REVIEW OF METHODS FOR DETERMINING GLOW PEAK KINETICS PARAMETERS OF THERMOLUMINESCENCE DOSEMETERS

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1 REVIEW OF METHODS FOR DETERMINING GLOW PEAK KINETICS PARAMETERS OF THERMOLUMINESCENCE DOSEMETERS & M. Hajek AIAU 7605 August 007 UID ATU DVR TU Handelsgericht Wien Bankverbindung: Bank Austria-Creditanstalt AG Konto BLZ 1000 BIC BKAUATWW IBAN AT

2 Review of ethods for the deterination of the kinetic paraeters of theroluinescence dosieters Project thesis by Atoic Institute of the Austrian Universities Stadionallee, 100 Vienna, Austria Abstract. In the field of theroluinescence dosietry the daily analysis of ulti-peak glow curves includes coputerized curve-fitting ethods, the so-called deconvolutions. These are in need of restricting the kinetic paraeters E and s in order to obtain physically relevant results. There have been suggested various ethods for the deterination of these kinetic paraeters based on a theory treating single peaks. Therefore, the applicability of these ethods to non-single peaks is still vague. In this work the initial rise ethod, different peak shape ethods and the ethod of different heating rates are probed by eans of easureents with the dosieters TLD-600, TLD-700 and TLD Introduction A very short and easy to understand introduction to theroluinescence phenoena and their applications can be found in the work of F.O. Ogundare et al [1]: Theroluinescence phosphors generally exhibit glow curves with one or ore peaks when the charge carriers are released. The glow curve is characteristic of the different trap levels that lie in the band gap of the aterial. The traps are characterized by certain physical paraeters that include trap depth (E) and frequency factor (s). For any TL applications, a clear knowledge of these physical paraeters is essential. In the study of relatively deep trapping defect-states in various solid state aterials as well as TL dating, a detailed analysis of TL glow curves is indispensable. In order to obtain these physical paraeters, one needs to fit the glow curve data to a TL odel that best describes the TL intensity as a function of these paraeters. The widely used TL odels are first-order (Randall and Wilkins, 1945) [], second-order (Garlick and Gibson, 1948) [3] and the general-order (GO) (May and Partridge, 1964) [4] kinetics odels. A ore extensive and highly recoendable paper Theory of theroluinescence has been written by A.J.J. Bos [5]. Today s daily work in the field of study of theroluinescence phenoena and their applications to theroluinescence dosietry includes coputerized curve-fitting ethods, deconvolutions, of the ulti-peak structure of TL glow curves. These at first purely atheatical, analytical approaches iply the necessity of both estiating the nuber of peaks within the relevant regions of the glow curve and restricting the values of the trapping paraeters (naely, trap depth or activation energy E and frequency factor s). The forer, estiating the nuber of peaks, can be executed by the T -T stop -ethod presented in a work of S.W.S McKeever [6], the latter, an estiate of E and s, uses different ethods whose 1

3 discussion shall be the ain topic of this work. The entioned ethods are applied in order to obtain unequivocal deconvolutions results for the peak separation. The ai of this work was to investigate the following techniques for the deterination of the activation energy and the frequency factor: the initial rise ethod corrected by Christodoulides, various peak shape ethods introduced by Lushchik, Halperin and Braner and Chen and the different heating rates ethod suggested by Hoogenstraaten. All of these ethods were priarily developed for single (i.e. isolated) peaks. Therefore the applicability for ulti-peak structure glow curves had to be questioned. The analysis techniques were applied to different theroluinescence dosieters (TLDs): TLD-300 (CaF : T), TLD-600 ( 6 LiF : Mg, Ti) and TLD-700 ( 7 LiF : Mg, Ti). Methods.1 Initial Rise The ethod of initial rise was originally suggested by G.F.J. Garlick and Gibson [3] as a eans of deterining trap depths fro theroluinescence easureents and is today widely used. The well-known Randall-Wilkins expression for the shape of a TL glow peak (A.J.J. Bos [5]) is: T E s E I( T ) = n s exp exp dt, 0 (1) kt β kt 0 where E is the energy depth of the traps, s is the frequency factor, k is Boltzann s constant, β is the (constant) heating rate, T is the absolute teperature, n 0 is the initial nuber of trapped charge carriers (electrons and holes) and I is the rate of escape of the carriers fro the traps or theroluinescence intensity. This equation reduces to E I( T ) = const exp kt () for the initial rise region of a glow peak, where T << T and I << I. Therefore, plotting ln(i) against 1/T a linear plot is obtained with slope equal to E/k. Hence it is possible to evaluate E without any knowledge of the frequency factor s by eans of the equation d(ln I) E k d(1/ T ) The axiu of the peak satisfies the equation =. (3) βe kt E s exp kt = (4) where T is the teperature at the axiu intensity of the glow peak. Once the value of E is deterined, the frequency factor s can be obtained by this expression.

