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Long term study of Harshaw TLD LiF – Glow curve peaks and sensitivities
Radiation Measurements 46 (2011) 1448e1452
Contents lists available at ScienceDirect
Radiation Measurements journal homepage: www.elsevier.com/locate/radmeas
Long term study of Harshaw TLD LiF e Glow curve peaks and sensitivities Ling Z. Luo* Thermo Fisher Scientific, One Thermo Fisher Way, Oakwood Village, OH 44146, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 October 2010 Received in revised form 23 June 2011 Accepted 27 June 2011
A series of work has been published in previous papers for the long term study of Harshaw TLD LiF materials for a 24-month period. Parts I and II were focused on the characteristic of the material fading, Lower Limit of Detection (LLD), and uncertainty. They were presented in SSD15 (2007) and LumDetr (2009). This work is the continuation of this series e Part III: Glow Curve Peaks and Sensitivities. It presents the analysis and sensitivity change over 24 months for LiF:Mg,Ti and LiF:Mg,Cu,P materials stored at 0 C, 20 C, and 40 C. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Harshaw TLD Fade Glow curve deconvolution LiF:Mg,Ti LiF:Mg,Cu,P Dosimeter
1. Introduction In Part I of this series of long term study, the overall fade rates for Harshaw TLD LiF respective to Signal and Sensitivity loss, at storage temperature of 0 C, 20 C, and 40 C, were presented (Luo, 2008). The stability or the fade rate of individual peak at these three representative temperatures over a period of 24 months is the focus of this current work (Part III). Over decades, research and experiments have been devoted to study and understand the properties of different thermoluminescent (TL) materials. The best known TLD is LiF:Mg,Ti, recognized as TLD-100 (or its ‘sisters’ 7Li-enriched TLD-700 and 6Li-enriched TLD600). Owing to its popularity and extended efforts toward it, this material is understood reasonably well. The kinetic models and simplified mathematical function were developed (Moscovitch, 1986; Horowitz and Yossian, 1995; Da Rosa et al., 1999; Horowitz et al., 2002). Various commercial computerized glow curve deconvolution/analysis (CGCD or CGCA) are available. Most of these CGCD/CGCA programs work well for LiF:Mg,Ti material. The firstorder kinetics (Randall & Wilkins) is one of them. With growing use of the high sensitive material LiF:Mg,Cu,P, attention on deconvoluting this material has grown. Luo et al. (2006), in a previous work, presented a combination of first-order kinetics fit with a modified Gaussian function to peak 4 that worked relatively well. However, that is not a commercial program. * Tel.: þ1 440 703 1405. E-mail address: ling.z.luo@thermofisher.com. 1350-4487/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.radmeas.2011.06.065
An increasing interest is expressed on whether a commercial curvefitting package is suitable for this material for the glow curve deconvolution purpose. In this work, two different fitting methods are experienced: first-order kinetics with modified Gaussian and Weibull area fit from the commercially available software PeakFitÒ. 2. Setup and study 2.1. Setup TLD materials studied were described in Luo’s previous papers (Luo, 2008 and 2010). They were LiF:Mg,Ti (TLD-1776) and LiF:Mg,Cu,P (TLD-1776H) card with a configuration such that detector 1 is a natural Li, detectors 2 and 3 are 7Li-enriched Li, and detector 4 is 6Lienriched Li. The dosimeters were respectively stored in three temperatures: standard laboratory temperature 20 C; low temperature 0 C and high temperature 40 C. Irradiation of 3 mSv was performed at either the beginning or the end of the scheduled fading period, which ranged from 2 days to 24 months. Then the dosimeters were read using the readout profiles described in Table 1. 2.2. Fitting techniques As mentioned, it is well known for LiF:Mg,Ti material that glow peaks 1e5 follow first-order kinetics theory (Moscovitch, 1986). This theory was first developed by Randall & Wilkins and expressed as (1) below.
L.Z. Luo / Radiation Measurements 46 (2011) 1448e1452 Table 1 Readout Time-temperature Setup used for studied material. Readout Setup Preheat Heat Rate Acquire
TLD-1776 (LiF:Mg,Ti)
TLDe1776H (LiF:Mg,Cu,P)
No-Preheat
No-Preheat
W/Preheat
50 C for 0 s 25 C/s 13(16*)s to Max 300 C
50 C for 0 s 15 C/s 23(26*)s to Max 260 C
165 C for 10 s 15 C/s 13(16*)s to Max 260 C
Note: * is for is 6Li-enriched element.
E 1 1 E 1 1 I ¼ Io exp 1 þ exp K Tm T K Tm T
(1)
where I is the intensity of glow signal; I0 is the glow peak height; Tm is the peak temperature; T is the heating temperature; E is the peak activation energy, and K is Boltzmann’s constant. For LiF:Mg,Cu,P material, fitting glow peaks 1e4 with Randall & Wilkins function leaves a few percentages of the total TL readout value that were contributed from higher temperature peaks when performing the readout using the time-temperature setups in Table 1. To take these few percentages into account, Luo et al. (2006) demonstrated that a modified Gaussian for peak 4 resulted in a better Figure-of-Merit fit. This modified Gaussian function is expressed as (2). Parameters A, B, and C are the modified Gaussian parameters.
