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Peculiarities of the glow-peak 5a of LiF:Mg,Ti
Nuclear Instruments and Methods in Physics Research B 160 (2000) 262±273
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Peculiarities of the glow-peak 5a of LiF:Mg,Ti G. Kitis a
a,b,*
, T. Otto
b
Aristotle University of Thessaloniki, Nuclear Physics Laboratory, GR-540 06, Thessaloniki, Greece b CERN, CH 1211, Geneva 23, Switzerland Received 8 June 1999; received in revised form 23 July 1999
Abstract The glow-peak 5a of LiF:Mg,Ti is a glow-peak, with peak maximum temperature between those of glow-peaks 5 and 6. This glow-peak is not seen in the usual glow-curve, resulting after normal annealing at 400°C for 1 h and at 100°C for 2 h. However, its existence is con®rmed ®rst experimentally and then as the necessity to achieve a very good glow-curve ®tting. In the present work it is found that the glow-peak 5a can be very well isolated from its neighbouring glow-peaks, after special thermal treatment between 140°C and 160°C. The isolation permits the study of its individual behaviour, which was found to have the following peculiarities. (i) This glow-peak is clearly seen only after thermal treatment between 140°C and 160°C. (ii) It appears with the same properties after both pre-irradiation and post-irradiation annealing in the above temperature region. (iii) Its activation energy was found to be above 3 eV and its frequency factor above 1030 sÿ1 . These values are extremely high and outside the physically accepted limits. Ó 2000 Elsevier Science B.V. All rights reserved. PACS: 78.60.Kn; 78.60.ÿb; 29.40.Wk Keywords: Thermoluminescence; Activation energy; Annealing; LiF:Mg,Ti
1. Introduction The existence of the glow-peak 5a with peak maximum temperature (Tmax ) between the main glow-peak 5 and glow-peak 6, was originally introduced by Fairchild et al. [1], as a requirement to obtain a good ®t to the experimental glow-curve of
* Corresponding author. Tel.: +30-31-99-8175; fax: +30-3199-8175. E-mail address: [email protected], [email protected] (G. Kitis).
LiF:Mg,Ti. Later, Bos et al. [2] found that the above requirement appears only for some batches of LiF (TLD) but not for others. Concerning early experimental evidences, in our opinion, the glowpeak called 6 by Zimmerman et al. [3], Johnson [4] and Blak and Watanabe [5], is the glow-peak 5a. Kitis et al. [6] observed glow-peak 5a, as an isolated one in TLD-700, after muon irradiation at the elevated temperature of 125°C. Kitis and Furetta [7] had found in LiF:Mg,Ti (DTG-4) that glow-peak 5a can be isolated after special lowtemperature pre-irradiation annealing between 140°C and 160°C.
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G. Kitis, T. Otto / Nucl. Instr. and Meth. in Phys. Res. B 160 (2000) 262±273
In the same material (DTG-4) Kitis et al. [8] had estimated that the activation energy of the glow-peak 5a must be greater than 3 eV. This value is even higher than that of the main glowpeak 5 of LiF:Mg,Ti, whose activation energy has been found to be (2:0 E 2:3 eV) and frequency factor (1019 s 1023 sÿ1 ) [9±13]. The main dosimetric glow-peak of the other hypersensitive LiF based dosemeter, LiF:Mg,Cu,P has even higher values of E and s ( 2:5 eV and 1025 sÿ1 , respectively) [14]. The above values of the trapping parameters are considered as extremely high and outside of the physically accepted region of 107 ±1013 sÿ1 , given by Mott and Gurney [15], whereas Bohm and Sharmann [16,17] had proposed as an upper limit for s, the value of 3 1015 sÿ1 at 300 K. For the explanation of the high values of trapping parameters various models have been proposed [1,18±21], which are extensively discussed in a series of books [9±11]. The objective of this work is: (a) to establish the appropriate conditions under which the glow-peak 5a appears completely isolated and without any doubts of confusion with the glow-peak 6, (b) to estimate its trapping parameters and (c) to give an explanation based on minor modi®cations of the existing models. 2. Experimental procedure and analysis LiF:Mg,Ti(TLD-700) chips were used in the present work. The chips were annealed, before their use, in a furnace at 400°C for 1 h and were rapidly cooled to room temperature. The measurements were performed with the Harshaw model 3500 manual TLD reader, with a heating rate of 2°C/s and continuous nitrogen ¯ow. The irradiations were performed in the Studsvik irradiator with a 90 Sr±90 Y beta ray source delivering 1.1 mGy per exposure. The test dose used was 11 mGy. According to the objectives of the present work the following measurements were performed. 1. Low-temperature pre-irradiation annealing between 140°C and 160°C for 1 h. 2. Pre-irradiation annealing at 150°C for times 10 min up to 12 h.
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3. Post-irradiation annealing at 150°C for times 10 min up to 4 h. In another series of test measurements it was examined if this glow-peak appears in: (i) TLD-100 and TLD-600, (ii) in other two batches of LiF:Mg,Ti and (iii) under neutron irradiation. 3. Experimental results 3.1. Glow-curve analysis All the experimental glow-curves obtained in the present work were analysed by glow-curve deconvolution (GCD) using the MINUIT program [22]. The goodness of ®t was tested by the ®gure of merit (FOM) of Balian and Eddy [23]. It was assumed that the glow-peaks follow ®rst order kinetics, except in a few cases. So, for the GCD analysis the ®rst and the general kinetics order algorithms proposed by Kitis et al. were used [24]. The FOM values obtained from the GCD analysis of all glow-curves obtained from the preirradiation annealing, were between 0.87% and 1.1%, which are satisfactory. In the case of the post-irradiation annealing, the ®rst order kinetic algorithm fails to ®t the region of glow-peak 5, and the FOM values obtained from GCD were above 4%. The FOM values were reduced to between 1% and 3% when one more glow-peak with Tmax very close to that of the main 5 was introduced. This behaviour is similar to that described by Yossian and Horowitz [13]. Following these authors, in the case of post-irradiation annealing, the glow-peak 5 was ®tted with a general order algorithm, whereas for the remaining glow-curve the ®rst order kinetic was used again. The FOM values obtained in this case were between 1% and 2%, which must be considered satisfactory. Fig. 1 shows an analysed glow-curve obtained after annealing at 400°C for 1 h and fast cooling to room temperature. Here, the glow-peak 5a appears as a weak peak necessary to improve the FOM values. The high temperature glow-peaks 6 and 7 appear at 525 K and 550 K, respectively. Fig. 2 shows an analysed glow-curve obtained after pre-irradiation annealing at 152°C for 2 h. The known [3,7,8] strong glow-curve modi®cations
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Fig. 1. Glow-curve of LiF:Mg,Ti after annealing at 400°C for 1 h followed by fast cooling.
Fig. 3. Glow-curve of LiF:Mg,Ti after post-irradiation annealing at 152°C for 30 min.
for the TL intensity). The high temperature glowpeaks 6 and 7 appear at 525 K and 550 K, respectively (as in the case of Fig. 1). Fig. 4 shows the glow-curve after post-irradiation annealing at 152°C for 4 h. In this case the glow-peak 5a is almost isolated. The glow-peak 7 appears again at 550 K, whereas glow-peak 6 appears at approximately the same temperature as the glow-peak 5a. From the ®gures above it becomes apparent that it is necessary to make the appropriate dis-
Fig. 2. Glow-curve of LiF:Mg,Ti after low-temperature preirradiation annealing at 152°C for 2 h.
have appeared. The glow-peak 5a becomes very clear. The glow-peak 7 appears again at 550 K, whereas glow-peak 6 appears at the same temperature as the glow-peak 5a. Fig. 3 shows the glow-curve after post-irradiation annealing at 152°C for 30 min. As was stated above, the glow-peak 5 was ®tted with a general kinetic order algorithm. The glow-peak 5a appears as a shoulder at the high temperature part of the main peak 5 (this shoulder becomes very clear if one draws the glow-curve using a logarithmic axis
Fig. 4. Glow-curve of LiF:Mg,Ti after post-irradiation annealing at 152°C for 4 h.
