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Numerical solutions of the randall-wilkins and one trap one recombination models for first order kinetic

Yıl 2021, Cilt: 42 Sayı: 2, 372 - 379, 30.06.2021

Erdem Uzun

https://doi.org/10.17776/csj.796263

Öz

Randall-Wilkins and One Trap One Recombination (otor) models have been proposed to explain thermoluminescence emission and it should be emphasized that each model has its own allowed charge carrier transitions, trapping parameters and differential equations set. The equations are generally first or higher order linear differential equations with constant coefficients and their numerical solutions are an initial value problem. From this point on, numerical solutions of the thermoluminescence equations have been effectively used. In this paper the models were solved, numerically by using Euler and Runge-Kutta methods on Mathematica 8.0. In this work, although the fastest result calculated by Explicit Euler method, the most accurate results were calculated Linearly Implicit Euler method.

Anahtar Kelimeler

Thermoluminescence simulation Euler Runge-Kutta otor

Destekleyen Kurum

Karamanoğlu Mehmetbey University Commission of Scientific Research

Proje Numarası

20-M-16

Kaynakça

  • [1] Chen R., Pagonis V., Thermally and Optically Stimulated Luminescence: A Simulation Approach. 1st ed. Wilthshire, (2011) 245-272.
  • [2] Pagonis V., Kitis G., Furetta C., Numerical and Practical Exercises in Thermoluminescence. 1st ed. New York, (2006) 1-21.
  • [3] McKeever S. W. S., Thermoluminescence of Solids. 1st ed. Cambridge, (1985) 20-198.
  • [4] Chen R., McKeever S. W. S., Theory of Thermoluminescence and Related Phenomena. 1st ed. Singapore, (1997) 17-205.
  • [5] Kemmey P. J., Townsend P. D. Levy, P. W., Numerical Analysis of Charge-Redistribution Processes Involving Trapping Centers, Phys. Rev., 155 (1967) 917–920.
  • [6] Kelly P., Laubitz M. J., Bräunlich P., Exact Solutions of the Kinetic Equations Governing Thermally Stimulated Luminescence and Conductivity, Phys. Rev. B., 4 (1971) 1960–1968.
  • [7] Shenker D., Chen R., Numerical Solution of the Glow Curve Differential Equations, J. Comput. Phys., 10 (1972) 272–283.
  • [8] Chen R., Hornyak W. F., Mathur V. K., Competition Between Excitation and Bleaching of Thermoluminescence, J. Phys. D. Appl. Phys., 23 (1990) 724–728.
  • [9] Randall J. T., Wilkins M. H. F., Phosphorescence and Electron Traps - I. The Study of Trap Distributions, Proc. R. Soc. London. Ser. A. Math. Phys. Sci., 184 (1945) 365–389.
  • [10] Randall J. T., Wilkins M. H. F., Phosphorescence and Electron Traps II. The Interpretation of Long-Period Phosphorescence, Proc. R. Soc. London. Ser. A. Math. Phys. Sci., 184 (1945) 390–407.
  • [11] McKeever S. W. S., Chen R., Luminescence Models, Radiat. Meas., 27 (1997) 625–661.
