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A new approach towards anomalous fading correction for feldspar IRSL dating — tests on samples in field saturation
Radiation Measurements 43 (2008) 786 – 790 www.elsevier.com/locate/radmeas
A new approach towards anomalous fading correction for feldspar IRSL dating — tests on samples in field saturation R.H. Kars a,b , J. Wallinga a,∗ , K.M. Cohen b a Netherlands Centre for Luminescence Dating, Technical University of Delft, Mekelweg 15, Delft, The Netherlands b Department of Physical Geography, Utrecht University, Heidelberglaan 2, Utrecht, The Netherlands
Abstract Anomalous fading of the feldspar infrared stimulated luminescence (IRSL) signal hampers possibilities of using feldspar IRSL to obtain burial ages for sediments beyond the dating range of quartz optically stimulated luminescence. Here, we propose a new approach to quantify anomalous fading of the feldspar IRSL signal over geological burial times based on laboratory fading experiments. The approach builds on the description of the quantum mechanical tunnelling process recently proposed by Huntley [2006. An explanation of the power-law decay of luminescence. J. Phys. Condensed Matter 18, 1359–1365]. We show that our methods allow the construction of un-faded and natural IRSL dose–response curves as well as anomalous fading rates in field saturation. The predicted level of field saturation closely approximates the measured saturation level for five samples from fluvial deposits (Lower Rhine) known to be older than 1 Ma. The modelled anomalous fading rate in field saturation (13.4% per decade) is close to the measured value of 11.2% per decade. These results indicate that the proposed method may allow anomalous fading corrected IRSL dating beyond the linear part of the IRSL dose–response curve. © 2008 Elsevier Ltd. All rights reserved. Keywords: Quantum mechanical tunnelling; Luminescence dating; Fading correction
1. Introduction Luminescence dating is an important tool to obtain age constraints for Quaternary sediments. The optically stimulated luminescence (OSL) signal of quartz is most commonly used for dating, but has a limited age range (usually up to ∼150 ka) due to saturation of the quartz OSL signal. Because feldspar infrared stimulated luminescence (IRSL) signals saturate at higher doses, IRSL of feldspars can potentially be used for dating well beyond the range of quartz OSL. However, the trapped charge giving rise to the IRSL signal may be affected by quantum-mechanical tunnelling, where charge recombines without travelling through the conduction band (e.g. Visocekas, 2002; Huntley, 2006). This process, referred to as anomalous fading by the luminescence dating community, leads to underestimation of the equivalent dose and therefore the age of the deposits (e.g. Wintle, 1973).
∗ Corresponding author.
E-mail address: [email protected] (J. Wallinga). 1350-4487/$ - see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.radmeas.2008.01.021
On laboratory timescales, fading can be described by logarithmic decay expressed as a percentage of signal loss per decade (g%: Aitken, 1985—Appendix F), where a decade is a factor 10 increase in delay time since irradiation. Huntley and Lamothe (2001) and Lamothe et al. (2003) proposed fading correction methods based on extrapolation of logarithmic decay. These methods have been shown to provide age estimates in agreement with independent age information for relatively young samples (20–50 ka) with equivalent doses in the linear part of the dose–response curve (DRC) (Huntley and Lamothe, 2001). However, the logarithmic approximation of decay of the IRSL signal is not valid for very short and very long delay times (Huntley and Lamothe, 2001). Huntley (2006) recently proposed an improved description of the fading decay of the IRSL signal, describing quantum-mechanical tunnelling as a function of trap lifetimes, the probability distribution of trapto-recombination-centre distances and the recombination centre density. After considerable geological burial time (∼1 Ma) the feldspar IRSL signal will reach an equilibrium state where no further signal builds up as charge recombination due to
R.H. Kars et al. / Radiation Measurements 43 (2008) 786 – 790
tunnelling equals charge trapping due to exposure to ionizing radiation (e.g. Huntley and Lian, 2006). In such situations of ‘field saturation’, traps with long lifetimes are truly saturated whereas traps with short lifetimes remain largely empty. The eventual distribution of available traps thus is skewed towards the short-lifetime traps that cause fading, and as a consequence fading rates will increase during geological burial (Lamothe et al., 2003; Huntley and Lian, 2006; Wallinga et al., 2007). In this research we test the applicability of the Huntley (2006) model for time dependence of the tunnelling process for predicting the behaviour of feldspar IRSL signals in the high dose region in natural situations. We present a model that: (1) predicts the field saturation level based on laboratory fading measurements, (2) allows construction of a natural (faded) DRC, and (3) predicts fading rates in field saturated systems. 