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

Abstract

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.

Analysis of thermally stimulated luminescence and conductivity without quasi-equilibrium approximation

“…It may contribute to dominating presence of the first-order shape of the TSL curve in nature. These conclusions concerning the influence of the retrapping process on the TSL and TSC properties are in agreement with the corresponding conclusions in the earlier works [19,20,[22][23][24]. Our results suggest that the range of the heating rate of a crystal allowing occurrence of the QS state of TSL and TSC processes can be approximately estimated from the dependences: (1) very weak increase of the symmetry factor of the TSL (TSC) curve with increasing heating rate (2) approximately linear dependence of the TSL (TSC) peak-maximum intensity on the heating rate, and (3) exponential dependence of the TSL (TSC) peak-maximum intensity on the reciprocal peakmaximum temperature.…”

“…The results are as follows: (1) the QE approximation is correct with accuracy 1% when the density of the recombination centers and traps is higher than 10 14 cm -3 and the recombination coefficient is higher than 10 -12 cm 3 s -1 , (2) the QE assumption is valid for the strong retrapping case, and (3) the TSL curve calculated for the strong retrapping case can have the firstorder shape. These results have been later confirmed by the results of Sunta and colleagues that analysed the TSL processes using different models [22][23][24][25]. Sunta and colleagues [24] found also that the level of QE during the TSL emission depends on the heating rate of a sample, and that near the turning point from the QE to non-QE state the TSL begins to change its shape.…”

“…They found that the QE approximation is not adequate for the low trap density (<10 15 cm -3 ). Later several more authors carried out the numerical solutions of the kinetic equations and calculated the TSL and TSC characteristics [14][15][16][17][18][19][20][21][22][23][24][25]. Shenker and Chen [14] found that the QE approximation in description of TSL is true both in the weak and strong retrapping cases and that the level of QE deteriorates in the high temperature part of the TSL peak calculated for the strong retrapping case.…”

Prevalence of first‐order kinetics in thermoluminescence materials: An explanation based on multiple competition processes

“…These simulated data show that as the trap filling becomes very small, the TL glow curves tend systematically toward first-order kinetics b ¼ 1. This result is consistent with the previous suggestion of Sunta et al [27], who investigated and summarized the conditions under which first-order TL glow peaks are produced within a generalized IMTS model. One of their important conclusions was that simulated TL glow always become of first-order at low trap occupancies.…”

“…6-12 by including an irradiation stage followed by a relaxation period, and by the heating stage of TL. At the start of the irradiation stage the traps and centers are considered to be empty, that is, the initial concentrations are taken as n 10 [21,27] posed clearly the central question addressed by this paper: ''The question then arises why is first-order prevalent in TL emission? The answer on the basis of the results and discussions in the preceding pages appears to be the following: it is because (i) the QE condition may always be satisfied as discussed earlier; (ii) there is an abundance of TDDTs in the temperature range in which the TL glow peaks are usually recorded.…”