason for the contradicting result is essentially due to the complex nature of the glow curve. Peaks 1 & 2 of LCB:Tm are not single well isolated peaks, but have shoulders on both sides of the main peak. Because of the presence of these shoulder peaks, depending on their intensity and position, half width parameters d, s and u can get enhanced and in turn may introduce error in the shape parameters mg and g. Hence, for complex glow curves the behavior of Tm as a function of dose can be used as good indicator to determine the order of kinetics. On above argument it is appropriate to assign first and second order kinetics process for peaks 1 and 2 respectively. Therefore, in complex glow curves having satellite peaks, Tm characteristic on radiation dose also may be used in place of peak shape parameters for determining the order of kinetics in TL materials. Table 3 Experimental peak parameters at various heating rates of 510 and 660 K peaks in LCB:Tm.

b (K s1) Peak 1 at 510 K 0.1 0.3 1 3 10 Average

Peak 2 at 660 K

Tm (K) u

d

s

mg

g

Tm (K) u

d

s

mg

g

464 476 489 503 516

42 51 46 49 51

41 42 36 39 44

0.51 0.55 0.56 0.56 0.54

1.02 1.21 1.28 1.26 1.16

589 609 626 647 663

36 38 40 44 48

46 51 53 57 64

0.44 0.43 0.43 0.44 0.43

0.78 0.75 0.76 0.77 0.75

83 93 82 88 95

0.54 1.19

82 87 93 101 112

0.43 0.76

1030

M.T. Jose et al. / Radiation Measurements 46 (2011) 1026e1032 Table 5 Half width parameters d, s and u calculated for peak 1 and peak 2 in LCB:Tm phosphor at various heating rates from average E values obtained by VHR and IR methods (for Peak 1, E ¼ 1.61 eV & b ¼ 1 and for peak 2, E ¼ 1.91 eV & b ¼ 2).

f

120

TL Intensity (a.u.)

d e

e

a

d

f

e

a

a

40

f

d

s

u

Tm (K)

d

s

u

464 476 489 503 516

11.3 11.8 12.5 13.2 13.9

16.1 17.0 17.9 18.9 19.8

27.7 29.1 30.7 32.4 34.0

589 609 626 647 663

26.7 28.6 30.2 32.2 33.8

25.6 27.3 28.8 30.6 32.1

52.6 56.2 59.3 63.2 66.3

c

c

0 100

200

300

400

500

0

Temperature ( C) Fig. 4. TL glow curves of LCB:Tm at different gamma doses: (a) 3.7 Gy; (b) 22.5 Gy; (c) 75 Gy; (d) 675 Gy; (e) 1175 Gy; (f) 17,625 Gy (intensities are not in same scale for comparison, heating rate e 10 K s1).

The activation energy (E) can be calculated by the general expressions formulated by Chen (1984), valid for any kinetics, and is given by:

a

Tm (K) 0.1 0.3 1 3 10

Peak 2 at 660 K

b b

2 kTm

Peak 1 at 510 K

d

80

E ¼ ca

b (K s1)

 ba 2kTm

(10)

where a stands for s, d and u respectively. ca and ba are obtained using the expressions given below:



 cs ¼ 1:51 þ 3:0 mg  0:42 ; bs ¼ 1:58 þ 4:2 mg  0:42
 cd ¼ 0:976 þ 7:3 mg  0:42 ; bd ¼ 0
 cu ¼ 2:52 þ 10:2 mg  0:42 ; bu ¼ 1 Activation energy E of peaks 1& 2 in LCB:Tm3þ phosphor is calculated using equation (10) for different heating rates from 0.1 to 10 K s1. For the calculation, first and second order kinetics equations (mg ¼ 0.42 & 0.52) are applied for peaks 1 and 2 respectively. The mean Ed, Es and Eu values calculated for different b values are given in Table 4. The Ed, Es and Eu obtained for peak 1 are 0.45  0.01, 0.60  0.03 and 0.51  0.01 eV respectively. The average values of Ed, Es and Eu obtained for peak 2 are 1.42  0.07, 0.93  0.04 and 1.16  0.05 respectively. The inconsistency in E values with different half width parameters is due to error in s, d, and u values imparted by shoulder peaks. Activation energy decreases with increase in s, d, and u values. For peak 1, Ed, is the lowest that indicates the shoulder peak at upper side may have a dominant influence on the glow curve shape. Similarly for peak 2, Es is the lowest which indicates that the presence of the shoulder at the rising part of the glow peak has a dominant influence on the glow curve shape. Half width shape parameters d, s and u of the two peaks were calculated for different heating rates from Eq. (10), using the experimental Tm values and mean E values obtained from VHR and IR methods. The results are tabulated in Table 5. These new d, s and u values and the experimentally obtained Tm may be