I4 ¼ A þ I04 exp
! T Tm4 C 0:5 B
(2)
PeakFit is a commercial automated peak separation software from Systat Software. Here it is investigated whether it is suitable for the glow curve deconvolution purpose. Weibull area fit is one of the fit functions tested. It is tested on both LiF:Mg,Ti and LiF:Mg,Cu,P cards. This function is expressed as (3) below. Where a0, a1, a2, and a3 are the parameters respectively for peak area, center, width, and shape.
2 3a3 1 1 a0 a3 6 a3 1 a3 7 I ¼ a3 4x þ a2 a1 5 a3 a2 2
0
6 B 6 Bx þ a2 6 B exp6 6B 6 B 4 @
1a3 3 1 a 3 7 a3 1 a1 C C 7 a3 C 7 C 7 C 7 a2 A 7 5
ð3Þ
Each time-temperature profile in Table 1 consists of a linear heating portion and a temperature plateau portion. However, the first-order kinetics theory assumes a linear heating throughout the readout; this temperature is then referred to as hypothetical temperature (Figel and Sprunck, 1999). The hypothetical linear temperature is used in this work. In summary, for a comparison, both first-order kinetics fit and Weibull area fit are used for LiF:Mg,Ti, whereas first-order kinetics with modified Gaussian fit and Weibull area fit are used for LiF:Mg,Cu,P. 3. Results and discussion As described in Part I (Luo, 2008), TL fading comes from two components: signal loss and sensitivity loss, in terms of irradiation that occurred at the beginning and end of storage time,
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respectively. Dosimeters were stored in different temperatures for a time period from 2 days to 24 months; both signal and sensitivity loss data were collected. Fade rates due to signal or sensitive or average loss are expressed in the function form F ¼ a$lnðtÞ þ b. Parameters a and b are provided in Table 2 of Part I (Luo, 2008). To find the fade rate for each glow peak, all glow curves are processed through the two appropriated fitting techniques as mentioned above. Data shows that the isotopic difference (Li-natural, 7Li, or 6 Li) causes insignificant variance in glow peaks. Therefore, discussion in this paper will not differentiate between the isotopes. Fig. 1 shows typical glow curves of 2-day fade at room temperature. The glow curves on the left represent LiF:Mg,Ti read with no-preheat. The middle and right glow curves are the representatives of LiF:Mg,Cu,P read with no-preheat and with preheat, respectively. The upper three glow curves are fitted by first-order kinetics (and modified Gaussian to peak 4 for LiF:Mg,Cu,P) and the lower glow curves are fitted using Weibull fit. The two-day fade is set as the baseline. At the baseline, for LiF:Mg,Ti, the asymmetric first-order kinetics deconvolutes peaks 2 to 5 such that each weighs 8%, 18%, 25%, and 47% to the whole-glowcurve-value, respectively; in contrast, Weibull method separates them to 10%, 19%, 31%, and 38%. Though the weight of peak 5 appears 9% (47%38%) in difference between the two methods, the main dosimetric peaks 4 þ 5 are close (72% vs. 69%). This is in agreement with the published work of others. Similar results are observed for the LiF:Mg,Cu,P no-preheat readout. As with preheat readout, the lower temperature peaks are eliminated, leaving only the main dosimetric peaks 3 þ 4. Therefore, both fitting methods produce very comparable results, 89% vs. 88%. Representative results in Fig. 2 shows the weight of each peak to the baseline-whole-glow-curve-value changes in 24-months at room temperature. The left two graphs are for LiF:Mg,Ti. The middle ones are for LiF:Mg,Cu,P read with no-preheat and the right two graphs are LiF:Mg,Cu,P read with preheat. The top three are generated by first-order kinetics method and the bottom three are from Weibull fit. Though Weibull fit offers better overall Figure-of-Merit (not shown in the graphs), it is more sensitive to glow curve shape and has greater errors in allocating the weight of each peak. This is indicated by the data points being more scattered around its trend line. However, in the case of LiF:Mg,Cu,P with preheat readout, both methods agree with each other and are consistent. In previous paper (Luo, 2008), it was observed that at 0 C storage temperature, LiF:Mg,Cu,P response appeared to increase as a function of fade time. All four LiF:Mg,Cu,P graphs in Fig. 2 show that this increase come from peak 4. The increase is due to the charge transfer from shallow traps to deeper traps not just a deconvolution effect. In fact this is also true for the cases of 0 C and 40 C storing temperatures (not shown in the graph). Over a 24-month period, each peak at different temperature demonstrates its signal loss and sensitivity loss. The rate of loss, in other words the