- Email: [email protected]
Analysis of the BeO thermoluminescent glow curve by the deconvolution method
Applied Radiation and Isotopes 150 (2019) 53–56
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Analysis of the BeO thermoluminescent glow curve by the deconvolution method
T
Rodrigo Martínez Baltezar∗, Juan Azorín Nieto Departamento de Física, Universidad Autónoma Metropolitana, Unidad Iztapalapa, Ciudad de México, Mexico
HIGHLIGHTS
parameters and TL response as a function of dose of BeO were determined by two different deconvolution methods. • Kinetic curve of BeO obtained at a heating rate of 5 Ks-1 was resolved in two peaks at temperatures of approximately 477 and 586 K respectively. • Glow • TL response as a function of dose of BeO obtained by both deconvolution methods fit a quadratic function for first peak and a linear one for the second peak. ARTICLE INFO
ABSTRACT
Keywords: Thermoluminescence glow curve Deconvolution TL kinetic parameters
Results of studying the behavior of the thermoluminescent glow curve of beryllium oxide (BeO) obtained in a wide range of absorbed doses are presented. The kinetic parameters and the TL response as a function of dose were determined using two deconvolution methods: Glow-Fit (Puchalska and Bilski 2006) and “tgcd” in “R” (Peng et al., 2016). Both methods showed that the glow curve of BeO obtained at a heating rate of 5 Ks−1 can be resolved in two peaks at temperatures of approximately 477 and 586 K respectively, with an activation energy of 1.1 eV for both peaks. The Glow-Fit method assumes first-order kinetics; while the “tgcd” in “R” method allows to determine the order of kinetics, finding that both peaks follow a kinetic of first order. Regarding the TL response as a function of dose, it was found that the first peak exhibits a quadratic dependence while the second peak exhibits a linear behavior with respect to the dose throughout the dose range studied, thus showing great advantages for its application as a TL dosimeter.
1. Introduction During the last decades the dosimetric properties of beryllium oxide (BeO) have been investigated by different research groups for applications in thermoluminescent dosimetry (TLD) (Azorín et al., 2016; Ogorodnikov et al., 2016) as well as in optically stimulated dosimetry (OSL) (Tausenev et al., 2008). Due to its excellent physical properties, such as, high heat conductivity, high electrical resistivity and high thermal shock resistance. BeO is widely used as an insulating heat sink in the electronic industry (Greenwood and Earnshaw, 1997); while its high melting point (2570 °C) and high thermal shock resistance makes it a suitable refractory material (Watanabe et al., 2010) as well as nuclear reactors moderator (McClure et al., 2014). In addition to the above characteristics, BeO is a tissue equivalent material (effective atomic number 7.13) that has a very wide energy gap (10.6 eV) (Sashin et al., 2003) as well as a good thermal conductivity, which guarantees rapid and uniform transmission of heat
∗
during the reading process; It is also easily moldable and resistant to most chemical agents, which makes it an attractive material for its application in thermoluminescent dosimetry. However, its applications have had several difficulties due to its high toxicity in powder form and to its high sensitivity to light (Bulur 2007). Yamashita et al. (1974) has obtained BeO by mixing purified BeO powder and alkali sulfate, pressing the resulting mixture to obtain discs or rods and then sintering at high temperature (1500 °C) and cooling gradually to room temperature. BeO has been also synthesized in powder form by the sol-gel method (Zahedifar et al., 2012). Although no details are known about its preparation in the form of ceramic discs 4 mm in diameter and 0.8 mm thick, it is commercially available under the name Thermalox 995 (Beryllium Brush Co., Elmore, OH, USA) with total contents of impurities not exceeding 0.5% distributed in silicon (2150 ppm), magnesium (945 ppm), iron (100 ppm), calcium (61 ppm), aluminum (54 ppm), chrome (10 ppm), titanium (4 ppm) and copper (3 ppm) (Spurny and Hobzova (1977).
Corresponding author. E-mail address: [email protected] (R.M. Baltezar).
https://doi.org/10.1016/j.apradiso.2019.04.003 Received 29 November 2018; Received in revised form 15 March 2019; Accepted 2 April 2019 Available online 03 April 2019 0969-8043/ © 2019 Published by Elsevier Ltd.
