The µ Dose-system: determination of environmental dose rates by combined alpha and beta counting – performance tests and practical experiences

. The µ Dose-system is a recently developed analytical instrument applying a combined α - and β -sensitive scintillation technique for determining the radioactivity arising from the decay chains of 235 U , 238 U and 232 Th as well as from the decay of 40 K . The device was designed to meet the particular requirements of trapped charge dating methods and allows the assessment of environmental (i


Introduction
Over the last two decades, trapped charge dating techniques have become commonly applied standard tools for age determination of sediments in palaeo-environmental and geo-archaeological research.The vast arsenal of luminescence and electron spin resonance (ESR) dating methods (e.g., Bateman, 2019;Grün, 1989;Preusser et al., 2008) allows the direct dating of sedimentation processes, heating events, and for ESR the precipitation of minerals.Ages gained with trapped charge dating are derived from doses (energy per mass unit), stored by minerals such as quartz and feldspars, which are ubiquitously present in natural sediments and other materials such as tooth enamels and ceramics.These minerals may therefore be used as dosimeters.The dating events are associated with processes which involve the energetic stimulation of these minerals either by sunlight exposure (e.g., during sediment transport) or by natural or artificial heating (e.g., rocks fritted during volcanic eruptions; ceramics heated in kilns).The optical or thermal stimulation releases the dose previously stored within the crystal lattices of the involved dosimeters thus "zeroing" the "luminescence clock" (e.g., Bateman, 2019;Wagner, 1998).When the minerals are no longer stimulated (e.g. after sediment deposition or after the end of the heating event), they remain exposed to the natural ionizing radiation arising from both cosmic radiation and the radioactive decay of members of the 238 U, 235 U and 232 Th decay chains as well as from the decay of 40 K in the surrounding sediments.This ongoing exposure to ionizing radiation results in a timedependent accumulation of radiation doses within the minerals (e.g., Preusser et al., 2008).The total amount of dose absorbed under natural conditions since the last stimulation event is termed the palaeodose and can be determined in the laboratory by means of luminescence or ESR measurements, based on a comparison with a corresponding amount of artificially administered (usually mono-energetic βor γ-) dose, which is called the equivalent dose.ESR and luminescence ages are derived from this palaeodose and the total environmental dose rate.The dose rate describes the location-specific strength of natural ionizing radiation per time and is formally defined as the rate at which energy is absorbed by a dosimeter from the flux of radiation to which the dosimeter is exposed (e.g., Aitken, 1998).
While the cosmic component of the environmental dose rate is typically derived from information on the exact sampling position by applying well established formulas (e.g., Prescott and Hutton, 1994), the contribution of ionizing radiation arising from the surrounding sediments is calculated by determining the activity concentrations of the relevant natural radionuclides.
For dose rate determination, several in situ procedures using either portable gamma-spectrometers or sensitive dosimeters such as BeO or Al 2 O 3 have been developed.Additionally, laboratory analyses of bulk material are applied, inter alia including emission counting methods such as thick source alpha counting (TSAC; e.g., Turner et al., 1958) and beta counting (e.g., Sanderson, 1988), spectrometric approaches like low-level high-resolution gamma spectrometry (HRGS) and neutron activation analysis (NAA) as well as geochemical techniques such as inductively coupled plasma mass spectrometry (ICP-MS) and inductively coupled plasma optical emission spectrometry (ICP-OES).
Recently, a laboratory-based, combined αand β-particle detection instrument called µDose-system has been developed (e.g., Miłosz et al., 2017;Tudyka et al., 2018).Providing a cost-efficient approach, this novel device allows the determination of radionuclide concentrations of 238 U, 235 U, 232 Th and 40 K. Up to now, this measurement system has not been tested systematically.Therefore, we present a performance test based on three µDose-devices and compare the results obtained with the new approach with those from established analytical techniques.The comprehensive study includes measurements on a total of ~50 samples, covering natural samples as well as IAEA standards, and involves five different laboratories.In addition, we provide recommendations for sample handling and data analysis for the µDose-results derived from practical experiences so far made in the Giessen Luminescence Laboratory.

Technical description
The µDose-system (Fig. 1) is a compact and easy to handle analytical instrument allowing the simultaneous detection of αand β-particles.For this purpose, the system is equipped with a dual-layer scintillator (Fig. 1b) consisting of a plate of β-sensitive (synthetic) material, which is coated with a thin film of ZnS : Ag for detecting α-particles.This dual-layer scintillator is part of the cover plate of the sample container and thus placed between the sample material and the photomultiplier.Since the scintillator does not have direct contact to the sample material under investigation and is additionally protected by an approximately 0.2 µm thin silver foil, the scintillator is reusable.In addition, this silver foil reflects photons emitted by the scintillators which increases photon counting efficiency and guarantees an equal level of efficiency independent of the respective sample material.
For measurements, the sample material is placed on a thin disc of filter paper, which is stored in a gas tight sample container (Fig. 1e).The diameter of the disc matches the diameter of the photomultiplier tube (PMT), which may vary from 30 mm to 70 mm.For the present study, a PMT with a diameter of 70 mm was used.A detailed description of the technical setup is given by Tudyka et al. (2018).
αand β-particles are discriminated based on the different shapes of the pulses induced by the particles.Amplified by the PMT, these pulses are identified and analysed by a pulse analyser unit that has previously been described in detail by Miłosz et al. (2017).During the measurement process, an Analogue to Digital Converter (ADC) samples and transforms the incoming pulses into digital values (ADC values).These ADC values are time-stamped and stored in a database.Thus, a re-evaluation of data is possible at any time without the need to repeat the measurement.Data analyses is performed by applying a special algorithm.This algorithm determines pulse height and pulse shape of the stored pulses allowing the discrimination between αand β-induced pulses as well as the elimination of background pulses caused by interfering variables.Data analysis is possible after finishing the measurement as well as during a still running measurement process.The µDose-system is not only capable of discriminating between αand β-particles, but also allows the detection of decay pairs.Such decay pairs arise from the fast succession of two decays and thus two incoming pulses (pairs) detected within a very short and specific period of time.These pairs are the results of short half-lives of some members of the involved decay chains.This principle has long been used in TSAC to derive the particular contributions from the uranium and thorium series (e.g., Aitken, 1985).Whereas the TSAC technique is restricted to α-α-pairs, the µDose-system is also able to make use of β-α-pairs, which can be identified based on the individual timestamp of each detected pulse.Thus, the determination of the activities arising from the 238 U-, 235 Uand 232 Th-series as well as from the decay of 40 K is based on two α-α-pairs and two β-α-pairs.A summary is given in Table 1.One α-α-pair is part of the 235 U-series and caused by the successive α-decays of 219 Rn and 215 Po, with the latter showing a half-life of 1.78 ms.With 220 Rn/ 216 Po (half-life of 216 Po: 145 ms) a second α-α-pair is part of the 232 Th-series.One β-α-pair arises from the successive decay of 212 Bi and 212 Po, which has a half-life of only 299 ns.Finally, the β-decay of 214 Po (half-life: 164 µs) following an α-decay of 214 Bi is a characteristic component of the 238 U-series.On condition that the investigated sample is in or at least close to secular equilibrium, the αand β-counts associated with the above mentioned decay pairs allow to calculate the concentrations of 238 U, 235 U as well as 232 Th and thus provide the possibility to derive the series-specific activities.The particular 40 K activity is determined as residual value derived from the excess of observed β-counts over the β-counts expected to arise from the determined 238 U-, 235 Uand 232 Th-series.
For details on how decay pairs are statistically identified and for a thorough description of formulas and assumptions used for calculating the specific contributions arising from the different decay series, the reader is referred to Tudyka et al. (2018).

