ARTICLE IN PRESS

Journal of Luminescence 130 (2010) 1216–1220

Contents lists available at ScienceDirect

Journal of Luminescence

0022-23

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/jlumin

Dependence of peak height of glow curves on heating ratein thermoluminescence

Munish Kumar a,n, G. Chourasiya a, B.C. Bhatt b, C.M. Sunta c

a Radiological Physics & Advisory Division, Bhabha Atomic Research Centre, Mumbai 400 094, Indiab CSIR Emeritus Scientist, C/o Radiological Physics & Advisory Division, Bhabha Atomic Research Centre, Mumbai 400 094, Indiac C30/257 MIG Colony, Bandra (E), Mumbai, India

a r t i c l e i n f o

Article history:

Received 17 December 2008

Received in revised form

11 January 2010

Accepted 19 February 2010Available online 24 February 2010

Keywords:

Glow peak height

Thermal quenching

Heating rate

Glow curve

13/$ - see front matter & 2010 Elsevier B.V. A

016/j.jlumin.2010.02.027

esponding author. Tel.: +91 22 25570928.

ail address: munish_pms@rediffmail.com (M.

a b s t r a c t

The area under the glow curve (no thermal quenching and same dose) is conserved only in TL–time

plots and is not conserved (scales by a factor by which heating rate is increased) in TL–temperature

plots. This increase in area under TL–temperature glow curves with increase in heating rate at a

constant dose should not be interpreted as increase in sensitivity of the dosimeter and is the

consequence of transformation of time to temperature scale (temperature scale obtained from time

scale by multiplying with b, T¼T0+bt). This is further supported by the fact that the light output or

integrated counts seen by the PMT do not change (ignoring statistical fluctuations) with increase in

heating rate at a constant dose. Further for a given heating rate, the glow peak height is similar in time

and temperature plots and the glow peak height increases with increase in heating rate. However to

conserve area in TL–temperature plots, the TL intensity should be divided by the respective heating

rate, which will lead to the decrease of glow peak height in I/b–temperature plots and is the artifact of

the normalization process. However for normalized glow curves (I/b–temperature), the glow peak

height decreases with increase in heating rate, which is actually true for I/b or TL/b versus temperature

plots. Hence it is recommended that in such cases where normalized glow curves (I/b versus

temperature) are presented, the obtained peak height must be multiplied by b. By doing so, glow peak

height increases with increase in heating rate. In addition to the above, studies are also carried out by

considering thermal quenching effect and it is found that a logical way to measure thermal quenching

quantitatively is to record the decrease of integrated counts (PMT current) with increase in heating rate

at a constant dose, i.e. the integrated peak area (PMT current or TL–time or TL/b–temperature) must be

plotted against the heating rate and the same should be used for interpretation of thermal quenching

effect. Only this proves the fact whether the decrease of TL intensity (TL/b–temperature) is due to

thermal quenching or not.

& 2010 Elsevier B.V. All rights reserved.

1. Introduction

Heating rate has always been an important parameter for theinvestigation of various kinetic parameters of glow curves inthermoluminescence (TL) phenomena. In addition, it plays acritical role in deciding the time required to record the TL glowcurves because thousands of dosimeters have to be processed in ashort time when personnel monitoring is carried out using TLdosimeters. This is also important because higher heating rate notonly increases the glow peak height but also records the glowcurves faster, which forms the basis of TL dosimetry in large scalepersonnel monitoring [1]. One of the additional facts a dosimetermust satisfy is that it should not exhibit thermal quenching,

ll rights reserved.

