In the present work, the response of peak positions in Linearly Modulated Optically Stimulated Luminescence (LM-OSL) curves as a function of physical and technical parameters were investigated and compared theoretically; specifically, the time or temperature values (tm, Tm) of their maximum intensity (Im).
Radiation Measurements 153 (2022) 106735 Contents lists available at ScienceDirect Radiation Measurements journal homepage: www.elsevier.com/locate/radmeas Electron trap filling and emptying through simulations: Studying the shift of the maximum intensity position in Thermoluminescence and Linearly Modulated Optically Stimulated Luminescence curves E Tsoutsoumanos a, b, *, P.G Konstantinidis c, G.S Polymeris b, T Karakasidis a, G Kitis c a b c Condensed Matter Physics Laboratory, Physics Department, University of Thessaly, GR-35100, Lamia, Greece Institute of Nanoscience and Nanotechnology, NCSR “Demokritos”, GR-15310, Ag Paraskevi, (Athens), Greece Nuclear and Elementary Particle Physics Laboratory, Physics Department, Aristotle University of Thessaloniki, GR-54214, Thessaloniki, Greece A R T I C L E I N F O A B S T R A C T Keywords: Linearly modulated optically stimulated luminescence One trap one recombination center model Thermoluminescence Simulation Python In the present work, the response of peak positions in Linearly Modulated Optically Stimulated Luminescence (LM-OSL) curves as a function of physical and technical parameters were investigated and compared theoreti cally; specifically, the time or temperature values (tm , Tm ) of their maximum intensity (Im ) The stimulation modes of Thermoluminescence (TL) and LM-OSL differ slightly in terms of peak resemblance (geometrical structure) but differ greatly as physical phenomena, so it could be ideal to study the effects responsible for electron trap filling or trap emptying These simulations could also extend our knowledge in Stimulated Lumi nescence phenomena regarding expected experimental outcomes In the present study, four simulation experi ments were conducted based on the One Trap – One Recombination center (OTOR) model for the case of equal re-trapping and recombination probabilities signifying second order kinetics The first experiment defines the Tm shifting for various heating and optical stimulation rates The second depicts an electron trap filling process, in which dose progresses from a low value until the saturation state In the third experiment, a trap emptying procedure was simulated via thermal bleaching (Isothermal Decay), whereas in the final one, the same trap emptying procedure was conducted via optical bleaching (Continuous wave optically stimulated luminescence) for different time spans Generally the tm , Tm shifting in trap emptying processes, is proven, according to sim ulations, to follow a similar behavior to the tm , Tm shift as a function of heating or optical stimulation rate Regarding trap filling, tm and Tm shift to lower values as the dose increases Introduction Linearly modulated optically stimulated luminescence (LM-OSL) is a technique which can be used in luminescence research and applications The LM-OSL bell-shape is the fundamental component of various com plex experimental LM-OSL curves, and it has its own set of character istics In comparison to the voluminous theoretical and experimental literature for the comparable TL peaks, in pioneer and cornerstone ăhm and works since the 1970s (Becker, 1973; Chen and Kirsh, 1981; Bo Scharmann, 1981; Chen and McKeever, 1997; Martini and Meinardi, 1997; Bøtter-Jensen et al., 2003; Furetta, 2003; Pagonis et al., 2006; Chen and Pagonis, 2011; McKeever, 1985) LM-OSL features, in com parison with TL, have received less attention since 1996 (Bulur, 1996, 1999; Bøtter-Jensen et al., 2003; Polymeris et al., 2006, 2008, 2009; Kitis and Pagonis, 2007; Dallas et al., 2008a; Kiyak et al., 2008; Kitis and Pagonis, 2007) This is even more accurate for the case of simulation research; despite the existing literature on TL simulations, there are few articles reporting simulated LM-OSL results (Kitis et al., 2009, 2019; Pagonis et al., 2019) However, the knowledge collected by the com munity as a result of studying the behavior of TL peaks could be effec tively used towards this direction In both cases of bell-shaped