System calibration
Since the activities are derived from the net count rates of the detected decay pairs using equations for which pair-specific calibration parameters are needed (cf., Tudyka et al., 2018), these parameters have to be determined for each µDose-device by performing calibration measurements on material of known activities.The µDose-systems can be calibrated for different amounts of sample material using calibration material distributed by the manufacturer.
For the calibration of the µDose-systems at the Giessen Luminescence Laboratory, three standards prepared on behalf of the IAEA are used, i.e.IAEA-RGU-1, IAEA-RGTh-1 and IAEA-RGK-1 (hereafter always mentioned as RGU-1, RGTh-1 and RGK-1).For a detailed description of the calibration material, see Sect.3.1 of this article.Moreover, a device-and location-specific background value has to be determined using a background disc placed on the sample holder.Since all three calibration materials have high activities, the respective calibration measurements were performed for only 24 hours.For the background determination, a longer lasting measurement of seven days was executed.In order to increase the accuracy of the calibration, we advise to use repeated measurements of all standards and to derive the calibration parameters from the means of these repeated measurements.This will substantially reduce the impact of random errors potentially affecting single measurements.In the Giessen Luminescence Laboratory, the means of three repeated measurements for each standard and one background measurement are combined to define the device-specific calibration.Comprising 10 separate measurements (3x3 IAEA standards + 1 background measurement), the whole calibration procedure requires a total duration of ~14 days.The µDose software offers a user-friendly calibration module to define and manage calibrations.
Since raw data of finished measurements (i.e. the ADC coded pulses) are stored in a database, data evaluation can be performed at any time using different calibration settings.This allows recalculating the determined activities without the need of conducting another time-consuming measurement.Furthermore, this database solution provides the opportunity to identify significant changes in the technical specifications of the devices.
Although there were no such significant changes detected so far during the ~1.5 years of µDose-usage in the Giessen Luminescence Laboratory, such changes seem possible and might predominantly be attributed to various ageing effects.These ageing effects may affect the used silver foil, the dual-layer scintillator or other electronic components of the devices, in particular the efficiency of the built-in PMTs.Thus, we strongly recommend a re-calibration of the µDose-systems at regular intervals in order to guarantee that the determined calibration parameters still match the actual technical status of the measurement setup.In the Giessen Luminescence Laboratory, a re-calibration of the µDose-systems is performed twice a year with time intervals of not more than six to eight months.This re-calibration is not only based on an isolated measurement of a specific test sample, but comprises the whole calibration procedure as described above, including nine separate measurements of IAEA standards as well as a prolonged measurement of the device-specific background signal.

Determination of uncertainties
The µDose-system considers several sources of uncertainties that are associated either with the measurement procedure or with the sample preparation.The most dominant uncertainties are derived from the counting statistics of calibration measurements (here IAEA standards and background) and investigated samples.Additionally, there is a relative counting rate uncertainty of 0.001 that corresponds to sample preparation reproducibility or other unknown sources of error.This component of uncertainty will not decrease with increasing measurement time.The µDose-system allows adjusting the (recommended) default values for each device by user-specified values.Uncertainty propagation considers correlations between the individual uncertainties determined for the different radionuclide activities/concentrations. A detailed description on the mode of uncertainty propagation used for µDose-analysis is provided by Tudyka et al. (2020).
3 Sample materials for the performance test

IAEA standards
Provided by the IAEA, RGU-1, RGTh-1 and RGK-1 standards were not only used as calibration material for the µDosesystems (see above) but also for performance tests validating the quality of calibration.The RGU-1 and RGTh-1 standards were both prepared by the Canada Centre for Mineral and Energy Technology.The standards were derived from a uranium ore (BL-5) and a thorium ore (OKA-2), respectively.These raw materials were diluted with floated silica powder of negligible uranium and thorium contents.For both raw materials, the IAEA was able to show them to be in radioactive equilibrium (for details see IAEA, 1987).

Nussy loess standard
The Nussy reference material is a loess sample from a well-known loess section near Nußloch (e.g., Antoine et al., 2001;Bente and Löscher, 1987;Sabelberg and Löscher, 1978) located ~10 km south of the city of Heidelberg, at the eastern shoulder of the Upper Rhine Graben, Germany (49°19' N, 8°43' E, 217 m a.s.l.).Here, loess sediments revealing a total thickness of ~16 m are covering a basement of Middle Triassic limestone and dolomite formations.The sample was collected from the Upper Weichselian loess deposits accumulated during the last glacial-interglacial cycle.The Nussy sample reveals grain sizes characteristic for loess sediments, ranging from 2−63 µm.The material was first used as a reference material in the Heidelberg Luminescence Laboratory (e.g., Kalchgruber, 2002;Rieser, 1991) and prepared as the first certified reference material (CRM) for loess by Kasper et al. (2001).Based on an inter-laboratory comparison with contributions from three different laboratories, Preusser and Kasper (2001) Preusser and Kasper (2001).All values are summarized in Table 4.

Volkegem loess standard
The Volkegem reference material is a loess sample that has been collected in a former quarry in the city of Volkegem (East-Flanders, Belgium).Originally, the reference material was characterized in a comprehensive study by De Corte et al. (2007).
After drying at 110°C and milling, the sample material was sieved to grain diameters < 50 µm and homogenized.This material was investigated applying k 0 -INAA and HPGe gamma spectrometry and additionally cross-checked by in situ gamma spectrometry, TSAC and Geiger-Muller beta-counting (for a detailed description see De Corte et al., 2007).As reference data, they were able to determine mean radionuclide concentrations of 2.79 ± 0.12 mg • kg −1 for U, 10.4 ± 0.6 mg    Durcan et al., 2015).All calculations are based on the radionuclide concentrations provided in this table, applying the dose rate conversion factors given by Guérin et al. (2011).Please note that a constant water content of 15 ± 5 % and a constant contribution of 0.150 ± 0.015 Gy • ka −1 arising from cosmic radiation were assumed for all calculations.We would like to point out that these assumed values do not correspond to the values that might actually be determined for Nussy and Volkegem sampling sites.Therefore, the calculated dose rates are referred to as 'simulated environmental dose rates' in the table and in the text.

Natural samples
For this study, 47 natural samples covering a great variety of environmental settings and landscapes were analysed in order to validate the performance of µDose-measurements.The samples were provided by and measured in five laboratories in Germany and Poland, including the luminescence laboratories at the universities of Bayreuth, Cologne, Giessen and Heidelberg as well as the Institute of Physics in Gliwice.All analysed samples are summarized in Table B1 in Appendix B. A detailed description of sampling locations including geological, stratigraphic and morphological settings is provided in Appendix C.
4 Experimental settings for the µDose-measurements in the Giessen Luminescence Laboratory

Sample preparation
All analysed samples were dried in a drying chamber at an elevated temperature of 105°C for several days.The dried sample material was gently crushed using a porcelain mortar and then homogenized.Approximately 10 g of this homogenized material were pulverized in a ball mill (Retsch M 400) using a frequency of 29.5 Hz for 45 minutes and dry sieved with analytical sieves showing mesh sizes of 63 µm.This sieving procedure is used as an additional backstop in the sample preparation, which is based on the idea that coarse-grained residuals of > 63 µm indicate that the applied milling duration was not sufficient to provide fully pulverized material.Thus, the sieving step is not used to exclude resilient grains with diameters > 63 µm, since this would cause a mineral-specific fractionation and introduce bias to the µDose-measurements.The additional sieving step merely aims at surveying the quality of the preparation procedure applied in the Giessen Luminescence Laboratory.With respect to the samples investigated in this study, we were not able to detect any residual material > 63 µm.Therefore, we conclude that the applied milling duration of 45 minutes was sufficient to provide pulverized material adequate for µDose-measurements.
After weighing 3.00 g of this pulverized material with a high precision balance (Fig. 1c), the sample material was placed on a sample carrier and carefully fixed on top of a disc of filter paper, using a stamp made of acrylic glass (Fig. 1a & Fig. 1d).
The discs show diameters matching the diameters of the used PMTs (here 70 mm).For the measurement procedure, the filled sample carriers were stored in a device-specific, gas-tight measurement container (Fig. 1e) which prevents migration of radon from and into the container.
Additionally, the bottom of the measurement container is filled with granular active carbon, which contributes to reducing the radon concentration of the air within the container.This aims at avoiding an accumulation of radon gas right in front of the scintillator module, which may impact the alpha count rate.

