Krishna Madhav

Sebastian Murari

Georgina Kreutzer

Marine King

Sumiko Frouin

Christoph Tsukamoto

Tobias Schmidt

Nicole Lauer

Daniel Klasen

Johannes Richter

Friedrich

Madhav Krishna Murari

Sebastian Kreutzer
email: sebastian.kreutzer@aber.ac.uk

Georgina King

Marine Frouin

Sumiko Tsukamoto

Christoph Schmidt

Tobias Lauer

Nicole Klasen

Daniel Richter

Johannes Friedrich

Norbert Mercier

Markus Fuchs

Infrared radiofluorescence (IR-RF) dating: A review

Keywords: Infrared radiofluorescence, Radioluminescence, Feldspar, Chronology, Luminescence dating

est destinée au dépôt

Introduction

In the late 1990s, [START_REF] Trautmann | Investigations of feldspar radioluminescence: potential for a new dating technique[END_REF] characterized radioluminescence signals, the emission stimulated by ionizing radiation, from various feldspar specimens to investigate their potential for dating applications. Focusing first on radiation-induced emissions in the UV and yellow wavelength range, where luminescence signal increases with radiation dose, they incidentally observed the opposite for potassium bearing (K-) feldspar specimen such as microcline and orthoclase: a dose-dependent signal decrease of the emission centred at 854 nm (1.45 eV; based on peak tail fitting only). Later, Trautmann et al. (1999a, b), [START_REF] Schilles | Die Infrarot-Radiolumineszenz von Feldspäten und ihr Einsatz in der Lumineszenzdatierung[END_REF] and Erfurt and Krbetschek (2003a) determined that the emission peak was centred at 865 nm (1.43 eV). [START_REF] Trautmann | Investigations of feldspar radioluminescence: potential for a new dating technique[END_REF] recognized that this emission energy is similar to the excitation energy used for infrared stimulated luminescence (IRSL, Hütt et al., 1988) and consequently interpreted this process as a luminescent transition (trapping) of electrons. Their pioneer work paved the way to what is known today as infrared radiofluorescence (IR-RF) dating; the method first proposed by Trautmann et al. (1999a, b) and termed by Erfurt and Krbetschek (2003a, b).

The IR-RF signal is believed to be a direct measure of the fraction of empty electron traps, unlike conventional luminescence dating methods such as those based on thermoluminescence (TL, cf. Aitken, 1985a), optically stimulated luminescence (OSL, [START_REF] Huntley | Optical dating of sediments[END_REF][START_REF] Aitken | An introduction to optical dating[END_REF] and infrared stimulated luminescence (IRSL, [START_REF] Hütt | Optical dating: K-Feldspars optical response stimulation spectra[END_REF], for which the signals are associated with more complex recombination pathways. Since the IR-RF signal intensity decreases with increasing dose, it can be used for dosimetry and dating purposes. IR-RF may provide advantages over conventional single aliquot regenerative (SAR, [START_REF] Murray | Luminescence dating of quartz using an improved singlealiquot regenerative-dose protocol[END_REF] dose, IRSL dating methods (e.g., SAR IRSL, [START_REF] Wallinga | The single-aliquot regenerative-dose (SAR) protocol applied to coarse-grain feldspar[END_REF] or its derivatives deploying higher reading temperatures (post-IR IRSL, [START_REF] Thomsen | Laboratory fading rates of various luminescence signals from feldspar-rich sediment extracts[END_REF]MET-pIRIR, Li and Li, 2011a) in terms of required measurement time (relatively short protocol, cf. Erfurt and Krbetschek, 2003b), resolution of the dose-response curve (continuous recording of data points) and dating range (Sec. 7). Nevertheless, IR-RF as a dating method is still subject to ongoing research, with its general applicability being questioned [START_REF] Buylaert | IR-RF dating of sandsized K-feldspar extracts: A test of accuracy[END_REF]. On the contrary, recent technological and methodological work, e.g., on the optical resetting of the IR-RF signal, and improved routines for dose estimation have yielded promising results [START_REF] Frouin | Les feldspaths comme support pour la datation par luminescence de gisements archéologiques et de séquences quaternaires d'Aquitaine[END_REF]Frouin et al., 2015Frouin et al., , 2017;;[START_REF] Huot | Evidence of shallow TL peak contributions in infrared radiofluorescence[END_REF][START_REF] Kreutzer | Always remain suspicious: a case study on tracking down a technical artefact while measuring IR-RF[END_REF][START_REF] Murari | Further investigations on IR-RF: Dose recovery and correction[END_REF].

This contribution provides an overview of past and recent developments of IR-RF from Kfeldspar as a dating method. We summarize current knowledge on existing models on the origin of IR-RF, outline commonly applied measurement procedures and equipment, and highlight shortfalls, challenges and open questions. Understanding what remains unknown may stimulate discussions and lead to improved experimental designs towards a full establishment of IR-RF as a valuable chronological tool.

Origin of the IR-RF signal and relevant models

The 1.43 eV (865 nm) IR-RF emission of K-feldspar (Trautmann et al., 1999a, b;1.45 eV in Trautmann et al., 1998, see below for an explanation) has the same energy as the typical excitation maximum of IRSL [START_REF] Hütt | Optical dating: K-Feldspars optical response stimulation spectra[END_REF]Poolton et al. 2002a, b), which led Trautmann et al. (1998) to suggest that both signals are derived from the same principal electron trap. More recent observations of infrared photoluminescence (IR-PL; [START_REF] Prasad | Optical dating in a new light: A direct, non-destructive probe of trapped electrons[END_REF] seem to support this hypothesis (see also [START_REF] Kumar | Towards direct measurement of electrons in metastable states in K-feldspar: Do infrared-photoluminescence and radioluminescence probe the same trap?[END_REF]. Further studies by [START_REF] Kumar | Site-selective mapping of metastable states using electron-beam induced luminescence microscopy[END_REF] generally confirmed this view but extended the understanding by assigning two different defect sites to the principal trap based on their cathodoluminescence measurements. Trautmann et al. (1999a, b) and [START_REF] Trautmann | A study of radioluminescence kinetics of natural feldspar dosimeters: experiments and simulations[END_REF] proposed a model for the IR-RF emission of feldspar whereby IR-RF results from the transition of an electron from the conduction band to the ground state of the IRSL trap through the excited state. the ultraviolet (UV)-RF and visible light (VIS)-RF emissions at higher doses (Trautmann et al., 1999a). However, this model raises two major questions: (1) why does the IR-RF signal not fully saturate during laboratory irradiation, resulting in a zero or negligible IR-RF signal, and (2) to bleach, why does the IR-RF signal require exposure to light of higher energies than IR (e.g.,

Preprint for QG revision 4 -Infrared Radiofluorescence (IR-RF) dating: a review

Page 5 of 64 [START_REF] Trautmann | Investigations of feldspar radioluminescence: potential for a new dating technique[END_REF]Trautmann et al., , 1999a, b;, b;[START_REF] Frouin | The issue of laboratory bleaching in the infrared-radiofluorescence dating method[END_REF][START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF], whereas the IRSL signal from the same trap could be efficiently reset through exposure to infrared light?

Figure 1 (Models)

To explain why the IR-RF signal does not appear to saturate, Trautmann et al. (1999a) first considered electron release throughout irradiation due to the low thermal stability of the IRSL trap, resulting in the replenishment of free electron-hole pairs and thus a continuously decaying IR-RF signal. However, this hypothesis contradicts a measured lifetime of the IRSL trap in the range of Ga [START_REF] Murray | The effect of preheating on the IRSL signal from feldspar[END_REF]). An alternative explanation not considered by Trautmann et al. (1999a) is the loss of trapped electrons by athermal tunnelling, known as anomalous fading of feldspar (e.g., [START_REF] Wintle | Anomalous fading of thermoluminescence in mineral samples[END_REF][START_REF] Spooner | Feldspar flotation as a quartz-purification method in cosmogenic nuclide dating: A case study of fluvial sediments from the Pamir[END_REF][START_REF] Visocekas | Tunneling radiative recombination in K-feldspar sanidine[END_REF][START_REF] Huntley | Some observations on tunnelling of trapped electrons in feldspars and their implications for optical dating[END_REF]) and more specifically, the anomalous fading of the IRSL feldspar trap (e.g., [START_REF] Spooner | Feldspar flotation as a quartz-purification method in cosmogenic nuclide dating: A case study of fluvial sediments from the Pamir[END_REF]Huntley and Lamothe, 2001) (transition [d] in Fig. 1), which we summarised in Sec. 5.6. Instead, Trautmann et al. (1999a) preferred a model already suggested by [START_REF] Schön | Zum Leuchtmechanismus der Kristallphosphore[END_REF] and [START_REF] Klasens | Transfer of energy between centres in zinc sulphide phosphors[END_REF] for sulphide phosphors, with a proposed transfer of holes from the valence band to the IRSL trap throughout irradiation, effectively increasing the defects trapping capacity (transition [e] in Fig. 1).

To address the different bleaching behaviour of IR-RF and IRSL signals, Trautmann et al. (2000a) modified their earlier model, relating the bleaching of the IRSL signal to localized electron transitions after the suggestion by [START_REF] Poolton | Thermo-optical properties of optically stimulated luminescence in feldspars[END_REF]. Following IR exposure, an electron is only excited to the excited state of the trap ([f] in Fig. 1), which is paired with the excited state of a neighbouring recombination centre, allowing a localized transition.

Thus, the IRSL emission would relate to the radiative relaxation of the electron to the ground state of the recombination centre. [START_REF] Trautmann | A study of radioluminescence kinetics of natural feldspar dosimeters: experiments and simulations[END_REF] and Trautmann et al. (2000a) determined from pulse-annealing experiments that bleaching of the IRSL trap is limited by the number of available recombination centres, suggesting thermal instability of trapped electrons could reduce the density of holes. They drew this conclusion from the IR-RF signal's stability up to temperatures of 400 °C, whereas IRSL and the related VIS-RF signals depleted at temperatures >300 °C. [START_REF] Trautmann | A study of radioluminescence kinetics of natural feldspar dosimeters: experiments and simulations[END_REF] and Trautmann et al. (2000a) concluded that the IRSL electron-hole population accounts for only ~1.5 % of the total potential IRSL trap occupancy, implying that most of these trapped electrons do not have the possibility of recombining with a hole during IR stimulation. A phenomenon that [START_REF] Trautmann | A study of radioluminescence kinetics of natural feldspar dosimeters: experiments and simulations[END_REF] and Trautmann et al. (2000a) did not consider, and which may influence these effects to some extent, is athermal signal loss (i.e., anomalous fading). Following the model of [START_REF] Huntley | An explanation of the power-law decay of luminescence[END_REF], ground state tunnelling [d in Fig. 1] would result in preferential recombination of unstable charge with proximal recombination centres, which may otherwise have been involved in localized transitions from the IRSL trap.