helpful in the deconvolution of complex glow curves by reconstructing the main and satellite peaks. No systematic change or large variations in activation energies are observed with heating rates suggesting that temperature lag between the samples and heating element is not significant up to 10 K s1. The ratios of T2m/u, T2m/d and T2m/s are given in Table 6 against heating rates appear to have rather less scattered distribution. It is also expected that the ratio T2m/a should be constant for all used heating rates for reduced temperature lag (Montalvo et al., 2004). The distribution of these ratios again confirms the good thermal contact of the sample with heating element during measurements. The frequency factor ‘s’ can be obtained using the following general expression by substituting the E value;

s ¼

bE expðE=kTm Þ½1 þ ðb  1Þ2kTm =E1 2 kTm

(11)

where ‘b’ is order of kinetics and b is the linear heating rate. In this expression ‘s’ depends on Tm and in second order kinetics Tm depends on the absorbed dose (Chen, 1969). Hence in the case of second order kinetics instead of s, another quantity s00 called the pre-exponential factor which is a dose dependant quantity is obtained. s00 ¼ sn0/N where n0 is concentration of trapped electrons and N is concentration of traps. The pre-exponential factor s00 is a constant for a given dose, but varies with change in the absorbed dose, i.e. with n0. In the special case when n0 ¼ N, i.e., the dose of saturation, s00 coincides with s. Frequency factor calculated using Eq. (11) for peaks 1 and 2 of LCB:Tm irradiated to 128 Gy is given in Table 4. ‘s’ value of peaks 1 and 2 is 4.37  105 s1 and 7.47  104 s1 respectively. First and second order of kinetics is applied for peaks 1 and 2 respectively. At saturation dose the preexponential factor s00 coincides with the frequency factor s for the second order peak 2. 3.2. Heating rate effects on glow curve It is experimentally observed that the maximum peak temperature varies as a function of linear heating rate of the sample. At a low heating rate, the glow peak occurs at the lower temperature and as b increases it has shifted toward higher temperature. The variation of Tm with different heating rates from 0.1 to 10 K s1 for peaks 1 and 2 in LCB:Tm is shown in Fig. 5. Tm has shifted to higher temperatures as a function of linear heating rate. For both peaks, Tm showed sharp increase at low heating rates up to 3 K s1 and

Table 4 Experimentally evaluated activation energy and frequency factor of 510 and 660 K peaks in LCB:Tm by PS method (irradiation dose ¼ 128 Gy). Peak 1 at 510 K

Peak 2 at 660 K 5

Ed (eV)

Es (eV)

Eu (eV)

s 10 s

0.45  0.01

0.60  0.03

0.51  0.01

43.7

1

Ed (eV)

Es (eV)

Eu (eV)

s 104 s1

1.42  0.07

0.93  0.04

1.16  0.05

7.47

M.T. Jose et al. / Radiation Measurements 46 (2011) 1026e1032 Table 6 Experimental value of T2m/a at various heating rates for 510 and 660 K peaks in LCB:Tm.

b (K s1)

