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Quartz Optically Stimulated Luminescence Configurational Coordinate Model
Journal Pre-proof Quartz Optically Stimulated Luminescence Configurational Coordinate Model Owen M. Williams, Nigel A. Spooner PII:
S1350-4487(20)30023-8
DOI:
https://doi.org/10.1016/j.radmeas.2020.106259
Reference:
RM 106259
To appear in:
Radiation Measurements
Received Date: 19 August 2019 Revised Date:
21 January 2020
Accepted Date: 1 February 2020
Please cite this article as: Williams, O.M., Spooner, N.A., Quartz Optically Stimulated Luminescence Configurational Coordinate Model, Radiation Measurements, https://doi.org/10.1016/ j.radmeas.2020.106259. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Crown Copyright © 2020 Published by Elsevier Ltd. All rights reserved.
Quartz Optically Stimulated Luminescence Configurational Coordinate Model Owen M. Williams1 and Nigel A. Spooner1, 2 Abstract In a recent study using pulsed stimulation we revealed that optically stimulated luminescence (OSL) and photo-transferred thermoluminescence (PTTL) in quartz are characterised by a common pulse response. We interpreted this result as indicating that both emissions are governed by the same detrapping mechanisms. In the present study we develop a common configurational coordinate model to describe the mechanisms. Within our model we identify the energy associated with the thermal assistance effect as the vibrational energy of the ground state of the dimer that represents the trap. Further, we model the OSL stimulation process as an optical transition between a vibrationally-excited ground state level and a dimer excited state. By introducing additional luminescence parameters, we reveal that the processes that underlie thermal quenching and the room temperature OSL response to pulsed stimulation can be represented by competing modes which empty the excited state. In particular, we find that the room temperature pulse response can be modelled in terms of an optical transition from the excited state to a lower antibonding level from which a hole is ejected. In contrast, thermal quenching is explained by excited state vibrational dissociation at large dimer component separations.
1. Institute of Photonics and Advanced Sensing, School of Physical Sciences, University of Adelaide, Adelaide, Australia 5005 2. Weapons and Combat Systems Division, Defence Science and Technology Group, P.O. Box 1500, Edinburgh, Australia 5111 1
2
1. Introduction In a series of recent studies (Williams and Spooner, 2018, Williams et. al, 2018, Spooner et. al., 2019), we have shown that the defect pair model introduced by Itoh et al. (2001, 2002) to explain the mechanisms associated with quartz luminescence can be extended. In particular, we attributed the 160 ºC and 220 ºC intermediate temperature thermoluminescence bands to the same electron/hole recombination reaction pair as that associated with the 110 ºC predose band. Further, we applied the model to explain the series of steps observed when long OSL shines are plotted on a log/log scale.
In this paper we employ the defect pair model to investigate several well-known quartz OSL phenomena. Our analysis is based on data from our recent experimental study (Spooner et al., 2019). There, we presented an extensive set of pulsed OSL measurements covering a number of South Australian quartzes measured across a wide temperature range. Notably, we found that the OSL and photo-transferred thermoluminescence (PTTL) contributions could be separated and revealed that each was characterised by the same temporal response. This outcome was somewhat unexpected since, according to the defect pair model, the luminescence centre reactions are quite different. We therefore were led to the conclusion that the slow processes governing the temporal response occur at the trap, and further, that the processes are common to OSL and PTTL.
The above conclusion represents a departure from previous OSL studies; in particular, in relation to the subject of thermal quenching (Bailiff, 2000, Galloway, 2002a, 2002b, Bailiff and Mikhailik, 2003, Denby et al., 2006, Chithambo, 2007, Pagonis et. al., 2010, 2011, Chithambo et al., 2016). Within the associated mechanisms studies (see, for example, Pagonis et al., 2010, 2011, Chithambo et al., 2016), it has commonly been assumed that thermal quenching occurs at the luminescence
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centre and is governed by the Mott-Seitz mechanism (Mott, 1938, Seitz, 1938, Gurney and Mott, 1939). It is this subject that defines the theme of the present study.
In Section 2 we review the Mott-Seitz mechanism and its adaption for use in the luminescence field before turning our attention to the defect pair model. There, we reveal that solution of an OSLspecific rate equation leads to the same analytical outcome as that of the Mott-Seitz mechanism. In order to identify the underlying reasons we proceed towards the development of an appropriate configurational coordinate model. Within Section 3 we initially review the thermal assistance energy identified by Spooner (1994) and introduce a new configurational framework within which we argue that the OSL stimulating photon drives an optical transition between the ground state and an excited state. Within this framework we show that thermal assistance is necessarily required in order to ensure that the OSL stimulating photon can successfully effect the transition.
In Section 4, we introduce additional information from the quartz luminescence literature and utilise it to extend the geometrical coverage of the configurational coordinate diagram towards greater separation of the dimer components. We find that the processes that govern both the room temperature pulse time constant and the thermal quenching effect can be linked through their joint contributions in emptying an excited state potential well. The net result is that the OSL pulse response at room temperatures can be associated with an optical transition to a lower antibonding state from which a hole is ejected and the thermal quenching effect with vibrational dissociation of the excited state dimer. We show further that the same type of configurational framework can be applied to account for the presence of the faint long-lived pulse component we identified earlier (Spooner et al., 2019).
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2. OSL models 2.1 Mott-Seitz mechanism The Mott-Seitz mechanism was proposed independently by prominent researchers Mott (1938) and Seitz (1938) for explaining observations that the efficiency of phosphors fell with rising temperature. The advances are best explained in the subsequent Gurney and Mott (1939) paper. In Fig. 1 we have sketched the configurational coordinate diagram associated with the Mott-Seitz mechanism.
Fig. 1: Sketch of original Mott-Seitz mechanism [after Seitz (1938) and Gurney and Mott (1939)].
The widths of the adiabatic potential energy curves reflect the property that the excited state is characterised by lower vibrational frequencies than those in the more tightly bound ground state, to the extent that at wide separations the ground and excited state curves approach each other. Crossing states are not allowed (Seitz, 1938) and hence the two curves assume the distorted nonoverlapping forms sketched in Fig. 1. The excited state population can decay by optical emission and by a crossover mechanism which occurs at high vibrational levels, the latter process being followed by thermal relaxation towards the lower vibrational levels of the ground state.
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Within the standard Mott-Seitz model, the relevant decay paths are spontaneous emission, phononassisted vibronic transitions and the crossover effect, the latter occurring at the excited state energy E, as is illustrated in Fig. 1. [Refer to Krbetschek et. al, 1997.] Following Akselrod et al. (1998), the overall transition probability Γ can be expressed as
hω Γ = Γ 0 + p coth kT
E − kT +ν e .
(1)
Here, Γ0 is the optical transition probability, p is a temperature-independent multiplier, h and k are the reduced Planck constant and the Boltzmann constant respectively, T is the absolute temperature,
ω is the phonon vibrational frequency, E is the well depth and ν is the associated frequency factor. In following Akselrod et al. (1998) by assuming that the vibronic transitions can be neglected, eqn (1) can be reformulated as
τ=
τ0
−E 1 +ντ 0 exp kT
.
(2)
This result (within which the time constants τ = 1/Γ and τ0 = 1/ Γ0 are defined in normal manner) is the standard analytical expression that describes the Mott-Seitz mechanism. As is well-known, the temperature dependence displayed in the eqn (2) denominator is the same as that which determines the OSL thermal quenching effect in quartz (Chithambo, 2007, Spooner et al., 2019). Accordingly, in spite of the fact that OSL and phosphorescence represent different phenomena, the Mott-Seitz mechanism has been adopted widely within the OSL literature. [Refer, for example, to Pagonis et al., 2010, 2011, Chithambo et al., 2016.] In each case, a Mott-Seitz type of configurational coordinate diagram has been invoked to predict the thermal quenching effect.
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A difficulty appeared, however, when Pagonis et al. (2010) attempted to replicate the known timeresolved OSL observations within the structure of the Bailey (2001) energy band model. Within their simulations they found a relaxation time of the order of 0.1 s, more than three orders of magnitude larger than the well-known ~40 µs pulsed OSL room temperature time constant (Chithambo, 2007, Chithambo et al., 2016, Spooner et al., 2019). Pagonis et al. (2010) also noted that the thermal quenching effect was not predicted within the Bailey model. Although these problems have been known for some time, we are not aware that they have been satisfactorily resolved. More recently another dilemma has become apparent. As part of our recent pulsed OSL study (Spooner et al., 2019), we reported on the presence of several faint OSL pulse components, the strongest of which we characterised by the significantly longer room temperature time constant of 1.60 ± 0.02 ms. This component also displayed a thermal quenching effect. The presence of the faint components suggests that separate Mott-Seitz mechanisms need to be applied. If this is true, each of the relevant configurational coordinate diagrams must then involve the same type of crossover as that we have sketched in Fig. 1. Such an outcome would appear to be somewhat of a coincidence.
In view of the above problems, it appears that the models used to explain OSL need revision. In the case of the energy band model, perhaps it needs to be further developed to enable satisfactory pulsed OSL predictions. In the case of the Mott-Seitz model, perhaps the problem lies with the adoption of a mechanism that was originally designed to account for phosphorescence.
It is the latter problem that defines our present theme. Accordingly, within Sections 3 and 4 below we develop a case that shows that the Mott-Seitz model can be replaced by an OSL-specific configurational framework. Moreover, we show that the replacement leads not only to an alternative derivation of the eqn (2) thermal quenching relationship but also to physical justification 7
for the presence of both the room temperature time constant and the processes that underpin both thermal assistance (Spooner, 1994) and thermal quenching. Further, we show that the difference between the rise and fall time constants we reported within our pulsed OSL study (Spooner et al., 2019) can be explained if we reinstate the coth function term in eqn (1). It is to these subjects that we now turn.
2.2 Quartz defect pair model
Within our earlier studies (Williams and Spooner, 2018, Williams et al., 2018, Spooner et al., 2019) we described how the defect pair model of Itoh et al. (2001, 2002) can be applied successfully to explain a number of features of both thermoluminescence and OSL. As its name suggests, the defect pair model is based on the generation of defect pairs during an ionising radiation event.