luminescence curves, namely TL and LMOSL, the maximum intensity (Im ) and the stimulation position corre sponding to maximum intensity (Tm or tm ) are quite important Due to the use of these parameters, several other geometrical structural char acteristics such as the glow peak’s width at the half of its maximum intensity (ω) are also defined for Peak Shape Methods (PSM) analysis in order to evaluate the kinetic parameter of an isolated glow peak Finally, * Corresponding author Condensed Matter Physics Laboratory, Physics Department, University of Thessaly, GR-35100, Lamia, Greece E-mail addresses: etsoutsoum@uth.gr, e.tsoutsoumanos@inn.demokritos.gr (E Tsoutsoumanos) https://doi.org/10.1016/j.radmeas.2022.106735 Received 27 November 2021; Received in revised form 28 February 2022; Accepted March 2022 Available online March 2022 1350-4487/© 2022 Elsevier Ltd All rights reserved E Tsoutsoumanos et al Radiation Measurements 153 (2022) 106735 these properties are also responsible for the derivation of the analytical expressions that are used for Computerized Glow Curve Deconvolution (CGCD) of complex luminescence glow curves, provided that the su perposition principle is taken into consideration (Kitis and Pagonis, 2007; Kitis et al., 2009; Kitis and Vlachos, 2013; Pagonis, 2021) The dependence of such parameters on experimental settings such as the heating rate and the dose has been a major topic especially for TL glow curves over the last 30 years In the former case, the well-known behavior has led to establishing experimental methodologies to either calculate the activation energy via the method for various heating rates (Hoogenstraaten, 1958) or the thermal quenching efficiency in materials such as quartz (Petrov and Bailiff, 1997) and Al2O3:C (Dallas et al., 2008b) For the latter case, the dependence of the delocalization of a TL glow peak on the radiation dose, but only for second order kinetics, stands as fundamental knowledge in the literature of TL and related applications (Garlick and Gibson, 1948; May and Partridge, 1964; Chen and McKeever, 1997) Nevertheless, experimental verification of shifting of the Tm towards lower temperatures with increasing dose has not been systematically reported in the literature, neither for TL nor LM-OSL curves The lack of shifting is regarded as the ideal experimental indication for the preva lence for first order kinetics in all luminescence phenomena (Chen and McKeever, 1997; McKeever, 1985) Thus, a scientific argument emerges, regarding whether Stimulated Luminescence analysis has a premise only for first order kinetics, which is based on the assumption that no re-trapping occurs in the material, and thus there are no competition phenomena between traps and centers Also, such competition phe nomena have not been undoubtedly verified experimentally, but there are cases where this supposition seems to have a strong basis Otherwise, in well-known and studied cases where first order kinetics applies to the experimental data, the corresponding equations are dominant for describing the phenomenon (lack of shifting) In a previous paper, Kitis et al (2020) have studied the behavior of the Tm as a function of various experimental parameters such as (a) heating rate, (b) dose (trap filling) and (c) trap decay (trap emptying) for a variety of thermoluminescence dosimeters (TLDs hereafter) Regarding this study, three issues become extremely important: (a) this is predominantly an experimental study; (b) the TLDs were purposefully chosen so that the TL signals generate kinetics order spanning from first to second order; and (c) the results revealed that the change of Tm is noticeable as a function of both heating rate and trap emptying None theless, it was difficult to track such a change in relation to the radiation dose (trap filling) The present study follows the work of Kitis et al (2020) but in this case the aim is two-fold, namely (a) the shifting behavior of the delocalization temperature of the TL peak via simula tions using the One Trap – One Recombination center (OTOR) model to be verified; and (b) theoretically such behavior in the case of LM-OSL stimulation to be simulated accordingly In the current case, since the stimulation modalities of TL and LM-OSL are slightly different in terms of structure, as