

ORIGINAL ARTICLE 

Year : 2014  Volume
: 37
 Issue : 2  Page : 6367 


An attempt to correlate shift in thermoluminescence peak with heating rate and black body radiation
NS Rawat, MS Kulkarni, DR Mishra, BC Bhatt, D. A. R. Babu
Radiological Physics and Advisory Division, Bhabha Atomic Research Centre, Trombay, Mumbai, Maharashtra, India
Date of Web Publication  18Dec2014 
Correspondence Address: N S Rawat Radiological Physics and Advisory Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, Maharashtra India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09720464.147273
Shift in the maxima of a thermoluminescence (TL) glow peak, with an increase in heating rate, is a wellknown and readily observed phenomena with its mathematical treatment/formalism in the paper from Randal and Wilkins in 1945. The occurrence of TL glow peak is observed at high temperature and earlier in time domain with increase in heating rate. The explanation of this phenomenon is not obvious at first instance and hasn't been addressed satisfactorily in the literature. The shift in TL peak with the heating rate has been ignored as far as its physical interpretation is concerned. This communication suggests an approach to explaining this observation, and an attempt has been made to associate a physical significance to it using the concept that evolves from blackbody radiation, a wellknown and thoroughly explored quantum phenomenon in modern physics. Keywords: Blackbody radiation, StefanBoltzmann law, thermoluminescence
How to cite this article: Rawat N S, Kulkarni M S, Mishra D R, Bhatt B C, Babu D. An attempt to correlate shift in thermoluminescence peak with heating rate and black body radiation. Radiat Prot Environ 2014;37:637 
How to cite this URL: Rawat N S, Kulkarni M S, Mishra D R, Bhatt B C, Babu D. An attempt to correlate shift in thermoluminescence peak with heating rate and black body radiation. Radiat Prot Environ [serial online] 2014 [cited 2022 Jan 19];37:637. Available from: https://www.rpe.org.in/text.asp?2014/37/2/63/147273 
Introduction   
Thermoluminescence (TL) is a luminescence phenomenon exhibited by insulator or semiconductor materials and is observed when irradiated solid is thermally stimulated. TL should not be confused with the light spontaneously emitted from a substance when it is heated to incandescence. At higher temperatures (say in excess of 200°C) a solid emits (infra) red radiation of which the intensity increases with increasing temperature. This is thermal or blackbody radiation (BBR). TL, however, is the thermally stimulated emission of light following the previous absorption of energy from radiation.
Shift in the maxima of a TL glow curve with the heating rate is well known and readily observed phenomena since the model of TL has evolved and proposed by Randall and Wilkins in 1945. ^{[1],[2]} The TL glow peak shifts toward high temperature but occurs earlier in the time domain, with an increase in heating rate. The explanation of this phenomenon is not obvious at first instance.
Shift in TL peak with the heating rate has empirical explanation as proposed by Kitis. ^{[3]} The shift of T_{max} versus heating rate is empirically very easily understood. At a low heating rate β_{1} , the time spent by the phosphor at a temperature T_{1} , is long enough, so that the amount of the thermal release of electrons depending on the halflife at this temperature could take place. As the heating rate increases to β_{2} > β_{1} the time spent at the same temperature T_{1} decreases and therefore the thermal release of electrons is also decreased. Hence, a higher temperature T_{2}, is needed for the same amount of the thermal release to take place at β_{2} . In this way, the whole glowpeak is shifted to higher temperatures as the heating rate increases in a manner depending on the halflife and the time spent at each temperature.
In this communication we suggest another approach to explaining the same and associate a physical significance to this effect, using the concept that evolves from BBR  a wellknown and thoroughly explored quantum phenomenon in modern physics. The concept of BBR is coupled with the heating rate to explain the shift in TL peak (T _{m} ). The suggested theory deals quantitatively as well as qualitatively with the observed shift in TL peak. However, it overestimates the shift in TL peak toward higher temperatures and lower time with an increase in heating rate. However, still it throws some light and deals well with the observed phenomenon.
Since the method of TL dosimetry is widely used in various fields such as personnel, environmental, medical, retrospective accident dosimetry as well as TL dating, better understanding of effect of heating rate on T _{m} may be helpful in interpretation and resolving of cases of accident exposures in various situations.
Here, an important point that authors would exclusively like to highlight is that they do not intend to correlate the phenomena of TL and BBR as these two phenomena are entirely different from each other in terms of underlying physics and thus, no dependence of one on the other should be claimed. The TL phenomena have been dealt using the one trap  one recombination center model. In spite of its simplicity, the kinetics of this model appears very useful in the understanding all fundamental features of the luminescence production and provides a framework to interpret many observations.
Theory   
Blackbody radiation
It is wellknown that hot objects glow, and that hotter objects glow brighter than cooler ones. The reason is that the electromagnetic field obeys laws of motion just like a mass on a spring, and can come to thermal equilibrium with hot atoms. When a hot object is in equilibrium with light, the amount of light it absorbs is equal to the amount of light it emits. If the object is black, meaning it absorbs all the light that hits it, and then it emits the maximum amount of thermal light too. It implies that a perfectly black body has reflection and transmission coefficient as zero.
The emission spectrum due to BBR is the curve that gives spectral radiance [Figure 1]. Spectral radiance, R (λ, T) is defined such that R (λ, T) d0λ is power per unit area whose wavelength lies between λ and λ + dλ.
Plank's expression for spectral radiance is
λ is the emitted wavelength, c is the speed of light, k is Boltzmann's constant.