Kumar).

which can be verified by investigating the TL response withincrease in heating rates. If at a constant dose, the response of theselected glow curve is independent of heating rate, then it doesnot exhibit thermal quenching. One of the additional considera-tions that is critical in TL dosimetry is the plotting of light outputwith time or temperature and the relation between time andtemperature is decided by the nature of the heating profile. For agiven glow curve at a constant dose (assuming no thermalquenching), the light seen by the photomultiplier remainsconstant and is related to the area under the glow curve. In theliterature there are large numbers of reports that demonstratethat for a constant dose, the glow peak height decreases withincrease in heating rate [2]. However there are also reportsindicating that the glow peak height increases with increase inheating rate [3–5]. A similar issue was also raised by Pradhan whospeculated that there is ambiguity in the presentation of effect ofheating rate on TL glow curves [6]. In this paper, we will present

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M. Kumar et al. / Journal of Luminescence 130 (2010) 1216–1220 1217

the variation of glow peak height as well as the area under theglow curve at different increasing heating rates and ambiguity onthe effect of heating rate on TL glow curves is sorted out.

2. Theoretical investigations

In order to study the dependence of glow peak height onheating rate, any one of the models of TL, namely Randall–Wilkins,Garlick–Gibson or the general order kinetics, can be used. In thisstudy, the general order kinetics model is used. According to thegeneral order kinetics model, the intensity of TL is [7]

I¼�dn

dt¼

nb

Nb�1

� �sexpð�E=kTÞ ð1:1Þ

where n is the number density of trapped electrons (m�3) and N isthe total number of empty traps (m�3). This also implies that out ofN, n are filled and (N�n) are empty. Further b is the order ofkinetics and is dependent on the relative probabilities of retrappingand recombination cross-section and radiation dose, E is activationenergy (eV), s is the frequency factor or attempt to escape factor(Hz), T¼T0+bt is the linear heating profile and T0 is the startingtemperature, b¼dT/dt is the heating rate (K/s) and k is theBoltzman’s constant (eV/K).

For b¼1, Eq. (1.1) reduces to the Randall–Wilkins model,which represents first order kinetics:

dn

dt¼�np¼�nsexpð�E=kTÞ ð1:2Þ

whereas for b¼2, we have the Garlick–Gibson model representingsecond order kinetics.

I¼�dn

dt¼

n2

Np¼

n2

Ns expð�E=kTÞ ð1:3Þ

For the sake of simplicity, the analytical dependence of peakheight on heating rate for first order kinetics seen from Eq. (1.2) is

I¼ n0s expð�E=kTÞexp �

Z T

T0

s expð�E=kTÞ

bdT

� �ð1:4Þ

From the derivative of Eq. (1.4), it follows

bE

kTm2¼ s expð�E=kTmÞ ð1:5Þ

By using Eq. (1.5) in Eq. (1.4), the maximum value of TLintensity or glow peak height Im at peak temperature, Tm, is

Im ¼n0bE

kT2m

exp �

Z Tm

T0

s expð�E=kTÞ

bdT

� �ð1:6aÞ

Using T¼T0+bt, b¼dT/dt and Tm¼T0+btm in Eq. (1.6a), thevalue of the maximum TL intensity or peak height at tm is

Im ¼n0bE

kðT0þbtmÞ2

exp �

Z tf

t0

s expð�E=kðT0þbtÞ

� �dt ð1:6bÞ

From Eqs. (1.6a) and (1.6b), the value of Im obtained at Tm is thesame as it is at tm. It follows that glow peak height increases withincrease of heating rate. Further from Eqs. (1.6a) or (1.6b), it can beseen that if radiation doses/exposures are selected inverselyproportional to heating rate (n0a1/b), even then the resulting glowcurves will not exhibit the same peak height but a decreasing peakheight pattern with the increase of b. This is because the peakheight does not increase in direct proportion with the increase ofheating rate b as demonstrated by Eq. (1.6a) [8,9].

Further the luminescence efficiency Z(T) depends on tempera-ture T and is given by

ZðTÞ ¼ 1

1þC expð�W=kTÞð1:7Þ

where W is the thermal activation energy and is interpreted as anenergy barrier, which must be overcome for an excited stateelectron to make transition non-radiatively to the ground state,with emission of phonons, and C is a constant. The intensity of TLin the presence of thermal quenching is given by

ITL ¼ IZ Tð Þ ð1:8Þ

where I is the TL intensity in the absence of thermal quenchingand is given by Eq. (1.1).