Aluminium is a significant quartz impurity. As is well-known, when aluminium is incorporated within the quartz structure, the Al3+ ions that displace Si4+ ions are accompanied by interstitial protons or alkali ions, thus ensuring that local charge balance is preserved. [Refer, for example, to Haliburton et al., 1981.] H+, Li+ and Na+ are common charge-compensating interstitial impurities. Within their landmark paper, Itoh et al. (2002) explained that while the main charge carriers generated by β or γ ionising radiation are electron/hole pairs, the ionisation also results in the release of the interstitial ions into the quartz c-channel; viz.,
[AlO−4 / M+ ]0 → AlO−4 + M+.
(3)
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−
The tetrahedral AlO4 defect group is located within the quartz c-channel wall and M+ represents the cation (e.g., H+, Li+ and Na+) that is released. The cation migrates along the c-channel until it is trapped by one or another of several types of defects X within the wall structure; viz.,
XO4 + M+ → [XO4/M+ ]+.
(4)
Here, we choose XO4 to generically label the defect tetrahedron of interest. We note that the present study holds regardless of the identification of X. The latter is still open to debate. Vaccaro et al. (2017) have provided interesting measurements that suggest that X is Ge. However, as we have discussed earlier (Williams and Spooner, 2018), the higher concentration Ti option has yet to be eliminated.
In the specific OSL case of interest here, Itoh et al. (2002) proposed that when the stimulating photon is absorbed, a hole is ejected from the defect site at which the displaced M+ was trapped; viz.,
[XO4/M+ ]+ + hν → [XO4/M+ ]+* → [XO4−/M+ ]0 + h+.
(5)
The hole migrates by hopping along the c-channel wall. If and when it reaches the site of the −
uncompensated AlO4 reaction (3) product, OSL is emitted via the association reaction
AlO−4 + h+ → [AlO−4 / h+ ]0 + photon (365 nm band).
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(6)
A complementary reaction sequence also can occur. This arises since the reaction (5) dimer product is thermally unstable (Itoh et al., 2002). After a temperature-dependent period, the dimer reverts into its more stable positively-charged form by releasing an electron. The latter migrates, also by hopping along the c-channel wall, allowing electron/hole recombination to subsequently occur if and when the electron reaches the location of the reaction (6) product. In this case a midtemperature band thermoluminescent photon is released; viz.,
[AlO−4 / h + ]0 + e − → AlO−4 + photon (110, 160 or 220 o C TL band emission),
(7)
where the respective bands are centred on 380, 394 and 408 nm (Williams and Spooner, 2018). Since the reaction sequence (5) to (7) is optically-driven, the emission is commonly termed phototransferred thermoluminescence or PTTL. [Refer, for example, to Chithambo et al. (2019).]
Although all processes occurring at the aluminium luminescence centre lie within our interest, it is the optical stimulation process (5) that we wish to investigate here. We note there that we have highlighted the presence of an excited defect state. Within Sections 3 and 4 below we reveal the significant role that this state plays in providing the essential links amongst the separate processes that govern the overall hole untrapping mechanism.
It is convenient at this point to recall our earlier observation that OSL and PTTL display the same temporal responses to pulsed stimulation (Spooner et al., 2019). As seen above, the OSL and PTTL luminescence centre reactions (6) and (7) are quite different. As such, we would expect that they would be characterised by different reaction speeds. However, we see no such difference. On logical grounds, then, we are obliged to accept that both reactions are fast compared to the speed of
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the optical stimulation process, reaction (5). In effect, the only logical explanation is that the pulse responses we record are instead governed by slower processes that occur at the hole trap.
In order to provide consistency with eqn (2), it is not difficult to formulate an appropriate rate equation; viz., the population of the reaction (5) excited defect state needs to be governed by
− ta − d [XO 4 /M + ]+* = k 0 e kT [XO 4 /M + ]+ Φ (t ) − Γ 0 [XO 4 /M + ]+ * − ν [XO 4 /M + ]+ * e dt E
E well kT
(8)
Here, T is the absolute temperature and k is the Boltzmann constant in eV/K, while the specific parameters are as follows: k0 is a rate constant, Eta is the energy that governs the strength of the thermal assistance process, [XO4/M+]+ is the population of the ground state dimer, Φ(t) represents the stimulating photon flux, Γ0 = 1/τ0 is a transition probability, Ewell is the depth of a potential well and ν is the associated frequency factor.
Within (8), we see that the rate at which the population changes is governed by three processes: an optical stimulation rate (which is influenced by the amount of thermal assistance), a temperatureindependent decay rate and a third term which accounts for thermal quenching. We justify the inclusion of each of these terms within Sections 3 and 4 below. We note in passing that, for the time being, we have chosen to neglect any possible vibronic contribution (Di Bartolo, 2010). We relax this assumption in Section 4.2 below. We note further that in formulating eqn (8) it is implied that all processes occur at the [XO4/M+]+ site.
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.
Eqn (8) may readily be solved in order to generate the common OSL and PTTL pulse response. In the special case where the optical stimulus Φ(t) = Φ0 is applied suddenly, the rate at which the population of [XO4/M+]+* grows can be derived simply as
E − ta e kT [XO 4 /M + ]+* ( t ) = k0 [XO 4 /M + ]+ Φ 0 τ 0 Ewell 1 + ντ e − kT 0
− t /τ 1 − e ,
(9)
where the time constant τ is determined by the temperature-dependent equation
τ=
τ0 E 1 +ντ 0 exp − well kT
.
(10)
Eqn (10) is clearly interesting in that it displays the same analytical form as the Mott-Seitz equation (2). The latter has now been derived within the OSL context. This leads us towards our next step; namely, the development of a model which enables the application of eqn (8) to be justified.
3. Thermal assistance in quartz
3.1 Spectral and temperature dependencies
We recall the results from the quartz OSL spectral study by Spooner (1994), within which the existence of a thermal assistance effect was revealed and its spectral characteristics were quantified. In that study a wide range of sample temperatures was investigated and in each case the OSL level 12
was recorded at the start of each shine, covering optical stimulation from a number of different narrowband spectral sources. Details are described by Spooner (1994).
For convenience, in Fig. 2 we present interpolated data we have extracted from the Spooner study. We see that the luminescence rises steeply from low temperatures before falling at higher temperatures. Spooner (1994) invoked the term “thermal assistance” to describe the rise while the fall is characteristic of the thermal quenching process. [For the latter, refer, for example, to Bailey, 2001, Chithambo, 2007, Pagonis et al., 2010, Chithambo et al., 2016, Spooner et al., 2019.]
Fig. 2: Sampled replica of the Spooner (1994) spectral luminescence data; quartz from Deaf Adder gorge, northern Australia. The data are not normalised. Best fits to the bracketed factor within eqn (9).
As seen in Fig. 2, the spectral data can readily be fitted by application of the bracketed temperaturedependent factor that appears within eqn (9) above. Within our fitting procedure, it has been convenient to adopt the rounded value τ0 = 40 µs to represent the room temperature time constant (Spooner et al., 2019). The remaining fitting parameters are the thermal assistance energy Eta, the 13
well depth Ewell, the frequency factor ν and the overall amplitude. Although according to eqn (9) the amplitude should be constant, we were only able to achieve satisfactory fits by allowing its value to vary. This reflects the fact that the original spectral data recorded by Spooner (1994) were not normalised.
We note also that although our fitting procedure yielded global values for Ewell and ν, both parameters displayed significant scatter. Accordingly, we instead relied on the higher precision values of Ewell = 0.694 ± 0.004 eV and ν = (9.6 ± 0.8) × 1011 s-1 that we extracted from our recent pulsed OSL study (Spooner et al., 2019).
More significantly, we confirm the earlier Spooner (1994) finding that thermal assistance energy is spectrally dependent; that is, Eta = Eta (λ). We summarise our results in Fig. 3 where it is seen that less thermal assistance is required as the energy of the stimulating photons is increased; that is, at lower optical stimulation wavelengths. This result is clearly consistent with the smaller values assumed by the Boltzmann numerator seen within eqn (9).
Fig. 3: Thermal assistance energies derived from Fig. 2 curve fitting. Note the small measurement scatter. Refer to Section 3.3 for justification of the dashed extrapolation.
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We note further that within Fig 3 we have fitted the thermal assistance energy data to a quadratic curve. We justify the extrapolation shown there within Section 3.3 below.
3.2 Optical stimulation configurational coordinate diagram
The presence of the Boltzmann numerator within eqn (9) is interesting since it suggests that it may be possible to represent the optical stimulation process in a more physically insightful manner. In particular, we are interested in examining the implications within a configurational coordinate model framework; that is, within a structure where the ground and excited state potential energy curves that characterise the [XO4/M+]+ dimer are presented in terms of the separation of the dimer components.
We have previously used configurational coordinate diagrams to explain the spectral variations that characterise the 110 ºC, 160 ºC and 220 ºC thermoluminescence bands in quartz (Williams and Spooner, 2018). In particular, within that study we highlighted the relevance of the earlier densityfunctional theory calculation by Magagnini et al. (1999). In that, it was revealed that three different antibonding impurity states can be occupied when a hole is trapped to form the compensated aluminium defect complex [AlO4¯/h+]0. We note that this complex appears within the OSL and PTTL luminescence centre reactions (6) and (7) above. By representing the Magagnini et al. (1999) information within a configurational framework, we were then able to predict the presence of the three mid-temperature thermoluminescence bands.
The use of configurational coordinate diagrams to represent the energy states of diatomic molecules such as oxygen (Morrill et al., 1998) and nitrogen (Heays, 2010) is well-known. In such cases,
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thermal energy is equivalent to vibrational and rotational energy. Since a configurational framework is appropriate to any dimer species it is useful to explore its application here. As a first step in constructing an appropriate diagram, we presume that thermal assistance energy can similarly be represented, in this case by the ground state vibrational energy of the radiation-induced dimer [XO4/M+]+. Consistent with the detrapping reaction (5) above, this is the trap from which the hole that carries the exiting charge is released.