Peak 1 at 510 K T2m/u

T2m/d

T2m/s

T2m/u

T2m/d

T2m/s

0.1 0.3 1 3 10

2594 2436 2916 2875 2803

5126 4943 5198 5163 5221

5251 5395 6642 6487 6051

4231 4167 4214 4145 3925

9637 9760 9797 9514 9158

7542 7272 7394 7344 6868

Average

2725

5130

5965

4136

9573

7284

110

b

FWHM

Peak 2 at 660 K

a steady increase was seen at higher heating rates. However, shape of the glow curve has not changed with heating rate. A similar behavior of Tm with heating rates has been reported for other TL materials also (Kitis et al., 1993). The shift of Tm versus heating rate can be empirically explained by the following way. At the low heating rate b1, the time spent by the phosphor at a temperature T1, is long enough so that an amount of thermal release of electrons depending on half life at this temperature could take place. As heating rate increases to b2 > b1 the time spent at same temperature T1 decreases and therefore the thermal release of electrons is also decreased. Then a higher temperature T2 is needed for the same amount of thermal release to take place at b2. In this way the whole glow peak is shifted to higher temperatures as heating rate increases in a manner depending on the half life and time spent at each temperature. The behavior of the full width at half maximum (FWHM) of peaks 1 and 2 in LCB:Tm as a function of linear heating rate is shown in Fig. 6. FWHM of peak 1 has a slow increase with b value but for peak 2 a rapid increase was seen above 1 K s1. Kitis et al. (1993) studied the heating rate effects on the TL glow peaks of quartz, TLD-700 and natural CaF2 and reported a similar behavior, but the difference in variation is very small for Tm shifting and it is large in the case of FWHM. The normalized integral area and height of peaks 1 and 2 versus heating rates are plotted in Fig. 7.The integral area of peak 2 was the area under the peak in the temperature region from 570 to 720 K. As a general trend the TL intensity decreases as a function of linear heating rate. For peak 2, integral area showed a sharp decrease of 20% from 0.1 to 0.6 K s1, then an increase at 1 K s1 and a slow reduction of 10% at 10 K s1. Integral area of peak 1 is not included due to the complex nature of the peak. The variation of peak height

100 a

90

80 0

2

4

6

8

10

-1

Heating rate (Ks ) Fig. 6. FWHM of the glow peaks as a function of heating rates; (a) peak 1 and (b) peak 2 in LCB:Tm phosphor.

is similar to that of integral area and it was prominent in peak 2 than peak 1. Height of peak 2 is reduced by 40% and peak 1 by 25% at the heating rate of 10 K s1. According to Gorbics et al. (1968) both integral and peak height versus heating rate have decreased because of the thermal quenching. Thermal quenching affects the efficiency of the glow curve with increasing heating rate. The thermal quenching effect is more in peak 2 and its peak temperature occurs at 660 K which is 150 K above peak 1. Taylor and Lilley (1982) have proposed the intensity reduction for peak 5 of LiF occurring probably due to the trapped species (fluorine atoms according to them) thermally released from their traps before there is time for peak 5 traps to be formed (MgeV dipole clusters). Different authors have given detailed explanations for the variation in integral and peak height TL intensity with heating rate by considering the influence for more than one situation (Ogundare et al., 2005; Gokce et al., 2009). Thermal quenching effect and cluster formation of impurities with heating rate can be taken as a possible situation for these variations. Some authors explained this phenomenon in terms of thermal quenching and clustering. Cluster formation has been reported in host materials doped with rare earth impurities (Holsa et al., 2004; Karali

1.0

700 b

Normolised TL intensity

Maximum peak temperature (K)

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650

600

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c

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5

6

7

8

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Heating rate (Ks ) Fig. 5. The plot between the maximum peak temperatures (Tm) as a function of linear heating rates: (a) peak 1 and (b) peak 2 of LCB:Tm phosphor.

0

2

4

6

8

10

Heating rate (Ks-1) Fig. 7. The normalized TL intensity as a function of linear heating rate in LCB:Tm phosphor: (a) integral area of peak 2, (b) height of peak 1 and (c) height of peak 2.