3. Results and discussions

3.1. No thermal quenching

Initially studies are carried out without assuming any thermalquenching effect for various kinetic order values viz. b¼1, 1.5 and 2.It has been found that at a fixed dose, the plot of glow curves inTL–time shows that: (i) glow peak height increases, (ii) peakposition comes earlier, (iii) area under the glow curve isindependent of the heating rate and (iv) full width at the halfmaximum (FWHM) decreases [10–12]. This is exactly the samesituation when TL is recorded for a large number of dosimetersirradiated to the same dose at various increasing heating rates.Moreover light output is constant and independent of heating rateand is always reflected as charge integrated/collected across thecapacitor attached to PMT for a given time, i.e. output current ofphotomultiplier tube (PMT), is independent of heating rate. Forsimplicity, the simulated glow curves are shown in Fig. 1a for firstorder kinetics at heating rates of 2 and 4 K/s.

Time and temperature are correlated to each other and aredecided by the nature of the heating profile, which for linearheating is T¼T0+bt. In fact temperature scale is obtained from timescale by multiplying with the heating rate, b; the area expectedunder TL–temperature glow curve would be b times the TL–timeglow curve if dose is constant. Further from Eqs. (1.6a) or (1.6b), itcan be seen that glow peak height or maximum TL intensity is thesame at peak temperature Tm or peak time tm and the maximum TLintensity or the peak height increases with increase in heating rate.

As argued above, the TL–temperature glow curves must exhibitthe following properties with increase of heating rate: (i) maximumTL intensity or glow peak height increases with increase in heatingrate and the peak heights are same at tm or Tm, (ii) peak positionshifts toward higher temperature, (iii) area under the glow curve isnot conserved and is a function of heating rate and (iv) FWHMincreases. Point (iii) is surprising because area under TL–tempera-ture glow curves increases with increase in heating rate at aconstant dose. However, this should not be interpreted as theincrease in sensitivity of the dosimeter with increase in heating rate.This is the consequence of transformation of time to temperaturescale and the light output or integrated counts seen by the PMT donot change (ignoring statistical fluctuations) with increase in heatingrate at a constant dose. This is further supported by the fact thatPMT integrates charge for a given time and does not see any plottingartifacts, which are later introduced while plotting glow curves atvarious heating rates at a constant dose. Such TL–temperature glowcurves corresponding to Fig. 1a are shown in Fig. 1b. The TL–temperature glow curves (Fig. 1b) corresponding to TL–time plots(Fig. 1a) differ from one another in—(a) total area under the curveand (b) FWHM. Hence area under TL–temperature plots increases asthe heating rate increases and the same is predicted theoretically,and the glow peak height also increases with the increase in heatingrate. Sometimes TL–temperature plots are divided by the heatingrate, so that area under TL/b–temperature curve is constant and isequal to the corresponding TL–time plots. After the normalizationthe area under the glow curve (TL/b–temperature) is independent of

ARTICLE IN PRESS

β=4 K/s

β=2 K/s

Time in Seconds (s)

β=2 K/s

β=4 K/s

Temperature in°C

0

1x1021

2x1021

3x1021

4x1021

5x1021

6x1021

7x1021

8x1021

9x1021

1x1022

0

1x1021

2x1021

3x1021

4x1021

5x1021

6x1021

7x1021

8x1021

9x1021

1x1022

0.0

5.0x1020

1.0x1021

1.5x1021

2.0x1021

2.5x1021

β=4 K/s

β=2 K/s

Temperature in°C

0 20 40 60 80 100

50 100 150 200 250 300

50 100 150 200 250 300

TL In

tens

ity α

-dn/

dt

TL In

tens

ity α

-dn/

dt

Nor

mal

ised

TL

Inte

nsity

α -(

1/β)