In supporting this representation, we note that a large number of potential energy curves exist in the case of diatomic molecules, some of which represent bonding states and others antibonding states. Analytically, the bonding states can be approximated by various functions such as a Lennard-Jones 6-12 potential or a Morse potential (Wikipedia, referenced below). It is convenient here to apply the Morse potential since this can be described by a simple analytic equation; namely,
− a d −d V (d ) = Edissoc 1 − e ( min ) 2.
(11)
Here, V(d) is the potential energy at separation d of the XO4 and X+ dimer components, V(d) = 0 when d = dmin , a is a constant the determines the width of the Morse potential curve and Edissoc is the dissociation energy, the value towards which V(d) tends at large values of d.
At this point in our analytical development we pause to emphasise that our primary objective here is to seek improved physical insights into the processes that govern OSL in quartz; that is, we are not at this point seeking precise quantitative representations. Given this caveat, we proceed in Fig. 4 to show how the Morse potential can be applied in order to guide our construction process.
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Fig. 4: Representative optical stimulation configurational coordinate diagram (c-channel only)
As we have proposed, thermal assistance energy can be represented as being synonymous with ground state vibrational energy. Within our Fig. 4 construction we have also introduced a second proposal; namely, that the OSL stimulation process is driven by an optical transition between the ground state of the [XO4/M+]+ dimer and the excited state that we introduced earlier within the optical stimulation reaction (5). In constructing the potential energy curve that characterises the excited state we have utilised the Fig. 3 thermal assistance data at each of the seven Spooner (1994) stimulation wavelengths. As part of this process we have appropriately adjusted the values assumed by the horizontal separation parameter in such a way that a smooth continuous excited state curve is generated.
As can be seen from the Fig. 4 construction, the overall energy of the excited state then equals the sum of the thermal assistance energy (i.e., the ground state vibrational energy) and the energy Eq = hc/λ carried by the stimulating photon. In effect, then, at each stimulating wavelength a precise amount of ground state vibrational energy Eta (λ) must be made available in order to allow the 17
optical transition to proceed. The probability that this will occur is clearly equal to the Boltzmann factor exp[-Eta (λ)/kT]. The presence of this factor within the optical stimulation term of the eqn (8) rate equation is therefore physically justified.
3.3 Construction details
It is important to emphasise that our Fig. 4 configurational coordinate diagram is relevant only to successful processes. In this respect, we believe that there is a further restriction; namely, that Eta (λ) is not only spectrally-dependent but also is directionally-dependent. OSL measurements then necessarily reflect successful processes and only successful processes. In the case of quartz, each stimulation can only succeed if the hole is released to hop along the c-channel wall. The scheme shown in Fig. 4 is therefore confined to c-channel thermal assistance processes alone.
If we examine the stimulation processes in relation to the random directionality we might expect of thermal vibrations, we find that in the vast majority of cases the value of Eta (λ) needed to ensure a successful transition to the excited state will not be achieved. In such cases, the vibrational energy will either be ill-directed or of incorrect magnitude. OSL will not then occur. Instead, the optical stimulation energy will be dissipated and the ground state conditions restored. In essence then, it is the unique directionality associated with the c-channel that contributes to explaining why OSL is such a weak process.
Regarding constructional detail, we reiterate our assertion that Fig. 4 is just a representation, the principal role of which is to assist in the identification of the underlying physical processes. In this respect, the actual parameters we have used within eqn (11) to derive the ground state Morse potential energy curve are not of great significance. We note further that we applied the Morse 18
potential only to the rightmost rising section of the ground state curve. The reason is that the Morse potential is insufficiently strong to properly represent the sharp repulsive rise that occurs at low separations. In the absence of any quantitative information, we have therefore simply used a freehand sketch to represent the latter.
The reader may further notice that our Fig. 4 construction has relied on an additional source of information. As discussed by Itoh et al. (2002), Kristianpoller et al. (1994) earlier reported that the quantum yield for OSL in quartz increases as the stimulating photon energy is increased, up to a maximum that occurs at 330 nm (3.76 eV). Here, we interpret the maximum as determining the point of zero thermal assistance energy. In that case, the transition process is entirely opticallydriven. It has thereby been convenient to include the Kristianpoller et al. (1994) data within our Fig. 4 sketch. We note in passing that we earlier used this information to justify the dashed extrapolation shown within Fig. 3 above.
4. Carrier release mechanisms
4.1 Carrier release configurational coordinate diagram
In order to proceed, we find it useful to introduce several additional parametric values:
• the 1.66 eV thermal dissociation energy that characterises [XO4/M+]+ (Itoh et al., 2002); • the pulsed OSL room temperature time constants we have measured earlier; namely, the 39.9 ± 0.2 µs and 40.9 ± 0.2 µs rise and fall times (Spooner et al., 2019);
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• the 0.694 ± 0.004 eV well depth and frequency factor ν = (9.6 ± 0.8) × 1011 Hz that together characterise the thermal quenching process (Spooner et al., 2019).
In Fig. 5 we show how this information can be incorporated in order to logically extend the range of the configurational coordinate diagram. There, the Fig. 4 optical stimulation data appear in compressed form at the lower values of the separation variable. We note also the 1.66 eV dissociation energy which determines the asymptotic energy to which the potential energy curves trend at large separations.
Fig. 5: Primary OSL extended configurational coordinate diagram (c-channel only). The potential energy curves and other details are described in the text.
In order to provide consistency with the rate equation (8), we propose that the curve associated with the Fig. 4 excited state evolves into a potential well as the separation is increased. The well can only be occupied via the optical stimulation process and hence is unique to OSL. As shown in Fig. 5, at large separations the excited state curve asymptotes at the 1.66 eV thermal dissociation level. Further, we choose the well depth to be consistent with the experimental value of Ewell = 20
0.694 ± 0.04 eV we extracted from our recent pulsed OSL study (Spooner et al., 2019). We also assume that both the ground and excited state levels of the [XO4/M+]+ dimer dissociate at the same level. As is illustrated in Fig. 5, both lead to the thermal release of the cation M+.
As highlighted within Fig. 5, we see that the ground state thermal dissociation process also represents (via vibrational excitation) the source of the 325 ºC thermoluminescent emission band in quartz; that is, via the defect pair model reactions (Itoh et al., 2002):
[XO4/M+ ]+ → [XO4 ]0 + M+ ,
(12)
and
AlO4− + M+ → [AlO4− / M+ ]0 + photon (420 nm peak).
(13)
Hence, as is well-known (Itoh et al., 2002), OSL is annealed out by heating above ~300 ºC while the application of OSL leads to reduced 325 ºC band thermoluminescent emissions.
Several additional features within Fig. 5 need explanation. Firstly, we have postulated the presence of a lower level antibonding state. As shown, this state (which represents the path along which a hole is ejected) provides consistency with the Itoh et al. (2002) optical stimulation reaction (5). Its presence also accounts for the eqn (8) temperature-independent decay term (which is represented in Fig. 5 by the vertical red arrow). The eqn (8) coefficient Γ0 can then be identified as an optical transition probability, the reciprocal of which represents the room temperature time constant τ0 = 1/ Γ0. We discuss the significance of the assignment of τ0 within Section 4.3 below.
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Given the Fig. 5 configurational coordinate diagram, we are now able to justify the three terms that appear within the OSL rate equation (8) above. The first term represents the thermally assisted optical stimulation we discussed above in Section 3. The second term represents an optical transition from the excited state to an antibonding state while the third term represents the rate at which the excited state is emptied by thermal dissociation, resulting in the ejection of the cation M+. We have therefore been able to associate each of the three terms with a physical process. Further, since the Mott-Seitz relationship (10) follows from the solution of eqn (8), we have now physically justified its use within the OSL thermal quenching context.
We also find that the rate at which holes are generated is governed by
E − ta dh e kT = Γ 0 [XO 4 /M + ]+* = k0 [XO 4 /M + ]+ Φ 0 Ewell dt 1 + ντ e − kT 0 +
−t /τ 1 − e ,
(14)
where the time constant τ is again determined by eqn (10). Given that the luminescence centre reactions we have replicated in (6) and (7) are assumed to be fast, the pulse responses of OSL and PTTL are both governed by (14) and hence display the same character. Further, since eqn (14) applies across the extent of the entire shine we find that the pulse response is time-invariant, consistent with well-known experimental observations. [See, for example, Chithambo et al., 2016, Spooner et al., 2019].
Before we proceed to discuss further implications arising from our configurational coordinate model, we note that within Fig. 5 we have also included potential energy curves that represent retrapping paths for both the holes and cations that are ejected. Although we regard retrapping as a
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subject of considerable interest, its discussion lies beyond the scope of our study. We therefore defer it here for future consideration.
4.2 Rise and fall time differences
We are now in a position to provide a physical explanation for the rise and fall time difference noted in our Fig. 5 configurational coordinate diagram. Within our pulsed OSL study (Spooner et al., 2019) we emphasised that the observed difference was statistically significant but were unable to explain its presence. We subsequently have identified the difference as arising from a finite vibronic contribution to the optical transition.
A vibronic contribution is included within eqn (1) above. Following other researchers (Akselrod et al., 1998, Chithambo, 2007), we earlier assumed that this could be neglected. We now have changed our view. Accordingly, given the assignment E = Ewell, we choose to rewrite eqn (1) as
E − well hν kT Γ = Γ 0 + p coth , +ν e 2 kT
(15)
within which we have specifically chosen the same vibrational frequency to represent both the vibronic and thermal quenching terms. This is consistent with the notion that the frequency factor ν that appears within the thermal quenching term is just the excited state vibrational frequency. We note further that our doubling of kT factor within the coth function argument is consistent with the derivation of the vibronic contribution by Di Bartolo (2010).
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Given time constants τ = 1/Γ and τ0 = 1/ Γ0, the Mott-Seitz eqn (2) can now be rewritten in the extended form
τ =
τ0 hν
1 + p τ 0 coth +ν τ 0e 2 kT
−
E well kT
.