Applied Radiation and Isotopes 150 (2019) 53–56
R.M. Baltezar and J.A. Nieto
This paper reports the results of analyzing the glow curve of BeO by using two deconvolution methods: Glow-Fit (Puchalska and Bilski 2006) and “tgcd” in “R” (Peng et al., 2016) for determining its TL kinetic parameters as well as its TL response as a function of gamma dose in the range of 1.3–23.4 Gy.
the one trap-one recombination (OTOR) model (Kitis and Vlachos, 2013) using the Levenberg-Marquardt algorithm (plus supports for constraining and fixing parameters). Kitis et al. (1998) developed the general order empirical expression for a Glow peak which is given by
I (T ) = Im bb / b
2. Materials and methods
xa =
By this method, the TL glow curve is separated in individual component using Randall-Wilkins model which assumes a first order kinetics. Horowitz and Yossian, 1995 proposed the following expression. This expression can be derived by using the maximum condition and the Randall-Wilkins expression. Equation (1) represents the TL intensity of an isolated glow-peak of the TL glow curve
E exp kT
E KTm2
T Tm
E exp KTm
E KT
dT
xb =
exp 0
E kT
dT
E k
(x )
2
exp( x ) dx =
x
E1 E2 (x ) k x
(1)
E kT
E 1 kTM
T2 exp v + Zm exp v Tm2
b/ b 1
(6)
T E exp Tm kTm
E kT
(3)
E kTm
exp
E T Tm kT Tm
)
1) xb
Materials studied were constituted by disc shaped BeO ceramics commercially available under the name Thermalox 995 (Brush Beryllium Co., Elmore, OH, USA), 4 mm diameter and 0.8 mm thickness. The impurities content in BeO ceramics reported in the literature (Spurny and Hobzova (1977) not exceeds 0.5% and is distributed as follows: silicon (2150 ppm), magnesium (945 ppm), iron (100 ppm), calcium (61 ppm), aluminum (54 ppm), chrome (10 ppm), titanium (4 ppm) and copper (3 ppm). Before use, all samples were submitted to thermal annealing treatment at 600 °C during 30 min in order to erase any remaining information. Irradiations at different absorbed doses of 60Co gamma radiation were carried out in a Gammacell 200 irradiator (Atomic Energy of Canada Limited) at a dose rate of 130 mGy min−1. TL readings were made in a Harshaw 3500 TL analyzer (Thermo Scientific, USA) from 30 °C up to 360 °C at a heating rate of 5 °C·s−1 under Nitrogen atmosphere in order to reduce the thermal noise resulting from the heating planchet of the TL reader. In order to determine both the kinetic parameters and the TL response as a function of dose, the glow curve analysis was carried out by using two different deconvolution methods: the Glow-Fit and “tgcd” in “R”, by assuming first and general order kinetics respectively (Puchalska and Bilski 2006, Peng et al., 2016). The fit effectiveness was evaluated using the figure of merit (FOM). A FOM equal or less than 5% meaning very good fit. To obtain the TL response as a function of dose for an isolated peak both deconvolution methods were used. The samples of BeO were randomly divided into six groups and irradiated at 1.3, 2.6, 5.2, 10.4, 15.6, and 23.4 Gy respectively in order to obtain the dose-response curve for each individual glow peak.
E kTm (4)
This equation shows that the glow-curve is a non-linear function of Tm, Im and E parameters. To find the best-fit values of peak parameters an iterative procedure must be used. GlowFit is able of simultaneously deconvoluting as many as ten glow peaks of the TL glow-curve. The minimization process starts with trial values. In this program the Levenberg-Marquardt method for non-linear function minimization was chosen. To enable the user to control the fitting peak parameters, the original algorithm was modified by Puchalska and Bilski (2006) to exclude or constrain any given parameter of the peak. Also, this software uses three unknown parameters in the background expression (equation (4))
Ig = a + beT / c
x a)
2.2. Experimental
Then, finally, the following expression is used to describe a single glow peak (Horowitz and Yossian 1995)
I (T ) = Im exp
1)(1
where b is the kinetics order, I is the TL intensity, E is the activation energy, k is the Boltzmann constant, T is the temperature, Tm is the temperature at the maximum of a peak and Im is the maximum TL intensity. This model contains four free parameters that which are Im, E, Tm and b. This deconvolution model also let us to set both parameters and restrictions. Like Glow-Fit this software let set up to ten peaks.