2. Samples and methods We collected samples from exposed Rhine deposits that occur as stacked formations in a sand and gravel quarry at Hoher Stall (Lower Rhine Embayment, Dutch–German border). Based on palynological evidence and stratigraphical correlation the sampled strata are of Late Pliocene and Early Pleistocene age (e.g. Kemna, 2005; Kemna and Westerhoff, 2007). For this investigation we concentrate on five samples (NCL-4406042 to 4406047) taken from formations dating between ∼3 and ∼1 Ma ago (strata that define the Reuverian and Tiglian chronostratigraphical stages). The IRSL signals for these samples are expected to have reached field saturation. The 180.212 m grain-size fraction was isolated through wet sieving. The samples were treated with HCl and H2 O2 to remove carbonates and organic matter and the potassium-rich feldspar grains were obtained through separating the lighter fraction using a 2.58 kg dm−3 sodiumpolytungstate solution. We calculated the external dose rate from the radionuclide concentration obtained through gamma spectrometry, assuming gradual burial since deposition for calculation of the cosmic dose rate. For the internal dose rate we assumed an internal K-content of 12.5% (Huntley and Baril, 1997) and Rb-content of 400 ppm (Huntley and Hancock, 2001). Exposure of the outer rim of the grains to external alpha radiation was taken into account as no HF etching was used. All luminescence measurements were made using a RisZ TL-DA-15 TL/OSL reader equipped with infrared (IR) diodes (870 nm) for stimulation (BZtter-Jensen et al., 2003). IRSL signals were collected using an LOT/Oriel D410/30 interference filter, selecting the K-feldspar emission around 410 nm (Krbetschek et al., 1997). For dose–response and fading measurements we employed the single aliquot regenerative (SAR) dose protocol for feldspars (Wallinga et al., 2000) using the same preheating procedure (60 s at 260 ◦ C) for regenerative and test doses (Auclair et al., 2003; Blair et al., 2005). At the end of each SAR cycle an IR bleach (100 s at 280 ◦ C) was included as a precaution to avoid recuperation effects. IR measurements were made at 30 ◦ C for 100 s, we used the net IRSL signal obtained by subtracting the normalized background (90–100 s) from the initial signal (0–2 s). This protocol yielded good dose
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recovery (1.01 ± 0.01), recuperation (< 0.2%) and recycling ratios (1.02 ± 0.02). For fading measurements, three aliquots per sample were bleached (100 s at 280 ◦ C), given a 10 Gy dose and measured after storage periods ranging from prompt measurement after 216 s (including half of the irradiation time; Aitken, 1985), to a delay of 208 ks (∼3 decades). The preheat was applied immediately after irradiation and prior to storage (following Auclair et al., 2003). For each sample the sensitivity corrected IRSL signals were normalized to the first measurement. In additional experiments, we measured fading using the single aliquot additive dose (SAAD) protocol (Duller, 1991), for bleached samples and for samples still bearing their large natural dose. In a first SAAD experiment, four aliquots per sample were bleached, given a 50 Gy dose, preheated (60 s at 260 ◦ C), and measured with short shines (0.1 s, 10% intensity) at consecutive storage times. Of four other aliquots per sample the natural was measured to monitor IRSL signal decay due to the short-shine measurements. In a second SAAD experiment, four aliquots per sample were given a 525 Gy dose additional to their natural (N + ) and subsequently measured as described above for the SAAD fading experiment. Of four other aliquots per sample, the natural (N ) was measured in the same way. After the SAAD experiment the IRSL signal was reset (100 s IR stimulation at 280 ◦ C) and subsequently we measured the response to a test dose; this response was used to normalize all measurements. The normalized readings on the natural aliquots were used to correct all measurements (N and N + ) for measurement-induced signal loss. Then the normalized and corrected N signals were subtracted from the N + to isolate the induced IRSL signal. The fading rate in field saturation is obtained from the decay of this signal after storage. 3. Description of the model 3.1. Assumptions Following Huntley (2006), we assume that within the feldspar crystal recombination centres are randomly distributed with a density (but see Poolton et al., 2007), and electrons tunnel to their nearest recombination centre only. The mean lifetime of tunnelling decay () for an electron-recombination centre pair with tunnelling distance r is given by = s −1 er ,
(1)
where is a constant and s is the attempt-to-escape frequency (taken to be 3 × 1015 s−1 , Huntley, 2006). For the sake of simplicity, r is introduced, given by r ≡ {4/3}1/3 r.
(2)
The probability that the nearest recombination centre lies between distance r and dr from a given trap is shown in Fig. 1 and follows from: p(r ) dr = 3(r )2 exp{−(r )3 } dr .