  • [12] Bos A. J. J., Theory of Thermoluminescence, Radiat. Meas., 41 (2006) 45–56.
  • [13] Uzun E., Characterization of Thermoluminescent Properties of Seydisehir Alumina and Investigation of Properties of Dose Response, PD, Yıldız Technical University, Science and Engineering, 2008.
  • [14] Uzun E., Yarar Y., Yazıcı A. N., Electron Immigration From Shallow Traps to Deep Traps by Tunnel Mechanism on Seydiehir Aluminas, J. Lumin., 131 (2011) 2625–2629.
  • [15] Kitis G., Pagonis V., Peak Shape Methods for General Order Thermoluminescence Glow-Peaks: A Reappraisal, Nucl. Instruments Methods Phys. Res. Sect. B Beam Interact. with Mater. Atoms., 262 (2007) 313–322.
  • [16] Sunta C. M., Feria A. W. E., Piters T. M., Watanabe S., Limitation of Peak Fitting and Peak Shape Methods for Determination of Activation Energy of Thermoluminescence Glow Peaks, Radiat. Meas., 30 (1999) 197–201.
  • [17] Chen R., Winer S. A. A., Effects of Various Heating Rates on Glow Curves, J. Appl. Phys., 41 (1970) 5227–5232.
  • [18] Chen R., Methods for Kinetic Analysis of Thermally Stimulated Processes, J. Mater. Sci., 11 (1976) 1521–1541.
  • [19] Stoer J., Bulirsch R., Introduction to Numerical Analysis, 3rd ed. New York, (2002) 471-480.
  • [20] Hoffman J. D., Numerical Methods for Engineers and Scientists, 2nd ed. West Lafayette, (2015) 352-414.
  • [21] Conte S. D. D., de Boor C., The Solution of Differential Equations. In: Conte S. D. D., de Boor C., (Eds). Elementary Numerical Analysis: An Algorithmic Approach, 1st ed. Philadelphia: Siam, (2017) 346-405.
  • [22] Shampine L. F., Some practical Runge-Kutta formulas, Math. Comput., 46 (1986) 135–135.
  • [23] Dormand J. R., Prince P. J., Runge-Kutta triples, Comput. Math. with Appl., 12 (1986) 1007–1017.
  • [24] Nearing J., Mathematical Tools for Physics, 1st ed. Miami, (2010) 320-350.
  • [25] Sofroniou M., Knapp R., Advanced Numerical Differential Equation Solving in Mathematica, 1st ed. Online, (2008) 17-162.
  • [26] Balian H. G., Eddy N. W., Figure-of-merit (FOM), an improved criterion over the normalized chi-squared test for assessing goodness-of-fit of gamma-ray spectral peaks, Nucl. Instruments Methods, 145 (1977) 389–395.
  • [27] Uzun E., Theoretical Modeling and Numerical Solutions of the Some Standard Thermoluminescence Detector Crystals, Turkish J. Phys., 37 (2013) 304–311.
  • [28] Uzun E., On the Numerical Solution of the One Trap One Recombination Model for First Order Kinetic, AASCIT J. Phys., 3(5) 2017 36-43.
  • [29] Uzun E., Korkmaz M. E., Numerical Solutions of Schön-Klasens Model for Luminescence Efficiency, EPJ Web Conf., 100 (2015) 04005p1-p3.
  • [30] Uzun E., Discussions on the Numerical Solutions of Schön-Klasens Model: Charge Carrier Traps Depth, Sigma J. Eng. Nat. Sci., 33 (2015) 421–426.