4 The single peak region and the range of applicability in which the initial rise ethod can be eployed are often not pointed out sufficiently in the literature. In the introduction of the analysis of C Christodoulides [7] on the topic, however, there is given a very clear and transparent explanation of what to understand as initial rise region of a single peak, in case of first-order kinetics: [ ] As the ethod is based on the assuption that during the initial rise of the TL peak the nuber of trapped charge carriers causing the peak does not change to any significant extent, the results will be accurate only if the level of signal used is a sall fraction of the peak height, usually quoted as less than 10%. This is not however always possible, and in situations where the signal-to-noise ratio is low, soe investigators apply the ethod to signal levels exceeding, in soe cases, 50% of peak height. While these high signal levels should be avoided, even for lower levels of signal the systeatic error introduced ay be of the order of a few per cent. Due to the fact that the activation energy E is partly seriously underestiated by the siple initial rise ethod C Christodoulides subsequently derives a corrected expression for the calculation of the activation energy by nuerical analysis: In estiating the systeatic errors introduced in energy deterinations by the initial rise ethod, we assued a peak of energy E and peak teperature T [ ]. Between teperatures T 1 and T (both < T ) corresponding to values of I equal to α 1 I and α I respectively, a nuber of points were taken at equal intervals on the teperature scale, [see figure 1.a]. These points were plotted in a plot of ln(i) against 1/T [see figure 1.b]. Using the ethod of least squares we fitted a straight line to these points, the slope of which gives the value E c as the energy deterined by the initial rise ethod. The value is less than the actual energy E by an aount which increases with increasing α 1 and α. Our ai was to find an expression for the correct energy E in ters of the easured value E c, and α 1, α and T. C. Christodoulides corrected expression is: T E = ( α α ) E (α + 0.α ) (5) 1 c fro which, given α 1, α and the energy value E c found by the initial rise ethod, the correct energy E can be calculated. The ranges of applicability of this equation (5) are E , kt α 0.5, α / α 5 1 (6) which are said to cover ost of the cases et in practice in theroluinescence. C Christodoulides has been criticised for the restriction of his forulae to first-order kinetics. T S C Singh et al [8] have derived soe further elaborated expressions for generalorder kinetics dependent on the exact (interediate) value of the order of kinetics of the glow peaks, which have, however, not been used in this work.. Peak Shape Methods The peak shape ethods eployed in this work were those of Lushchik [9], Halperin and Braner [10] and Chen [11]. The glow peak paraeters required for these techniques (see figure ) are: 3

5 δ = T T τ = T ω = T T δ µ = g ω T 1 1 (7) with the low teperature half width τ, the high teperature half width δ, the full width of half axiu ω, and the so-called geoetry factor µ g. 1.a 1.b Figure 1. (taken fro C. Christodoulides work [7]) The ethod of initial rise as applied between teperatures T 1 and T, corresponding to values of I between α 1 I and α I. Figure. (taken fro the work of Azorin et al [1]) An isolated glow peak with the paraeters ω, τ and δ, where T is the teperature of the axiu and T 1 and T are the low and high half-intensity teperatures respectively. 4

6 C. B. Lushchik and A. Halperin and A. A. Braner have derived their equations for both firstorder and second-order kinetics: Halperin and Braner: kt E = kt τ kt E = kt τ first-order kinetics second-order kinetics. (8a) (8b) Lushchik: kt E = δ first-order kinetics (9a) kt E = 1.71 δ second-order kinetics. (9b) R. Chen anaged to establish expressions for general-order kinetics, dependent on the geoetry factor of the glow peaks: Chen s equation: kt E C b ( kt ) η η η = (10) where η stands for δ, τ, ω and the values or C η and b η for the three ethods are: C C C b b b τ τ δ δ ω ω = ( µ 0.4) = ( µ 0.4) = ( µ 0.4) = ( µ 0.4) = 0 = 1. g g g g (11) After the deterination of the activation energy E and the kinetic order, an estiate of the frequency s can be ade using the following expressions: βe kt βe kt E sexp kt = E = sexp kt 1 + kt E (1a) (1b) for first- and second-order kinetics respectively. 5