G. Kitis, T. Otto / Nucl. Instr. and Meth. in Phys. Res. B 160 (2000) 262±273
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crimination between glow-peaks 5a and 6. In the next subsection it will be shown that the glow-peak 5a is a new glow-peak, which must not be confused with glow-peak 6. 3.2. Glow-peak 5a through the glow-curves In the normal glow-curve of LiF:Mg,Ti, shown in Fig. 1, the glow-peak 5a is a weak peak necessary to improve the ®tting. In the following, the evolution of the glow-peak 5a will be shown from a weak shoulder to a discrete glow-peak. Fig. 5 shows the glow-curves obtained after low-temperature pre-irradiation annealing between 143°C and 160°C for 1 h (see ®gure caption). The evolution of the glow-peak 5a from a shoulder in the glow-peak 5 at 143°C (curve a) to a discrete glow-peak at higher temperatures (curves b±f) becomes very clear. On the other hand the dierence of glow-peak 5a from the system of the glowpeaks 6 and 7 becomes also clear. Fig. 6 shows the glow-curves obtained after low-temperature pre-irradiation annealing at 152°C for various times, as it is shown in the ®gure caption. Glow-peak 5a appears clearly as a shoulder of the main glow-peak 5 for an annealing time of 30 min. At higher annealing times it is completely discriminated from the glow-peak 5.
Fig. 5. Glow-curves of LiF:Mg,Ti after low-temperature preirradiation annealing for 1 h at (a) 143°C, (b) 146°C, (c) 148°C, (d) 152°C, (e) 155°C and (f) 160°C.
Fig. 6. Glow-curve of LiF:Mg,Ti after low temperature preirradiation annealing at 152°C for times (a) 300 min, (b) 60 min, (c) 100 min, (d) 2 h, (e) 4 h and (f) 12 h.
Moreover, one can see that it is dierent from the system of glow-peaks 6 and 7. Fig. 7 shows the glow-curves obtained after post-irradiation annealing at 152°C for various times shown in the ®gure caption. In this ®gure glow-peak 5 is also included. As in the previous cases the dierence between glow-peak 5a and the system of glow-peaks 6 and 7 is clear. The net conclusion from the above listed ®gures is that under the conditions studied, the glow-peak 5a is a discrete glow-peak, which exists also in the
Fig. 7. Glow-curve of LiF:Mg,Ti after post-irradiation annealing at 152°C for times (a) 30 min, (b) 40 min, (c) 1 h, (d) 2 h and (e) 4 h.
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normal (after 400°C/1 h annealing) glow-curve of LiF:Mg,Ti. The results of the test measurements with TLD100, TLD-600, and with the other two batches of LiF:Mg,Ti, show that the glow-peak 5a appears in all cases. A slight dierence from batch to batch was found. This glow-peak was observed after muon irradiation [6]. In the present work it was found that the glow-peak 5a appears also under thermal neutron irradiation. 3.3. Behaviour of peak maximum position, Tmax The low-temperature pre-irradiation annealing in the region of 140±160°C induces strong modi®cations in the glow-curve structure of LiF:Mg,Ti [6,7,25,26] and of the LiF:Mg,Cu,P [8]. These modi®cations were also observed in the present work. However, results presented in [7,8,14,26] are not repeated here except for a few cases and only when they have a very close relation to the glowpeak 5a, which is the main subject of this work. The Tmax of glow-peaks 2, 3, 6 and 7 are not in¯uenced at all for all conditions studied. On the other hand the Tmax of the glow-peak 4, 5 and 5a is in¯uenced. Fig. 8 shows how the Tmax of the glowpeak 5a is shifted towards higher temperatures as the low-temperature pre-irradiation annealing for 1 h, is increased from 140°C to 160°C. On the
Fig. 8. Glow-peak maximum Tmax of the glow-peak 5a after low temperature pre-irradiation annealing between 143°C and 160°C for 1 h.
other hand in this short temperature region the Tmax of glow-peaks 4 and 5 is not altered. Fig. 9 shows the Tmax of glow-peaks 4, 5 and 5a, as a function of low-temperature pre-irradiation annealing at 152°C for various times. It is interesting to observe that the Tmax of the glow-peaks 4 and 5 is shifted towards lower temperatures in a similar way, both qualitatively and quantitatively. Whereas the Tmax of the glow-peak 5a is shifted towards higher temperatures. Fig. 10 shows the Tmax of the glow-peaks 5 and 5a as a function of post-irradiation annealing time at 152°C (glow-peak 4 is drained). It is interesting to note that the behaviour is similar to that of Fig. 9. The conclusions from the above listed results are that the thermal treatment between 140°C and 160°C aects only the Tmax of glow-peaks 4, 5 and 5a. A very interesting conclusion is that the Tmax for the glow-peaks 5 and 5a behaves in exactly the same way irrespective if the annealing is performed prior to irradiation or after the irradiation (see Figs. 9 and 10). 3.4. Activation energy Before the presentation of the GCD analysis results, concerning the value of the activation energy of the glow-peak 5a, we will show that a
Fig. 9. Glow-peak maximum Tmax as a function of time of the low temperature pre-irradiation annealing at 152°C: (a) glowpeak 5, (b) glow-peak 4 and (c) glow-peak 5a (left axis).
G. Kitis, T. Otto / Nucl. Instr. and Meth. in Phys. Res. B 160 (2000) 262±273
Fig. 10. Glow-peak maximum Tmax of glow-peaks 5 and 5a, as a function of the post-irradiation annealing time at 152°C.
preliminary information can be extracted by a simple observation of the temperature interval covered by this glow-peak. We can use Figs. 2 and 4 as examples. From these ®gures one can see that the full width at half maximum (FWHM) of the glow-peak 5a is less than 20°C. This is the highest possible value of FWHM, because it does not include any corrections from the obvious interferences from the neighbouring glow-peaks. For a Tmax 525 K, any peak shape method [27] provides for the lower limit of the activation energy of the glow-peak 5a a value of 3 eV. The activation energy values obtained by the GCD analysis are as follows. Fig. 11 gives the values of the activation energies of the glow-peak 5a as a function of the low-temperature pre-irradiation annealing for 1 h between 143°C and 160°C. The activation energy increases as the pre-irradiation temperature increases arriving at a value of about 3.8 eV. The activation energies of the glow-peaks 4 and 5 vary within the experimental errors, in this temperature interval and for the 1 h annealing time. Fig. 12 gives the values of the activation energies as a function of the low-temperature preirradiation annealing time at 152°C, of the glow-peaks 5 (a) and glow-peak 4 (b). The activation energy of the glow-peak 5 is strongly reduced as the duration of the annealing time at 152°C increases.
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Fig. 11. Activation energy E of the glow-peak 5a as a function of the low-temperature pre-irradiation annealing between 143°C and 160°C, for 1 h.
Fig. 12. Activation energy as a function of the low temperature pre-irradiation annealing time at 152°C: (a) glow-peaks 5 and (b) glow-peak 4.
Fig. 13 gives three sets of values of the activation energies of the glow-peak 5a as a function of the pre-irradiation annealing time at 152°C. Each set of values corresponds to dierent constraints of the deconvolution analysis. The constraints concern the position and the intensity of the glowpeak 6 only. The position and the intensity of the glow-peak 7 had an appreciable repeatability for all cases studied. Its peak position is at 550 2.5 K whereas its intensity varies within 15% (the
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Fig. 13. Activation energy of glow-peak 5a as a function of the low temperature pre-irradiation annealing time at 152°C. Curves (a), (b) and (c) correspond to various constraints of the deconvolution analysis, see text.
statistics of the glow-curve at the high temperatures glow-peaks is low). In the normal glow-curve of LiF shown in Fig. 1, the intensity of the glow-peak 6 is lower than the intensity of the glow-peak 7 and its peak position is around 525 K. In the set of values (a) of Fig. 13 the intensity of the peak 6 was not allowed to become higher than the intensity of the peak 7 and its peak position was left to vary between 517 K and 525 K. Under these constraints its integral was stable within 15% and the average peak position was 519 2 K. In the set of values (b) of Fig. 13, the intensity of the peak 6 was not allowed to become higher than the intensity of the peak 7 and its peak position was left to vary between 525 K and 535 K. Under these constraints its integral was stable within 15% and the average peak position was 530 2 K. In the set of values (c) of Fig. 13, the intensity of the peak 6 was allowed to vary freely and its peak position was left to vary between 517 K and 535 K. Under these constraints the average peak position was at 520 2.5 K, whereas its integral for annealing times greater than 1 h, was increased by a factor of three relative to the integral for lower annealing times. The FOM values in all set of deconvolution were between 0.87% and 1.1%.
Fig. 14. Activation energy of glow-peak 5a as a function of the post-irradiation annealing time at 152°C.
