UV light effect - Experimental Result - 基於光刺激發光技術用於Al2O3:C材料之劑量消光研究

Chapter 3 Experimental Result

3.3 UV light effect

A UV light bleach result is displayed in Figure 3-10. Two background dose (nearly under 200 Conv. Val. = under 1mGy) badges were exposed to UV. The “step” in horizontal axis stands for 3 min UV exposure. Form “step1” to “step8”, a pump effect was discovered. “step8” to “step9” is that badges were laid on the table without UV exposure. Form “step9” to “step11”, another pump effect was discovered too. It means UV light for Luxel^TM Al2O3:C badge not only has “bleach effect” (Fig. 3-11), but also has

Fig. 3-10. UV light pumping effect for background dose badge. Note that each “step”

stands for 3 min UV exposure and “step8” to “step9” is 12 hours.

0 2 4 6 8 10 Before 1 Hour UV Bleach After 1 Hour UV Bleach

Fig. 3-11. UV light bleach effect for 1~10 Gy badge.

4.1 Set differential equation

Chapter 4 Simulation and Discussion

4.1 Set differential equation

Chapter 2 has already introduced how to use band diagram to describe electron behavior in the Al2O3:C and how to write down the ordinary differential equation (ODE) according to band diagram. As ODE is a dynamic system, choosing a proper numerical method must be considered. After that, tune the parameter in each ODE because each parameter has its own physical probability meaning. Finally, compare the simulation data with experimental data.

Checking if they match or not, if not we should modify band diagram or tune a new set of parameters, as shown in Fig. 4-1.

Put ODE into Matlab 2007 software and use “ode23” to solve this dynamic simulation Writing down proper

Ordinary Differential Equation (ODE)

Tune the parameter in the ODE and compare with experimental result

Put ODE into Matlab 2007 software and use “ode23” to solve this dynamic simulation Writing down proper

Ordinary Differential Equation (ODE)

Tune the parameter in the ODE and compare with experimental result

Fig. 4-1. The flow chart of simulation process.

4.1 Set differential equation

There are four steps (Fig. 4-2) or four strategies to describe electron behavior in the Al2O3:C. First, simulate Al2O3:C under high energy radiation explosion such as X-rays or beta-rays. Follow that, the system has to obey thermal equilibrium process. Electrons in this step should be distributed to another state by thermal energy. Theoretically, ODE dynamic system should be added with some thermal excitation term. Third, writing down a set of bleach ODE by adding bleach factors to simulate electron for pumping away electrons from the original states. Finally, same as bleaching step, POSL also need to pump away electrons in dosimetric trap. Thus, change bleach factors to POSL bleach factors. Then read out the concentration variance to calculation OSL intensity (so called “glow curve”).

Valence Band

Fig. 4-3. Schematic R. Chen’s multi-trap, multi-recombination-center energy model.

The used model is shown in Fig. 4-3, N1 which is an “active” dosimetric trap, meaning that the stimulating light is capable of releasing electrons from it, and N2, a competitor, which the electrons can be trapped, but the stimulating light cannot release

1. Material be bombarded with high energy 1. Material be bombarded

with high energy

Fig. 4-2. The steps of ordinary differential equation in Matlab 2007 software.

4.1 Set differential equation

electrons from it. Two recombination centers are assumed to exist, M1, radioactive center, and M2 a non-radioactive competitor. The set of six coupled differential equations are governing each process. The repeated simulation of R. Chen’s is in the figure 4-4.

Bombard with high energy radiation

Physical description Unit

M1 The concentration of radioactive hole centers (cm⁻³) M2 The concentration of non-radioactive hole centers (cm⁻³)

m₁ Instantaneous occupancy (cm⁻³)

m₂ Instantaneous occupancy (cm⁻³)

N₁ The concentration of the electron active trap state (dosimetric trap, shallow trap)

(cm⁻³)

N2 The concentration of the trapping state (cm⁻³)

n1 Instantaneous occupancy (cm⁻³)

n₂ Instantaneous occupancy (cm⁻³)

n_c The concentrations of the electrons in the conduction bands (cm⁻³) nv The concentrations of holes in the valence bands (cm⁻³)

4.1 Set differential equation

X The rate of production of electron-hole pairs, which is proportional to the excitation dose rate

(cm⁻³)(s⁻¹)

B1, B2

The trapping probability coefficients of free holes in Recombination centers 1 and 2

(cm⁻³)(s⁻¹)

Am1, A_m2

Recombination probability coefficients for free electrons with holes in centers 1 and 2,

(cm⁻³)(s⁻¹)

An1 The re-trapping probability coefficient of free electrons into the active trapping state N1 (dosimetric trap)

(cm⁻³)(s⁻¹)

An2 The trapping probability coefficient of the free electrons into the competing trapping state N2

(cm⁻³)(s⁻¹)

(X*T) If we denote the time of excitation by (T) and the rate of production of electron-hole pairs per cm³ by (X), then represents the total concentration of electrons and holes produced, which is proportional to the total dose imparted.