7 A siilar suary of the presented peak shape ethods can be found in a paper of J. Azorin et al [1], whose easureents and therein applied ethods also served as a guide for this work..3 Different Heating Rates Method The different heating rates ethod was suggested by W. Hoogenstraaten [13] and uses various heating rates for first-order kinetics. Dividing equation (4) by E/k and taking the natural logarith on both sides yields the following expression: T E 1 ln = β k T + const. (13) Hence, a plot of ln(t / β) against (1/ T ) there results in a straight line with slope +E/k fro which the activation energy E can be calculated by the equation E d(ln( T / β )) = + k. (14) d(1/ T ) 3 Measureents & Results 3.1 TLD-600 & TLD-700 The theroluinescence dosieters TLD-600 ( 6 LiF : Mg, Ti) and TLD-700 ( 7 LiF : Mg, Ti) consist of lithiu fluoride, enriched with 6 Li and 7 Li respectively, and are doped with titaniu (about 11.5 pp) and agnesiu (about 300 pp). The standard annealing and irradiation procedure of the dosieters before easuring their glow curves is listed in table 1. Figure 3 shows two exeplary glow curves of TLD-600 and TLD-700 with peaks nubered. The easureent device used was: TL-DAT.II, at the ATI. Annealing: C Cooling down in the oven: 4 hours Irradiation: 3 hours with 137Cs gaa source (ATI) = 3.08 Gy Resting: 4 hours to reach the equilibriu state. Table 1. Standard annealing and irradiation procedure of the dosieters TLD-600 and TLD-700 before the easureents. 6

8 TLD-700 TLD-600 I(T) [cts] T [ C] Figure 3. Exeplary glow curves of TLD-600 and TLD-700 with peaks nubered. Figure 4. The graphs depict the way of calculating the initial rise activation energy E c and the corrected activation energy E fro the intensity of the glow curves according to the equations (3) and (5). TLD-600 on the left, TLD-700 on the right Initial Rise No pre-readout annealing procedure was used with the TLDs-600 and Therefore the initial rise ethod could only be tested with peak. Unfortunately this iplies the uncertainty of not knowing the exact annealing conditions which are, in this case, equivalent to the ubiquitous but elusive fading effects. By the use of equation (5) the corrected value of the activation energy E could be calculated fro the easured activation energy E c (see figure 4), α and α /α 1, which had to be chosen fairly high (with 0.4 and 5 respectively) due to the very low intensity of peak. Because of the considerably high standard deviations 1 the calculation of the frequency factor 1 All given standard deviations are eant to be the standard deviations of individual easureents and were calculated by the use of the well-known equation σ = i ( x x ) n 1 i. 7

9 s, which would hence give a spread over several orders of agnitude, was renounced in this case. TLD 600 M e t h o d Peak Peak 5 E [ev] E [ev] Initial Rise Initial Rise (by Christodoulides) 1,7 ± 0,16 ( α = 0.4, α /α 1 = 5 ) Initial Rise (without corrections) 1,58 ± 0,15 Peak Shape Halperin-Braner 1,66 ± 0,15 Lushchik 1,75 ± 0,09 Different Heating Rates Hoogenstraaten 0,75 ± 0,14 1,6 ± 0,1 Table. Results of all eployed ethods for TLD-600. TLD 700 M e t h o d Peak Peak 5 E [ev] E [ev] Initial Rise Initial Rise (by Christodoulides) 1,78 ± 0,33 ( α = 0.4, α /α 1 = 5 ) Initial Rise (without corrections) 1,64 ± 0,31 Peak Shape Halperin-Braner 1,81 ± 0,5 Lushchik 1,73 ± 0,10 Different Heating Rates Hoogenstraaten 0,51 ± 0,06 1,10 ± 0,14 Table 3. Results of all eployed ethods for TLD Peak Shape The ulti-peak structure of the glow curve of TLD-600 and TLD-700, especially the well-hiding peak 4, restricts the peak shape ethods reasonably applicable to Halperin-Braner s (equations (8)) for peak (left side) and Lushchik s (equations (9)) for peak 5 (right side). Both peaks were assued to follow first-order kinetics, ensuing fro the literature [14]. The uncertainty of the result for peak is again due to the unbeknown fading effects, which were not dwelled on in this work. However, concerning peak 5 there exists legitiate hope that the peak s right side is sufficiently independent of all preceding curve axia. Again, the evaluation of the frequency factor was renounced due to high standard deviations. 8