However, it must be noticed that for the set (c) the FOM values were somewhat better. Fig. 14 gives the activation energies of the glow-peak 5a as a function of the post-irradiation annealing time at 152°C. As was stated above, in the post-irradiation annealing glow-curves, the glow-peak 5 was ®tted by a second order kinetic algorithm. The activation energy found for the glow-peak 5 was 2.5 0.1 eV. No systematic behaviour of the kinetic order was found. Finally, it must be noticed that an activation energy value of 3.62 eV i.e. similar to those presented above was that of Pohlit [28] for the glow-peak 5 of the Harshaw LiF. It is reasonable to think that the glow-peak studied by Pohlit was, possibly, the glow-peak 5a. 3.5. Frequency factors The frequency factors are evaluated from the condition for the maximum of ®rst order kinetics [27]. As it is expected these values are extremely high. The values of frequency factors are in the region 1030 ±1040 sÿ1 . 4. Discussion The occurrence of very high E and s values was mainly a characteristic of the main glow-peak 5 of LiF:Mg,Ti and the main glow-peak 4 of
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LiF:Mg,Cu,P. The various models proposed for the explanation of the high E and s values are summarised and extensively discussed by McKeever [9±11]. The current work presents the case of the glow-peak 5a, which has even higher E and s values. However, the results of the present work show that glow-peak 5a has a very close relation with the glow-peak 5. So, one can conclude that the mechanism responsible for the high E and s values is, in general, similar in both cases. First of all it is assumed that the high E values of glow-peaks 5 and 5a are not real values, but apparent ones (Eapp ) [10,21]. The responsible mechanism causes an arti®cial narrowing [21] of the experimentally received glow-peak, decreasing its FWHM. Therefore, due the inverse relation between E and FWHM the Eapp will be larger than the expected. Furthermore, due to the high Eapp an anomalously high value of the frequency factor is derived. The explanation that we intend to give for the high Eapp of both glow-peaks 5 and 5a, is that of McKeever [19] with minor modi®cations and an elementary formulation. From the numerous and extensive work on Mg precipitations in LiF:Mg,Ti during annealing and readout [9±11,29±31] (and references therein) we adopt that peak 5 appears to be a combination of (Mg2 ±V) pairs, which is used by McKeever for his model [19]. According to this model the TL of the glow-peak 5 is related to the trimer dissociation. The activation energy of peak 5 is the sum of the trimer binding energy (0.89 eV) and a term related to the release of charge from the dissociated dipoles. The simulation of the arti®cial narrowing of a glow-peak will be attempted using the simple energy band diagram shown in Fig. 15. E0 is the binding energy of an electron to the Mg2 ±V trimer and accounts for the normal (unknown) activation energy of the glow-peak 5. The activation energy E0 must be high enough, so that the corresponding trapping level is not in¯uenced in the temperature region where the trimer dissociates. This temperature region, according to McKeever [19], is the temperature where the experimental glow-peak 5 appears. If during the dissociation the Mg2 ±V dipoles are removed from the trimer, then the activation energy is reduced to E1 E0 ÿ DE
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Fig. 15. Energy band diagram used to derive Eq. (3).
and represents the new activation energy of the resulting dipole. This reduced activation energy corresponds to a ®lled shallow trapping level (E1 , s1 ). However, the temperature of the sample is high enough and the new situation is that of a shallow trapping level, which is suddenly found in a high temperature environment. This will cause the fast thermal release from the trapping level (E1 , s1 ). Therefore, the dissociation is followed by thermal release and recombination. Due to this sequence of processes the probability for thermal release becomes p pd p 0 sd exp
Ed ÿ kT
s0 exp
E0 ÿ DE ; ÿ kT
1
where sd , s0 and Ed , E0 are the frequency factors and activation energies of the dissociation process and of the (unknown) glow-peak 5, respectively. Theoretical ®rst order kinetic glow-peaks corresponding to the dissociation process (sd , Ed ) and to the resulting trapping level, (E1 , s1 ) were evaluated using a heating rate of 2 K/s (equal to the experimental one). The parameters used were: the value of the dissociation energy of trimers, Ed was taken equal to 0.89 eV [11]. The value of sd was chosen equal to 3 108 sÿ1 , so that the maximum of the dissociation process occurs at about 473 K (200°C) [19]. For the sake of simplicity, the dissociation process was arbitrarily considered to be a ®rst order like process in order to evaluate and to show the temperature region where it takes place. The value of E1 was taken to be 1.2 eV whereas for s1 values between 1013 ±6 ´ 1013 sÿ1 were tested. The simulated glow-peaks are shown in Fig. 16. It is
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Fig. 16. Simulation of the glow-peak 5: curve (a) glow-peak corresponding to the trapping level (E1 , s1 ) resulting from the dissociation of trimers; curve (b) a glow-peak showing the temperature region where the dissociation process of trimers take place; curve (c) the glow-peak with activation energy E0 ; and curve (d) the glow-peak with activation energy E Ed E0 ÿ DE corresponding to the experimentally observed glow-peak 5.
observed that the trapping level (E1 , s1 ) resulting from the dissociated dipoles, corresponds to a glow-peak, curve (a) of Fig. 16, which under normal conditions would appear between 415 K and 435 K (for the region of s1 used), i.e. at temperatures lower than the temperatures where the trimers dissociate, shown by the dashed curve (b) of Fig. 16. However, the dipoles come from the dissociation of trimers, so the glow-peak with trapping parameters (E1 , s1 ) must appear at least in the temperature region where the trimers dissociate depending upon the time between trimer dissociation and thermal release from the dissociated dipole. If this time is negligible then the thermal release from the trapping level (E1 , s1 ) must coincide with the dissociation process. At these high temperatures and for the heating rate used (2 K/s) the term p1 s1 exp E1 =kT becomes extremely high, whereas the R T state function F E1 ; s1 ; b; T exp ÿs1 =b T0 exp ÿE1 =kT dT tends to zero. This, from the kinetic point of view, means that the glow-peak with trapping parameters (E1 , s1 ) has, at these high temperatures, very low eciency. However, the eciency of the glowpeak (E1 , s1 ) becomes high at these temperatures,
when a time delay between the dissociation process and the thermal release exists, because this time delay reduces the value of p1 and increases the value of F E1 ; s1 ; b; T . A possible origin of the time delay between dissociation and thermal release is the time needed by the dissociation products i.e. Mg±V dipoles to have an appreciable separation before thermal release takes place. This is a dicult approach because one has to know the mobilities of the Mg±V dipoles in LiF matrix as a function of temperature. In the following a physical procedure will be described, which reduces the value of p1 and increases the value of F E1 ; s1 ; b; T . The result will be an increased eciency of the trapping level (E1 , s1 ) at the temperatures where the trimer dissociation takes place. The physical procedure is based on the fact that as the heating rate increases a glow-peak is shifted to higher temperatures. For example, the new trapping level (E1 ,s1 ) for a heating rate of say 20 K/s is shifted to about 470 K, i.e. at temperatures where the dissociation of the trimers take place. However, one must keep in mind that the heating rate used is 2 K/s. The question is how a higher heating rate emerges. This can be understood by looking carefully at the situation arising after the trimer dissociation. The situation is that of the trapping level with (E1 , s1 ) and peak maximum at 425 K, which is abruptly found at temperatures much higher than its peak maximum temperature. It is equivalent to saying that as far as this trapping level is concerned, the sample is heated not with the normal heating rate of 2 K/s, but with a hypothetical one (say beff ), which depends on the dierence between the real temperature of the sample and the temperature of the peak maximum with the heating rate of 2 K/s. i.e beff increases as the temperature increases. The time s spent at each temperature interval DT is DT/ b. For the normal readout and the dissociation process s is DT/2. However, for the thermal release from the trapping level (E1 , s1 ) is DT/beff (T). Since the beff is greater than b the time spent by (E1 , s1 ) at each temperature interval is reduced as the temperature increases. This causes a shift of the thermal release from (E1 , s1 ) to higher temperatures. Therefore, the term p0 is aected by the quantity s DT/beff (T). Due to this eect, Eq. (1) becomes
G. Kitis, T. Otto / Nucl. Instr. and Meth. in Phys. Res. B 160 (2000) 262±273
Ed DT s0 p pd p0 sd exp ÿ kT beff T E0 ÿ DE : exp ÿ kT
