C M Sunta

Limitation of peak fitting and peak shape methods for determination of activation energy of thermoluminescence glow peaks

This paper shows the limitation of general order peak fitting and peak shape methods for determining the activation energy of the thermoluminescence glow peaks in the cases in which retrapping probability is much higher than the recombination probability and the traps are filled up to near saturation level. Right values can be obtained when the trap occupancy is reduced by using small doses or by post-irradiation partial bleaching. This limitation in the application of these methods has not been indicated earlier. In view of the unknown nature of kinetics in the experimental samples, it is recommended that these methods of activation energy determination should be applied only at doses well below the saturation dose.

General order and mixed order fits of thermoluminescence glow curves—a comparison

Abstract General order (GO) and mixed order (MO) kinetics expressions are applied to a series of synthetic thermoluminescence (TL) glow peaks derived from different physical models. The correlation between kinetic order (KO) parameter b of the GO kinetics expression and the parameter α (=n 0 /(n 0 +M) where n0 is the initial filled concentration of the active traps and M that of the thermally disconnected deep traps) of the MO expression is checked. It is found that the correlation is not universal except at the limiting values of α and b, when α=0 and 1 always correspond to b=1 and 2 as expected. In the intermediate region the graphical plot does not produce a smooth line. An examination of all the results along with those from the published literature shows that the overall scatter in the values found for b corresponding to any value found of α is within about ±10%. This scatter is attributed to the influence of parameters other than α and b on the symmetry of the glow peak. A conclusion of greater significance reached from this study is that MO expression is a superior alternative to GO for the glow peak characterization. This is because the parameter α remains constant at all temperatures T in the glow curve whereas b, though assumed constant in the GO expression, changes with T when GO is applied to any physically plausible model of TL emission, except when b turns out to be 1 or 2. Due to this variation of b, the value found for E always has some error which increases systematically as the fitted b deviates farther away from 1 and 2. Parallel to the error in E, the figure of merit (FOM) of the fit also deteriorates. The paper also discusses the relevance of other fitted parameters, both in GO and MO fits.

General-order kinetics of thermoluminescence and its physical meaning

Thermoluminescence glow peaks are calculated numerically for a one-trap - one-recombination-centre model using a generalized approach. Except in extreme cases the peaks are seen to change in position and shape with a change in dose. These glow peaks are fitted to the general-order kinetics model and the values of the kinetic parameters, namely the activation energy, pre-exponential factor and order of kinetics are determined by finding the best fit. In this way an attempt is made to correlate the empirical parameters with the physically meaningful ones in the framework of the adopted model. The fitted value of the activation energy matches reasonably its input value used in the generalized approach model calculations. The fitted values of the order of kinetics and the pre-exponential factor parameters change with the initial occupancy of the traps (dose) in all cases in which the order of kinetics (KO) is found to be in the range in which 1< KO< 2. The KO decreases with increasing trap occupancy whereas the pre-exponential factor increases. The latter parameter undergoes a change also in its units. It is observed that, when the found value of the KO is such that 1< KO<2, the best fitted general-order kinetics peak deviates significantly from the computed peak. A better fit is found with two peaks, one of which is approximately of first order and the other approximately of second order. The KO parameter at saturation dose has been correlated with the ratio of the re-trapping and recombination cross sections. These theoretical results are discussed in the perspective of experimental observations in general. Plausible reasons for disagreements between theory and experiment are also discussed.

A critical look at the kinetic models of thermoluminescence: I. First-order kinetics

Using a generalized scheme of multiple traps, thermoluminescence (TL) glow curves are calculated for different sets of systems parameters. In particular, the conditions under which glow peaks of first-order kinetics are produced are highlighted. The major findings and conclusions are as follows. (1) In the generalized scheme the glow peaks always reduce to first order at low trap occupancies. It is therefore suggested that the peak analysis to determine the parameters should be carried out only at low doses. (2) Glow peaks which follow first-order kinetics can be obtained irrespective of whether the recombination rate is faster, equal to or slower than the retrapping rate (Rret). (3) Quasi-equilibrium (QE) of free carriers in the delocalized band, which is the essential condition for the derivation of the conventional analytical expressions of TL and thermally stimulated conductivity, can be realized irrespective of whether RrecRret. (4) The realization of the QE condition depends on the concentrations of the traps and the recombination centres (RCs) and their cross sections for free carrier capture. It is discussed and shown that, in doped insulating and semiconducting materials, the values of these parameters are sufficiently high for the QE condition to be comfortably held. It is thus concluded that the doubts raised by earlier workers regarding the validity of the QE assumption in the derivation of the analytical expressions are unnecessary as far as these materials are concerned. (5) It is shown that a system in which some of the untrapped charge carriers recombine within the germinate centres and some become delocalized may satisfactorily explain the mechanism of TL emission in most of the phosphors. The properties of first-order, supralinearity and pre-dose sensitization may be easily explained under the framework of this system. (6) Conclusions (2) and (3) above disprove those of earlier workers who had concluded that QE and fast retrapping together do not form a consistent set of conditions and that the apparent dominance of first-order kinetics in nature is due to slow retrapping.