Athermal de-trapping results in a non-linear increase of IRSL with dose, an effect recorded and highlighted by [START_REF] Trautmann | A study of radioluminescence kinetics of natural feldspar dosimeters: experiments and simulations[END_REF] and Trautmann et al. (2000a).

Defects related to IR-RF and IRSL

The exact identification of defects responsible for electron and hole trapping in feldspar is subject to ongoing research, and as such, the physical nature of the IRSL and IR-RF trap remains under debate. The traps and recombination centres of K-feldspars have mainly been assigned based on indirect measurements and correlation studies (e.g., Baril and Huntley, 2003a;Erfurt 2003a, b;Erfurt and Krbetschek, 2003b). [START_REF] Krbetschek | Spectral information from minerals relevant for luminescence dating[END_REF] discussed the principal Kfeldspar luminescence emissions and their possible origins for different excitation methods. The most common emission bands for K-feldspar are listed in Table 1 (please also note the references given therein).

Table 1 (Traps and recombination centres)

It appears that in the literature Fe 3+ and Pb + ions have been identified as the main centres which are believed to be responsible for the presence of the red to deep-red emission (~ 1.7 eV; Prasad and Jain, 2018) in feldspar. [START_REF] Kumar | Towards direct measurement of electrons in metastable states in K-feldspar: Do infrared-photoluminescence and radioluminescence probe the same trap?[END_REF] tried to correlate their IR-PL findings [START_REF] Prasad | Understanding defect related luminescence processes in wide bandgap materials using low temperature multi-spectroscopic techniques[END_REF] with the IR-RF signal. Their work suggested that the same defect participated in the production of IR-RF and IR-PL. However, they speculated that IR-PL, contrary to IR-RF, is "site-selective", i.e. IR-PL preferentially probes centres leading to the emission at ca 1.30 eV (955 nm) whereas the IR-RF emission may be 'contaminated' by emissions from other centres, such as Fe 3+ , related to the emission band near 680 nm to 740 nm (e.g., [START_REF] Geake | The cause and significance of luminescence in lunar plagioclase[END_REF][START_REF] Telfer | Optical detection of Fe 3+ in lunar plagioclase[END_REF][START_REF] White | Absorption and luminescence of Fe 3+ in single-crystal orthoclase[END_REF][START_REF] Brooks | The red to near-infrared luminescence in alkali feldspar[END_REF][START_REF] Finch | The causes and petrological significance of cathodoluminescence emissions from alkali feldspars[END_REF]Krbetschek et Preprint for QG revision 4 -Infrared Radiofluorescence (IR-RF) dating: a review Page 7 of 64 al., 2002;[START_REF] Prasad | Dynamics of the deep red Fe 3+ photoluminescence emission in feldspar[END_REF]. Most recent work by [START_REF] Kumar | Site-selective mapping of metastable states using electron-beam induced luminescence microscopy[END_REF], reporting infrared cathodoluminescence (IRCL) experiments at 7 K, give evidence for a correlation of emission peak position and K-concentration. They further propose Fe 4+ as a defect competing for electrons with the principal trap. Furthermore, the red emission's peak location has been observed to be related to the composition of feldspar samples (e.g., [START_REF] Finch | The causes and petrological significance of cathodoluminescence emissions from alkali feldspars[END_REF][START_REF] Krbetschek | The red luminescence emission of feldspar and its wavelength dependence on K, Na, Ca ± composition[END_REF]. In contrast, the Pb + centre appears to be related to the IR-RF emission bands between ca. 860 nm and 910 nm (e.g., [START_REF] Nagli | Influence of a vcvacancy on luminescence of Pb + centres in alkali halides[END_REF]Erfurt 2003a, b;Erfurt and Krbetschek, 2003a). Erfurt (2003a) and Erfurt and Krbetschek (2003a) observed an increase of IR-RF signal intensity with increasing Pb content for concentrations on the order of 30 ppm to 1,400 ppm, and proposed that the IR-RF emission may be associated with the excitation of Pb 2+ to monovalent (Pb + ) * which subsequently relaxes to the ground state of Pb + , emitting photons at 1.43 eV.

Schematically it reads (adapted from Ostrooumov 2016, p. 152 for amazonite):

Pb 2+ + e o → Pb 2+ e -+ e + → (Pb + ) + e + → Pb + ~hν865 + … + O -Al
However, this hypothesis remains unproven, and earlier electron paramagnetic resonance (EPR) studies have indicated that Pb + is only found in amazonite, a specific type of microcline where Pb + occupies a K + position [START_REF] Marfunin | Paramagnetic in feldspars and their possible crystalchemical and petrological significance (ПАРАМАГНИТНЫЕ ЦЕНТРЫ В ПОЛЕВЫХ ШПАТАХ И ИХ ВОЗМОЖНОЕ КРИСТАЛЛОХИМИЧЕСКОЕ И ПЕТРОГРАФИЧЕСКОЕ ЗНАЧЕНИЕ)[END_REF][START_REF] Marfunin | Spectroscopy, luminescence and radiation centers in minerals[END_REF]. In contrast, Poolton et al. (2002b) hypothesised that the IRSL trap is a simple hydrogenic defect, calculating an optical transition at 1.48 ± 0.04 eV, close to that observed in the K-Na feldspar series. Since Trautmann et al. (1998, 1999a, 2000a) proposed a model to explain the processes of (IR)-RF of feldspar, our understanding of luminescence processes in feldspar has improved considerably, driven mainly by the developments around conventional IRSL (e.g., [START_REF] Wallinga | The single-aliquot regenerative-dose (SAR) protocol applied to coarse-grain feldspar[END_REF][START_REF] Huntley | Ubiquity of anomalous fading in K-feldspars and the measurement and correction for it in optical dating[END_REF][START_REF] Lamothe | Towards a prediction of long-term anomalous fading of feldspar IRSL[END_REF][START_REF] Auclair | Measurement of anomalous fading for feldspar IRSL using SAR[END_REF][START_REF] Murray | The effect of preheating on the IRSL signal from feldspar[END_REF][START_REF] Kars | IRSL dating of K-feldspars: Modelling natural dose response curves to deal with anomalous fading and trap competition[END_REF][START_REF] Pagonis | Monte Carlo simulations of tunneling phenomena and nearest neighbor hopping mechanism in feldspars[END_REF][START_REF] Pagonis | Further investigations of tunneling recombination processes in random distributions of defects[END_REF][START_REF] Pagonis | Excited state luminescence signals from a random distribution of defects: A new Monte Carlo simulation approach for feldspar[END_REF][START_REF] Lamothe | Circumvention of anomalous fading in feldspar luminescence dating using Post-Isothermal IRSL[END_REF], the post-IR IRSL (also pIRIR) measurement protocols [START_REF] Thomsen | Laboratory fading rates of various luminescence signals from feldspar-rich sediment extracts[END_REF]Buylaert et al., 2009), time-resolved IRSL investigations (e.g., Jain and[START_REF] Jain | Towards a non-fading signal in feldspar: Insight into charge transport and tunnelling from time-resolved optically stimulated luminescence[END_REF] as well as IR-PL [START_REF] Prasad | Understanding defect related luminescence processes in wide bandgap materials using low temperature multi-spectroscopic techniques[END_REF][START_REF] Prasad | Optical dating in a new light: A direct, non-destructive probe of trapped electrons[END_REF][START_REF] Prasad | Dynamics of the deep red Fe 3+ photoluminescence emission in feldspar[END_REF][START_REF] Kumar | Site-selective mapping of metastable states using electron-beam induced luminescence microscopy[END_REF].

IR-RF model and related phenomena

Figure 1 shows a band-gap diagram which describes models for IRSL, post-IR IRSL and IR-RF.

The presence and importance of the sub-conduction band tail-states are now widely recognized (Poolton et al., 2002a[START_REF] Poolton | Direct evidence for the participation of band-tails and excited-state tunnelling in the luminescence of irradiated feldspars[END_REF][START_REF] Jain | Towards a non-fading signal in feldspar: Insight into charge transport and tunnelling from time-resolved optically stimulated luminescence[END_REF] and anomalous fading (athermal signal loss; Wintle, 1973 for TL;[START_REF] Spooner | Feldspar flotation as a quartz-purification method in cosmogenic nuclide dating: A case study of fluvial sediments from the Pamir[END_REF] for stimulation at 514.5 nm and ~880 nm) from the IRSL trap is generally regarded as ubiquitous in feldspar (e.g., [START_REF] Huntley | Ubiquity of anomalous fading in K-feldspars and the measurement and correction for it in optical dating[END_REF] (transition [d] in Fig. 1). The largest inconsistency between the IR-RF models and more recent studies is that the former models did not consider the effects of hole distribution (i.e., recombination distance) and anomalous fading.