Gy, Sv

f A magnitude proportional to the stimulating light source

intensity. (s⁻¹)

Take out rate of production of electron-hole pairs X, comparing (3-5) with (3-11)

4.1 Set differential equation

Radiative Center Occupancy / Integral OSL

m10 m1f m10-m1f

Fig. 4-4. Repeat R. Chen’s simulation result. The right side of the figure is the simulation of integral OSL versus dosimetry (log scale) and is fully matched with the result of R Chen’s proposed (left side) [10].

4.2 Modification

4.2.1 Bombard with high energy radiation

The main OSL emission band at ~420nm (Akselrod et al., 1990 [26]; Markey et.,1995 [27]) is attributed to radioactive relaxation of excited F-centers, which are created after electron recombination with F+-centers (Springis et al., 1995 [28]). When F-center accepts 206nm UV light, it will convert back to F+ center (F-center + 206 nm Æ F+-center + e-). F+ center is the luminescence center in Al2O3:C [29]. It is one of dominate factors for OSL intensity. Thus back to R. Chen’s model, we modified Eq.3-3 &

Eq.3-4 to Eq.3-25 & Eq.3-26 respectively and added C m n and ₁ ₂ _c C m n into the ₂ ₂ _c equations. These two terms represent the probability that F-center (M2) would accept enough high energy and become F+-center (F-center + high energy (beta-rays) Æ F+-center + e-). The phenomena depends on m2 concentration (F-center) and electron concentration nc. Conversion rate C1 was set equal to C2 with opposite sign. This setting represents the 100% F-center conversion will change to F+-center. Figure 4-5 is C1 & C2 parameter simulation. This figure shows the F-center conversion must occur in the Al2O3:C. Comparing with Figure 4-5(b), experimental result, we chose C1 = C2 = 50 for the following simulation.

1 1 1

(

1 1

)

1 2

m c v c

d m A m n B M m n C m n

d t = − + − +

^(3-25)

2 2 2

(

2 2

)

2 2

m c v c

dm A m n B M m n C m n

dt = − + − −

^(3-26)

4.2 Modification

Relatice OSL Intesity / OSL Count

Dose (Gy) C1 = C2 = 100 C1 = C2 = 50 C1 = C2 = 25 C1 = C2 = 0

Fig. 4-5. (a)F-center conversion simulation result and (b) experimental data.

4.2.2 Optical Bleach

The mathematical term(−V n_f) ₁ was set into n1 state, same as in the set of equations for OSL process. This is base on the assumption that visible light only cleans electrons in the dosimetric trap and there is no enough energy to bleach electrons in deep trap. The simulation result is shown in Fig 4-6. Point “A “to “H” is the experimental data and they are roughly match our simulation result in Fig. 4-6, Fig. 4-7 and Fig. 4-8.

Fig. 4-6. Optical bleach simulation result with experimental data.

4.2 Modification

0 100000 200000 300000 400000 500000 600000 700000 800000

0 2 4 6 8 10

Dose (Gy) Element-2 Conv. Val. ^{Time = 0}

Time ~ 10 min Time ~ 20 min

Fig. 4-8. Detail bleach effect of optical bleach effect in 1~ 10Gy with simulation result.

Fig. 4-7. Simulation matches the OSL decay speed with different dose.

0 5 10 15 20

0 0.5 1 1.5 2 2.5

3x 10⁴

Time (min)

OSL Relative Intensity / OSL Count 5Gy

10Gy 50Gy 100Gy

4.2 Modification

4.2.3 Maximum Bleach

Fig. 4-9. Bleach effect with UV filter in the visible light system.

