# Single-Grain Quartz OSL Characteristics: Testing for Correlations within and between Sites in Asia, Europe and Africa

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## Abstract

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_{0}), and a standardized growth curve (SGC) can be established for each of the DRC groups. There is no distinctive difference in the shape of OSL decay curves among different DRC groups, but samples from different regions have a difference in the OSL sensitivities and decay shapes for different groups. Many of the quartz grains have low D

_{0}values (30–50 Gy), and more than 99% of the grains have D

_{0}values of <200 Gy. Our results raise caution against the dating of samples with equivalent dose values higher than 100 Gy, if there are many low-D

_{0}and ‘saturated’ grains.

## 1. Introduction

_{e}estimation can be dependent on these behaviors, e.g., the shape of the dose response curve (DRC) (or characteristic saturation dose, D

_{0}) [9,10,11,12,13,14,15], OSL sensitivity (or brightness) [16], and shape of OSL decay curves [17,18,19].

_{e}estimates and the variability of a particular OSL characteristic for single grains, e.g., luminescence sensitivity [1,7,15,20], shape of OSL decay curve [1,6,7,15,19,20], and measurement uncertainties (including counting errors and instrument irreproducibility errors) [21]. However, none of these studies have systematically investigated correlations between multiple luminescence behaviors. In this paper, we studied quartz grains extracted from three sites in China, Italy, and Libya. We compared the OSL characteristics of different grains from the same and different samples from different sites. We investigated the relationship and correlation between the OSL characteristics, and discuss their implications for optical dating.

## 2. Sample Description, Preparation, and Measurements

^{90}Sr/

^{90}Y beta sources. For single-grain OSL measurements, standard Risø single grain discs were used (each disc contains 100 holes, each 300 μm in diameter and 300 μm deep) [29]. For the samples of 150 to 180 µm in diameter, extra care was taken to ensure that each hole contained only one grain (e.g., by picking up extra grains with a needle of static electricity). The discs were visually checked under a microscope to ensure that each hole contained only one grain. The spatial variation in the dose rate for individual grain positions was calibrated using gamma-irradiated calibration quartz standards. For the readers used in this study, the maximum difference of single-grain dose rates ranged from ~30% to ~60% (with relative standard deviation from ~5% to ~15%). The ultraviolet OSL emissions were detected by an Electron Tubes Ltd. 9235QA photomultiplier tube fitted with a 7.5-mm Hoya U-340 filter.

_{t}= ~10 Gy) was given after each natural and regenerative dose, with the induced test dose OSL signals used to monitor any sensitivity change that may have occurred during the SAR sequence. A cutheat to a temperature (180 °C) was applied to the test dose. From seven to nine regenerative doses (up to ~1200 Gy) were measured for each sample, including a duplicate regenerative dose to check on the validity of sensitivity correction and a ‘zero dose’ to monitor the extent of any ‘recuperation’ or ‘thermal transfer’ induced by the preheating. We also applied the OSL IR depletion-ratio test [32] at the end of the SAR sequence, using an infrared bleach of 40 s at 50 °C, to check for feldspar contamination.

## 3. Comparing OSL Characteristics

#### 3.1. OSL Decay Curves and Signal Intensities

_{n}) range from a few tens to several tens of thousands of counts per 0.1 s of stimulation time (Figure 1d). The samples from HF have much brighter grains and a wider range of T

_{n}intensities, followed by those from THD. In contrast, the samples from VISO are comparatively dimmer and have a much narrower range of T

_{n}intensities. We calculated the cumulative percentage of luminescence intensities for all the samples, and it is observed that for most of the samples, 15% to 20% of the grains contribute ~80% of the total luminescence (Figure 1e).