10 3.1.3 Different Heating Rates This ethod was applied to the second and the fifth peak using the following heating rates: 1, 3, 4, 5 and 7 K/s. The evaluation was done by the use of equation (14) according to the plot represented by figure 5. Also for this ethod the evaluation of the frequency factor was renounced due to high standard deviations Discussion Tables and 3 show the results for the activation energies E of TLD-600 and TLD-700. They reveal treendous differences of the values and their standard deviations between the different ethods, in particular for peak but also for peak 5. Above all the ethod of different heating rates sees to fail copletely. Concerning peak this could be explained by the fact that there was no standard annealing procedure perfored expect the natural one, i.e. fading. Regarding peak 5 the ost probable reason for this is the undeterined influence and order of kinetics of the preceding peaks 3 and 4 (see figure 3) whose shift with increasing heating rate reains unsettled. Altogether there could not be obtained any eaningful result for peak. The probably ost reliable value (also in ters of standard deviation) is yielded by Lushchik s ethod (right peak side) eployed for peak 5, which justifies the rough assuption of approxiate independence of this region of peak 5 fro the other curve axia. 3. TLD-300 The theroluinescence dosieter TLD-300 (CaF : T) consists of calciu fluoride and is doped with an undisclosed aount of thuliu. The standard annealing and irradiation procedure of the dosieters before easuring their glow curves is listed in table 4. The easureent device used was again: TL-DAT.II, at the ATI. There were investigated the kinetic paraeters E and s of 3 different batches of TLD-300 sorted by forer easureents. The respective chips with their nubers are listed in table 5. Figure 6 shows 3 exeplary glow curves of the different batches of TLD-300 with peaks nubered. Annealing: C Cooling down in the oven: 4 hours Irradiation: or 3 hours with 137Cs gaa source (ATI) =.05 or 3.08 Gy Resting: 4 hours to reach the equilibriu state. Pre-readout annealing: 15 85, 90 or 100 C Table 4. Standard annealing and irradiation procedure of TLD-300 before the easureents. TLD 300 Chip # Batch 1 4, 4, 53, 84 Batch 16, 49, 56 Batch 3 109, 16, 13, 137 Table 5. Batches 1-3 of chips with respective chip nubers. 9

11 Figure 5. The graphs depict the way of calculating the activation energy E fro a plot according to equation (14). TLD-600 on the left, TLD-700 on the right TLD-300 Batch 1 TLD-300 Batch TLD-300 Batch 3 I(T) [cts] T [ C] Figure 6. Exeplary glow curves of the 3 different batches of TLD-300 with peaks nubered Initial Rise For the use of the initial rise ethod for peak 3 there had to be added a pre-readout annealing procedure in order to erase peak. As table 4 shows the respective conditions were: 15 in additional annealing at teperatures of 85, 90 or 100 C. Figure 7 shows the glow curves of a TLD-300 of batch 3 after different annealing conditions. One should be aware of the loss of axiu intensity of peak 3 in coparison to the glow curves of figure 6. By the use of equation (5) the corrected value of the activation energy E could be calculated fro the easured activation energy E c (see figure 8), α and α /α 1. The exact initial rise peak region, deterined by the values of α and α /α 1, was chosen in consideration 10

12 of sufficient intensity as well as an adequate nuber of data points to be fitted according to equation (3). So α and α /α 1 were fixed with 0.33 and 10 respectively. The values of the frequency factor s were obtained by the evaluation of equation (4), again. Table 6 shows the results (corrected and values without corrections) for the initial rise ethod for all batches of TLD No annealing C C C I(T) [cts] T [ C] Figure 7. Glow curves of one TLD-300 of batch 3 after different annealing procedures. One should be aware of the loss of axiu intensity of peak 3 in coparison to the glow curves of figure (without annealing). The slight shift of the glow curve corresponding to annealing conditions of C (dashed plot) only results fro a different heating rate of 1 K/s instead of K/s for the other curves. Figure 8. The graph depicts the way of calculating the initial rise activation energy E c and the corrected activation energy E fro the intensity of the glow curves according to the equations (3) and (5). TLD-300, batch 3. 11