The Planck's expression is used to plot the black body curves for each temperature by working out the power emitted at each wavelength as shown in [Figure 1], [Figure 2].
As the temperature decreases, the peak of the BBR curve moves to lower intensities and longer wavelengths [as evident from [Figure 1]], which is quantified in terms of Wein's displacement law that is, λ_{p}T_{p} = 2.898 × 10 ^{− 3} mK which is a constant.
StefanBoltzmann law
The total energy radiated per unit surface area of a black body in unit time is directly proportional to the fourth power of the black body's thermodynamic temperature. Mathematically it can be expressed as,
This equation gives thermal energy that is delivered to the sample in time 't' during linear heating profile with the heating rate "β". Clearly, from equation (7) the time and final temperature until which the energy, E (t) delivered to the sample is a function of heating rate.
Now we consider that thermal energy E (t) is responsible for the detrapping of charge carriers that are pumped to the conduction band and subsequently recombine at RC that leaves later in an excited state. The radiative relaxation of RC to the ground state gives luminescence signal. This expression for E (t) (refer equation (7)) is explored further to account for the shift in TL maxima of glow peak with the heating rate.
Case of variable heating rate and shift in thermoluminescence peak
Let us consider the two different heating rates β_{1} and β_{2} Then thermal energies imparted to the sample/TL material in time t _{1} andt _{2} at heating rates β_{1} and β_{2} are given by,
Results and discussion   
Interpretation of equation (8)
Now to interpret equation (8), let's assume β_{2} > β_{1} .
If thermal energy associated with the material by raising its temperature up to T_{1} with a heating rate β_{1} , then to impart the same energy at different heating rate β_{2} the material needs to be heated up to temperature T_{2} such that
That is, for heating rate β_{1} if some energy is imparted up to temperature T_{1,} then to deliver the same amount of energy at higher heating rate β_{2} we need to heat the sample to temperature T_{2} that is higher than T_{1} . This is accordance with the observation that TL peak shifts toward high temperature as heating rate increases. Therefore, equation (8) gives qualitative as well as quantitative explanation for a shift in TL glow peak with the heating rate in temperature domain.
Interpretation of equation (9)
Let's analyze and interpret equation (9) which is
"If sample is heated up to temperature T_{1} with heating rate β_{1} and T_{2} with the heating rate β_{2} such that the thermal energies imparted in two cases are same, then it takes less time if heating rate is high that is, t_{2} <<i> t1 . This is again in accordance with the shift in TL intensity when plotted w.r.t. time for various heating rates."
Numerical simulations of the derived results
The BBR is correlated with thermal energy imparted (E (t)) to the material that is, energy imparted to the material is assumed to be proportional to the BBR emitted from the sample. Therefore, this energy may be responsible for the detrapping of charge carriers that are pumped to the conduction band. Subsequently, these pumped charge carriers recombine at luminescent centers to give luminescence signal.
[Figure 3] shows shift plot of TL peak w.r.t. heating rate for first order glow curves with parameters S = 10 ^{12} /s, E = 1.0 eV and S = 10 ^{12} /s, E = 1.2 eV. This plot is obtained by graphical solution of equation (3) that is transcendental in nature. The trend as shown in [Figure 3]. Is predicted by Randall and Wilkins for first order glow curve.
If we simulate equation (8) as deduced using concept of BBR and StefanBoltzmann law, for shift in TL peak we obtain a curve shown in [Figure 4]. Here, initially we assume that for heating rate 1 K/s, the TL peak occurs at temperature as predicted by equation (3).
From [Figure 3] and [Figure 4] it is evident that the proposed theory based on the approach of BBR satisfactorily explains the nature of the shift in TL peak with the heating rate and shows qualitative trend similar to the one predicted by Randall and Wilkins. However, quantitatively the approach of BBR overestimates this shift and, therefore, needs to be treated more extensively and rigorously. The experimentally obtained TL maxima are also obtained at temperatures higher than what is predicted by TL equations.  Figure 1: Spectral radiance versus wavelength plot of blackbody radiation (as predicted by Planck law) (a) in the temperature range 15003000 K, (b) in the temperature range 30006000 K
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 Figure 2: Variation of background due to blackbody radiation w.r.t time for a linear heating profile at various heating rates
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 Figure 3: Shift in thermoluminescence (TL) peak for a first order TL glow curve (with parameters as shown in the figure) as predicted by Randall and Wilkins
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 Figure 4: Shift in thermoluminescence (TL) peak for first order TL glow curves a
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Conclusions   
Using the concept of BBR it is now intuitive that TL maxima shift toward high temperature with increase in heating rate (equation (8)). Furthermore, as heating rate increases TL peak occurs earlier in the time domain (equation (9)). Approach to perceive and interpret TL phenomenon using BBR, associates a physical significance to shift in T_{m} with "β" . However, this approach overestimates the shift in TL peak toward high temperature and lower time domain with increase in heating rate. TL measurements performed at isothermal conditions that are frequently used in routine personnel monitoring can also be explained using the suggested approach. The results may be improved by incorporating temperature dependent emissivity corrections of the surface and other aspects of thermodynamics and statistical mechanics.
References   
1.  Randall JT, Wilkins MH. Proc R Soc A 1945;184:366. 
2.  Chen R, McKeever SW. Theory of Thermoluminescence and Related Phenomena. World Scientific; 1997. 
3.  Kitis G, Spiropulu M, Papadopoulos J, Charalambous S. Nucl Instrum Methods Phys Res 1993;73:36772. 
[Figure 1], [Figure 2], [Figure 3], [Figure 4]