(3)
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R.H. Kars et al. / Radiation Measurements 43 (2008) 786 – 790
Fig. 1. The probability distribution (p(r )) of trap-to-recombination-centre distances (r ) (following Huntley, 2006); the area under the curve represents the entire trapped-charge population. Trapped charge with nearby recombination centres (left-hand side) recombines through quantum-mechanical tunnelling.
Combining Eqs. (1) and (3) allows us to add a top axis to Fig. 1 displaying the life times of the traps. The position of this axis shifts when changes. The density of recombination centres can be derived from laboratory fading measurements. We express the density as a dimensionless variable (Huntley, 2006—Eq. (5)): 4 ≡ 3 . 3
(4)
The portion of trapped electrons remaining after a delay time (t) depends on the density of recombination centres in the crystal (Eq. (7) from Huntley, 2006). Since the IRSL signal reflects the amount of trapped charge, we have rewritten the equation to IRSLfaded = IRSLinitial exp{− [ln(1.8 st)]3 }.
(5)
3.2. Fading results The measured signal in the laboratory experiments is the faded signal. By plotting the Li /Ti ratios from the SAR fading experiments against time, we obtain a through fitting the data with Eq. (5) using Origin 7.5 software. The distributions of trap lifetimes can now be calculated (top-axis, Fig. 1) using Eqs. (1) and (3). For the five samples we obtained an average value of 3.6 ± 0.5 × 10−6 (Eq. (5)) using the SAR method (Fig. 2). This equals a fading rate (g2 days ) of 5.3 ± 0.9% per decade (Huntley and Lamothe, 2001—Eq. (4)). On a separate set of bleached aliquots, SAAD experiments yielded a g value 2.2 ± 0.4% per decade. Results for individual aliquots in both methods varied widely but all agreed within uncertainty with the average value. The measurements of N + , performed with SAAD, yielded a much higher fading rate of 11.2 ± 0.9% per decade (Fig. 2). No value was derived from these data because the measured
Fig. 2. Decay of the IRSL signal with delay time after irradiation. Results are shown for the low dose region (SAR, triangles) and for samples in field saturation (SAAD, squares). The dotted line represents IRSL fading in field saturation according to our simulation model. The inset shows a comparison of extrapolation of the measured data assuming logarithmic decay (dashed line) and using Eq. (5) (solid line).
fading is not sourced from the entire population of traps and can therefore not be used to calculate the recombination centre density. 3.3. Dose–response curves Owing to fading during laboratory irradiation the measured DRC underestimates the DRC that would be obtained assuming immediate measurement (i.e. no fading). We measured DRCs for three aliquots of all five samples. The results show similar DRCs for all samples and we used an average DRC for further analysis. From this data we constructed an un-faded DRC (Fig. 3) using Eq. (5) and the density of recombination centres ( ) obtained from the SAR fading experiment. Fig. 1 illustrates the difference between the measured and un-faded DRC to be caused by the traps with lifetimes shorter than ∼7 ks. For high doses (irradiation times of a few thousand seconds) most charge from these traps will have tunnelled out by the time of measurement. Where fading in the entire trap-recombination centre system is described by a power law, that of a group of traps with a given r will follow a simple exponential decay. We exploit this to construct a faded DRC for each trap-type where trap filling is described by ˙ dn D(N − n) n − , = dt D0
(6)
where n is the amount of trapped electrons in N electron traps, D˙ is the dose rate, D0 the characteristic dose in the saturating exponential of the un-faded DRC and the trap life time (Huntley and Lian, 2006, Appendix A). We calculated a DRC for 250 values of r ranging from 0 to 2.5, with the saturation
R.H. Kars et al. / Radiation Measurements 43 (2008) 786 – 790
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The shape of the simulated natural DRC shown in Fig. 3 determines the datable age range of these samples. Following Wintle and Murray (2006), we assume that equivalent doses can be measured up to two times D0 for a single saturating ˙ exponential DRC. For our samples (D0 ∼500 Gy, D∼2.5 Gy) this suggests that fading corrected IRSL dating could be possible up to an age of ∼400 ka. We do consider however that the model slightly underestimates the natural level of field saturation and this may result in inaccurate results especially when approaching saturation. 5. Conclusions We present a novel method to quantify IRSL anomalous fading in geological samples based on laboratory fading measurements. Our natural fading simulation model builds on a description of quantum-mechanical tunnelling in feldspars presented by Huntley (2006) and hindcasts the build up of IRSL signal during geological storage. Our simulation model allows: Fig. 3. Measured (solid line), un-faded (dashed line) and simulated natural (dotted line) dose–response curves.
