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Effect of heating rate on thermoluminescence output of LiF: Mg, Ti (TLD-100) in dosimetric applications
Nuclear Inst, and Methods in Physics Research B 426 (2018) 22–29
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Nuclear Inst. and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Effect of heating rate on thermoluminescence output of LiF: Mg, Ti (TLD100) in dosimetric applications
T
⁎
Ranjit Singha,b, , Harpreet Singh Kaintha a b
Department of Physics, Panjab University, Chandigarh 160014, India Department of Radiotherapy, PGIMER, Chandigarh 160012, India
A R T I C LE I N FO
A B S T R A C T
Keywords: TLD-100 Heating rate Temperature lag Quenching
The luminiscence characteristics of thermoluminscence dosimeter LiF: Mg, Ti (TLD-100) irradiated to X-rays from 6 MV linac have been studied for wide range of 2–50 K/s readout linear heating rates. The reproducibility of glow curves for TLDs is found to be better at lower heating rates and depreciate at higher heating rates. The glow curve spectra were analysed using deconvolution procedure based on general-order kinetics. Shift in the peak maximum temperature per unit rise in heating rate for various peaks were found to decrease with heating rate. The TLDs irradiated with same dose exhibit decreasing TL counts with increase in the heating rate, which indicate the thermal quenching effect in TLD-100. The value of activation energy for each peak within the glow curve increases with heating rate. Calibration curves plotted for the dose range 0.4–1020 cGy exhibit decreasing slope with increasing readout heating rate. Corrections for temperature lag between the heating element and the dosimeter, and the effective heating rate (βeff) across the sample estimated using formulation proposed by Kitis and Tuyn and are found to be fairly applicable.
1. Introduction In-vivo dosimetry has become mandatory for the radiotherapy procedures involving high dose per fractions (sterotactic radiosurgery) [7,11], large volume irradiation (total skin electron and total or partial body irradiation) [9,38] and modern techniques with complex dose distribution, viz., intensity modulated radiotherapy (IMRT) [10,31], image guided radiotherapy (IGRT) and volumetric arc therapy (VMAT) [25]. The in vivo dosimetric procedures are performed either using active dosimeter, e.g., diode dosimeter, or passive dosimeter, e.g., thermoluminiscence dosimeter (TLD) or radiographic film. The diode dosimeters require cables or auxiliary equipment during the dose assessment and use of a large number of diodes is not cost-effective and also not physically possible for various in vivo applications. Also, its response is temperature dependent. In the medical applications, the passive dosimeters, especially, the thermo luminescent crystals [4,37,34] are frequently used for dosimetric applications because of their small energy dependence, small physical size and different shapes, reusability, ability to measure radiation dose from almost all types of ionizing radiation over wide dose range and easy adaptation with the patient’s body [17]. The TLDs are widely used as free standing dosimeter in radiotherapy applications to assess the radiation doses to the critical organs such as skin, lens, scrotal, fetal, thyroid, contra-lateral
⁎
Corresponding author. E-mail address: [email protected] (R. Singh).
https://doi.org/10.1016/j.nimb.2018.04.025 Received 9 February 2018; Received in revised form 16 April 2018; Accepted 16 April 2018 0168-583X/ © 2018 Elsevier B.V. All rights reserved.
breast and esophagus during the routine treatment both in external beam radiotherapy and brachytherapy. Considerable research work related to TL materials has been carried out to study their dosimetric characteristics, e.g., energy and radiation type dependency and sensitivity of different TL materials available for radiation dosimetry [32,16,1,18]. Despite the lower sensitivity, the LiF based material (TLD-100; LiF: Mg, Ti) is widely used in radiotherapy as compared to other more sensitive TL materials based on CaF2 (TLD-200, TLD-300, TLD-400), CaSO4: Dy (TLD −900) and Li2B4O7 (TLD-800). Its effective atomic number (Zeff = 8.14) is nearly tissue equivalent and hence closely approximates the absorption and scattering properties to that of the human tissue (Zeff = 7.42) [33,30]. The presence of 12Mg and 22Ti at concentrations of approximately 100 and 10 mol ppm, respectively, is responsible for the thermoluminiscence properties [27,15]. The 12Mg is intimately involved in the trapping process, and 22Ti in the recombination event [29,8]. The evaluation of the doses from large number of TLDs utilized for in vivo dosimetry also increases overall dose evaluation time if readout is performed at slow heating rate. The fast linear heating rates ∼10 K/s considerable reduces the time to evaluate absorbed doses by reading out large number of TLDs in the shortest possible time. It forms the basis of TL dosimetry in large scale monitoring. Increasing the heating rate during readout often appears necessary to reduce the time between
Nuclear Inst, and Methods in Physics Research B 426 (2018) 22–29
R. Singh, H.S. Kainth
were irradiated for the same dose of 186 cGy. The TLDs readouts were carried out at a linear heating rate (β) of 5 K/s. The Element correction coefficient (ECC) for each TLDs are calculated by dividing the average TL counts of all TLDs with individual TL counts. This process was repeated thrice and the ECC [2] of each TLD was evaluated as ECCi = Cavg / Ci;where Cavg is the average counts of all TLDs irradiated with same exposed dose and Ci is the counts from individual TLD, respectively. Only TLDs within ± 10% variation were included and others were discarded. The first part of the present experiment was related to study the effect of heating rate on thermoluminescence spectra. Ninty three TLDs were taken from the lot sorted after ECC determination and pre-irradiation annealed. The TLDs were immediately irradiated with the same dose of 186 cGy using the same experimental setup and the monitor units. After the pre-readout annealing, the TLDs were divided into 14 batches of 6 TLDs each. The TLDs from each batch were readout at 2, 3, 4, 5, 6, 7, 8, 10, 15, 20, 25, 30, 40 and 50 K/s linear heating rates using Rexon readout system. The spectra exhibits shape, size and location of dosimetric glow curve from different batches of TLDs readout were recorded at increasing heating rates. Background data for 14 batches each of 4 un-irradiated (pre-irradiation annealed) TLD-100 were also taken at same set of heating rates. The background spectra exhibit almost no background counts up to ∼573 K followed by slowly increasing trend up to 673 K. Various parameters, e.g., area under the glow curve, total counts, integrated counts over the temperature range 373 K-673 K, and peak temperature were recorded. The second part of the present experiment involved studies the dose readout on the calibration of TLDs at different heating rate. The sorted lot of TLDs with known Element correction factor (ECCi) were divided into 14 batches with each one consisting of 6 TLDs. Different batches were irradiated with doses ranging from 0.4 cGy to 1020 cGy in the varying dose step. After the pre-readout annealing, the readouts of TLDs from different batches were carried out at 5, 10, 15 and 30 K/s heating rates using Rexon readout system and the areas under the glow curves were used for dose calibration.