2
Taking into account Eq. (2) the TL intensity will be given by Eapp sapp kT 2 I T sapp exp ÿ exp ÿ kT bEapp Eapp 2kT 1ÿ ; 3 exp ÿ kT Eapp where Eapp Edis E0 ÿ DE eV; sapp sd s0
DT ÿ1 s : beff
4 5
It must be noted that this equation is, in general, similar to the equations that have been proposed by Fairchild et al. [1] and Townsend et al. [18] in their models for the explanation of high E and s values in LiF:Mg,Ti. The above model can predict the experimentally observed glow-peak 5 when the following requirements are ful®lled. 1. According to McKeever [19] the dissociation of the trimer takes place in the temperature range where the experimental glow-peak 5 appears. 2. The real glow-peak 5 must have such values of E0 and s0 , that the probability for thermal release in the temperature range of the trimer dissociation is negligible. A glow-peak was simulated using Eq. (3) according to the above requirements. The result is shown in Fig. 16. The value of E0 was taken equal to 1.5 eV and the value of s0 5.8 ´ 1013 sÿ1 (which is the lattice vibration frequency of LiF [32]). The values of E0 and s0 give the glow-peak (c) of Fig. 16. The value of DE was taken equal to 0.3 eV. So, the expected E value of the simulated experimental glow-peak must be equal to 2.09 eV. The beff (T) was evaluated using two relations: (a) beff T 0:5 and (b) beff 1 T ÿ 300=12. The temperature interval DT was taken equal to 1 K. The simulated glow-peak, using beff T 0:5 , is the curve (d) (open circles) of Fig. 16, which accounts for the experi-
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mental glow-peak 5. The simulated glow-peak was ®tted with the ®rst kinetic order algorithm [24]. The ®tted glow-peak is represented by the solid line of curve (d) of Fig. 16. The FOM value of the ®t was 1.5 ´ 10ÿ4 , the activation energy 2.07 eV and the frequency factor 4.76 ´ 1020 sÿ1 . The stimulation with beff 1 T ÿ 300=12 gave E 2.0 eV and s 9 ´ 1019 sÿ1 . Practically, the arti®cial narrowing of the experimental glow-peak is done as follows. The probability of thermal release from E0 is negligible in the temperature region of trimer dissociation. The trimer dissociation reduces the activation energy E0 to E1 . The result is the creation of a shallow trap in a high temperature environment. It is obvious that the thermal release and recombination will take place in time much faster than that expected for a trap with E0 . Obviously, the faster the dissociation the faster the thermal release and recombination sequence and, therefore, the larger the arti®cial narrowing. One can refer to this arti®cial narrowing process as a dissociation stimulated TL (DSTL). For the explanation of the even higher values of the glow-peak 5a we will stay with the interesting observation of McKeever [19], that peak 5 appears exactly in the range where both trimer dissociation and precipitate dissolution are taking place. Observing Figs. 9 and 10 we can see that the Tmax of both peaks diers only by approximately 10±15°C. However, as the low-temperature pre-(and post-) irradiation annealing time increases, the Tmax of glow-peak 5 is reduced whereas the Tmax of glowpeak 5a is increased. This means that Tmax of glowpeak 5 goes to temperatures where the dissociation becomes weaker and the Tmax of glow-peak 5a goes to temperatures where the dissociation or precipitation dissolution becomes faster. This can explain the behaviour of the activation energy shown in Figs. 11±14. When the Tmax of glow-peak 5 goes to lower temperature the dissociation is weaker so the arti®cial narrowing is also weak and the Eapp of glow-peak 5 is decreased. When the Tmax of the glow-peak 5a shifts to higher temperatures, where the dissociation and the precipitation dissolution becomes very fast, the arti®cial narrowing is substantially increased and the Eapp of glow-peak 5a takes enormously high values.
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The amount of precipitates formed during the readout is restricted [33]. This is the reason why the glow-peak 5a is sometimes observed and sometimes not [2]. On the other hand, the lowtemperature pre-irradiation annealing can cause a substantial amount of precipitation. The precipitated Mg2 ±V is known [19,30,31] not to contribute to the TL. However, under the circumstances described above the dissolved precipitates can lead to the TL emission. An interesting observation of the present work is that the appearance and the properties of the glow-peak 5a are the same for both pre- and postirradiation annealing between 140°C and 160°C. This means that if the TL of the peak 5a is due to the dissolution of precipitates, then the precipitation formation is equally ecient in the following two cases. (i) from Mg2 ±V dipoles which has not captured an electron (pre-irradiation annealing and (ii) from Mg2 ±V dipoles which had captured an electron (post-irradiation annealing). The temperature region of the precipitation formation is 140±160°C. In this temperature region the Mg2 ±V trimers are dissociated. This is followed by a serious reduction of the TL intensity of glow-peak 5 [7,33]. Part of the trimer dissociation products are Mg2 ±V dimers, which contribute to the defect structure responsible for the glow-peak 2 [11,19] whose TL intensity is highly increased [7]. Another part of them contribute to the formation of tetramers, pentamers i.e. precipitates. However, the Mg2 ±V dipoles are held together by coulombic forces, which are fairly modi®ed during electron capture [11]. So, the question is how a trimer which has captured an electron is held together with a dipole in the same way as a trimer that has not captured an electron. LiF is among the strongest insulators. Its energy gap is 13.6 eV [34]. So, deep traps of the order of 2 or 3 eV and more are possible. The dissociation stimulated TL mechanism can also explain a direct thermal release of electrons from such deep traps under some special conditions such as: (i) when modi®cations are induced to the defect structure responsible for the deep trap in the intermediate temperature region and (ii) when the time needed for the modi®cations to take place is relatively low.
5. Conclusions · The glow-peak 5a of LiF:Mg,Ti is an individual one and dierent from the neighbouring glowpeaks 5, 6 and 7. · The glow-peak 5a appears in all forms of LiF:Mg,Ti (TLD-100, TLD-600 and TLD-700). · The glow-peak 5a, is also induced by neutron and muon irradiation [6]. · This glow-peak is isolated under special thermal treatments between 140°C and 160°C. · The isolated glow-peak 5a has the same characteristics irrespective of the thermal treatment between 140°C and 160°C done prior to irradiation or after the irradiation. · The activation energy E of glow-peak 5a was found to vary between 3 and 3.8 eV. · The above values of activation energy are among the highest known. · Due to the high E values, the frequency factors were found to be extremely high, i.e. of the order of 1030 ±1040 sÿ1 . · The high values of activation energy were explained with a model based on the fact that the defect responsible for the trapping level of this glow-peak, dissociates in the temperature region where the glow-peak appears. The dissociation lowers the trap depth of the trapping level, thus prompting the thermal release of trapped electron in a time faster than that predicted by its original trap depth. Acknowledgements G.K. acknowledges the hospitality of M. Hoefert, group leader of the CERNÕs radiation protection group. The technical help and co-operation of G. Roubaud, J. Wolf are gratefully acknowledged. Prof. S. Ves and Dr. N. Tsirliganis are also acknowledged for their useful suggestions. References [1] R.G. Fairchild, P.L. Mattern, K. Longweiler, P.W. Levy, J. Appl. Phys. 49 (1978) 4523. [2] A.J.J. Bos, T.M. Piters, W. De Vries, J.E. Hoogenboom, Radiat. Prot. Dosim. 33 (1990) 7.
G. Kitis, T. Otto / Nucl. Instr. and Meth. in Phys. Res. B 160 (2000) 262±273 [3] D.W. Zimmerman, G.R. Rhyner, J.R. Cameron, Health Phys. 12 (1996) 525. [4] T.L. Johnson, in: Fourth International Conference on Luminescence Dosimetry, Krakow, Poland, 1974, p. 197. [5] A.R. Blak, S. Watanabe, in: Fourth Internal Conference on Luminescence Dosimetry, Krakow, Poland, 1974, p. 169. [6] G. Kitis, S. Charalambous, J.W.N. Tuyn, Radiat. Prot. Dosim. 40 (1992) 117. [7] G. Kitis, C. Furetta, Nucl. Instr. and Meth. B 94 (1994) 441. [8] G. Kitis, C. Charitidis, C. Furetta, Nucl. Sci. J. 31 (1994) 465. [9] S.W.S. McKeever, Thermoluminescence in Solids, Cambridge University Press, Cambridge, 1985, p. 111. [10] S.W.S. McKeever, M. Moscovitch, P.D. Townsend, Thermoluminescence Dosimetry Materials: Properties and Uses, Nuclear Technology Publishing, 1995, p. 52. [11] R. Chen, S.W.S. McKeever, Theory of Thermoluminescence and Related Phenomena, World Scienti®c, Singapore, 1997, p. 465. [12] S. Mahajna, D. Yossian, Y.S. Horowitz, A. Horowitz, Radiat. Prot. Dosim. 47 (1993) 73. [13] D. Yossian, Y.S. Horowitz, J. Phys. D 28 (1995) 1495. [14] G. Kitis, A. Tzima, G.G. Cai, C. Furetta, J. Phys. D 29 (1996) 1601. [15] N.F. Mott, R.W. Gurney, Electronic Processes in Ionic Crystals, Oxford University Press, Oxford, 1948. [16] M. Bohm, O. Erb, A. Scharmann, Appl. Phys. A 37 (1985) 165.