Excitation spectra of feldspar revealed the characteristic resonance at ~1.4 eV (1.43 eV, [START_REF] Hütt | Optical dating: K-Feldspars optical response stimulation spectra[END_REF]; see also above), which is superimposed on a rising continuum, now recognized as relating to the sub-conduction band-tail states (Poolton et al., 2002a[START_REF] Poolton | Direct evidence for the participation of band-tails and excited-state tunnelling in the luminescence of irradiated feldspars[END_REF]. IRSL preferentially samples electrons which can recombine with proximal holes, either through tunnelling from the ground state of the IRSL trap (transition [d] in Fig. 1) or via a localized transition (transition [f] in Fig. 1). Higher energy stimulation of the IRSL trap or higher temperature stimulation (phonon-assisted diffusion) allows electrons to recombine via diffusion through the band-tail states (Poolton et al. 2002a;Jain and Ankjaergaard, 2011) (transition [g] in Fig. 1). For post-IR IRSL signals, which are measured at elevated temperatures of typically 225 ˚C or 290 ˚C (pIRIR225 or pIRIR290), this enables more distal recombination centres to be accessed [START_REF] Jain | Towards a non-fading signal in feldspar: Insight into charge transport and tunnelling from time-resolved optically stimulated luminescence[END_REF], which have greater athermal [START_REF] Huntley | An explanation of the power-law decay of luminescence[END_REF][START_REF] Jain | Towards a non-fading signal in feldspar: Insight into charge transport and tunnelling from time-resolved optically stimulated luminescence[END_REF] and thermal stability [START_REF] Thomsen | Stability of IRSL signals from sedimentary K-feldspar samples[END_REF]Li andLi, 2011b, 2013;[START_REF] Fu | Comparison of the properties of various optically stimulated luminescence signals from potassium feldspar[END_REF]. However, pIRIR signals are systematically harder to bleach than IRSL signals (e.g., Li and Li, 2011a).

In general, the IR-RF signal is known to bleach less efficiently than the low-temperature IRSL signal with infra-red light [START_REF] Trautmann | Radiolumineszenzuntersuchungen an Feldspat[END_REF]Trautmann et al., 1999a;[START_REF] Frouin | Les feldspaths comme support pour la datation par luminescence de gisements archéologiques et de séquences quaternaires d'Aquitaine[END_REF]Frouin et al., 2015) and recently it has been shown that the bleaching rate is similar to that observed for the pIRIR290 signal [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF]. This comparably slow bleachability agrees with the apparently high thermal stability of the IR-RF signal (at least up to 350 ˚C, cf. preheat vs curve shape experiments by Erfurt and Krbetschek, 2003b, their Fig. 7). However, further investigations are required to constrain the thermal stability of IR-RF signal and its susceptibility to anomalous fading.

Measurement devices

The first IR-RF studies were carried out on home-made systems [START_REF] Trautmann | Investigations of feldspar radioluminescence: potential for a new dating technique[END_REF](Trautmann et al., , 1999a;;[START_REF] Schilles | Radioluminescence dating: the IR emission of feldspar[END_REF]Erfurt et al., 2003), which differ from the ready-to-use systems available today [START_REF] Lapp | New luminescence measurement facilities in retrospective dosimetry[END_REF][START_REF] Richter | lexsyg -a new system for luminescence research[END_REF]. The device described in [START_REF] Trautmann | Investigations of feldspar radioluminescence: potential for a new dating technique[END_REF] was equipped with a spectrometer for K-feldspar IR-RF exploration. However, because the spectrometer was limited to 800 nm [START_REF] Trautmann | Investigations of feldspar radioluminescence: potential for a new dating technique[END_REF](Trautmann et al., , 1999b)), first peak investigations were based on signal extrapolation [START_REF] Trautmann | Investigations of feldspar radioluminescence: potential for a new dating technique[END_REF]. After identifying the dosedependent peak (Trautmann et al., 1999a) at 865 nm, the integrated RF signal around this peak was used for RF dose estimation. [START_REF] Schilles | Radioluminescence dating: the IR emission of feldspar[END_REF] and [START_REF] Erfurt | Radiolumineszenzspektroskopie und -dosimetrie an Feldspäten und synthetischen Luminophoren für die geochronometrische Anwendung[END_REF] went one step further and attached a photomultiplier tube with a filter combination optimized to limit the measured luminescence to the 865 nm emission closely. Tables 3 and4

Stimulation or irradiation unit

Radiofluorescence (RF) is the light emission caused by ionizing radiation. Therefore, stimulation sources can either be ionizing charged particles (ions, electrons or protons) or high energy photons (X-ray or γ-ray). The custom-made devices were equipped with 137 Cs/ 137 Ba sources (t1/2 ~ 30.08 a) [START_REF] Schilles | Radioluminescence dating: the IR emission of feldspar[END_REF], while other (commercially) available RF equipment has 90 Sr/ 90 Y sources (t1/2 ~ 28.8 a) [START_REF] Lapp | New luminescence measurement facilities in retrospective dosimetry[END_REF][START_REF] Richter | A novel beta source design for uniform irradiation in dosimetric applications[END_REF][START_REF] Richter | lexsyg -a new system for luminescence research[END_REF]. Details of the radiation sources are provided in Table 2. The major differences between these radiation sources are activity, radiation type and energy spectra. The 137 Cs/ 137 Ba radiation sources in the homemade devices, e.g., used by Trautmann et al. (1999a), [START_REF] Schilles | Die Infrarot-Radiolumineszenz von Feldspäten und ihr Einsatz in der Lumineszenzdatierung[END_REF] and Erfurt et al. (2003), emit β-particles and γ-photons with mean energies of 187.1 keV and 662 keV, respectively. At the same time, 137 Cs is also a γ-photon emitter, but the IR-RF stimulation by γ-rays was considered being negligible in comparison to the β-particles (Trautmann, 1999, p. 16). The 90 Sr/ 90 Y source emits a broad energy spectrum with mean β-energies around 195.8 keV. Other Page 10 of 64 differences regarding the stimulation sources are the design and the way of irradiating the sample (planar radiation source geometry vs ring source geometry). The ring source design [START_REF] Richter | A novel beta source design for uniform irradiation in dosimetric applications[END_REF] allows the detector to be mounted directly above the source. For the planar sources, the light collection is realized by an optical light guide [START_REF] Lapp | New luminescence measurement facilities in retrospective dosimetry[END_REF] or using light reflected to the detector [START_REF] Schilles | Die Infrarot-Radiolumineszenz von Feldspäten und ihr Einsatz in der Lumineszenzdatierung[END_REF]. The indirect light collection has the advantage of reducing unwanted signal contributions induced in the detection system due to bremsstrahlung, but it usually comes at the cost of reduced detection efficiency. Additionally, the ring-type sources have been reported as delivering a highly spatially homogenous dose rate [START_REF] Richter | A novel beta source design for uniform irradiation in dosimetric applications[END_REF], relative to planar sources. Common to all types of sources and geometries is the underlying assumption of measuring a comparable IR-RF signal.

Detection and filter combination

Initial studies on IR-RF were based on spectrometer measurements to identify IR-RF peaks and characterize their behaviour. [START_REF] Trautmann | Investigations of feldspar radioluminescence: potential for a new dating technique[END_REF] identified the presence and behaviour of the IR-RF peak around 854 nm based on curve fitting of a partially measured peak, but later (Trautmann et al., 1999a, b) reassigned the peak position to 865 nm using an improved spectrometer. [START_REF] Erfurt | Radiolumineszenzspektroskopie und -dosimetrie an Feldspäten und synthetischen Luminophoren für die geochronometrische Anwendung[END_REF] and [START_REF] Schilles | Die Infrarot-Radiolumineszenz von Feldspäten und ihr Einsatz in der Lumineszenzdatierung[END_REF] studied this peak in detail with a spectrometer and a photomultiplier tube in conjunction with optical filters (Sec. 5.1). The spectrometers' relevant details are provided in Table 3, and Fig. 3 shows the efficiency of different spectrometer systems.

Table 3 (Spectrometer overview) Figure 3 (Spectrometer transmission)

Table 4 provides detailed detector settings applied to measure the IR-RF signal. The main difference between the devices is the filter combination, and thus the detection window.

However, all types of filters centre around 865 nm and the usage of different filters reflects mainly the availability of filters when the equipment was delivered. Trautmann et al. (1999a) recommended centring around 865 nm and avoiding interference from the 710 nm peak. This idea was also followed by Erfurt and Krbetschek (2003b) using a detection window of 865 ± 20 nm, considering the broadening effect of the 710 nm peak with increasing dose (Sec. 5.1). The devices used by [START_REF] Schilles | Die Infrarot-Radiolumineszenz von Feldspäten und ihr Einsatz in der Lumineszenzdatierung[END_REF] and [START_REF] Erfurt | Radiolumineszenzspektroskopie und -dosimetrie an Feldspäten und synthetischen Luminophoren für die geochronometrische Anwendung[END_REF] both had the same type of photomultiplier tube (PMT) (Hamamatsu R943-02) with a quantum efficiency of ~5 % at 865 nm. The quantum efficiency of commercial lexsyg and Risø readers is about ~12 % at that wavelength, both employing the same PMT (Hamamatsu H7421-50), but the efficiency drops to 0.001 % for wavelengths > 900 nm. The PMTs of these commercial devices have a lower efficiency for the potentially interfering signals > 900 nm but relatively high efficiency for the 710 nm peak (Erfurt and Krbetschek, 2003b), which might significantly interfere with the main IR-RF peak. The bandpass for different systems used in the past and present are shown in Figs. 4 A andB.

Table 4 (detector settings)

Bleaching units

Table 5 summarizes the information on the commonly used bleaching units. In the device used by past researchers (e.g., [START_REF] Schilles | Radioluminescence dating: the IR emission of feldspar[END_REF]Erfurt et al., 2003) the sample geometry was fixed, i.e., the sample was not moved between different measurement steps. Thus, the IR-RF signal's bleaching was done by connecting a solar lamp using an optical fibre. In this design, IR cut-off filters were used to avoid excess heating due to the high intensity of light of the solar lamp. In contrast, inside commercial devices for IR-RF measurement and bleaching (e.g., lexsyg and Risø) the sample moves to different positions. The Risø system is equipped with powerful UV LEDs (~700 mW), and the lexsyg device has an inbuilt LED solar simulator that combines up to six wavelengths with the option of varying the power of each LED [START_REF] Richter | lexsyg -a new system for luminescence research[END_REF]see Table 5).

Table 5

Preprint for QG revision 4 -Infrared Radiofluorescence (IR-RF) dating: a review Page 12 of 64 (bleaching units) Krbetschek et al. (2000) and Erfurt and Krbetschek (2003b) recommended a fixed geometry during IR-RF measurements. They observed a high dispersion in IR-RF dose distributions attributed to geometry changes (e.g., grain movements) when samples were bleached outside the reader. [START_REF] Buylaert | IR-RF dating of sandsized K-feldspar extracts: A test of accuracy[END_REF] did not observe any changes in the IR-RF signal due to the movement of the sample from one position to another (cf. Fig 3b in [START_REF] Buylaert | IR-RF dating of sandsized K-feldspar extracts: A test of accuracy[END_REF].