(16)
In this expression τ0 is defined as the fall time at low temperatures. In the case of the fall, the multiplier p is set to zero. In contrast, in the case of the rise, a nonzero value is chosen for p and adjusted to enable the low temperature rise time to be matched. Accordingly, the rate equation (8) also needs modification; viz.,
E − ta − well hν d [XO 4 /M + ]+* kT e = k 0 e kT [XO 4 /M + ]+ Φ (t ) − Γ 0 + p coth + ν dt 2 kT E
+ + [XO 4 /M ] *. (17)
In Fig. 6 we show an example within which the solution (16) has been applied to fit our earliermeasured time constant data (Spooner et al., 2019), using the fall time τ0 and the multiplier p as fitting parameters. Given appropriate choice of the value of p for the rise, we can see that a low temperature difference between the rise and fall is predicted. Further, we find that the fit is only marginally different from that we achieved earlier by empirically assigning different τ0 values for the rise and fall. In particular, it is seen that the presence of the vibronic term leads to the rise time falling slowly at low temperatures while the fall time remains constant until thermal quenching becomes a significant contributor.
24
Fig. 6: Time constants and fit to eqn (16); Woakwine quartz (Williams et al., 2018); p = 0 (fall); p = 42 ± 2 s-1 (rise).
It is interesting that the vibronic term only affects the rise and not the fall. Presumably, the vibronic mechanism in only active during the period when the strong optical stimulation field is applied. We currently have no physical explanation.
4.3 Predicted optical transition
We have a number of comments regarding the presence of the optical decay path we have illustrated in Fig. 5. Firstly, we note that the eqn (9) time dependence we derived above for the OSL pulse response is characterised by a single exponential time constant, consistent with a spontaneous emission process. Secondly, the relative slowness of the ~40 µs rise and fall times compared to the nanosecond and picosecond time constants that characterise allowed transitions leads us to suggest
25
that the optical transition to the antibonding level is electric dipole forbidden; that is, the excited state [XO4/M+]+* is metastable.
Thirdly, and rather unexpectedly, within our model we appear to have predicted the existence of an internal infrared transition. As sketched in Fig. 5, the transition energy appears to be of the order of 0.5 eV. The equivalent 2.5 µm emission wavelength therefore lies within one of the atmospheric transmission windows between the visible and medium wave infrared regions of the optical spectrum. We are not aware that emissions within this spectral region have been investigated in relation to OSL. It would clearly be of considerable interest if the presence or otherwise of such an emission within OSL spectra could in future be verified.
4.4 Width of the excited state potential well
We note from our Fig. 5 sketch that we have chosen to widely-space the excited state potential well compared to that which characterises the ground state. Further, we have not specified the scale of the separation variable. Regarding the latter, we do not know whether the separation axis should be linearly or logarithmically scaled.
We recall the value of (9.6 ± 0.8) × 1011 Hz we earlier measured for the frequency factor associated with the thermal quenching process (Spooner et al., 2019). As we have discussed above, within our configurational coordinate model we find that frequency factor is synonymous with the vibrational frequency associated with the Fig. 5 excited state. We therefore have succeeded in associating the thermal quenching frequency factor with a physical process.
26
In comparative terms, the measured frequency is small compared to the known values that are typical of tightly coupled molecules such as oxygen and nitrogen (where the vibrational frequencies lie in the 1013 – 1014 Hz range). The relatively small vibrational frequency identified here is therefore consistent with the concept that the dimer excited state is loosely bound.
4.5 Secondary pulse response
As we noted above in Section 2.1, within our experimental pulsed OSL study (Spooner et al., 2019) we detected several faint long-lived pulse components. The strongest of these was characterised by a 1.60 ± 0.02 ms room temperature time constant and by potential well parameters of 1.1 ± 0.05 eV for the depth and 8 × 1013 Hz for the vibrational frequency. Evidently, the weaker OSL levels we measured in this case are associated with optical stimulation to a significantly more tightly bound excited state.
In Fig. 7 we show how the secondary OSL data can be incorporated within the same configurational framework. There, we have included two additional potential energy curves: a more tightly-bound potential well characterised by 1.1 eV depth and an associated antibonding curve. As in the case of the primary OSL discussed above, we again propose that an optical transition occurs between the excited state and its associated antibonding state. On the basis of the Fig. 7 sketch, it appears that the relevant photon energy would be of the order of 0.2 eV. For the secondary OSL component, then, the optical transition would appear to lie between the medium-wave and long-wave regions of the atmospheric transmission spectrum, being characterised by a wavelength of the order of 6 µm.
27
Fig. 7: Primary and secondary OSL extended configurational coordinate diagram (c-channel only)
Incidentally, the large difference between the vibrational frequencies associated with the primary and secondary OSL components suggests that a logarithmic scale might be the more appropriate for the separation variable employed within Figs. 5 and 7. We also see from Fig. 7 that at higher temperatures (where the higher vibrational levels become better populated) the width of the secondary component potential energy curve enlarges, indicative of lower vibrational frequencies. Although somewhat speculative, this observation may account for the observed high temperature deviation from the Mott-Seitz relationship we observed earlier within Fig. 9(b) of our pulsed OSL study (Spooner et al., 2019).
In completing this Section, we recall that within our pulsed OSL study we found that the secondary OSL pulse response also is characterised by a single exponential time constant. The analysis presented above within Section 2.2 is therefore applicable also to the secondary OSL case. Although we also detected two additional even slower pulse components, the signals were 28
insufficiently strong to enable proper characterisation. It may be the case that curves representing these components need also to be added in future within the configuration framework.
5. Summary
In this paper, we have applied information from our recent pulsed OSL study (Spooner et al., 2019) to develop a new configurational coordinate model that enables a number of characteristics exhibited by quartz OSL to be physically explained. For the first time, we have offered an explanation for the well-known ~40 µs room temperature OSL time constant; namely, that it governs the transition probability for an infrared emission that occurs from an excited state potential well to a lower antibonding level. Further, we have shown that the time constant and the associated OSL processes of thermal assistance and thermal quenching are strongly linked within a common configurational framework, the development of which has enabled the use of an expanded version of the Mott-Seitz equation to be justified within the OSL context.
References
Akselrod, M.S., Agersnap Larsen, N., Whitley, V., and McKeever, S.W.S., 1998. Thermal quenching of F-center luminescence in Al2O3:C. J. Appl. Phys. 84, 3364-3373 https://doi.org/10.1063/1.368450 Bailey, R.M., 2001. Towards a general kinetic model for optically and thermally stimulated luminescence in quartz. Rad. Meas. 33, 17-45. https://doi.org/10.1016/S1350-4487(00)00100-1
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Bailiff, I.K., 2000. Characteristics of time-resolved luminescence in quartz. Rad. Meas. 32, 401405. https://doi.org/10.1016/S1350-4487(00)00126-8 Bailiff, I.K., and Mikhailik, V.B., 2003. Spatially-resolved measurement of optically stimulated luminescence and time-resolved luminescence. Rad. Meas. 37, 151-159. https://doi.org/10.1016/S1350-4487(02)00187-7 Chithambo, M.L., 2007. The analysis of time-resolved optically stimulated luminescence: II. Computer simulations and experimental results. J. Phys. D: Appl. Phys. 40, 1880-1889. https://doi.org/10.1088/0022-3727/40/7/007 Chithambo, M.L., Ankjærgaard, C., and Pagonis, V., 2016. Time-resolved luminescence from quartz: An overview of contemporary developments and applications. Physica B. 481, 8-18. https://doi.org/10.1016/j.physb.2015.10.014 Chithambo, M.L., Folley, D.S., and Chikwembani, S., 2019. Phototransferred thermoluminescence from natural quartz annealed at 1000 °C: Analysis of time-dependent evolution of intensity and competition effects. J. Luminescence 216, 116730, 9 pp. https://doi.org/10.1016/j.jlumin.2019.116730 Denby, P.M., Bøtter-Jensen, L., Murray, A.S., Thomsen, K.J., and Moska, K. 2006. Application of pulsed OSL to the separation of the luminescence components from a mixed quartz/feldspar sample. Rad. Meas. 41, 271-276. https://doi.org/10.1016/j.radmeas.2006.05.017 Di Bartolo, B. 2010. Optical interactions in solids. 2nd edition. World Scientific, Singapore. https://doi.org/10.1142/7649 Galloway, R.B., 2002a. Luminescence lifetimes in quartz: dependence on annealing temperature prior to beta irradiation. Rad. Meas. 35, 67-77. https://doi.org/10.1016/S1350-4487(01)00258-X Galloway, R.B., 2002b. Comparison of luminescence lifetimes in quartz following alpha and beta irradiation. Rad. Meas. 35, 591-593. https://doi.org/10.1016/S1350-4487(02)00066-5 30
Gurney, R.W., and Mott, N.F., 1939. Luminescence in solids. Trans. Faraday. Soc., 35, 69-73. https://doi.org/10.1039/TF9393500069 Halliburton, L.E., Koumvakalis, N., Markes, M.E., and Martin, J.J., 1981. Radiation effects in crystalline SiO2: the role of aluminium. J. Appl. Phys. 52, 3565-3574. https://doi.org/10.1063/1.329138 Heays, A.N., 2010. Photoabsorption and photodissociation in molecular nitrogen. PhD thesis. The Australian National University, Canberra, ACT, Australia. https://openresearch-repository.anu.edu.au/bitstream/1885/7360/1/02whole.pdf Itoh, N., Stoneham, D., Stoneham, A.M., 2001. The predose effect in thermoluminescent dosimetry. J. Phys: Condens. Matter 13, 2201-2209. https://doi.org/10.1088/0953-8984/13/10/314 Itoh, N., Stoneham, D. and Stoneham, A.M., 2002. Ionic and electronic processes in quartz: Mechanisms of thermoluminescence and optically stimulated luminescence. J. Appl. Phys. 92, 5036-5044. https://doi.org/10.1063/1.1510951 Krbetschek, M.R., Göetz, J., Dietrich, A., and Trautmann, T., 1997. Spectral information from minerals relevant for luminescent dating. Rad. Meas. 27, 695-748. https://doi.org/10.1016/S13504487(97)00223-0 Kristianpoller, N., Abu-Rayya, M., and Chen, R., 1994. Optically stimulated luminescence in synthetic quartz. J. Lumin. 60&61, 540-543. https://doi.org/10.1016/0022-2313(94)90211-9 Magagnini, M., Giannozzi, P., and Dal Sorso, A., 1999. Microscopic structure of the substitutional Al defect in α quartz. Phys. Rev. B 61, 2621-2625. https://doi.org/10.1103/PhysRevB.61.2621 Morrill, J.S., Ginter, M.L., Lewis., B.R., Gibson, S.T., 1998. https://physics.nist.gov/Icamdata/PDF/3DataProduction/33Molecules/morrill.pdf