stability or fade of each peak, is estimated using function F ¼ c$ln2 ðtÞ þ a$lnðtÞ þ b, where t is fading time in day (which is the period from clearing the dosimeter to reading it out, t 1); a, b, and c are linear parameters. Note that the whole-glow-curve-value (Peaks 1e5) fading is estimated by linear logarithm function: F ¼ a$lnðtÞ þ b. However, the individual peak is best fitted by second-order polynomial logarithm. Author is lack of an explanation. Table 2 summarizes the test and provides these parameters for all test temperatures and all cases. In part I of this study, it showed that the Signal faded faster than the Sensitivity at low storage temperature, and vice versa at higher temperature, the Sensitivity fade accelerated faster than the Signal did. It was discussed then this might due to the preservation of low temperature peak 2. The current work however show that the main peaks (4 þ 5) also
1450 Table 2 Summary of parameters a, b, and c for fade function F ¼ c$ln2 ðtÞ þ a$lnðtÞ þ b for the main dosimetric peaks, where t is the fading time from clearing to readout in day t 1. Column “Total” is re-generated from Table 2 of Luo (2008) and shown here for reference. LiF:Mg,Cu,P e NoPreheat
LiF:Mg,Ti Total
0.0569 1.003 0.0524 1.0018 0.0425 1.0531
0.0726 1.0075 0.0736 1.0832 0.0333 1.0568
0.0647 1.0053 0.0630 1.0425 0.0379 1.0550
Weibull
Total
Peak5
Peak4
Peak5
Peak4
0.0076 0.0528 0.6161 0.0065 0.0749 0.4238 0.0035 0.0036 0.4768
0.0086 0.0953 0.2902 0.0040 0.0729 0.3275 0.0101 0.0537 0.1807
0.0132 0.1003 0.5632 0.0048 0.0256 0.3626 0.0074 0.0415 0.3813
0.0072 0.0261 0.2714 0.0054 0.0605 0.4092 0.0043 0.0158 0.3079
0.0078 0.0400 0.6348 0.0086 0.0795 0.4397 0.0024 0.0123 0.4532
0.0107 0.1179 0.3282 0.0011 0.0539 0.3074 0.0077 0.0377 0.1926
0.0028 0.0142 0.4014 0.0014 0.0140 0.3641 0.0012 0.0028 0.3502
0.0006 0.0335 0.3351 0.0046 0.0019 0.3388 0.0004 0.0003 0.2825
0.0077 0.0464 0.6255 0.0076 0.0772 0.4317 0.0030 0.0043 0.4650
0.0096 0.1066 0.3092 0.0025 0.0634 0.3175 0.0089 0.0457 0.1867
0.0052 0.0430 0.4823 0.0031 0.0198 0.3633 0.0043 0.0222 0.3657
0.0033 0.0037 0.3032 0.0004 0.0312 0.3740 0.0020 0.0078 0.2952
0.0225 1.0073 0.0187 1.0032 0.0153 1.0256
0.0315 1.0240 0.0249 1.0339 0.0060 1.0111
0.0270 1.0156 0.0218 1.0186 0.0107 1.0183
1st-order/Mod Gaussian
Weibull
Total
Peak4
Peak3
Peak4
Peak3
0.0069 0.0431 0.7882 0.0003 0.0116 0.7683 0.0060 0.0462 0.8495
0.0063 0.0648 0.1644 0.0010 0.0339 0.1769 0.0063 0.0376 0.0853
0.0092 0.0668 0.7210 0.0030 0.0398 0.6799 0.0036 0.0077 0.6818
0.0063 0.0657 0.1699 0.0017 0.0394 0.1916 0.0043 0.0107 0.1609
0.0036 0.0095 0.8208 0.0025 0.0153 0.7659 0.0062 0.0490 0.8478
0.0045 0.0533 0.1731 0.0011 0.0101 0.1489 0.0042 0.0255 0.0990
0.0053 0.0238 0.7617 0.0067 0.0573 0.6472 0.0022 0.0034 0.7024
0.0039 0.0441 0.1566 0.0025 0.0386 0.1981 0.0016 0.0011 0.1424
0.0052 0.0263 0.8045 0.0014 0.0134 0.7671 0.0061 0.0476 0.8487
0.0054 0.0591 0.1688 0.0000 0.0220 0.1629 0.0052 0.0316 0.0922
0.0072 0.0453 0.7414 0.0048 0.0485 0.6636 0.0029 0.0056 0.6921
0.0051 0.0549 0.1633 0.0021 0.0390 0.1948 0.0029 0.0048 0.1517
0.0165 1.0122 0.0065 1.0243 0.0056 0.9992
0.0292 1.0343 0.0139 1.0513 0.0043 1.0033
0.0228 1.0233 0.0102 1.0378 0.0049 1.0012
1st-order/Mod Gaussian
Weibull
Peak4
Peak3
Peak4
Peak3
0.0029 0.0179 0.8595 0.0018 0.0252 0.8108 0.0022 0.0037 0.8507
0.0016 0.0195 0.0647 0.0000 0.0097 0.0700 0.0021 0.0120 0.0407
0.0026 0.0166 0.8358 0.0015 0.0208 0.8081 0.0019 0.0005 0.8210
0.0036 0.0332 0.0776 0.0015 0.0028 0.0683 0.0037 0.0216 0.0523
0.0036 0.0080 0.8654 0.0044 0.0311 0.8145 0.0018 0.0051 0.8557
0.0021 0.0205 0.0655 0.0000 0.0064 0.0651 0.0019 0.0129 0.0388
0.0033 0.0050 0.8577 0.0043 0.0314 0.7994 0.0010 0.0081 0.8076
0.0013 0.0148 0.0632 0.0016 0.0072 0.0502 0.0015 0.0068 0.0675
0.0033 0.0129 0.8625 0.0031 0.0281 0.8126 0.0020 0.0044 0.8532
0.0019 0.0200 0.0651 0.0000 0.0080 0.0676 0.0020 0.0124 0.0398
0.0029 0.0108 0.8467 0.0029 0.0261 0.8038 0.0014 0.0043 0.8143
0.0024 0.0240 0.0704 0.0015 0.0022 0.0593 0.0026 0.0142 0.0599
L.Z. Luo / Radiation Measurements 46 (2011) 1448e1452
Signal Loss c 40 C a b c 20 C a b c 0 C a b Sensitivity Loss c 40 C a b c 20 C a b c 0 C a b Average c 40 C a b c 20 C a b c 0 C a b
1st-order
LiF:Mg,Cu,P e W/Preheat
L.Z. Luo / Radiation Measurements 46 (2011) 1448e1452
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Fig. 1. Glow curves and deconvoluted peaks for LiF:Mg,Ti (left) and LiF:Mg,Cu,P (middle e no-preheat readout; right e w/preheat readout). Upper glow curves are fitted by firstorder kinetics (modified Gaussian to peak 4 for LiF:Mg,Cu,P) and the lower glow curves are fitted using Weibull fit.