_{n}signal against its intensities. The fast ratios were calculated using the following equation:

_{n}and FR for samples from each of the three sites. It appears that brighter grains tend to have larger FR ratios, which is indicated by the positive correlation coefficients (R values) and is especially prominent for samples from VISO (R = 0.13) and THD (R = 0.18), although many dimmer grains also have larger FR ratios and uncertainties. We also tested using a later integral (0.9–1.0 s) for S, and we found no detectable change in the pattern of the relationship. This result suggests that selecting brighter grains may preferentially select grains dominated by the fast component.

#### 3.2. Dose Response Curves

_{n}) was too dim, i.e., the initial intensity was below the instrument detection limit (3σ below background intensity) and/or the relative standard error on the test dose measurement was more than 20%; (2) recuperation or thermal transfer was too high, i.e., the ratio between the sensitivity-corrected OSL signals for the zero dose and the largest regenerative dose was greater than 5%; and (3) the DRC data were too scattered to be fitted with suitable functions (e.g., a single saturating exponential function or a general-order kinetic (GOK) function [35]). We used a figure-of-merit (FOM) value of 10% and a reduced-chi-square (RCS) value of 5, as recommended by Peng and Li [36], as the upper limits for selecting satisfactory DRCs. The implementation of the rejection process was achieved using the functions provided in the R-package ‘numOSL’ [36]. The numbers of grains measured and rejected for each sample are summarized in Table 1. About 25%, 40%, and 65% of the grains from each of the three sites were rejected due to signals being too weak. Less than 5% of the grains in all samples had recuperation values greater than 5%. It is interesting to note that the proportions of grains with poor DRCs differed significantly from site to site, e.g., ~40% for HF, ~11% to 29% for THD, and 22% for VISO. Since the samples from HF are generally much brighter than those from the other sites, it is likely that the brighter grains may be preferentially rejected by the criterion of ‘poor DRC’. In order to test this, we compared the signal intensity distributions of the T

_{n}signal from the grains being associated with ‘good’ and ‘bad’ DRCs, respectively (Figure 1d). It shows that there was no distinctive difference between the T

_{n}intensity distributions of the two groups, indicating that the different proportions of grains with poor DRCs reflects the variability of the grain’s behavior among different sites.

_{n}) and OSL decay curve shapes (using the FR as proxy) of grains to their recuperation value and recycling ratio. For recuperation, we compared all grains with recuperation values <5% (accepted) and >5% (rejected). For the recycling ratio, we compared the grains that had ratios consistent with unity at 2σ (accepted) and those that were inconsistent with unity (rejected). Figure 3a,b shows the T

_{n}and FR values for all accepted and rejected grains based on either the recuperation or recycling ratio from different samples. No distinctive differences were observed. Figure 4 shows all test-dose normalized sensitivity-corrected signals (L

_{x}/T

_{x}*D

_{t}) from a total of 1146 grains that passed the rejection criteria. It shows large between-grain variability in DRCs from the same site, and a similar range of DRCs between grains from different sites. We also measured the DRCs for sample THD-OSL4 using different preheating temperatures ranging from 180 to 280 °C (Figure 4b), and no distinctive difference was observed in the variability in DRCs for different preheating temperatures. The results suggest that the variation in the DRCs is an intrinsic physical behavior rather than an artefact caused by the preheating conditions.

#### 3.3. Sensitivity Change

_{e}determination relies on a successful correction of the sensitivity change, which is usually monitored through the use of a recycling ratio as part of the SAR procedure. Grains with poor recycling ratios are usually rejected for D

_{e}analysis [1]. In this section, we investigated the extent of the sensitivity change for different grains during the SAR measurement procedure and its relationship to different OSL characteristics, such as the brightness, decay curve shape, recuperation, and reproducibility (e.g., recycling ratio). We used the ratio between T

_{x}and T

_{n}as an indicator of the extent of the sensitivity change through SAR cycles. Figure 5 plots the T

_{x}/T

_{n}values obtained for all grains from each site. The test dose signals measured during the first five SAR cycles (including those corresponding to the natural dose, T