Sample geometry

Similarly, [START_REF] Frouin | The issue of laboratory bleaching in the infrared-radiofluorescence dating method[END_REF][START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF] did not report dose dispersions caused by the movement of the sample inside the reader for their measurements using a lexsyg research reader. Later, [START_REF] Kreutzer | Always remain suspicious: a case study on tracking down a technical artefact while measuring IR-RF[END_REF] attributed a large part of the inter-aliquot scatter to unwanted machineinduced geometry changes, which, however, may have affected only their particular reader.

Nevertheless, in summary, it appears to be advisable to aim for a stable sample geometry and check the results for unwanted effects, enlarging the De distribution (cf. [START_REF] Kreutzer | Always remain suspicious: a case study on tracking down a technical artefact while measuring IR-RF[END_REF].

Sample preparation methods

IR-RF sample preparation methods extract K-feldspar enriched mineral grains following routine procedures (e.g., [START_REF] Preusser | Luminescence dating: basics, methods and applications[END_REF]. After sieving and chemical treatments with HCl and H2O2, density separation using heavy-liquids (e.g., lithium heteropolytungstates or sodium polytungstate) extract feldspar grains. Additional (froth) flotation (e.g., [START_REF] Herber | Separation of Feldspar from Quartz by Flotation[END_REF]application examples: Miallier et al., 1983;Sulaymonova et al., 2018) can be applied to enrich the Kfeldspar concentration further; a procedure that the Freiberg group has mainly used in the context of IR-RF (e.g., Trautmann, 1999;[START_REF] Erfurt | Radiolumineszenzspektroskopie und -dosimetrie an Feldspäten und synthetischen Luminophoren für die geochronometrische Anwendung[END_REF]. Flotation likely provides a better yield in terms of better separation of quartz and feldspar mineral phases. Despite requiring extra laboratory equipment and staff training, flotation has unmined potential for further enriching the K-feldspar fraction (e.g., via selective flotation: [START_REF] Larsen | Selective flotation of Kfeldspar from Na-feldspar in alkaline environment[END_REF] with possible implications for measured IR-RF signals.

To remove the outer α-irradiation affected layer of coarse K-feldspar grains (> 90 µm) a low concentration (≤ 10 %) HF treatment was often used (e.g., [START_REF] Wagner | Radiometric dating of the type-site for Homo heidelbergensis at Mauer, Germany[END_REF][START_REF] Lauer | Infrared radiofluorescence (IR-RF) dating of middle pleistocene fluvial archives of the Heidelberg Basin (Southwest Germany)[END_REF]. However, the practice of etching of coarse grain K-feldspar was already questioned by Preprint for QG revision 4 -Infrared Radiofluorescence (IR-RF) dating: a review Page 13 of 64 [START_REF] Duller | Luminescence chronology of raised marine terraces, South-West North Island[END_REF], who described non-uniform etching along the lines of weakness within the mineral. [START_REF] Porat | Re-examination of common extraction and purification methods of quartz and feldspar for luminescence dating[END_REF] recalled caution if HF is applied to feldspar grains because HF etching might significantly modify the luminescence properties of K-feldspar, and thus [START_REF] Porat | Re-examination of common extraction and purification methods of quartz and feldspar for luminescence dating[END_REF] suggest etching times <15 min. [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF] reported inconclusive, younger and highly scattered, IR-RF results for two samples (BT714, BT715) after prolonged HF treatment (10 %, 40 min), while this was not observed for another, non-etched, sample from the same site (BT706). Although the systematic effect of HF treatments with different timings and concentration on the IR-RF signal remains unexplored, HF treatment appears to be dispensable.

IR-RF signal characteristics

IR-RF spectroscopy: Signal identification and measurement optimization

The IR-RF signal composition was extensively studied using a home-made spectrometer in combination with a liquid nitrogen-cooled charged coupled device (CCD) detector [START_REF] Trautmann | Investigations of feldspar radioluminescence: potential for a new dating technique[END_REF](Trautmann et al., , 2000b;;Krbetschek and Trautmann, 2000). Their spectroscopic investigations of IR-RF from feldspar revealed many peaks centred at various wavelengths. However, the 865 nm emission peak was found to be stable with its intensity decreasing with increasing dose. Kfeldspar showed the highest signal intensity at this wavelength compared to other feldspar compositions. [START_REF] Trautmann | Radiolumineszenzuntersuchungen an Feldspat[END_REF] and [START_REF] Schilles | Die Infrarot-Radiolumineszenz von Feldspäten und ihr Einsatz in der Lumineszenzdatierung[END_REF] noticed that the spectrum of K-feldspar could be fitted with two Gaussian functions centred at 710 nm (1.75 eV) and 865 nm (1.43 eV).

Later, [START_REF] Erfurt | Radiolumineszenzspektroskopie und -dosimetrie an Feldspäten und synthetischen Luminophoren für die geochronometrische Anwendung[END_REF] improved the spectrometer used by [START_REF] Trautmann | Radiolumineszenzuntersuchungen an Feldspat[END_REF] and recognized that the data required a minimum of three Gaussian functions to fit the emission spectrum, with a third emission centred at ~910 nm (1.35 eV; Erfurt and Krbetschek, 2003a). The spectroscopic study of these peaks provided the appropriate detection range (filter combination) required for isolating the main IR-RF peak at 865 nm from other neighbouring emissions (Krbetschek et al., 2000). A typical raw spectrum for K-feldspar shows many emission peaks (Fig. 5C after [START_REF] Schilles | Die Infrarot-Radiolumineszenz von Feldspäten und ihr Einsatz in der Lumineszenzdatierung[END_REF] and Trautmann et al. (1999a) demonstrated that the peak intensity at 865 nm decreases with increasing dose, whereas the intensity of the 710 nm peak increases with dose. Furthermore, [START_REF] Trautmann | Investigations of feldspar radioluminescence: potential for a new dating technique[END_REF] observed that the 710 nm peak is unstable and vanished within a few hours following irradiation.

Both the 710 nm and 910 nm1 emissions may interfere with the main IR-RF peak (865 nm), which filters can minimise. The effect of such a filter can be simulated using three superimposed Gaussian functions (Fig. 5A and Fig. 5B similar to Erfurt and Krbetschek, 2003b). Table 4 summarizes all devices' filter combinations to isolate the peak centred at a wavelength of 865 nm.

Figure 5 A B C (IR-RF peaks in feldspar)

IR-RF signal resetting

The success of (optical) luminescence dating methods relies on resetting the luminescence signal during sediment transport prior to burial. For IR-RF, the signal intensity increases with light exposure after several minutes to several hours and reaches its highest value when all traps are empty. The bleachability of the IR-RF signal was assessed by bleaching until a plateau is formed between the IR-RF signal vs bleaching time. A constant plateau indicates no further signal increase, i.e., the IR-RF signal is at its maximum, and all IR-RF related traps are empty. In the first IR-RF bleaching experiments (Trautmann et al., 1999a), natural direct sunlight (VIS to UV component, Fig. 6A) was used for a few hours (between 2 h and 5 h of daylight exposure in February in Freiberg, Germany) to bleach the IR-RF signal. Later, Trautmann et al. (2000a) showed that wavelengths shorter than 500 nm were more efficient at resetting the IR-RF signal (Fig. 6B) and Krbetschek et al. (2000) demonstrated that only a few minutes (~5-10 min) were required to reset the signal, using a 200 W Hg-lamp (Table 5 for an overview of the settings)

along with a heat-absorbing filter (Fig. 6C). Further bleaching experiments were conducted using a 300 W OSRAM 'Ultravitalux' sunlamp placed at a distance of 35 cm from the aliquot for 6.5 h (Krbetschek et al., 2000) or an on-board lamp (250 W OSRAM metal halide), using fibre optics, which delivered ~100 mW cm -2 to the aliquot for 30 min. obtained different values between aliquots that were bleached with UV LEDs (delivering 700 mW cm -2 ) with an exposure time of 25 min, compared to bleaching with a Hönle SOL 2 solar simulator for 4 h. Samples bleached with the Hönle SOL2 resulted in older, but partly also more consistent ages compared to the independent age control (cf. Buylaert et al., 2012, their Fig. 7).

Later [START_REF] Varma | Aspects of infrared radioluminescence dosimetry in K-feldspar[END_REF] concluded that exposure of 800 s is optimal for resetting the IR-RF signal using the aforementioned UV LED (delivering 700 mW cm -2 ).

Frouin et al. ( 2015) systematically compared the bleaching behaviour of monochromatic light and a solar simulator spectrum. In their study, they showed that: i) K-feldspars of various origins exhibit the same behaviour during bleaching experiments, and ii) the IR-RF signal can be bleached by all wavelengths, ranging from 365 nm to 850 nm, and iii) the IR-RF signal can be completely reset in nature and cannot be "over-bleached" in the laboratory even with the use of longer time exposures. Finally, they recommend a solar spectrum close to the terrestrial solar spectrum with minimal UV light contribution. They achieved this by individually adjusting the monochromatic LEDs' power in their luminescence reader and stated that this spectrum delivered a sufficient amount of power (375 mW cm -2 ) to bleach the IR-RF signal in minimum time at ambient temperature [START_REF] Frouin | The issue of laboratory bleaching in the infrared-radiofluorescence dating method[END_REF]. Furthermore, they showed that the onset of a bleaching plateau started after 3 h to 4 h of light exposure (cf. Fig. 4 in [START_REF] Frouin | The issue of laboratory bleaching in the infrared-radiofluorescence dating method[END_REF].

Specifically, within this light spectrum, the power of the UV (325 nm) LED was reduced to 10 mW cm -2 as this wavelength is absorbed by the atmosphere and its presence in the terrestrial solar spectrum is minimal. Regardless, this low power, Frouin (2014, her Fig. 28) showed that UV bleaches most efficiently within the first seconds before it reaches a plateau after ca. 40 h.