levels for each determined by its probability (p(r ) in Fig. 1). Summation of these DRCs gives a single DRC that describes the entire trap population for a given dose rate. The IRSL field saturation level relative to the un-faded saturation level may also be obtained without calculating a natural DRC. In field saturation the rate of trapping charge is equal to the rate of charge recombination due to tunnelling (Eq. (6); dn/dt = 0). When is known from laboratory fading experiments, can be calculated for each trap type and Eq. (6) can be used to determine the saturation level (n/N ) at a given dose rate for each trap type. Summation of these results, taking into account the probability distribution (Fig. 1), gives the field saturation level relative to the un-faded saturation level. 4. Results The measured value for recombination centre density ( = 3.6 × 10−6 ), the natural dose rate and the characteristics of the un-faded DRC are the parameters in the model. Because the model results are insensitive to the small variations in the natural dose rate of the samples we used an average value of 2.5 Gy ka−1 . The model yields a level of field saturation of 37% of the un-faded saturation level, which is close to the measured natural saturation level of 46% (Fig. 3). The modelled charge distribution in field saturation is now used as input to model fading in the high-dose region. The model simulates exposure of this distribution to a dose of 525 Gy at laboratory dose rate. Modelling the decay of the signal after the end of irradiation yields a fading rate of 13.4% per decade, which is close to the measured value in the high-dose region using SAAD (11.2% per decade, Fig. 2). We do not attempt here to quantify the uncertainties of the model. We note however that the model results depend strongly on and on the accuracy of the measured DRC.
(a) reconstruction of a un-faded IRSL DRC, (b) reconstruction of the IRSL DRC at environmental dose rates, (c) prediction of IRSL field saturation levels, (d) prediction of IRSL fading rates in field saturation. The simulation model has the potential of providing fadingcorrected IRSL ages up to the saturation dose of feldspar IRSL. The potential dating range depends on the natural dose rate and the fading rate: IRSL dating of deposits up to ∼400 ka seems feasible for sites in the Lower Rhine Embayment. Acknowledgements The research described here was supported through NWO Grants 863.03.006 and 834.03.003. Clarity of the manuscript was improved following suggestions from an anonymous referee. We enjoyed discussions with Nigel Poolton, Adrie Bos and Andrew Murray. We thank Candice Johns for guidance and lab support. References Aitken, M.J., 1985. Thermoluminescence Dating. Academic Press, London. Auclair, M., Lamothe, M., Huot, S., 2003. Measurement of anomalous fading for feldspar IRSL using SAR. Rad. Meas. 37, 487–492. Blair, M.W., Yukihara, E.G., McKeever, S.W.S., 2005. Experiences with single-aliquot OSL procedures using coarse-grain feldspars. Rad. Meas. 39, 361–374. BZtter-Jensen, L., Andersen, C.E., Duller, G.A.T., Murray, A.S., 2003. Developments in radiation, stimulation and observation facilities in luminescence measurements. Rad. Meas. 37, 535–541. Duller, G.A.T., 1991. Luminescence dating of sediments using single aliquots: new procedures. Quat. Geochr. 13, 149–156. Huntley, D.J., 2006. An explanation of the power-law decay of luminescence. J. Phys. Condensed Matter 18, 1359–1365. Huntley, D.J., Baril, M.R., 1997. The K content of the K-feldspars being measured in optical dating or thermoluminescence dating. Ancient TL 15-1, 11–13.
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Huntley, D.J., Hancock, R.G.V., 2001. The Rb contents of the K-feldspars being measured in optical dating. Ancient TL 19-2, 43–46. Huntley, D.J., Lamothe, M., 2001. Ubiquity of anomalous fading in K-feldspars and the measurement and correction for it in optical dating. Can. J. Earth Sci. 38, 1039–1106. Huntley, D.J., Lian, O.B., 2006. Some observations on tunnelling of trapped electrons in feldspar and their implications for optical dating. Quat. Sci. Rev. 25, 2503–2512. Kemna, H.A., 2005. Pliocene and Pleistocene stratigraphy of the Lower Rhine Embayment, Germany. Kölner Forum Geol. Paläontol. 14, 1–22. Kemna, H.A., Westerhoff, W.E., 2007. Remarks on the palynology-based chronostratigraphical subdivision of Pliocene terrestrial deposits in NWEurope. Quat. Int. 164,165, 184–196. Krbetschek, M.R., Götze, J., Dietrich, A., Trautmann, T., 1997. Spectral information from minerals relevant for luminescence dating. Rad. Meas. 27 (5/6), 695–748. Lamothe, M., Auclair, M., Hamzaoui, C., Huot, S., 2003. Towards a prediction of long-term anomalous fading of feldspar IRSL. Rad. Meas. 37, 493–498.