contribute to it. Let us look at an example. From Table 2, using the parameters provided in the columns “LiF:Mg,Ti, 1st-order, Peak 5 and Peak 4”, it can be calculated that, for LiF:Mg,Ti, the 24-month Signal fade from peaks 4 þ 5 at 0 C and 40 C are 70% and 67%,
respectively. While during the same period, the Sensitivity fade are 75% and 58% respectively at 0 C and 40 C. Hence, at low storage temperature 0 C, Signal from main peaks loss 5% (75%70%) more in 24 months. At the same period, Sensitivity loss from main peaks
Fig. 2. The weight of each peak to the baseline-whole-glow-curve-value changes in 24-months in room temperature for LiF:Mg,Ti (left) and LiF:Mg,Cu,P (middle e no-preheat readout; right e w/preheat readout). Upper graphs are generated by first-order kinetics (modified Gaussian to peak 4 for LiF:Mg,Cu,P) method and bottoms are from Weibull fit. The dotted lines are predicted trend lines for Total, Peak 5, Peak 4 or Peak 3. The solid line is for main peaks (Peak 4 þ 5 for LiF:Mg,Ti and Peak 3 þ 4 for LiF:Mg,Cu,P). Individual points are the actual data for each peak.
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L.Z. Luo / Radiation Measurements 46 (2011) 1448e1452
advanced 9% (67%58%) more at 40 C. The work in Part I, also can be calculated from Table 2 column “LiF:Mg,Ti, Total”, shows these two fade rates of whole-glow-curve-value differences are 7% (84% 77%) and 10% (63%53%) at 0 C and 40 C, respectively. Hence the contribution from low temperature peaks in fact is only a couple of percents, much less than author previously thought. The similar is observed for LiF:Mg,Cu,P as well.
4. Summary The isotopic difference (Li-natural, 7Li, or 6Li) causes insignificant variance in glow peaks. Two fitting methods were used: first-order kinetics with modified Gaussian and Weibull area fit. The first-order kinetics functions fit LiF:Mg,Ti well in all temperature cases. For LiF:Mg,Cu,P, using modified Gaussian function for peak 4 to include the contribution from higher temperature peaks yields better fit. Weibull area fit results in greater errors in allocating the relative weight of individual peak, though the overall Fit-of-Merit is better. The main peak has less percentage compared to that of the first-order kinetic fit. Both fitting methods show that the dosimetric peaks 4 þ 5 (or 3 þ 4 for LiF:Mg,Cu,P) are relatively stable in all temperatures cases. Two fitting methods agreed with each other for LiF:Mg,Cu,P TLD card in storage temperature of 20 C, with specified preheated
readout setup. Parameters (a, b, and c) of fade function are provided. Acknowledgments The author wishes to thank her colleagues for all the support in this series of work. References Da Rosa, L.A.R., Regulla, D.F., Fill, U.A., 1999. Precision for low Dose assessment using TLD-100 Chips and computerised glow curve analysis. Radiat. Protec. Dosim. 85, 175e178. Figel, M., Sprunck, M., 1999. Fast cooling and computerised glow curve deconvolution in routine personnel monitoring with TLD-100. Radiat. Protec. Dosim. 81, 259e264. Horowitz, Y., Yossian, D., 1995. Computerised glow curve deconvolution: application to thermoluminescence dosimetry. Radiat. Protec. Dosim. 60. Horowitz, Y., Delgado, A., Pradhan, A.S., Yoder, R.C., 2002. Topics under debate e the use of Computerised glow curve analysis will optimise personal thermoluminescence dosimetry measurements. Radiat. Protec. Dosim. 102, 269e277. Luo, L.Z., 2008. Extensive fade study of Harshaw LiF TLD materials. Radiat. Meas. 43, 365e370. Luo, L.Z., 2010. Long term study of Harshaw TLD LiF e LLD and Uncertainty. Radiat. Meas 45, 569e572. Luo, L.Z., Velbeck, K.J., Moscovitch, M., Rotunda, J.E., 2006. LiF: Mg, Cu, P glow curve shape dependence on heating rate. Radiat. Protec. Dosim. 119, 184e190. Moscovitch, M., 1986. Automatic method for Evaluating Elapsed time between irradiation and readout in LiF-TLD. Protec. Dosim. 17, 165e169.