(2)
a0 + a1 x + a2 x 2 + a3 x 3 + a4 x 4 b0 + b1 x + b2 x 2 + b3 x 2 + b4 x 4
(
Zm = 1 + (b
where x = E kT , x = E kT , and E2(x) is the second exponential integral function which can be evaluated by E2(x) = α(x)exp (-x), where α(x) is a quotient of two 4th order polynomials (Abramowitz and Stegun, 1972):
(x ) = 1
2kT E 2KTm E
exp v = exp
where I is the glow peak intensity, E is the activation energy, k is the Boltzmann constant, T is the absolute temperature and Tm and Im are the temperature and the intensity of the maximum, respectively. Because the exponential integral in equation (1) cannot be solved analytically, several different approximations have been proposed (Chen 1969; Horowitz and Yossian 1995) for the function describing a single glow peak. In the case of Glow-Fit (Puchalska and Bilski 2006) the exponential integral is approximated by the following expression (Abramowitz and Stegun 1972; Bos et al., 1993). T
(b
where
2.1. Glow-Fit deconvolution
E I (T ) = Im exp kTm
1
3. Results
(5)
Fig. 1 displays the glow curve of BeO obtained after exposing the sample to gamma irradiation at an absorbed dose of 15.6 Gy. This glow curve exhibited two well-separated peaks centered at 477 and 586 K. Fig. 2 shows the TL glow curve of BeO irradiated at an absorbed dose of 15.6 Gy, deconvoluted by using the Glow-Fit. This deconvolution method decomposed the glow curves in two TL glow peaks centered at around 471 and 590 K. The results obtained applying the ‘tgcd’
where a, b and c are the three unknown parameters.‘tgcd’ in ‘R’ deconvolution This package was developed by Peng et al. (2016). Function tgcd is used for deconvoluting thermoluminescence glow curves represented by the empirical expression of general order kinetics (Kitis et al., 1998; Pagonis et al., 2006) or by the semi-analytical expression derived from 54
Applied Radiation and Isotopes 150 (2019) 53–56
R.M. Baltezar and J.A. Nieto
Fig. 1. Experimental TL glow curve of BeO irradiated with 60Co gamma radiation at an absorbed dose of 15.6 Gy and registered at a heating rate of 5 K s−1.
Figure 3. Glow curve of BeO irradiated with 60Co gamma radiation, deconvoluted by Glow-Fit method. Table 1 Kinetic parameters obtained for the first peak of the BeO TL glow curve by applying two different deconvolution methods. Parameter
Glow-Fit
‘tgcd’ on ‘R’.
Kinetic order Frequency factor (s−1) Activation energy (eV)
1 2.57 × 1011 1.10 ± 0.03
1.04 ± 0.01 4.4603 × 1010 1.04 ± 0.01
Table 2 Kinetic parameters obtained for the second peak of the BeO TL glow curve by applying two different deconvolution methods. Parameter
Glow-Fit
‘tgcd’ on ‘R’.
Kinetic order Frequency factor (s−1) Activation energy (eV)
1 4.71 × 1008 1.06 ± 0.01
1.00003 ± 0.00001 1.89 × 1009 1.17 ± 0.01
used, it is expected that both the parameters and the maximum temperature differ from one method to other. Glow-Fit uses first-order kinetics, while “tgcd” considers general-order kinetics and, as can be seen, the approximations used to adjust the TL peak are different in both methods. At naked eye, it can be observed that temperature values are more in agreement with the “tgcd” method than with Glow-Fit method. The results also showed that, while the activation energy values obtained by applying both deconvolution methods were very close to 1.1 eV for each peak, the values found for the frequency factor differ by two orders of magnitude between one method and another. This is probably because Glow-fit assumes first-order kinetics while the order of kinetics found using “tgcd” was very close but not exactly equal to 1. TL response as a function of dose shows a quadratic response for the first peak and a linear response for the second one using both deconvolution methods. Although the same experimental glow curves were analyzed by two different deconvolution methods, the integrated signals of each peak were not the same because it must be considered that to determine the TL response as a function of dose using the “Glow-Fit” method, the data provided by the TL reader (expressed in nC) are used directly; whereas when the “tgcd” method is used the data are exported to an external program that determines the area under the glow curve in arbitrary units and not in “nC”. However, it can be seen that the behavior of the TL response as a function of dose, obtained using both
Fig. 2. Glow curve of BeO irradiated with 60Co gamma radiation, deconvoluted by ‘tgcd’ in R method.