both cases result in similar experimental observation exhibiting a glow peak resemblance, and since they differ greatly as physical phenomena in terms of physical mechanism producing those peaks, studying the effects that cause electron trap filling or trap emptying for both cases will be beneficial Thus, for both cases, specific trap filling as well as trap emptying procedures will be applied band in OTOR are: dn / dt = An ⋅(N − n)⋅nc − n⋅p(t) (2.1) m = n + nc (2.2) dnc / dt = n⋅p(t) − An ⋅(N − n)⋅nc − Am ⋅m⋅nc (2.3) dm / dt = dn/dt + dnc /dt (2.4) I(t) = − dm/dt = Am ⋅m⋅nc (2.5) where N (cm− 3) is the total concentration of electron traps inside the crystal, n (cm− 3) is the concentration of the filled electron traps in the crystal, nc (cm− 3) is the concentration of the free carriers in the con duction band, m (cm− 3) is the concentration of filled recombination centers of the crystal and represents the charge neutrality condition, An (cm3 ⋅ s− 1) is the capture probability of the electron traps and Am (cm3 ⋅ s− 1) is the capture probability of the recombination center, I(t) repre sents the luminescence intensity (a.u.) The term p(t) represents the rate of thermal or optical excitation of trapped electrons, expressed by p(t)TL = s⋅exp[ − E /kb ⋅T(t)] and p(t)LM− OSL = (λ /P)⋅t Since both expressions 2.1 and 2.3 include the term p(t), which describes the stimulation process, there is a unique, single main equation for peak shaped TL and LM-OSL curves; referred to as ‘master equation’ (Kitis et al., 2013, 2019) For TL, E (eV) is the activation energy of the trap, s (s− 1) is the fre quency factor, kb is the Boltzmann constant and T(t) = T0 + β⋅t repre sents the heating function, in which T0 = 273 Κ, β is the constant heating rate for linearly ramping the temperature, while t (s) is time For LM-OSL, λ (s− 1) is the decay constant, P(t) = 1/a⋅I is the total illumination time and represents the time dependence during the LMOSL signal recording The stimulation rate a (1/s) is expressed as a function of the changing rate in light stimulus, where a⋅I is the decaying time-constant of luminescence or more specifically the probability of trapped electrons’ escape at a light intensity I (a.u.) of stimulation Each time I (a.u.) expresses the initial intensity value that forms the possible OSL component (e.g the OSL fast component) if the stimulus was con stant at that point, in this case it resembles the form of Continuous Wave Optically Stimulated Luminescence (CW-OSL) signal (Bulur, 1996) The summation of those components, form the final LM-OSL bell shape curve, where the I (a.u.) linearly ramped up for a specific illumination ăksu, 1999; Pagonis, 2021; Kon time P(t) (Bulur, 1996; Bulur and Go stantinidis et al., 2021) In all cases, all simulation protocols were conducted in Python, with the OTOR model equations being numerically integrated, by importing “odeint” (ordinary differential equation integration), as a part of Scipy, for solving initial-value issues in ordinary differential equations Data visualization was achieved with the help of Matplotlib that creates interactive plots and graphs 2.2 Simulation protocols The four theoretical processes focus on the investigation of maximum intensity position shifting due to various alterations via computer simulations, based on the work of Kitis et al (2020) After a specific (steady) dose, the first procedure (Protocol І) defines the maximum intensity position, Tm , shifting for multiple heating rate values for the case of TL For the case of LM-OSL, the same protocol studies the shift of the tm versus the varying stimulation rate Protocol ІІ depicts the electron trap filling process, which progresses from a low dose until a maximum possible dose according to Table In Protocol III, a signal resetting process was simulated using the Isothermal Decay (ID) method, whereas in Protocol IV, the same signal resetting process was carried out through a simulated CW-OSL measurement In Stimulated Luminescence, the ID method is a well-known approach for measuring the trap’s activation energy It mostly entails Method of analysis 2.1 The differential equations governing the OTOR model In both cases of TL and LM-OSL, their theoretical processes can be described efficiently by the One Trap – One Recombination