Technical settings for the µDose-devices
All measurements have been performed on µDose-devices installed in the Luminescence Laboratory of the Department of Geography at the Justus Liebig University Giessen.The devices are situated in a laboratory that is exclusively designated for sedimentological analyses and for the preparation of dose rate samples.Thus, neither luminescence measurement systems with their integrated radioactive sources nor other technical devices that might generate radiation fields or electromagnetic fields 215 had any kind of potentially distracting impact on the µDose-measurements.
Three measurement systems with identical technical features are installed -named "005-Ahnert", "006-Bremer" and "007-Rohdenburg" (Fig. 1f).All devices are equipped with internal high voltage power supplies and photomultiplier tubes (PMT) that have a photocathode diameter of 70 mm.The measurement units are controlled by a single PC with distinct, systemspecific measurement software.Measurement data are primarily stored on the built-in SSD-drive of this PC and additionally saved on backup servers provided by the Department of Geography.A device-specific unique measurement ID is assigned for each measurement.
The µDose-systems at the Giessen laboratory are calibrated for a total amount of 3 g of sample material.In order to guarantee that all investigated samples matched this specification, the samples were checked using a high precision balance prior to the measurements.Only those samples lying within a range of 2.995 g to 3.005 g were accepted for measurement.
In order to minimize the possible bias of α-counts due to the adhesion of radon bearing particles from ambient air, a delayed start of the measurement procedure is advised.In the Giessen Luminescence Laboratory, the applied time delay was at least one hour, i.e. after storing the sample in the measurement container and sealing it, the operator has to wait for at least one hour before initiating the start of the measurement procedure.For ease of use, upcoming versions of the µDose software will provide the possibility to define an automated and user specified time delay.
The respective measurement times strongly depended on the sample-specific activities.For the experiment analysing the impact of measurement duration (see Sect. 4.3.2),various measurement times were applied.Due to their high activities, relatively short measurement times of ~24 hours were used for the IAEA-standards RGU-1, RGTh-1 and RGK-1, yielding excellent counting statistics.For the remaining samples, including both loess standards and natural samples, measurements were continued until the number of detected α-counts reached the level of approximately 3,000 counts, an empirically determined threshold that was derived from long lasting experiences with TSAC at the University of Bayreuth (pers.comm.L. Zöller).
Depending on the respective activities of a sample, this value corresponds to measurement durations of two to four days for samples revealing average environmental dose rates in the range of 2 Gy • ka −1 to 4 Gy • ka −1 .

Experimental setups
For this study, a total of three different experiments were conducted which aimed at assessing the performance and reliability of the µDose-systems.

Accuracy and reproducibility of results
A first experimental setting aimed at assessing the reproducibility and accuracy of measurement results gained with the µDosesystems.Therefore, repeated measurements were performed on the certified IAEA standards and on the two loess standards.
For these measurements, one 3 g subsample of each standard was prepared.These subsamples were used for all measurements on all devices.So, there was no re-sampling.Once stored in the device-specific measurement container, the subsamples were not removed from the container until all measurements on the respective device were completed.Measurements for the IAEA standards were restricted to ~24 hours, while the loess standards were each measured for approximately four to five days.
Measurements have been performed on all three devices.

The impact of the measurement duration
The measurement duration required for a reliable result might be a crucial point since accuracy and precision of the µDosemeasurements strongly depend on the net count rates of αand β-particles.In TSAC, device-specific numbers of α-counts are often used as thresholds to ensure count rates that enable the calculation of radionuclide concentrations with a sufficiently high precision.As already mentioned above, a value of approximately 3, 000 α-counts is routinely used in the Giessen laboratory to guarantee reliable results.However, this value is merely an arbitrary threshold, which is derived from long lasting experiences with TSAC in the luminescence laboratory at the University of Bayreuth (pers.comm.Ludwig Zöller).With particular respect to environmental samples revealing low radionuclide concentrations the usage of such a high threshold may lead to prolonged measurement times that would not be desirable for routine dose rate measurements.In the Giessen Luminescence Laboratory for instance, several samples originating from the Negev desert (Israel) were measured, for which dose rates of < 1 Gy • ka −1 could be determined.Applying the 3, 000 α-counts criterion, each sample had to be measured for more than 15 days.
In order to investigate the impact of measurement duration and to test whether shorter measurement times also provide reliable results, 3 g subsamples of both loess standards Nussy and Volkegem were repeatedly measured applying various measurement times.The measurement times lasted from a minimum of approximately ten hours to more than seven days, corresponding to total α-counts of ~200 to more than 8, 000.All measurements were performed as stand-alone measurements, i.e. the results for short-and medium-time measurements were calculated from numerous separate measurements and not derived from one long-lasting master-measurement.Both subsamples were measured on all three µDose-systems.Once stored in the measurement container, the subsamples were not removed from the container until all measurements were finished for the respective device.For all measurements, the same subsamples of Nussy and Volkegem loess standards were used.

Comparison to established measurement procedures
In order to test the overall performance of the µDose-system, we initiated a comprehensive inter-laboratory comparison including five different laboratories from Germany and Poland, which applied different measurement procedures.The involved laboratories were: (i) the Giessen Luminescence Laboratory, (ii) the Bayreuth Luminescence Laboratory, (iii) the Cologne Luminescence Laboratory, (iv) the Heidelberg Luminescence Laboratory and (v) the Institute of Physics (Division of Geochronology and Environmental Isotopes) in Gliwice.
For this performance test, we re-investigated a total of 47 environmental samples for which either radionuclide concentrations or activities had already been determined by either TSAC in combination with ICP-OES (Bayreuth) or low-level HRGS (Cologne, Heidelberg, Gliwice).Details on sample preparation and technical specifications of the µDose-systems in Giessen are provided in Sect.4.1 and 4.2.The measurement configurations applied in the other participating laboratories are briefly summarized in Table 5.Details of sample preparation and information on the applied measurement procedures including used gamma lines are provided in Appendix A. The investigated samples represent a broad variety of regions and environmental settings (see Table B1 and sample characterization in the Appendix).5 Results and discussion

Accuracy and reproducibility of measurement results
The accuracy and reproducibility of measurement results were tested by repeated measurements of three certified IAEA standards that had also been used for the calibrations of the µDose-devices.Due to their high radionuclide concentrations these standards provide high decay rates improving the statistics of αand β-counts.Figure 2 shows the results of repeated measurements of these standards expressed as relative deviations of measured results from the expected reference values provided by the IAEA.For the plot, only the results obtained for the dominant radioactive emitter of the respective standard were con-  sidered.So, for RGK-1 only the activity of 40 K, for RGTh-1 the activity of 232 Th and for the uranium standard RGU-1 the combined activities of 235 U and 238 U were analysed.
From the results shown in Fig. 2 we are able to draw two important conclusions: (i) µDose-measurements of IAEA standards reveal an excellent accuracy.For potassium, thorium and uranium, all measured values are within the respective 95 % confidence intervals certified by the IAEA.The majority of relative deviations of measured activities from the certified values are < 1 %.The mean relative calibration deviations are: −0.0001 % for 40 K, −0.4554 % for 232 Th and −0.0298 % for 235+238 U.
These values correspond to measured-to-given ratios of 1.0000 for 40 K, 0.9955 for 232 Th and 0.9997 for 235+238 U and indicate an excellent quality of the implemented µDose calibrations.(ii) The repeated measurements of IAEA standards are characterized by an excellent reproducibility.The determined results reveal neither statistically significant outliers nor distinct differences between the different measurement devices.The relative standard deviations (RSD) obtained from statistics and averaged for all devices are: 0.10 % for 40 K, 0.80 % for 232 Th and 0.45 % for 235+238 U.An overview summarizing accuracy and statistical reproducibility is provided in Table 6.
These results may be attributed to the high content of radionuclides characteristic for the investigated IAEA standards.
Although only measured for ~24 hours, the net α-counts detected for RGU-1 and RGTh-1 show mean values of ~46, 000 cts and ~30, 000 cts, respectively.These total numbers of α-counts are more than 10 times higher than the threshold value of  3, 000 α-counts typically applied in the Giessen Luminescence Laboratory for µDose-measurements of sediment samples.In summary, these results indicate the excellent quality of µDose-calibration and a good reproducibility of measurements.
Figure 3 shows the accuracy and reproducibility of results gained for the two loess standards Nussy (Preusser and Kasper, 2001) and Volkegem (De Corte et al., 2007).For the Nussy standard, the mean values of the determined concentrations averaged over all three devices are: 1.08 % (SD: 0.07 %) for potassium, 8.53 mg • kg −1 (SD: 1.30 mg • kg −1 ) for thorium and 2.43 mg • kg −1 (SD: 0.32 mg • kg −1 ) for uranium.These values correspond to mean measured-to-given-ratios of 1.13 for potassium, 1.15 for thorium and 0.91 for uranium.
For both samples, the uranium contents are slightly underestimated by ~10 %, whereas thorium contents are overestimated by ~15 % and ~18 %, respectively.For the Nussy standard, potassium is also overestimated by ~13 % while there is a nearly perfect agreement with the reference value for the Volkegem standard.
At a first glance, the results obtained for the loess standards seem to indicate some kind of problems concerning the accuracy of the µDose-measurements.In order to check this and to assess intra-sample variability, we re-sampled and re-measured both loess standards.The results of these additional measurements did not significantly differ from the results reported in this study and showed similar deviations of ~9 % up to ~17 %.However, when talking about deviations determined for specific radionuclides, it should be considered that uranium and thorium concentrations are not detected independently in µDose-measurements (see Sec. 2.1).This dependency can clearly be seen when looking at the Th-and U-concentrations of  the Volkegem loess standard in the lower part of Fig. 3. Whenever Th-concentrations are higher than the expected value, the corresponding U-concentration is lower and vice versa.For the Nussy loess standard, the results shown in the upper part of Fig. 3 are similar, but not as obvious as for the Volkegem loess standard.When deriving environmental dose rates, the exact 325 Th/U-ratio has some relevance.However, the conversion of alpha count rates to dose rates in TSAC shows that the conversion factor for the beta dose rate is higher for uranium and lower for thorium, while the conversion factor for the gamma contribution is higher for thorium and lower for uranium (e.g., Aitken, 1985).In the end, there is at least a partial compensation.As a result, the total environmental dose rate does not vary much with the exact Th/U-ratio (e.g., Li and Tso, 1995).With respect to the determination of environmental dose rates, deviations in the individual concentrations/activities of uranium and thorium are