the measurements and dose evaluation, especially in routine dosimetry. Further, the readout at fast heating rate will result in change in shape, size, and position of the dosimetric peak. Investigations regarding read out of TLDs at fast heating rates is an active area of research in thermoluminescent dosimetry [12,21,39,6,36,20,3,26]. The knowledge of kinetic parameters trap depth (E), frequency curve (s), order of kinetics (b) and variation of peak maximum temperature (Tm) and intensity (Im), play vital role in understanding the TL phenomenon and its practical utility as radiation dosimeters. Other important observations include variation of Tm and Im with the heating rate [40,24,19]. The aim of present study is to evaluate the TL glow curves of cuboid shaped LiF: Mg, Ti (TLD-100) phosphor into its component peaks using general order kinetics proposed by May and Patridge [28]. The effect of linear heating rate over a wide range 2–50 K/s was studied for various parameters, viz., peak height, maximum peak temperature, total counts, integrated counts, area under various peaks in the TL glow spectrum of TLD-100 dosimeter. The reproducibility of TLDs at different heating rate was analyzed. Corrections for temperature lag between the heating element and the dosimeter and the effective heating rate (βeff) across the sample were estimated [22]. The dose calibration curves were obtained for the dose ranging 0.4 cGy-1000 cGy at different heating rates. 2. Method and material The samples used in the present study were LiF: Mg, Ti (trade name TLD 100) cuboid shaped rods with dimension 1 mm × 1 mm × 6 mm (Rexon TLD Systems and Components, Ohio, USA). The radiation dose was delivered by photon beam from 6 MV linear accelerator (Clinac DHX, Varian, CA). Rexon UL-300 readout system (Rexon TLD Systems and Components, Ohio, USA) (Model UL 300) interfaced to PC was used for recording and analyzing the thermoluminscence spectra from TLDs after irradiation. To erase any residual information before irradiation, all the TLDs were pre-irradiation annealed by the procedure involving heating at 400 °C for 1 h followed by 105 °C for 2 h as recommended by Yu and Luxton [42]. The absorbed dose was measured using A19 Exradin Ion chamber (Standard Imaging, Middleton, USA), RW3 solid water phantom (area 30 × 30 cm2, thickness range 0.1–1 cm, density 1.04 gm/cm3) and Supermax Electrometer (Standard Imaging, Middleton, USA). The active volume of A19 Exradin Ion chamber is 0.6 cc and readings are traceable to Reference Standard Laboratory of Radiation Standardization Section, Bhabha Atomic Research Centre, Mumbai, India. The monitor units required to deliver a dose of 186 cGy were obtained by placing the 0.6 cc ionization chamber in RW3 solid water phantom at the depth of 5 cm with source-to-surface distance of 100 cm and irradiation field size 10 × 10 cm2. The heating profile used for the TLD-100 readout consisted of (i) heating at linear rate from the room temperature 25 °C (298 K) to 100 °C (373 K) in 10 s, (ii) constant temperature at 100 °C (373 K) up to 15 s, (iii) heating from 100 °C (373 K) to 400 °C (673 K) as per the requisite linear rate (β), (iv) constant temperature at 400 °C (673 K) for 10 s, and (v) cooling cycle from 400 °C (673 K) to room temperature 25 °C (298 K) in 10 s. The glow curve spectrum of a TLD-100 crystal taken just after the exposure and readout at very low heating rate ∼0.1 K/s constitutes five peaks labeled as 1–5. Lowest peak 1 is occurring at temperature 338 K. It has half life of 10 min at 298 K. Although in the present work, heating rate below 2 K/s is not possible due to limitation of readout system. Throughout the present work, prereadout annealing of all the irradiated TLDs was done by heating at 105 °C (378 K) for 15 min. to eliminate the contribution from peak 1. Peaks 2 and 3 are known to be associated with Mg2+-cation vacancy pairs and peaks 4 and 5 with higher-order clusters of dipoles, possibly trimers [5]. To sort good quality TLDs, the response sensitivity factor for each individual TLD was determined. All the pre-irradiation annealed TLDs
3. Theoretical formulations The basic first-order kinetic theory for the thermal untrapping of electrons was first developed by Randall and Wilkins [35]. In case of readout of the irradiated thermoluminescence material, the rate of electrons released from the traps, dn/dt, is proportional to nb, where n (m−3) is the concentration of hole at the recombination centre and b is defined as the general-order kinetic parameter. The intensity of thermoluminescence (I) at any time (t) for TL kinetics of May and Patridge [28] order b is written as I (t ) = −dn/ dt = nbs′exp (−E / kT ) ; where E (in eV) is the activation energy, k (eV K−1) is the Boltzmann constant and T is the absolute temperature. The term s′ is called the frequency factor or attempt-to-escape factor and has dimensions of m3(b−1) s−1. In case of linear readout heating rate (β), i.e., T = To + βt, the intensity as a function of temperature [28] is given by
I (T ) = −
s′nob dn = exp (−E dt β
⎡ (b−1) s′nob − 1 / kT ) ⎢1 + β ⎢ ⎣
T
∫ T0
b (1 − b)
⎤ [exp (−E /kT ′)] dT ′⎥ ⎥ ⎦
(1)
Also, for the general order kinetics in terms of peak maximum intensity (Im) and peak maximum temperature (Tm) can be derived as [13] b
I (T ) = Im ⎡ ⎢ ⎣
(b−1) T 2 ⎛ 2kT ⎞ Z 1 −b 1− exp(D) + m ⎤ exp(D) b T2m ⎝ E ⎠ b ⎥ ⎦
where D =
E kT
(
T − Tm Tm
) and Z
m
=1+
(2)
2kT (b−1) Em .
By setting dI/dt = 0 at the peak maximum, T = Tm, one gets the condition 23
Nuclear Inst, and Methods in Physics Research B 426 (2018) 22–29
R. Singh, H.S. Kainth
Fig. 1. The glow spectra plotted on logarithmic scale from TLDs of different batches at different readout heating rates (a) 2 K/s (b) 5 K/s and (c) 10 K/s.
(b−1) s′ β
1+
T
∫
[exp (−E /kT ′)] dT ′ =
T0
s′bkTm2 exp (−E / kTm) βE
from peak 5 (dosimetric peak). The glow spectra obtained at heating rates 2, 5 and 10 K/s are plotted on log scale in Fig. 1(a)-(c). In addition to the complex peaks labeled 2–5 under the main glow curve, two more small peaks labeled ‘a’ and ‘b’ are also observed in the spectra. Peak ‘a’ is not observed in the background spectra taken with virgin TLD, while peak ‘b’ is also observed in the background spectra [shown in Fig. 1(a)-(c) as dotted lines]. Both these peaks also shift with increase in readout heating rate. The readout spectra with different heating rates were analysed using simple multi-gaussian peak fitting analysis using Origin 8.5 software. The dosimetric glow spectra of TLDs exposed to the same dose of 186 cGy and readout at different heating rates exhibit that the glow
(3)
The frequency factor s′is written as
s′ =
βE exp(−E / kTm) kZm Tm2
(4)
4. Results and discussion The typical glow peak spectrum of TLD-100 consisted mainly of peaks 2–5, with the major contribution to the glow curve spectra is 24
Nuclear Inst, and Methods in Physics Research B 426 (2018) 22–29
R. Singh, H.S. Kainth
Table 1 The values of peak temperature (peak 5) and maximum thermoluminiscence (TL) counts for different heating rates to readout TLD-100. Heating rate (K/s)
Maximum Peak temperature (K)
Maximum Peak Intensity (counts)
Heating rate (K/s)
Maximum Peak temperature (K)
Maximum Peak Intensity (counts)
2 3 4 5 6 7 8
493.7 501.3 505.0 509.1 511.8 514.3 519.6
514.3 ± 15.5 778.6 ± 19.2 989.6 ± 30.8 1273.8 ± 37.0 1519.0 ± 40.8 1890.1 ± 74.0 2029.3 ± 12.5
10 15 20 25 30 50
527.6 536.0 556.5 568.0 579.9 596.6
2459.8 3490.0 4337.9 5184.1 6042.9 7476.7
± ± ± ± ± ± ±
1.4 1.6 0.6 1.0 1.9 1.1 1.7
± ± ± ± ± ±
2.1 1.8 4.8 3.6 5.1 10.4
± ± ± ± ± ±
191.1 150.6 231.8 310.6 374.7 347.0
The glow peak due to βj is shifted towards the higher temperature keeping the integral stable and reducing slightly in the peak height. Ignoring the thermal quenching effects and assuming the peak shapes to be the same at different heating rates, the shift in the glow peak towards higher temperature as the rate of heating is given as
Ti−Tj = Ti Tj
k ⎛ βi ⎞ log E e ⎜ βj ⎟ ⎝ ⎠
(5)
The approximation is valid over a wide range of E and s values. The effective rate of heating of TLD (βeff) is smaller than the rate at which element is heated (β) and hence, within the first approximation, the effective heating rate [22] is given as
Tg−To−ΔT ⎞ βeff = ⎜⎛ ⎟β ⎝ Tg−To ⎠ Fig. 2. Recorded/observed and corrected heating rate for peaks 2,3,4,5.
(6)
where ‘Tg’ is the peak maximum temperature of a glow peak recorded with temperature lag (ΔT = Tg − Tm), ‘Tm’ is the real peak temperature of same glow peak without temperature lag and ‘To’ is the starting temperature usually of the room temperature (∼298 K). The effective heating rate and temperature position of the glow peak has been calculated using Eqs. (6) and (5), respectively. All calculations are made assuming no temperature lag at the lowest heating rate 2 K/s used in the present study. The different peaks have different effective heating rates. The observed and effective heating rates are deviated from linear behaviour as shown in Fig. 2. The difference between the recorded peak position and the corrected peak position between the same peaks increases with heating rate as shown in Fig. 3. From Fig. 4(a), it appears that the peak area under the glow curve increases for the TLD batches irradiated with same radiation dose as the heating rate is increased. This increase in area under TL-temperature glow curves of TLDs and read at increasing heating rates was also reported by Kumar et al. [24] who speculated that there is ambiguity in the presentation of effect of heating rate on TL glow curves. The TL phenomenon has been basically derived as time derivative of luminescence signal from sample during constant linear heating of samples.