*dn/

dt

Fig. 1. (a) Plot of TL intensity (�dn/dt; m�3s�1) with respect to time. The

parameters assumed are activation energy, E¼1.1 eV, frequency factor, s¼1011 Hz,

b¼1, T0¼300 K and number of trapped electrons, n0¼1023 m�3. (b) Plot of TL

intensity (�dn/dt; m�3s�1) with respect to temperature. The other parameters

assumed are the same as in (a). (c) Normalized TL glow curves (TL/b; �dn/bdt;

m�3K�1) corresponding to (b). The other parameters assumed are the same as in (a).

M. Kumar et al. / Journal of Luminescence 130 (2010) 1216–12201218

heating rate; however the obtained glow curves exhibit decrease ofpeak height with increase in heating rate. Hence normalized glowcurves only exhibit decrease in glow peak height or maximum TL

intensity with increase in heating rate. However such statements,like the peak height or maximum TL intensity decreases withincrease in heating rate, should be avoided because they are againsttheoretical predictions and also violates principles of dosimetrywhere higher heating rate is always an advantage because of theincreased peak height and shorter time needed to record the glowcurve. Such normalized TL glow curves (I/b versus temperature)corresponding to Fig. 1b are shown in Fig. 1c. In view of this, Spoonerand Franklin [13] manipulated the TL data while comparing theexperimental measurements with the theoretically generated TL–temperature glow curves, considering the normalized TL intensitygiven by I/b¼�dn/bdt¼�dn/dT. It means the TL reader’s algorithmdirectly presents TL/b–temperature or I/b versus temperature. Insuch TL readers, the glow curves are inherently I/b versustemperature and the area is independent of heating rate for aconstant dose. However looking at glow curves (Fig. 1c), it appearsthat glow peak height or maximum TL intensity decreases withincrease in heating rate, which is actually true for I/b or TL/b. Henceit is recommended that in such cases where normalized glow curves(I/b versus temperature) are presented, the obtained peak heightmust be multiplied by b. By doing so, glow peak height increaseswith increase in heating rate.

These above mentioned facts: (i) increase of glow peak heightfor TL–temperature (I-temperature) glow curves, (ii) increase ofarea under the TL–temperature (I–temperature) glow curve and(iii) decrease of glow peak height for normalized glow curves, i.e.TL/b or I/b versus temperature, with increase in heating rate, aregenerally neglected while presenting the effect of heatingrate on glow curves at a constant dose Hence utmost care must betaken while dealing with TL readers that display normalizedTL intensity versus temperature, i.e. TL/b or I/b versustemperature.

3.2. With thermal quenching

Further in the presence of thermal quenching but at a constantdose, it has been found from Eq. (1.8) that with increase in heatingrate, the area under the glow curve in TL–time plot decreases.Further the area under TL–temperature glow curves does notincrease by b as was the case in the absence of thermal quenching.Also for normalized glow curves, i.e. TL/b–temperature or I/b versustemperature, the area under the glow curves decreases withincrease in heating rate and the area obtained is the same asobtained from the corresponding TL–time plots. Such graphs areshown in Fig. 2a–c for TL–time, TL–temperature and TL/b–temperature plots, respectively. Looking at these plots, it isevident that glow peak height increases with increase in heatingrate even in the presence of thermal quenching, but the increase isslower compared to the case when thermal quenching is absent.However for normalized glow curves (I/b versus temperature), thedecrease in normalized glow peak height is faster compared to thecase when thermal quenching is absent. The variation of maximumTL intensity, i.e. Im as well as normalized TL intensity, i.e. Im/b, withincrease in heating rate is shown in Fig. 3a and b, which shows thatthe decrease in Im/b is faster in the presence of thermal quenching.

