Developing an internally consistent methodology for K-feldspar MAAD TL thermochronology

Luminescence thermochronology and thermometry can quantify recent changes in rock exhumation rates and rock surface temperatures, but these methods require accurate determination of several kinetic parameters. For K-feldspar thermoluminescence (TL) glow curves, which comprise overlapping signals of different thermal stability, it is challenging to develop measurements that capture these parameter values. Here, we present multiple-aliquot additive-dose (MAAD) TL dose response and fading measurements from bedrock-extracted K-feldspars. These measurements are compared with Monte Carlo simulations to identify best-fit values for recombination center density (ρ) and activation energy (∆E). This is done for each dataset separately, and then by combining dose-response and fading misfits to yield more precise ρ and ∆E values consistent with both experiments. Finally, these values are used to estimate the characteristic dose (D0) of samples. This approach produces kinetic parameter values consistent with comparable studies and results in expected fractional saturation differences between samples.


Introduction
heating measurement can alter the shape of subsequent regenerative glow curves, rendering this approach of 'stripping out' sensitivity change by monitoring test dose responses as inadequate, because 26 only certain regions within the curve will become more or less sensitive to irradiation (in some cases, 27 this is overcome by monitoring the changes in peak heights through measurement cycles, although 28 this incorporates further assumptions; Adamiec et al., 2006). In the case of such TL shape changes 29 upon heating, the MAAD approach is ideal for constructing dose-response curves, as all of the dose 30 responses should exhibit natural luminescence efficiency (an exception would be a radiation-induced 31 change in sensitivity; Zimmerman, 1971).

Samples and instrumentation 33
The K-feldspar samples analyzed in this study were extracted from bedrock outcrops across the 34 southern San Bernardino Mountains of Southern California. Young apatite (U-Th)/He ages (Spotila 35 et al., 1998(Spotila 35 et al., , 2001 and catchment-averaged cosmogenic 10 Be denudation rates from this region 36 (Binnie et al., 2007(Binnie et al., , 2010 reveal a landscape which is rapidly eroding in response to transpressional 37 uplift across the San Andreas fault system. Accordingly, we expect the majority of these samples to 38 have cooled rapidly during the latest Pleistocene, maintaining natural trap occupancy below field 39 saturation which is a requirement for luminescence thermochronometry (King et al., 2016a).

40
Twelve bedrock samples were removed from outcrops using a chisel and hammer. After collec-41 tion, samples were spray-painted with a contrasting color and then broken into smaller pieces under 42 dim amber LED lighting. The sunlight-exposed, outer-surface portions of the bedrock samples were 43 separated from the inner portions. The unexposed inner portions of rock were then gently ground 44 with a pestle and mortar and sieved to isolate the 175 -400 µm size fraction. These separates were 45 treated with 3% hydrochloric acid and separated by density using lithium metatungstate heavy 46 liquid (ρ < 2.565 g/cm 3 ; Rhodes 2015) in order to isolate the most potassic feldspar grains. Under 47 a binocular scope, three K-feldspar grains were manually placed into the center of each stainless 48 steel disc for luminescence measurements.

49
All luminescence measurements were performed at the UCLA luminescence laboratory using a 50 TL-DA-20 Risø automated reader equipped with a 90 Sr/ 90 Y beta source which delivers 0.1 Gy/s 51 at the sample location (Bøtter-Jensen et al., 2003). Emissions were detected through a Schott 52 BG3-BG39 filter combination (transmitting between ∼325 -475 nm). Thermoluminescence mea-53 surements were performed in a nitrogen atmosphere and glow curves were measured at a heating 54 rate of 0.5 • C/s to avoid thermal lag between the disc and the mounted grains.

61
Thermoluminescence signals following laboratory irradiation (regenerative TL) of K-feldspar 62 samples are known to fade on laboratory timescales (Wintle, 1973;Riedesel et al., 2021). To 63 quantify this effect in our samples, we prepared 10 natural aliquots per sample. These aliquots 64 were first preheated to 100 • C for 10 s at a rate of 10 • C/s and then heated to 310 • C at a rate of 0.5 • C/s. The first heat treatment is identical to the preheat used in the dose response experiment 66 described in the previous section. The second heat is analogous to the subsequent TL glow curve 67 readout (step 3 in Table 1), but the peak temperature of 310 • C is significantly lower than the peak 68 temperature used in the MAAD dose response experiment. This lower peak temperature was chosen 69 to be just higher than the region of interest within the TL glow curve (150-300 • C), to minimize 70 changes in TL recombination kinetics induced by heating, and ultimately, to evict the natural TL 71 charge population within this measurement temperature bin.