_{n}, and four regenerative doses, T

_{1}–T

_{4}) were normalized to T

_{n}. Most of the grains show some sensitivity change from cycle to cycle, and were sensitized or de-sensitized by <50% during the first two measurement cycles (T

_{1}/T

_{n}). Most of them, however, gradually sensitized during subsequent measurement cycles, indicated by the systematic increase in T

_{x}/T

_{n}values. There are a small proportion of grains that produced a >100% change in sensitivity during two successive measurement cycles; this is most prominent for samples from HF and THD. Furthermore, the extent of sensitivity change is not significantly correlated to the sensitivity of the grains (Figure 5) or rate of decay of the OSL signals (Figure S1).

## 4. Grouping of Grains According to the Shape of Their DRCs

_{x}/T

_{x}values between two regenerative dose points, and used the least-square normalization (LS-normalization) procedure to establish a standardized growth curve (SGC) for each of the groups. To test the variability of DRCs of samples from different regions, we grouped and applied the LS-normalization procedure to all grains measured for all the samples investigated in this study.

_{0})], where x is the dose, D

_{0}is the characteristic saturation dose, and A is a constant, and then use the D

_{0}estimate for comparison. However, there are several drawbacks to this method. Firstly, D

_{0}estimates are usually imprecise when only a few regenerative data (e.g., 5–7) and a relatively narrow dose range (e.g., <2D

_{0}) are measured. Li et al. [21] demonstrated that the D

_{0}estimates are influenced significantly by measurement uncertainties and also the measurement strategy (such as the number and range of regenerative doses applied). Another issue with D

_{0}is that it only works when all the DRCs follow a single saturating exponential function, and it becomes problematic when there are many grains follow different growth patterns, such as double exponential or exponential plus linear. For this reason, we followed the method of Li et al. [13] by calculating the L

_{x}/T

_{x}ratios to quantify the saturation characteristic (e.g., shape of DRC) of different grains. We chose the L

_{x}/T

_{x}values of two regenerative doses, ~300 and ~70 Gy, respectively (see Li et al. [13] for a full discussion about how to choose the two regenerative doses). Since different grains have different regenerative doses due to the spatial variation in the dose rates of the beta sources, it is impossible to find exactly the same regenerative doses for all grains. To deal with this, we first fitted the measured L

_{x}/T

_{x}data for individual grains using a GOK function, and then estimated the L

_{x}/T

_{x}values at 300 and 70 Gy based on the best-fit DRCs for individual grains. In order to estimate the uncertainties of individual L

_{x}/T

_{x}ratios, we applied a Monte Carlo method. This involved generating random L

_{x}/T

_{x}values based on the experimental L

_{x}/T

_{x}values and their uncertainties according to Gaussian distributions (by taking the uncertainty of each L

_{x}/T

_{x}value as the standard deviation of the distribution). After that, the generated data were fitted using a GOK function, and an L

_{x}/T

_{x}ratio was calculated for each simulation. This process was repeated 500 times, so that a total of 500 L

_{x}/T

_{x}ratios were obtained. The final L

_{x}/T

_{x}ratio estimate and its uncertainty were then derived directly from the mean and the standard deviation of the sampling distribution of the 500 ratios.

_{x}/T

_{x}ratios close to 1 correspond to early saturated grains (i.e., there was a negligible increase in the OSL signal beyond 70 Gy). In contrast, grains with higher L

_{x}/T

_{x}ratios have a larger saturation dose level.