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[17] M. Bohm, A. Scharmann, Appl. Phys. A 43 (1987) 29. [18] P.D. Townsend, G.C. Taylor, M.C. Wintersgill, Radiat. Eects 41 (1979) 11. [19] S.W.S. McKeever, Radiat. Prot. Dosim. 6 (1984) 49. [20] T.M. Piters, A.J.J. Bos, J. Phys. D 26 (1993) 2255. [21] R. Chen, A. Hag-Yahya, Radiat. Meas. 27 (1997) 205. [22] F. James, MINUIT, CERN program library entry D506 http://consult.cern.ch/writeups/minuit. [23] H.G. Balian, N.W. Eddy, Nucl. Instr. and Meth. 145 (1997) 389. [24] G. Kitis, J.M. Gomez-Ros, J.W.N. Tuyn, J. Phys. D 31 (1998) 2636. [25] P. Spanne, C.A. Carlson, in: V. Mejdahl (Ed.), Third International Conference on Luminescence Dosimetry, Riso, Denmark, 1971, p. 48. [26] G. Kitis, J.W.N. Tuyn, Nucl. Instr. and Meth. B 132 (1997) 639. [27] R. Chen, Y. Kirsh, Analysis of Thermally Stimulated Processes, Pergamon Press, Oxford, 1981. [28] W. Pohlit, Biophysik 5 (1969) 341. [29] A.J.L. Bos, R.N.M. Vijverberg, T.M. Piters, S.W.S. McKeever, J. Phys. D 25 (1992) 1249. [30] G.C. Taylor, E. Lilley, J. Phys. D 15 (1982) 1243. [31] G.C. Taylor, E. Lilley, J. Phys. D 15 (1982) 1253. [32] C. Kittel, Introduction to Solid State Physics, Wiley, 1976, p. 309. [33] G. Kitis, J.W.N. Tuyn, Nucl. Instr. and Meth. B 132 (1997) 639. [34] W.A. Harrison, Electronic Structure and Properties of Solids, Freeman, New York, p. 321.
www.elsevier.nl/locate/nimb
Peculiarities of the glow-peak 5a of LiF:Mg,Ti G. Kitis a
a,b,*
, T. Otto
b
Aristotle University of Thessaloniki, Nuclear Physics Laboratory, GR-540 06, Thessaloniki, Greece b CERN, CH 1211, Geneva 23, Switzerland Received 8 June 1999; received in revised form 23 July 1999
Abstract The glow-peak 5a of LiF:Mg,Ti is a glow-peak, with peak maximum temperature between those of glow-peaks 5 and 6. This glow-peak is not seen in the usual glow-curve, resulting after normal annealing at 400°C for 1 h and at 100°C for 2 h. However, its existence is con®rmed ®rst experimentally and then as the necessity to achieve a very good glow-curve ®tting. In the present work it is found that the glow-peak 5a can be very well isolated from its neighbouring glow-peaks, after special thermal treatment between 140°C and 160°C. The isolation permits the study of its individual behaviour, which was found to have the following peculiarities. (i) This glow-peak is clearly seen only after thermal treatment between 140°C and 160°C. (ii) It appears with the same properties after both pre-irradiation and post-irradiation annealing in the above temperature region. (iii) Its activation energy was found to be above 3 eV and its frequency factor above 1030 sÿ1 . These values are extremely high and outside the physically accepted limits. Ó 2000 Elsevier Science B.V. All rights reserved. PACS: 78.60.Kn; 78.60.ÿb; 29.40.Wk Keywords: Thermoluminescence; Activation energy; Annealing; LiF:Mg,Ti
1. Introduction The existence of the glow-peak 5a with peak maximum temperature (Tmax ) between the main glow-peak 5 and glow-peak 6, was originally introduced by Fairchild et al. [1], as a requirement to obtain a good ®t to the experimental glow-curve of
* Corresponding author. Tel.: +30-31-99-8175; fax: +30-3199-8175. E-mail address: [email protected], [email protected] (G. Kitis).
LiF:Mg,Ti. Later, Bos et al. [2] found that the above requirement appears only for some batches of LiF (TLD) but not for others. Concerning early experimental evidences, in our opinion, the glowpeak called 6 by Zimmerman et al. [3], Johnson [4] and Blak and Watanabe [5], is the glow-peak 5a. Kitis et al. [6] observed glow-peak 5a, as an isolated one in TLD-700, after muon irradiation at the elevated temperature of 125°C. Kitis and Furetta [7] had found in LiF:Mg,Ti (DTG-4) that glow-peak 5a can be isolated after special lowtemperature pre-irradiation annealing between 140°C and 160°C.
0168-583X/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 0 5 8 9 - 3
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In the same material (DTG-4) Kitis et al. [8] had estimated that the activation energy of the glow-peak 5a must be greater than 3 eV. This value is even higher than that of the main glowpeak 5 of LiF:Mg,Ti, whose activation energy has been found to be (2:0 E 2:3 eV) and frequency factor (1019 s 1023 sÿ1 ) [9±13]. The main dosimetric glow-peak of the other hypersensitive LiF based dosemeter, LiF:Mg,Cu,P has even higher values of E and s ( 2:5 eV and 1025 sÿ1 , respectively) [14]. The above values of the trapping parameters are considered as extremely high and outside of the physically accepted region of 107 ±1013 sÿ1 , given by Mott and Gurney [15], whereas Bohm and Sharmann [16,17] had proposed as an upper limit for s, the value of 3 1015 sÿ1 at 300 K. For the explanation of the high values of trapping parameters various models have been proposed [1,18±21], which are extensively discussed in a series of books [9±11]. The objective of this work is: (a) to establish the appropriate conditions under which the glow-peak 5a appears completely isolated and without any doubts of confusion with the glow-peak 6, (b) to estimate its trapping parameters and (c) to give an explanation based on minor modi®cations of the existing models. 2. Experimental procedure and analysis LiF:Mg,Ti(TLD-700) chips were used in the present work. The chips were annealed, before their use, in a furnace at 400°C for 1 h and were rapidly cooled to room temperature. The measurements were performed with the Harshaw model 3500 manual TLD reader, with a heating rate of 2°C/s and continuous nitrogen ¯ow. The irradiations were performed in the Studsvik irradiator with a 90 Sr±90 Y beta ray source delivering 1.1 mGy per exposure. The test dose used was 11 mGy. According to the objectives of the present work the following measurements were performed. 1. Low-temperature pre-irradiation annealing between 140°C and 160°C for 1 h. 2. Pre-irradiation annealing at 150°C for times 10 min up to 12 h.
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3. Post-irradiation annealing at 150°C for times 10 min up to 4 h. In another series of test measurements it was examined if this glow-peak appears in: (i) TLD-100 and TLD-600, (ii) in other two batches of LiF:Mg,Ti and (iii) under neutron irradiation. 3. Experimental results 3.1. Glow-curve analysis All the experimental glow-curves obtained in the present work were analysed by glow-curve deconvolution (GCD) using the MINUIT program [22]. The goodness of ®t was tested by the ®gure of merit (FOM) of Balian and Eddy [23]. It was assumed that the glow-peaks follow ®rst order kinetics, except in a few cases. So, for the GCD analysis the ®rst and the general kinetics order algorithms proposed by Kitis et al. were used [24]. The FOM values obtained from the GCD analysis of all glow-curves obtained from the preirradiation annealing, were between 0.87% and 1.1%, which are satisfactory. In the case of the post-irradiation annealing, the ®rst order kinetic algorithm fails to ®t the region of glow-peak 5, and the FOM values obtained from GCD were above 4%. The FOM values were reduced to between 1% and 3% when one more glow-peak with Tmax very close to that of the main 5 was introduced. This behaviour is similar to that described by Yossian and Horowitz [13]. Following these authors, in the case of post-irradiation annealing, the glow-peak 5 was ®tted with a general order algorithm, whereas for the remaining glow-curve the ®rst order kinetic was used again. The FOM values obtained in this case were between 1% and 2%, which must be considered satisfactory. Fig. 1 shows an analysed glow-curve obtained after annealing at 400°C for 1 h and fast cooling to room temperature. Here, the glow-peak 5a appears as a weak peak necessary to improve the FOM values. The high temperature glow-peaks 6 and 7 appear at 525 K and 550 K, respectively. Fig. 2 shows an analysed glow-curve obtained after pre-irradiation annealing at 152°C for 2 h. The known [3,7,8] strong glow-curve modi®cations
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Fig. 1. Glow-curve of LiF:Mg,Ti after annealing at 400°C for 1 h followed by fast cooling.