In the personnel dosimetry and environmental dosimetry, maximum bleach for badge is very important. Both of dosimetry estimate dose range in mGy range. Figure 4-9 and figure 4-10 are under visible light system with UV filter and without UV filter respectively. With UV-filter and 10 min exposure case, the dose of badge will decrease to 0.1 mGy (=10 Conv. Val.) as shown in Fig. 4-10. On the other hand, in Fig. 4-11 without UV-filter, the dose of badge will left 0.2 mGy (=20 Conv. Val.). This phenomenon describes UV light in the visible light tube will increase dose in the badge. In physical explanation, UV light source can not only bleach electrons trap center but also add extra electron into trap center. Therefore, ODE dynamic system should be modified as following:

1 1 1 1 1

( _f ) ( _v) _n ( ) _c

dn V n U n A N n n

dt = − + − − (3-28)

1 2 2 2

(

)

( )

dn U n A N n n

dt = − + −

(3-29)

1 1

( )(

1 1

)

m c v

dm A m n U M m

dt = − + −

(3-23)

4.2 Modification

For UV light could pump electrons from dosimetric trap and deep trap, (−U n_v) ¹was written into N1 state and N2 state in the ODE, where Uv is the coefficient of UV impact factor. On the other hand, UV light also could add electron into dosimetric trap and deep trap. Therefore, (U_v)(M₁−m₁) was put into M1 state. In order to determine the simulation parameter Uv and Vf, , we calculate minimum photon unit by bleach light source spectrum intensity (Fig. 2-16&2-18) and then estimate photon number of wavelengths. We assume 400nm is a critical wavelength between bleach and pump effect. Moreover, we set 50 to 50 percentages for UV pump and bleach effect respectively. Finally, set the simulation parameter of bleach photon number of visible light as 0.5 and others proportional to this value. The simulation result is shown in Fig.

4-12.

Table 4-1. Calculation of lowest common multiple for bleaching photon 420nm = 2.95ev, 560nm=2.21ev, 640nm=1.93ev, 1ev = 1.6*10¹⁹J 90W*60sec=5400J

Visible

Lamp 5400J/(80*3.1+200*2.95+400*2.21+350*1.93)/10¹⁹=2.25714*10¹⁹ (Minimum photon unit for visible light)

350nm=3.54ev, 1ev = 1.6*10¹⁹J 4w*60sec=240J

UV Lamp

240J/3.54/10¹⁹=6.7796*10²⁰

(Minimum photon unit for UV lamp)

154

Fig. 4-10. Visible Light bleach without UV filters. (Each step has 10 min time gap)

4.2 Modification

Table 4-2. Simulation parameter dependence Photon

Number UV (<400nm) Visible(>400nm)

UV pump (50%) UV bleach (50%) 40*2.25*10¹⁹=9.02*10²⁰ 40*2.25*10¹⁹=9.02*10²⁰

(200+400+350)*

2.25*10¹⁹

=2.14*10²²

Simulation Simulation Simulation

Visible Lamp

0.021 0.021 0.5

0.5*6.77*10²⁰=3.38*10²⁰ 0.5*6.77*10²⁰=3.38*10²⁰

Simulation Simulation

Relative OSL Intensity / OSL Count

Time (min)

Normalized Relative OSL Intensity / OSL Count

Time (min)

Uv = 0.021, Vf = 0.5+0.021,Without UV filter Uv = 0.004, Vf = 0.504,With UV filter

Fig. 4-11. Bleach effect will achieve to a saturation point.

Fig. 4-12. Different light source has different saturation point.

The simulation results are shown in Figure 4-11 and Fig. 4-12. It successfully explains UV bleach effect with pumping function and the OSL intensity saturate at the same place. In Fig. 4-11, different n1 initial concentration represents different

experimental condition in Fig. 4-9. The other simulation result in Fig. 4-12 demonstrates different bleach light source has different saturation effect. This simulation explain even though Visible light tube is for bleach usage, but it also has pumping factors to achieve low saturation. Therefore, UV filter usage in visible light system is necessary for deep bleach in OSL badge.

4.2 Modification

4.2.4 Predictions by this model

What if the stimulated light source changes from Green light to UV light?

There suppose to have possibilities that UV light could pump deep trap electron n2. Therefore, using UV light as a stimulated light source not only pump shallow trap electrons (dosimetric trap n1), but also pump deep trap n2 as well, as shown in Fig. 4-13.