Poolton, N.R.J., Towlson, B.M., Hamilton, B., Wallinga, J., Lang, A., 2007. Micro-imaging synchrotron-laser interactions in wide band-gap luminescent materials. J. Phys. D—Appl. Phys. 40, 3557–3562. Visocekas, R., 2002. Tunnelling in afterglow, its coexistence and interweaving with thermally stimulated luminescence. Rad. Prot. Dosim. 100, 45–54. Wallinga, J., Murray, A.S., Wintle, A.G., 2000. The single aliquot regenerativedose (SAR) protocol applied to coarse-grain feldspar. Rad. Meas. 32, 529–533. Wallinga, J., Bos, A.J.J., Dorenbos, P., Murray, A.S., Schokker, J., 2007. A test case for anomalous fading correction in IRSL dating. Quat. Geochr. 2, 216–221. Wintle, A.G., 1973. Anomalous fading of thermoluminescence in mineral samples. Nature 245, 143–144. Wintle, A.G., Murray, A.S., 2006. A review of quartz optically stimulated luminescence characteristics and their relevance in single-aliquot regeneration dating protocols. Rad. Meas. 41, 369–391.
A new approach towards anomalous fading correction for feldspar IRSL dating — tests on samples in field saturation R.H. Kars a,b , J. Wallinga a,∗ , K.M. Cohen b a Netherlands Centre for Luminescence Dating, Technical University of Delft, Mekelweg 15, Delft, The Netherlands b Department of Physical Geography, Utrecht University, Heidelberglaan 2, Utrecht, The Netherlands
Abstract Anomalous fading of the feldspar infrared stimulated luminescence (IRSL) signal hampers possibilities of using feldspar IRSL to obtain burial ages for sediments beyond the dating range of quartz optically stimulated luminescence. Here, we propose a new approach to quantify anomalous fading of the feldspar IRSL signal over geological burial times based on laboratory fading experiments. The approach builds on the description of the quantum mechanical tunnelling process recently proposed by Huntley [2006. An explanation of the power-law decay of luminescence. J. Phys. Condensed Matter 18, 1359–1365]. We show that our methods allow the construction of un-faded and natural IRSL dose–response curves as well as anomalous fading rates in field saturation. The predicted level of field saturation closely approximates the measured saturation level for five samples from fluvial deposits (Lower Rhine) known to be older than 1 Ma. The modelled anomalous fading rate in field saturation (13.4% per decade) is close to the measured value of 11.2% per decade. These results indicate that the proposed method may allow anomalous fading corrected IRSL dating beyond the linear part of the IRSL dose–response curve. © 2008 Elsevier Ltd. All rights reserved. Keywords: Quantum mechanical tunnelling; Luminescence dating; Fading correction
1. Introduction Luminescence dating is an important tool to obtain age constraints for Quaternary sediments. The optically stimulated luminescence (OSL) signal of quartz is most commonly used for dating, but has a limited age range (usually up to ∼150 ka) due to saturation of the quartz OSL signal. Because feldspar infrared stimulated luminescence (IRSL) signals saturate at higher doses, IRSL of feldspars can potentially be used for dating well beyond the range of quartz OSL. However, the trapped charge giving rise to the IRSL signal may be affected by quantum-mechanical tunnelling, where charge recombines without travelling through the conduction band (e.g. Visocekas, 2002; Huntley, 2006). This process, referred to as anomalous fading by the luminescence dating community, leads to underestimation of the equivalent dose and therefore the age of the deposits (e.g. Wintle, 1973).
∗ Corresponding author.
