Analysis of Numeric Glow Curves by using the Method of Isothermal Decay and Calculating of the Trap Parameters

Abstract

Within this work, some fundamental models describing the TL glow are revised and resolved numerically. For this purposes, differential equation systems representing the charge carrier traffic are derived for each model. Some executable computer codes in Mathematica 8.0 are written to solve the systems numerically. Some trap parameters are given to the computer code as initial conditions and glow curves are obtained. The isothermal decay method used in the calculation of the thermoluminescence trap parameters are converted into a computer algorithm and is applied for every model. Trap parameters are calculated numerically by using thermoluminescence models and isothermal decay method. The calculated parameters are compared with the initial conditions and one can be seen that they are in a good agreement.

Keywords

• thermoluminescence; TL trap parameters; TL models; numerical analysis; isothermal decay

Sayısal Işıldama Eğrilerinin İzotermal Bozunum (Isothermal Decay) Yöntemi ile İncelenmesi ve Tuzak Parametrelerinin Hesaplanması

Abstract

Bu çalışma kapsamında termolüminesans (TL) ışımayı açıklayan bazı temel modeller yeniden gözden geçirilmiş ve nümerik olarak çözümlenmiştir. Bu amaçla her bir model için yük taşıyıcı trafiğini ifade eden diferansiyel denklem sistemleri türetilmiştir. Bu denklem sistemlerini sayısal olarak çözümleyebilmek için Mathematica 8.0 bilgisayar programı üzerinde koşturulabilen kodlar yazılmıştır. Belirli tuzak parametre değerleri başlangıç koşulu olarak bilgisayar programına verilmiş ve ışıldama eğrileri elde edilmiştir. Termolüminesans tuzak parametrelerinin hesaplanmasında kullanılan izotermal bozunum (ID) yöntemi bir bilgisayar algoritması haline dönüştürülmüş ve her bir modele uygulanmıştır. Termolüminesans modeller ve izotermal bozunum yöntemi kullanılarak tuzak parametreleri nümerik olarak hesaplanmıştır. Hesaplanan parametreler başlangıç koşulları ile karşılaştırılmış ve uyum içerisinde oldukları görülmüştür.

Keywords

• Termolüminesans; TL tuzak parametreleri; TL modeller; sayısal çözümleme; eş sıcaklık bozunum

References

1. Chen, R. (1968). Glow curves with general order kinetics. J. Electrochem. Soc., 116: 1254-1257.
2. Chen, R. (1969). On the calculation of activation energies and frequency factors from glow curves. J. Appl. Phys., 40-2: 570 – 585.
3. Chen R. (1970). On the computation of the generalized integral in glow curve theory. J. Comput. Phys., 6-2: 314 - 316.
4. Mohan, N. M., Chen, R. (1970). Numerical curve fitting for calculating glow parameters.
5. J. Phys: D. Appl. Phys., 3: 243 – 247. Shenker D., Chen, R. (1970). Numerical curve fitting of general order kinetics glow peaks. J. Phys: D. Appl. Phys., 4: 287 – 291.
6. Shenker D., Chen, R. (1972). Numerical solution of the glow curve differantial equations, J. Comput. Phys., 10-2: 272 – 283.
7. Chen R., Kristianpoller, N., Davidson, Z., Visocekas, R. (1981a). Mixed, first and second order kinetics in thermally stimulated processes. J. Lumin., 23: 293-303.
8. Chen, R., McKeever S.W.S., Durrani, A. D. (1981b). Solutuion of the kinetic equations governing trap filling. Consequences concerning dose dependence and dose - rate effects. Phys. Rev. B, 24-9: 4931 – 4944.