For UV light source has different impact factors for dosimetric trap and deep trap, an impact factor “d” was set to deal with this question. Impact factor “d” was set from zero to one. When “d” is zero or one that means stimulated light source can only pump electrons in dosimetric trap or deep trap respectively. Therefore, OSL intensity only attribute to one trap state. When “d” is equal to “0.5”, in the middle of zero and one, which means stimulated light source can pump electrons in both traps and it is a pumping competition. Therefore, stimulating light source impact factor f1 and f2 (in the Figure 3-24) are set (-f)(1-d) and (-f)(d), in the Eq. 3-13.&Eq. 3-14. “-f” is correlated with stimulating light source and “d” is associated with one trap stimulated or two trap stimulated.

The simulation results are shown in Fig. 4-14. When “d=0%”, the result is again back to R. Chen’s paper (or Fig. 4-4). When “d=50%”, two trap stimulated competition occur, the OSL intensity is still similar to one trap stimulation. This is an important prediction for POSL using UV light source. Because POSL only consume little amount of

Valence Band

Fig. 4-13. Two trap stimulated competition band diagram [30].

4.2 Modification

electrons in the traps and two traps concentration will not run out completely, thus pumping probabilities will follow with two trap concentration ratio condition. In 2009, We proposed a quantum selection rule for OSL and indicated pumping probabilities depend on two traps energy level ratio with concentration ratio [30]. For long time stimulation, the pumping probability of two traps should reduce to 1:1 which is the same function in this simulation “d=50%”. In the extreme case “d=100%”, shallow trap ran out of electron concentration and only deep trap can do the function. In reality, this phenomenon can only take place in the pre-bleach process. Dosimetric trap (shallow trap) had been already bleached out by pre-heat or optical bleach before UV-Pulse OSL measurement.

According to this mathematical model prediction, pre-bleach shallows process seems to enlarge linear dose dependence from 10Gy to 50 Gy.

0 20 40 60 80 100

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

Relative OSL Intensity (104 count)

Dose (Gy)

d = 0%

d = 50%

d = 80%

d = 90%

d = 100%

Fig. 4-14. OSL intensity for two traps stimulates competition.

Chapter 5 Conclusions

Although maximum precision measurement of Landauer POSL Reader with Luxel Al2O3: C badge is 10Gy, the high dose exceeds 10Gy measurement still can finish roughly by the decay slope of optical bleach process and standard deviation calculation in our experiment (Figure 5-1). We also find out the modification model to explain this bleach decay phenomena successfully. Those two methods enlarge the estimate scale for the Landauer reader with Luxel Al2O3: C badge in the case of nuclear event or nuclear emergency.

Suspected Badge

Fig. 5-1 The proposed flowchart to distinguish the over dose and under safety margin situation.

Chapter 5 Conclusions

Using the UV lamp as bleach light source has not only bleach function, but also pump effect [20]. Therefore, we use commercial visible light source with UV filter instead of UV lamp to avoid pump effect [16]. Moreover, in our optical bleach simulation, the saturation point with UV filter and without UV filter is different. These simulations totally match experimental evidence. That is the saturation point for maximum bleach could be attributed to balance of the bleach effect and pump effect.

So that we could make a prediction that the higher energy photon incidents will cause the pumping effect and bleaching effect simultaneously. When the competition approaches the equilibrium, the higher residue of the electrons will be staying the trapped level so that we could make a fine tune to set the electrons quantitatively trapped in the desired energy level.

When F-center accepts 206nm UV light, it will convert back to F+ center (F-center + 206 nm Æ F+-center + e-) [20]. Therefore, we assumed that F-center converts to F+-center (F-center + high energy (beta-rays) Æ F+-center + e-) should occur in Luxel Al2O3: C badges. This assumption successfully describes the phenomena of OSL intensity saturation in high dose in our simulation.

By modified simulation result, changing light source energy from green LED to higher energy light UV lamp in POSL system seems no apparent signal change and maintains its original OSL curve. Therefore, using two trap model by changing light source energy seems provide another idea for new type of OSL reader. Moreover, according to simulation result in UV stimulation, clean shallow trap electron concentration left deep trap dose the function seems to enlarge linearity dose dependence from 10Gy to 60Gy in Al2O3: C. This phenomena provided us an idea in deep trap usage to retrospect nuclear emergency event.

Chapter 5 Conclusions

In the future, a prototype UV-light-source OSL reader should be set up to verify the simulation result of two traps competition model (as shown in Fig). For further study, the flexible light source design in Fig. 5-2 can do the OSL light source modulation experiment. Meanwhile, a preliminary medical image reconstruction experiment can use the optical fiber design. Hoping those works will be helpful for evolution in radiation dosimetry technique in Taiwan.