Supralinearity and sensitization of thermoluminescence. I. A theoretical treatment based on an interactive trap system

A theoretical treatment is presented for the supralinearity of thermoluminescence glow peaks. The model assumes part of the thermoluminescence trap population as interactive with the thermally disconnected deep traps. These traps produce supralinear growth of the thermoluminescence response. The initial linear part of the response curve is assumed to be produced by the non-interactive part of the thermoluminescence trap population. The treatment enables determination of the relative concentration of deep traps. Resolution of the observed response curve into linear and supralinear parts allows determination of the relative trap populations responsible for producing the linear and supralinear parts of the response. We have also shown the procedure for determining the trap filling constant using the growth profile of the thermoluminescence glow peak of pre-dose sensitized samples. Apart from interpreting the linear and supralinear behaviour of the thermoluminescence response, the treatment provides a quantitative explanation for the pre-dose sensitization effect.

Supralinearity and sensitization factors in thermoluminescence

Abstract Supralinearity and pre-dose sensitization are two characteristics of thermoluminescence (TL) glow peaks which are seen together in many of the TL phosphors. In this paper, theoretical expressions are derived for the supralinearity and pre-dose sensitization factors, based on the interactive trap system model. A new term called sensitization factor ( S n F ) is introduced, which differs from the pre-dose sensitization factor ( PDSF ) but is related directly to the supralinearity factor ( SF ). The factors SF and S n F coincide in the low and medium dose range. At high doses the latter departs considerably from the former. The case of LiF TLD-100 is used to demonstrate the application of the theory to actual experimental results.

Supralinearity and sensitization of thermoluminescence. II. Interactive trap system model applied to LiF:Mg,Ti

For Part I see ibid., vol.27, pp.852-60 (1994). A theoretical treatment based on a partly interactive trap system (PITS) described in Part I is applied to peak 5 of LiF:Mg,Ti. The model assumes two types of thermoluminescence traps for the given glow peak: (i) those which produce a linear response with dose and (ii) those which produce a supralinear response. The former are spatially associated with the luminescent recombination centres. The latter are randomly distributed and the carriers released from them during readout heating may be recaptured by the thermally disconnected deeper traps non-radiatively in addition to undergoing recombination to produce luminescence. The trap filling constant, defined as the fraction of traps filled per unit dose, is determined using the intensity growth profile of the related optical absorption band and that of the thermoluminescence of pre-dose sensitized sample. The value of this constant is 1.16*10-3 Gy-1 for peak 5. For peak 12 it is an order of magnitude lower. Fractions of the thermoluminescence trap population responsible for linear and supralinear parts of the response are determined using pre-dose sensitization. The ratio of these two populations is calculated to be 1:13. A method is suggested to determine the relative concentration of the deep traps with respect to the shallower thermoluminescence traps. This estimation is carried out by separating the supralinear part of the response curve and calculating its under response factor at low doses. The relative concentration of deep traps is seen to be dependent on the relative coefficients for trapping and recombination. The calculated parameters are backfitted into the theoretical expression and the response profile so obtained is compared with the experimental response curve. The two are found to be in good agreement.

Test for quasi-equilibrium in thermally stimulated luminescence and conductivity

The uncertainty about the existence of quasi-equilibrium (QE) condition during the readout of thermoluminescence and thermally stimulated conductivity glow peaks in real materials causes doubts about the validity of applying the QE-based analytical expressions to analyse these glow peaks. In this paper a simple method is given to verify the QE condition during the readout of these glow peaks in real materials. The method is based on changes in the glow peak shapes caused by changing the heating rate in non-QE cases. It is illustrated by using synthetic glow peaks derived from two different physically meaningful models.

Anomalies in the determination of the activation energy of thermoluminescence glow peaks by general-order fitting

Thermoluminescence glow curves calculated from three physically meaningful models are fitted into the empirical general-order (GO) kinetics expression to find the fitted values of activation energy E and the kinetic order b. The results show that the figure of merit of the fit deteriorates progressively as the best fitted value of b deviates from 1 and 2. At the same time the fitted E value also departs from its true value. This result is used to reinterpret the observed change in E of glow peak 5 of LiF (TLD-100) in post-irradiation annealed samples. It is concluded that the application of GO kinetics to glow peak 5 of LiF (TLD-100) leads to inconsistencies and that the changes in E found by GO fitting may not be real.

The quasi-equilibrium approximation and its validity for the thermoluminescence of inorganic phosphors

The validity of the quasi-equilibrium (QE) assumption in the analytical models of thermoluminescence (TL) which assume delocalization of the untrapped charge carriers has often been questioned. In this paper, this problem is further considered using three different physical models of TL emission. The numerically computed glow curves without the QE approximation are compared with those calculated analytically to verify whether the QE condition is satisfied. QE is assessed also by using a mathematical relation between the excitation and relaxation rates. The results lead to the following conclusions. (i) Under a wide variety of parametric combinations QE is attained even when retrapping predomines over recombination. (ii) Glow peaks with first-order character are obtained even when the retrapping rate far exceeds the recombination rate in multiple-trap systems. This is contrary to the premise on which the Randall-Wilkins model is based. These two conclusions contradict also the assertions of Lewandowski and McKeever that QE and fast retrapping are not self-consistent conditions and that the apparent dominance of first-order TL kinetics in nature is due solely to the predominance of recombination over retrapping. (iii) QE depends critically on the product of the trap concentration and the cross section. A new criterion for the validity of the QE assumption is derived, according to which should be greater than , where and are the concentration and the cross section of the traps at the active and deeper levels in a system exhibiting multiple glow peaks. (iv) Evidence from studies of point defects in insulating and semiconducting materials shows that the N and values of the defect centres concerned are high enough to satisfy the QE condition. It is thus inferred that the use of the analytical expressions based on the QE approximation for analysing the glow curves of the common TL phosphors is legitimate.