13 TLD 300 Pre-Readout Annealing Peak 3 M e t h o d 15 E [ev] s [1/s] Initial Rise Initial Rise (by Christodoulides) ( α = 0.33, α /α 1 = 10) Batch 1 85 C 1,4 ± 0,014 9,6E+1 Batch 1 90 C 1,45 ± 0,010 9,6E+1 Batch C 1,58 ± 0,03 9,8E+1 Batch 85 C 1,40 ± 0,09 9,1E+1 Batch 90 C 1,44 ± 0,04 8,3E+1 Batch 100 C 1,55 ± 0,00 9,1E+1 Batch 3 85 C 1,4 ± 0,00 1,5E+13 Batch 3 90 C 1,50 ± 0,016 1,E+13 Batch C 1,60 ± 0,054 1,3E+13 Initial Rise (without corrections) Batch 1 85 C 1,35 ± 0,014 9,E+1 Batch 1 90 C 1,38 ± 0,010 9,E+1 Batch C 1,51 ± 0,031 9,4E+1 Batch 85 C 1,34 ± 0,0776 8,7E+1 Batch 90 C 1,37 ± 0,040 8,0E+1 Batch 100 C 1,48 ± 0,00 8,7E+1 Batch 3 85 C 1,36 ± 0,019 1,4E+13 Batch 3 90 C 1,44 ± 0,016 1,E+13 Batch C 1,53 ± 0,051 1,E+13 Table 6. Results (corrected and values without corrections) for the initial rise ethod for all batches of TLD Peak Shape The peak shape ethods were also applied to non-annealed saples of TLD-300 for the evaluation of peak 3. However, after a check of the geoetry factor s (µ g ) value, which was significantly lower than 0.4 for first-order kinetics, it got clear that, in this case, only the very siple peak shape ethods of Halperin-Braner and Lushchik for first-order peaks are suitable. This is again caused by the undeterined influence of peak on peak 3. Likewise, for the annealed saples of TLD-300 the geoetry factor was used as a rough easure of the independence of peak 3 fro peak. A calculation of its value fro the easured glow curve after the various pre-readout annealing procedures justified the application of all peak shape ethods presented in section.. Additionally, there was tried to get at least one value fro Halperin-Braner s ethod for peak 5, in spite of the fact that it cannot at all be regarded as isolated fro the preceding and following peaks (see figure 7). Peak 5 was assued to follow second-order kinetics. Again, the values of the frequency factor s were obtained by the evaluation of equation (4). Table 7 shows the results for the peak shape ethods for all batches of TLD-300 with all annealing conditions. 1