Light Source

This module could be designed in reflection mode.

Transmission mode Grating

Transmitting Mode

Fig. 5-2. Schematic diagram of prototype design for UV-light-source OSL reader.

References

1. Boetter-Jensen, L., S.W.S. McKeever, and A.G. Wintle, Optically Stimulated Luminescence Dosimetry. 1 edition ed. 2003: Elsevier Science.

2. Yukihara, E.G. and S.W.S. McKeever, Optically stimulated luminescence (OSL) dosimetry in medicine. Physics in Medicine and Biology, 2008. 53(20): p.

R351-R379.

3. Huston, A.L., et al., Optically stimulated luminescent glass optical fibre dosemeter.

Radiation Protection Dosimetry, 2002. 100(1-4): p. 23-26.

4. Huei-Fu-Tsu, Safety Standards for Protection against Ionizing Radiation. Atomic Energy Council, Taiwan, 2003.

5. Aznar, M.C., et al., Real-time optical-fibre luminescence dosimetry for radiotherapy:

physical characteristics and applications in photon beams. Physics in Medicine and Biology, 2004. 49(9): p. 1655-1669.

6. Gaza, R., S.W.S. McKeever, and M.S. Akselrod, Near-real-time radiotherapy dosimetry using optically stimulated luminescence of Al2O3 : C: Mathematical models and preliminary results. Medical Physics, 2005. 32(4): p. 1094-1102.

7. Marckmann, C.J., et al., Optical fibre dosemeter systems for clinical applications based on radioluminescence and optically stimulated luminescence from Al2O3 : C.

Radiation Protection Dosimetry, 2006. 120(1-4): p. 28-32.

8. Spooner, N.A., et al., ARCHAEOLOGICAL DATING BY INFRARED-STIMULATED LUMINESCENCE USING A DIODE-ARRAY. Radiation Protection Dosimetry, 1990.

34(1-4): p. 83-86.

9. Magne, S., et al. Multichannel dosemeter and Al2O3:C optically stimulated luminescence fibre sensors for use in radiation therapy: evaluation with electron beams. 2008: Oxford Univ Press.

10. Miller, S.D. and M.K. Murphy, Technical performance of the Luxel Al2O3 : C optically stimulated luminescence dosemeter element at radiation oncology and nuclear accident dose levels. Radiation Protection Dosimetry, 2007. 123(4): p.

435-442.

11. Yukihara, E.G., et al., Effect of high-dose irradiation on the optically stimulated luminescence of Al2O3 : C. Radiation Measurements, 2004. 38(3): p. 317-330.

12. Adirovitch, E.I., La formule de Becquerel et la loi élémentaire du déclin de la luminescence des phosphores cristallins. J. Phys. Radium, 1956. 17: p. 705-707.

13. 傅利德 and 翁寶山, 熱發光的過程、理論與方法. 1990: 新竹黎明書店.

14. Chen, R., D. Lo, and J.L. Lawless, Non-monotonic dose dependence of thermoluminescence. Radiat Prot Dosimetry, 2006. 119(1-4): p. 33-36.

References

15. Lawless, J.L., et al., A model for non-monotonic dose dependence of thermoluminescence (TL). Journal of Physics-Condensed Matter, 2005. 17(4): p.

737-753.

16. Pagonis, V., R. Chen, and J.L. Lawless, Nonmonotonic dose dependence of OSL intensity due to competition during irradiation and readout. Radiation Measurements, 2006. 41(7-8): p. 903-909.

17. Chen, R., V. Pagonis, and J.L. Lawless, The nonmonotonic dose dependence of optically stimulated luminescence in Al2O3 : C: Analytical and numerical simulation results. Journal of Applied Physics, 2006. 99(3).

18. Akselrod, M.S. and S.W.S. McKeever, A radiation dosimetry method using pulsed optically stimulated luminescence. Radiation Protection Dosimetry, 1999. 81(3): p.

167-176.

19. Edmund, J.M., et al., CW-OSL measurement protocols using optical fibre Al2O3:C dosemeters. Radiat Prot Dosimetry, 2006. 119(1-4): p. 368-374.

20. Bulur, E., An alternative technique for optically stimulated luminescence (OSL) experiment. Radiation Measurements, 1996. 26(5): p. 701-709.

21. H. Whitely, V. and S. W. S. McKeever, Linear Modulation Optically Stimulated Luminescence and Thermoluminescence Techniques in Al2O3:C. Radiat Prot Dosimetry, 2002. 100(1-4): p. 61-65.