Nussy loess standard
Volkegem loess standard Volkegem loess standard  a value of 2.71 ± 0.15 Gy • ka −1 is expected.The simulated environmental dose rates calculated for the µDose-results show a range from 2.70 Gy • ka −1 to 2.98 Gy • ka −1 and average at a value of 2.77 ± 0.02 Gy • ka −1 , which corresponds to a mean measured-to-given ratio of 1.02.If the above mentioned extreme outliers are not considered for data analysis, the average simulated dose rate for the remaining measurements is 2.75 ± 0.01 Gy • ka −1 and the measured-to-given ratio improves to 1.01.In summary, we can conclude that the µDose-measurements are able to provide results that allow the calculation of simulated environmental dose rates that are in good agreement with the expected benchmark value for the Volkegem loess standard.
For the Nussy loess standard the results are less satisfying.With an average combined uranium and thorium activity of 66.01 Bq • kg −1 , the µDose-measurements overestimate the benchmark of 64.74 Bq • kg −1 derived from the values published by Preusser and Kasper (2001) by only ~2 %.This would correspond to a promising overall measured-to-given ratio of 1.02.
However, the bulk uranium and thorium values determined by the µDose-measurements show a rather large relative standard deviation of ~10 %.Furthermore, there are distinct inter-device differences reflected by pronounced variations in the devicespecific mean measured-to-given ratios.These ratios range from 0.92 for the devices "006-Bremer" and "007-Rohdenburg" to 1.13 for device "005-Ahnert".While the first two devices underestimate the expected value, the latter shows a considerable overestimation.
When looking at the calculated simulated environmental dose rates, the results are slightly better than for the combined activities of uranium and thorium.The mean value averaged for all measurements is 2.04 ± 0.02 Gy • ka −1 and is slightly higher than the benchmark of 1.93 ± 0.07 Gy • ka −1 .With device-specific measured-to-given ratios of 1.09 (Ahnert), 1.03 (Bremer) and 1.04 (Rohdenburg), the average measured-to-given ratio for all devices corresponds to 1.06.Except for the values of two µDose-measurements, all simulated environmental dose rates are beyond the range of the 95 % confidence interval given for the benchmark of Preusser and Kasper (2001).But still, all simulated environmental dose rates are within the range of benchmarks calculated for the IAG values and for the values provided by Murray et al. (2018), which can clearly be seen on the left side of Fig. 4b.
For a meaningful interpretation of results it has to be considered that the published reference values were derived from a limited number of gamma spectrometry and k 0 -INAA measurements that were carried out under specific laboratory conditions.
Therefore, they may suffer from distinct methodological problems.On a closer inspection, it thus becomes apparent that intermethodological deviations of more than 10 % are neither unusual for dosimetry measurements (e.g., Murray et al., 2015) nor necessarily indicate serious deficits in the respective measurement procedures.On contrary, the results obtained for the IAEA standards (see above) suggest good accuracy and reproducibility of µDose-measurements.
A closer look at the publication of Preusser and Kasper (2001) shows that the authors do not only provide results derived from HRGS, but also ICP-MS based values from three different laboratories.The magnitude of scatter in the data reported for the Nussy loess standard is comparable to the maximum deviations determined for the µDose-measurements.For the K content, values from 0.96 % to a maximum of 1.14 % are reported, while the Th and U contents range from 7.4 mg

Measurement time and associated alpha count rates
Dosimetry measurements can be time-consuming.This might either be caused by the need of extensive preparation procedures and long-lasting storage times or due to the measurement process itself.For the µDose-system, sample preparation is relatively rapid and samples can be measured immediately after the preparation procedure without the need for storage for specific periods of time.Since accuracy and precision of µDose-measurements strongly depend on the net alpha and beta count rates, the measurement duration is a decisive factor for the quality of the obtained results.In terms of net αand β-counts, this becomes obvious when comparing the results gained from the investigated IAEA standards (up to ~30, 000−46, 000 α-counts) to the results determined for the loess standards (up to ~3, 000 α-counts; see Sect.5.1).In theory, longer measurement times will provide better counting statistics (i.e., higher numbers of αand β-counts) which should improve both, accuracy and precision of the results.From a theoretical point of view, long lasting measurements thus should be favoured.However, it is obviously impossible to implement such an approach in practice since for typical environmental samples trying to reach count rates similar to those reported for the IAEA standards would mean having to accept long lasting measurements of several weeks or even months.
Figure 5 shows the results of an experiment aiming at identifying whether there is a particular lower limit of measurement durations for which still reliable results can be expected.The plots show radionuclide concentrations (y-axis) plotted against the total number of detected α-counts (x-axis).All measurements were conducted as separate stand-alone measurements on the same subsamples of the Nussy and Volkegem loess standards.
The majority of results is clustering rather closely to the median values indicated by the bold lines.Overall, this seems to be true for all measurement durations.For the thorium and uranium contents of the Volkegem loess standard, short-time measurements with a total number of α-counts < 2, 000 show a larger deviation from the median.This also applies to extremely short measurements of only few hours for U-and Th-values obtained for the Nussy standard.Apart from that, other short-time measurements for Nussy do not show such a distinct deviation from the median, but only reveal a slightly larger scatter compared to long-time measurements.With respect to the potassium results, the picture is not so clear.For Volkegem, shorttime measurements of < 2, 000 α-counts at least show a large scatter and a slightly larger deviation from the median than measurements with longer durations.For Nussy however, neither the deviation from the median nor the inter-measurement scatter indicate that this group of measurements might be less precise than measurements of longer duration.Unlike for thorium and uranium, even measurements with a duration of only some hours do not differ from the median value.
Although there are some sources of uncertainty which do not get smaller with time (see Sect. 2.3), longer lasting measurements in theory should be expected to be associated with considerably smaller uncertainties due to better counting statistics.
In summary, our results are confirming this relationship, which might be derived from Fig. 5 and becomes quite obvious when looking at the average measurement uncertainties for different groups of measurements arranged by their respective durations (expressed by their total number of α-counts), which are summarized in Table 8.
Overall, the measurement uncertainties are reduced by longer measurement times.This applies to both loess standards and to all radionuclides.The biggest reduction, however, is observed when comparing short-time measurements of < 2, 000 α-counts to those showing a total number of α-counts of 2, 000 − 4, 000 (i.e.medium-time measurements).For the Nussy loess standard for instance, relative reductions of uncertainties of ~8 % (K), ~44 % (Th) and ~45 % (U) are achieved.With 4 % (K), 29 % (Th) and 29 % (U) similar but smaller relative reductions in uncertainties can be determined for the Volkegem loess standard when short-time and medium-time measurements are compared.
A further increase to long measurement durations corresponding to more than 4, 000 α-counts (long-time measurements) further reduces the uncertainties, yet typically not to the same extent as for the medium-time measurements.For the Nussy loess standard, prolonged measurements of > 4, 000 α-counts correspond to relative reductions of the original (short-time) uncertainties of 13 % (K), 59 % (Th) and 60 % (U).Particularly for U and Th, these values are only slightly higher than those 425 of the reduction for medium-time measurements.With total relative reductions of 9 % (K), 49 % (Th) and 48 % (U) compared to the short-time measurements, similar results can be found for the Volkegem loess standard.
In Fig. 6 the obtained results for radionuclide concentrations are illustrated as box-whisker-plots.This allows identifying statistically relevant outliers which were determined based on the 1.5 interquartile-range-(IQR-)criterion, i.e. the difference of the third and the first quartile of the whole data set as shown by the box, extended both in the lower and upper direction by a factor 1.5 * IQR as illustrated by the whiskers.Values outside this range are highlighted by red circles and labelled with their respective measurement durations expressed as the total number of α-counts.From Fig. 6 it can be concluded that the majority of outliers arises from short-time measurements of < 2, 000 α-counts, which equals measurement durations of approximately one day or only a few hours.Only three medium-time measurements revealing α-counts of ~2, 400, ~2, 900 and ~3, 500 have been identified as outliers.Therefore, we conclude that the probability of obtaining results not consistent with the average values is higher for short-time measurements showing a total number of α-counts of less than 2, 000.
For Fig. 7 the data were grouped according to measurement durations, which illustrates the impact of measurement time even more evidently and supports the conclusions drawn from Fig. 5 and 6.With respect to the uranium and thorium contents of the Volkegem loess standard (Fig. 7 lower part), medium-and long-time measurements agree rather well.For uranium, the median values are 2.35 mg • kg −1 (long) and 2.37 mg • kg −1 (medium) with associated relative standard deviations (RSD) of 3 % and 14 %, respectively.For thorium, median values of 12.5 mg • kg −1 (RSD = 9 %; long) and 12.5 mg • kg −1 (RSD = 15 %, medium) were derived.These group medians are identical within errors and reveal rather small intra-group scatter (at least when compared to the short-time group).For the short-time measurements, the results are completely different.Here, median values of 1.76 mg • kg −1 (RSD = 43 %) for uranium and 17.2 mg • kg −1 (RSD = 24 %) for thorium were calculated.These median values differ clearly from those determined for either the long-time or the medium-time group.For uranium, the short-time measurements underestimate the medium-and long-time measurements by ~25 %.For thorium, an overestimation of ~38 % can be observed.With respect to the results obtained for potassium, the picture is not as clear as for uranium and thorium.The median values (short: 1.67 mg • kg −1 ; medium: 1.65 mg • kg −1 ; long: 1.68 mg • kg −1 ) show rather good agreement.Only the slightly larger scatter in data observed for the short-time measurements (RSD = 4 %) compared to the medium-(RSD = 2 %) and long-time (RSD = 2 %) groups suggests that the short-time measurements might not provide reliable results (see also Table 9).
For the Nussy loess standard (Fig. 7, upper part), the results are more difficult to interpret.The median values indicate differences between the groups of measurement duration.However, the results summarized in  as evident as for the Volkegem loess standard.Potassium contents calculated for long-time and medium-time measurements agree very well (long: 1.04 %; medium: 1.05 %), whereas the short-time value of 1.10 % is deviating from these two values.