9. McKeever, S.W.S., Rhodes, J.F., Mathur, V.K., Chen, R., Brown, M.D., Bull, R.K. (1985). Numerical solutions to the rate equations governing the simultaneous release of electrons and holes during thermoluminescence and isothermal decay. Phys. Rev. B, 32-6: 3835 – 3843.
10. McKeever, S.W.S., Bull, R.K. (1985). Numerical solutions to the rate equations governing the simulations relaese of electrons and holes during thermoluminescence and isothermal decay. Phys. Rev. B, 32-6: 3835 – 3843.
11. Bertucci M., Veronese I., Cantone M.C. (2011). Photo-transferred thermoluminescence from deep traps in quartz. Radiat. Meas., 46:6–7, 588-590.
12. Jose M.T., Anishia S.R., Annalakshmi O., Ramasamy V. (2011). Determination of thermoluminescence kinetic parameters of thulium doped lithium calcium borate. Radiat. Meas., 46-10: 1026-1032.
13. Denis G., Deniard P., Rocquefelte X., Benabdesselam M., Jobic S. (2010). The thermally connected traps model applied to the thermoluminescence of Eu 2+ doped Ba 13−x 0.6)Al 22−2x Si 10+2x O 66 (x~0.6) materials. Opt. Mater., 32-9: 941-945.
14. Cruz-Zaragoza E., Ortiz A., Furetta C., Flores J.C., Hernández A.J., Murrieta S.H. (2011). Thermoluminescence analysis of co-doped NaCl at low temperature irradiations. Appl. Radiat. Isotopes, 69-2: 334-339.
15. Geeta S., Lochab S.P., Nafa S. (2010). Investigation of thermoluminescence characteristics of CaSrS: Ce nanophosphors. Physica B: Condens. Matter., 405-21: 452645
16. Singh M., Kaur N., Singh L. (2012). Thermoluminescence characteristics of high gamma dose irradiated natural quartz. Nucl. Instr. Meth. B: 276: 19-24.
17. Wu H., Hu Y., Ju G., Chen L., Wang X., Yang, Z. (2011). Photoluminescence and thermoluminescence of Ce 3+ and Eu 2+ in Ca 2 Al 2 SiO 7 matrix. J. Lumin. 131-12: 2441-2445.
18. Zahedifar M., Harooni S., Sadeghi E. (2011). Thermoluminescence kinetic analysis of quartz using an improved general order model for exponential distribution of activation energies. Nucl. Instr. Meth. A: 654-1: 569-574.
19. Mandowski A., Bos J.J. (2011). Explanation of anomalous heating rate dependence of thermoluminescence in YPO4:Ce 3+ ,Sm 3+ based on the semi-localized transition (SLT) model. Radiat. Meas., 46-12: 1376-1379.
20. Chen R., Lawless J.L., Pagonis V. (2012). Two-stage thermal stimulation of thermoluminescence, Radiat. Meas., 47- 9: 809-813 .
21. Pagonis V., Chen R., Lawless J. L. (2012). Superlinear dose response of thermoluminescence (TL) and optically stimulated luminescence (OSL) signals in luminescence materials: An analytical approach. J. Lumin., 132-6: 1446-1455.
22. González P.R., Furetta C., Cruz-Zaragoza E. (2011). New modified expressions for isothermal decay of Teflon embedded LiF:Mg,Cu,P and BaSO4:Eu phosphors. Appl. Radiat. Isotopes, 69-2: 511-515.
23. Kucuk İ., Yildirim T., Gasanly N. M., Özkan H. (2010). Computational modeling of isothermal decay curves of trapping centers in TlGaSeS layered single crystals. J. Alloys Compounds, 507-2, 517-520.
24. Choubey A., Das S., Sharma S.K., Manam J. (2010). Calculation for the trapping parameters of K 3 Na(SO 4 ) 2 phosphor by isothermal luminescence decay method. Mater. Chem. Phys., 120-3: 472-475.
25. McKeever, S.W.S. (1985). Thermoluminescence of Solids, Cambridge University Press, London, s.98-101.
26. Chen R., Lockwood D.J. (2002). Developments in luminescence and display materials over the last 100 years as reflected in electrochemical society publications. J. Electrochem. Soc., 149-9: 69-78.
27. Randall J.T., Wilkins M.H.F. (1945a). Phosphorescence and electron traps I. A study of trap distributions. Proceedings of the Royal Soc. A, Math. Phys. Sci., 184: 366-389.
28. Randall J.T., Wilkins M.H.F. (1945b). Phosphorescence and electron traps II. The interpretation of long period phosphorescence. Proceedings of the Royal Soc. A, Math. Phys. Sci., 184: 390-407.
29. Garlick G.F.J, Gibson A.F. (1948). The electron trap mechanism of luminescence in sulphide and silicate phosphors. Proc. Phys. Soc., 60: 574-590.
30. May C.E., Partridge, J.A. (1964). Thermoluminescence kinetics of alpha irradiated alkali halides. J. Chem. Phys., 40: 1401–1409.
31. Partridge J.A., May, C.E. 1965. Anomalous thermoluminescence kinetics of irradiated alkali halides. J. Chem. Phys., 42: 797-798
32. Furetta, C. (2003). Handbook of Thermoluminescence, Word Scientific, New Jersey, s. 176-1
33. Chen, R., McKeever, S.W.S. (1997). Theory of thermoluminescence and Related Phenomena, Word Scientific, Singapore s.88-96.
34. Chen, R., Pagonis V. (2011). Thermally and optically stimulated luminescence. A simulation approach. Wiley&Sons, Wiltshire, s.81.