A COMPUTER PROGRAM FOR THE DECONVOLUTION OF THERMOLUMINESCENCE GLOW CURVES K. S. Chung 1,, H. S. Choe 1, J. I. Lee 2, J. L. Kim 2 and S. Y.

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1 Radiation Protection Dosimetry (200), Vol. 11, No. 1, pp doi: /rpd/nci073 A COMPUTER PROGRAM FOR THE DECONVOLUTION OF THERMOLUMINESCENCE GLOW CURVES K. S. Chung 1,, H. S. Choe 1, J. I. Lee 2, J. L. Kim 2 and S. Y. Chang 2 1 The Research Institute of Natural Science and Department of Physics, Gyeongsang National University, Jinju , Korea 2 Health Physics Department, Korea Atomic Energy Research Institute, P.O. Box 10 Yuseong, Daejeon , Korea A quick and efficient computer program was developed in order to resolve the peaks from the thermoluminescence (TL) glow curve. The program was designed to be easily used on any MS Windows-based computer with a graphical user interface. In this program, a new method based on the general one-trap TL equation was adopted to analyse the TL glow curve with the traditional first-order, second-order and general-order kinetics model. The method described here, general approximation, generates TL glow peaks and interpolates the relevant TL parameters from the glow data. The program was tested with simulated and experimental TL glow data and the results were found to be adequate and reliable. INTRODUCTION Computerised glow curve deconvolution is widely used for studying the thermoluminescence (TL) mechanism as well as for TL dosimetry (1,2). In this paper, a general one-trap (GOT) model (3), which assumes that the TL material has only one trap, is used as a background. The original GOT is a model which assumes the temperature rise to be linear, but in this study, we do not use this kind of assumption and therefore it can be applied to situations where the temperature changes in an arbitrary manner. Because of this, the numerical analysis performed in this study is also called a general approximation (GA) (). This paper describes a computer program, TLanal, which is designed for the deconvolution of the TL glow curves with not only a GA but also a traditional first-order kinetics (1OK), second-order kinetics (2OK), general-order kinetics (GOK) and a full iteration (FI). In this paper, FI is a designation where there is no assumption of the three coupled differential equations in the paper by Halperin and Braner (). As there is no restriction in the temperature profile, this program can be used in the case where the temperature changes linearly as well as arbitrarily. A full functional demonstration version of this program and example files can be downloaded from The registration code can be obtained from the author upon request. COMPUTER PROGRAM This program is written in C# of the Visual Studio Dot Net and has been tested in the Microsoft Corresponding author: chungks@gsnu.ac.kr Windows XP operating system. It is possible to convert this program to an ActiveX control which can run in a web browser. Figure 1 shows the graphical user interface of the TLanal program with the experimental data and the results of the deconvolution. We tested the program with standard TL materials such as LiF:Mg,Ti(TLD-100) or MCP-N which are the most intensively studied ones. One of the results for TLD-100 is shown in Figure 1. The deconvoluted glow curve is shown in the left panel of the main program. It appears that the glow data of TLD-100 is best fitted with five peaks of the GA. In the case of GA, there are five parameters, the activation energy E (ev), the frequency factor s (s 1 ), the initial electron density n 0 (cm 3 ), the ratio of retrap and recombination coefficient R and the concentration of electron trap N (cm 3 ) (). The number of unknown parameters is 3, 3,, and 8 for 1OK, 2OK, GOK, GA and FI, respectively. Among all the parameters, n 0, the initial value of n, contains the information of previous exposure to ionising radiation and is the most important in practical dosimetric applications. In the example reported here, we use GA for all five kinds of traps. So the total number of unknown parameters is 28 ( þ 3) where the additional three parameters arise from the fitting of the background and the global amplification of the TL reader. The background is fitted using an expression of the form a þ b exp ( /T ), where the factor a stands for the white noise and dark current of the photomultiplier tube and the factor b originates from the black body radiation which depends on the temperature of the TL material. If a wellknown TL material is used, the number of unknown parameters could be reduced. If all the TL parameters of a specific TL material should be determined from a prior analysis, only the parameter ª The Author 200. Published by Oxford University Press. All rights reserved. For Permissions, please journals.permissions@oxfordjournals.org

n 0 is allowed to vary in the course of fitting and the other parameters can be treated as fixed values. Figure 2 shows the user interface for choosing the parameters of a one trap.