curve maxima shift towards higher temperature region (shown in table 1) and the peak area increases with increase in the heating rate (Fig. 1). The temperature of the glow peak maximum is mainly determined by two processes (i) increase of released charge carriers with increasing temperature (ii) the decrease of charge carriers due to depletion of the trap. For a low heating rate, the TLD will be held at a certain temperature for a longer time which implies that the trap is emptied at lower temperature resulting in a lower glow peak temperature. The situation is just opposite in case of higher heating rate of the TLD and results in higher glow peak temperature. Also, the temperature difference between the heating element and the TLD increases at fast heating rate, i.e., the actual temperature at TLD lags the recorded temperature. This difference is associated with the thermoluminescence measurements set up involving temperature gradient within the heating element, non-ideal thermal contact between heater element, planchet and sample, and temperature gradient across the TL sample. The recorded temperature is obtained using non-contact infrared sensor positioned beneath the planchett. At higher heating rates, the glow curves of different TLDs within a given batch are widely spread and reproducibility of glow curve in these TLDs within a given batch is observed to be poorer. The values of standard deviation for position of dosimetric peak (peak 5) at various readout heating rates are given in Table 1. They were found to be ± 5.1 K, ± 13.6 K and ± 10.4 K, respectively, for β = 30 K, 40 K and 50 K while the average value of standard deviation is < ± 2.1 K for heating rate below β = 10 K/s. The average shift in glow curve main peak position per unit increase in heating rate βeff is found to be ∼4 K for low heating rate and decreases to ∼0.8 K at higher heating rates, respectively (Table 1. The spread in glow curve maxima at higher heating rates is also because of contact heating of the TLD placed on the planchett, which can give rise to spurious shift in the glow peaks [41]. The temperature lag between the heating element and the TL dosimeter was corrected to first approximation using the formulation given by Kitis and Tuyn [22] for the general-order kinetics. The glow peaks obtained at two different heating rates, βi and βj (> βi), have the peak maximum temperatures Ti and Tj (> Ti), respectively.
Fig. 3. Temperature lag between observed and corrected peak position for peak No. 5 plotted as function of heating rate. 25
Nuclear Inst, and Methods in Physics Research B 426 (2018) 22–29
R. Singh, H.S. Kainth
Fig. 4. (a) The typical glow curve spectra obtained from TLDs exposed to same dose verses different heating rates and (b) shows the same spectra normalized w.r.t. their corresponding heating rate (β).
However, traditionally luminescence signal has been plotted against temperature. But this plot is linear transformed temperature scale of independent time scale. This observation/appearance of increase in area under TL–temperature glow curves with increase in heating rate at a constant dose is the consequence of transformation of time to temperature scale (temperature scale obtained om time scale by multiplying with β, T= To + βt . The observations are better presented in Fig. 4(a) and (b). Fig. 4(a) shows the typical glow curve spectra obtained from TLDs exposed to same dose and readout at different heating rates and Fig. 4(b) shows the same spectra with the counts divided by the corresponding heating rate (β). For normalized glow curves (I/ β–temperature), the glow peak height decreases with increase in heating rate, which is actually true for I/β or TL/β versus temperature plots. It is further pointed out that increase in heating rate for TLD readout does not lead to increase in sensitivity of the dosimeter. With increase in heating rate more rapidly, the phonon density increases that possibly may make thermal energy transfer to trap charged at defects less efficient. This forces equilibrium condition of maximum in temperature scale higher. More fundamental treatment formulation of lattice vibration and TL phenomenon will bring out same more facts about this question. Under Randall and Wilkins [35] conditions, the total light output is determined by the trapped charged, which is proportional to the absorbed dose and the heating rate influences only the time at which the trapped charge is released but not the total light output. From the various TLD spectra obtained at different heating rates, the average values of integrated counts are obtained between the two specified temperatures covering the main glow curve (Peak 5). The Fig. 5 shows the plot of average integrated counts corrected for the sensitivity of the respective TLDs. The integrated counts under the
Fig. 5. The observed integrated TL peak area plotted as a function of heating rate.
main glow curve are observed to decrease smoothly with increase in observed heating rate (βeff). It is because the luminescence intensity of the TL material is a temperature sensitive factor which decreases with increase in temperature and heating rate due to competition between radiative and non-radiative transitions. The increases in the probability of non-radiative transition with rise in temperature and heating rate was also explained by Kafadar [19] and Kadari and Kadri [18]. Apart from the increased probability of non-radiative transitions at higher temperatures, the observed effects have also been assigned to the effects of heating rate on the migration of charge carriers released during the TL readout. Then, it was inferred that the glow peaks occurring at high temperatures must exhibit higher thermal quenching than those occurring at lower temperatures in any TLD material. 26
Nuclear Inst, and Methods in Physics Research B 426 (2018) 22–29
R. Singh, H.S. Kainth
Fig. 6. Peak fitting of the observed glow curves us glow curve deconvolution (GCD) software for peaks (2–5) within the glow curve.
at 5 K/s to 1.89 eV for 30 K/s. The peak temperature values (Tm) were deduced for the peaks labeled 2–5. These values are given in Table 3 and plotted in Fig. 7 for the observed and corrected temperature position with heating rates. In composite glow curves, where an excellent fit can be obtained with many pairs of different E and s values. Kitis [23] has discussed preliminary acceptance criteria for E and s values resulting from the glow-curve deconvolution analysis. Some effort must be made in order to formulate some criteria according to which some E and s pairs are accepted. Indeed, the reliability of the resulting E and s values is questionable when these values are deduced from analysis of spectra taken at the higher heat rates, which are not corrected for temperature lag. The knowledge of temperature lag between the heating element and dosimeter is an essential part for extracting physical information from glow curve. The experimental data at higher heating rates must be corrected for temperature lag before fitting. The Fig. 7 demonstrates the observed peak positions and those corrected for the temperature lag [22]for the peaks 2–5. And taking first order kinetics, the plot of ln(Tm2 /) vs 1/(kTm), must be a straight line with slope E. This method is very much dependent upon Tm, so it would be a very good test for the
A Microsoft Windows-operated user-friendly computer program, TLAnal (TL Glow curve Analyser) has been used in the present work to resolve complex composite TL glow-curve in the readout spectra consisting of strongly overlapping peaks. The program involves fitting of experimental points to a non-linear function describing the general order kinetics thermoluminescence glow curve using the least squares Levenberg-Marquardt method [14]. Its graphical interface enables easy intuitive manipulation of glow peaks by pre-selecting the various parameters and their ranges at the initial stage. Fig. 6(a)-(d) show the fitted spectra recorded at different heating rates. The procedure continues by sequentially changing the fitting parameter until a minimum value of FOM [14] is obtained. This program can accommodate fitting of the glow curve spectrum readout up to heating rate 30 K/s and delivers the trap parameters, viz., activation energy (E), order of kinetics (b) and frequency factor (s), and initial concentration of traps (no) corresponding to various fitted peaks. The values of activation energy (E), frequency factor (s) and trap concentration (no) are shown in Table 2. The values of the order of kinetics parameter (b) are 2.09–2.29 and ∼1.91–2.12, respectively, for peaks 2 and 3, 1.8–2.10 for peaks 4 and 5. The value of activation energy (E) for peak 5 varies from 1.58 eV
Table 2 The value of activation energy ‘E’, frequency factor ‘s’, general order parameter ‘b’ and trap concentration ‘no’ for different peaks at heating rates ≤30 K/s. Hea-ting rate (K/s)
5 10 15 20 30
Peak 2
Peak 3 −1
E (eV)
s (s
1.04 1.10 1.04 1.16 1.07
1.32E+15 3.59E+15 5.30E+13 1.52E+15 7.16E+14
)
b
no (m
2.25 2.1 2.23 2.11 2.09
978 945 935 848 918
−3
)
Peak 4 −1
E (eV)
s (s
)
1.13 1.18 1.21 1.21 1.24
6.28E+15 5.57E+15 7.67E+16 3.60E+14 5.40E+14
b
no (m
1.94 1.91 2.04 2.08 2.12
1212 2004 1387 1599 1532
27
−3
)
Peak 5 −1
E (eV)
s (s
)
1.20 1.26 1.31 1.37 1.37
5.45E+15 4.09E+15 2.40E+15 1.34E+16 2.95E+15
b
no (m
2.06 1.95 1.99 1.91 2.1
1877 2573 1871 1873 3366
−3
)
E (eV)
s (s−1)
b
no (m−3)
1.58 1.71 1.7 1.79 1.89
2.80E+15 1.17E+17 2.09E+16 4.71E+16 5.70E+17
1.92 1.91 1.91 1.85 2.1
5812 4448 5625 5107 4381
Nuclear Inst, and Methods in Physics Research B 426 (2018) 22–29
R. Singh, H.S. Kainth
Table 3 The average value of peak temperature for different peaks and corrected peak position (temperature lag) at different heating rates. The effective heating rate corresponds to peak no 5. Heating rate (K/s)
2.0 3.0 4.0 5.0 6.0 7.0 8.0 10.0 15.0 20.0 25.0 30.0 50.0
Effective heating rate (K/s)
2.0 3.0 3.9 4.9 5.8 6.8 7.6 9.3 13.7 17.2 20.9 24.3 39.5
Average Peak position (K)
Average corrected peak position (K)
Peak 2
Peak 3
Peak 4
Peak 5
Peak 2
Peak 3
Peak 4
Peak 5
436.6 442.1 447.5 452.0 457.2 457.7 460.7 473.5 485.6 499.8 513.6 522.1 530.9
464.6 469.4 477.5 484.8 487.1 489.0 490.1 503.5 509.1 534.5 538.9 547.3 556.4
474.9 482.2 487.9 494.8 496.4 498.5 502.1 513.0 518.3 535.4 551.1 560.1 573.2
493.7 501.3 505.0 509.1 511.8 514.3 519.6 527.6 536.0 556.5 568.0 579.9 596.6
436.6 439.9 442.2 444.1 445.6 446.9 448.1 450.3 454.2 457.3 459.9 462.0 467.3
464.6 468.3 471.0 473.1 474.9 476.3 477.6 480.1 484.2 488.1 490.6 492.9 498.8
474.9 478.7 481.4 483.7 485.5 487.0 488.4 491.0 495.2 498.9 502.0 504.4 510.8
493.7 497.8 500.8 503.2 505.1 506.8 508.3 510.9 515.6 519.7 522.8 525.6 532.7
Fig. 9. Dose calibration curve (net TL counts versus absorbed dose) for 6 MV Xrays at heating rate 2, 5, 15 and 30 K/s.