Contents lists available at ScienceDirect
Radiation Measurements journal homepage: www.elsevier.com/locate/radmeas
Long term study of Harshaw TLD LiF e Glow curve peaks and sensitivities Ling Z. Luo* Thermo Fisher Scientific, One Thermo Fisher Way, Oakwood Village, OH 44146, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 October 2010 Received in revised form 23 June 2011 Accepted 27 June 2011
A series of work has been published in previous papers for the long term study of Harshaw TLD LiF materials for a 24-month period. Parts I and II were focused on the characteristic of the material fading, Lower Limit of Detection (LLD), and uncertainty. They were presented in SSD15 (2007) and LumDetr (2009). This work is the continuation of this series e Part III: Glow Curve Peaks and Sensitivities. It presents the analysis and sensitivity change over 24 months for LiF:Mg,Ti and LiF:Mg,Cu,P materials stored at 0 C, 20 C, and 40 C. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Harshaw TLD Fade Glow curve deconvolution LiF:Mg,Ti LiF:Mg,Cu,P Dosimeter
1. Introduction In Part I of this series of long term study, the overall fade rates for Harshaw TLD LiF respective to Signal and Sensitivity loss, at storage temperature of 0 C, 20 C, and 40 C, were presented (Luo, 2008). The stability or the fade rate of individual peak at these three representative temperatures over a period of 24 months is the focus of this current work (Part III). Over decades, research and experiments have been devoted to study and understand the properties of different thermoluminescent (TL) materials. The best known TLD is LiF:Mg,Ti, recognized as TLD-100 (or its ‘sisters’ 7Li-enriched TLD-700 and 6Li-enriched TLD600). Owing to its popularity and extended efforts toward it, this material is understood reasonably well. The kinetic models and simplified mathematical function were developed (Moscovitch, 1986; Horowitz and Yossian, 1995; Da Rosa et al., 1999; Horowitz et al., 2002). Various commercial computerized glow curve deconvolution/analysis (CGCD or CGCA) are available. Most of these CGCD/CGCA programs work well for LiF:Mg,Ti material. The firstorder kinetics (Randall & Wilkins) is one of them. With growing use of the high sensitive material LiF:Mg,Cu,P, attention on deconvoluting this material has grown. Luo et al. (2006), in a previous work, presented a combination of first-order kinetics fit with a modified Gaussian function to peak 4 that worked relatively well. However, that is not a commercial program. * Tel.: þ1 440 703 1405. E-mail address: ling.z.luo@thermofisher.com. 1350-4487/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.radmeas.2011.06.065
An increasing interest is expressed on whether a commercial curvefitting package is suitable for this material for the glow curve deconvolution purpose. In this work, two different fitting methods are experienced: first-order kinetics with modified Gaussian and Weibull area fit from the commercially available software PeakFitÒ. 2. Setup and study 2.1. Setup TLD materials studied were described in Luo’s previous papers (Luo, 2008 and 2010). They were LiF:Mg,Ti (TLD-1776) and LiF:Mg,Cu,P (TLD-1776H) card with a configuration such that detector 1 is a natural Li, detectors 2 and 3 are 7Li-enriched Li, and detector 4 is 6Lienriched Li. The dosimeters were respectively stored in three temperatures: standard laboratory temperature 20 C; low temperature 0 C and high temperature 40 C. Irradiation of 3 mSv was performed at either the beginning or the end of the scheduled fading period, which ranged from 2 days to 24 months. Then the dosimeters were read using the readout profiles described in Table 1. 2.2. Fitting techniques As mentioned, it is well known for LiF:Mg,Ti material that glow peaks 1e5 follow first-order kinetics theory (Moscovitch, 1986). This theory was first developed by Randall & Wilkins and expressed as (1) below.
L.Z. Luo / Radiation Measurements 46 (2011) 1448e1452 Table 1 Readout Time-temperature Setup used for studied material. Readout Setup Preheat Heat Rate Acquire
TLD-1776 (LiF:Mg,Ti)
TLDe1776H (LiF:Mg,Cu,P)
No-Preheat
No-Preheat
W/Preheat
50 C for 0 s 25 C/s 13(16*)s to Max 300 C
50 C for 0 s 15 C/s 23(26*)s to Max 260 C
165 C for 10 s 15 C/s 13(16*)s to Max 260 C
Note: * is for is 6Li-enriched element.
E 1 1 E 1 1 I ¼ Io exp 1 þ exp K Tm T K Tm T
(1)
where I is the intensity of glow signal; I0 is the glow peak height; Tm is the peak temperature; T is the heating temperature; E is the peak activation energy, and K is Boltzmann’s constant. For LiF:Mg,Cu,P material, fitting glow peaks 1e4 with Randall & Wilkins function leaves a few percentages of the total TL readout value that were contributed from higher temperature peaks when performing the readout using the time-temperature setups in Table 1. To take these few percentages into account, Luo et al. (2006) demonstrated that a modified Gaussian for peak 4 resulted in a better Figure-of-Merit fit. This modified Gaussian function is expressed as (2). Parameters A, B, and C are the modified Gaussian parameters.