Although an artificial bleaching spectrum using only six wavelengths (LEDs) cannot match the terrestrial solar spectrum, it may remain a good approximation of natural bleaching conditions (typical irradiance on Earth of 90-100 mW cm -2 ; ASTM international, 2012). A comparison between the bleaching behaviour of the IR-RF signal measured at 70 °C (Sec. 6.1) with other variants of the IRSL signals of K-feldspar showed that IR-RF seems to bleach at a similar rate to the pIRIR290 signal but much slower than the IRSL50 signal [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF]; Fig. 6D).

However, a similar bleaching rate compared to the pIRIR290 signal does not guarantee a complete reset of either signal (i.e., pIRIR290 and IR-RF); various studies have shown that the pIRIR290 signal is hard to bleach and can have large residual doses even after 4 h of solar simulator bleaching (e.g., [START_REF] Buylaert | IR-RF dating of sandsized K-feldspar extracts: A test of accuracy[END_REF][START_REF] Li | A single-aliquot luminescence dating procedure for K-feldspar based on the dose-dependent MET-pIRIR signal sensitivity[END_REF]. It may take up to ~300 h to reach a constant residual dose (Yi et al., 2016). In summary, [START_REF] Frouin | The issue of laboratory bleaching in the infrared-radiofluorescence dating method[END_REF] recommended a minimum of 3 h bleaching using the inbuilt solar simulator of their equipment with the following settings: 365 nm (10 mW cm -2 ), 462 nm (63 mW cm -2 ), 525 nm (54 mW cm -2 ), 590 nm (37 mW cm -2 ), 623 nm (115 mW cm -2 ), and 850 nm (96 mW cm -2 ).

Phosphorescence

In the context of IR-RF, two types of phosphorescence have been observed: (1) Phosphorescence after bleaching (Fig. 7) and ( 2) phosphorescence after irradiation (so-called radiophosphorescence). Phosphorescence after bleaching was considered by Erfurt and Krbetschek (2003b). They recognized that K-feldspar samples, bleached with a solar simulator, show a very strong phosphorescence at 865 nm. For a sediment sample with a palaeodose of ~1,500 Gy, extrapolation of the phosphorescence signal at room temperature using an exponential decay shows that its effect lasts beyond 1,000 s after bleaching (cf. Fig. 6 in Erfurt and Krbetschek, 2003b). To accommodate this effect in IR-RF measurement protocols, Erfurt and Krbetschek (2003b) recommended a pause of one hour after bleaching, before starting the next IR-RF measurement. In contrast, [START_REF] Buylaert | IR-RF dating of sandsized K-feldspar extracts: A test of accuracy[END_REF] showed that after bleaching the phosphorescence signal intensity is lower by two orders of magnitude than IR-RF, its effect on the main IR-RF signal will be negligible. However, it should be noted that their setup differs from the one used by Erfurt and Krbetschek (2003b) (Sec. 3). [START_REF] Varma | Aspects of infrared radioluminescence dosimetry in K-feldspar[END_REF] reported that although the IR-RF signal of their sample was almost at its saturation level, it did not show significant phosphorescence after bleaching the sample for 800 s. Hence, they concluded that no extra pause is needed and suggested that a delay of 500 s is sufficient to reduce the phosphorescence down to the background level if the bleaching time is less than 800 s. Similarly, [START_REF] Schaarschmidt | pIRIR and IR-RF dating of archaeological deposits at Badahlin and Gu Myaung Caves -First luminescence ages for Myanmar[END_REF] reported a weak phosphorescence compared to the IR-RF signal and reduced the pause to 900 s for their samples. In summary, it seems that phosphorescence caused by bleaching can be avoided by introducing a pause of 15 min to 1 h prior to IR-RF measurements (Erfurt and Krbetschek, 2003b;[START_REF] Frouin | The issue of laboratory bleaching in the infrared-radiofluorescence dating method[END_REF][START_REF] Schaarschmidt | pIRIR and IR-RF dating of archaeological deposits at Badahlin and Gu Myaung Caves -First luminescence ages for Myanmar[END_REF] in the case of solar simulator bleaching and may not be required if the sample is bleached with a UV LED for 800 s or longer [START_REF] Varma | Aspects of infrared radioluminescence dosimetry in K-feldspar[END_REF].

Radiophosphorescence is a known phenomenon used in the past to characterize luminescence spectra from feldspar (e.g., [START_REF] Krbetschek | Luminescence spectra of alkali feldspars and plagioclases[END_REF]Baril and Huntley, 2003b). [START_REF] Varma | Aspects of infrared radioluminescence dosimetry in K-feldspar[END_REF] observed phosphorescence with an intensity of ~35 % of the IR-RF signal (cf. Fig 2b

in [START_REF] Varma | Aspects of infrared radioluminescence dosimetry in K-feldspar[END_REF] immediately after irradiation up to 800 Gy. Phosphorescence caused by irradiation can be a severe issue since IR-RF measurements need continuous irradiation during signal measurement. Thus, phosphorescence superposition onto the main IR-RF signal can be problematic and might be as high as 35 % of the IR-RF signal [START_REF] Varma | Aspects of infrared radioluminescence dosimetry in K-feldspar[END_REF].

Nevertheless, if the phosphorescence intensity is independent of the previously administered radiation dose, it might be neglected. In contrast, if the radiophosphorescence is dose-dependent, it will be impossible to isolate it from the IR-RF signal. This possible superposition of IR-RF and radiophosphorescence needs to be further investigated. Natural and commercial samples showed different bleaching levels and a relative change of signal intensity of 3.6-4.8 % for natural sunlight and 5.1-8.9 % for artificial solar simulation (SOL2, Hönle). These variations in signal intensity indicated sensitivity changes due to bleaching and/or irradiation during the measurement. In order to cope with this, [START_REF] Schilles | Die Infrarot-Radiolumineszenz von Feldspäten und ihr Einsatz in der Lumineszenzdatierung[END_REF] suggested using a separate aliquot and measuring its IR-RF for two bleaching cycles. Based on these additional measurements, a dimensionless correction factor could be derived from the ratio of the regenerated IR-RF intensities (Fig. 8A).

Similarly, [START_REF] Varma | Aspects of infrared radioluminescence dosimetry in K-feldspar[END_REF] reported sensitivity changes during measurement and could not recover a given dose using IR-RF. They derived a sensitivity correction factor FS by repeating the bleaching and regenerative IR-RF six times. FS (also Sec. 6.1) is estimated from the ratio of IR-RF intensity of the first regenerated cycle to the extrapolated intensity of the zeroth cycle (Fig. 8B). Furthermore, [START_REF] Varma | Aspects of infrared radioluminescence dosimetry in K-feldspar[END_REF] recognized that all six sediment samples investigated in their study needed a sensitivity correction to obtain reasonable dose recovery results. Erfurt and Krbetschek (2003b) while all the samples were able to recover the known dose from the RFreg signal with an uncertainty of 4 %. Their findings showed the discrepancy in dose recovery and the mismatch of the shape of RFreg curves compared to RFnat curves. The latter is attributed to the change in IR-RF sensitivity. Possible causes for these sensitivity changes are the high photon flux of the builtin solar simulator, the high laboratory dose rate and/or the interference from other neighbouring peaks with the main IR-RF signal (i.e., 710 nm and 910 nm emissions ;[START_REF] Trautmann | Radiolumineszenzuntersuchungen an Feldspat[END_REF]Erfurt and Krbetschek, 2003b). In summary, it seems that IR-RF is affected by sensitivity changes that should be monitored and corrected. Based on their findings, [START_REF] Murari | Further investigations on IR-RF: Dose recovery and correction[END_REF] suggested a new analysis and correction method named the 'horizontal and vertical correction' method (Sec. 6.2).

Figure 8

(Sensitivity change monitoring)

IR-RF initial rise

A few IR-RF studies mentioned an unexpected signal rise at the beginning of the IR-RF measurement (e.g., [START_REF] Schilles | Die Infrarot-Radiolumineszenz von Feldspäten und ihr Einsatz in der Lumineszenzdatierung[END_REF][START_REF] Buylaert | IR-RF dating of sandsized K-feldspar extracts: A test of accuracy[END_REF][START_REF] Frouin | Les feldspaths comme support pour la datation par luminescence de gisements archéologiques et de séquences quaternaires d'Aquitaine[END_REF][START_REF] Huot | Evidence of shallow TL peak contributions in infrared radiofluorescence[END_REF][START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF]. It was often described as a bump, a TL-like peak or an initial rise of the RF signal (Fig. 9A; for further discussions on the dynamic range see below) and it typically persisted for the first few hundred seconds (~6-12 Gy) before the IR-RF starts decaying monotonically [START_REF] Huot | Evidence of shallow TL peak contributions in infrared radiofluorescence[END_REF]. According to [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF], the initial rise in the natural signal seemed to be positively correlated with the equivalent dose (De) (cf. Fig. S7 in [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF]) of a sample and was observed for every K-feldspar sample used in their study.

In contrast, the Freiberg group never reported such IR-RF behaviour (e.g., Krbetschek et al., 2000;[START_REF] Erfurt | Radiolumineszenzspektroskopie und -dosimetrie an Feldspäten und synthetischen Luminophoren für die geochronometrische Anwendung[END_REF] leading to speculation that differences in instrumental design (overall system efficiency, different detection bandpass filter combinations or radiation source strengths) may cause the effect or favour its detection. Measurements using both commercial devices (lexsyg research and Risø, Sec. Error! Reference source not found.) showed the initial rise behaviour (e.g., [START_REF] Huot | Evidence of shallow TL peak contributions in infrared radiofluorescence[END_REF][START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF][START_REF] Qin | Initial sensitivity change of K-feldspar pIRIR signals due to uncompensated decrease in electron trapping probability: Evidence from radiofluorescence measurements[END_REF]). However, this is not discussed in detail by [START_REF] Buylaert | IR-RF dating of sandsized K-feldspar extracts: A test of accuracy[END_REF] who discarded the signal corresponding to the first ~20 Gy from their data analysis considering it as a sample-specific behaviour. [START_REF] Huot | Evidence of shallow TL peak contributions in infrared radiofluorescence[END_REF] thoroughly investigated the origin of the initial rise after bleaching (regenerated signal). They hypothesized that the rapid increase in RF observed at the beginning of the irradiation, is not due to higher electron trapping, but can be explained by thermally assisted phosphorescence. "Minute variations in sample temperature" (Huot et al., 2015, p. 241) can cause this peak because of the existence of shallow traps which emit phosphorescence in the near-infrared region. Their recommendation to avoid this peak was to wait at least 1 h after bleaching, let the sample cool down to room temperature, or measure IR-RF at elevated temperatures of around 70 °C to 100 ˚C. Nevertheless, the phenomenon does not seem to disappear from the IR-RF signal even when measured at elevated temperatures of 70 °C and waiting for one h after bleaching (cf. Fig. 2 vs Fig. 7 in [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF].

