SIMULATION OF COMPETING FADING AND IRRADIATION EFFECTS IN THERMOLUMINESCENCE (TL) DOSIMETRY: 1 st ORDER KINETICS

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1 IMULATION OF COMPETING FADING AND IRRADIATION EFFECT IN THERMOLUMINECENCE (TL) DOIMETRY: 1 st ORDER KINETIC C.Furetta 1, J.Azorin 1, T.Rivera 1, G.Kitis 2 1. Dep.to de Fisica, Edif. T, cub. 331 Universidad Autonoma Metropolitana Iztapalapa (UAMI) Av. an Rafael Atlixco 186 Col Vicentina Iztapalapa D.F., Mexico Nuclear Physics Laboratory, Aristotle University of Thessaloniki Thessaloniki, Greece Abstract The aim of this paper is to give some useful expressions for fading correction in practical situations as they can be encountered in radiation protection dosimetry monitoring, i.e. personal, environmental and clinical dosimetry. They are obtained considering the first order TL process and the general case in which, during the experimental period of time, two effects are in competition between them: one is the trapping rate due to a continuous irradiation over all the experimental period, i.e. environmental background irradiation; the second one is the detrapping rate which takes place at the same time, i.e. thermal fading. Keywords: thermoluminescence dosimetry, first order kinetics, fading 1. Introduction The fading effect in thermoluminescence phenomena is the most serious problem when the TL phopsphors are used for monitoring ionizing or UV radiations. This phenomena has been theoretically studied by several authors [1-6], but no practical expressions have been given up to now. The kinetics expressions [7-9], namely the first, second and general-order equations, allow to characterise the TL decay after irradiation, i.e. exponential for a first-order decay, hyperbolic for the second-order and intermediate for the generalorder. This is a typical laboratory situation which allows to study the decay behaviour of the filled TL traps at room temperature or at any other temperature of storage. The kinetic equations must be modified in case of situations quite different from the previous one, i.e. the irradiation is performed during all the storage time, or

2 more irradiations are superposed. In these cases the fading is in competition with the irradiation: the former effect produces a progressive extinction of the accumulated charges, whereas the second produces an increase of the trapped charges. The aim of the present work is to propose equations relative to different practical situations as they can be encountered in the monitoring of ionizing or UV radiations. The equations are given for the first-order kinetics. 2. Modified equations Let us start considering a first order TL process which is described by the Randall Wilkins equation dn = nλ (1) dt Eq.(1) gives the charge change rate, dn/dt, as a function of the detrapping rate, n. n is the trapped electron concentration (cm-3) at time t, is the escape probability per unit of time, i.e. E = s exp kt λ where s is the so called frequency factor (sec-1), E (ev) is the activation energy, i.e. the energy associated to the trapping state located in the band gap of the crystal, k the Boltzmann s constant (0.862x10-4 ev/k) and T the absolute temperature (K). is also called fading factor. Integration of Eq.(1), at constant temperature, gives = n exp( λ t) (2) n( t ) 0 where n0 is the concentration of the initial trapped charges at t = 0. The TL intensity, I(t), is given by n 0 I( t ) dn dt = n λ = (3) λ exp( t) (4) = λ By integration of the basic equation (3), we get ( t ) n( ) = Idt n (5) Dealing with only one single peak, n( ) = 0 and therefore t = t n ( t ) Idt (6)

3 The integral in Eq.(6) gives the total area,, of the peak. Then, it turns out that the peak area coincides numerically with n. In this way, Eq.s (1) and (2) can be rewritten as dφ = Φ λ dt (1)' and Φ () t = Φ 0 exp( λ t) (2)' This kind of writing is much more useful for the following development of this work because the peak area is a quantity easily available from the TL reading. 3. Modified 1 st order kinetics expression Let us consider a general case in which, during the experimental period of time, two effects are in competition between them: one is the trapping rate due to a continuous irradiation over all the experimental period, i.e. environmental background irradiation; the second one is the detrapping rate which takes place at the same time, i.e. thermal fading. uch a situation can be described by the following first order differential equation: dφ D = λ Φ + (7) dt F C where is the total TL light of a given peak in the glow curve; D is the dose rate of the irradiation field (Gy/time); F C is the calibration factor of the thermoluminescence system, expressed in dose/tl. Eq.(7) represents a dynamic situation where two competing effects are taken into account. This equation tends to an asymptotical limit as the fading produces a progressive extinction of the accumulated charges, whereas the continuous irradiation leads to an increase of them. Eq.(7) only holds in the case to be far from saturation. The solution of Eq.(7) is then easily obtained as: D Φ = Φ 0 exp( λt) + λfc [ 1 exp( λt) ] (8) Eq.(8) depicts a situation where a non-zero charge population is already trapped at the beginning of the experimental time, i.e. Φ 0 0. Considering the practical situation where the TLDs are annealed before use, all the traps are empty at the beginning of the experimental period. In such a case Eq.(8) becomes