I4 ¼ A þ I04 exp
! T Tm4 C 0:5 B
(2)
PeakFit is a commercial automated peak separation software from Systat Software. Here it is investigated whether it is suitable for the glow curve deconvolution purpose. Weibull area fit is one of the fit functions tested. It is tested on both LiF:Mg,Ti and LiF:Mg,Cu,P cards. This function is expressed as (3) below. Where a0, a1, a2, and a3 are the parameters respectively for peak area, center, width, and shape.
2 3a3 1 1 a0 a3 6 a3 1 a3 7 I ¼ a3 4x þ a2 a1 5 a3 a2 2
0
6 B 6 Bx þ a2 6 B exp6 6B 6 B 4 @
1a3 3 1 a 3 7 a3 1 a1 C C 7 a3 C 7 C 7 C 7 a2 A 7 5
ð3Þ
Each time-temperature profile in Table 1 consists of a linear heating portion and a temperature plateau portion. However, the first-order kinetics theory assumes a linear heating throughout the readout; this temperature is then referred to as hypothetical temperature (Figel and Sprunck, 1999). The hypothetical linear temperature is used in this work. In summary, for a comparison, both first-order kinetics fit and Weibull area fit are used for LiF:Mg,Ti, whereas first-order kinetics with modified Gaussian fit and Weibull area fit are used for LiF:Mg,Cu,P. 3. Results and discussion As described in Part I (Luo, 2008), TL fading comes from two components: signal loss and sensitivity loss, in terms of irradiation that occurred at the beginning and end of storage time,
1449
respectively. Dosimeters were stored in different temperatures for a time period from 2 days to 24 months; both signal and sensitivity loss data were collected. Fade rates due to signal or sensitive or average loss are expressed in the function form F ¼ a$lnðtÞ þ b. Parameters a and b are provided in Table 2 of Part I (Luo, 2008). To find the fade rate for each glow peak, all glow curves are processed through the two appropriated fitting techniques as mentioned above. Data shows that the isotopic difference (Li-natural, 7Li, or 6 Li) causes insignificant variance in glow peaks. Therefore, discussion in this paper will not differentiate between the isotopes. Fig. 1 shows typical glow curves of 2-day fade at room temperature. The glow curves on the left represent LiF:Mg,Ti read with no-preheat. The middle and right glow curves are the representatives of LiF:Mg,Cu,P read with no-preheat and with preheat, respectively. The upper three glow curves are fitted by first-order kinetics (and modified Gaussian to peak 4 for LiF:Mg,Cu,P) and the lower glow curves are fitted using Weibull fit. The two-day fade is set as the baseline. At the baseline, for LiF:Mg,Ti, the asymmetric first-order kinetics deconvolutes peaks 2 to 5 such that each weighs 8%, 18%, 25%, and 47% to the whole-glowcurve-value, respectively; in contrast, Weibull method separates them to 10%, 19%, 31%, and 38%. Though the weight of peak 5 appears 9% (47%38%) in difference between the two methods, the main dosimetric peaks 4 þ 5 are close (72% vs. 69%). This is in agreement with the published work of others. Similar results are observed for the LiF:Mg,Cu,P no-preheat readout. As with preheat readout, the lower temperature peaks are eliminated, leaving only the main dosimetric peaks 3 þ 4. Therefore, both fitting methods produce very comparable results, 89% vs. 88%. Representative results in Fig. 2 shows the weight of each peak to the baseline-whole-glow-curve-value changes in 24-months at room temperature. The left two graphs are for LiF:Mg,Ti. The middle ones are for LiF:Mg,Cu,P read with no-preheat and the right two graphs are LiF:Mg,Cu,P read with preheat. The top three are generated by first-order kinetics method and the bottom three are from Weibull fit. Though Weibull fit offers better overall Figure-of-Merit (not shown in the graphs), it is more sensitive to glow curve shape and has greater errors in allocating the weight of each peak. This is indicated by the data points being more scattered around its trend line. However, in the case of LiF:Mg,Cu,P with preheat readout, both methods agree with each other and are consistent. In previous paper (Luo, 2008), it was observed that at 0 C storage temperature, LiF:Mg,Cu,P response appeared to increase as a function of fade time. All four LiF:Mg,Cu,P graphs in Fig. 2 show that this increase come from peak 4. The increase is due to the charge transfer from shallow traps to deeper traps not just a deconvolution effect. In fact this is also true for the cases of 0 C and 40 C storing temperatures (not shown in the graph). Over a 24-month period, each peak at different temperature demonstrates its signal loss and sensitivity loss. The rate of loss, in other words the stability or fade of