455
However, the relative deviation is only ~6 %.For thorium, we have a similar result.The median values of the medium-and long-time measurements are identical within errors, but do not significantly deviate from the results obtained for the short-time group which is slightly underestimating (~10 %) the results calculated for the other two groups.For uranium, the long-time measurements are slightly overestimating (~13 %) while short-time and medium-time groups show rather good agreement.
With respect to the median values, the results are suggesting that the short-time measurements might be problematic.However, the evidence is not as clear as for the Volkegem loess standard.Showing values of 29 % and 34 % for uranium and thorium, respectively, at least the RSDs are rather large for the short-time measurements.Here, medium-and long-time groups show distinct lower RSDs of 12 % and 13 % (medium) as well as 4 % and 7 % (long).However, this does not apply to potassium for which a RSD of only 5 % could be determined for the short-time measurements.With respect to the outliers identified based on the 1.5 IQR-criterion, the majority belongs to short-time measurements of < 2, 000 α-counts.
Finally, there seems not to be a straightforward answer to the question whether there is a particular lower limit of measurement durations for which still reliable results can be expected.Our findings suggest that short-time measurements hold the greatest risk of providing results not in agreement with results obtained by longer-lasting measurements.This might be interpreted as an indicator of an unreliable measurement setup.At least, this is true for very short measurement durations of less than one day which should therefore be avoided.However, since our findings are somehow contradictory and might even 470 point to a more or less sample-specific pattern, this conclusion should be regarded as a conservative rule of thumb.
In summary, we conclude that reliable results for the loess standards investigated in this study could be obtained by µDosemeasurements revealing total numbers of α-counts of 2, 000 to 4, 000.For our samples this number of α-counts corresponds to measurement durations of approximately two to four days (also see Table D1 in Appendix D).Extremely short measurement durations delivering α-counts < 2, 000 should be avoided due to insufficient counting statistics.Despite the benefit of further reducing measurement uncertainties, prolonged measurements of more than five days (i.e.> 4, 000 α-counts) are normally not necessary to ensure results of reasonable accuracy and precision.Since the counting statistic strongly depends on the samplespecific activity, we advise to use the total number of α-counts as an indicator for an adequate measurement duration.In our experiments, samples (Nussy and Volkegem) measured for approximately two to four days revealed a mean number of ~2, 400 α-counts.Therefore, we suggest a threshold value of ~2, 500 α-counts as a minimum value in order to guarantee reliable measurement results.