in R method showed that the glow curve of BeO is composed by two glow peaks centered at around 476 and 585 K, as is shown in Fig. 3. The value of activation energy obtained applying both deconvolution methods was 1.1 eV for each peak. The frequency factor value for first peak obtained using the Glow-fit method was 2.57 × 1011 s−1 and for second peak 4.71 × 108 s−1. Also it was found, by using the ‘tgcd’ deconvolution method, that the frequency factor was 1.89 × 109 s−1 and 4.46 × 1010 s−1 for first and second peak respectively. These results are shown in Table 1 and Table 2. The TL response of first peak, isolated by both deconvolution methods, as a function of gamma absorbed dose was fit a quadratic function in the range of 1.3–23.4 Gy, while the second peak fit a linear response in the same dose range, as it is shown in Fig. 4. 4. Conclusions From the results, it can be concluded that Glow-fit method gives peak maximum temperatures 471 K and 590 K whereas ‘tgcd’ in R method 476 K and 585 K. It is well known that peak temperatures and TL parameters depend strongly on the order of the kinetics responsible for the TL process. If methods that consider different kinetic orders are 55
Applied Radiation and Isotopes 150 (2019) 53–56
R.M. Baltezar and J.A. Nieto
Fig. 4. TL response as a function of absorbed dose obtained for isolated peaks of BeO TL glow curve. a) First peak b) Second peak.
methods, is the same. Then, if it is required to use this material for ionizing radiation dosimetry, it will be necessary to specify the deconvolution method used to separate the glow peaks and calculate the TL response as a function of dose for each peak. Watanabe et al. (2010) have shown that BeO TL glow curve is composed by three isolated peaks centered at 75 °C, 220 °C, 340 °C. However due to high fading this peak has not been reported by ourselves and by other authors. Recently, Algarve and Caldas (2018) have reported that the BeO glow curve is composed for two peaks centered at 475 and 621 K. Although these results differ of those obtained in this work, are according in the fact that the TL glow curve is composed by two well separated peaks, as well as in the activation energy values obtained; these results are according also with previous studies (Azorín et al., 2016). Recent researches have shown the advantages of BeO for its application in optically stimulated luminescence dosimetry (Bulur, 2007; Watanabe et al., 2010), however TL response of this phosphor by deconvolution method for individual peaks is not reported yet.
thermoluminescent samples using different methods. Braz. J. Radiat. Sci. 6 (2), 1–12. Azorín, J., Azorín, C., Rivera, T., Torijano, E., 2016. Determination of the kinetic parameters of BeO using isothermal decay method. Appl. Radiat. Isot. 108, 8–11. Bos, A.J.J., Piters, T.M., Gŏmez Ros, J.M., Delgado, A., 1993. An intercomparison of glow curve analysis computer programs. IRI-CIEMAT Report 131-93-005. Bulur, E., 2007. Photo-transferred luminescence from BeO ceramics. Radiat. Meas. 42, 334–340. Chen, R., 1969. Glow curves with general order kinetics. J. Electrochem. Soc. 116, 1254–1257. Greenwood, N., Earnshaw, A., 1997. Chemistry of the Elements, second ed. ButterworthHeinemann0-08-037941-9. Horowitz, Y.S., Yossian, D., 1995. Computerised glow curve deconvolution: application to thermoluminescence dosimetry. Radiat. Protect. Dosim. 60, 1–114. Kitis, G., Gomes-Ros, J.M., Tuyn, J.W.N., 1998. Thermoluminescence glow curve deconvolution functions for first, second and general orders of kinetics. J. Phys. D Appl. Phys. 31 (19), 2636–2641. Kitis, G., Vlachos, N.D., 2013. General semi-analytical expressions for TL, OSL and other luminescence stimulation modes derived from the OTOR model using the Lambert Wfunction. Radiat. Meas. 48, 47–54. McClure, P.R., Poston, D.I., Gibson, M., Bowman, C., Creasy, J., 2014. KiloPower Space Reactor Concept - Reactor Materials Study. 2014 LA-UR-14-23402. Los Alamos National Laboratory, USDOE. Ogorodnikov, I.N., Petrenko, M.D., Ivanov, V.Y., 2016. Low-temperature luminescence and thermoluminescence from BeO:Zn single crystals. Opt. Mater. 62, 219–226. Pagonis, V., Kitis, G., Furetta, C., 2006. Numerical and Practical Exercises in Thermoluminescence. Springer Science & Business Media978-0-387-26063-1. Peng, J., Dong, Z., Han, F., 2016. tgcd: an R package for analyzing thermoluminescence glow curves. Software X 5, 112–120. Puchalska, M., Bilski, P., 2006. Glow-Fit—a new tool for thermoluminescence glow-curve deconvolution. Radiat. Meas. 41 (6), 659–664. Sashin, V.A., Bolorizadeh, M.A., Kheifets, A.S., Ford, M.J., 2003. Electronic band structure of beryllium oxide. J. Phys. Condens. Matter 15 (21), 3567–3581. Spurny, Z., Hobzova, L., 1977. A band model of energy levels and thermoluminescence mechanism in BeO ceramics. Radiochem. Radioanal. Lett. 29, 287–295. Tausenev, D.S., Milman, I.I., Ivanov, V.Io, Kruzhalov, A.V., 2008. Thermally and optically stimulated processes in additively colored beryllium oxide crystals. Radiat. Meas. 43, 349–352. Watanabe, S., Rao, G, T.K., Page, P.S., Bhatt, B.C., 2010. TL, OSL and ESR studies on beryllium oxide. J. Lumin. 130, 2146–2152. Yamashita, T., Yasuno, Y., Ikedo, Y., 1974. Beryllium oxide doped with lithium or sodium for thermoluminescence dosimetry. Health Phys. 27 (2), 201–206. Zahedifar, M., Mehrabi, M., Modarres, M., Harooni, S., 2012. Thermoluminescence properties of BeO:Mg nanoparticles produced by sol-gel method. J. Nanostruct. 1 (3), 199–203.