Fig. 7. The TL glow peak positions with observed heating rate and effective heating rate obtained after temperature lag correction.
heating rate (K/s). It depicts the effect on dose calibration curve of TLD 100 with heating rate. As has been observed, the TL output of TLD-100 decreases with increase in the heating rate due to thermal quenching effects. At higher heating rates and low doses ∼few tens of cGy, the contribution due to the background spectrum obtained with virgin TLD becomes significant. Hence for TLDs irradiated with low doses readout cannot be performed reliably at high heating rates ∼40–50 K/s.
5. Conclusion The luminescence characteristics of the thermoluminescence (TL) from TLD 100 were examined using the heating rate dependence of the TL signal. As the heating rate varies the TL peaks shift to different temperatures and become affected by thermal quenching to different extents. In this work the heating rate was varied over several orders of magnitude and, through deconvolution of the TL glow curve the behaviour of the main TL peaks was followed as a function of the temperature at which the peak appeared in the glow curve. Through an analysis of the glow peak areas as a function of glow peak temperature the decrease in the efficiency of TL production with increasing temperature could be monitored and the analysis supports the quenching phenomenon. The General order kinetics (GPK) is used in the present study to analyze the effect of heating rate on the dosimetric properties of TLD-100. The heating rate has a significant effect not only on sensitivity and intensity of TL material but also on shape, size and position of glow curve of TLD-100. The dose calibration curve is dependent on
Fig. 8. The plot of ln(Tm2 /) vs 1/(kTm) for peaks 2–5 corrected for temperature lag.
validity of temperature lag corrections. Fig. 8 shows the plot of ln(Tm2 /) vs 1/(kTm) for peaks 2–5. The application of this method to gives straight line for corrected peak temperature for peak 2–5. The values of E deduced are ∼1.65 eV. The dose calibration curves over the dose 0.4–1020 cGy are plotted as shown in Fig. 9 for 2, 5, 15 and 30 K/s 28
Nuclear Inst, and Methods in Physics Research B 426 (2018) 22–29
R. Singh, H.S. Kainth
the heating rate due to thermal quenching. The variation between TL counts for same doses varies significantly at high dose irradiation and background counts also increase in the main glow curve region and hence high heating rates ∼50 K/s are not suitable for TLD readout for low dose measurements ∼10 cGy. At lower heating rates the reproducibility in shape, size and location of glow curve for TLDs having nearly same sensitivity and irradiated with same dose (same radiation type) are better and it depreciate at higher heating rates. The peaks under the glow curve were shifted to higher temperature region with rise in heating rate and average shift in peak position (in K) per unit rise in heating rate is found to be larger for heating rate below 10 K/s. The decreases in TL output, sensitivity and area under glow curve with increase in heating rate are elucidated in TL/heating rate (s/K) versus temperature (K) plot. It has been proposed that the accuracy in dosimetric evaluation for personnel or in vivo dosimetry in medicine will be maintained if the TL dosimeter is readout at an appropriate heating rate at which its calibration was done and for low dose evaluations, lower possible heating rates are recommended.
and mixed order kinetics, Radiat. Prot. Dosim. 101 (2002) 47. [14] J.A. Harvey, M.L. Rodrigues, K.J. Kearfott, A computerized glow curve analysis (GCA) method for WinREMS thermoluminescent dosimeter data using MATLAB, Appl. Radiat. Isot. 69 (2011) 1282. [15] S. Hashim, et al., Thermoluminescence dosimetry properties and kinetic parameters of lithium potassium borate glass co-doped with titanium and magnesium oxides, Appl. Radiat. Isot. 91 (2014) 126. [16] W.R. Hendee, G.S. Ibbott, D.B. Gilbert, Effects of total dose on energy dependence of TLD-100 LiF dosimeters, Int. J. Appl. Radiat. Isot. 19 (1968) 431. [17] IAEA Report 8, Development of procedures for In-vivo dosimetry in Radiotherapy. Internat. Atomic Energy Agency, Vienna, 2013. [18] A. Kadari, D. Kadri, New numerical model for thermal quenching mechanism in quartz based on two-stage thermal stimulation of thermoluminescence model, Arabian J. Chem. 8 (2015) 798. [19] V.E. Kafadar, Thermal quenching of thermoluminescence in TLD-200, TLD-300 and TLD-400 after β-irradiation, Phys. B: Condens. Matter 406 (2011) 537. [20] V.E. Kafadar, K.F. Majeed, The effect of heating rate on the dose dependence and thermoluminescence characteristics of CaSO4: Dy (TLD-900), Thermochim. Acta 590 (2014) 266. [21] G. Kitis, J.M. Gomez-Ros, J.W.N. Tuyn, Thermoluminescence glow-curve deconvolution functions for first, second and general orders of kinetics, J. Phys. D Appl. Phys. 31 (1998) 2636. [22] G. Kitis, J.W.N. Tuyn, A simple method to correct for the temperature lag in TL glow-curve measurements, J. Phys. D Appl. Phys. 31 (1998) 2065. [23] G. Kitis, TL glow-curve deconvolution functions for various kinetic orders and continuous trap distribution: Acceptance criteria for E and s values, J. Radioanal. Nucl. Chem. 247 (2001) 697. [24] M. Kumar, G. Chourasiya, B.C. Bhatt, C.M. Sunta, Dependence of peak height of glow curves on heating rate in thermoluminescence, J. Lumin. 130 (2010) 1216. [25] G. Leunens, et al., Experience of in vivo dosimetry investigations in Leuven. Radiation dose in radiotherapy from prescription to delivery. IAEA Report TECDOC-734, 283, 1994. [26] L.Z. Luo, K.J. Velbeck, M. Moscovitch, J.E. Rotunda, LiF: Mg, Cu, P glow curve shape dependence on heating rate, Radiat. Prot. Dosim. 119 (2006) 184. [27] E. Mandowska, P. Bilski, E. Ochab, J. Wiatek, A. Mandowski, TL emission spectra from differently doped LiF: Mg detectors, Radiat. Prot. Dosim. 100 (2002) 451. [28] C.E. May, J.A. Partridge, Thermoluminescent kinetics of alpha irradiated alkali halides, J. Chem. Phys. 40 (1964) 1401. [29] M.R. Mayhugh, R.W. Christy, N.M. Johnson, Thermoluminescence and color center correlations in dosimetry LiF, J. Appl. Phys. 41 (1970) 2968. [30] S.W.S. McKeever, M. Moscovitch, P.D. Townsend, Thermoluminescence dosimetry materials: properties and uses, 1995. [31] B. Mijnheer, S. Beddar, J. Izewska, C. Reft, In vivo dosimetry in external beam radiotherapy, Med. Phys. 40 (2013) 070903 1. [32] S. Miljanic, et al., Main dosimetric characteristics of some tissue-equivalent TL detectors, Radiat. Prot. Dosim. 100 (2002) 437. [33] T. Nakajima, et al., Development of a new highly sensitive LiF thermoluminescence dosimeter and its applications, Nucl. Instrum. Methods 157 (1978) 155. [34] A.S. Pradhan, Thermoluminescence dosimetry and its applications, Radiat. Prot. Dosim. 1 (1981) 153. [35] J.T. Randall, M.H.F. Wilkins, Proc. R. Soc. London, 184, 347-365, 366-389, 390-407 (1945). [36] M.S. Rasheedy, E.M. Zahran, The effect of the heating rate on the characteristics of some experimental thermoluminescence glow curves, Phys. Scr. 73 (2005) 98. [37] T. Rivera, Thermoluminescence in medical dosimetry, Appl. Radiat. Isot. 71 (2012) 30. [38] R.J. Shalek, Determination of Absorbed Dose in a Patient Irradiated by Beams of X or Gamma Rays in Radiotherapy Procedures, Med. Phys. 4 (1977) 461. [39] H. Stadtmann, A. Delgado, J.M. Gómez-Ros, Study of real heating profiles in routine TLD readout: Influences of temperature lags and non-linearities in the heating profiles on the glow curve shape, Radiat. Prot. Dosim. 101 (2002) 141. [40] N.A. Spooner, A.D. Franklin, Effect of the heating rate on the red TL of quartz, Radiat. Meas. 35 (2002) 59. [41] G.C. Taylor, E. Lilley, Rapid readout rate of studies of thermoluminescence in LiF (TLD-100) crystals. III, J. Phys. D Appl. Phys. 15 (1982) 2053. [42] C. Yu, G. Luxton, TLD dose measurement: a simplified accurate technique for the dose range from 0.5 cGy to 1000 cGy, Med. Phys. 26 (1999) 1010.