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Following these initial heatings, aliquots were given a beta dose of 50 Gy, preheated to 100 • C 73 for 10 s at a rate of 10 • C/s and then held at room temperature for a set time (Auclair et al., 2003).

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Per sample, two aliquots each were stored for times of approximately 3 ks, 10 ks, 2 d, 1 wk and 75 3 wk. Following storage, aliquots were measured following steps 3 -8 of Table 1. Typical fading 76 behavior is shown for sample J1499 in Fig. 2 and for all samples in Fig. S2.

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The kinetic model is expressed as: where n(r ) and N (r ) are the concentrations (m −3 ) of occupied and total trapping sites, respec-92 tively, at a dimensionless recombination distance r ;Ḋ is the geologic dose rate (Gy/ka); D 0 is the 93 characteristic dose of saturation (Gy); ∆E is the activation energy difference between the ground-94 and excited-states (eV); T is the absolute temperature of the sample (K); k B is the Boltzmann con-95 stant (eV/K); P (r ) is the tunneling probability at some distance r (s −1 ); and s is the frequency 96 factor (s −1 ).

Kinetic parameters 98
We compared results from Eq. 1 with the fading and dose response datasets to estimate the 99 recombination center density ρ (m −3 ) and the activation energy ∆E of each sample using a Monte 100 Carlo approach. First, we compared the T 1/2 values from room temperature fading measurements 101 ( Fig. 2) with modeled values produced using Eq. 1 (Fig. 2). For each of the 5000 iterations, values of 102 ρ and ∆E were randomly selected within the ranges of 10 24 −10 28 m −3 and 0.8 -1.2 eV, respectively.

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As illustrated in Fig. 2, higher ∆E values produce less time dependence of T 1/2 decay and higher slight differences (Fig. 3). Using the same approach and parameter ranges as above, we plot the 112 best-fit fifth and tenth percentile contours in red in Fig. 4. Significantly, the best-fit contours for ρ 113 and ∆E overlap when the fading and curve shape datasets are combined. Values consistent with 114 both the tenth percentile contours of each sample are listed in Table 2.

115
Notice that we evaluate the dimensional ρ rather than the commonly used dimensionless ρ ∆E. Therefore, we isolate these two parameters during data misfit analysis, though we ultimately 120 translate the best-fit ρ into ρ using the independently optimized ∆E value.

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D 0 values were estimated by comparing measured and simulated TL dose response intensities.

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Simulated growth curves were produced with Eq. 1, using the best-fit ρ and ∆E values listed 123 in Table 2. We assume that frequency factors P 0 and s equal 3 × 10 15 s −1 (Huntley, 2006) and  Figure 6 shows the ratio of the natural TL signals to the 'natural + 5 kGy' TL signals. Each 129 ratio shown in Fig. 6 represents the mean and standard deviation of ratios from 6 natural and 3

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The additive dose responses were corrected for fading during laboratory irradiation, prior to 133 measurement using the kinetic parameters in Table 2  is assumed to scale with exhumation rate, it is encouraging that the calculated N/(N + 5 kGy) 147 ratios for these samples follow this pattern.

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The kinetic parameters (Table 2) determined using the approach described here and summarized the best-fit region is considerably reduced, giving more precise estimates of both ρ and ∆E (Fig. 4) 1806629.     Table 2. Monte Carlo iterations from the best-fit 5 th percentile are used to calculate the D 0 , represented by the diamond with error bars and also listed in Table 2. Figure 6: (a -c) The sensitivity-corrected natural (red curves), 'natural + 1 kGy' (green Xs), and 'natural + 5 kGy' (dark blue circles) TL glow curves are shown for samples J0172, J0216, and J1502, with a logarithmic y-axis. Each glow curve is a separate aliquot. (d -f) The 'natural / (natural + 5 kGy)' data are plotted as measured (red Xs) and unfaded (blue circles). Tables   242   Table 1: Thermoluminescence measurement sequence.

Main Text
Step   Figure S1: The sensitivity-corrected natural (red curves), 'natural + 1 kGy' (green Xs), and 'natural + 5 kGy' (dark blue circles) TL glow curves are shown for all samples, with a logarithmic y-axis. Each glow curve is a separate aliquot. Figure S2: Intensity normalized TL glow curves following a laboratory dose of 50 Gy followed by a preheat and then various room temperature storage durations, ranging from about 3 ks to 3 wk. Each delay time is represented by two aliquots per sample.