Acknowledgments The authors thank CONACYT for the scholarship granted to one of the authors (Martínez-Baltezar R) and also thank the Institute of Nuclear Sciences of the National Autonomous University of Mexico for providing irradiation facilities. Appendix A. Supplementary data Supplementary data related to this article can be found at https:// doi.org/10.1016/j.apradiso.2019.04.003. References Abramowitz, M., Stegun, I.A., 1972. Handbook of Mathematical Functions. Tenth Printing. National Bureau of Standards, Applied Mathematical Series, Washington, D.C 1972. Algarve, F.J., Caldas, L.V.E., 2018. Determination of the kinetic parameters of BeO
56
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Analysis of the BeO thermoluminescent glow curve by the deconvolution method
T
Rodrigo Martínez Baltezar∗, Juan Azorín Nieto Departamento de Física, Universidad Autónoma Metropolitana, Unidad Iztapalapa, Ciudad de México, Mexico
HIGHLIGHTS
parameters and TL response as a function of dose of BeO were determined by two different deconvolution methods. • Kinetic curve of BeO obtained at a heating rate of 5 Ks-1 was resolved in two peaks at temperatures of approximately 477 and 586 K respectively. • Glow • TL response as a function of dose of BeO obtained by both deconvolution methods fit a quadratic function for first peak and a linear one for the second peak. ARTICLE INFO
ABSTRACT
Keywords: Thermoluminescence glow curve Deconvolution TL kinetic parameters
Results of studying the behavior of the thermoluminescent glow curve of beryllium oxide (BeO) obtained in a wide range of absorbed doses are presented. The kinetic parameters and the TL response as a function of dose were determined using two deconvolution methods: Glow-Fit (Puchalska and Bilski 2006) and “tgcd” in “R” (Peng et al., 2016). Both methods showed that the glow curve of BeO obtained at a heating rate of 5 Ks−1 can be resolved in two peaks at temperatures of approximately 477 and 586 K respectively, with an activation energy of 1.1 eV for both peaks. The Glow-Fit method assumes first-order kinetics; while the “tgcd” in “R” method allows to determine the order of kinetics, finding that both peaks follow a kinetic of first order. Regarding the TL response as a function of dose, it was found that the first peak exhibits a quadratic dependence while the second peak exhibits a linear behavior with respect to the dose throughout the dose range studied, thus showing great advantages for its application as a TL dosimeter.