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Mott, N.F., 1938. On the absorption of light by crystals. Proc. Roy. Soc. A, 167, 384-391. https://doi.org/10.1098/rspa.1938.0137 Pagonis, V., Ankjærgaard, C., Murray, A.S., Jain, M., Chen, R., Lawless, J., and Greilich, S., 2010. Modelling the thermal quenching mechanism in quartz based on time-resolved optically stimulated luminescence. J. Luminescence 130, 902-909. https://doi.org/10.1016/j.jlumin.2009.12.032 Pagonis, V., Lawless, J., Chen, R., and Chithambo, M.L., 2011. Analytical expressions for timeresolved optically stimulated luminescence experiments in quartz. J. Luminescence 131, 1827-1835. https://doi.org/10.1016/j.jlumin.2011.04.040 Seitz, F., 1939. An interpretation of crystal luminescence. Trans. Faraday. Soc., 35, 74-85. https://doi.org/10.1039/TF9393500074 Spooner, N.A., 1994. On the optical dating signal from quartz. Rad. Meas. 23, 593-600. https://doi.org/10.1016/1350-4487(94)90105-8 Spooner, N.A., Williams, O.M., and Moffatt, J.E., 2019. Pulsed optically stimulated luminescence data for mechanisms studies in quartz. Rad. Meas. 128, 106176, 10pp. https://doi.org/10.1016/j.radmeas.2019.106176 Vaccaro, G., Panzeri, L., Paleari, S., Martini, M., and Fasoli, M., 2017. EPR investigation of the role of germanium centres in the production of the 110ºC thermoluminescence peak in quartz. Quaternary Geochronology 39, 99-104. https://doi.org/10.1016/j.quageo.2017.02.005 Wikipedia, https://en.wikipedia.org/wiki/Lennard-Jones_potential Wikipedia, https://en.wikipedia.org/wiki/Morse_potential Williams, O.M., and Spooner, N.A., 2018. Defect pair mechanism for quartz intermediate temperature thermoluminescence bands. Rad. Meas. 108, 41-44. https://doi.org/10.1016/j.radmeas.2017.11.005
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Williams, O.M., Spooner, N.A., Smith, B.W, and Moffatt, J.E., 2018. Extended duration optically stimulated luminescence in quartz. Rad. Meas. 119, 42-51. https://doi.org/10.1016/j.radmeas.2018.09.005
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Common untrapping mechanisms govern the speed of both optically stimulated luminescence and photo-transferred thermoluminescence in quartz. A defect pair model configurational coordinate model is developed to explain the untrapping mechanisms. The optical stimulation process is modelled as an optical transition between a vibrationallyexcited ground state level of the trap and a dimer excited state. The room temperature pulse response and thermal quenching are represented by competing decay modes which empty a potential well within the excited state.
Declaration of Interest Statement - RADMEAS-S-19-00071 The work in this paper is original and has not been published elsewhere. The principal author (OMW) engages in voluntary research at the University of Adelaide. No funding has been received from any source.
Owen M. Williams Principal author RADMEAS-S-19-00071
S1350-4487(20)30023-8
DOI:
https://doi.org/10.1016/j.radmeas.2020.106259
Reference:
RM 106259
To appear in:
Radiation Measurements
Received Date: 19 August 2019 Revised Date:
21 January 2020
Accepted Date: 1 February 2020
Please cite this article as: Williams, O.M., Spooner, N.A., Quartz Optically Stimulated Luminescence Configurational Coordinate Model, Radiation Measurements, https://doi.org/10.1016/ j.radmeas.2020.106259. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Crown Copyright © 2020 Published by Elsevier Ltd. All rights reserved.
Quartz Optically Stimulated Luminescence Configurational Coordinate Model Owen M. Williams1 and Nigel A. Spooner1, 2 Abstract In a recent study using pulsed stimulation we revealed that optically stimulated luminescence (OSL) and photo-transferred thermoluminescence (PTTL) in quartz are characterised by a common pulse response. We interpreted this result as indicating that both emissions are governed by the same detrapping mechanisms. In the present study we develop a common configurational coordinate model to describe the mechanisms. Within our model we identify the energy associated with the thermal assistance effect as the vibrational energy of the ground state of the dimer that represents the trap. Further, we model the OSL stimulation process as an optical transition between a vibrationally-excited ground state level and a dimer excited state. By introducing additional luminescence parameters, we reveal that the processes that underlie thermal quenching and the room temperature OSL response to pulsed stimulation can be represented by competing modes which empty the excited state. In particular, we find that the room temperature pulse response can be modelled in terms of an optical transition from the excited state to a lower antibonding level from which a hole is ejected. In contrast, thermal quenching is explained by excited state vibrational dissociation at large dimer component separations.
1. Institute of Photonics and Advanced Sensing, School of Physical Sciences, University of Adelaide, Adelaide, Australia 5005 2. Weapons and Combat Systems Division, Defence Science and Technology Group, P.O. Box 1500, Edinburgh, Australia 5111 1
2
1. Introduction In a series of recent studies (Williams and Spooner, 2018, Williams et. al, 2018, Spooner et. al., 2019), we have shown that the defect pair model introduced by Itoh et al. (2001, 2002) to explain the mechanisms associated with quartz luminescence can be extended. In particular, we attributed the 160 ºC and 220 ºC intermediate temperature thermoluminescence bands to the same electron/hole recombination reaction pair as that associated with the 110 ºC predose band. Further, we applied the model to explain the series of steps observed when long OSL shines are plotted on a log/log scale.
In this paper we employ the defect pair model to investigate several well-known quartz OSL phenomena. Our analysis is based on data from our recent experimental study (Spooner et al., 2019). There, we presented an extensive set of pulsed OSL measurements covering a number of South Australian quartzes measured across a wide temperature range. Notably, we found that the OSL and photo-transferred thermoluminescence (PTTL) contributions could be separated and revealed that each was characterised by the same temporal response. This outcome was somewhat unexpected since, according to the defect pair model, the luminescence centre reactions are quite different. We therefore were led to the conclusion that the slow processes governing the temporal response occur at the trap, and further, that the processes are common to OSL and PTTL.
The above conclusion represents a departure from previous OSL studies; in particular, in relation to the subject of thermal quenching (Bailiff, 2000, Galloway, 2002a, 2002b, Bailiff and Mikhailik, 2003, Denby et al., 2006, Chithambo, 2007, Pagonis et. al., 2010, 2011, Chithambo et al., 2016). Within the associated mechanisms studies (see, for example, Pagonis et al., 2010, 2011, Chithambo et al., 2016), it has commonly been assumed that thermal quenching occurs at the luminescence
3
centre and is governed by the Mott-Seitz mechanism (Mott, 1938, Seitz, 1938, Gurney and Mott, 1939). It is this subject that defines the theme of the present study.
In Section 2 we review the Mott-Seitz mechanism and its adaption for use in the luminescence field before turning our attention to the defect pair model. There, we reveal that solution of an OSLspecific rate equation leads to the same analytical outcome as that of the Mott-Seitz mechanism. In order to identify the underlying reasons we proceed towards the development of an appropriate configurational coordinate model. Within Section 3 we initially review the thermal assistance energy identified by Spooner (1994) and introduce a new configurational framework within which we argue that the OSL stimulating photon drives an optical transition between the ground state and an excited state. Within this framework we show that thermal assistance is necessarily required in order to ensure that the OSL stimulating photon can successfully effect the transition.
In Section 4, we introduce additional information from the quartz luminescence literature and utilise it to extend the geometrical coverage of the configurational coordinate diagram towards greater separation of the dimer components. We find that the processes that govern both the room temperature pulse time constant and the thermal quenching effect can be linked through their joint contributions in emptying an excited state potential well. The net result is that the OSL pulse response at room temperatures can be associated with an optical transition to a lower antibonding state from which a hole is ejected and the thermal quenching effect with vibrational dissociation of the excited state dimer. We show further that the same type of configurational framework can be applied to account for the presence of the faint long-lived pulse component we identified earlier (Spooner et al., 2019).
4
2. OSL models 2.1 Mott-Seitz mechanism The Mott-Seitz mechanism was proposed independently by prominent researchers Mott (1938) and Seitz (1938) for explaining observations that the efficiency of phosphors fell with rising temperature. The advances are best explained in the subsequent Gurney and Mott (1939) paper. In Fig. 1 we have sketched the configurational coordinate diagram associated with the Mott-Seitz mechanism.
Fig. 1: Sketch of original Mott-Seitz mechanism [after Seitz (1938) and Gurney and Mott (1939)].
The widths of the adiabatic potential energy curves reflect the property that the excited state is characterised by lower vibrational frequencies than those in the more tightly bound ground state, to the extent that at wide separations the ground and excited state curves approach each other. Crossing states are not allowed (Seitz, 1938) and hence the two curves assume the distorted nonoverlapping forms sketched in Fig. 1. The excited state population can decay by optical emission and by a crossover mechanism which occurs at high vibrational levels, the latter process being followed by thermal relaxation towards the lower vibrational levels of the ground state.
5
Within the standard Mott-Seitz model, the relevant decay paths are spontaneous emission, phononassisted vibronic transitions and the crossover effect, the latter occurring at the excited state energy E, as is illustrated in Fig. 1. [Refer to Krbetschek et. al, 1997.] Following Akselrod et al. (1998), the overall transition probability Γ can be expressed as
hω Γ = Γ 0 + p coth kT
E − kT +ν e .