_{x}/T

_{x}ratios from two regenerative doses do not necessarily tell us the shape of DRC, it is still possible that two grains with the same L

_{x}/T

_{x}ratios have different shaped DRC (e.g., one grain could follow a single-saturation exponential function, and the other could follow a single-saturation exponential plus linear function). Whether different grains share the same shape of DRCs can only be proved by establishing SGCs and investigating the goodness-of-fit of SGC to the data. In order to test whether the eight groups identified in Figure 6 actually did represent their difference in DRCs, the LS-normalization procedure was used to analyze the DRCs from each group. The GOK function was used to construct the DRCs for data from the same groups. Figure 6b shows the LS-normalized regenerative-dose data and their corresponding SGC curves for the eight groups. It can be seen that different groups have considerably different saturation dose levels. When the data for each group were fitted using a single saturating exponential function, D

_{0}values of 32 ± 2, 39 ± 2, 57 ± 1, 76 ± 2, 97 ± 2, 120 ± 5, 144 ± 6, and 197 ± 12 Gy were calculated for groups 1 to 8. To test the validity of the groupings and establishment of the SGCs, the ratios between the measured L

_{x}/T

_{x}values and the expected values based on the best-fitted SGCs were calculated and are shown in Figure S2. The results show that most of the measured-to-expected signal ratios (~90% or more) are statistically consistent with unity at 2σ for all the groups, indicating that most of the grains from the same groups classified based on the L

_{x}/T

_{x}ratios follow the same DRC shape.

## 5. Comparison of OSL Characteristics between Different DRC Groups

_{n}) and decay curve shapes (FR) of the grains from different groups. The T

_{n}of individual grains of different groups for the samples from different sites were compared and are shown in boxplots in Figure 7b. It shows that all groups contain grains with a wide range of sensitivities. There is no distinctive difference in the range of the sensitivities for different groups from the same site. However, it appears that the HF and VISO samples tend to have a larger number of brighter grains in the high-number groups associated with higher saturation doses than THD.

_{x}/T

_{n}values for the first five SAR cycles (similar to those shown in Figure 5) for the grains from different groups for each site (Figure 8). Again, no discernible difference in the extent of sensitivity changes among different DRC groups was observed.

## 6. Discussions and Conclusions

_{e}estimation [10,11,44], indicating that the decay shape of laser-based OSL curves does reflect the physical behavior of the grains to some extent. Furthermore, if the stimulation mode is the primary cause, then we should see a similar correlation between the FR and T

_{n}for different samples, which is not the case, as shown in Figure 2.

_{0}< 50 Gy). Groups 4 to 6, making up 40% to 50% of the accepted grains, have higher saturation doses (D

_{0}from ~70 to 110 Gy), and <5% of the grains fall into groups 7 and 8 that have D

_{0}values of up to ~200 Gy. Among the analyzed grains, only one ‘super-grain’ with a D

_{0}value as high as ~600 Gy was identified. Our results suggest that more than 99% of the grains have D

_{0}value <200 Gy, restricting the dating samples with natural doses higher than ~400 Gy (2D

_{0}) when using the conventional SAR method [45], in which D

_{e}is determined for individual grains based on their corresponding DRCs.

_{0}values (~30–50 Gy), it may result in “truncated” D

_{e}distributions (and, hence, D

_{e}underestimation) for samples with natural doses >100 Gy [21]. As a result, caution should be taken when dating samples with a large proportion of early saturation grains (e.g., [9,10,11,46]). For this case, it would be important to identify only the grains that have relatively larger D

_{0}values to estimate D

_{e}values. To overcome this problem, previous studies suggested the selection of grains based on a range of different D

_{0}thresholds (e.g., [10,11,12,47]). However, this method has limitations if the D

_{0}values are obtained by fitting a few regenerative dose points for each grain, because they strongly depend on measurement uncertainties (e.g., especially for the signal from the largest regenerative dose) and strategy (e.g., the number and range of regenerative doses applied) [21]. This method is also not straightforward when a large number of grains are analyzed and different grains follow different growth patterns. For example, some grains may require a single-saturating exponential plus a linear component to fit their data (in this case, the D

_{0}value does not reflect the saturation dose), and some grains may require a double-saturating exponential function (with two different D

_{0}values, and only the larger one reflects the saturation dose), which makes the comparison of D

_{0}values not straightforward. In contrast, we demonstrated that it is possible to establish SGCs for different groups of quartz [48], which means that one can use the scaling factors of individual grains obtained from SGC analysis to normalize their corresponding natural signals and then apply the new method of Li et al. [21], which involves analyzing the re-normalized L