Acknowledgement One of the author, Ranjit Singh wants to convey special thanks to Director, PGIMER, Chandigarh, India, for provide us facility and Prof. Devinder Mehta, Physics Department, Panjab University, India, for their valuable suggestions regarding this work. References [1] M. Angelone, M. Chiti, A. Esposito, Measurement of supralinearity factor of CaF2: Tm (TLD-300) thermoluminescent dosimeter, Nucl. Instrum. Methods Phys. Res., Sect. B 117 (1996) 428. [2] N. Banaee, H.A. Nedaie, EP-1441: Evaluating the effect of energy on calibration of thermoluminesent dosimeters 7-LiF: Mg, Cu, P (GR-207A), Radiother. Oncol. 111 (2014) S137. [3] S. Bauk, S.F. Hussin, M.S. Alam, Analysis of read-out heating rate effects on the glow peaks of TLD-100 using WinGCF software, AIP Conference Proceedings, AIP Publishing, 2016, p. 030016. [4] A.J.J. Bos, High sensitivity thermoluminescence dosimetry, Nucl. Instrum. Methods B 184 (2001) 3. [5] M.H. Bradbury, B.C.E. Nwosu, E. Lilley, The effect of cooling rate on the performance of thermoluminescent dosimeter crystals (TLD-100) and LiF crystals, J. Phys. D Appl. Phys. 9 (1976) 1009. [6] P.F. Caprile, B. Sánchez-Nieto, A.M. Pino, J.F. Delgado, Effects of heating rate and dose on trapping parameters of TLD-100 crystals, Health Phys. 104 (2013) 218. [7] J.V. Dam, G. Marinell, Methods for In-vivo Dosimetry in External Radiotherapy, 2nd ed., Garant, Leuven, 2006. [8] J.J. Davies, EPR and ENDOR of titanium-doped fluoride, J. Phys. C: Solid State Phys. 7 (1974) 599. [9] M.A. Duch, M. Ginjaume, H. Chakkor, X. Ortega, N. Jornet, M. Ribas, Thermoluminescence dosimetry applied to in vivo dose measurements for total body irradiation techniques, Radiother. Oncol. 47 (1998) 319. [10] P.E. Engström, et al., In vivo dose verification of IMRT treated head and neck cancer patients, Acta Oncol. 44 (2005) 572. [11] M. Essers, B. Mijnheer, In vivo dosimetry during external photon beam radiotherapy, Int. J. Radiat. Oncol. Biol. Phys. 43 (1999) 245. [12] C. Furetta, G. Kitis, J.H. Kuo, L. Vismara, P.S. Weng, Impact of non-ideal heat transfer on the determination of thermoluminescent kinetics parameters, J. Lumin. 75 (1997) 341. [13] Ros J.M. Gómez, G. Kitis, Computerised glow curve deconvolution using general
29
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Nuclear Inst. and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Effect of heating rate on thermoluminescence output of LiF: Mg, Ti (TLD100) in dosimetric applications
T
⁎
Ranjit Singha,b, , Harpreet Singh Kaintha a b
Department of Physics, Panjab University, Chandigarh 160014, India Department of Radiotherapy, PGIMER, Chandigarh 160012, India
A R T I C LE I N FO
A B S T R A C T
Keywords: TLD-100 Heating rate Temperature lag Quenching
The luminiscence characteristics of thermoluminscence dosimeter LiF: Mg, Ti (TLD-100) irradiated to X-rays from 6 MV linac have been studied for wide range of 2–50 K/s readout linear heating rates. The reproducibility of glow curves for TLDs is found to be better at lower heating rates and depreciate at higher heating rates. The glow curve spectra were analysed using deconvolution procedure based on general-order kinetics. Shift in the peak maximum temperature per unit rise in heating rate for various peaks were found to decrease with heating rate. The TLDs irradiated with same dose exhibit decreasing TL counts with increase in the heating rate, which indicate the thermal quenching effect in TLD-100. The value of activation energy for each peak within the glow curve increases with heating rate. Calibration curves plotted for the dose range 0.4–1020 cGy exhibit decreasing slope with increasing readout heating rate. Corrections for temperature lag between the heating element and the dosimeter, and the effective heating rate (βeff) across the sample estimated using formulation proposed by Kitis and Tuyn and are found to be fairly applicable.
1. Introduction In-vivo dosimetry has become mandatory for the radiotherapy procedures involving high dose per fractions (sterotactic radiosurgery) [7,11], large volume irradiation (total skin electron and total or partial body irradiation) [9,38] and modern techniques with complex dose distribution, viz., intensity modulated radiotherapy (IMRT) [10,31], image guided radiotherapy (IGRT) and volumetric arc therapy (VMAT) [25]. The in vivo dosimetric procedures are performed either using active dosimeter, e.g., diode dosimeter, or passive dosimeter, e.g., thermoluminiscence dosimeter (TLD) or radiographic film. The diode dosimeters require cables or auxiliary equipment during the dose assessment and use of a large number of diodes is not cost-effective and also not physically possible for various in vivo applications. Also, its response is temperature dependent. In the medical applications, the passive dosimeters, especially, the thermo luminescent crystals [4,37,34] are frequently used for dosimetric applications because of their small energy dependence, small physical size and different shapes, reusability, ability to measure radiation dose from almost all types of ionizing radiation over wide dose range and easy adaptation with the patient’s body [17]. The TLDs are widely used as free standing dosimeter in radiotherapy applications to assess the radiation doses to the critical organs such as skin, lens, scrotal, fetal, thyroid, contra-lateral
⁎
Corresponding author. E-mail address: [email protected] (R. Singh).
https://doi.org/10.1016/j.nimb.2018.04.025 Received 9 February 2018; Received in revised form 16 April 2018; Accepted 16 April 2018 0168-583X/ © 2018 Elsevier B.V. All rights reserved.