E-mail address: [email protected] (J. Wallinga). 1350-4487/$ - see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.radmeas.2008.01.021
On laboratory timescales, fading can be described by logarithmic decay expressed as a percentage of signal loss per decade (g%: Aitken, 1985—Appendix F), where a decade is a factor 10 increase in delay time since irradiation. Huntley and Lamothe (2001) and Lamothe et al. (2003) proposed fading correction methods based on extrapolation of logarithmic decay. These methods have been shown to provide age estimates in agreement with independent age information for relatively young samples (20–50 ka) with equivalent doses in the linear part of the dose–response curve (DRC) (Huntley and Lamothe, 2001). However, the logarithmic approximation of decay of the IRSL signal is not valid for very short and very long delay times (Huntley and Lamothe, 2001). Huntley (2006) recently proposed an improved description of the fading decay of the IRSL signal, describing quantum-mechanical tunnelling as a function of trap lifetimes, the probability distribution of trapto-recombination-centre distances and the recombination centre density. After considerable geological burial time (∼1 Ma) the feldspar IRSL signal will reach an equilibrium state where no further signal builds up as charge recombination due to
R.H. Kars et al. / Radiation Measurements 43 (2008) 786 – 790
tunnelling equals charge trapping due to exposure to ionizing radiation (e.g. Huntley and Lian, 2006). In such situations of ‘field saturation’, traps with long lifetimes are truly saturated whereas traps with short lifetimes remain largely empty. The eventual distribution of available traps thus is skewed towards the short-lifetime traps that cause fading, and as a consequence fading rates will increase during geological burial (Lamothe et al., 2003; Huntley and Lian, 2006; Wallinga et al., 2007). In this research we test the applicability of the Huntley (2006) model for time dependence of the tunnelling process for predicting the behaviour of feldspar IRSL signals in the high dose region in natural situations. We present a model that: (1) predicts the field saturation level based on laboratory fading measurements, (2) allows construction of a natural (faded) DRC, and (3) predicts fading rates in field saturated systems. 2. Samples and methods We collected samples from exposed Rhine deposits that occur as stacked formations in a sand and gravel quarry at Hoher Stall (Lower Rhine Embayment, Dutch–German border). Based on palynological evidence and stratigraphical correlation the sampled strata are of Late Pliocene and Early Pleistocene age (e.g. Kemna, 2005; Kemna and Westerhoff, 2007). For this investigation we concentrate on five samples (NCL-4406042 to 4406047) taken from formations dating between ∼3 and ∼1 Ma ago (strata that define the Reuverian and Tiglian chronostratigraphical stages). The IRSL signals for these samples are expected to have reached field saturation. The 180.212 m grain-size fraction was isolated through wet sieving. The samples were treated with HCl and H2 O2 to remove carbonates and organic matter and the potassium-rich feldspar grains were obtained through separating the lighter fraction using a 2.58 kg dm−3 sodiumpolytungstate solution. We calculated the external dose rate from the radionuclide concentration obtained through gamma spectrometry, assuming gradual burial since deposition for calculation of the cosmic dose rate. For the internal dose rate we assumed an internal K-content of 12.5% (Huntley and Baril, 1997) and Rb-content of 400 ppm (Huntley and Hancock, 2001). Exposure of the outer rim of the grains to external alpha radiation was taken into account as no HF etching was used. All luminescence measurements were made using a RisZ TL-DA-15 TL/OSL reader equipped with infrared (IR) diodes (870 nm) for stimulation (BZtter-Jensen et al., 2003). IRSL signals were collected using an LOT/Oriel D410/30 interference filter, selecting the K-feldspar emission around 410 nm (Krbetschek et al., 1997). For dose–response and fading measurements we employed the single aliquot regenerative (SAR) dose protocol for feldspars (Wallinga et al., 2000) using the same preheating procedure (60 s at 260 ◦ C) for regenerative and test doses (Auclair et al., 2003; Blair et al., 2005). At the end of each SAR cycle an IR bleach (100 s at 280 ◦ C) was included as a precaution to avoid recuperation effects. IR measurements were made at 30 ◦ C for 100 s, we used the net IRSL signal obtained by subtracting the normalized background (90–100 s) from the initial signal (0–2 s). This protocol yielded good dose
787
recovery (1.01 ± 0.01), recuperation (< 0.2%) and recycling ratios (1.02 ± 0.02). For fading measurements, three aliquots per sample were bleached (100 s at 280 ◦ C), given a 10 Gy dose and measured after storage periods ranging from prompt measurement after 216 s (including half of the irradiation time; Aitken, 1985), to a delay of 208 ks (∼3 decades). The preheat was applied immediately after irradiation and prior to storage (following Auclair et al., 2003). For each sample the sensitivity corrected IRSL signals were normalized to the first measurement. In additional experiments, we measured fading using the single aliquot additive dose (SAAD) protocol (Duller, 1991), for bleached samples and for samples still bearing their large natural dose. In a first SAAD experiment, four aliquots per sample were bleached, given a 50 Gy dose, preheated (60 s at 260 ◦ C), and measured with short shines (0.1 s, 10% intensity) at consecutive storage times. Of four other aliquots per sample the natural was measured to monitor IRSL signal decay due to the short-shine measurements. In a second SAAD experiment, four aliquots per sample were given a 525 Gy dose additional to their natural (N + ) and subsequently measured as described above for the SAAD fading experiment. Of four other aliquots per sample, the natural (N ) was measured in the same way. After the SAAD experiment the IRSL signal was reset (100 s IR stimulation at 280 ◦ C) and subsequently we measured the response to a test dose; this response was used to normalize all measurements. The normalized readings on the natural aliquots were used to correct all measurements (N and N + ) for measurement-induced signal loss. Then the normalized and corrected N signals were subtracted from the N + to isolate the induced IRSL signal. The fading rate in field saturation is obtained from the decay of this signal after storage. 3. Description of the model 3.1. Assumptions Following Huntley (2006), we assume that within the feldspar crystal recombination centres are randomly distributed with a density (but see Poolton et al., 2007), and electrons tunnel to their nearest recombination centre only. The mean lifetime of tunnelling decay () for an electron-recombination centre pair with tunnelling distance r is given by = s −1 er ,
(1)
where is a constant and s is the attempt-to-escape frequency (taken to be 3 × 1015 s−1 , Huntley, 2006). For the sake of simplicity, r is introduced, given by r ≡ {4/3}1/3 r.