Fig. 3. Glow-curve of LiF:Mg,Ti after post-irradiation annealing at 152°C for 30 min.
for the TL intensity). The high temperature glowpeaks 6 and 7 appear at 525 K and 550 K, respectively (as in the case of Fig. 1). Fig. 4 shows the glow-curve after post-irradiation annealing at 152°C for 4 h. In this case the glow-peak 5a is almost isolated. The glow-peak 7 appears again at 550 K, whereas glow-peak 6 appears at approximately the same temperature as the glow-peak 5a. From the ®gures above it becomes apparent that it is necessary to make the appropriate dis-
Fig. 2. Glow-curve of LiF:Mg,Ti after low-temperature preirradiation annealing at 152°C for 2 h.
have appeared. The glow-peak 5a becomes very clear. The glow-peak 7 appears again at 550 K, whereas glow-peak 6 appears at the same temperature as the glow-peak 5a. Fig. 3 shows the glow-curve after post-irradiation annealing at 152°C for 30 min. As was stated above, the glow-peak 5 was ®tted with a general kinetic order algorithm. The glow-peak 5a appears as a shoulder at the high temperature part of the main peak 5 (this shoulder becomes very clear if one draws the glow-curve using a logarithmic axis
Fig. 4. Glow-curve of LiF:Mg,Ti after post-irradiation annealing at 152°C for 4 h.
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crimination between glow-peaks 5a and 6. In the next subsection it will be shown that the glow-peak 5a is a new glow-peak, which must not be confused with glow-peak 6. 3.2. Glow-peak 5a through the glow-curves In the normal glow-curve of LiF:Mg,Ti, shown in Fig. 1, the glow-peak 5a is a weak peak necessary to improve the ®tting. In the following, the evolution of the glow-peak 5a will be shown from a weak shoulder to a discrete glow-peak. Fig. 5 shows the glow-curves obtained after low-temperature pre-irradiation annealing between 143°C and 160°C for 1 h (see ®gure caption). The evolution of the glow-peak 5a from a shoulder in the glow-peak 5 at 143°C (curve a) to a discrete glow-peak at higher temperatures (curves b±f) becomes very clear. On the other hand the dierence of glow-peak 5a from the system of the glowpeaks 6 and 7 becomes also clear. Fig. 6 shows the glow-curves obtained after low-temperature pre-irradiation annealing at 152°C for various times, as it is shown in the ®gure caption. Glow-peak 5a appears clearly as a shoulder of the main glow-peak 5 for an annealing time of 30 min. At higher annealing times it is completely discriminated from the glow-peak 5.
Fig. 5. Glow-curves of LiF:Mg,Ti after low-temperature preirradiation annealing for 1 h at (a) 143°C, (b) 146°C, (c) 148°C, (d) 152°C, (e) 155°C and (f) 160°C.
Fig. 6. Glow-curve of LiF:Mg,Ti after low temperature preirradiation annealing at 152°C for times (a) 300 min, (b) 60 min, (c) 100 min, (d) 2 h, (e) 4 h and (f) 12 h.
Moreover, one can see that it is dierent from the system of glow-peaks 6 and 7. Fig. 7 shows the glow-curves obtained after post-irradiation annealing at 152°C for various times shown in the ®gure caption. In this ®gure glow-peak 5 is also included. As in the previous cases the dierence between glow-peak 5a and the system of glow-peaks 6 and 7 is clear. The net conclusion from the above listed ®gures is that under the conditions studied, the glow-peak 5a is a discrete glow-peak, which exists also in the
Fig. 7. Glow-curve of LiF:Mg,Ti after post-irradiation annealing at 152°C for times (a) 30 min, (b) 40 min, (c) 1 h, (d) 2 h and (e) 4 h.
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normal (after 400°C/1 h annealing) glow-curve of LiF:Mg,Ti. The results of the test measurements with TLD100, TLD-600, and with the other two batches of LiF:Mg,Ti, show that the glow-peak 5a appears in all cases. A slight dierence from batch to batch was found. This glow-peak was observed after muon irradiation [6]. In the present work it was found that the glow-peak 5a appears also under thermal neutron irradiation. 3.3. Behaviour of peak maximum position, Tmax The low-temperature pre-irradiation annealing in the region of 140±160°C induces strong modi®cations in the glow-curve structure of LiF:Mg,Ti [6,7,25,26] and of the LiF:Mg,Cu,P [8]. These modi®cations were also observed in the present work. However, results presented in [7,8,14,26] are not repeated here except for a few cases and only when they have a very close relation to the glowpeak 5a, which is the main subject of this work. The Tmax of glow-peaks 2, 3, 6 and 7 are not in¯uenced at all for all conditions studied. On the other hand the Tmax of the glow-peak 4, 5 and 5a is in¯uenced. Fig. 8 shows how the Tmax of the glowpeak 5a is shifted towards higher temperatures as the low-temperature pre-irradiation annealing for 1 h, is increased from 140°C to 160°C. On the
Fig. 8. Glow-peak maximum Tmax of the glow-peak 5a after low temperature pre-irradiation annealing between 143°C and 160°C for 1 h.
other hand in this short temperature region the Tmax of glow-peaks 4 and 5 is not altered. Fig. 9 shows the Tmax of glow-peaks 4, 5 and 5a, as a function of low-temperature pre-irradiation annealing at 152°C for various times. It is interesting to observe that the Tmax of the glow-peaks 4 and 5 is shifted towards lower temperatures in a similar way, both qualitatively and quantitatively. Whereas the Tmax of the glow-peak 5a is shifted towards higher temperatures. Fig. 10 shows the Tmax of the glow-peaks 5 and 5a as a function of post-irradiation annealing time at 152°C (glow-peak 4 is drained). It is interesting to note that the behaviour is similar to that of Fig. 9. The conclusions from the above listed results are that the thermal treatment between 140°C and 160°C aects only the Tmax of glow-peaks 4, 5 and 5a. A very interesting conclusion is that the Tmax for the glow-peaks 5 and 5a behaves in exactly the same way irrespective if the annealing is performed prior to irradiation or after the irradiation (see Figs. 9 and 10). 3.4. Activation energy Before the presentation of the GCD analysis results, concerning the value of the activation energy of the glow-peak 5a, we will show that a
Fig. 9. Glow-peak maximum Tmax as a function of time of the low temperature pre-irradiation annealing at 152°C: (a) glowpeak 5, (b) glow-peak 4 and (c) glow-peak 5a (left axis).
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Fig. 10. Glow-peak maximum Tmax of glow-peaks 5 and 5a, as a function of the post-irradiation annealing time at 152°C.
preliminary information can be extracted by a simple observation of the temperature interval covered by this glow-peak. We can use Figs. 2 and 4 as examples. From these ®gures one can see that the full width at half maximum (FWHM) of the glow-peak 5a is less than 20°C. This is the highest possible value of FWHM, because it does not include any corrections from the obvious interferences from the neighbouring glow-peaks. For a Tmax 525 K, any peak shape method [27] provides for the lower limit of the activation energy of the glow-peak 5a a value of 3 eV. The activation energy values obtained by the GCD analysis are as follows. Fig. 11 gives the values of the activation energies of the glow-peak 5a as a function of the low-temperature pre-irradiation annealing for 1 h between 143°C and 160°C. The activation energy increases as the pre-irradiation temperature increases arriving at a value of about 3.8 eV. The activation energies of the glow-peaks 4 and 5 vary within the experimental errors, in this temperature interval and for the 1 h annealing time. Fig. 12 gives the values of the activation energies as a function of the low-temperature preirradiation annealing time at 152°C, of the glow-peaks 5 (a) and glow-peak 4 (b). The activation energy of the glow-peak 5 is strongly reduced as the duration of the annealing time at 152°C increases.
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Fig. 11. Activation energy E of the glow-peak 5a as a function of the low-temperature pre-irradiation annealing between 143°C and 160°C, for 1 h.
Fig. 12. Activation energy as a function of the low temperature pre-irradiation annealing time at 152°C: (a) glow-peaks 5 and (b) glow-peak 4.