Also the variation of peak height with heating rate may not bea suitable technique to measure thermal quenching effect becausethe peak height at a given heating rate demands prior knowledgeof kinetic parameters to study thermal quenching effect. Hence alogical way to predict/measure the thermal quenching quantita-tively is the observation of decrease of integrated counts (PMTcurrent; area under TL–time plot or area under TL/b temperatureplot) with increase of heating rate at constant dose, i.e. theintegrated peak area (PMT current or TL–time or TL/b–tempera-ture) must be plotted against the heating rate and any decrease in

ARTICLE IN PRESS

40 Ks-1

20 Ks-1

Time (s)

10 Ks-1

40 Ks-1

20 Ks-1

Temperature (K)

10 Ks-1

0

1x1021

2x1021

3x1021

4x1021

5x1021

0.00E+000

1.00E+021

2.00E+021

3.00E+021

4.00E+021

5.00E+021

0.0

2.0x1019

4.0x1019

6.0x1019

8.0x1019

1.0x1020

1.2x1020

1.4x1020

20 Ks-1

40 Ks-1

TL In

tens

ity α

−dn/

dt

TL In

tens

ity α

-dn/

dt

TL In

tens

ity α

-dn/

βdt

Temperature (K)

10 Ks-1

0 5 10 15 20 25 30

300 350 400 450 500 550 600 650 700

300 350 400 450 500 550 600 650

Fig. 2. (a) Plot of TL intensity (�dn/dt) with respect to time. The parameters

assumed are, activation energy, E¼1.0 eV, frequency factor, s¼1011 Hz, b¼2,

T0¼300 K and number of trapped electrons, n0¼1022 m�3. Further for thermal

quenching W¼0.5 eV and C¼105. The red line represents glow curves in the

presence of thermal quenching effect. (b) Plot of TL intensity (�dn/dt) with respect

to temperature. The other parameters assumed are the same as in (a). The red line

represents glow curves in the presence of thermal quenching effect. (c) Plot of TL

intensity/heating rate (�dn/bdt) with respect to temperature. The other

parameters assumed are the same as in (a). The red line represents glow curves

in the presence of thermal quenching effect. (For interpretation of the references

to colour in this figure legend, the reader is referred to the web version of this

article.)

b=2

b=2

b=1

Heating rate (Ks-1)

b=1

b=1.5

b=1.5

-1x1021

0

1x1021

2x1021

3x1021

4x1021

5x1021

6x1021

7x1021

8x1021

9x1021

4.0x1019

8.0x1019

1.2x1020

1.6x1020

2.0x1020

2.4x1020

2.8x1020

3.2x1020

3.6x1020

b=1

b=1

b=1.5

b=1.5

b=2

Pea

k he

ight

Pea

k he

ight

/hea

ting

rate

Heating rate (Ks-1)

b=2

0 10 20 30 40

0 10 20 30 40

Fig. 3. (a) Plot of glow peak height Im with heating rate. The other parameters are

the same as given in Fig. 2a. The red line represents variation of peak height in

the presence of thermal quenching effect. (b) Plot of glow peak height/heating rate

(Im/b) with heating rate. The other parameters are the same as given in Fig. 2a. The

red line represents variation of peak height in the presence of thermal quenching

effect. (For interpretation of the references to colour in this figure legend, the

reader is referred to the web version of this article.)

M. Kumar et al. / Journal of Luminescence 130 (2010) 1216–1220 1219

integrated counts with increase in heating rate at a constant doseshould be used for measuring the thermal quenching effect. Onlythis proves the fact whether the decrease of TL intensity (I/b or TL/b–temperature) is due to thermal quenching or not. Further if theexposures are kept inversely proportional to heating rate (n0 a 1/b),even then the resulting glow curves will not exhibit the samepeak height, but a decreasing peak height pattern with theincrease of b. Hence peak height measurements may not besuitable for measuring thermal quenching effect quantitatively.