2 K. S. CHUNG ET AL. Figure 1. Graphical user interface of the main program used to analyse TL glow data which have many peaks. The deconvoluted glow curve of TLD-100 appears in the left panel and the fitting parameters appear in the right panel. n 0 is allowed to vary in the course of fitting and the other parameters can be treated as fixed values. Figure 2 shows the user interface for choosing the parameters of a one trap. The TL kinetic model can be chosen among 1OK, 2OK, GOK, GA and FI. Also, the corresponding parameters can be easily chosen with the assistance of the graph in the top panel of the dialogue window. This program can be applied not only to one type of exposure to ionising radiation with one kind of heating rate function but also to many types of exposures with many kinds of heating rate functions (Figure 3). The only restriction in the application of this program is that the TL reader used to measure the TL glow curve should be of a singular type and the TL material should be a singular kind. (1) Case of applying different types of heating rate functions: To analyse a specific peak accurately, there should be a change in temperature other than linear. This program can accommodate any type of heating function. So, if there are some peaks that cannot be deconvoluted well or any parameter that cannot be determined well, the heating scheme can be changed with a proper type such as a hyperbolic or stepwise one. (2) Case of applying different types of radiation sources and irradiation conditions: For example, if it can be assumed that the parameters Figure 2. Dialogue window for editing the peak corresponding to one kind of trap. The models used in glow curve analysis can be chosen from the combo box and the initial values of the corresponding parameters can be adjusted by the slide bars. The editing result appears immediately in the top panel with a shaded curve. 36

3 COMPUTERISED TL GLOW CURVE DECONVOLUTION Table 1. Kinetic parameters of the glow peaks of TLD-100 deconvoluted by 1OK. Peak E (ev) s (s 1 ) n 0 (cm 3 ) (a) n 0 (cm 3 ) (b) In this table, the two columns of n 0 values are relative values for irradiation by (a) 100 mgy and (b) 6 mgy 137 Cs gamma rays respectively. Figure-of-merit (FOM) ¼ 1.19% Table 2. Typical kinetic parameters for peaks 2 in TLD-100. Peak E (ev) s (s 1 ) Figure 3. Window for editing the temperature profile for a given material for which all physical parameters are known. (E, s, N and R) of each trap TL materials of the same kind are independent of radiation sources and exposure dose and that n 0 is dependent, then the data set obtained from the samples irradiated differently can be analysed all together. That is, under the condition of choosing the same values of trap parameters, one can obtain the different deconvoluted peak shapes and n 0 s from each sample and also estimate the kind of radiation sources and exposure dose. It is possible to find out the response of each trap of the TL material for various kinds of radiation sources. (3) Case of general circumstances: This program can be simultaneously applied to general circumstances such as any type of heating rate functions and various irradiation conditions. To determine the unknown parameters with the TL glow curves, we adopted two curve-fitting algorithms: one is the Hessian method and the other is the simplex method (6). Among these two curvefitting techniques, the simplex method is more efficient than the Hessian method in this case. But the simplex method imposes restrictions on the parameters and gives rise to problems like discontinuities in parameter values and other singularities. So the simplex method was adopted in the first stage of the iteration and when the result is not so good or a more accurate one is required, the Hessian method was introduced. But in case of many peaks in a TL glow curve, the dimension of the parametric space is too high to handle with the Hessian matrix () Adapted from Horowitz et al. (2) EXAMPLES OF APPLICATION To demonstrate the application of this computer program, we analysed the glow curve of LiF:Mg, Ti(TLD-100) which was irradiated to 100 mgy and 6 mgy as air kerma with 137 Cs gamma rays at the Korea Atomic Energy Research Institute. The glow curve measurement of the samples was performed using a manual-type commercial TLD reader (Model 00, Harshaw) in the range between 300 and 60 K with a heating rate of 1 K sec 1 in a N 2 atmosphere. TLD-100 samples were annealed at temperatures of 00 C for and 1 h 100 C for 2 h before irradiation. TLD-100 is the most popular and commonly used dosimeter even though it is a very complex material (2,7). It is well known that the TLD-100 has 1 glow peaks between room temperature and 00 C. Each peak may have distinctly different dosimetric characteristics. Six peaks were deconvoluted between 300 and 60 K with 1OK, GOK and GA and the results are summarised in Table 1. To determine the kinetic parameters for the three fitting model, TLD-100 was irradiated simultaneously with 100 mgy 137 Cs and 6 mgy of 137 Cs gamma rays. The results of deconvolution by 1OK are given in Table 1. The value of the figure-of-merit (FOM) originally defined by Misra and Eddy (8) is 1.19% and is considered a satisfactory fit. The values of trap depth E and the frequency factor s for the peaks appear to be different from typical average values reported previously (Table 2). However, the 37