(1)
Here, Γ0 is the optical transition probability, p is a temperature-independent multiplier, h and k are the reduced Planck constant and the Boltzmann constant respectively, T is the absolute temperature,
ω is the phonon vibrational frequency, E is the well depth and ν is the associated frequency factor. In following Akselrod et al. (1998) by assuming that the vibronic transitions can be neglected, eqn (1) can be reformulated as
τ=
τ0
−E 1 +ντ 0 exp kT
.
(2)
This result (within which the time constants τ = 1/Γ and τ0 = 1/ Γ0 are defined in normal manner) is the standard analytical expression that describes the Mott-Seitz mechanism. As is well-known, the temperature dependence displayed in the eqn (2) denominator is the same as that which determines the OSL thermal quenching effect in quartz (Chithambo, 2007, Spooner et al., 2019). Accordingly, in spite of the fact that OSL and phosphorescence represent different phenomena, the Mott-Seitz mechanism has been adopted widely within the OSL literature. [Refer, for example, to Pagonis et al., 2010, 2011, Chithambo et al., 2016.] In each case, a Mott-Seitz type of configurational coordinate diagram has been invoked to predict the thermal quenching effect.
6
A difficulty appeared, however, when Pagonis et al. (2010) attempted to replicate the known timeresolved OSL observations within the structure of the Bailey (2001) energy band model. Within their simulations they found a relaxation time of the order of 0.1 s, more than three orders of magnitude larger than the well-known ~40 µs pulsed OSL room temperature time constant (Chithambo, 2007, Chithambo et al., 2016, Spooner et al., 2019). Pagonis et al. (2010) also noted that the thermal quenching effect was not predicted within the Bailey model. Although these problems have been known for some time, we are not aware that they have been satisfactorily resolved. More recently another dilemma has become apparent. As part of our recent pulsed OSL study (Spooner et al., 2019), we reported on the presence of several faint OSL pulse components, the strongest of which we characterised by the significantly longer room temperature time constant of 1.60 ± 0.02 ms. This component also displayed a thermal quenching effect. The presence of the faint components suggests that separate Mott-Seitz mechanisms need to be applied. If this is true, each of the relevant configurational coordinate diagrams must then involve the same type of crossover as that we have sketched in Fig. 1. Such an outcome would appear to be somewhat of a coincidence.
In view of the above problems, it appears that the models used to explain OSL need revision. In the case of the energy band model, perhaps it needs to be further developed to enable satisfactory pulsed OSL predictions. In the case of the Mott-Seitz model, perhaps the problem lies with the adoption of a mechanism that was originally designed to account for phosphorescence.
It is the latter problem that defines our present theme. Accordingly, within Sections 3 and 4 below we develop a case that shows that the Mott-Seitz model can be replaced by an OSL-specific configurational framework. Moreover, we show that the replacement leads not only to an alternative derivation of the eqn (2) thermal quenching relationship but also to physical justification 7
for the presence of both the room temperature time constant and the processes that underpin both thermal assistance (Spooner, 1994) and thermal quenching. Further, we show that the difference between the rise and fall time constants we reported within our pulsed OSL study (Spooner et al., 2019) can be explained if we reinstate the coth function term in eqn (1). It is to these subjects that we now turn.
2.2 Quartz defect pair model
Within our earlier studies (Williams and Spooner, 2018, Williams et al., 2018, Spooner et al., 2019) we described how the defect pair model of Itoh et al. (2001, 2002) can be applied successfully to explain a number of features of both thermoluminescence and OSL. As its name suggests, the defect pair model is based on the generation of defect pairs during an ionising radiation event.
Aluminium is a significant quartz impurity. As is well-known, when aluminium is incorporated within the quartz structure, the Al3+ ions that displace Si4+ ions are accompanied by interstitial protons or alkali ions, thus ensuring that local charge balance is preserved. [Refer, for example, to Haliburton et al., 1981.] H+, Li+ and Na+ are common charge-compensating interstitial impurities. Within their landmark paper, Itoh et al. (2002) explained that while the main charge carriers generated by β or γ ionising radiation are electron/hole pairs, the ionisation also results in the release of the interstitial ions into the quartz c-channel; viz.,
[AlO−4 / M+ ]0 → AlO−4 + M+.
(3)
8
−
The tetrahedral AlO4 defect group is located within the quartz c-channel wall and M+ represents the cation (e.g., H+, Li+ and Na+) that is released. The cation migrates along the c-channel until it is trapped by one or another of several types of defects X within the wall structure; viz.,
XO4 + M+ → [XO4/M+ ]+.
(4)
Here, we choose XO4 to generically label the defect tetrahedron of interest. We note that the present study holds regardless of the identification of X. The latter is still open to debate. Vaccaro et al. (2017) have provided interesting measurements that suggest that X is Ge. However, as we have discussed earlier (Williams and Spooner, 2018), the higher concentration Ti option has yet to be eliminated.
In the specific OSL case of interest here, Itoh et al. (2002) proposed that when the stimulating photon is absorbed, a hole is ejected from the defect site at which the displaced M+ was trapped; viz.,
[XO4/M+ ]+ + hν → [XO4/M+ ]+* → [XO4−/M+ ]0 + h+.
(5)
The hole migrates by hopping along the c-channel wall. If and when it reaches the site of the −
uncompensated AlO4 reaction (3) product, OSL is emitted via the association reaction
AlO−4 + h+ → [AlO−4 / h+ ]0 + photon (365 nm band).
9
(6)
A complementary reaction sequence also can occur. This arises since the reaction (5) dimer product is thermally unstable (Itoh et al., 2002). After a temperature-dependent period, the dimer reverts into its more stable positively-charged form by releasing an electron. The latter migrates, also by hopping along the c-channel wall, allowing electron/hole recombination to subsequently occur if and when the electron reaches the location of the reaction (6) product. In this case a midtemperature band thermoluminescent photon is released; viz.,
[AlO−4 / h + ]0 + e − → AlO−4 + photon (110, 160 or 220 o C TL band emission),
(7)
where the respective bands are centred on 380, 394 and 408 nm (Williams and Spooner, 2018). Since the reaction sequence (5) to (7) is optically-driven, the emission is commonly termed phototransferred thermoluminescence or PTTL. [Refer, for example, to Chithambo et al. (2019).]
Although all processes occurring at the aluminium luminescence centre lie within our interest, it is the optical stimulation process (5) that we wish to investigate here. We note there that we have highlighted the presence of an excited defect state. Within Sections 3 and 4 below we reveal the significant role that this state plays in providing the essential links amongst the separate processes that govern the overall hole untrapping mechanism.
It is convenient at this point to recall our earlier observation that OSL and PTTL display the same temporal responses to pulsed stimulation (Spooner et al., 2019). As seen above, the OSL and PTTL luminescence centre reactions (6) and (7) are quite different. As such, we would expect that they would be characterised by different reaction speeds. However, we see no such difference. On logical grounds, then, we are obliged to accept that both reactions are fast compared to the speed of
10
the optical stimulation process, reaction (5). In effect, the only logical explanation is that the pulse responses we record are instead governed by slower processes that occur at the hole trap.
In order to provide consistency with eqn (2), it is not difficult to formulate an appropriate rate equation; viz., the population of the reaction (5) excited defect state needs to be governed by
− ta − d [XO 4 /M + ]+* = k 0 e kT [XO 4 /M + ]+ Φ (t ) − Γ 0 [XO 4 /M + ]+ * − ν [XO 4 /M + ]+ * e dt E
E well kT
(8)
Here, T is the absolute temperature and k is the Boltzmann constant in eV/K, while the specific parameters are as follows: k0 is a rate constant, Eta is the energy that governs the strength of the thermal assistance process, [XO4/M+]+ is the population of the ground state dimer, Φ(t) represents the stimulating photon flux, Γ0 = 1/τ0 is a transition probability, Ewell is the depth of a potential well and ν is the associated frequency factor.
Within (8), we see that the rate at which the population changes is governed by three processes: an optical stimulation rate (which is influenced by the amount of thermal assistance), a temperatureindependent decay rate and a third term which accounts for thermal quenching. We justify the inclusion of each of these terms within Sections 3 and 4 below. We note in passing that, for the time being, we have chosen to neglect any possible vibronic contribution (Di Bartolo, 2010). We relax this assumption in Section 4.2 below. We note further that in formulating eqn (8) it is implied that all processes occur at the [XO4/M+]+ site.
11
.
Eqn (8) may readily be solved in order to generate the common OSL and PTTL pulse response. In the special case where the optical stimulus Φ(t) = Φ0 is applied suddenly, the rate at which the population of [XO4/M+]+* grows can be derived simply as
E − ta e kT [XO 4 /M + ]+* ( t ) = k0 [XO 4 /M + ]+ Φ 0 τ 0 Ewell 1 + ντ e − kT 0
− t /τ 1 − e ,
(9)
where the time constant τ is determined by the temperature-dependent equation
τ=
τ0 E 1 +ντ 0 exp − well kT
.
(10)
Eqn (10) is clearly interesting in that it displays the same analytical form as the Mott-Seitz equation (2). The latter has now been derived within the OSL context. This leads us towards our next step; namely, the development of a model which enables the application of eqn (8) to be justified.
3. Thermal assistance in quartz
3.1 Spectral and temperature dependencies
We recall the results from the quartz OSL spectral study by Spooner (1994), within which the existence of a thermal assistance effect was revealed and its spectral characteristics were quantified. In that study a wide range of sample temperatures was investigated and in each case the OSL level 12
was recorded at the start of each shine, covering optical stimulation from a number of different narrowband spectral sources. Details are described by Spooner (1994).
For convenience, in Fig. 2 we present interpolated data we have extracted from the Spooner study. We see that the luminescence rises steeply from low temperatures before falling at higher temperatures. Spooner (1994) invoked the term “thermal assistance” to describe the rise while the fall is characteristic of the thermal quenching process. [For the latter, refer, for example, to Bailey, 2001, Chithambo, 2007, Pagonis et al., 2010, Chithambo et al., 2016, Spooner et al., 2019.]