Furthermore, the reported a correlation between the intensity of the initial rise in the natural signal and the sample's De (cf. [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF] their Fig. S7), indicated that shallow TL traps alone cannot explain this phenomenon. Nevertheless, from the perspective of dating, it seems that the effect of the initial rise does not affect dose estimation as it appears only for 100 s to 200 s (typically ~6-12 Gy) in every IR-RF signal (i.e., natural and regenerated IR-RF signals).

However, further investigations combined with modelling are needed to better understand the origin of the IR-RF signal increase during the first seconds.

Figure 9 (Initial rise and dynamic range)

IR-RF signal stability

The IR-RF signal stability has two dimensions: thermal stability and athermal stability. The first is directly related to the depth of the trap and represents the stability of the electrons captured by the defect over time, dependent on the 'burial' temperature. The second, also known as 'anomalous fading' [START_REF] Wintle | Anomalous fading of thermoluminescence in mineral samples[END_REF], is temperature independent.

The thermal stability of the IR-RF signal was investigated by Trautmann et al. (1999a) who used pulse annealing experiments, and they reported thermal stability of the IR-RF signal up to 450 °C (Fig. 10A). However, this result was observed only for one sample (Ook1), which is >1 Ma old;

two younger samples showed a decrease in signal intensity after 250 °C (Fig. 10A). Later experiments by Erfurt and Krbetschek (2003b) and [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF] (Fig. 10B) confirmed these findings. Further, it was noticed that for temperatures of 250 °C and higher, natural IR-RF (RFnat) signal intensities decreased with pulse annealing temperature (Fig. 10B) while they increased slightly for regenerated IR-RF signals (RFreg). If annealing at high temperatures resets the IR-RF signal, the IR-RF intensity should not decrease, which is in accordance with observations on RFreg, but in contradiction to that for RFnat. This contrasting feature may be explained by a change of the IR-RF sensitivity with temperature. In thermoluminescence (TL) studies on K-feldspar rapid, temperature-induced luminescence sensitivity decreases were frequently reported (Aitken, 1985a[START_REF] Aitken | An introduction to optical dating[END_REF]. Those changes are non-repeatable in subsequent dose cycles (cf. reasoning in [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF].

Nevertheless, while temperatures above ca. 250 °C may impact the De, these observations should not be used to draw general conclusions on the thermal stability of the defect responsible for the

Preprint for QG revision 4 -Infrared Radiofluorescence (IR-RF) dating: a review

Page 21 of 64 IR-RF emission. Erfurt (2003a, b) referred to works on amazonite (cf. Ostrooumov, 2016 for an overview) and argued that the Pb + centres are stable up to ~450 ˚C [START_REF] Speit | Radiation defects in feldspars[END_REF] or even up to 700 ˚C (assumption in Erfurt, 2003b: 500 ˚C;700 ˚C in Ostrooumov, 2016). Above this temperature, the Pb + centre disappears (a process also referred to as de-amazonitization).

IR-RF dose limits

The minimum measurable dose has not yet been systematically determined with IR-RF. While [START_REF] Erfurt | Radiolumineszenzspektroskopie und -dosimetrie an Feldspäten und synthetischen Luminophoren für die geochronometrische Anwendung[END_REF] estimated a dose of ca 40 Gy, [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF] reported measurable doses of 0.5 ± 1.0 Gy and 1.2 ± 1.9 Gy for two modern analogue samples. Current instrument configurations allow signals with a few photon-counts per second to be distinguished. In available luminescence measurement systems (Sec. 3), the IR-RF signal of K-feldspar is usually of the order of a million photon counts per second with signal intensities at its maximum when the sample is bleached, i.e., for zero dose samples. Thus, the minimum measurable dose (limit) is a function of stimulation dose-rate (Gy s -1 ), the measurement channel resolution (s channel -1 ) and the applied statistical procedure to distinguish two bright signals and determine the De (e.g., the sliding method causes discretization effects, Sec. 6.2). For example, a sampling rate as applied by [START_REF] Murari | Further investigations on IR-RF: Dose recovery and correction[END_REF] of 10 s channel -1 for a dose rate of ca. 0.06 Gy s -1 would theoretically correspond to a minimum distinguishable dose of 0.6 Gy on average.

The IR-RF dynamic range is defined as the ratio of the maximum to the minimum of the IR-RF signal intensity. In other words, this is the ratio of the IR-RF signal from saturation to the bleaching level of the sample, which in general varies about a factor of 2 (Erfurt and Krbetschek, 2003a). The IR-RF signal dynamic range is minimal (Fig. 9B) compared to the signal dynamics from the other variants of luminescence such as OSL or IRSL, where it typically is at least an order of magnitude higher. Due to low signal dynamic ranges, the slope of IR-RF intensity (I)

with respect to dose (De) changes gradually and finally approaches zero. In terms of resolving dose estimates, the resolution becomes impoverished in the higher dose region as a slight change in intensity (dI) may lead to a large uncertainty in dose estimation (dDe). Erfurt and Krbetschek (2003b) recommended determining the dose where the slope of signal intensity vs dose approaches a value of zero (i.e., dI/dDe ≈ 0). Based on this parameter, they found that for their reader configuration, IR-RF curves allow dose estimation up to ~650 Gy.

Preprint for QG revision 4 -Infrared Radiofluorescence (IR-RF) dating: a review

Page 23 of 64 However, the upper dose limit of IR-RF, and with it, the temporal range, is subject to ongoing research. Krbetschek et al. (2000) reported a saturation De value of 1,440 ± 215 Gy (nature of the error not reported) for a single sample, and in a recent IR-RF dating study Kreutzer et al. (2018a) reported a measurable mean dose of 1,064 ± 41 Gy (mean ± standard deviation). [START_REF] Erfurt | Radiolumineszenzspektroskopie und -dosimetrie an Feldspäten und synthetischen Luminophoren für die geochronometrische Anwendung[END_REF] estimated a mean saturation dose as high as 1,500 Gy. However, [START_REF] Erfurt | Radiolumineszenzspektroskopie und -dosimetrie an Feldspäten und synthetischen Luminophoren für die geochronometrische Anwendung[END_REF] and Erfurt and Krbetschek (2003b) also estimated the maximum resolvable dose at 600 Gy to 650 Gy as the small IR-RF signal dynamic range can limit the precision of signal interpolation. The highest, single aliquot, IR-RF dose of 4,181 ± 371 Gy (mean ± standard deviation) was reported by [START_REF] Wagner | Radiometric dating of the type-site for Homo heidelbergensis at Mauer, Germany[END_REF] (cf. their "Supporting Information", Table S2) using the same instrument as Erfurt et al. (2003).

On a lexsyg research system Frouin et al. ( 2017) recently reported successful measurement of a ~2,100 Gy dose using a regenerated IR-RF signal that was recorded up to 4,000 Gy cumulative dose (cf. their Fig. 7 for sample TML1). Furthermore, [START_REF] Murari | Further investigations on IR-RF: Dose recovery and correction[END_REF] demonstrated accurate laboratory dose recovery up to 3,600 Gy by interpolating onto a regenerated IR-RF curve measured up to 3,900 Gy. However, it should be pointed out that the intensity difference between 2,000 Gy and 3,500 Gy was only around 4 % (Fig. 9B for the dynamic range of IR-RF), which leaves the results susceptible to minimal intensity changes. Hence, at this moment, we cannot refer to a saturation limit of IR-RF. However, the one single value published by Murari et al.

(2018) of ca. 3,600 Gy would allow age determinations (dose rates in the order of 2-3 Gy ka -1 ) of 1.2 Ma to 1.8 Ma. Whether this dose (and temporal) range is feasible for routine dating is still under debate.

The IR-RF alpha-efficiency

The ionisation efficiency and, with it, the efficiency of induced luminescence per unit dose, depends on the type of irradiation (i.e., αvs βvs γ-radiation). Commonly, the luminescence produced by α-particles per unit dose is substantially lower than for βor γ-radiation. Thus, the α-efficiency needs to be determined to correctly calculate the β-equivalent α-dose rate contribution (cf. Aitken, 1985a) Sα-value [START_REF] Guérin | Thermoluminescence dating of volcanic plagioclases[END_REF][START_REF] Valladas | Effet de l'irradiation alpha sur des grains de quartz[END_REF] obtained from four finegrain K-feldspar samples (84 aliquots) was 9.26 ± 1.62 µGy/(10 3 α cm -2 ). The corresponding (dimensionless) value in the a-value system (cf. Aitken 1985b) of 0.067 ± 0.012 is similar to avalues reported for IRSL polymineral fine grain (e.g., [START_REF] Kadereit | Holocene relief and soil changes in loess-covered areas of south-western Germany: The pedosedimentary archives of Bretten-Bauerbach (Kraichgau)[END_REF]. Based on these findings and if the α-efficiency cannot be determined, an estimated a-value of 0.07 ± 0.01 (applied to fine grain and unetched coarse grains, cf. Kreutzer et al., 2018b) appears to be justified.

Measurement protocols and data analysis

Like other luminescence measurement protocols for equivalent dose (De) determination (e.g., for TL, OSL or IRSL), over the years, several measurement protocols and data analysis techniques have been proposed to determine the De for IR-RF.

IR-RF measurement protocols

The first comprehensive IR-RF measurement protocol named IRSAR (infrared single-aliquot regenerative-dose) was presented by Erfurt and Krbetschek (2003b). [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF] introduced a modified version of this protocol and entitled it RF70 (where the subscript '70' refers to the applied measurement temperature of 70 ˚C). Additionally, several other protocols have been reported in the literature and are summarized in Table 6.