4 D Φ = λf [ exp( λt) ] C 1 (9) When a very long time has elapsed, i.e to the asymptotical value F C t D Φ = (10) λ, Φ gets more and more similar uch a value grows larger as the dose rate and /or the sensitivity (1/F C ) increases, or as the fading effect decreases. The asymptotical value given by Eq.(10) may be explained assuming that, at infinity, a dynamical equilibrium is attained, providing the trapped charges to compensate at each instant those escaping owing the fading phenomenon. ome expressions can be now developed in relation to some practical situations 3.1. Initial and instantaneous irradiation followed by fading at room temperature Fig.1 depicts the situation. In this case the irradiation is delivered to the dosimeters at the beginning of the experimental period and the duration of irradiation, t i, is very short so that any fading effect during irradiation can be neglected. After irradiation the irradiated samples are stored, at room temperature or at any other controlled temperature, for a time t >> t i. The situation depicted in Fig.1 is the usual for fading studies. Eq.(8) reduces to the simply expression from which Φ ( t ) = Φ exp( λ ) 0 (11) t 0 = Φ ( t ) exp( λ ) Φ (12) t Through the calibration factor F C, the initial delivered dose is then obtained: D 0 CΦ ( t ) exp( λt ) = F (13) 3.2. Initial but not instantaneous irradiation, followed by fading at room temperature An initial irradiation is delivered at the beginning of the experimental period, but the irradiation time, t i, is long enough so that a fading effect is not any more negligible during the period of irradiation. After the irradiation the samples are stored for the time t. Fig.2 depicts the situation. During the irradiation time, Eq.(8) reduces to the following expression

5 D ( ti ) = λfc [ 1 exp( λti )] (14) Φ which gives the TL emission at the end of the irradiation time. As the irradiation stops, the samples are only subjected to fading at room temperature, so that ( t ) = Φ( t ) ( λt ) Combining Eq.(14) and Eq.(15), we get Φ Φ exp (15) i D ( t ) = [ exp( λti )] exp( λt ) λfc 1 (16) from which the true delivered dose is obtained, taking into account that D = D t, i ( t ) t exp( λt )[ 1 exp( λt )] 1 D = λ FC Φ i i (17) 3.3. The irradiation is carried out over all the experimental period. This is the case of environmental background measurements or self-dose irradiation. ee Fig.3. The irradiation time, t i, is now equal to the storage time t. The TLD samples are prepared and exposed to the irradiation field, then the initial condition is Φ 0 = 0 and Eq.(8) reduces to the following expression: having indicated t = t t. i = D Φ = λf [ exp( λt) ] C 1 (18) If D is the environmental background dose rate or the internal dose rate due to the self irradiation of the samples, the total dose is obtained as [ 1 exp( )] 1 D = Φλ FC t λt (19) 3.4. An initial and short irradiation is superposed to a background irradiation Let us indicate with D B the background irradiation, which acts over all the period of storage, t, and D 0 the initial delivered irradiation dose which acts for a short time t i ; t i is negligible compared to the storage time t.fig.4 shows the situation. The fading during the short irradiation is neglected. The equation simulating this case is always Eq.(8), written in the following way:

6 Φ = Φ 0 exp B ( λt ) + [ 1 exp( λt )] D! λf C (20) which gives, in explicit form Φ 0 D! = Φ λf B C [ 1 exp( λt )] exp( λt ) (21) from which the initial delivered dose is obtained: D F (22) 0 = C Φ 0 4. Discussion and conclusions Fig.5 shows the behaviour of the TL response as a function of the elapsed time from the initial irradiation. The data used for the simulation are given in the inset. Fig.6 depicts three different situations according to different values of the initial delivered dose D. As an example, considering that the TL sample has been irradiated for a period of 3 days, the storage time t s is equal to 50 days and that the TL emission measured at the end of storage is 2000 reader units, Eq.(17) gives a total dose of Gy. Fig.s 7 and 8 show the behaviour of the TL emission according to Eq.(18). In particular, the plot given in Fig.8 shows the effect of the saturation of the TL sample: in practical applications it is necessary to verify accurately the linear range of the phosphor used to avoid this effect. Fig.9, finally, shows the TL behaviour analitically described by Eq.(20). Also in this case the characteristics of the TLD used have to be accurately studied; a high fading factor may provoke a final readout very close to zero or to the intrinsic background of the sample as shown by the plot (a). Concluding, the previous equations, simulating different experimental and practical situations, may be very useful in all fields of dosimetry where a more or less long delay time exists between the end of the irradiation and the readout time, i.e. clinical dosimetry, and in personal and environmental monitoring, where during the exposure time the fading effect could be in competition with the irradiation.

7 References 1. Levy P.W. (1985) Recent developments in thermoluminescence kinetics. Nucl. Tracks Rad. Meas. 10, Furetta C., Tuyn J.W.N.., Louis F., Azorin J. and Driscoll C.M.H. (1986) imultaneous determination of dose and elapsed time in accident dosimetry using thermoluminescent material. Rad. Prot. Dos. 17, Furetta C. (1988) New calculations concerning the fading of thermoluminescent materials. Nucl. Tracks Rad. Meas. 14,, Delgado A. and Gomez Ros J.M.(1990) Evolution of TLD-100 glow-peaks IV and V at elevated ambient temperatures. J.Phys. D: Appl. Phys. 23, Delgado A., Gomez Ros J.M. and Muñiz J.L.(1992) Temperature effects in LiF TLD-100 based environmental dosimetry. Rad. Prot. Dos. 45, Gomez Ros J.M., Delgado A., Furetta C.and cacco A.(1996) Effects of simulteneous release of trapped carriers and pair production on fading in thermoluminescent materials during storage in radiation fields. Rad. Meas. 26, Randall J.T.and Wilkins M.H.F. (1945) Phosphorescence and electron traps I. The study of trap distribution. Proc. Roy. oc. Lond. A 184,

8 8. Garlick G.F.J.and Gibson A.F. (1948) The electron trap mechanism of luminescence in sulphide and silicate phosphors. Proc. Phys. oc. 60, May C.E.and Partridge J.A., (1964) J. Chem. Phys. 40,1401 Figure captions Fig.1. Case 3.1. Initial irradiation followed by storage at R.T. Fig.2. Case 3.2. Long irradiation followed by storage at RT. Fig.3. Case 3.3. The irradiation is carried out over all the storage time. Fig.4. Case 3.4. Initial and short irradiation plus background irradiation over all the experimental period. Fig.5. Behaviour of the TL response as a function of the elapsed time from the initial irradiation: Case 3.1, Eq.(12). Fig.6. Behaviour of TL response as a consequence of long irradiation and fading: Case 3.2, Eq.(16). Fig.7. Behaviour of TL response according to Eq.(18).Case 3.3. Fig.8. ame of Case 3.3 showing dosimeter saturation effect. Fig.9. TL behaviour according to the situation of Fig.4 (Case 3.4) and Eq.(20).

10 D 0 Φ(t ) storage time t Fig.1.Case 3.1. Initial irradiation followed by storage at R.T.

11 D t i t s Fig.2. Case 3.2. Long irradiation followed by storage at RM

12 D! t s = t i = t Fig.3.Case 3.3. The irradiation is carried out over all the storage time

13 D 0 D! B t s Fig.4. Case 3.4. Initial and short irradiation plus background irradiation over all the experimental period

14 1.1 1 NORMALIZED TL λ =6x10-3 day -1 F c =10-3 Gy/TL Φ 0 =10 3 D 0 =1Gy 0.5 Fig DAY

15 TL EMIION [a.u TL (1 day) TL (3 days) TL (5 days) DAY Fig.6

16 80 70 TL EMIION [a.u.] DAY Fig.7

17 TL EMIION [a.u.] DAY Fig.8

18 NORMALIZED TL (b) (a) DAY Fig.9

Mechanism of Thermoluminescence

International Journal of Scientific & Engineering Research, Volume 3, Issue 10, October-2012 1 Mechanism of Thermoluminescence Haydar Aboud *a,b, H. Wagiran a, R. Hussin a a Department of Physics, Universiti