Fig. 13 gives three sets of values of the activation energies of the glow-peak 5a as a function of the pre-irradiation annealing time at 152°C. Each set of values corresponds to dierent constraints of the deconvolution analysis. The constraints concern the position and the intensity of the glowpeak 6 only. The position and the intensity of the glow-peak 7 had an appreciable repeatability for all cases studied. Its peak position is at 550 2.5 K whereas its intensity varies within 15% (the
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Fig. 13. Activation energy of glow-peak 5a as a function of the low temperature pre-irradiation annealing time at 152°C. Curves (a), (b) and (c) correspond to various constraints of the deconvolution analysis, see text.
statistics of the glow-curve at the high temperatures glow-peaks is low). In the normal glow-curve of LiF shown in Fig. 1, the intensity of the glow-peak 6 is lower than the intensity of the glow-peak 7 and its peak position is around 525 K. In the set of values (a) of Fig. 13 the intensity of the peak 6 was not allowed to become higher than the intensity of the peak 7 and its peak position was left to vary between 517 K and 525 K. Under these constraints its integral was stable within 15% and the average peak position was 519 2 K. In the set of values (b) of Fig. 13, the intensity of the peak 6 was not allowed to become higher than the intensity of the peak 7 and its peak position was left to vary between 525 K and 535 K. Under these constraints its integral was stable within 15% and the average peak position was 530 2 K. In the set of values (c) of Fig. 13, the intensity of the peak 6 was allowed to vary freely and its peak position was left to vary between 517 K and 535 K. Under these constraints the average peak position was at 520 2.5 K, whereas its integral for annealing times greater than 1 h, was increased by a factor of three relative to the integral for lower annealing times. The FOM values in all set of deconvolution were between 0.87% and 1.1%.
Fig. 14. Activation energy of glow-peak 5a as a function of the post-irradiation annealing time at 152°C.
However, it must be noticed that for the set (c) the FOM values were somewhat better. Fig. 14 gives the activation energies of the glow-peak 5a as a function of the post-irradiation annealing time at 152°C. As was stated above, in the post-irradiation annealing glow-curves, the glow-peak 5 was ®tted by a second order kinetic algorithm. The activation energy found for the glow-peak 5 was 2.5 0.1 eV. No systematic behaviour of the kinetic order was found. Finally, it must be noticed that an activation energy value of 3.62 eV i.e. similar to those presented above was that of Pohlit [28] for the glow-peak 5 of the Harshaw LiF. It is reasonable to think that the glow-peak studied by Pohlit was, possibly, the glow-peak 5a. 3.5. Frequency factors The frequency factors are evaluated from the condition for the maximum of ®rst order kinetics [27]. As it is expected these values are extremely high. The values of frequency factors are in the region 1030 ±1040 sÿ1 . 4. Discussion The occurrence of very high E and s values was mainly a characteristic of the main glow-peak 5 of LiF:Mg,Ti and the main glow-peak 4 of
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LiF:Mg,Cu,P. The various models proposed for the explanation of the high E and s values are summarised and extensively discussed by McKeever [9±11]. The current work presents the case of the glow-peak 5a, which has even higher E and s values. However, the results of the present work show that glow-peak 5a has a very close relation with the glow-peak 5. So, one can conclude that the mechanism responsible for the high E and s values is, in general, similar in both cases. First of all it is assumed that the high E values of glow-peaks 5 and 5a are not real values, but apparent ones (Eapp ) [10,21]. The responsible mechanism causes an arti®cial narrowing [21] of the experimentally received glow-peak, decreasing its FWHM. Therefore, due the inverse relation between E and FWHM the Eapp will be larger than the expected. Furthermore, due to the high Eapp an anomalously high value of the frequency factor is derived. The explanation that we intend to give for the high Eapp of both glow-peaks 5 and 5a, is that of McKeever [19] with minor modi®cations and an elementary formulation. From the numerous and extensive work on Mg precipitations in LiF:Mg,Ti during annealing and readout [9±11,29±31] (and references therein) we adopt that peak 5 appears to be a combination of (Mg2 ±V) pairs, which is used by McKeever for his model [19]. According to this model the TL of the glow-peak 5 is related to the trimer dissociation. The activation energy of peak 5 is the sum of the trimer binding energy (0.89 eV) and a term related to the release of charge from the dissociated dipoles. The simulation of the arti®cial narrowing of a glow-peak will be attempted using the simple energy band diagram shown in Fig. 15. E0 is the binding energy of an electron to the Mg2 ±V trimer and accounts for the normal (unknown) activation energy of the glow-peak 5. The activation energy E0 must be high enough, so that the corresponding trapping level is not in¯uenced in the temperature region where the trimer dissociates. This temperature region, according to McKeever [19], is the temperature where the experimental glow-peak 5 appears. If during the dissociation the Mg2 ±V dipoles are removed from the trimer, then the activation energy is reduced to E1 E0 ÿ DE
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Fig. 15. Energy band diagram used to derive Eq. (3).
and represents the new activation energy of the resulting dipole. This reduced activation energy corresponds to a ®lled shallow trapping level (E1 , s1 ). However, the temperature of the sample is high enough and the new situation is that of a shallow trapping level, which is suddenly found in a high temperature environment. This will cause the fast thermal release from the trapping level (E1 , s1 ). Therefore, the dissociation is followed by thermal release and recombination. Due to this sequence of processes the probability for thermal release becomes p pd p 0 sd exp
Ed ÿ kT
s0 exp
E0 ÿ DE ; ÿ kT
1
where sd , s0 and Ed , E0 are the frequency factors and activation energies of the dissociation process and of the (unknown) glow-peak 5, respectively. Theoretical ®rst order kinetic glow-peaks corresponding to the dissociation process (sd , Ed ) and to the resulting trapping level, (E1 , s1 ) were evaluated using a heating rate of 2 K/s (equal to the experimental one). The parameters used were: the value of the dissociation energy of trimers, Ed was taken equal to 0.89 eV [11]. The value of sd was chosen equal to 3 108 sÿ1 , so that the maximum of the dissociation process occurs at about 473 K (200°C) [19]. For the sake of simplicity, the dissociation process was arbitrarily considered to be a ®rst order like process in order to evaluate and to show the temperature region where it takes place. The value of E1 was taken to be 1.2 eV whereas for s1 values between 1013 ±6 ´ 1013 sÿ1 were tested. The simulated glow-peaks are shown in Fig. 16. It is
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Fig. 16. Simulation of the glow-peak 5: curve (a) glow-peak corresponding to the trapping level (E1 , s1 ) resulting from the dissociation of trimers; curve (b) a glow-peak showing the temperature region where the dissociation process of trimers take place; curve (c) the glow-peak with activation energy E0 ; and curve (d) the glow-peak with activation energy E Ed E0 ÿ DE corresponding to the experimentally observed glow-peak 5.