µDose-system performance for environmental samples
So far, the performance of the µDose-system has only been tested on one synthetic sample with known activity composed as a mixture of different IAEA standards and on a very limited number of natural loess and archaeological samples (cf.Tudyka et al., 2018Tudyka et al., , 2020)).In order to assess the performance of the µDose-system for natural samples on a broader data basis, we carried out a series of inter-laboratory comparisons including TSAC, ICP-OES and low-level HRGS measurements.As our primary aim was to assess the potential of the µDose-system to produce reliable data for calculating dose rates of samples with low radionuclide contents typical of natural environments, a total number of 47 samples from various environmental settings were re-measured on the µDose-devices at the Giessen Luminescence Laboratory. Figure 8 shows the results for samples that were measured at the University of Bayreuth, applying TSAC for the determination of uranium and thorium contents and ICP-OES for potassium.For most samples, the findings indicate a very good agreement between the values derived from µDose-measurements (blue symbols) and those obtained by TSAC and ICP-OES (red symbols).For uranium and thorium contents, the majority of samples agree within the 2σ-level (U: 63 %, Th: 79 %).
The calculated potassium contents often show a perfect match.95 % of the investigated samples are within the 2σ-level of agreement, 83 % even within the limits of 1σ.
However, there are also some samples for which the determined values -particularly the determined contents of uranium and thorium -do not coincide on the 2σ-level.Among these problematic samples are Gi311, Gi343, Gi360, Gi455, Gi465, Gi466 and Gi649.With respect to the last four of these samples, this pronounced difference of TSAC and µDose values might be attributed to the possible presence of radioactive disequilibria caused by chemical and/or physical differentiation processes potentially affecting long-living members in the U and Th decay chains such as 234 U, 230 Th, 226 Ra, 228 Th and 228 Ra (e.g., Degering and Degering, 2020;Krbetschek et al., 1994).This explanation is based on the specific context of the respective sampling locations.All four samples originate from Holocene fluvial flood plain sediments covering Pleistocene gravel beds.
For such sediments, strongly alternating ground water levels are characteristic.Generally, sediments exposed to fluctuating ground water levels are regarded as typical candidates for radioactive imbalances (e.g., Degering and Degering, 2020;Olley et al., 1996Olley et al., , 1997) ) since they are subjects of various translocation processes and potentially significant periodic changes in fundamental environmental conditions such as the pH value.With respect to the differing chemical properties of the individual elements in the decay chains, such imbalances can take several and complex forms, which may manifest either in a loss or in an accumulation of specific parent and daughter nuclides (e.g., Prescott and Hutton, 1995).Therefore, it appears not unlikely that the samples mentioned above suffer from distinct increases and/or decreases of particular radioactive daughter nuclides in the U and Th decay chains.Regardless of the specific nature of these potential imbalances, their existence would violate a central assumption of the specific algorithms used by the µDose-system, which would most probably cause inadequate results for the calculated activities.
For the other samples, a lack of secular equilibrium might also be a suitable explanation for the detected deviations of measurement values.This might at least be true for samples Gi311 and Gi343.Both are colluvial samples which were taken from locations within profiles that were identified in the field as M-Go horizons according to the German soil classification system (Ad-Hoc-AG Boden, 2005).These horizons showed typical features of a gleysol revealing inter alia a characteristic accumulation of sesquioxides, which indicate periodical impact of ground water.As a result, secular disequilibria appear to be possible for these samples.
Figure 9 illustrates the results for the comparison of µDose-measurements (blue symbols) with low-level HRGS (red symbols) performed in different laboratories.Figure 9a shows the results for the samples from the Heidelberg Luminescence Laboratory.On average, the obtained values are characterized by rather small discrepancies between µDose-results and HRGS.
Figure 9b shows various samples that were measured at the Gliwice laboratory.Apart from samples provided by the Gliwice laboratory itself, these measurements also included some samples provided by the Giessen Luminescence Laboratory, which had previously been measured at the University of Bayreuth applying TSAC and ICP-OES.With respect to these latter samples, the results gained in Gliwice largely confirm the findings already discussed for the comparison of µDose-measurements to TSAC and ICP-OES.For samples Gi311, Gi453 and Gi360, there is again a pronounced deviation of the µDose-results to the independently obtained data.Sample Gi437, which was just within the limit of 2σ-deviation for the TSAC-comparison, did not conform on the 2σ-level when compared to the results from Gliwice.Particularly, this applies to the activities arising from 232 Th and 238 U.However, with respect to sample Gi455, the situation is different.While this sample showed the largest differences for the comparison to TSAC and ICP-OES, the values obtained by HRGS reveal a 2σ-agreement with the µDoseresults.A straightforward interpretation of this finding is hardly possible, but it casts doubt on the above suggested explanation that Gi455 might suffer from a distinct radioactive disequilibrium.In fact, the extraordinary large discrepancies observed for Gi455 in the TSAC/ICP-OES comparison and the good agreement of µDose-results and low-level HRGS values might rather indicate a serious problem during the TSAC/ICP-OES measurements.Particularly the amount of discrepancy observed for Gi455 is supporting this interpretation since other samples originating from the same sampling location (Gi450-Gi453) do not show similar discrepancies.Furthermore, Gi455 was identified as a sample originating from floodplain loams of the Lahn river (see detailed description of sample materials in Appendix C).Based on long lasting experience with sediments from the Lahn catchment in the Giessen Luminescence Laboratory, floodplain material from the Lahn catchment is expected to show significant higher concentrations of thorium and uranium than material originating from fluvial gravels of the region.However, the TSAC/ICP-OES results obtained for Gi455 are in the same order of magnitude as the results obtained for Gi450-Gi453, which originate from the underlying terrace gravels.In the end we cannot be sure whether the distinct deviations observed for Gi455 were caused by problems during the TSAC/ICP-OES measurements or whether they can be explained by the presence of a radioactive disequilibrium.
Overall, the 2σ-level proportions of agreement for all samples measured in Gliwice (including those from Giessen) are: 64 % (U), 50 % (Th) and 64 % (K).At a first glance, this could be misinterpreted as indication of serious methodological shortcomings.However, it has to be kept in mind that these measurements included a large number of samples from the Giessen laboratory which were previously identified as potentially problematic.Although the HRGS measurements in Gliwice did not give clear evidence of radioactive disequilibria, the presence of such disequilibria seems to be likely for at least 8 out of 14 measured samples when the specific sampling locations are considered.
Restricting the analysis to those five samples provided by the Institute of Physics in Gliwice for which no radioactive disequilibria were expected, the results are completely different.Except for sample U1_19, all samples reveal a very good or even excellent agreement with the µDose-results from Giessen.On the 2σ-level, the proportions of agreement between HRGS and µDose are 80 % for K and Th and 100 % for U.So far, we were not able to find any reasonable explanation for the pronounced deviation of K and Th activities determined for sample U1_19.
With respect to the samples from the Cologne Luminescence Laboratory, the findings are also very good.Except for the potassium contents of three samples (COL_GGW1, COL_GGW6 and COL_UGW1) for which a distinct difference in the respective values is obvious, all values show excellent agreement with the µDose-results.But also 50 % of the results for 40 K conform on the 2σ-level.For the activity of 235+238 U, 90 % of the determined values agree on the 2σ-level and still 60 % coincide within 1σ.For 232 Th, activities determined by µDose and HRGS show a nearly perfect match.100 % of the values agree within 2σ and still 70 % within 1σ.
Surprisingly, this is also true for four samples for which radioactive disequilibria had been identified (COL_UGW1 -COL_UGW4).With respect to 235+238 U and 232 Th activities, a 100 % proportion of agreement on the 1σ-level can be derived from the data, and for 40 K still 50 %.In theory, the algorithm applied by the µDose-software should not yield correct results since a major assumption of this algorithm is violated in the presence of radioactive disequilibria.As a consequence, we should expect large discrepancies between the applied methods since the determination of radionuclide activities in low-level HRGS and in the µDose-system are based on differing approaches.Yet, our findings suggest that radioactive disequilibria are not necessarily associated with such large inter-methodological discrepancies.Although such discrepancies were detected for some of the analysed natural samples, this did obviously not apply to samples COL_UGW1 to COL_UGW4.A convincing explanation for this inconsistency can hardly be found at this moment.The findings for the Cologne samples are only based on a limited number of samples and are not supported by results obtained from the comparisons to the other laboratories (cf.(Durcan et al., 2015).Please be aware that these calculated values do not correspond to the actual dose rates and are thus referred to as 'simulated environmental dose rates'.For details the reader is referred to the table notes of Table 4.
Bayreuth and Gliwice).In the end, it can not be excluded that the results obtained for the four Cologne samples only match by chance.At the moment, we cannot decide whether these results are only odd anomalies or whether they represent the normal case for samples in radioactive disequilibria.In order to give a final answer, further detailed and systematic investigations are required, including the question whether the magnitude of radioactive disequilibria is a decisive factor for the µDose-system's capability to determine values for the radionuclide concentrations that are in good agreement with results obtained by other methodological approaches.Regardless of the final answer to this question, we would like to point out that dose rates calculated from radionuclide concentrations of samples for which radioactive disequilibria have to be assumed will never be an accurate measure for trapped charge dating and should therefore be treated with care.
The overall good performance of µDose-measurements is confirmed by the rate of agreement observed for the simulated environmental dose rates illustrated in Fig. 10.As described for the Nussy and Volkegem loess standards (see Sec. 5.1), these dose rates were calculated for the coarse (90 − 200 µm) grain fraction of HF-etched quartz using DRAC v1.2 (Durcan et al., 2015).For calculation, we applied the conversion factors provided by Guérin et al. (2011) and used a constant water content of 15 ± 5 % as well as a constant cosmic radiation of 0.150 ± 0.015 Gy • ka −1 .We would like to point out that these values were arbitrarily chosen and do not represent the actual moisture and cosmic radiation values that might be detected for the different sampling locations.
Figure 10a shows a comparison of µDose-based simulated environmental dose rates to values derived from TSAC/ICP-OES measurements performed at the Bayreuth Luminescence Laboratory.With samples Gi343, Gi455 and Gi465, there are three samples for which neither an agreement on the 1σ-level nor on the 2σ-level could be achieved.These samples have already been identified to be problematic (see discussion above).With respect to the Bayreuth samples, 88 % of the simulated environmental dose rates coincide within 2σ, and still 79 % within 1σ.(Gliwice) and 50 % (Cologne), the proportions of samples for which an agreement on the 1σ-level can be observed is substantially lower than for the µDose-TSAC/ICP-OES comparison.On the 2σ-level of agreement, 100 % (Heidelberg), 86 % (Gliwice) and 80 % (Cologne) of the calculated simulated dose rates coincide with the respective dose rate values derived from µDose-measurements.
Overall, 55 % of the simulated environmental dose rates for all investigated samples coincide within 1σ and 88 % show an agreement on the 2σ-level.In total, the measured-to-given-ratios range from 0.48 to 2.81 and average at a value of 1.04, which improves to 1.00 if the above mentioned three problematic samples are not considered.80 % of the calculated measured-togiven ratios lie within 15 % of unity, indicating an overall very good rate of agreement for the simulated environmental dose rates.In summary, we can conclude that µDose-measurements provide results which allow the calculation of dose rates that are in accordance with dose rate values derived from well-established methods of environmental dose rate determination.
Our findings do not point to significantly differing results for samples from different sedimentary environments.For aeolian sediments, 2σ-levels of agreement of 80 % for uranium as well as 90 % for thorium and potassium were determined.For samples originating from fluvial environments, only ~68 % of the uranium measurements agree on the 2σ-level, what is slightly lower than for the aeolian sediments and might be attributed to potential radioactive disequilibria (see discussion above) or to a stronger heterogeneity of the mineralogical composition of the fluvial deposits.With respect to thorium (89 %) and potassium (84 %), however, no significant differences between fluvial and aeolian samples were observed.Similar results were derived for littoral samples as well as for hillslope sediments and soils (see summary in Table 10).With respect to colluvial samples, our findings at a first glance seem to point to slightly worse 2σ-proportions of agreement for thorium (57 %) and uranium (71 %).
A closer look at the results, however, shows that only seven colluvial samples were considered for this study.Two of them clearly revealed features of changing ground water levels and thus might most probably exhibit radioactive disequilibria.For at least three more samples, such disequilibria are likely if considering their sampling positions.Thus, due to the very specific conditions at the respective sampling locations the colluvial samples investigated in this study proved to be problematic.Yet, we would like to emphasize that this result should not be generalized for colluvial samples.As a result, our study does not give evidence that samples from particular sedimentary environments are generally not suitable for analyses with the novel µDosesystem and should therefore a priori be excluded from µDose-analyses.However, we would like to emphasize that the specific on-site conditions at the sampling locations are of decisive importance.The µDose-system will only provide reliable results for radionuclide concentrations if the fundamental requirement of secular equilibrium is met.Thus, a careful documentation of sampling locations, inter alia comprising sedimentological and hydrographic aspects, is indispensable for providing the database for a convincing interpretation of µDose-results.