center (OTOR) model (Randall and Wilkins, 1945; Garlick and Gibson, 1948) A thorough explanation of this model is given by Chen and Pagonis (2011) The differential equations that govern the electron flow between the unique trapping level, the recombination center, and the conduction E Tsoutsoumanos et al Radiation Measurements 153 (2022) 106735 Step 1: Delivering of a Dose Di Step 2: Readout for a specific heating/optical stimulation rate Step 3: Repeat of Steps and for a higher Di Step 4: Recording its highest dose signal as N, and integrated signal as n0 Table Symbols, Units and Values of parameters that are used for the Simulations of OTOR processes Symbol (Units) Value Alterability N (cm− 3) An (cm3 ⋅ s− 1) Am (cm3 ⋅ s− 1) s (s− 1) E (eV) kb (eV/K) ⋅ 1010 ⋅ 109 Constant throughout Constant throughout ⋅ 109 Constant throughout 12 ⋅ 10 8.617 ⋅ 10− 0.5 λ(photons s− 1) β(K/s) α(eV/s) 10 ⋅ 1010 11 Di (electrons) Tiso (K) 12 13 tiso (s) tcwi (s) – – – Protocol III: trap emptying through thermal bleaching (isothermal decay) Step 1: Delivering of maximum dose, integrating and recording its signal as N Step 2: Thermal bleaching through Isothermal decay at a T iso for TL and tiso for LM-OSL Step 3: Readout at rate one point per step in order to obtain the re sidual signal Step 4: Recording of its characteristics, such as integrated signal, n0 , and peak maximum position Step 5: Repeat of steps to for a new higher T iso Constant throughout Constant throughout Constant throughout Constant throughout Constant throughout, except Protocol I; (0.25–20) Constant throughout, except Protocol I; (0.25–20) Constant throughout, except Protocol II; (5 ⋅ 105–1 ⋅ 1010) Only in Protocol III, where ranges (350–385) in TL and remains constant in LM-OSL (352) Only in Protocol III, where ranges (5–175) Only in Protocol IV, where ranges (10–50,000) Protocol IV: trap emptying through optical bleaching (contin uous wave optically stimulated luminescence) Step 1: Delivering of maximum dose, integrating and recording its signal as N Step 2: Optical bleaching through Continuous wave optically stim ulated luminescence for different readouts spans (tcwi ) Step 3: Readout at rate one point per step in order to obtain the re sidual signal Step 4: Recording of its characteristics, such as integrated signal, n0 , and peak maximum position Step 5: Repeat of Steps to for a new higher readout span value tcwi determining the decreasing intensity of light (phosphorescence) emitted by a previously irradiated material while held at a constant temperature higher than the irradiation temperature After that, the form of the decay curve is used to determine the values of several parameters that char acterize the trap engaged in the luminous process (Furetta et al., 2007) In case of TL, when an irradiated sample is kept at a high temperature (T), the isothermal TL signal decays with a temperature-dependent thermal deteriorate constant (λ) The decay constant, in protocol III, is determined by equation (2.6) (Chithambo and Niyonzima, 2014): − λ = s⋅e It is quite important to note that, according to the selected stimula tion parameters, the isothermal decay for the case of the LM-OSL curve takes place at 352 K This temperature can be calculated using equation (2.6) by solving versus Tiso Thus, tiso is not the isothermal decay tem perature; instead, the duration of the isothermal decay In the particular case of OTOR, the ratio R (R = An /Am ) has replaced the kinetic parameter b Shifting of either Tm or tm is anticipated mainly for the case of second order kinetics, in which the values of An and Am were selected so that R = (2.6) E k⋅Tiso Here s (s− 1) is the frequency factor, E (eV) is the activation energy, and the Tiso is a selected temperature position for decaying For the case of LM-OSL tiso corresponds to the time duration in which decaying Tiso applied The CW-OSL is the most conventional method for measuring opti cally stimulated luminescence by recording the prompt light emission during a constant light-intensity stimulation In this case the OSL signal decays with time (Bulur and Gă oksu, 1999) Pagonis et al (2019) used Monte Carlo methods in OTOR in order to simulate Stimulated Luminescence phenomena In their work they numerically integrated the differential equations using the term