Yıl 2021, Cilt: 42 Sayı: 2, 372 - 379, 30.06.2021

Erdem Uzun

https://doi.org/10.17776/csj.796263

Öz

Proje Numarası

20-M-16

Kaynakça

  • [1] Chen R., Pagonis V., Thermally and Optically Stimulated Luminescence: A Simulation Approach. 1st ed. Wilthshire, (2011) 245-272.
  • [2] Pagonis V., Kitis G., Furetta C., Numerical and Practical Exercises in Thermoluminescence. 1st ed. New York, (2006) 1-21.
  • [3] McKeever S. W. S., Thermoluminescence of Solids. 1st ed. Cambridge, (1985) 20-198.
  • [4] Chen R., McKeever S. W. S., Theory of Thermoluminescence and Related Phenomena. 1st ed. Singapore, (1997) 17-205.
  • [5] Kemmey P. J., Townsend P. D. Levy, P. W., Numerical Analysis of Charge-Redistribution Processes Involving Trapping Centers, Phys. Rev., 155 (1967) 917–920.
  • [6] Kelly P., Laubitz M. J., Bräunlich P., Exact Solutions of the Kinetic Equations Governing Thermally Stimulated Luminescence and Conductivity, Phys. Rev. B., 4 (1971) 1960–1968.
  • [7] Shenker D., Chen R., Numerical Solution of the Glow Curve Differential Equations, J. Comput. Phys., 10 (1972) 272–283.
  • [8] Chen R., Hornyak W. F., Mathur V. K., Competition Between Excitation and Bleaching of Thermoluminescence, J. Phys. D. Appl. Phys., 23 (1990) 724–728.
  • [9] Randall J. T., Wilkins M. H. F., Phosphorescence and Electron Traps - I. The Study of Trap Distributions, Proc. R. Soc. London. Ser. A. Math. Phys. Sci., 184 (1945) 365–389.
  • [10] Randall J. T., Wilkins M. H. F., Phosphorescence and Electron Traps II. The Interpretation of Long-Period Phosphorescence, Proc. R. Soc. London. Ser. A. Math. Phys. Sci., 184 (1945) 390–407.
  • [11] McKeever S. W. S., Chen R., Luminescence Models, Radiat. Meas., 27 (1997) 625–661.
  • [12] Bos A. J. J., Theory of Thermoluminescence, Radiat. Meas., 41 (2006) 45–56.
  • [13] Uzun E., Characterization of Thermoluminescent Properties of Seydisehir Alumina and Investigation of Properties of Dose Response, PD, Yıldız Technical University, Science and Engineering, 2008.
  • [14] Uzun E., Yarar Y., Yazıcı A. N., Electron Immigration From Shallow Traps to Deep Traps by Tunnel Mechanism on Seydiehir Aluminas, J. Lumin., 131 (2011) 2625–2629.
  • [15] Kitis G., Pagonis V., Peak Shape Methods for General Order Thermoluminescence Glow-Peaks: A Reappraisal, Nucl. Instruments Methods Phys. Res. Sect. B Beam Interact. with Mater. Atoms., 262 (2007) 313–322.
  • [16] Sunta C. M., Feria A. W. E., Piters T. M., Watanabe S., Limitation of Peak Fitting and Peak Shape Methods for Determination of Activation Energy of Thermoluminescence Glow Peaks, Radiat. Meas., 30 (1999) 197–201.
  • [17] Chen R., Winer S. A. A., Effects of Various Heating Rates on Glow Curves, J. Appl. Phys., 41 (1970) 5227–5232.
  • [18] Chen R., Methods for Kinetic Analysis of Thermally Stimulated Processes, J. Mater. Sci., 11 (1976) 1521–1541.
  • [19] Stoer J., Bulirsch R., Introduction to Numerical Analysis, 3rd ed. New York, (2002) 471-480.
  • [20] Hoffman J. D., Numerical Methods for Engineers and Scientists, 2nd ed. West Lafayette, (2015) 352-414.
  • [21] Conte S. D. D., de Boor C., The Solution of Differential Equations. In: Conte S. D. D., de Boor C., (Eds). Elementary Numerical Analysis: An Algorithmic Approach, 1st ed. Philadelphia: Siam, (2017) 346-405.
  • [22] Shampine L. F., Some practical Runge-Kutta formulas, Math. Comput., 46 (1986) 135–135.
  • [23] Dormand J. R., Prince P. J., Runge-Kutta triples, Comput. Math. with Appl., 12 (1986) 1007–1017.
  • [24] Nearing J., Mathematical Tools for Physics, 1st ed. Miami, (2010) 320-350.
  • [25] Sofroniou M., Knapp R., Advanced Numerical Differential Equation Solving in Mathematica, 1st ed. Online, (2008) 17-162.
  • [26] Balian H. G., Eddy N. W., Figure-of-merit (FOM), an improved criterion over the normalized chi-squared test for assessing goodness-of-fit of gamma-ray spectral peaks, Nucl. Instruments Methods, 145 (1977) 389–395.
  • [27] Uzun E., Theoretical Modeling and Numerical Solutions of the Some Standard Thermoluminescence Detector Crystals, Turkish J. Phys., 37 (2013) 304–311.
  • [28] Uzun E., On the Numerical Solution of the One Trap One Recombination Model for First Order Kinetic, AASCIT J. Phys., 3(5) 2017 36-43.
  • [29] Uzun E., Korkmaz M. E., Numerical Solutions of Schön-Klasens Model for Luminescence Efficiency, EPJ Web Conf., 100 (2015) 04005p1-p3.
  • [30] Uzun E., Discussions on the Numerical Solutions of Schön-Klasens Model: Charge Carrier Traps Depth, Sigma J. Eng. Nat. Sci., 33 (2015) 421–426.
Toplam 30 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Klasik Fizik (Diğer)
Bölüm Natural Sciences
Yazarlar

Erdem Uzun 0000-0002-8001-0334

Proje Numarası 20-M-16
Yayımlanma Tarihi 30 Haziran 2021
Gönderilme Tarihi 17 Eylül 2020
Kabul Tarihi 18 Mart 2021
Yayımlandığı Sayı Yıl 2021Cilt: 42 Sayı: 2

Kaynak Göster

APA Uzun, E. (2021). Numerical solutions of the randall-wilkins and one trap one recombination models for first order kinetic. Cumhuriyet Science Journal, 42(2), 372-379. https://doi.org/10.17776/csj.796263