Conclusions
The µDose-system is an easy to handle device that provides the possibility of determining the sample-specific concentrations of uranium, thorium and potassium.Equipped with a dual layer scintillator sensitive to αand β-radiation, the system is able to discriminate between αand β-particles interacting with the scintillator and thus determine the total αand β-counts.Based on four decay pairs comprising two α-α-pairs and two β-α-pairs, the measurement system allows discriminating series-specific  and combined using a weighted mean.This allowed detecting possible radioactive disequilibria in the uranium chain, which, however, were not an issue for the Heidelberg samples presented here.A detailed overview of used gamma lines can be found in Table A1.Regular measurements of an identically treated standard (Kasper et al., 2001;Preusser and Kasper, 2001) were implemented to calibrate the detector and monitor its performance.

MEASUREMENT CONFIGURATION APPLIED AT THE INSTITUTE OF PHYSICS IN GLIWICE
The decay chains of 238 U and 232 Th as well as 40 K concentrations were measured by low-level HRGS using a HPGe detector (Canberra GX 4518) and Genie-PC software (Canberra).The investigated samples were stored in a laboratory dryer for a few days, depending on moisture.The dried samples were crushed and 100 g of each sample were sealed in gBeakers (Poręba et al., 2020).Prior to measurement, samples were stored for at least three weeks.This delay was necessary to allow 222 Rn to reach a radioactive equilibrium with 226 Ra.The measurement time for each sample was about 24 hours (Moska et al., 2021).To obtain the 238 U content the following gamma lines were considered: 295 keV, 352 keV, 609 keV and 1, 120 keV.To calculate the 232 Th activity the following gamma lines were considered: 583 keV, 911 keV and 2, 614 keV.For 40 K the gamma line at 1, 461 keV was used.For a summarizing compilation of used gamma lines, the reader is referred to Table A1.The HRGS-system was calibrated using the RGU-1, RGTh-1 and RGK-1 reference materials provided by the IAEA.Regularly applied quality controls are implemented in the measurement routines in Gliwice using reference material IAEA-385.
Appendix B: Overview of natural samples C3 Samples provided by the Cologne Luminescence Laboratory (Germany) The Cologne Luminescence Laboratory overall provided ten samples which were subject of different research projects including littoral environments and geo-archaeological settings as well as alluvial sediments and aeolian deposits.Finally, Col_UGW4 is a loess sample from the Matmata Plateau (Tunesia).The lithology of the plateau is dominated by mid-Cretaceous limestones showing several basins filled with sandy loess deposits.The sample was taken near the village of Matmata (33.54°N, 9.95°E, 351 m a.s.l.).A detailed description of the Matmata loess region is given by Faust et al. (2020).
C4 Samples provided by the Institute of Physics in Gliwice (Poland) U_1_2 and U_1_19 -were collected for studies on soil erosion and sedimentation processes applying fallout radionuclides.
Both samples were collected from an agricultural field located on a gentle slope within the Proboszczowicki tableland near the village of Ujazd (South Poland).The samples are colluvial sediments and were collected at the base of the slope.The sampling site is located in an area overall characterized by Pleistocene loess sediments that were described as "transition loess formation" by Jersak (1973).While the mean grain size of sample U_1_2 is equal to 40 µm (very coarse silt), it is about 139 µm for sample U_1_19 (very fine sand).

Figure 1 .
Figure 1.Photos showing the µDose-devices and equipment: (a) Sample carrier and equipment for sample preparation.(b) Scintillator unit with silver foil.(c) High-precision balance used for weighing 3.00 g of sample material.(d) Prepared sample on a sample carrier with a diameter of 70 mm.(e) Prepared sample material and measurement container.(f) Three µDose-devices installed in the Giessen Luminescence Laboratory.

Figure 2 .
Figure 2. Results for repeated measurements of the investigated IAEA standards.The different colours of the symbols represent three different measurement devices (see legend).All plots show the relative deviation of measured values from the respective reference values provided for the IAEA standards.Sample RGK-1 is illustrated on the left, the thorium standard RGTh-1 is shown in the centre and RGU-1 is depicted on the right.Bold lines illustrate the 0 %-deviation (i.e., a perfect agreement of measured and expected values).Please note that only activities arising from the dominant radioactive emitter of the respective standard were considered for this figure.

Figure 3 .
Figure 3. Results from repeated µDose-measurements for the loess standards Nussy (upper part) and Volkegem (lower part).The different colours of the symbols represent three different measurement devices (see legend).All plots show radionuclide concentrations either in mg • kg −1 (U and Th) or in % (K).Please note that the bold reference lines indicate radionuclide contents originally published for the Nussy loess standard by Preusser and Kasper (2001) and for the Volkegem loess standard by De Corte et al. (2007).Dashed lines characterize the corresponding 95 % C.I. Error bars indicate measurement uncertainties on the 2σ-level.

Figure 4 .
Figure 4. Bulk uranium and thorium activities given in Bq • kg −1 (a) and simulated environmental dose rates given in Gy • ka −1 (b) for both investigated loess standards.The Nussy loess standard is depicted on the left, the Volkegem loess standard is shown on the right.The different colours of the symbols represent three different measurement devices (see legend).Please note that the bold reference lines centred within the grey area indicate radionuclide contents originally published for the Nussy loess standard by Preusser and Kasper (2001) and for the Volkegem loess standard by De Corte et al. (2007) whereas the bold lines centred within the yellow area represent benchmark values derived from the results published by Murray et al. (2018).

Figure
Figure4ashows the combined activity arising from the uranium and thorium decay chains for the Nussy loess standard (left) and for the Volkegem loess standard (right).With respect to the latter, the values determined with the µDose-system are in good agreement with the expected benchmark value published by DeCorte et al. (2007).With individual measured-to-given ratios ranging from 0.96 (measurement VR1) to 1.24 (measurement VA4), the mean measured-to-given ratio averaged for all devices 335

Figure 5 .
Figure 5. Results from µDose-measurements of two loess standards (Nussy = upper part; Volkegem = lower part).Values on the x-axis represent the number of total α-counts.Y-axis-values give the respective radionuclide concentration either in % (K) or in mg • kg −1 (Th and U).The different colours of the symbols represent three different µDose-devices (see legend).The bold lines illustrate the median values derived from the determined results.Dashed lines indicate the 2σ-deviation.

Figure 6 .
Figure 6.Radionuclide concentrations determined by µDose-measurements given as % for K (left) and as mg • kg −1 for Th (centre) and U (right).The different colours represent the different loess standards investigated (see legend).Outliers (red circles) were identified based on the 1.5 IQR-criterion and labelled with their respective number of total α-counts.

Figure 7 .
Figure7.Radionuclide concentrations determined by µDose-measurements given as % for K (left) and as mg • kg −1 for Th (centre) and U (right).Results of individual measurements and boxplots for the loess standards Nussy (top) and Volkegem (bottom).Data grouped by measurement duration in three classes: short-time (< 2, 000 α-counts; green symbols); medium-time (2, 000 − 4, 000 α-counts; yellow symbols); long-time (> 4, 000 α-counts; grey symbols).Outliers (red symbols) as identified by the 1.5 IQR-criterion and labelled with their respective numbers of total α-counts.Classification not based on specific statistical arguments but reflecting the realisation of the experiments.

Figure 8 .
Figure 8.Comparison of results obtained by TSAC (U and Th) in combination with ICP-OES (K) (red symbols) to the findings derived from µDose-measurements (blue symbols).Please note that the values are given as radionuclide concentrations ( % for K; mg • kg −1 for U and Th).