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et al., 1998). The cluster formation can be a simple or a large one depending on the heating rate or the thermal history. Ogundare et al. reported that, at some heating rates enhancement of TL due to cluster formation is greater than the total effect of reduction by thermal quenching effect on TL. 4. Discussion The activation energies and frequency factors determined for peaks 1 and 2 of LCB:Tm material using VHR and IR methods have been tabulated in Table 2. Trap depth and frequency factor calculated by VHR (graphical and calculation) and IR methods which are independent of glow peak shape or kinetic orders have given matching values for both peaks. The mean trap depth and frequency factor of peak 1 and peak 2 are 1.61 & 1.91 eV and 1.36  1016 & 3.75  1014 s1 respectively. E and s calculated by PS method showed relatively lesser values than other two methods i.e. in PS method trap depth of peaks 1 and 2 is 1/3rd and 2/3rd of the values obtained by other methods. The main reason for lower values in PS method is due to the complex nature of the glow curve. As mentioned earlier peaks at 510 and 660 K have satellite peaks at rising and lowering sides of the glow curve. These satellite peaks increase the width of the main peaks and this has resulted in the increase of half width parameters d, s and u. Activation energy decreases with increase in s, d, and u value and it is evidently seen in our lower E values. Complex nature of the peaks has introduced error in the determination of order of kinetics also, i.e., b evaluated from peak shape parameters mg and g for peak 1 (second order) and peak 2 (first order) is not in support with the response of Tm with absorbed dose. In the case of complex glow curves, for the determination of order of kinetics, Tm response to dose is a good approximation to predict particularly the first order kinetics where no shift of Tm as a function of dose. PS method is not suitable for the evaluation of kinetic parameters in complex glow curves without deconvolution of the curves. Sunta et al. discussed the limitations of peak fitting and peak shape methods for the determination of activation energy of thermoluminescence glow peaks. The failure of the peak shape and peak fitting methods is not because of the improper application of the methods, but is for reasons inherent in the shape of the peak itself. High values of d, s and u coupled with low value of Tm at n0/N z 1 lead to a lower value of E (Sunta et al., 1999). 5. Conclusion The trap depth and frequency factor determined for the peaks at 510 (peak 1) and 660 K (peak 2) of LCB:Tm phosphor using the variable heating rate and initial rise methods are in good agreement. The mean trap depth of peak 1 and peak 2 obtained by these methods is 1.61 eV and 1.91 eV respectively. The frequency factor of peaks 1 & 2 is in the range of 1013e16 and 1012e14 s1 respectively. VHR and IR methods are independent of glow curve shape or order of the kinetic process. E and s from the glow peak shape dependent PS method are found to be relatively smaller than other methods. Large reduction in E and s is essentially due to the complex nature of the glow curves. Main peaks of LCB:Tm are wider due to the presence of shoulder peaks which resulted in the increase of half width parameters and subsequent reduction in E and s. For the estimation of E and s, PS method is not suitable for complex glow