each peak, is estimated using function F ¼ c$ln2 ðtÞ þ a$lnðtÞ þ b, where t is fading time in day (which is the period from clearing the dosimeter to reading it out, t 1); a, b, and c are linear parameters. Note that the whole-glow-curve-value (Peaks 1e5) fading is estimated by linear logarithm function: F ¼ a$lnðtÞ þ b. However, the individual peak is best fitted by second-order polynomial logarithm. Author is lack of an explanation. Table 2 summarizes the test and provides these parameters for all test temperatures and all cases. In part I of this study, it showed that the Signal faded faster than the Sensitivity at low storage temperature, and vice versa at higher temperature, the Sensitivity fade accelerated faster than the Signal did. It was discussed then this might due to the preservation of low temperature peak 2. The current work however show that the main peaks (4 þ 5) also
1450 Table 2 Summary of parameters a, b, and c for fade function F ¼ c$ln2 ðtÞ þ a$lnðtÞ þ b for the main dosimetric peaks, where t is the fading time from clearing to readout in day t 1. Column “Total” is re-generated from Table 2 of Luo (2008) and shown here for reference. LiF:Mg,Cu,P e NoPreheat
LiF:Mg,Ti Total
0.0569 1.003 0.0524 1.0018 0.0425 1.0531
0.0726 1.0075 0.0736 1.0832 0.0333 1.0568
0.0647 1.0053 0.0630 1.0425 0.0379 1.0550
Weibull
Total
Peak5
Peak4
Peak5
Peak4
0.0076 0.0528 0.6161 0.0065 0.0749 0.4238 0.0035 0.0036 0.4768
0.0086 0.0953 0.2902 0.0040 0.0729 0.3275 0.0101 0.0537 0.1807
0.0132 0.1003 0.5632 0.0048 0.0256 0.3626 0.0074 0.0415 0.3813
0.0072 0.0261 0.2714 0.0054 0.0605 0.4092 0.0043 0.0158 0.3079
0.0078 0.0400 0.6348 0.0086 0.0795 0.4397 0.0024 0.0123 0.4532
0.0107 0.1179 0.3282 0.0011 0.0539 0.3074 0.0077 0.0377 0.1926
0.0028 0.0142 0.4014 0.0014 0.0140 0.3641 0.0012 0.0028 0.3502
0.0006 0.0335 0.3351 0.0046 0.0019 0.3388 0.0004 0.0003 0.2825
0.0077 0.0464 0.6255 0.0076 0.0772 0.4317 0.0030 0.0043 0.4650
0.0096 0.1066 0.3092 0.0025 0.0634 0.3175 0.0089 0.0457 0.1867
0.0052 0.0430 0.4823 0.0031 0.0198 0.3633 0.0043 0.0222 0.3657
0.0033 0.0037 0.3032 0.0004 0.0312 0.3740 0.0020 0.0078 0.2952
0.0225 1.0073 0.0187 1.0032 0.0153 1.0256
0.0315 1.0240 0.0249 1.0339 0.0060 1.0111
0.0270 1.0156 0.0218 1.0186 0.0107 1.0183
1st-order/Mod Gaussian
Weibull
Total
Peak4
Peak3
Peak4
Peak3
0.0069 0.0431 0.7882 0.0003 0.0116 0.7683 0.0060 0.0462 0.8495
0.0063 0.0648 0.1644 0.0010 0.0339 0.1769 0.0063 0.0376 0.0853
0.0092 0.0668 0.7210 0.0030 0.0398 0.6799 0.0036 0.0077 0.6818
0.0063 0.0657 0.1699 0.0017 0.0394 0.1916 0.0043 0.0107 0.1609
0.0036 0.0095 0.8208 0.0025 0.0153 0.7659 0.0062 0.0490 0.8478
0.0045 0.0533 0.1731 0.0011 0.0101 0.1489 0.0042 0.0255 0.0990
0.0053 0.0238 0.7617 0.0067 0.0573 0.6472 0.0022 0.0034 0.7024
0.0039 0.0441 0.1566 0.0025 0.0386 0.1981 0.0016 0.0011 0.1424
0.0052 0.0263 0.8045 0.0014 0.0134 0.7671 0.0061 0.0476 0.8487
0.0054 0.0591 0.1688 0.0000 0.0220 0.1629 0.0052 0.0316 0.0922
0.0072 0.0453 0.7414 0.0048 0.0485 0.6636 0.0029 0.0056 0.6921
0.0051 0.0549 0.1633 0.0021 0.0390 0.1948 0.0029 0.0048 0.1517
0.0165 1.0122 0.0065 1.0243 0.0056 0.9992
0.0292 1.0343 0.0139 1.0513 0.0043 1.0033
0.0228 1.0233 0.0102 1.0378 0.0049 1.0012
1st-order/Mod Gaussian
Weibull
Peak4
Peak3
Peak4
Peak3
0.0029 0.0179 0.8595 0.0018 0.0252 0.8108 0.0022 0.0037 0.8507
0.0016 0.0195 0.0647 0.0000 0.0097 0.0700 0.0021 0.0120 0.0407
0.0026 0.0166 0.8358 0.0015 0.0208 0.8081 0.0019 0.0005 0.8210
0.0036 0.0332 0.0776 0.0015 0.0028 0.0683 0.0037 0.0216 0.0523
0.0036 0.0080 0.8654 0.0044 0.0311 0.8145 0.0018 0.0051 0.8557
0.0021 0.0205 0.0655 0.0000 0.0064 0.0651 0.0019 0.0129 0.0388
0.0033 0.0050 0.8577 0.0043 0.0314 0.7994 0.0010 0.0081 0.8076
0.0013 0.0148 0.0632 0.0016 0.0072 0.0502 0.0015 0.0068 0.0675
0.0033 0.0129 0.8625 0.0031 0.0281 0.8126 0.0020 0.0044 0.8532
0.0019 0.0200 0.0651 0.0000 0.0080 0.0676 0.0020 0.0124 0.0398
0.0029 0.0108 0.8467 0.0029 0.0261 0.8038 0.0014 0.0043 0.8143
0.0024 0.0240 0.0704 0.0015 0.0022 0.0593 0.0026 0.0142 0.0599
L.Z. Luo / Radiation Measurements 46 (2011) 1448e1452
Signal Loss c 40 C a b c 20 C a b c 0 C a b Sensitivity Loss c 40 C a b c 20 C a b c 0 C a b Average c 40 C a b c 20 C a b c 0 C a b
1st-order
LiF:Mg,Cu,P e W/Preheat
L.Z. Luo / Radiation Measurements 46 (2011) 1448e1452
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Fig. 1. Glow curves and deconvoluted peaks for LiF:Mg,Ti (left) and LiF:Mg,Cu,P (middle e no-preheat readout; right e w/preheat readout). Upper glow curves are fitted by firstorder kinetics (modified Gaussian to peak 4 for LiF:Mg,Cu,P) and the lower glow curves are fitted using Weibull fit.