Fig. 2: Sampled replica of the Spooner (1994) spectral luminescence data; quartz from Deaf Adder gorge, northern Australia. The data are not normalised. Best fits to the bracketed factor within eqn (9).
As seen in Fig. 2, the spectral data can readily be fitted by application of the bracketed temperaturedependent factor that appears within eqn (9) above. Within our fitting procedure, it has been convenient to adopt the rounded value τ0 = 40 µs to represent the room temperature time constant (Spooner et al., 2019). The remaining fitting parameters are the thermal assistance energy Eta, the 13
well depth Ewell, the frequency factor ν and the overall amplitude. Although according to eqn (9) the amplitude should be constant, we were only able to achieve satisfactory fits by allowing its value to vary. This reflects the fact that the original spectral data recorded by Spooner (1994) were not normalised.
We note also that although our fitting procedure yielded global values for Ewell and ν, both parameters displayed significant scatter. Accordingly, we instead relied on the higher precision values of Ewell = 0.694 ± 0.004 eV and ν = (9.6 ± 0.8) × 1011 s-1 that we extracted from our recent pulsed OSL study (Spooner et al., 2019).
More significantly, we confirm the earlier Spooner (1994) finding that thermal assistance energy is spectrally dependent; that is, Eta = Eta (λ). We summarise our results in Fig. 3 where it is seen that less thermal assistance is required as the energy of the stimulating photons is increased; that is, at lower optical stimulation wavelengths. This result is clearly consistent with the smaller values assumed by the Boltzmann numerator seen within eqn (9).
Fig. 3: Thermal assistance energies derived from Fig. 2 curve fitting. Note the small measurement scatter. Refer to Section 3.3 for justification of the dashed extrapolation.
14
We note further that within Fig 3 we have fitted the thermal assistance energy data to a quadratic curve. We justify the extrapolation shown there within Section 3.3 below.
3.2 Optical stimulation configurational coordinate diagram
The presence of the Boltzmann numerator within eqn (9) is interesting since it suggests that it may be possible to represent the optical stimulation process in a more physically insightful manner. In particular, we are interested in examining the implications within a configurational coordinate model framework; that is, within a structure where the ground and excited state potential energy curves that characterise the [XO4/M+]+ dimer are presented in terms of the separation of the dimer components.
We have previously used configurational coordinate diagrams to explain the spectral variations that characterise the 110 ºC, 160 ºC and 220 ºC thermoluminescence bands in quartz (Williams and Spooner, 2018). In particular, within that study we highlighted the relevance of the earlier densityfunctional theory calculation by Magagnini et al. (1999). In that, it was revealed that three different antibonding impurity states can be occupied when a hole is trapped to form the compensated aluminium defect complex [AlO4¯/h+]0. We note that this complex appears within the OSL and PTTL luminescence centre reactions (6) and (7) above. By representing the Magagnini et al. (1999) information within a configurational framework, we were then able to predict the presence of the three mid-temperature thermoluminescence bands.
The use of configurational coordinate diagrams to represent the energy states of diatomic molecules such as oxygen (Morrill et al., 1998) and nitrogen (Heays, 2010) is well-known. In such cases,
15
thermal energy is equivalent to vibrational and rotational energy. Since a configurational framework is appropriate to any dimer species it is useful to explore its application here. As a first step in constructing an appropriate diagram, we presume that thermal assistance energy can similarly be represented, in this case by the ground state vibrational energy of the radiation-induced dimer [XO4/M+]+. Consistent with the detrapping reaction (5) above, this is the trap from which the hole that carries the exiting charge is released.
In supporting this representation, we note that a large number of potential energy curves exist in the case of diatomic molecules, some of which represent bonding states and others antibonding states. Analytically, the bonding states can be approximated by various functions such as a Lennard-Jones 6-12 potential or a Morse potential (Wikipedia, referenced below). It is convenient here to apply the Morse potential since this can be described by a simple analytic equation; namely,
− a d −d V (d ) = Edissoc 1 − e ( min ) 2.
(11)
Here, V(d) is the potential energy at separation d of the XO4 and X+ dimer components, V(d) = 0 when d = dmin , a is a constant the determines the width of the Morse potential curve and Edissoc is the dissociation energy, the value towards which V(d) tends at large values of d.
At this point in our analytical development we pause to emphasise that our primary objective here is to seek improved physical insights into the processes that govern OSL in quartz; that is, we are not at this point seeking precise quantitative representations. Given this caveat, we proceed in Fig. 4 to show how the Morse potential can be applied in order to guide our construction process.
16
Fig. 4: Representative optical stimulation configurational coordinate diagram (c-channel only)
As we have proposed, thermal assistance energy can be represented as being synonymous with ground state vibrational energy. Within our Fig. 4 construction we have also introduced a second proposal; namely, that the OSL stimulation process is driven by an optical transition between the ground state of the [XO4/M+]+ dimer and the excited state that we introduced earlier within the optical stimulation reaction (5). In constructing the potential energy curve that characterises the excited state we have utilised the Fig. 3 thermal assistance data at each of the seven Spooner (1994) stimulation wavelengths. As part of this process we have appropriately adjusted the values assumed by the horizontal separation parameter in such a way that a smooth continuous excited state curve is generated.
As can be seen from the Fig. 4 construction, the overall energy of the excited state then equals the sum of the thermal assistance energy (i.e., the ground state vibrational energy) and the energy Eq = hc/λ carried by the stimulating photon. In effect, then, at each stimulating wavelength a precise amount of ground state vibrational energy Eta (λ) must be made available in order to allow the 17
optical transition to proceed. The probability that this will occur is clearly equal to the Boltzmann factor exp[-Eta (λ)/kT]. The presence of this factor within the optical stimulation term of the eqn (8) rate equation is therefore physically justified.
3.3 Construction details
It is important to emphasise that our Fig. 4 configurational coordinate diagram is relevant only to successful processes. In this respect, we believe that there is a further restriction; namely, that Eta (λ) is not only spectrally-dependent but also is directionally-dependent. OSL measurements then necessarily reflect successful processes and only successful processes. In the case of quartz, each stimulation can only succeed if the hole is released to hop along the c-channel wall. The scheme shown in Fig. 4 is therefore confined to c-channel thermal assistance processes alone.
If we examine the stimulation processes in relation to the random directionality we might expect of thermal vibrations, we find that in the vast majority of cases the value of Eta (λ) needed to ensure a successful transition to the excited state will not be achieved. In such cases, the vibrational energy will either be ill-directed or of incorrect magnitude. OSL will not then occur. Instead, the optical stimulation energy will be dissipated and the ground state conditions restored. In essence then, it is the unique directionality associated with the c-channel that contributes to explaining why OSL is such a weak process.
Regarding constructional detail, we reiterate our assertion that Fig. 4 is just a representation, the principal role of which is to assist in the identification of the underlying physical processes. In this respect, the actual parameters we have used within eqn (11) to derive the ground state Morse potential energy curve are not of great significance. We note further that we applied the Morse 18
potential only to the rightmost rising section of the ground state curve. The reason is that the Morse potential is insufficiently strong to properly represent the sharp repulsive rise that occurs at low separations. In the absence of any quantitative information, we have therefore simply used a freehand sketch to represent the latter.
The reader may further notice that our Fig. 4 construction has relied on an additional source of information. As discussed by Itoh et al. (2002), Kristianpoller et al. (1994) earlier reported that the quantum yield for OSL in quartz increases as the stimulating photon energy is increased, up to a maximum that occurs at 330 nm (3.76 eV). Here, we interpret the maximum as determining the point of zero thermal assistance energy. In that case, the transition process is entirely opticallydriven. It has thereby been convenient to include the Kristianpoller et al. (1994) data within our Fig. 4 sketch. We note in passing that we earlier used this information to justify the dashed extrapolation shown within Fig. 3 above.
4. Carrier release mechanisms
4.1 Carrier release configurational coordinate diagram
In order to proceed, we find it useful to introduce several additional parametric values:
• the 1.66 eV thermal dissociation energy that characterises [XO4/M+]+ (Itoh et al., 2002); • the pulsed OSL room temperature time constants we have measured earlier; namely, the 39.9 ± 0.2 µs and 40.9 ± 0.2 µs rise and fall times (Spooner et al., 2019);
19
• the 0.694 ± 0.004 eV well depth and frequency factor ν = (9.6 ± 0.8) × 1011 Hz that together characterise the thermal quenching process (Spooner et al., 2019).
In Fig. 5 we show how this information can be incorporated in order to logically extend the range of the configurational coordinate diagram. There, the Fig. 4 optical stimulation data appear in compressed form at the lower values of the separation variable. We note also the 1.66 eV dissociation energy which determines the asymptotic energy to which the potential energy curves trend at large separations.
Fig. 5: Primary OSL extended configurational coordinate diagram (c-channel only). The potential energy curves and other details are described in the text.
In order to provide consistency with the rate equation (8), we propose that the curve associated with the Fig. 4 excited state evolves into a potential well as the separation is increased. The well can only be occupied via the optical stimulation process and hence is unique to OSL. As shown in Fig. 5, at large separations the excited state curve asymptotes at the 1.66 eV thermal dissociation level. Further, we choose the well depth to be consistent with the experimental value of Ewell = 20
0.694 ± 0.04 eV we extracted from our recent pulsed OSL study (Spooner et al., 2019). We also assume that both the ground and excited state levels of the [XO4/M+]+ dimer dissociate at the same level. As is illustrated in Fig. 5, both lead to the thermal release of the cation M+.
As highlighted within Fig. 5, we see that the ground state thermal dissociation process also represents (via vibrational excitation) the source of the 325 ºC thermoluminescent emission band in quartz; that is, via the defect pair model reactions (Itoh et al., 2002):
[XO4/M+ ]+ → [XO4 ]0 + M+ ,
(12)
and
AlO4− + M+ → [AlO4− / M+ ]0 + photon (420 nm peak).
(13)
Hence, as is well-known (Itoh et al., 2002), OSL is annealed out by heating above ~300 ºC while the application of OSL leads to reduced 325 ºC band thermoluminescent emissions.