peaks without deconvolution of the peaks. The order of the kinetic process assigned from the shape parameters of complex peaks is may be in error. Tm response to absorbed dose can be used as simple method to distinguish a first order or non-first order kinetic process. Here in LCB:Tm, as a function of dose no shift in Tm is observed for peak 1 and it obeys a first order kinetics. But maximum peak temperature Tm for peak 2 showed downward movement with dose which confirms a non-first order kinetics process. Heating rate effects on the glow curve shape, peak temperature, integral and peak height and integral area studies in LCB:Tm confirmed its glow curve stability. Acknowledgments The authors are grateful to Dr. B. Venkatraman, Head, RSD & Dr. V. Meenakshisundaram, Head, RSS, RSD for their support and encouragement and wish to acknowledge Dr. U. Madhusoodanan, for the useful discussions. References Anishia, S.R., Jose, M.T., Annalakshmi, O., Ponnusamy, V., Ramasamy, V., 2010. Dosimetric properties of rare earth doped LiCaBO3 thermoluminescence phosphors. J. Lumin. 130, 1834e1840. Azorin, J., 1986. Determination of thermoluminescence parameters from glow curves e I. a review. Nucl. Tracks 11 (3), 159e166. Balarin, M., 1975. Direct evaluation of activation energy from half width of glow peaks and a special nomogram. Phys. Stat. Sol. (a) 31, K111eK114. Chen, R., 1969. Glow curves with general order kinetics. J. Electrochem. Soc. 116, 1254e1257. Chen, R., 1984. Kinetics of Thermoluminescence Glow Peaks in Thermoluminescence and Thermoluminescence Dosimetry. CRC Press, Boca Raton, pp. 49e88. Garlick, G.F.J., Gibson, A.F., 1948. The electron traps mechanism of luminescence in sulphide and silicate phosphors. Proc. Phys. Soc. Lond. 60, 574e590. Gokce, M., Oguz, K.F., Karali, T., Prokic, M., 2009. Influence of heating rate on thermoluminescence of MgSiO4:Tb dosimeter. J. Phys. D: Appl. Phys. 42, 105412. 5pp. Gorbics, S.G., Nash, A.E., Attix, F.H., 1968. Thermal quenching of luminescent dosimetry phosphors. In: Proc. of 2nd Inter. Conf. on Lumin. Dosimetry, USA, 587 pp. Holsa, J., Aitasalo, T., Jungner, H., Lastusaari, M., Nittykoski, J., Spano, G., 2004. Role of defect states in persistent luminescence materials. J. Alloys Compd. 374, 56e59. Hoogenstraaten, W., 1958. Electron traps in zinc sulphide phosphors. Philips Res. Rep., vol. 13, pp. 515e562. Jiang, L.H., Zhang, Y.L., Li, C.Y., Pang, R., Hao, J.Q., Su, Q., 2008. Thermoluminescence characteristics of rare-earth doped LiCaBO3 phosphor. J. Lumin. 128, 1904e1908. Karali, T., Rowlands, A.P., Townsend, P.D., Prokic, M., Olivares, J., 1998. Spectral comparison of Dy, Tm and Dy/Tm in CaSO4 thermoluminescent dosimeters. J. Phys. D: Appl. Phys. 31, 754e765. Kitis, G., Spiropulu, M., Papadopoulos, J., Charalambous, Stef, 1993. Heating rate effects on the TL glow-peaks of three thermoluminescent phosphors. Nucl. Instr. Meth. Phys. Res. 73, 367e372. Kitis, G., Furetta, C., Prokic, M., Prokic, V., 2000. Kinetic parameters of some tissue equivalent thermoluminescent materials. J. Phys. D: Appl. Phys. 33, 1252e1262. McKeever, S.W.S., 1985. Thermoluminescence of Solids. Cambridge University Press, Cambridge. Montalvo, T.R., Furetta, C., Kitis, G., Azorin, J., Vite, R.M., 2004. Influence of heating rate on thermoluminescence of zirconium oxide UV irradiated. Radiat. Eff. Defects Solids 159, 217e222. Ogundare, F.O., Balogun, F.A., Hussaian, L.A., 2005. Heating rate effects on the thermoluminescence of fluorite. Radiat. Meas. 40, 60e64. Rawat, N.S., Kulkarni, M.S., Mishra, D.R., Bhatt, B.C., Sunta, C.M., Gupta, S.K., Sharma, D.N., 2009. Use of initial rise method to analyze a general-order kinetic thermo luminescent glow curve. Nucl. Instr. Meth. Phys. Res. B 267, 3475e3479. Sunta, C.M., Feria, Ayta W.E., Piters, T.M., Watanabe, S., 1999. Limitation of peak fitting and peak shape methods for determination of activation energy of thermoluminescence glow peaks. Radiat. Meas. 30, 197e201. Taylor, G.S., Lilley, E., 1982. Rapid readout rate studies of thermoluminescence in LiF (TLD-100) crystals: III. J. Phys. D: Appl. Phys. 15, 2053e2065.