contribute to it. Let us look at an example. From Table 2, using the parameters provided in the columns “LiF:Mg,Ti, 1st-order, Peak 5 and Peak 4”, it can be calculated that, for LiF:Mg,Ti, the 24-month Signal fade from peaks 4 þ 5 at 0 C and 40 C are 70% and 67%,
respectively. While during the same period, the Sensitivity fade are 75% and 58% respectively at 0 C and 40 C. Hence, at low storage temperature 0 C, Signal from main peaks loss 5% (75%70%) more in 24 months. At the same period, Sensitivity loss from main peaks
Fig. 2. The weight of each peak to the baseline-whole-glow-curve-value changes in 24-months in room temperature for LiF:Mg,Ti (left) and LiF:Mg,Cu,P (middle e no-preheat readout; right e w/preheat readout). Upper graphs are generated by first-order kinetics (modified Gaussian to peak 4 for LiF:Mg,Cu,P) method and bottoms are from Weibull fit. The dotted lines are predicted trend lines for Total, Peak 5, Peak 4 or Peak 3. The solid line is for main peaks (Peak 4 þ 5 for LiF:Mg,Ti and Peak 3 þ 4 for LiF:Mg,Cu,P). Individual points are the actual data for each peak.
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L.Z. Luo / Radiation Measurements 46 (2011) 1448e1452
advanced 9% (67%58%) more at 40 C. The work in Part I, also can be calculated from Table 2 column “LiF:Mg,Ti, Total”, shows these two fade rates of whole-glow-curve-value differences are 7% (84% 77%) and 10% (63%53%) at 0 C and 40 C, respectively. Hence the contribution from low temperature peaks in fact is only a couple of percents, much less than author previously thought. The similar is observed for LiF:Mg,Cu,P as well.
4. Summary The isotopic difference (Li-natural, 7Li, or 6Li) causes insignificant variance in glow peaks. Two fitting methods were used: first-order kinetics with modified Gaussian and Weibull area fit. The first-order kinetics functions fit LiF:Mg,Ti well in all temperature cases. For LiF:Mg,Cu,P, using modified Gaussian function for peak 4 to include the contribution from higher temperature peaks yields better fit. Weibull area fit results in greater errors in allocating the relative weight of individual peak, though the overall Fit-of-Merit is better. The main peak has less percentage compared to that of the first-order kinetic fit. Both fitting methods show that the dosimetric peaks 4 þ 5 (or 3 þ 4 for LiF:Mg,Cu,P) are relatively stable in all temperatures cases. Two fitting methods agreed with each other for LiF:Mg,Cu,P TLD card in storage temperature of 20 C, with specified preheated
readout setup. Parameters (a, b, and c) of fade function are provided. Acknowledgments The author wishes to thank her colleagues for all the support in this series of work. References Da Rosa, L.A.R., Regulla, D.F., Fill, U.A., 1999. Precision for low Dose assessment using TLD-100 Chips and computerised glow curve analysis. Radiat. Protec. Dosim. 85, 175e178. Figel, M., Sprunck, M., 1999. Fast cooling and computerised glow curve deconvolution in routine personnel monitoring with TLD-100. Radiat. Protec. Dosim. 81, 259e264. Horowitz, Y., Yossian, D., 1995. Computerised glow curve deconvolution: application to thermoluminescence dosimetry. Radiat. Protec. Dosim. 60. Horowitz, Y., Delgado, A., Pradhan, A.S., Yoder, R.C., 2002. Topics under debate e the use of Computerised glow curve analysis will optimise personal thermoluminescence dosimetry measurements. Radiat. Protec. Dosim. 102, 269e277. Luo, L.Z., 2008. Extensive fade study of Harshaw LiF TLD materials. Radiat. Meas. 43, 365e370. Luo, L.Z., 2010. Long term study of Harshaw TLD LiF e LLD and Uncertainty. Radiat. Meas 45, 569e572. Luo, L.Z., Velbeck, K.J., Moscovitch, M., Rotunda, J.E., 2006. LiF: Mg, Cu, P glow curve shape dependence on heating rate. Radiat. Protec. Dosim. 119, 184e190. Moscovitch, M., 1986. Automatic method for Evaluating Elapsed time between irradiation and readout in LiF-TLD. Protec. Dosim. 17, 165e169.