4. Conclusions

The area under the glow curve (no thermal quenching and samedose) is conserved only in thermoluminescence (TL)–time plots and isnot conserved (scales by a factor by which heating rate is increased)in TL–temperature plots. This increase in area under TL–temperatureglow curves with increase in heating rate at a constant dose shouldnot be interpreted as increase in sensitivity of the dosimeter and isthe consequence of transformation of time to temperature scale

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M. Kumar et al. / Journal of Luminescence 130 (2010) 1216–12201220

(temperature scale obtained from time scale by multiplying with b,T¼T0+bt). This is further supported by the fact that the light outputor integrated counts seen by the PMT do not change (ignoringstatistical fluctuations) with increase of heating rate at a constantdose. Further for a given heating rate, the glow peak height is thesame in time as well as in temperature plots and the glow peakheight increases with the increase of the heating rate. However toconserve area in TL–temperature plots, the TL intensity should bedivided by the respective heating rate, which will lead to the decreaseof glow peak height in I/b–temperature plots and is the artifact of thenormalization process. However for normalized glow curves (I/b–temperature), the glow peak height decreases with increase inheating rate, which is actually true for I/b or TL/b versus temperatureplots. Hence it is recommended that in such cases where normalizedglow curves (I/b versus temperature) are presented, the obtainedpeak height must be multiplied by b. By doing so, one always obtainsthat glow peak height increases with increase in heating rate. Inaddition to the above, studies are also carried out by consideringthermal quenching effect and it is found that a logical way to measurethermal quenching quantitatively is to record the decrease ofintegrated counts (PMT current) with increase of heating rate at aconstant dose, i.e. the integrated peak area (PMT current or TL–timeor TL/b–temperature) must be plotted against the heating rate andthe same should be used for interpretation of thermal quenchingeffect. Only this proves the fact whether the decrease of TL intensity(TL/b–temperature) is due to thermal quenching or not.

Acknowledgments

Shri H.S. Kushwaha, Director, Health, Safety & Environment(HS&E) Group, and Dr. Y.S. Mayya, Head, Radiological Physics andAdvisory Division, BARC, are the guiding forces behind this workand the authors are thankful to them for the encouragement. Theauthors are also thankful to the anonymous referees for theirvaluable suggestions.

References

[1] M. Kumar, E. Alagu Raja, L.C. Prasad, K.L. Popli, R.K. Kher, B.C. Bhatt, Radiat.Prot. Dosim. 113 (2005) 366.

[2] L.H. Jiang, Y.L. Zhang, C.Y. Li, J.Q. Haq, Q. Su, J. Lumin. 128 (2008) 1904.[3] M.S. Akselrod, V.S. Kortov, D.J. Kravetsky, V.I. Gotlib, Radiat. Prot. Dosim. 33

(1990) 119.[4] M.S. Akselrod, N.A. Larsen, V. Whitley, S.W.S. McKeever, J. Appl. Phys. 84

(1998) 3364.[5] M.S. Akselrod, V.S. Kortov, D.J. Kravetsky, V.I. Gotlib, Radiat. Prot. Dosim. 32

(1990) 15.[6] A.S. Pradhan, Radiat. Prot. Dosim. 65 (1996) 73.[7] M.S. Rasheedy, J. Phys.: Condens. Matter 5 (1993) 633.[8] S.G. Gorbics, A.E. Nash, F.H. Attix, Int. J. Radiat. Isot. 20 (1969) 829.[9] S.G. Gorbics, A.E. Nash, F.H. Attix, Int. J. Radiat. Isot. 20 (1969) 843.

[10] Munish Kumar, L.C. Prasad, R.K. Kher, Phys. Scr. 74 (2006) 293.[11] Munish Kuamr, G. Chourasiya, Meas. Sci. Technol. 20 (2009) 058001.[12] Munish Kumar, G. Chourasiya, R.K. Kher, B.C. Bhatt, C.M. Sunta, Indian J. Pure

Appl. Phys. 47 (2009) 402.[13] N.A. Spooner, A.D. Franklin, Radiat. Meas. 35 (2002) 59.