Several additional features within Fig. 5 need explanation. Firstly, we have postulated the presence of a lower level antibonding state. As shown, this state (which represents the path along which a hole is ejected) provides consistency with the Itoh et al. (2002) optical stimulation reaction (5). Its presence also accounts for the eqn (8) temperature-independent decay term (which is represented in Fig. 5 by the vertical red arrow). The eqn (8) coefficient Γ0 can then be identified as an optical transition probability, the reciprocal of which represents the room temperature time constant τ0 = 1/ Γ0. We discuss the significance of the assignment of τ0 within Section 4.3 below.
21
Given the Fig. 5 configurational coordinate diagram, we are now able to justify the three terms that appear within the OSL rate equation (8) above. The first term represents the thermally assisted optical stimulation we discussed above in Section 3. The second term represents an optical transition from the excited state to an antibonding state while the third term represents the rate at which the excited state is emptied by thermal dissociation, resulting in the ejection of the cation M+. We have therefore been able to associate each of the three terms with a physical process. Further, since the Mott-Seitz relationship (10) follows from the solution of eqn (8), we have now physically justified its use within the OSL thermal quenching context.
We also find that the rate at which holes are generated is governed by
E − ta dh e kT = Γ 0 [XO 4 /M + ]+* = k0 [XO 4 /M + ]+ Φ 0 Ewell dt 1 + ντ e − kT 0 +
−t /τ 1 − e ,
(14)
where the time constant τ is again determined by eqn (10). Given that the luminescence centre reactions we have replicated in (6) and (7) are assumed to be fast, the pulse responses of OSL and PTTL are both governed by (14) and hence display the same character. Further, since eqn (14) applies across the extent of the entire shine we find that the pulse response is time-invariant, consistent with well-known experimental observations. [See, for example, Chithambo et al., 2016, Spooner et al., 2019].
Before we proceed to discuss further implications arising from our configurational coordinate model, we note that within Fig. 5 we have also included potential energy curves that represent retrapping paths for both the holes and cations that are ejected. Although we regard retrapping as a
22
subject of considerable interest, its discussion lies beyond the scope of our study. We therefore defer it here for future consideration.
4.2 Rise and fall time differences
We are now in a position to provide a physical explanation for the rise and fall time difference noted in our Fig. 5 configurational coordinate diagram. Within our pulsed OSL study (Spooner et al., 2019) we emphasised that the observed difference was statistically significant but were unable to explain its presence. We subsequently have identified the difference as arising from a finite vibronic contribution to the optical transition.
A vibronic contribution is included within eqn (1) above. Following other researchers (Akselrod et al., 1998, Chithambo, 2007), we earlier assumed that this could be neglected. We now have changed our view. Accordingly, given the assignment E = Ewell, we choose to rewrite eqn (1) as
E − well hν kT Γ = Γ 0 + p coth , +ν e 2 kT
(15)
within which we have specifically chosen the same vibrational frequency to represent both the vibronic and thermal quenching terms. This is consistent with the notion that the frequency factor ν that appears within the thermal quenching term is just the excited state vibrational frequency. We note further that our doubling of kT factor within the coth function argument is consistent with the derivation of the vibronic contribution by Di Bartolo (2010).
23
Given time constants τ = 1/Γ and τ0 = 1/ Γ0, the Mott-Seitz eqn (2) can now be rewritten in the extended form
τ =
τ0 hν
1 + p τ 0 coth +ν τ 0e 2 kT
−
E well kT
.
(16)
In this expression τ0 is defined as the fall time at low temperatures. In the case of the fall, the multiplier p is set to zero. In contrast, in the case of the rise, a nonzero value is chosen for p and adjusted to enable the low temperature rise time to be matched. Accordingly, the rate equation (8) also needs modification; viz.,
E − ta − well hν d [XO 4 /M + ]+* kT e = k 0 e kT [XO 4 /M + ]+ Φ (t ) − Γ 0 + p coth + ν dt 2 kT E
+ + [XO 4 /M ] *. (17)
In Fig. 6 we show an example within which the solution (16) has been applied to fit our earliermeasured time constant data (Spooner et al., 2019), using the fall time τ0 and the multiplier p as fitting parameters. Given appropriate choice of the value of p for the rise, we can see that a low temperature difference between the rise and fall is predicted. Further, we find that the fit is only marginally different from that we achieved earlier by empirically assigning different τ0 values for the rise and fall. In particular, it is seen that the presence of the vibronic term leads to the rise time falling slowly at low temperatures while the fall time remains constant until thermal quenching becomes a significant contributor.
24
Fig. 6: Time constants and fit to eqn (16); Woakwine quartz (Williams et al., 2018); p = 0 (fall); p = 42 ± 2 s-1 (rise).
It is interesting that the vibronic term only affects the rise and not the fall. Presumably, the vibronic mechanism in only active during the period when the strong optical stimulation field is applied. We currently have no physical explanation.
4.3 Predicted optical transition
We have a number of comments regarding the presence of the optical decay path we have illustrated in Fig. 5. Firstly, we note that the eqn (9) time dependence we derived above for the OSL pulse response is characterised by a single exponential time constant, consistent with a spontaneous emission process. Secondly, the relative slowness of the ~40 µs rise and fall times compared to the nanosecond and picosecond time constants that characterise allowed transitions leads us to suggest
25
that the optical transition to the antibonding level is electric dipole forbidden; that is, the excited state [XO4/M+]+* is metastable.
Thirdly, and rather unexpectedly, within our model we appear to have predicted the existence of an internal infrared transition. As sketched in Fig. 5, the transition energy appears to be of the order of 0.5 eV. The equivalent 2.5 µm emission wavelength therefore lies within one of the atmospheric transmission windows between the visible and medium wave infrared regions of the optical spectrum. We are not aware that emissions within this spectral region have been investigated in relation to OSL. It would clearly be of considerable interest if the presence or otherwise of such an emission within OSL spectra could in future be verified.
4.4 Width of the excited state potential well
We note from our Fig. 5 sketch that we have chosen to widely-space the excited state potential well compared to that which characterises the ground state. Further, we have not specified the scale of the separation variable. Regarding the latter, we do not know whether the separation axis should be linearly or logarithmically scaled.
We recall the value of (9.6 ± 0.8) × 1011 Hz we earlier measured for the frequency factor associated with the thermal quenching process (Spooner et al., 2019). As we have discussed above, within our configurational coordinate model we find that frequency factor is synonymous with the vibrational frequency associated with the Fig. 5 excited state. We therefore have succeeded in associating the thermal quenching frequency factor with a physical process.
26
In comparative terms, the measured frequency is small compared to the known values that are typical of tightly coupled molecules such as oxygen and nitrogen (where the vibrational frequencies lie in the 1013 – 1014 Hz range). The relatively small vibrational frequency identified here is therefore consistent with the concept that the dimer excited state is loosely bound.
4.5 Secondary pulse response
As we noted above in Section 2.1, within our experimental pulsed OSL study (Spooner et al., 2019) we detected several faint long-lived pulse components. The strongest of these was characterised by a 1.60 ± 0.02 ms room temperature time constant and by potential well parameters of 1.1 ± 0.05 eV for the depth and 8 × 1013 Hz for the vibrational frequency. Evidently, the weaker OSL levels we measured in this case are associated with optical stimulation to a significantly more tightly bound excited state.
In Fig. 7 we show how the secondary OSL data can be incorporated within the same configurational framework. There, we have included two additional potential energy curves: a more tightly-bound potential well characterised by 1.1 eV depth and an associated antibonding curve. As in the case of the primary OSL discussed above, we again propose that an optical transition occurs between the excited state and its associated antibonding state. On the basis of the Fig. 7 sketch, it appears that the relevant photon energy would be of the order of 0.2 eV. For the secondary OSL component, then, the optical transition would appear to lie between the medium-wave and long-wave regions of the atmospheric transmission spectrum, being characterised by a wavelength of the order of 6 µm.
27
Fig. 7: Primary and secondary OSL extended configurational coordinate diagram (c-channel only)
Incidentally, the large difference between the vibrational frequencies associated with the primary and secondary OSL components suggests that a logarithmic scale might be the more appropriate for the separation variable employed within Figs. 5 and 7. We also see from Fig. 7 that at higher temperatures (where the higher vibrational levels become better populated) the width of the secondary component potential energy curve enlarges, indicative of lower vibrational frequencies. Although somewhat speculative, this observation may account for the observed high temperature deviation from the Mott-Seitz relationship we observed earlier within Fig. 9(b) of our pulsed OSL study (Spooner et al., 2019).
In completing this Section, we recall that within our pulsed OSL study we found that the secondary OSL pulse response also is characterised by a single exponential time constant. The analysis presented above within Section 2.2 is therefore applicable also to the secondary OSL case. Although we also detected two additional even slower pulse components, the signals were 28
insufficiently strong to enable proper characterisation. It may be the case that curves representing these components need also to be added in future within the configuration framework.
5. Summary
In this paper, we have applied information from our recent pulsed OSL study (Spooner et al., 2019) to develop a new configurational coordinate model that enables a number of characteristics exhibited by quartz OSL to be physically explained. For the first time, we have offered an explanation for the well-known ~40 µs room temperature OSL time constant; namely, that it governs the transition probability for an infrared emission that occurs from an excited state potential well to a lower antibonding level. Further, we have shown that the time constant and the associated OSL processes of thermal assistance and thermal quenching are strongly linked within a common configurational framework, the development of which has enabled the use of an expanded version of the Mott-Seitz equation to be justified within the OSL context.
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Common untrapping mechanisms govern the speed of both optically stimulated luminescence and photo-transferred thermoluminescence in quartz. A defect pair model configurational coordinate model is developed to explain the untrapping mechanisms. The optical stimulation process is modelled as an optical transition between a vibrationallyexcited ground state level of the trap and a dimer excited state. The room temperature pulse response and thermal quenching are represented by competing decay modes which empty a potential well within the excited state.
Declaration of Interest Statement - RADMEAS-S-19-00071 The work in this paper is original and has not been published elsewhere. The principal author (OMW) engages in voluntary research at the University of Adelaide. No funding has been received from any source.
Owen M. Williams Principal author RADMEAS-S-19-00071