breast and esophagus during the routine treatment both in external beam radiotherapy and brachytherapy. Considerable research work related to TL materials has been carried out to study their dosimetric characteristics, e.g., energy and radiation type dependency and sensitivity of different TL materials available for radiation dosimetry [32,16,1,18]. Despite the lower sensitivity, the LiF based material (TLD-100; LiF: Mg, Ti) is widely used in radiotherapy as compared to other more sensitive TL materials based on CaF2 (TLD-200, TLD-300, TLD-400), CaSO4: Dy (TLD −900) and Li2B4O7 (TLD-800). Its effective atomic number (Zeff = 8.14) is nearly tissue equivalent and hence closely approximates the absorption and scattering properties to that of the human tissue (Zeff = 7.42) [33,30]. The presence of 12Mg and 22Ti at concentrations of approximately 100 and 10 mol ppm, respectively, is responsible for the thermoluminiscence properties [27,15]. The 12Mg is intimately involved in the trapping process, and 22Ti in the recombination event [29,8]. The evaluation of the doses from large number of TLDs utilized for in vivo dosimetry also increases overall dose evaluation time if readout is performed at slow heating rate. The fast linear heating rates ∼10 K/s considerable reduces the time to evaluate absorbed doses by reading out large number of TLDs in the shortest possible time. It forms the basis of TL dosimetry in large scale monitoring. Increasing the heating rate during readout often appears necessary to reduce the time between
Nuclear Inst, and Methods in Physics Research B 426 (2018) 22–29
R. Singh, H.S. Kainth
were irradiated for the same dose of 186 cGy. The TLDs readouts were carried out at a linear heating rate (β) of 5 K/s. The Element correction coefficient (ECC) for each TLDs are calculated by dividing the average TL counts of all TLDs with individual TL counts. This process was repeated thrice and the ECC [2] of each TLD was evaluated as ECCi = Cavg / Ci;where Cavg is the average counts of all TLDs irradiated with same exposed dose and Ci is the counts from individual TLD, respectively. Only TLDs within ± 10% variation were included and others were discarded. The first part of the present experiment was related to study the effect of heating rate on thermoluminescence spectra. Ninty three TLDs were taken from the lot sorted after ECC determination and pre-irradiation annealed. The TLDs were immediately irradiated with the same dose of 186 cGy using the same experimental setup and the monitor units. After the pre-readout annealing, the TLDs were divided into 14 batches of 6 TLDs each. The TLDs from each batch were readout at 2, 3, 4, 5, 6, 7, 8, 10, 15, 20, 25, 30, 40 and 50 K/s linear heating rates using Rexon readout system. The spectra exhibits shape, size and location of dosimetric glow curve from different batches of TLDs readout were recorded at increasing heating rates. Background data for 14 batches each of 4 un-irradiated (pre-irradiation annealed) TLD-100 were also taken at same set of heating rates. The background spectra exhibit almost no background counts up to ∼573 K followed by slowly increasing trend up to 673 K. Various parameters, e.g., area under the glow curve, total counts, integrated counts over the temperature range 373 K-673 K, and peak temperature were recorded. The second part of the present experiment involved studies the dose readout on the calibration of TLDs at different heating rate. The sorted lot of TLDs with known Element correction factor (ECCi) were divided into 14 batches with each one consisting of 6 TLDs. Different batches were irradiated with doses ranging from 0.4 cGy to 1020 cGy in the varying dose step. After the pre-readout annealing, the readouts of TLDs from different batches were carried out at 5, 10, 15 and 30 K/s heating rates using Rexon readout system and the areas under the glow curves were used for dose calibration.
the measurements and dose evaluation, especially in routine dosimetry. Further, the readout at fast heating rate will result in change in shape, size, and position of the dosimetric peak. Investigations regarding read out of TLDs at fast heating rates is an active area of research in thermoluminescent dosimetry [12,21,39,6,36,20,3,26]. The knowledge of kinetic parameters trap depth (E), frequency curve (s), order of kinetics (b) and variation of peak maximum temperature (Tm) and intensity (Im), play vital role in understanding the TL phenomenon and its practical utility as radiation dosimeters. Other important observations include variation of Tm and Im with the heating rate [40,24,19]. The aim of present study is to evaluate the TL glow curves of cuboid shaped LiF: Mg, Ti (TLD-100) phosphor into its component peaks using general order kinetics proposed by May and Patridge [28]. The effect of linear heating rate over a wide range 2–50 K/s was studied for various parameters, viz., peak height, maximum peak temperature, total counts, integrated counts, area under various peaks in the TL glow spectrum of TLD-100 dosimeter. The reproducibility of TLDs at different heating rate was analyzed. Corrections for temperature lag between the heating element and the dosimeter and the effective heating rate (βeff) across the sample were estimated [22]. The dose calibration curves were obtained for the dose ranging 0.4 cGy-1000 cGy at different heating rates. 2. Method and material The samples used in the present study were LiF: Mg, Ti (trade name TLD 100) cuboid shaped rods with dimension 1 mm × 1 mm × 6 mm (Rexon TLD Systems and Components, Ohio, USA). The radiation dose was delivered by photon beam from 6 MV linear accelerator (Clinac DHX, Varian, CA). Rexon UL-300 readout system (Rexon TLD Systems and Components, Ohio, USA) (Model UL 300) interfaced to PC was used for recording and analyzing the thermoluminscence spectra from TLDs after irradiation. To erase any residual information before irradiation, all the TLDs were pre-irradiation annealed by the procedure involving heating at 400 °C for 1 h followed by 105 °C for 2 h as recommended by Yu and Luxton [42]. The absorbed dose was measured using A19 Exradin Ion chamber (Standard Imaging, Middleton, USA), RW3 solid water phantom (area 30 × 30 cm2, thickness range 0.1–1 cm, density 1.04 gm/cm3) and Supermax Electrometer (Standard Imaging, Middleton, USA). The active volume of A19 Exradin Ion chamber is 0.6 cc and readings are traceable to Reference Standard Laboratory of Radiation Standardization Section, Bhabha Atomic Research Centre, Mumbai, India. The monitor units required to deliver a dose of 186 cGy were obtained by placing the 0.6 cc ionization chamber in RW3 solid water phantom at the depth of 5 cm with source-to-surface distance of 100 cm and irradiation field size 10 × 10 cm2. The heating profile used for the TLD-100 readout consisted of (i) heating at linear rate from the room temperature 25 °C (298 K) to 100 °C (373 K) in 10 s, (ii) constant temperature at 100 °C (373 K) up to 15 s, (iii) heating from 100 °C (373 K) to 400 °C (673 K) as per the requisite linear rate (β), (iv) constant temperature at 400 °C (673 K) for 10 s, and (v) cooling cycle from 400 °C (673 K) to room temperature 25 °C (298 K) in 10 s. The glow curve spectrum of a TLD-100 crystal taken just after the exposure and readout at very low heating rate ∼0.1 K/s constitutes five peaks labeled as 1–5. Lowest peak 1 is occurring at temperature 338 K. It has half life of 10 min at 298 K. Although in the present work, heating rate below 2 K/s is not possible due to limitation of readout system. Throughout the present work, prereadout annealing of all the irradiated TLDs was done by heating at 105 °C (378 K) for 15 min. to eliminate the contribution from peak 1. Peaks 2 and 3 are known to be associated with Mg2+-cation vacancy pairs and peaks 4 and 5 with higher-order clusters of dipoles, possibly trimers [5]. To sort good quality TLDs, the response sensitivity factor for each individual TLD was determined. All the pre-irradiation annealed TLDs
3. Theoretical formulations The basic first-order kinetic theory for the thermal untrapping of electrons was first developed by Randall and Wilkins [35]. In case of readout of the irradiated thermoluminescence material, the rate of electrons released from the traps, dn/dt, is proportional to nb, where n (m−3) is the concentration of hole at the recombination centre and b is defined as the general-order kinetic parameter. The intensity of thermoluminescence (I) at any time (t) for TL kinetics of May and Patridge [28] order b is written as I (t ) = −dn/ dt = nbs′exp (−E / kT ) ; where E (in eV) is the activation energy, k (eV K−1) is the Boltzmann constant and T is the absolute temperature. The term s′ is called the frequency factor or attempt-to-escape factor and has dimensions of m3(b−1) s−1. In case of linear readout heating rate (β), i.e., T = To + βt, the intensity as a function of temperature [28] is given by
I (T ) = −
s′nob dn = exp (−E dt β
⎡ (b−1) s′nob − 1 / kT ) ⎢1 + β ⎢ ⎣
T
∫ T0
b (1 − b)
⎤ [exp (−E /kT ′)] dT ′⎥ ⎥ ⎦
(1)
Also, for the general order kinetics in terms of peak maximum intensity (Im) and peak maximum temperature (Tm) can be derived as [13] b
I (T ) = Im ⎡ ⎢ ⎣
(b−1) T 2 ⎛ 2kT ⎞ Z 1 −b 1− exp(D) + m ⎤ exp(D) b T2m ⎝ E ⎠ b ⎥ ⎦
where D =
E kT
(
T − Tm Tm
) and Z
m
=1+
(2)
2kT (b−1) Em .
By setting dI/dt = 0 at the peak maximum, T = Tm, one gets the condition 23
Nuclear Inst, and Methods in Physics Research B 426 (2018) 22–29
R. Singh, H.S. Kainth
Fig. 1. The glow spectra plotted on logarithmic scale from TLDs of different batches at different readout heating rates (a) 2 K/s (b) 5 K/s and (c) 10 K/s.