4 theoretical curve deconvoluted with six peaks fits well the experimental curve, as shown in Figure. The results of the application of the GOK model and the GA model are listed in Tables 3 and, respectively. In GOK, the order of kinetics b is introduced additionally to 1OK. The parameters b listed in Table 3 indicate that the behaviour of each peak is nearly of 10K and it is natural that similar results of E K. S. CHUNG ET AL. are obtained in the case of 1OK and GOK. The ratio of the retrap and the recombination coefficient R and the trap density N are also introduced to 1OK. It was suggested that the value of b in GOK is strongly related with the value of R in GA (,9). The value of N in the GA model indicates the condition of saturation. On comparing each peak of Figures 6 the shape of peak 6 appears to be quite different. TL intensity (arb.unit) 1OK fitting Temperature (K) Figure. Glow curve of TLD-100 irradiated by 100 mgy 137 Cs gamma rays and deconvoluted by 1OK. The thick Table 3. Kinetic parameters of the glow peaks of TLD-100 deconvoluted by GOK. Peak E (ev) s 0 (s 1 cm 3(b 1) ) b n 0 (cm 3 ) (a) n 0 (cm 3 ) (b) In this table, the two columns of n 0 values are relative values for irradiation by (a) 100 mgy and (b) 6 mgy 137 Cs gamma rays, respectively. Figure-of-merit (FOM) ¼ 0.88% TLintensity (arb.unit) GOK fitting Temperature (K) 6 7 Figure. Glow curve of TLD-100 irradiated by 100 mgy 137Cs gamma rays and deconvoluted by GOK. The thick TL intensity (arb.unit) GA fitting Temperature(K) Figure 6. Glow curve of TLD-100 irradiated by 100 mgy 137Cs gamma rays and deconvoluted by GA. The thick Table. Kinetic parameters of the glow peaks of TLD-100 deconvoluted by GA. Peak E (ev) s (s 1 ) R N (cm 3 ) n 0 (cm 3 ) (a) n 0 (cm 3 ) (b) In this table, the two columns of n 0 values are relative values for irradiation by (a) 100 mgy and (b) 6 mgy Cs gamma rays respectively. Figure-of-merit (FOM) ¼ 1.6% 38

5 CONCLUSION A computer program for the deconvolution of TL glow curves and for the analysis of TL materials has been developed in this study. Exemplary deconvolutions have been performed for TL-100 with three different models: the 1OK model, the GOK model and the GA model. The program can be simultaneously applied to various sets of TL glow data of a TL material exposed to different types of radiation sources and/or recorded with different types of heating schemes. The program has been proved to be a fast and reliable tool for analysing TL materials. ACKNOWLEDGEMENTS This research was supported by the national longterm project of nuclear energy development funded by the Ministry of Science. REFERENCES COMPUTERISED TL GLOW CURVE DECONVOLUTION 1. McKeever, S. W. S. Thermoluminescence of Solids (Cambridge: Cambridge University Press) (198). 2. Horowitz, Y. S. and Yossian, D. Computerised glow curve deconvolution: application to thermoluminescence dosimetry. Radiat. Prot. Dosim. 60, 1 11 (199). 3. Levy, P. W. Recent developments in thermoluminescence kinetics. Nucl. Tracks Meas. 10, 7 (198).. Lee, J. I. A study on the development of highly sensitive LiF, Mg, Cu, Na, Si thermoluminescent detector and its physical and dosimetric characteristics, Gyeongsang National University, Ph.D. Thesis, 1 (2003).. Halperin, A. and Braner, A. A. Evaluation of thermal activation energies from glow curves. Phys. Rev. 117, 08 (1960). 6. Gerald, C. F. and Wheatley, P. O. Applied Numerical Analysis (New York: Addison Wesley) (199). 7. Horowitz, Y. S. and Yossian, D. Computerised glow curve deconvolution applied to the analysis of the kinetics of peak in LiF:Mg,Ti(TLD-100). J. Phys. D Appl. Phys. 28, (199). 8. Misra, S. K. and Eddy, N. W. IFOM, a formula for universal assessment of goodness-of-fit of gamma ray spectra. Nucl. Instrum. Methods 166, 37 0 (1979). 9. Sunta, C. M., Ayta, W. E. F., Kulkarni, R. N., Piters T. M. and Watanabe, S. General-order kinetics of thermoluminescence and its physical meaning. J. Phys. D Appl. Phys. 30, 123 (1997). 39

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