(2)
The probability that the nearest recombination centre lies between distance r and dr from a given trap is shown in Fig. 1 and follows from: p(r ) dr = 3(r )2 exp{−(r )3 } dr .
(3)
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Fig. 1. The probability distribution (p(r )) of trap-to-recombination-centre distances (r ) (following Huntley, 2006); the area under the curve represents the entire trapped-charge population. Trapped charge with nearby recombination centres (left-hand side) recombines through quantum-mechanical tunnelling.
Combining Eqs. (1) and (3) allows us to add a top axis to Fig. 1 displaying the life times of the traps. The position of this axis shifts when changes. The density of recombination centres can be derived from laboratory fading measurements. We express the density as a dimensionless variable (Huntley, 2006—Eq. (5)): 4 ≡ 3 . 3
(4)
The portion of trapped electrons remaining after a delay time (t) depends on the density of recombination centres in the crystal (Eq. (7) from Huntley, 2006). Since the IRSL signal reflects the amount of trapped charge, we have rewritten the equation to IRSLfaded = IRSLinitial exp{− [ln(1.8 st)]3 }.
(5)
3.2. Fading results The measured signal in the laboratory experiments is the faded signal. By plotting the Li /Ti ratios from the SAR fading experiments against time, we obtain a through fitting the data with Eq. (5) using Origin 7.5 software. The distributions of trap lifetimes can now be calculated (top-axis, Fig. 1) using Eqs. (1) and (3). For the five samples we obtained an average value of 3.6 ± 0.5 × 10−6 (Eq. (5)) using the SAR method (Fig. 2). This equals a fading rate (g2 days ) of 5.3 ± 0.9% per decade (Huntley and Lamothe, 2001—Eq. (4)). On a separate set of bleached aliquots, SAAD experiments yielded a g value 2.2 ± 0.4% per decade. Results for individual aliquots in both methods varied widely but all agreed within uncertainty with the average value. The measurements of N + , performed with SAAD, yielded a much higher fading rate of 11.2 ± 0.9% per decade (Fig. 2). No value was derived from these data because the measured
Fig. 2. Decay of the IRSL signal with delay time after irradiation. Results are shown for the low dose region (SAR, triangles) and for samples in field saturation (SAAD, squares). The dotted line represents IRSL fading in field saturation according to our simulation model. The inset shows a comparison of extrapolation of the measured data assuming logarithmic decay (dashed line) and using Eq. (5) (solid line).