1. Introduction During the last decades the dosimetric properties of beryllium oxide (BeO) have been investigated by different research groups for applications in thermoluminescent dosimetry (TLD) (Azorín et al., 2016; Ogorodnikov et al., 2016) as well as in optically stimulated dosimetry (OSL) (Tausenev et al., 2008). Due to its excellent physical properties, such as, high heat conductivity, high electrical resistivity and high thermal shock resistance. BeO is widely used as an insulating heat sink in the electronic industry (Greenwood and Earnshaw, 1997); while its high melting point (2570 °C) and high thermal shock resistance makes it a suitable refractory material (Watanabe et al., 2010) as well as nuclear reactors moderator (McClure et al., 2014). In addition to the above characteristics, BeO is a tissue equivalent material (effective atomic number 7.13) that has a very wide energy gap (10.6 eV) (Sashin et al., 2003) as well as a good thermal conductivity, which guarantees rapid and uniform transmission of heat
∗
during the reading process; It is also easily moldable and resistant to most chemical agents, which makes it an attractive material for its application in thermoluminescent dosimetry. However, its applications have had several difficulties due to its high toxicity in powder form and to its high sensitivity to light (Bulur 2007). Yamashita et al. (1974) has obtained BeO by mixing purified BeO powder and alkali sulfate, pressing the resulting mixture to obtain discs or rods and then sintering at high temperature (1500 °C) and cooling gradually to room temperature. BeO has been also synthesized in powder form by the sol-gel method (Zahedifar et al., 2012). Although no details are known about its preparation in the form of ceramic discs 4 mm in diameter and 0.8 mm thick, it is commercially available under the name Thermalox 995 (Beryllium Brush Co., Elmore, OH, USA) with total contents of impurities not exceeding 0.5% distributed in silicon (2150 ppm), magnesium (945 ppm), iron (100 ppm), calcium (61 ppm), aluminum (54 ppm), chrome (10 ppm), titanium (4 ppm) and copper (3 ppm) (Spurny and Hobzova (1977).
Corresponding author. E-mail address: [email protected] (R.M. Baltezar).
https://doi.org/10.1016/j.apradiso.2019.04.003 Received 29 November 2018; Received in revised form 15 March 2019; Accepted 2 April 2019 Available online 03 April 2019 0969-8043/ © 2019 Published by Elsevier Ltd.
Applied Radiation and Isotopes 150 (2019) 53–56
R.M. Baltezar and J.A. Nieto
This paper reports the results of analyzing the glow curve of BeO by using two deconvolution methods: Glow-Fit (Puchalska and Bilski 2006) and “tgcd” in “R” (Peng et al., 2016) for determining its TL kinetic parameters as well as its TL response as a function of gamma dose in the range of 1.3–23.4 Gy.
the one trap-one recombination (OTOR) model (Kitis and Vlachos, 2013) using the Levenberg-Marquardt algorithm (plus supports for constraining and fixing parameters). Kitis et al. (1998) developed the general order empirical expression for a Glow peak which is given by
I (T ) = Im bb / b
2. Materials and methods
xa =
By this method, the TL glow curve is separated in individual component using Randall-Wilkins model which assumes a first order kinetics. Horowitz and Yossian, 1995 proposed the following expression. This expression can be derived by using the maximum condition and the Randall-Wilkins expression. Equation (1) represents the TL intensity of an isolated glow-peak of the TL glow curve
E exp kT
E KTm2
T Tm
E exp KTm
E KT
dT
xb =
exp 0
E kT
dT
E k
(x )
2
exp( x ) dx =
x
E1 E2 (x ) k x
(1)
E kT
E 1 kTM
T2 exp v + Zm exp v Tm2
b/ b 1
(6)
T E exp Tm kTm
E kT
(3)
E kTm
exp
E T Tm kT Tm
)
1) xb
Materials studied were constituted by disc shaped BeO ceramics commercially available under the name Thermalox 995 (Brush Beryllium Co., Elmore, OH, USA), 4 mm diameter and 0.8 mm thickness. The impurities content in BeO ceramics reported in the literature (Spurny and Hobzova (1977) not exceeds 0.5% and is distributed as follows: silicon (2150 ppm), magnesium (945 ppm), iron (100 ppm), calcium (61 ppm), aluminum (54 ppm), chrome (10 ppm), titanium (4 ppm) and copper (3 ppm). Before use, all samples were submitted to thermal annealing treatment at 600 °C during 30 min in order to erase any remaining information. Irradiations at different absorbed doses of 60Co gamma radiation were carried out in a Gammacell 200 irradiator (Atomic Energy of Canada Limited) at a dose rate of 130 mGy min−1. TL readings were made in a Harshaw 3500 TL analyzer (Thermo Scientific, USA) from 30 °C up to 360 °C at a heating rate of 5 °C·s−1 under Nitrogen atmosphere in order to reduce the thermal noise resulting from the heating planchet of the TL reader. In order to determine both the kinetic parameters and the TL response as a function of dose, the glow curve analysis was carried out by using two different deconvolution methods: the Glow-Fit and “tgcd” in “R”, by assuming first and general order kinetics respectively (Puchalska and Bilski 2006, Peng et al., 2016). The fit effectiveness was evaluated using the figure of merit (FOM). A FOM equal or less than 5% meaning very good fit. To obtain the TL response as a function of dose for an isolated peak both deconvolution methods were used. The samples of BeO were randomly divided into six groups and irradiated at 1.3, 2.6, 5.2, 10.4, 15.6, and 23.4 Gy respectively in order to obtain the dose-response curve for each individual glow peak.