_{n}/T

_{n}values for grains sharing the same SGC (i.e., from the same group) and projecting the overall estimate (e.g., weighted mean) of L

_{n}/T

_{n}values onto the corresponding SGC to estimate the final D

_{e}. Unlike the conventional method, in which individual L

_{n}/T

_{n}values are projected onto the corresponding DRCs to estimate D

_{e}for individual grains, this method does not reject ‘saturated’ grains, so one can avoid the truncation problem and obtain the full distributions of L

_{n}/T

_{n}for individual DRC groups. This allows a reliable D

_{e}estimation beyond the conventional limit of ~2D

_{0}using the standard SAR procedure. For the cases where the early saturation groups are saturated (i.e., their mean L

_{n}/T

_{n}values are consistent with the saturation levels of corresponding SGCs), only the later saturation groups can yield finite D

_{e}values. This means that all the grains from the early saturation groups are rejected from the final D

_{e}estimation. This method has been successfully applied to date several archaeological sites from southwest China [48] and Russia [49,50].

## Supplementary Materials

_{x}) of the 2nd–5th SAR cycles (T

_{1}–T

_{4}) and the first cycle (T

_{n}) plotted against fast ratio for grains from different sites (shown in different rows); Figure S2, Radial plots showing the ratios between the LS-normalised L

_{x}/T

_{x}values and the expected values based on the best-fit SGC shown in Figure 6a; Table S1, The single-aliquot regenerative-dose (SAR) procedure for single grain.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Ten representative OSL decay curves from three samples (

**a**) HF6031, (

**b**) THD-OSL4, and (

**c**) VISO-OSL1. The inset panels show the same curves but with the y-axis on a logarithmic scale. (

**d**) The density distribution of the test dose signal intensity (T

_{n}) of individual grains from each site. Different colors represent the grains associated with poor or good DRCs, respectively (see Section 3.2). (

**e**) Cumulative light sum plotted against the proportion of grains for each sample.

**Figure 2.**Relationship between the test dose signal intensity (T

_{n}) and fast ratio of individual grains from each site.

**Figure 3.**Boxplots showing the (

**a**) sensitivity (T

_{n}) and (

**b**) fast ratio of grains with different recuperation percentages and recycling ratios. Grains that have recuperation values <5% or recycling ratios consistent with unity (at 2σ) are shown as ‘accepted’ (light blue bars), and those with recuperation values >5% or recycling ratios inconsistent with unity are shown as ‘rejected’ (pink bars). The center lines in each of the boxes show the data median. Boxes show the first and third quartiles (the 25th and 75th percentiles), and the whiskers extend from the upper and lower hinge to the largest and smallest values no further than 1.5 times the interquartile range from the hinge. Data beyond the end of the whiskers are outliers and are plotted individually.

**Figure 4.**(

**a**) Test-dose normalized sensitivity-corrected signal (L

_{x}/T

_{x}*D

_{t}) plotted as a function of regenerative doses for a total of 1146 grains from the study sites. (

**b**) Comparison of DRCs obtained for the sample THD-OSL4 using different preheating temperatures (shown in different symbols).

**Figure 5.**Ratios between test-dose signals (T

_{x}) of the second to fifth SAR cycles (T

_{1}–T

_{4}) and the first cycle (T

_{n}) plotted against inherent sensitivity (T

_{n}) for grains from different sites (shown in different rows). The dashed horizontal lines represent values at 0.5, 1.0, and 1.5, respectively.

**Figure 6.**(

**a**) Radial plot showing the distribution of the ratios of L

_{x}/T

_{x}values between two regenerative doses of 300 and 70 Gy for all accepted grains. The different colors and symbols represent different groups of grains identified using the FMM. (

**b**) The LS-normalized L

_{x}/T

_{x}values plotted against regenerative doses for different groups. The data set for each group was fitted using a GOK function (full lines) and then normalized to unity at 50 Gy.