14 TLD 300 Pre-Readout Annealing Peak 3 Peak 5 M e t h o d 15 E [ev] s [1/s] E [ev] s [1/s] Peak Shape Halperin-Braner Batch 1 none 1,17 ± 0,031 7,3E+1 1,69 ± 0,10 5,3E+10 Lushchik 1,6 ± 0,055 7,9E+1 Halperin-Braner 85 C 1,31 ± 0,070 8,9E+1 1,77 ± 0,144 7,E+10 Lushchik 1,8 ± 0,103 8,7E+1 Chen (τ) 1,1 ± 0,038 8,E+1 Chen (δ) 1,17 ± 0,059 7,9E+1 Chen (ω) 1,0 ± 0,046 8,E+1 Halperin-Braner 90 C 1,34 ± 0,035 8,9E+1 1,65 ± 0,087 4,5E+10 Lushchik 1,6 ± 0,11 8,4E+1 Chen (τ) 1,5 ± 0,038 8,4E+1 Chen (δ) 1,3 ± 0,058 8,E+1 Chen (ω) 1,5 ± 0,046 8,4E+1 Halperin-Braner 100 C 1,5 ± 0,04 9,4E+1 1,74 ± 0,141 6,6E+10 Lushchik 1,34 ± 0,080 8,3E+1 Chen (τ) 1,41 ± 0,011 8,8E+1 Chen (δ) 1,37 ± 0,031 8,5E+1 Chen (ω) 1,41 ± 0,018 8,7E+1 Halperin-Braner Batch none 1,18 ± 0,041 7,0E+1 1,71 ± 0,09 6,1E+10 Lushchik 1,6 ± 0,035 7,5E+1 Halperin-Braner 85 C 1,30 ± 0,044 8,4E+1 1,71 ± 0,051 7,E+10 Lushchik 1,30 ± 0,003 8,5E+1 Chen (τ) 1,1 ± 0,059 7,E+1 Chen (δ) 1,03 ± 0,076 6,7E+1 Chen (ω) 1,09 ± 0,066 7,1E+1 Halperin-Braner 90 C 1,34 ± 0,054 7,8E+1 1,87 ± 0,15 6,5E+10 Lushchik 1,3 ± 0,081 7,6E+1 Chen (τ) 1,17 ± 0,109 6,8E+1 Chen (δ) 1,08 ± 0,174 6,3E+1 Chen (ω) 1,15 ± 0,133 6,6E+1 Halperin-Braner 100 C 1,49 ± 0,050 8,7E+1 1,75 ± 0,18 7,1E+10 Lushchik 1,31 ± 0,004 7,7E+1 Chen (τ) 1,39 ± 0,07 8,1E+1 Chen (δ) 1,35 ± 0,08 7,9E+1 Chen (ω) 1,38 ± 0,077 8,1E+1 Halperin-Braner Batch 3 none 1,7 ± 0,056 1,1E+13 1,30 ± 0,06 5,0E+10 Lushchik 1, ± 0,06 1,1E+13 Halperin-Braner 85 C 1,41 ± 0,043 1,5E+13 1,5 ± 0,068 6,E+10 Lushchik 1, ± 0,058 1,3E+13 Chen (τ) 1,31 ± 0,08 1,4E+13 Chen (δ) 1,8 ± 0,097 1,3E+13 Chen (ω) 1,31 ± 0,088 1,4E+13 Halperin-Braner 90 C 1,44 ± 0,083 1,E+13 1,36 ± 0,061 4,4E+10 Lushchik 1,19 ± 0,05 9,6E+1 Chen (τ) 1,37 ± 0,139 1,1E+13 Chen (δ) 1,35 ± 0,149 1,1E+13 Chen (ω) 1,38 ± 0,143 1,1E+13 Halperin-Braner 100 C 1,53 ± 0,061 1,E+13 1,9 ± 0,175 5,6E+10 Lushchik 1, ± 0,064 9,8E+1 Chen (τ) 1,49 ± 0,106 1,E+13 Chen (δ) 1,47 ± 0,108 1,E+13 Chen (ω) 1,49 ± 0,106 1,E+13 Table 7. Results for the peak shape ethods for all batches of TLD-300 with all annealing conditions. 13

15 3..3 Discussion Initial Rise Method Table 6 shows the results for the activation energies E and the frequency factors s for the initial rise ethod applied with the TLD-300. The values of E easured and calculated with the initial rise ethod show a not treendous but considerable dependence on the exact teperature of the preceding annealing procedure, whereas the frequency factor s order of agnitude reains constant within the respective batches. The higher the annealing teperature had been, the higher is the obtained value for the corrected E, and this is valid for all of the three different batches of TLD-300. Another vagueness occurs when considering a possibly different choice of the paraeters α and α /α 1 of equation (5). The dependence of the corrected value E on these paraeters still reains undeterined. These circustances reveal the necessity of further probes into the influence of the pre-readout annealing procedure as well as into Christodoulides odified initial rise ethod itself. Peak Shape Method Table 7 shows the results for the activation energies E and the frequency factors s for the peak shape ethods applied with the TLD-300. The effect of the pre-readout annealing is ost obvious with the peak shape ethods. Priarily the Halperin-Braner values of E for peak 3 increase ost of all with increasing annealing teperature. This is on the one hand an evidence of the indispensability of the annealing procedure eployed to erase all peaks previous to peak 3. Yet, on the other hand, it discloses the influence of additional paraeters to analyse. For all batches it can be observed that the result for E calculated fro the highteperature side of peak 3 is very stable despite different annealing conditions, but unfortunately gives a slightly deviant result copared to the other ethods. For all batches of TLD-300 the convergence of the different peak shape ethods is best for the highest annealing teperature (100 C), which can, in this case, also be explained by the closest value of the geoetry factor µ g to 0.4, the value said to correspond with first-order kinetics. Concerning the frequency factor s the easureents gave a satisfyingly stable estiate of the order of agnitude, with low variation at different annealing conditions. Regarding peak 5 the only suitable ethod was Halperin-Braner s. However, due to it overlapping with at least other peaks (the previous and the following one) the obtained results, with rearkably high standard deviations, have to be seriously questioned. Coparison The initial rise ethod in general gives slightly higher results for the trapping paraeters E and s. Yet, the convergence with the peak shape ethods in the case of 100 C annealing teperature is not bad. Ensuing fro this an annealing procedure at the higher end of the teperature range sees to be recoendable for further easureents. 14