p(t), which represents the rate of thermal or optical excitation of trapped electrons, as described by equation (2.7): p(t)CW− OSL = σ⋅I(t) 2.3 Selection of the appropriate simulation parameters As the main effect that was simulated is either the trap filling or the trap emptying, it is quite convenient to use the trap occupancy as the simulation parameter Using the parameters of Table 1, the occupancy and thus the radiation dose are expressed by the ratio n0 ∕N, representing the filling degree of either the trap responsible for a TL glow peak or an LM-OSL component Here the term N represents the total concentration of electron traps inside the crystal and n0 is the integrated signal after filling or emptying For Protocol II, the dose increases in various steps; thus, the ratio n0 ∕N is increasing up to the maximum saturation n0 ∕N = On the other hand, in Protocols III and IV, as trap emptying takes place from an initial saturated state, the value of this ratio decreases Specifically, in Protocol III the varying value is Tiso in which the isothermal TL takes place, while in Protocol IV it is tcwi ; the duration of CW-OSL that is measured before either TL or LM-OSL Nevertheless, as both isothermal decay and bleaching result in decreasing the trap oc cupancy, the value of n0 ∕N is also presented in Table The simulation parameters in each protocol are presented as bold and italics at the same time (2.7) where σ (cm2), represents the optical cross section and I(t) the lumi nescence intensity (a.u.) (Equation (2.5)) Since λ = σ⋅ I(t), the value of the λ parameter was determined to be 0.5 s− as a preset value in order to avoid excessive calculations that could postpone the simulation re sults in terms of duration (Konstantinidis et al., 2021) The protocols were conformed accordingly for TL and LM-OSL and are the following: Protocol I: increase of heating/stimulation rate (β/a) Step 1: Delivering of a Dose Di Step 2: Readout for specific β for TL and specific a for LM-OSL Step 3: Repeat of Steps and for new β or a Results and discussion Protocol II: trap filling by increasing the dose The luminescence curves resulting from the simulation processes are E Tsoutsoumanos et al Radiation Measurements 153 (2022) 106735 Table Dose, maximum peak position, isothermal decay temperature and time, CW-OSL duration and trap occupancy in Protocols II, III and IV for TL and LM-OSL Protocol II Di , electrons 5⋅ 105 1⋅ 106 5⋅ 106 1⋅ 107 5⋅ 107 1⋅ 108 5⋅ 108 1⋅ 109 5⋅ 109 1⋅ 1010 Protocol III TL LM-OSL Protocol IV TL LM-OSL tcwi , s Tm , K n0 /N tm , s n0 /N Tiso , K Tm , K n0 /N tiso , s tm , s n0 /N 499 487 461 450 429 420 393 373 368 368 0.00005 0.0001 0.0005 0.001 0.005 0.01 0.05 0.1 0.5 1363 1363 621 441 198 198 63 45 45 18 0.00005 0.0001 0.0005 0.001 0.005 0.01 0.05 0.1 0.5 350 355 360 365 370 375 380 385 – 389 390 390 391 392 394 396 398 401 – 1.000 0.935 0.901 0.847 0.775 0.694 0.599 0.498 0.398 – 15 25 50 75 100 125 150 175 180 204 246 288 360 426 481 529 577 619 1.000 0.379 0.254 0.191 0.116 0.083 0.064 0.052 0.043 0.037 shown in Fig The shift of Tm in TL is shown in plots a, c, e and g whereas the shift of tm in LM-OSL is shown in plots b, d, f and h Moreover, the shift of Tm or tm versus the trap occupancy are presented in plots c, e, g and d, f, h respectively; plots c and d correspond to trap filling, while the rest to trap emptying Finally, plots a and b indicate the shift of Tm and tm respectively as a function of parameters that describe the stimulation moduli It is evident that for higher heating and optical stimulation rates, the intensity (TL and OSL) decreases, and the glow curves shift towards higher temperature and time values respectively Simulation describes very effectively the shift of the maximum position as both β and α increase 10 50 100 500 1000 5000 10,000 30,000 50,000 TL LM-OSL Tm , K n0 /N tm , s n0 /N 389 389 391 392 401 407 426 435 451 458 1.000 0.971 0.862 0.763 0.388 0.239 0.058 0.029 0.009 0.005 180 180 190 200 290 360 731 1012 1743 2244 1.000 0.498 0.442 0.388 0.195 0.120 0.028 0.014 0.004 0.002 Protocols III and IV respectively In all processes, before the emptying stages were initiated, the system was stimulated by the maximum dose (Di = ⋅1010 ) and n0 /N was equal to unity due to saturation In Protocol III, Fig 1e, after