Figure 10 .
Figure10.Comparison of simulated environmental dose rates for various natural samples.Assuming a constant water content of 15 ± 5 % and a constant cosmic radiation of 0.150 ± 0.015 Gy • ka −1 , all values were calculated for the 90−200 µm grain size fraction of HF-etched quartz using DRAC v1.2(Durcan et al., 2015).Please be aware that these calculated values do not correspond to the actual dose rates and

Samples Col_GGW1 -
Col_GGW3 were taken during an archaeological excavation of a Roman lime kiln situated on the western slope of a small hill within the Paffrather Mulde (50.98°N, 7.16°E, 135 m a.s.l.) near the city of Bergisch Gladbach (Germany).The local lithology is dominated by Devonian limestone and dolomite covered by silty weathered loam.Samples Col_GGW1 and Col_GGW2 were extracted from a fritted contact zone between the packing chamber and the surrounding sediments.Col_GGW3 originates from an oxidized, reddish-brown residual loam outside the contact area.For details, the reader is kindly referred toZander et al. (2019).Samples Col_GGW4 -Col_GGW6 represent fluvial environments.While Col_GGW4 was taken during an archaeological excavation in the city centre of Lyon (France, 45.76°N, 4.84°E, 180 m a.s.l.), Col_GGW5 originates from the alluvial plain of the Rhone river near the town of Pierrelatte (France, 44.337°N, 4.702°E, 50 m a.s.l.).Both samples were taken from fluvial sands of alluvial deposits accumulated by the Rhone river.Sample Col_GGW6 originates from alluvial sediments of the Rote Weißeritz river near the town of Schellerhau (Erzgebirge Mountains, Germany, 50.766°N, 13.716°E, 727 m a.s.l.).For a detailed description of the sampling location the reader is kindly referred toTolksdorf et al. (2020).Samples Col_UGW1 -Col_UGW3 originate from a littoral environment.They have originally been analysed as part of the investigation of washover fans at Point Lefroy (22.30°S, 114.15°E, 4 m a.s.l.), which is located in the Exmouth Gulf in the north-western part of Western Australia.All samples have been taken from littoral sandy deposits consisting of a mixture of siliciclastic sand, coral fragments and shells.A detailed description of the sampling location including the geological and geomorphologic settings as well as a thorough sedimentary characterization are given byBrill et al. (2017) andMay et al. (2017).

Table 1 .
Decay pairs used to derive the specific contributions arising from the 238 U-, 235 Uand 232 Th-series as well as from 40 K.

Table 2 .
Radionuclide concentrations as certified by the IAEA(IAEA, 1987).Uranium and thorium values are given in mg • kg −1 , potassium is given in %.Uncertainties represent the 95 % C.I.

Table 3 .
Recommended radionuclide-specific activities as provided on the homepage of the IAEA.All values are given in Bq • kg −1 .Please note that only those values were considered for this table for which information are provided by the IAEA.Uncertainties represent the 95 % C.I.

Table 4 .
Summary of concentrations and activities published for the Nussy and Volkegem loess standards.Values used as reference values for this study are

Table 5 .
Summary of measurement settings in the participating laboratories.Details of sample preparation and applied measurement procedures are described in the text and in Appendix A.

Table 6 .
Accuracy and precision of µDose-measurements of certified IAEA standards.The accuracy is expressed as measured-to-given ratios (MGR).Precision is given as relative standard deviation (RSD) of measured acitivities.Only results derived for the dominant emitter of the respective IAEA standard were considered for this table.
Murray et al. (2018)(2001)and from 2.3 mg • kg −1 to 2.7 mg • kg −1 , respectively.Referring to the reference value for the Nussy loess standard, this spread in data corresponds to relative deviations of approximately 15 % to 19 %.A smaller, but still considerable spread in the determined data can be observed, when the values published byPreusser and Kasper (2001)are compared to the IAG reference values for U and Th.Here, the IAG values exceed the originally published data by ~5 % (U) and ~10 % (Th).A similar finding can be noticed for Volkegem loess activities given by De Corte et al. (2007) when compared to results derived from the re-measurements ofMurray et al. (2018).For all radionuclides,Murray et al. (2018)reported substantially higher activities.While the 232 Th-activity exceeds the originally determined value by ~5 %, the deviations for 238 U and 40 K are considerably more pronounced revealing relative values of ~10 % and ~15 %, respectively.

Table 7 .
Preusser and Kasper (2001)ements and reference values for K, Th and U contents of Nussy loess standard (upper part) and Volkegem loess standard (lower part).The values for K are given in %, the values for U and Th are given in mg • kg −1 .Reference values (and their associated 95 % C.I.s) are according to Preusser and Kasper (2001) and De Corte et al. (2007).The 95 % C.I.s. for Nussy have been recalculated based on the SD-values provided byPreusser and Kasper (2001).Uncertainties of the µDose-measurements correspond to 95 % C.I.s.The table shows mean values for individual µDose-devices as well as average values calculated as mean of all measurements on the three devices.

Table 8 .
Averaged uncertainties for µDose-measurements of loess standards Nussy (upper part) and Volkegem (lower part) grouped by their respective total numbers of α-counts.

Table 9
(upper part)are not

Table 10 .
Proportions of agreement on the 2σ-level between µDose-results and results obtained by different techniques of determining radionuclide concentrations and/or activities (TSAC/ICP-OES and low-level HRGS).Results are grouped according to different sedimentary environments.
activities, arising from the decay chains of 238 U, 235 U and 232 Th.Based on the assumption that 40 K is the dominant β-emitter In summary, the µDose-system is a promising tool for measuring low level concentrations of radionuclides in samples from natural environments.It has the potential to become a standard method for dose rate determination in routine luminescence and electron spin resonance dating applications.Appendix A: Measurement configuration for comparison of natural samples MEASUREMENT CONFIGURATION APPLIED IN THE BAYREUTH LUMINESCENCE LABORATORY For the determination of uranium and thorium concentrations, thick source alpha counting (TSAC) was used whereas the potassium content was determined by ICP-OES, using a Varian Vista-Pro T M system.TSAC measurements were performed on a Littlemore Low Level Alpha Counter 7286 equipped with four photomultiplier tubes.Sample preparation included drying the sample material in a drying chamber at 105°C for several days, homogenizing and finally pulverizing the material using a ball mill.To ensure the complete coverage of the ZnS : Ag scintillation screen, the sample material was placed and gently compacted in a gas tight sample carrier consisting of acrylic glass.Before starting the TSAC measurements, all samples were stored for at least four weeks in order to account for radon emanation due to the sample preparation procedure.MEASUREMENT CONFIGURATION APPLIED IN THE COLOGNE LUMINESCENCE LABORATORYFor samples provided by the Cologne Luminescence Laboratory, uranium, thorium and potassium contents were determined by low level HRGS, using i) an Ortec Coaxial Profile M7080-S GEM high-precision Germanium Gamma-Ray detector with 60 % relative efficiency and connected to a Dspec jr 2.0; and ii) a Canberra Coaxial Profile GC4040 Germanium Gamma-Ray detector with a relative efficiency of 20 % connected to an Ortec 92x Spectrum Master.Samples were dried at 50°C for at least two days, crushed in a jaw breaker if necessary and homogenized.Depending on the available amount of sample material, polypropylene (PP) capsules with calibrated capacities of 200 g and 590 g were filled to the top, tape sealed and stored for four weeks to compensate for radon loss induced by sample preparation.The capsules were then placed on top of the detector surrounded by a 10 cm thick lead shield and measured for 42 hours.GammaVision 8.0 software with the LVis 3.0.9applicationwasused for measurements and analyses. 40activities were directly measured based on the gamma line at 1, 461 keV. 238activities were derived from the gamma lines at 295 keV, 352 keV, 609 keV, 1, 120 keV, 1, 764 keV and 2, 204 keV.For determining 232 Th activities, the following gamma lines were used: 209 keV, 338 keV, 911 keV, 965 keV, 969 keV, 727 keV, 583 keV, 861 keV and 2, 614 keV.A summarizing compilation of used gamma lines can be found in TableA1.Nussy loess was utilized for efficiency calibration of the individual sample containers, whereas 152 Eu (50 kBq) and 60 Co (37 kBq) check sources were used for periodic energy calibration and quality checks.In order to compensate for potential 222 Rn loss during the preparation process, the samples were stored for at least four weeks.Thereafter, a lead shielded broad energy Ge detector (Canberra, model BE 2020) was used to determine the sample concentration of 238 U, 232 Th and 40 K.While 40 K could be measured directly, for 238 U and 232 Th, the gamma lines

Table A1 .
Compilation of radioactive daughter nuclides and their associated gamma peaks used for low-level HRGS-based uranium, thorium and potassium determination in the participating laboratories of Cologne, Heidelberg and Gliwice. 234Th, 226 Ra, 214 Pb, 214 Bi and 210 Pb for 238 U; 228 Ac, 212 Pb and 208 Tl for 232 Th) were measured

Table B1 .
Compilation of 47 natural samples investigated for this study.These samples have been provided by four different laboratories and represent various environmental settings.A more detailed description of sample characteristics, sampling locations and research contexts is 715 given in Appendix C.