**Figure 7.**(

**a**) Proportional distribution of accepted grains that make up the different DRC groups for each sample. (

**b**) Boxplots showing the distribution of T

_{n}for all grains from different DRC groups and different sites (shown as different colors). (

**c**) Boxplots showing the fast ratio of T

_{n}for all grains from different DRC groups and different sites (shown as different colors). Centre lines in each of the boxes show the data median. Boxes show the first and third quartiles (the 25th and 75th percentiles), and the whiskers extend from the upper and lower hinge to the largest and smallest values no further than 1.5 times the interquartile range from the hinge. Data beyond the end of the whiskers are outliers and are plotted individually.

**Figure 8.**Boxplots showing the ratios between test-dose signals (T

_{x}) of the second to fifth SAR cycles (T

_{1}–T

_{4}) and the first cycle (T

_{n}) for grains from different groups and different sites (shown in different rows and colors). The center lines in each of the boxes show the data median. Boxes show the first and third quartiles (the 25th and 75th percentiles), and the whiskers extend from the upper and lower hinge to the largest and smallest values no further than 1.5 times the interquartile range from the hinge. Data beyond the end of the whiskers are outliers and are plotted individually.

**Table 1.**Number of single grains measured, rejected, and accepted for each sample, together with the reasons for their rejection. BG: background, RSE: relative standard error, FOM: figure of merit, RCS: reduced chi-squares.

Description | HF6008 | HF6023 | HF6031 | THD-OSL2 | THD-OSL4 | THD-OSL6 | VISO-OSL1 | |
---|---|---|---|---|---|---|---|---|

Total Measured | 300 | 200 | 500 | 300 | 3000 | 300 | 2500 | |

1. Weak signal | T_{n} < 3xBG | 32 (11%) | 17 (9%) | 68 (14%) | 59 (20%) | 1031 (34%) | 81 (27%) | 870 (35%) |

RSE of T_{n} > 20% | 36 (12%) | 27 (14%) | 55 (11%) | 59 (20%) | 715 (24%) | 61 (20%) | 673 (27%) | |

2. Recuperation | >5% | 8 (3%) | 7 (4%) | 26 (5%) | 2 (1%) | 15 (1%) | 2 (1%) | 56 (2%) |

3. Poor DRC | FOM > 10% | 89 (30%) | 26 (13%) | 117 (23%) | 42 (14%) | 374 (12%) | 29 (10%) | 426 (17%) |

RCS > 5 | 51 (17%) | 45 (23%) | 114 (23%) | 12 (4%) | 520 (17%) | 2 (1%) | 115 (5%) | |

Total rejected | 216 (%) | 122 (61%) | 380 (76%) | 174 (58%) | 2655 (89%) | 175 (58%) | 2140 (86%) | |

Total accepted | 84 (%) | 78 (39%) | 120 (24%) | 126 (42%) | 345 (12%) | 125 (42%) | 268 (11%) |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Hu, Y.; Li, B.; Jacobs, Z. Single-Grain Quartz OSL Characteristics: Testing for Correlations within and between Sites in Asia, Europe and Africa. *Methods Protoc.* **2020**, *3*, 2.
https://doi.org/10.3390/mps3010002

**AMA Style**

Hu Y, Li B, Jacobs Z. Single-Grain Quartz OSL Characteristics: Testing for Correlations within and between Sites in Asia, Europe and Africa. *Methods and Protocols*. 2020; 3(1):2.
https://doi.org/10.3390/mps3010002

**Chicago/Turabian Style**

Hu, Yue, Bo Li, and Zenobia Jacobs. 2020. "Single-Grain Quartz OSL Characteristics: Testing for Correlations within and between Sites in Asia, Europe and Africa" *Methods and Protocols* 3, no. 1: 2.
https://doi.org/10.3390/mps3010002