Table 6 (Measurement protocols)

All listed protocols consist of less than six measurement steps. Common to all protocols are three main steps: (I) measurement of the natural IR-RF signal (RFnat), (II) signal resetting by bleaching and (III) measurement of the regenerated IR-RF (RFreg) signal after bleaching. The duration of the IR-RF measurements (natural, regenerative) is determined by the chosen data analysis approach (Fig. 11). For example, De determination via curve fitting and signal extrapolation results in IR-RF measurements of longer duration for the natural IR-RF signal than for the regenerated signal and vice versa for a De determination via interpolation. Trautmann et al. (1999a), Krbetschek et al. (2000) and [START_REF] Schilles | Die Infrarot-Radiolumineszenz von Feldspäten und ihr Einsatz in der Lumineszenzdatierung[END_REF] distinguished between an additive (extrapolation) and a regenerative (interpolation) measurement approach, depending on the particular IR-RF signal (natural: additive; regenerative: regenerative) used for subsequent curve fitting. However, this distinction is misleading and should be avoided as it conflicts with the commonly accepted terminology used for TL/OSL. All recorded IR-RF signal curves are dose-response curves, and signal resetting is carried out by optical bleaching. Thus, natural IR-RF curves are always additive dose-response curves, irrespective of the technique used to analyse the data and to obtain the De, namely: extrapolation, interpolation or sliding (see the following section). For further details on the bleaching behaviour of the IR-RF signal see Sec. 5.2.

Pause duration: Five out of seven IR-RF protocols (Table 6) suggested a pause after the optical resetting of the IR-RF signal for at least 1,800 s. The pause is believed to account for an unwanted superposition of IR phosphorescence on the IR-RF signal (e.g., Erfurt and Krbetschek, 2003b). [START_REF] Varma | Aspects of infrared radioluminescence dosimetry in K-feldspar[END_REF] carried out the pause as a phosphorescence measurement just before the stimulation itself. Based on their results, it appears that the phosphorescence is induced only by the irradiation ('radiophosphorescence') and that it is not further increased by bleaching. They thus proposed an optimum bleaching time of 800 s to reduce phosphorescence to its residual

Preprint for QG revision 4 -Infrared Radiofluorescence (IR-RF) dating: a review

Page 26 of 64 level without implementing an additional pause within the measurement procedure. However, this study contradicted the observation made on the same system (Risø TL/OSL DA-20 with IR-RF attachment) by [START_REF] Buylaert | IR-RF dating of sandsized K-feldspar extracts: A test of accuracy[END_REF] who showed the appearance of IR phosphorescence even after bleaching of 1,500 s, though it was two orders of magnitude smaller than the IR-RF signal which can probably be considered negligible. Nevertheless, other studies contradicted these findings, e.g., [START_REF] Erfurt | Radiolumineszenzspektroskopie und -dosimetrie an Feldspäten und synthetischen Luminophoren für die geochronometrische Anwendung[END_REF], Erfurt and Krbetschek (2003b) and [START_REF] Huot | Evidence of shallow TL peak contributions in infrared radiofluorescence[END_REF] showed the presence of phosphorescence directly emitted after bleaching. The above-described observations suggest that an additional pause of 30 min up to 1 h might be beneficial to minimize the potential effects of unwanted signal superposition from the phosphorescence caused by bleaching (also Sec. 5.3).

Preheat and measurement temperature: The work of [START_REF] Trautmann | Radiolumineszenzuntersuchungen an Feldspat[END_REF] gave evidence for a strong temperature dependence of the IR-RF signal of K-feldspar, which appears to be related to the sample's age (see also [START_REF] Erfurt | Radiolumineszenzspektroskopie und -dosimetrie an Feldspäten und synthetischen Luminophoren für die geochronometrische Anwendung[END_REF]. Considering the dependency of the IR-RF signal intensity [START_REF] Trautmann | Radiolumineszenzuntersuchungen an Feldspat[END_REF][START_REF] Erfurt | Radiolumineszenzspektroskopie und -dosimetrie an Feldspäten und synthetischen Luminophoren für die geochronometrische Anwendung[END_REF][START_REF] Frouin | Les feldspaths comme support pour la datation par luminescence de gisements archéologiques et de séquences quaternaires d'Aquitaine[END_REF] on the preheat and measurement temperature, measurements under well-controlled temperature conditions appear advisable.

However, due to technical limitations, measurements under controlled (elevated) temperature conditions have only been applied by [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF]. They suggested a preheat of 70 ˚C based on the observation of thermally assisted phosphorescence. [START_REF] Huot | Evidence of shallow TL peak contributions in infrared radiofluorescence[END_REF] advised that a temperature range of 70 ˚C to 100 ˚C would be suitable. However, Erfurt and Krbetschek (2003b) neglected the need for any preheat prior to measurement following their observation of no change in IR-RF intensity from room temperature to 250 ˚C (cf. Fig. 2 in Erfurt and Krbetschek, 2003b). Nevertheless, a comparison of IR-RF ages with independent age control showed improvement in results when measurements are carried out at elevated temperature [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF]. Therefore, Frouin et al. ( 2017) recommended measurements at elevated temperature.

Sensitivity correction (also Sec. 5.4): Monitoring changes in the dose-response characteristics is an essential feature of every OSL SAR protocol. [START_REF] Schilles | Die Infrarot-Radiolumineszenz von Feldspäten und ihr Einsatz in der Lumineszenzdatierung[END_REF] and [START_REF] Varma | Aspects of infrared radioluminescence dosimetry in K-feldspar[END_REF] included treatments to correct for unwanted changes in IR-RF signal sensitivity by introducing a correction factor for IR-RF measurements. [START_REF] Murari | Further investigations on IR-RF: Dose recovery and correction[END_REF] investigated a new way of correction. In this method, the shapes of IR-RF curves are matched by moving the RFnat

Preprint for QG revision 4 -Infrared Radiofluorescence (IR-RF) dating: a review

Page 27 of 64 vertically along with horizontal sliding (Sec. 5.4 for sensitivity change). This method was able to recover a given dose with 3-10 % accuracy, compared to an offset by 15-23 % when recovered only using the horizontal sliding method proposed by [START_REF] Buylaert | IR-RF dating of sandsized K-feldspar extracts: A test of accuracy[END_REF]. The recommended method [START_REF] Kreutzer | Always remain suspicious: a case study on tracking down a technical artefact while measuring IR-RF[END_REF][START_REF] Murari | Further investigations on IR-RF: Dose recovery and correction[END_REF] does not need any extra measurements other than those implemented in the protocol suggested by [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF]. However, the RFnat measurement should be long enough to produce an RF signal with pronounced curvature to match the RFnat and RFreg curves.

Data analysis

Data analysis for De estimation is essential for age determination. De determination requires a comparison of the natural and a minimum of one regenerated IR-RF signal. The different methods available for making this comparison are described below.

Figure 11 (De determination methods)

Extrapolation and Interpolation method: Three different approaches were presented to analyse IR-RF data (Fig. 11): (I) extrapolation, (II) interpolation and (III) sliding. The first two approaches comprise a mathematical curve fitting for De determination. Extrapolation (Fig. 11A) and interpolation (Fig. 11B) requires that either the natural or regenerative signal is recorded over a more extended period (natural signal: extrapolation; regenerative signal: interpolation).

The chosen channel resolution and stimulation time determine the precision of the curve fitting and thus, the statistical error of the De. For curve fitting (extrapolation, interpolation), Trautmann et al. (1999a), Krbetschek et al. (2000) and [START_REF] Schilles | Die Infrarot-Radiolumineszenz von Feldspäten und ihr Einsatz in der Lumineszenzdatierung[END_REF] proposed a single exponential decaying function with three parameters. Later, Erfurt and Krbetschek (2003b) recognized that the curve shape could be best described using a so-called stretched exponential function (Fig. 12). This function was suggested in a general form by, e.g., [START_REF] Pavesi | Stretched-exponential decay of the luminescence in porous silicon[END_REF]. The stretched exponential function introduces a dispersion factor (ß), which accounts for the underlying physical processes in disordered condensed matter systems. Unfortunately, the mathematical expression of this function type is not consistent in the IR-RF literature (Fig. 12)

and differs regarding the placement of ß in the equation. Although the functions shown in Fig. 12 may result in consistent De estimations, they reveal different curve shapes for similar parameter

Preprint for QG revision 4 -Infrared Radiofluorescence (IR-RF) dating: a review

Page 28 of 64 sets. Therefore, parameters describing an IR-RF curve's decay cannot be compared without a statement on the applied mathematical expression.

Figure 12 (Equations used for IR-RF curve fitting)

Due to the general difficulties associated with De estimation by extrapolation (i.e., substantial uncertainties), this methodological approach appears to have been abandoned in later studies, and more recently only De estimation by interpolation has been applied (e.g., [START_REF] Wagner | Radiometric dating of the type-site for Homo heidelbergensis at Mauer, Germany[END_REF][START_REF] Novothny | Infrared stimulated luminescence and radiofluorescence dating of aeolian sediments from Hungary[END_REF][START_REF] Kreutzer | Chronology of the Quaternary profile Zeuchfeld in Saxony-Anhalt / Germany -a preliminary luminescence dating study[END_REF]. Nevertheless, every fitting method requires an assumption regarding the IR-RF curve shape, either based on a model or the best graphic adaption of the curve shape. Furthermore, IR-RF curves recorded only for a short time do not sufficiently reveal the curve shape and potential changes.

Sliding method: [START_REF] Buylaert | IR-RF dating of sandsized K-feldspar extracts: A test of accuracy[END_REF] suggested a data analysis method based on horizontal sliding of the RFnat curve until the best match is reached (inspired by the Australian slide method introduced initially by [START_REF] Prescott | Estimation of equivalent dose in thermoluminescence dating -the Australian slide method[END_REF]. This approach appears to be even more justified since [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF] pointed out an initial rise at the beginning of the natural IR-RF curve (Sec. 5.5). The observed initial rise at the beginning of the IR-RF curve does not allow an unbiased channel selection if curve fitting combined with interpolation or extrapolation is applied. In other words, for IR-RF data analysis, the (horizontal) sliding technique should be favoured over the curve fitting approach. However, it was often seen that RFnat and RFreg curves did not match after horizontal sliding. [START_REF] Kreutzer | Always remain suspicious: a case study on tracking down a technical artefact while measuring IR-RF[END_REF] 2018) used 100 channels. However, the precise number depends on the signal shape.

