I believe it means that there are clusters formed by traps and recombination centers putting them in close spatial vicinity. As a result of such close vicinity, the carriers released from traps will recombine in the nearby recombination center and thus the probability of recapture is very low compared to the probability of recombination. This explains why many phosphors exhibit a first order kinetic behavior.

Thank you Dr. Radu. Your answer is very clear for me. However, I may have a question. What is the impact of these cluster during the irradiation process? In other words, if the re-trapping probability is negligible, there would be no trapped electrons after the irradiation process. Because, we usually assume the re-trapping probabilities during both the irradiation and the heating stage are the same.

Thank you.

The difference is where you create the carriers. During the irradiation, the carriers are created in all the detector volume and not just in the trap - recombination center cluster. Some carriers will recombine and some will get trapped. During the heating stage, the carriers are taken out from the trap in the vicinity of the recombination center and then recombines. Maybe you could ask prof. Chen about this for a more comprehensive explanation. He is one of the gurus of the TLD, together with prof. McKeever and prof. Horowitz.

An important point to remember is that if the transition is localized, first order can be expected even if retrapping is not negligible. For example, you can see my 1976 paper in J. Mater. Sci., 11, 1521-1541 (1976). Therefore, the mentioned problem that if retrapping is negligible no trapping will take place during excitation, does not occur.

Dear Prof. Chen. Thank you so much for your answer.

-According to the above reference. You have mentioned, immediately after Eq.14, that in the case of localized transition, the excited electrons may either be retrapped or emit luminescence by falling down to the ground level of the center. Hence, the two possibilities can occur depending on the re-trapping and the recombination probabilities. So, why the first order is expected?

-Another point, when you say "first-order", does it mean a negligible re-trapping probability or a glow-peak has first-order geometrical properties? Because in some cases the geometrical properties of the glow-peak (kinetics order and/or symmetry factor) may not reflect the actual mechanism of the TL process. For example, in the case of competition, the glow-peaks are characterized by kinetics order values equal ~1 even in the cases with very high retrapping probability (prevalence of first-order kinetics).

Thank you.

Hi,

The main definition of first-order kinetics is that the rate of change of the carriers' concentration is proportional to this concentration, e.g. I(T)=-dn/dt=snexp(-E/kT). Note that in the case of localized transitions, the equation (Eq. 16 in the mentioned paper) is of the same form even when retrapping is substantial; only the effective frequency factor is different and depends on both the recombination and retrapping coefficients. Another possible definition of first-order kinetics in TL has to do with the characteristic asymmetric shape of a first-order peak.

You are absolutely right that in the case of a series of peaks related to a series of traps and one or more centers, and transitions through the conduction band, all the peaks excluding the highest-temperature one tend to look like typical first-order curves. In fact, even in these cases, one can show that the above mentioned first-order equation holds, at least approximately, with only a different effective frequency factor.

Spatial association between traps and recombintion centers implies that they can exchange charge carriers (electrons) without first exciting them to a delocalized band (conduction band). i will provide an experimental evidence  from our investigations in MgS:Eu,Sm. In this phosphor Sm acts as a trap and Eu as a recombination center. It was interesting to note that exciting the phosphor by 500 nm light, which is unable to excite electrons to conduction band, the Sm traps are populated as evidenced by TL and OSL. 500 nm light essentially excites Eu2+.ion and the excited electron is transferred to Sm3+ion, probably by 'tunneling'. For further details please refer to the paper and citations in 'Infrared-to-visible Conversion following Sub-Band-Gap Excitation in MgS:Eu,Sm' K.Chakrabarti, V.K.Mathur and R.j.Abbundi, PHYS. Rev. B 39, 10406 (1989).

Dear Dr. Mathur,

Thank you for your answer. The given reference is very helpful. 

Dear Dr Sadek, You may refer to publication of Dr. R. K. Bull (J. Phys D.:Applied Physics), Prof. C. M. Sunta (J. Phys.D: Appl. Phys. 39 4557 2006), Prof. P. D. Townsed (Radiation Protection Dosimetry, J. Phys D:Applied Physivs), Prof. Pagonis (J. Phys D.:Applied Physics), Prof. Mandowski (J. Phys D.:Applied Physics) and  Prof. Chen's Books on this issue.

Following paper may also be of interest to you.

Journal of Physics D: Applied Physics Volume 40 Number 19

Munish Kumar et al 2007 J. Phys. D: Appl. Phys. 40 5865 doi:10.1088/0022-3727/40/19/011.

Dear Dr. Kumar, Thank you for your valuable suggestion.