(b−1) s′ β
1+
T
∫
[exp (−E /kT ′)] dT ′ =
T0
s′bkTm2 exp (−E / kTm) βE
from peak 5 (dosimetric peak). The glow spectra obtained at heating rates 2, 5 and 10 K/s are plotted on log scale in Fig. 1(a)-(c). In addition to the complex peaks labeled 2–5 under the main glow curve, two more small peaks labeled ‘a’ and ‘b’ are also observed in the spectra. Peak ‘a’ is not observed in the background spectra taken with virgin TLD, while peak ‘b’ is also observed in the background spectra [shown in Fig. 1(a)-(c) as dotted lines]. Both these peaks also shift with increase in readout heating rate. The readout spectra with different heating rates were analysed using simple multi-gaussian peak fitting analysis using Origin 8.5 software. The dosimetric glow spectra of TLDs exposed to the same dose of 186 cGy and readout at different heating rates exhibit that the glow
(3)
The frequency factor s′is written as
s′ =
βE exp(−E / kTm) kZm Tm2
(4)
4. Results and discussion The typical glow peak spectrum of TLD-100 consisted mainly of peaks 2–5, with the major contribution to the glow curve spectra is 24
Nuclear Inst, and Methods in Physics Research B 426 (2018) 22–29
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Table 1 The values of peak temperature (peak 5) and maximum thermoluminiscence (TL) counts for different heating rates to readout TLD-100. Heating rate (K/s)
Maximum Peak temperature (K)
Maximum Peak Intensity (counts)
Heating rate (K/s)
Maximum Peak temperature (K)
Maximum Peak Intensity (counts)
2 3 4 5 6 7 8
493.7 501.3 505.0 509.1 511.8 514.3 519.6
514.3 ± 15.5 778.6 ± 19.2 989.6 ± 30.8 1273.8 ± 37.0 1519.0 ± 40.8 1890.1 ± 74.0 2029.3 ± 12.5
10 15 20 25 30 50
527.6 536.0 556.5 568.0 579.9 596.6
2459.8 3490.0 4337.9 5184.1 6042.9 7476.7
± ± ± ± ± ± ±
1.4 1.6 0.6 1.0 1.9 1.1 1.7
± ± ± ± ± ±
2.1 1.8 4.8 3.6 5.1 10.4
± ± ± ± ± ±
191.1 150.6 231.8 310.6 374.7 347.0
The glow peak due to βj is shifted towards the higher temperature keeping the integral stable and reducing slightly in the peak height. Ignoring the thermal quenching effects and assuming the peak shapes to be the same at different heating rates, the shift in the glow peak towards higher temperature as the rate of heating is given as
Ti−Tj = Ti Tj
k ⎛ βi ⎞ log E e ⎜ βj ⎟ ⎝ ⎠
(5)
The approximation is valid over a wide range of E and s values. The effective rate of heating of TLD (βeff) is smaller than the rate at which element is heated (β) and hence, within the first approximation, the effective heating rate [22] is given as
Tg−To−ΔT ⎞ βeff = ⎜⎛ ⎟β ⎝ Tg−To ⎠ Fig. 2. Recorded/observed and corrected heating rate for peaks 2,3,4,5.
(6)
where ‘Tg’ is the peak maximum temperature of a glow peak recorded with temperature lag (ΔT = Tg − Tm), ‘Tm’ is the real peak temperature of same glow peak without temperature lag and ‘To’ is the starting temperature usually of the room temperature (∼298 K). The effective heating rate and temperature position of the glow peak has been calculated using Eqs. (6) and (5), respectively. All calculations are made assuming no temperature lag at the lowest heating rate 2 K/s used in the present study. The different peaks have different effective heating rates. The observed and effective heating rates are deviated from linear behaviour as shown in Fig. 2. The difference between the recorded peak position and the corrected peak position between the same peaks increases with heating rate as shown in Fig. 3. From Fig. 4(a), it appears that the peak area under the glow curve increases for the TLD batches irradiated with same radiation dose as the heating rate is increased. This increase in area under TL-temperature glow curves of TLDs and read at increasing heating rates was also reported by Kumar et al. [24] who speculated that there is ambiguity in the presentation of effect of heating rate on TL glow curves. The TL phenomenon has been basically derived as time derivative of luminescence signal from sample during constant linear heating of samples.
curve maxima shift towards higher temperature region (shown in table 1) and the peak area increases with increase in the heating rate (Fig. 1). The temperature of the glow peak maximum is mainly determined by two processes (i) increase of released charge carriers with increasing temperature (ii) the decrease of charge carriers due to depletion of the trap. For a low heating rate, the TLD will be held at a certain temperature for a longer time which implies that the trap is emptied at lower temperature resulting in a lower glow peak temperature. The situation is just opposite in case of higher heating rate of the TLD and results in higher glow peak temperature. Also, the temperature difference between the heating element and the TLD increases at fast heating rate, i.e., the actual temperature at TLD lags the recorded temperature. This difference is associated with the thermoluminescence measurements set up involving temperature gradient within the heating element, non-ideal thermal contact between heater element, planchet and sample, and temperature gradient across the TL sample. The recorded temperature is obtained using non-contact infrared sensor positioned beneath the planchett. At higher heating rates, the glow curves of different TLDs within a given batch are widely spread and reproducibility of glow curve in these TLDs within a given batch is observed to be poorer. The values of standard deviation for position of dosimetric peak (peak 5) at various readout heating rates are given in Table 1. They were found to be ± 5.1 K, ± 13.6 K and ± 10.4 K, respectively, for β = 30 K, 40 K and 50 K while the average value of standard deviation is < ± 2.1 K for heating rate below β = 10 K/s. The average shift in glow curve main peak position per unit increase in heating rate βeff is found to be ∼4 K for low heating rate and decreases to ∼0.8 K at higher heating rates, respectively (Table 1. The spread in glow curve maxima at higher heating rates is also because of contact heating of the TLD placed on the planchett, which can give rise to spurious shift in the glow peaks [41]. The temperature lag between the heating element and the TL dosimeter was corrected to first approximation using the formulation given by Kitis and Tuyn [22] for the general-order kinetics. The glow peaks obtained at two different heating rates, βi and βj (> βi), have the peak maximum temperatures Ti and Tj (> Ti), respectively.
Fig. 3. Temperature lag between observed and corrected peak position for peak No. 5 plotted as function of heating rate. 25
Nuclear Inst, and Methods in Physics Research B 426 (2018) 22–29
R. Singh, H.S. Kainth
Fig. 4. (a) The typical glow curve spectra obtained from TLDs exposed to same dose verses different heating rates and (b) shows the same spectra normalized w.r.t. their corresponding heating rate (β).
However, traditionally luminescence signal has been plotted against temperature. But this plot is linear transformed temperature scale of independent time scale. This observation/appearance of increase in area under TL–temperature glow curves with increase in heating rate at a constant dose is the consequence of transformation of time to temperature scale (temperature scale obtained om time scale by multiplying with β, T= To + βt . The observations are better presented in Fig. 4(a) and (b). Fig. 4(a) shows the typical glow curve spectra obtained from TLDs exposed to same dose and readout at different heating rates and Fig. 4(b) shows the same spectra with the counts divided by the corresponding heating rate (β). For normalized glow curves (I/ β–temperature), the glow peak height decreases with increase in heating rate, which is actually true for I/β or TL/β versus temperature plots. It is further pointed out that increase in heating rate for TLD readout does not lead to increase in sensitivity of the dosimeter. With increase in heating rate more rapidly, the phonon density increases that possibly may make thermal energy transfer to trap charged at defects less efficient. This forces equilibrium condition of maximum in temperature scale higher. More fundamental treatment formulation of lattice vibration and TL phenomenon will bring out same more facts about this question. Under Randall and Wilkins [35] conditions, the total light output is determined by the trapped charged, which is proportional to the absorbed dose and the heating rate influences only the time at which the trapped charge is released but not the total light output. From the various TLD spectra obtained at different heating rates, the average values of integrated counts are obtained between the two specified temperatures covering the main glow curve (Peak 5). The Fig. 5 shows the plot of average integrated counts corrected for the sensitivity of the respective TLDs. The integrated counts under the
Fig. 5. The observed integrated TL peak area plotted as a function of heating rate.
main glow curve are observed to decrease smoothly with increase in observed heating rate (βeff). It is because the luminescence intensity of the TL material is a temperature sensitive factor which decreases with increase in temperature and heating rate due to competition between radiative and non-radiative transitions. The increases in the probability of non-radiative transition with rise in temperature and heating rate was also explained by Kafadar [19] and Kadari and Kadri [18]. Apart from the increased probability of non-radiative transitions at higher temperatures, the observed effects have also been assigned to the effects of heating rate on the migration of charge carriers released during the TL readout. Then, it was inferred that the glow peaks occurring at high temperatures must exhibit higher thermal quenching than those occurring at lower temperatures in any TLD material. 26
Nuclear Inst, and Methods in Physics Research B 426 (2018) 22–29
R. Singh, H.S. Kainth
Fig. 6. Peak fitting of the observed glow curves us glow curve deconvolution (GCD) software for peaks (2–5) within the glow curve.