fading is not sourced from the entire population of traps and can therefore not be used to calculate the recombination centre density. 3.3. Dose–response curves Owing to fading during laboratory irradiation the measured DRC underestimates the DRC that would be obtained assuming immediate measurement (i.e. no fading). We measured DRCs for three aliquots of all five samples. The results show similar DRCs for all samples and we used an average DRC for further analysis. From this data we constructed an un-faded DRC (Fig. 3) using Eq. (5) and the density of recombination centres ( ) obtained from the SAR fading experiment. Fig. 1 illustrates the difference between the measured and un-faded DRC to be caused by the traps with lifetimes shorter than ∼7 ks. For high doses (irradiation times of a few thousand seconds) most charge from these traps will have tunnelled out by the time of measurement. Where fading in the entire trap-recombination centre system is described by a power law, that of a group of traps with a given r will follow a simple exponential decay. We exploit this to construct a faded DRC for each trap-type where trap filling is described by ˙ dn D(N − n) n − , = dt D0
(6)
where n is the amount of trapped electrons in N electron traps, D˙ is the dose rate, D0 the characteristic dose in the saturating exponential of the un-faded DRC and the trap life time (Huntley and Lian, 2006, Appendix A). We calculated a DRC for 250 values of r ranging from 0 to 2.5, with the saturation
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The shape of the simulated natural DRC shown in Fig. 3 determines the datable age range of these samples. Following Wintle and Murray (2006), we assume that equivalent doses can be measured up to two times D0 for a single saturating ˙ exponential DRC. For our samples (D0 ∼500 Gy, D∼2.5 Gy) this suggests that fading corrected IRSL dating could be possible up to an age of ∼400 ka. We do consider however that the model slightly underestimates the natural level of field saturation and this may result in inaccurate results especially when approaching saturation. 5. Conclusions We present a novel method to quantify IRSL anomalous fading in geological samples based on laboratory fading measurements. Our natural fading simulation model builds on a description of quantum-mechanical tunnelling in feldspars presented by Huntley (2006) and hindcasts the build up of IRSL signal during geological storage. Our simulation model allows: Fig. 3. Measured (solid line), un-faded (dashed line) and simulated natural (dotted line) dose–response curves.
levels for each determined by its probability (p(r ) in Fig. 1). Summation of these DRCs gives a single DRC that describes the entire trap population for a given dose rate. The IRSL field saturation level relative to the un-faded saturation level may also be obtained without calculating a natural DRC. In field saturation the rate of trapping charge is equal to the rate of charge recombination due to tunnelling (Eq. (6); dn/dt = 0). When is known from laboratory fading experiments, can be calculated for each trap type and Eq. (6) can be used to determine the saturation level (n/N ) at a given dose rate for each trap type. Summation of these results, taking into account the probability distribution (Fig. 1), gives the field saturation level relative to the un-faded saturation level. 4. Results The measured value for recombination centre density ( = 3.6 × 10−6 ), the natural dose rate and the characteristics of the un-faded DRC are the parameters in the model. Because the model results are insensitive to the small variations in the natural dose rate of the samples we used an average value of 2.5 Gy ka−1 . The model yields a level of field saturation of 37% of the un-faded saturation level, which is close to the measured natural saturation level of 46% (Fig. 3). The modelled charge distribution in field saturation is now used as input to model fading in the high-dose region. The model simulates exposure of this distribution to a dose of 525 Gy at laboratory dose rate. Modelling the decay of the signal after the end of irradiation yields a fading rate of 13.4% per decade, which is close to the measured value in the high-dose region using SAAD (11.2% per decade, Fig. 2). We do not attempt here to quantify the uncertainties of the model. We note however that the model results depend strongly on and on the accuracy of the measured DRC.
(a) reconstruction of a un-faded IRSL DRC, (b) reconstruction of the IRSL DRC at environmental dose rates, (c) prediction of IRSL field saturation levels, (d) prediction of IRSL fading rates in field saturation. The simulation model has the potential of providing fadingcorrected IRSL ages up to the saturation dose of feldspar IRSL. The potential dating range depends on the natural dose rate and the fading rate: IRSL dating of deposits up to ∼400 ka seems feasible for sites in the Lower Rhine Embayment. Acknowledgements The research described here was supported through NWO Grants 863.03.006 and 834.03.003. Clarity of the manuscript was improved following suggestions from an anonymous referee. We enjoyed discussions with Nigel Poolton, Adrie Bos and Andrew Murray. We thank Candice Johns for guidance and lab support. References Aitken, M.J., 1985. Thermoluminescence Dating. Academic Press, London. Auclair, M., Lamothe, M., Huot, S., 2003. Measurement of anomalous fading for feldspar IRSL using SAR. Rad. Meas. 37, 487–492. Blair, M.W., Yukihara, E.G., McKeever, S.W.S., 2005. Experiences with single-aliquot OSL procedures using coarse-grain feldspars. Rad. Meas. 39, 361–374. BZtter-Jensen, L., Andersen, C.E., Duller, G.A.T., Murray, A.S., 2003. Developments in radiation, stimulation and observation facilities in luminescence measurements. Rad. Meas. 37, 535–541. Duller, G.A.T., 1991. Luminescence dating of sediments using single aliquots: new procedures. Quat. Geochr. 13, 149–156. Huntley, D.J., 2006. An explanation of the power-law decay of luminescence. J. Phys. Condensed Matter 18, 1359–1365. Huntley, D.J., Baril, M.R., 1997. The K content of the K-feldspars being measured in optical dating or thermoluminescence dating. Ancient TL 15-1, 11–13.
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