defining the Tm in saturation state, all the parameters remained constant except for the Tiso , which varies from 350 up to 385 K, in which the Im is observed (Table 2) Before every readout, an ID step with a duration of 30 s interpolated, in steps of K, followed by a residual measurement with Tm varied from 389.5 K to 401.2 K (ΔT = 11.7 K) For the LM-OSL simulation (Fig 1f), the Tiso , and by extension λ, is stable while the tiso value was set to vary from to 175 s (up to Im) Finally, similarly to TL, tm varied from 180.2 s to 619.2 s (Δt = 439 s), meaning that tiso reaches the tm of the saturation state In Protocol IV, Fig 1g & h, all the parameters remained constant except the tcwi value (CW-OSL stimulation duration) which varied from to 50,000 s In TL, as the CW-OSL duration sequentially increased Tm increased from 389.5 K to 458.8 K, meaning a shift of 69.3 K (ΔT = 69.3 K)) In LM-OSL, as the CW-OSL duration sequentially increased, tm increased from 180.2 s to 2244.5 s In this case, the shift was increased by 2064.3 s (Δt = 2064.3 s), while the total stimulation time of the LMOSL readout remained constant at 3000 s Regarding all the cases of trap emptying, Im decreased, while Tm and tm shifted to higher values It should be underlined that, regardless of the phenomena that occur during the trap filling, at the end of the irradia tion there will be a certain number of traps filled with n0 electrons, and no leaping motions will occur after that point, in that case the system falls into a pseudo-equilibrium state Thus, it can be assumed that n0 corresponds to the unbleached luminescence integral of N number of traps (n0 = N) During thermal or optical bleaching, a part of those trapped electrons (n01 ) will escape, leaving several traps (N1 ) empty in the crystal lattice Upon further electron stimulation (thermal or optical) a higher number of empty traps (N − N1 ) will increase the probability of re-trapping, which is responsible for the Tm and tm shift towards higher values The overall results of trap emptying protocols (Protocol III and IV) agree with the trap emptying theory described above and can also be seen in Table 2, which includes the maximum peak position and trap occupancy changes as the simulation parameters vary in each step (Kitis et al., 2020) 3.1 Shifting results in trap filling An interesting behavior of these shifts is presented in Fig 1c and d, where Tm & tm are presented as a function of trap filling Initially for both cases a small dose of electrons Di = 5⋅105 was delivered to the system representing a tiny fraction of the maximum trap occupancy (n0 / N = 0.00005) In the case of TL, the Tm was at 499.5 K and as the dose proportionally increased to the point where the number of electrons were equal to the number of available traps (Di = N = 1⋅ 1010 ), the Im occurred at 368.2 K, meaning that for an initial low dose until the state of saturation (Table 2), the Tm shifted 131.3 K lower (ΔT = − 131.3 K) For the lowest dose of LM-OSL, the tm was at 1363.4 s As the dose increased to the state of saturation the shift of tm was much greater, in contrast with TL, as tm occurred at 18 s Specifically the duration where the peak reaches its Im was decreased by 1345.4 s It should also be mentioned that the total duration of simulation process remained con stant in all cases at 3000s Regarding the case of trap filling, the Tm and tm decrease as the dose sequentially rises is caused by the fact, that at low doses, where n0 ≪ N, the chance of retrapping almost entirely depends on the number of accessible traps in the crystal lattice This implies that the released trapped electrons are leaping between the conduction band and the available empty traps, leaving an insufficient number of electrons for recombination As a result, electrons not spend enough time in the conduction band to find a recombination pathway, which probability can increase with the number of electrons in the conduction band This phenomenon is responsible for the cause of Tm & tm to appear at higher values However, as the dose increases to the state of saturation (n0 → N), the re-trapping reduces and recombination probability increases causing a shift to lower Tm & tm values The simulation results of trap filling protocol (Protocol II) can be seen in Table and are in