at 5 K/s to 1.89 eV for 30 K/s. The peak temperature values (Tm) were deduced for the peaks labeled 2–5. These values are given in Table 3 and plotted in Fig. 7 for the observed and corrected temperature position with heating rates. In composite glow curves, where an excellent fit can be obtained with many pairs of different E and s values. Kitis [23] has discussed preliminary acceptance criteria for E and s values resulting from the glow-curve deconvolution analysis. Some effort must be made in order to formulate some criteria according to which some E and s pairs are accepted. Indeed, the reliability of the resulting E and s values is questionable when these values are deduced from analysis of spectra taken at the higher heat rates, which are not corrected for temperature lag. The knowledge of temperature lag between the heating element and dosimeter is an essential part for extracting physical information from glow curve. The experimental data at higher heating rates must be corrected for temperature lag before fitting. The Fig. 7 demonstrates the observed peak positions and those corrected for the temperature lag [22]for the peaks 2–5. And taking first order kinetics, the plot of ln(Tm2 /) vs 1/(kTm), must be a straight line with slope E. This method is very much dependent upon Tm, so it would be a very good test for the
A Microsoft Windows-operated user-friendly computer program, TLAnal (TL Glow curve Analyser) has been used in the present work to resolve complex composite TL glow-curve in the readout spectra consisting of strongly overlapping peaks. The program involves fitting of experimental points to a non-linear function describing the general order kinetics thermoluminescence glow curve using the least squares Levenberg-Marquardt method [14]. Its graphical interface enables easy intuitive manipulation of glow peaks by pre-selecting the various parameters and their ranges at the initial stage. Fig. 6(a)-(d) show the fitted spectra recorded at different heating rates. The procedure continues by sequentially changing the fitting parameter until a minimum value of FOM [14] is obtained. This program can accommodate fitting of the glow curve spectrum readout up to heating rate 30 K/s and delivers the trap parameters, viz., activation energy (E), order of kinetics (b) and frequency factor (s), and initial concentration of traps (no) corresponding to various fitted peaks. The values of activation energy (E), frequency factor (s) and trap concentration (no) are shown in Table 2. The values of the order of kinetics parameter (b) are 2.09–2.29 and ∼1.91–2.12, respectively, for peaks 2 and 3, 1.8–2.10 for peaks 4 and 5. The value of activation energy (E) for peak 5 varies from 1.58 eV
Table 2 The value of activation energy ‘E’, frequency factor ‘s’, general order parameter ‘b’ and trap concentration ‘no’ for different peaks at heating rates ≤30 K/s. Hea-ting rate (K/s)
5 10 15 20 30
Peak 2
Peak 3 −1
E (eV)
s (s
1.04 1.10 1.04 1.16 1.07
1.32E+15 3.59E+15 5.30E+13 1.52E+15 7.16E+14
)
b
no (m
2.25 2.1 2.23 2.11 2.09
978 945 935 848 918
−3
)
Peak 4 −1
E (eV)
s (s
)
1.13 1.18 1.21 1.21 1.24
6.28E+15 5.57E+15 7.67E+16 3.60E+14 5.40E+14
b
no (m
1.94 1.91 2.04 2.08 2.12
1212 2004 1387 1599 1532
27
−3
)
Peak 5 −1
E (eV)
s (s
)
1.20 1.26 1.31 1.37 1.37
5.45E+15 4.09E+15 2.40E+15 1.34E+16 2.95E+15
b
no (m
2.06 1.95 1.99 1.91 2.1
1877 2573 1871 1873 3366
−3
)
E (eV)
s (s−1)
b
no (m−3)
1.58 1.71 1.7 1.79 1.89
2.80E+15 1.17E+17 2.09E+16 4.71E+16 5.70E+17
1.92 1.91 1.91 1.85 2.1
5812 4448 5625 5107 4381
Nuclear Inst, and Methods in Physics Research B 426 (2018) 22–29
R. Singh, H.S. Kainth
Table 3 The average value of peak temperature for different peaks and corrected peak position (temperature lag) at different heating rates. The effective heating rate corresponds to peak no 5. Heating rate (K/s)
2.0 3.0 4.0 5.0 6.0 7.0 8.0 10.0 15.0 20.0 25.0 30.0 50.0
Effective heating rate (K/s)
2.0 3.0 3.9 4.9 5.8 6.8 7.6 9.3 13.7 17.2 20.9 24.3 39.5
Average Peak position (K)
Average corrected peak position (K)
Peak 2
Peak 3
Peak 4
Peak 5
Peak 2
Peak 3
Peak 4
Peak 5
436.6 442.1 447.5 452.0 457.2 457.7 460.7 473.5 485.6 499.8 513.6 522.1 530.9
464.6 469.4 477.5 484.8 487.1 489.0 490.1 503.5 509.1 534.5 538.9 547.3 556.4
474.9 482.2 487.9 494.8 496.4 498.5 502.1 513.0 518.3 535.4 551.1 560.1 573.2
493.7 501.3 505.0 509.1 511.8 514.3 519.6 527.6 536.0 556.5 568.0 579.9 596.6
436.6 439.9 442.2 444.1 445.6 446.9 448.1 450.3 454.2 457.3 459.9 462.0 467.3
464.6 468.3 471.0 473.1 474.9 476.3 477.6 480.1 484.2 488.1 490.6 492.9 498.8
474.9 478.7 481.4 483.7 485.5 487.0 488.4 491.0 495.2 498.9 502.0 504.4 510.8
493.7 497.8 500.8 503.2 505.1 506.8 508.3 510.9 515.6 519.7 522.8 525.6 532.7
Fig. 9. Dose calibration curve (net TL counts versus absorbed dose) for 6 MV Xrays at heating rate 2, 5, 15 and 30 K/s.
Fig. 7. The TL glow peak positions with observed heating rate and effective heating rate obtained after temperature lag correction.
heating rate (K/s). It depicts the effect on dose calibration curve of TLD 100 with heating rate. As has been observed, the TL output of TLD-100 decreases with increase in the heating rate due to thermal quenching effects. At higher heating rates and low doses ∼few tens of cGy, the contribution due to the background spectrum obtained with virgin TLD becomes significant. Hence for TLDs irradiated with low doses readout cannot be performed reliably at high heating rates ∼40–50 K/s.
5. Conclusion The luminescence characteristics of the thermoluminescence (TL) from TLD 100 were examined using the heating rate dependence of the TL signal. As the heating rate varies the TL peaks shift to different temperatures and become affected by thermal quenching to different extents. In this work the heating rate was varied over several orders of magnitude and, through deconvolution of the TL glow curve the behaviour of the main TL peaks was followed as a function of the temperature at which the peak appeared in the glow curve. Through an analysis of the glow peak areas as a function of glow peak temperature the decrease in the efficiency of TL production with increasing temperature could be monitored and the analysis supports the quenching phenomenon. The General order kinetics (GPK) is used in the present study to analyze the effect of heating rate on the dosimetric properties of TLD-100. The heating rate has a significant effect not only on sensitivity and intensity of TL material but also on shape, size and position of glow curve of TLD-100. The dose calibration curve is dependent on
Fig. 8. The plot of ln(Tm2 /) vs 1/(kTm) for peaks 2–5 corrected for temperature lag.
validity of temperature lag corrections. Fig. 8 shows the plot of ln(Tm2 /) vs 1/(kTm) for peaks 2–5. The application of this method to gives straight line for corrected peak temperature for peak 2–5. The values of E deduced are ∼1.65 eV. The dose calibration curves over the dose 0.4–1020 cGy are plotted as shown in Fig. 9 for 2, 5, 15 and 30 K/s 28
Nuclear Inst, and Methods in Physics Research B 426 (2018) 22–29
R. Singh, H.S. Kainth
the heating rate due to thermal quenching. The variation between TL counts for same doses varies significantly at high dose irradiation and background counts also increase in the main glow curve region and hence high heating rates ∼50 K/s are not suitable for TLD readout for low dose measurements ∼10 cGy. At lower heating rates the reproducibility in shape, size and location of glow curve for TLDs having nearly same sensitivity and irradiated with same dose (same radiation type) are better and it depreciate at higher heating rates. The peaks under the glow curve were shifted to higher temperature region with rise in heating rate and average shift in peak position (in K) per unit rise in heating rate is found to be larger for heating rate below 10 K/s. The decreases in TL output, sensitivity and area under glow curve with increase in heating rate are elucidated in TL/heating rate (s/K) versus temperature (K) plot. It has been proposed that the accuracy in dosimetric evaluation for personnel or in vivo dosimetry in medicine will be maintained if the TL dosimeter is readout at an appropriate heating rate at which its calibration was done and for low dose evaluations, lower possible heating rates are recommended.
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