16 4 Suary & Conclusions The ai of this work was to assess different ethods for the deterination of the kinetic paraeters E and s and their applicability to ulti-peak structure glow curves by eans of easureents on the theroluinescence dosieters TLD-600, TLD-700 and TLD-300. The investigated techniques were the initial rise ethod, various peak shape ethods and the different heating rates ethod. The ain difficulty encountered results fro the fact that all these ethods were developed as techniques applicable to single isolated peaks, a fact often stated insufficiently in the literature. So the appropriateness of all ethods for ulti-peak glow curves was uncertain. Therefore it was tried to isolate the peaks (naely peak 3 of TLD-300) as good as possible and erase the dependence of other peaks by different pre-readout annealing conditions. These were not thoroughly successful, but pointed to a proising way of doing so. The ethod of different heating rates, tested with dosieters TLD-600 and TLD-700, working with the shift of axiu intensity teperature with different heating rates, sees to fail copletely when applied to ulti-peak glow curves. This is ost probably due to other overlapping axia whose order of kinetics rests undeterined. The various peak shape ethods, tested priarily with the dosieter TLD-300, exhibit high sensitivity to previous annealing conditions, which should as well be the object of future investigations. Nevertheless, a little hint to annealing conditions at the higher end of the teperature range is given by the convergence of all peak shape ethods in this case, which poses another difficulty of high loss of intensity of the glow curve. The initial rise ethod (with Christodoulides corrections), tested in particular with the dosieter TLD-300, shows both sensitivity to previous annealing conditions and a still undeterined dependence on the choice of paraeters selecting the peak s exact region of initial rise. Thus, if not further probed, the results obtained by the use of this ethod have to be questioned even if they are to soe extent in good agreeent with the different peak shape ethods. Acknowledgeents The author is grateful to M. Hajek and M. Fugger for their great organisational and technical support during the tie of easureents at the ATI. References [1] F.O. Ogundare, F.A. Balogun and L.A. Hussain, Evaluation of kinetic paraeters of traps in theroluinescence phosphors. [] J.T. Randall and M.H.F. Wilkins, Phosphorescence and electron traps I. The study of trap distributions, Proc. R. Soc. A 184 (1945), [3] G.F.J. Garlick and A.F. Gibson, The electron trap echanis of luinescence in sulphide and silicate phosphors, Proc. Phys. Soc. 60 (1948), [4] C.E. May and J.A. Partridge, Theroluinescence kinetics of alpha-irradiated alkali halides, J. Che. Phys. 40 (1964), [5] A.J.J. Bos, Theory of theroluinescence, Radiation Measureents 41 (007), [6] S.W.S McKeever, Analysis of Coplex theroluinescence Glow-Curves, Phys. Stat. Sol. (a) 6, 331 (1980). 15

17 [7] C. Christodoulides, Errors involved in the deterination of activation energies in TL and TSDC by the initial rise ethod, J. Phys. D: Appl. Phys. 18 (1985), [8] T.S.C. Singh et al, Letter to the editor: On the deterination of activation energy in theroluinescence by the initial rise ethod, J. Phys. D: Appl. Phys. 1 (1988) [9] C. B. Lushchik, Sov. Phys. JETP 3 (1956) [10] A. Halperin and A.A. Braner, Phys. Rev [11] R. Chen, On the Calculation of Activation Energies and Frequency Factors fro Glow Curves, J. Appl. Phys. 40 (1969) [1] J. Azorin et al, Evaluation of the kinetic paraeters of CaF : T (TLD-300) theroluinescence dosieters, J. Phys. D: Appl. Phys. (1989) [13] W. Hoogenstraaten, Philips Res. Rep. 13 (1958) [14] M. Puchalska et al, Theroluinescence glow peak paraeters for LiF : Mg, Ti with odified activator concentration, Radiation Measureents (006). 16