agreement with the trap filling theory described above (Kitis et al., 2020) 3.3 The appropriate representation As it was already mentioned in Section 2.3, the trap occupancy is expressed through the ratio n0 /N representing the filling degree and is plotted versus the heating (β) and stimulation (α) rate However, ac cording to Kitis et al (2020) the trap occupancy derived using the analytical equation of general order kinetics model (GOK) and the total pre-exponential factor is also affected in the same way, but in the opposite direction Specifically, when α and β rise, both Tm and tm in crease, while n0 /N decreases Due to this polarity, plotting the presen tation as a function of trap occupancy and stimulation rate on the same 3.2 Shifting results in trap emptying There is a shift of Tm and tm as functions of trap emptying via thermal bleaching (Fig 1e and f) and via optical bleaching (Fig 1g and h) in E Tsoutsoumanos et al Radiation Measurements 153 (2022) 106735 Fig Graphical representation of simulation protocols I - IV for TL (a, c, e and g) and LM-OSL (b, d, f, h) All simulation parameters were kept constant except for the heating rate (a), stimulation rate (b), dose (c & d), Tiso / tiso (e & f) and tcw (g & h) For the exact value of each parameter in each protocol, the readers could refer to Table E Tsoutsoumanos et al Radiation Measurements 153 (2022) 106735 x-axis is difficult and impractical So, by using the inverse expression of trap occupancy, N/n0 , one can avoid this polarity in terms of presenta tion and also acquire ascending plots for better comprehension of the results It is important to note that the attributed dose in saturation stage is equal to unity and it is expressed as N/n0 = In Fig 2, the parameters Tm , tm are given as a function of either corresponding rate β or α, as well as ordinary and inverse trap occupancy (n0 /N, N/n0 ) respectively, in order to emphasize the aforementioned polarity and the plots represent findings from theoretical glow peaks produced using Eq (2.1) - (2.5) for second order kinetics (R = An / Am = 1) In Figs and 3, the heating/stimulation parameters were regarded as mathematical variables rather than physical, allowing to take on a wide range of values Іt should be noted that, according to instrumental limitations of commercial luminescence readers in experimental pro cedures the heating rate applied is practically restricted within values ranging between 0.1 and 20 ◦ C/s Also, for higher rates, readers exhibit phenomena of fluctuations in signal recording due to instrumental concerns, something that in simulations is prevented due to their mathematical nature In the left plots of Figs and 3, when the x-axis is converted to logarithmic, the figures’ two branches regarding the behavior of peak maximum position become mirrored resulting to those presented at the right plots (Figs and – right plots) This leads to the conclusion that the common representation depicting the shift of Tm , tm as function of both β and a, are not practical at all Also, the representation of Tm and tm shifting in respect to different values of the parameter R is of high importance; these are reproduced by varying ratios of the values An and Am in order to get values ranging between (second order kinetics) and 10− (roughly first order ki netics) It is interesting that for a given stimulation rate, the peak maximum position shifting depends on the kinetic parameter and consequently the re-trapping ratio Shifting in TL and LM-OSL is more intense in the case when re-trapping and recombination are both probable Nevertheless, for the LM-OSL, infinitesimal shift takes place for the value of tm for the case of negligible re-trapping Fig shows the theoretical results concerning the cases of all pro tocols, in which curve (a), according to Protocol I, represents the shift of maximum temperature and time value (Tm & tm ) versus the heating or stimulation rate At the same time, curve (b) depicts the change in Tm & tm versus the dose, as measured by Protocol II in the framework of the trap filling procedure Curve (c) represents the change in Tm & tm versus the trap occupancy as a result of using Protocol III in trap emptying with thermal bleaching, while curve (d) represents the shift of Tm & tm versus the trap occupancy