E kTm (4)
This equation shows that the glow-curve is a non-linear function of Tm, Im and E parameters. To find the best-fit values of peak parameters an iterative procedure must be used. GlowFit is able of simultaneously deconvoluting as many as ten glow peaks of the TL glow-curve. The minimization process starts with trial values. In this program the Levenberg-Marquardt method for non-linear function minimization was chosen. To enable the user to control the fitting peak parameters, the original algorithm was modified by Puchalska and Bilski (2006) to exclude or constrain any given parameter of the peak. Also, this software uses three unknown parameters in the background expression (equation (4))
Ig = a + beT / c
x a)
2.2. Experimental
Then, finally, the following expression is used to describe a single glow peak (Horowitz and Yossian 1995)
I (T ) = Im exp
1)(1
where b is the kinetics order, I is the TL intensity, E is the activation energy, k is the Boltzmann constant, T is the temperature, Tm is the temperature at the maximum of a peak and Im is the maximum TL intensity. This model contains four free parameters that which are Im, E, Tm and b. This deconvolution model also let us to set both parameters and restrictions. Like Glow-Fit this software let set up to ten peaks.
(2)
a0 + a1 x + a2 x 2 + a3 x 3 + a4 x 4 b0 + b1 x + b2 x 2 + b3 x 2 + b4 x 4
(
Zm = 1 + (b
where x = E kT , x = E kT , and E2(x) is the second exponential integral function which can be evaluated by E2(x) = α(x)exp (-x), where α(x) is a quotient of two 4th order polynomials (Abramowitz and Stegun, 1972):
(x ) = 1
2kT E 2KTm E
exp v = exp
where I is the glow peak intensity, E is the activation energy, k is the Boltzmann constant, T is the absolute temperature and Tm and Im are the temperature and the intensity of the maximum, respectively. Because the exponential integral in equation (1) cannot be solved analytically, several different approximations have been proposed (Chen 1969; Horowitz and Yossian 1995) for the function describing a single glow peak. In the case of Glow-Fit (Puchalska and Bilski 2006) the exponential integral is approximated by the following expression (Abramowitz and Stegun 1972; Bos et al., 1993). T
(b
where
2.1. Glow-Fit deconvolution
E I (T ) = Im exp kTm
1
3. Results
(5)
Fig. 1 displays the glow curve of BeO obtained after exposing the sample to gamma irradiation at an absorbed dose of 15.6 Gy. This glow curve exhibited two well-separated peaks centered at 477 and 586 K. Fig. 2 shows the TL glow curve of BeO irradiated at an absorbed dose of 15.6 Gy, deconvoluted by using the Glow-Fit. This deconvolution method decomposed the glow curves in two TL glow peaks centered at around 471 and 590 K. The results obtained applying the ‘tgcd’
where a, b and c are the three unknown parameters.‘tgcd’ in ‘R’ deconvolution This package was developed by Peng et al. (2016). Function tgcd is used for deconvoluting thermoluminescence glow curves represented by the empirical expression of general order kinetics (Kitis et al., 1998; Pagonis et al., 2006) or by the semi-analytical expression derived from 54
Applied Radiation and Isotopes 150 (2019) 53–56
R.M. Baltezar and J.A. Nieto
Fig. 1. Experimental TL glow curve of BeO irradiated with 60Co gamma radiation at an absorbed dose of 15.6 Gy and registered at a heating rate of 5 K s−1.
Figure 3. Glow curve of BeO irradiated with 60Co gamma radiation, deconvoluted by Glow-Fit method. Table 1 Kinetic parameters obtained for the first peak of the BeO TL glow curve by applying two different deconvolution methods. Parameter
Glow-Fit
‘tgcd’ on ‘R’.
Kinetic order Frequency factor (s−1) Activation energy (eV)
1 2.57 × 1011 1.10 ± 0.03
1.04 ± 0.01 4.4603 × 1010 1.04 ± 0.01
Table 2 Kinetic parameters obtained for the second peak of the BeO TL glow curve by applying two different deconvolution methods. Parameter
Glow-Fit
‘tgcd’ on ‘R’.