observed that the trapping level (E1 , s1 ) resulting from the dissociated dipoles, corresponds to a glow-peak, curve (a) of Fig. 16, which under normal conditions would appear between 415 K and 435 K (for the region of s1 used), i.e. at temperatures lower than the temperatures where the trimers dissociate, shown by the dashed curve (b) of Fig. 16. However, the dipoles come from the dissociation of trimers, so the glow-peak with trapping parameters (E1 , s1 ) must appear at least in the temperature region where the trimers dissociate depending upon the time between trimer dissociation and thermal release from the dissociated dipole. If this time is negligible then the thermal release from the trapping level (E1 , s1 ) must coincide with the dissociation process. At these high temperatures and for the heating rate used (2 K/s) the term p1 s1 exp E1 =kT becomes extremely high, whereas the R T state function F E1 ; s1 ; b; T exp ÿs1 =b T0 exp ÿE1 =kT dT tends to zero. This, from the kinetic point of view, means that the glow-peak with trapping parameters (E1 , s1 ) has, at these high temperatures, very low eciency. However, the eciency of the glowpeak (E1 , s1 ) becomes high at these temperatures,
when a time delay between the dissociation process and the thermal release exists, because this time delay reduces the value of p1 and increases the value of F E1 ; s1 ; b; T . A possible origin of the time delay between dissociation and thermal release is the time needed by the dissociation products i.e. Mg±V dipoles to have an appreciable separation before thermal release takes place. This is a dicult approach because one has to know the mobilities of the Mg±V dipoles in LiF matrix as a function of temperature. In the following a physical procedure will be described, which reduces the value of p1 and increases the value of F E1 ; s1 ; b; T . The result will be an increased eciency of the trapping level (E1 , s1 ) at the temperatures where the trimer dissociation takes place. The physical procedure is based on the fact that as the heating rate increases a glow-peak is shifted to higher temperatures. For example, the new trapping level (E1 ,s1 ) for a heating rate of say 20 K/s is shifted to about 470 K, i.e. at temperatures where the dissociation of the trimers take place. However, one must keep in mind that the heating rate used is 2 K/s. The question is how a higher heating rate emerges. This can be understood by looking carefully at the situation arising after the trimer dissociation. The situation is that of the trapping level with (E1 , s1 ) and peak maximum at 425 K, which is abruptly found at temperatures much higher than its peak maximum temperature. It is equivalent to saying that as far as this trapping level is concerned, the sample is heated not with the normal heating rate of 2 K/s, but with a hypothetical one (say beff ), which depends on the dierence between the real temperature of the sample and the temperature of the peak maximum with the heating rate of 2 K/s. i.e beff increases as the temperature increases. The time s spent at each temperature interval DT is DT/ b. For the normal readout and the dissociation process s is DT/2. However, for the thermal release from the trapping level (E1 , s1 ) is DT/beff (T). Since the beff is greater than b the time spent by (E1 , s1 ) at each temperature interval is reduced as the temperature increases. This causes a shift of the thermal release from (E1 , s1 ) to higher temperatures. Therefore, the term p0 is aected by the quantity s DT/beff (T). Due to this eect, Eq. (1) becomes
G. Kitis, T. Otto / Nucl. Instr. and Meth. in Phys. Res. B 160 (2000) 262±273
Ed DT s0 p pd p0 sd exp ÿ kT beff T E0 ÿ DE : exp ÿ kT
2
Taking into account Eq. (2) the TL intensity will be given by Eapp sapp kT 2 I T sapp exp ÿ exp ÿ kT bEapp Eapp 2kT 1ÿ ; 3 exp ÿ kT Eapp where Eapp Edis E0 ÿ DE eV; sapp sd s0
DT ÿ1 s : beff
4 5
It must be noted that this equation is, in general, similar to the equations that have been proposed by Fairchild et al. [1] and Townsend et al. [18] in their models for the explanation of high E and s values in LiF:Mg,Ti. The above model can predict the experimentally observed glow-peak 5 when the following requirements are ful®lled. 1. According to McKeever [19] the dissociation of the trimer takes place in the temperature range where the experimental glow-peak 5 appears. 2. The real glow-peak 5 must have such values of E0 and s0 , that the probability for thermal release in the temperature range of the trimer dissociation is negligible. A glow-peak was simulated using Eq. (3) according to the above requirements. The result is shown in Fig. 16. The value of E0 was taken equal to 1.5 eV and the value of s0 5.8 ´ 1013 sÿ1 (which is the lattice vibration frequency of LiF [32]). The values of E0 and s0 give the glow-peak (c) of Fig. 16. The value of DE was taken equal to 0.3 eV. So, the expected E value of the simulated experimental glow-peak must be equal to 2.09 eV. The beff (T) was evaluated using two relations: (a) beff T 0:5 and (b) beff 1 T ÿ 300=12. The temperature interval DT was taken equal to 1 K. The simulated glow-peak, using beff T 0:5 , is the curve (d) (open circles) of Fig. 16, which accounts for the experi-
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mental glow-peak 5. The simulated glow-peak was ®tted with the ®rst kinetic order algorithm [24]. The ®tted glow-peak is represented by the solid line of curve (d) of Fig. 16. The FOM value of the ®t was 1.5 ´ 10ÿ4 , the activation energy 2.07 eV and the frequency factor 4.76 ´ 1020 sÿ1 . The stimulation with beff 1 T ÿ 300=12 gave E 2.0 eV and s 9 ´ 1019 sÿ1 . Practically, the arti®cial narrowing of the experimental glow-peak is done as follows. The probability of thermal release from E0 is negligible in the temperature region of trimer dissociation. The trimer dissociation reduces the activation energy E0 to E1 . The result is the creation of a shallow trap in a high temperature environment. It is obvious that the thermal release and recombination will take place in time much faster than that expected for a trap with E0 . Obviously, the faster the dissociation the faster the thermal release and recombination sequence and, therefore, the larger the arti®cial narrowing. One can refer to this arti®cial narrowing process as a dissociation stimulated TL (DSTL). For the explanation of the even higher values of the glow-peak 5a we will stay with the interesting observation of McKeever [19], that peak 5 appears exactly in the range where both trimer dissociation and precipitate dissolution are taking place. Observing Figs. 9 and 10 we can see that the Tmax of both peaks diers only by approximately 10±15°C. However, as the low-temperature pre-(and post-) irradiation annealing time increases, the Tmax of glow-peak 5 is reduced whereas the Tmax of glowpeak 5a is increased. This means that Tmax of glowpeak 5 goes to temperatures where the dissociation becomes weaker and the Tmax of glow-peak 5a goes to temperatures where the dissociation or precipitation dissolution becomes faster. This can explain the behaviour of the activation energy shown in Figs. 11±14. When the Tmax of glow-peak 5 goes to lower temperature the dissociation is weaker so the arti®cial narrowing is also weak and the Eapp of glow-peak 5 is decreased. When the Tmax of the glow-peak 5a shifts to higher temperatures, where the dissociation and the precipitation dissolution becomes very fast, the arti®cial narrowing is substantially increased and the Eapp of glow-peak 5a takes enormously high values.
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The amount of precipitates formed during the readout is restricted [33]. This is the reason why the glow-peak 5a is sometimes observed and sometimes not [2]. On the other hand, the lowtemperature pre-irradiation annealing can cause a substantial amount of precipitation. The precipitated Mg2 ±V is known [19,30,31] not to contribute to the TL. However, under the circumstances described above the dissolved precipitates can lead to the TL emission. An interesting observation of the present work is that the appearance and the properties of the glow-peak 5a are the same for both pre- and postirradiation annealing between 140°C and 160°C. This means that if the TL of the peak 5a is due to the dissolution of precipitates, then the precipitation formation is equally ecient in the following two cases. (i) from Mg2 ±V dipoles which has not captured an electron (pre-irradiation annealing and (ii) from Mg2 ±V dipoles which had captured an electron (post-irradiation annealing). The temperature region of the precipitation formation is 140±160°C. In this temperature region the Mg2 ±V trimers are dissociated. This is followed by a serious reduction of the TL intensity of glow-peak 5 [7,33]. Part of the trimer dissociation products are Mg2 ±V dimers, which contribute to the defect structure responsible for the glow-peak 2 [11,19] whose TL intensity is highly increased [7]. Another part of them contribute to the formation of tetramers, pentamers i.e. precipitates. However, the Mg2 ±V dipoles are held together by coulombic forces, which are fairly modi®ed during electron capture [11]. So, the question is how a trimer which has captured an electron is held together with a dipole in the same way as a trimer that has not captured an electron. LiF is among the strongest insulators. Its energy gap is 13.6 eV [34]. So, deep traps of the order of 2 or 3 eV and more are possible. The dissociation stimulated TL mechanism can also explain a direct thermal release of electrons from such deep traps under some special conditions such as: (i) when modi®cations are induced to the defect structure responsible for the deep trap in the intermediate temperature region and (ii) when the time needed for the modi®cations to take place is relatively low.
5. Conclusions · The glow-peak 5a of LiF:Mg,Ti is an individual one and dierent from the neighbouring glowpeaks 5, 6 and 7. · The glow-peak 5a appears in all forms of LiF:Mg,Ti (TLD-100, TLD-600 and TLD-700). · The glow-peak 5a, is also induced by neutron and muon irradiation [6]. · This glow-peak is isolated under special thermal treatments between 140°C and 160°C. · The isolated glow-peak 5a has the same characteristics irrespective of the thermal treatment between 140°C and 160°C done prior to irradiation or after the irradiation. · The activation energy E of glow-peak 5a was found to vary between 3 and 3.8 eV. · The above values of activation energy are among the highest known. · Due to the high E values, the frequency factors were found to be extremely high, i.e. of the order of 1030 ±1040 sÿ1 . · The high values of activation energy were explained with a model based on the fact that the defect responsible for the trapping level of this glow-peak, dissociates in the temperature region where the glow-peak appears. The dissociation lowers the trap depth of the trapping level, thus prompting the thermal release of trapped electron in a time faster than that predicted by its original trap depth. Acknowledgements G.K. acknowledges the hospitality of M. Hoefert, group leader of the CERNÕs radiation protection group. The technical help and co-operation of G. Roubaud, J. Wolf are gratefully acknowledged. Prof. S. Ves and Dr. N. Tsirliganis are also acknowledged for their useful suggestions. References [1] R.G. Fairchild, P.L. Mattern, K. Longweiler, P.W. Levy, J. Appl. Phys. 49 (1978) 4523. [2] A.J.J. Bos, T.M. Piters, W. De Vries, J.E. Hoogenboom, Radiat. Prot. Dosim. 33 (1990) 7.
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