22. Mishra, D.R., et al., Luminescence properties of alpha- Al2O3 : C crystal with intense low temperature TL peak. Radiation Measurements, 2007. 42(2): p. 170-176.

23. Yukihara, E.G. and S.W.S. McKeever, Spectroscopy and optically stimulated luminescence of Al2O3 : C using time-resolved measurements. Journal of Applied Physics, 2006. 100(8).

24. Miller, S.D. and M.K. Murphy, Technical performance of the Luxel Al2O3:C optically stimulated luminescence dosemeter element at radiation oncology and nuclear accident dose levels. Radiat Prot Dosimetry, 2007. 123(4): p. 435-442.

25. Kobayashi, I. and A. Suzuki, Discussion on light annealing methode of OSL dosemeter. 日本放射線安全管理學會誌, 2002: p. 84-88.

26. Akselrod, M.S., et al., HIGHLY SENSITIVE THERMOLUMINESCENT ANION-DEFECT ALPHA-AL2O3-C SINGLE-CRYSTAL DETECTORS. Radiation Protection Dosimetry, 1990. 33(1-4): p. 119-122.

27. Markey, B.G., L.E. Colyott, and S.W.S. McKeever, TIME-RESOLVED OPTICALLY STIMULATED LUMINESCENCE FROM ALPHA-AL2O3-C. Radiation Measurements, 1995. 24(4): p. 457-463.

28. Springis, M., et al., PHOTOSTIMULATED AND THERMOSTIMULATED PROCESSES IN ALPHA-AL2O3. Radiation Measurements, 1995. 24(4): p. 453-456.

29. Yukihara, E.G., et al., The effects of deep trap population on the thermoluminescence

Appendix I

of Al2O3: C. Radiation Measurements, 2003. 37(6): p. 627-638.

30. Hsieh, C.W., J. W. Li, K.B. Chen, T. L. Jong, Simulation on Optical Stimulated Luminescence Based on Two Competition Trap Model. in iCBBE 2009. 2009. Beijing, China.

Appendix I

Number Dose (Gy) Case Serial#

1 0 XA01131183T

2 500 XA00302618L

3 background XA00805731N

4 background XA008379254

5 background XA00000570J

6 1 XA008375385

7 1 XA000695848

8 1 XA008638270

9 5 XA008352888

10 5 XA00836603H

11 5 XA008389609

12 10 XA00227099F

13 10 XA00691630F

14 10 XA00867925Y

15 50 XA00061705I

16 50 XA00838950A

17 50 XA00031544Q

18 100 XA00867979L

19 100 XA00254080V

20 100 XA008685817

21 background XA008077692

22 background XA00834036M

23 background XA00669640C

Appendix II

% Bombard stage

function dy = vdp1000(t,y)

dm1=-3000*m1*nc+5000*(800000-m1)* nv+25*m2*nc;

dm2=-5*m2*nc+400*(240000-m2 )* nv-25*m2*nc;

dn1=800*(70000-n1)* nc;

dn2=200*(30000-n2)* nc;

dnv=17000-400*(240000-m2) * nv - 1000*(1000000-m1 )*nv ; dnc=dm1+dm2+dnv-dn1-dn2;

% relaxion balance (Thermal equilibrium) function dx = vdp2(t,x)

dm1=-3000*m1*nc+5000*(800000-m1 )*nv;

dm2=-5*m2*nc+400*(240000-m2) * nv;

dn1=800*(70000-n1)* nc;

dn2=200*(30000-n2)* nc;

dnv=-400*(240000-m2) * nv - 1000*(1000000-m1 )*nv ; dnc=dm1+dm2+dnv-dn1-dn2;

% OSL Read

dm1=-5000*m1*nc;

dm2=-5*m2*nc;

dn1=(-f)*(1-d)*n1+2000*(7000-n1)*nc;

dn2=(-f)*d*n2+200*(20000-n2)*nc;

dnv=0;

dnc=dm1+dm2-dn1-dn2;

% bleach

function dz = bleach(t,z) dm1=-4000*m1*nc;

dm2=-4000*m2*nc;

dn1=7000*(-VB)*n1+2000*(7000-n1)*nc;

dn2=200*(20000-n2)*nc;

dnv=0;

dnc=dm1+dm2-dn1-dn2;

在文檔中基於光刺激發光技術用於Al2O3:C材料之劑量消光研究 (頁 47-0)