based on Protocol IV, trap emptying with optical bleaching In all protocol processes regarding both TL and LM-OSL, the assumption that the phenomenological models lead to a single glow peak are predicated on the premise that the electron traps (N) are preexisting in the material and are simply filled during irradiation Furthermore, it is implied that there are no traps created during the irradiation Conclusions In the present study, the maximum temperature (Tm ) and time (tm ) of each glow curve for the case of TL and LM-OSL peaks were investigated and compared theoretically; specifically, as functions of heating/stim ulation rate, of dose, thermal bleaching, and optical bleaching In the first Protocol, it was observed that Tm and tm shift to higher values as the heating/optical stimulation rate increases Also, Protocol II shows that Tm and tm shift to lower temperature and time values as the dose increases Based on Protocol III, Tm and tm shift to higher temper ature and time values as Step (Thermal emptying) reaches the recor ded maximum positions Tm and tm of saturation of Step The last Protocol shows that Tm and tm shift to higher values as in Step (Optical emptying) the readout time spans tcwi extend to higher time values As the LM-OSL signal is used as a basic tool for the understanding the OSL recombination mechanisms, identification of individual OSL com ponents in experimental cases becomes quite important in processes of signal characterization LM-OSL components shifted at higher tm values could possibly enable deconvolution analysis with better resolution, when it comes to materials with luminescence described by the second order kinetics However, this change is not a favorable aspect from a dosimetric standpoint, as it is accompanied with a significant reduction in luminous intensity Additionally, it should be mentioned that the shift of Tm and tm as a function of trap emptying (Protocols III and IV) in TL and LM-OSL is proven, according to simulations, to follow similar behavior as the shift of Tm and tm in Protocol I, as they shift for higher heating and optical stimulation rates to higher values Concluding, when performing signal analysis due to better resolu tion, selecting the LM-OSL experimental conditions to favor the shifting of tm to higher values is strongly advised; although in those cases this aspect is not consider favorable due to light intensity reduction, it would be appealing for future dosimetric applications Declaration of competing interest The authors declare that they have no known competing financial Fig Tm versus the heating rate β (left plot) and versus the stimulation rate α (right plot), both expressed through trap occupancy (n0/N ) and inversed trap occupancy (N/n0) E Tsoutsoumanos et al Radiation Measurements 153 (2022) 106735 Fig Tm versus the heating rate β (left plot) and versus the stimulation rate α (right plot), both expressed through trap occupancy ( n0/N) and inversed trap occupancy (N/n0) and the x-axis on a logarithmic scale Fig Peak maximum position Tmversus the heating rate β, insert plot presents at detail Protocol III (left plot) and tm versus the stimulation rate α (right plot), alongside the inversed trap occupancy (N/n0) interests or personal relationships that could have appeared to influence the work reported in this paper Furetta, C., 2003 Handbook of Thermoluminescence World Scientific https://doi.org/ 10.1142/5167 Furetta, C., Marcazz´ o, J., Santiago, M., Caselli, E., 2007 Isothermal decay method for analysis 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Phosphorescence and electron traps II The interpretation of long-period phosphorescence Proc Math Phys Eng Sci 184 (999), 390–407 ... plotting the presen tation as a function of trap occupancy and stimulation rate on the same 3.2 Shifting results in trap emptying There is a shift of Tm and tm as functions of trap emptying via thermal... 0.037 shown in Fig The shift of Tm in TL is shown in plots a, c, e and g whereas the shift of tm in LM-OSL is shown in plots b, d, f and h Moreover, the shift of Tm or tm versus the trap occupancy... underlined that, regardless of the phenomena that occur during the trap filling, at the end of the irradia tion there will be a certain number of traps filled with n0 electrons, and no leaping