Kinetic order Frequency factor (s−1) Activation energy (eV)
1 4.71 × 1008 1.06 ± 0.01
1.00003 ± 0.00001 1.89 × 1009 1.17 ± 0.01
used, it is expected that both the parameters and the maximum temperature differ from one method to other. Glow-Fit uses first-order kinetics, while “tgcd” considers general-order kinetics and, as can be seen, the approximations used to adjust the TL peak are different in both methods. At naked eye, it can be observed that temperature values are more in agreement with the “tgcd” method than with Glow-Fit method. The results also showed that, while the activation energy values obtained by applying both deconvolution methods were very close to 1.1 eV for each peak, the values found for the frequency factor differ by two orders of magnitude between one method and another. This is probably because Glow-fit assumes first-order kinetics while the order of kinetics found using “tgcd” was very close but not exactly equal to 1. TL response as a function of dose shows a quadratic response for the first peak and a linear response for the second one using both deconvolution methods. Although the same experimental glow curves were analyzed by two different deconvolution methods, the integrated signals of each peak were not the same because it must be considered that to determine the TL response as a function of dose using the “Glow-Fit” method, the data provided by the TL reader (expressed in nC) are used directly; whereas when the “tgcd” method is used the data are exported to an external program that determines the area under the glow curve in arbitrary units and not in “nC”. However, it can be seen that the behavior of the TL response as a function of dose, obtained using both
Fig. 2. Glow curve of BeO irradiated with 60Co gamma radiation, deconvoluted by ‘tgcd’ in R method.
in R method showed that the glow curve of BeO is composed by two glow peaks centered at around 476 and 585 K, as is shown in Fig. 3. The value of activation energy obtained applying both deconvolution methods was 1.1 eV for each peak. The frequency factor value for first peak obtained using the Glow-fit method was 2.57 × 1011 s−1 and for second peak 4.71 × 108 s−1. Also it was found, by using the ‘tgcd’ deconvolution method, that the frequency factor was 1.89 × 109 s−1 and 4.46 × 1010 s−1 for first and second peak respectively. These results are shown in Table 1 and Table 2. The TL response of first peak, isolated by both deconvolution methods, as a function of gamma absorbed dose was fit a quadratic function in the range of 1.3–23.4 Gy, while the second peak fit a linear response in the same dose range, as it is shown in Fig. 4. 4. Conclusions From the results, it can be concluded that Glow-fit method gives peak maximum temperatures 471 K and 590 K whereas ‘tgcd’ in R method 476 K and 585 K. It is well known that peak temperatures and TL parameters depend strongly on the order of the kinetics responsible for the TL process. If methods that consider different kinetic orders are 55
Applied Radiation and Isotopes 150 (2019) 53–56
R.M. Baltezar and J.A. Nieto
Fig. 4. TL response as a function of absorbed dose obtained for isolated peaks of BeO TL glow curve. a) First peak b) Second peak.
methods, is the same. Then, if it is required to use this material for ionizing radiation dosimetry, it will be necessary to specify the deconvolution method used to separate the glow peaks and calculate the TL response as a function of dose for each peak. Watanabe et al. (2010) have shown that BeO TL glow curve is composed by three isolated peaks centered at 75 °C, 220 °C, 340 °C. However due to high fading this peak has not been reported by ourselves and by other authors. Recently, Algarve and Caldas (2018) have reported that the BeO glow curve is composed for two peaks centered at 475 and 621 K. Although these results differ of those obtained in this work, are according in the fact that the TL glow curve is composed by two well separated peaks, as well as in the activation energy values obtained; these results are according also with previous studies (Azorín et al., 2016). Recent researches have shown the advantages of BeO for its application in optically stimulated luminescence dosimetry (Bulur, 2007; Watanabe et al., 2010), however TL response of this phosphor by deconvolution method for individual peaks is not reported yet.
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Acknowledgments The authors thank CONACYT for the scholarship granted to one of the authors (Martínez-Baltezar R) and also thank the Institute of Nuclear Sciences of the National Autonomous University of Mexico for providing irradiation facilities. Appendix A. Supplementary data Supplementary data related to this article can be found at https:// doi.org/10.1016/j.apradiso.2019.04.003. References Abramowitz, M., Stegun, I.A., 1972. Handbook of Mathematical Functions. Tenth Printing. National Bureau of Standards, Applied Mathematical Series, Washington, D.C 1972. Algarve, F.J., Caldas, L.V.E., 2018. Determination of the kinetic parameters of BeO
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