Error estimation: Krbetschek et al. (2000) suggested that the primary source of random error in the IR-RF 'mean' De arises from changes in the sample geometry at a single-grain level (see also Page 29 of 64 Trautmann et al., 2000b). In contrast to OSL, where the dose-response curve is typically reconstructed with a few (e.g., 5-15) regenerative dose measurements, the number of channels used for constructing the IR-RF dose-response curve can be increased dramatically (e.g., >1,000 values) and is limited only by the instrumental signal-to-noise ratio and the total number of allowed channels by the system. Consequently, for IR-RF dating studies, individual (statistical)

errors have been ignored, and the standard error deduced from individual De distributions (e.g., [START_REF] Wagner | Radiometric dating of the type-site for Homo heidelbergensis at Mauer, Germany[END_REF][START_REF] Lauer | Infrared radiofluorescence (IR-RF) dating of middle pleistocene fluvial archives of the Heidelberg Basin (Southwest Germany)[END_REF][START_REF] Kreutzer | Chronology of the Quaternary profile Zeuchfeld in Saxony-Anhalt / Germany -a preliminary luminescence dating study[END_REF]. To account for potential errors [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF] (their supplement) developed an approach to estimate the standard error of an individual aliquot based on a non-parametric bootstrapping approach [START_REF] Efron | Bootstrap Methods: Another Look at the Jackknife[END_REF] for the sliding method. Nevertheless, the results of [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF] also showed that the obtained individual statistical standard error remains negligible in comparison to inter-aliquot scatter and becomes relevant only for dim IR-RF signals.

Data analysis software: To analyse IR-RF data, no specialized software is needed, and commercial software solutions, e.g., SigmaPlot TM or ORIGIN TM may be sufficient to analyse single measurements. However, within a dating study, the amount of data may demand more comprehensive and efficient solutions. Two freely available software solutions have been published to analyse IR-RF data based on the IRSAR Erfurt and Krbetschek (2003b) approach.

The MS Windows TM software RLanalyse [START_REF] Lapp | New luminescence measurement facilities in retrospective dosimetry[END_REF]latest version 1.20) has implemented the (horizontal) sliding method and works with BIN/BINX-files produced by a Risø TL/OSL reader. The most recent version of the function analyse_IRSAR.RF() implemented in the package 'Luminescence' [START_REF] Kreutzer | Introducing an R package for luminescence dating analysis[END_REF](Kreutzer et al., , 2018c) makes use of the platform-independent programming language R (R Core Team, 2018), and supports the horizontal and vertical sliding approach. The function also supports De estimation via curve fitting as described by Erfurt and Krbetschek (2003b) as well as via sliding including the individual standard error estimation approach described in [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF] and [START_REF] Murari | Further investigations on IR-RF: Dose recovery and correction[END_REF]. Through the 'Luminescence' environment, XSYG-files (Freiberg Instruments lexsyg readers), BIN/BINX-files (Risø TL/OSL reader) as well as various other data formats (e.g., file endings *.csv, *.txt) are supported as input data.

Application of IR-RF dating

The broader use of IR-RF as a dating method for sediments started mainly after introducing the IRSAR protocol by Erfurt and Krbetschek (2003b). Signal saturation levels of > 1,000 Gy (e.g., Erfurt and Krbetschek, 2003b and Sec. 5.7) favoured IR-RF dating applications on Middle Pleistocene sediments which are generally beyond the quartz OSL dating limit. The typical dose saturation for quartz OSL measured in the UV is reached around 150-200 Gy [START_REF] Wintle | A review of quartz optically stimulated luminescence characteristics and their relevance in single-aliquot regeneration dating protocols[END_REF] except for a few cases where quartz doses >300 Gy are reported (e.g., [START_REF] Lowick | Characterising the luminescence behaviour of `infinitely old' quartz samples from Switzerland[END_REF]. Until now, IR-RF dating has mainly been applied to coarse grain K-rich feldspar using multiple-grains (Secs. 7.17.2). Spatially resolved and single grain studies are limited to preliminary work (e.g., [START_REF] Schilles | Die Infrarot-Radiolumineszenz von Feldspäten und ihr Einsatz in der Lumineszenzdatierung[END_REF]Trautmann et al., 2000b) and a manuscript in an open discussion by Mittelstrass and Kreutzer (preprint) and are thus not further discussed here.

Applications of IR-RF on polymineral fine-grain samples (4-11 µm) are currently limited to three studies [START_REF] Schilles | Die Infrarot-Radiolumineszenz von Feldspäten und ihr Einsatz in der Lumineszenzdatierung[END_REF]Kreutzer et al., 2018b;[START_REF] Coussot | Séquence de Comblement d'un Paléovallon en Contexte de Plateau (290-10 Ka)[END_REF].

Application to glacio-fluvial and fluvial sediments

In the past, IR-RF dating has been favoured particularly for constraining the timing of the Saalian glacial cycle and the Eemian interglacial by dating fluvial deposits of sites located in Central/Eastern Germany [START_REF] Eissmann | Quaternary geology of eastern Germany (Saxony, Saxon-Anhalt, South Brandenburg, Thüringia), type area of the Elsterian and Saalian Stages in Europe[END_REF] by [START_REF] Degering | Dating of interglacial sediments by luminescence methods[END_REF], Krbetschek et al. (2008) and [START_REF] Kreutzer | Chronology of the Quaternary profile Zeuchfeld in Saxony-Anhalt / Germany -a preliminary luminescence dating study[END_REF]. [START_REF] Degering | Dating of interglacial sediments by luminescence methods[END_REF] presented IR-RF ages ranging from 120 ± 15 ka to 158 ± 21 ka for the Eemian site Klinge (Germany), and the results were in good agreement with quartz and K-feldspar OSL and IRSL luminescence dating results.

IR-RF dated fluvial sites (e.g., Wallendorf and Delitzsch, Germany) are highly relevant for establishing a chronology for Middle Pleistocene Palaeolithic human activity in Europe due to the presence of stone-artefacts embedded in fluvial sands and gravels. [START_REF] Krbetschek | Infrarot-Radiofluoreszenz-Alter (IR-RF) unter-saalezeitlicher Sedimente Mittel-und Ostdeutschlands[END_REF] presented IR-RF ages ranging from ~150 ka to ~306 ka for the Saalian period and highlighted human activity in Central Germany already at around 300 ka. Lauer and Weiss (2018) compared pIRIR290 luminescence ages from the important palaeolithic site of Markkleeberg [START_REF] Baumann | Die paläolithischen Neufunde von Markkleeberg bei Leipzig[END_REF][START_REF] Schäfer | Bericht zu den Ausgrabungen am altsteinzeitlichen Fundplatz Markkleeberg 1999 bis 2001[END_REF] with previously available IR-RF ages [START_REF] Krbetschek | Radiofluorescence dating: A novel method for age determination of clastic sediment deposits from about 20 ka to 300 ka[END_REF] and found the pIRIR290 and IR-RF ages were in excellent agreement and provided late MIS 6 ages for the upper fluvial sequence at the site. Also, for the key site of the Homo heidelbergensis, located at Mauer in south-west Germany, IR-RF was applied to fluvial deposits correlated to the archaeological horizon of the Mauer mandible. At this site, the IR-RF ages were in good agreement with results of combined electron spin resonance (ESR)/U-series dating on mammal teeth, yielding an age of around 0.6 Ma [START_REF] Wagner | Radiometric dating of the type-site for Homo heidelbergensis at Mauer, Germany[END_REF]. [START_REF] Lauer | Infrared radiofluorescence (IR-RF) dating of middle pleistocene fluvial archives of the Heidelberg Basin (Southwest Germany)[END_REF] (2017) reported a minimum age of >602 ± 77 ka, consistent with the magnetostratigraphic information which was not available in 2011. In light of the new findings, the IR-RF age of 643 ± 28 ka by [START_REF] Lauer | Infrared radiofluorescence (IR-RF) dating of middle pleistocene fluvial archives of the Heidelberg Basin (Southwest Germany)[END_REF] should be considered as minimum age. The reasons for this age underestimation should be subject to future research.

In general, studies presented by [START_REF] Krbetschek | Infrarot-Radiofluoreszenz-Alter (IR-RF) unter-saalezeitlicher Sedimente Mittel-und Ostdeutschlands[END_REF] and [START_REF] Wagner | Radiometric dating of the type-site for Homo heidelbergensis at Mauer, Germany[END_REF] demonstrated good agreement with independent age control. In contrast to these studies, [START_REF] Buylaert | IR-RF dating of sandsized K-feldspar extracts: A test of accuracy[END_REF] showed that IR-RF dating results of coastal marine sediments from Russia and Denmark as well as colluvial sediments from France were either overestimated (for ages between 20-45 ka) or underestimated (for older samples ~128 ka) compared to independent dating methods based on biostratigraphy, radiocarbon ( 14 C), OSL and pIRIR290 (for numerical values cf. Table S1 in [START_REF] Buylaert | IR-RF dating of sandsized K-feldspar extracts: A test of accuracy[END_REF].

Figure 13 ABC (Age comparison)

Application to aeolian deposits

Well-bleached sediments, such as wind-blown loess or dune sands seem to be most suitable for IR-RF dating applications, although the amount of sand-sized K-feldspars in silt-dominated loess is limited. Early aeolian samples used for IR-RF dating result originate from a sediment core from the Gaxun Nur Basin in North-West Chin [START_REF] Wünnemann | Interglacial and Glacial Fingerprints from Lake Deposits in the Gobi Desert, NW China[END_REF]. The IR-RF dating results2 significantly overestimated previously reported TL/IRSL ages and were discarded by the authors [START_REF] Wünnemann | Interglacial and Glacial Fingerprints from Lake Deposits in the Gobi Desert, NW China[END_REF], without presenting further technical details. [START_REF] Novothny | Infrared stimulated luminescence and radiofluorescence dating of aeolian sediments from Hungary[END_REF] were the first to extract coarse-grained K-feldspars from Hungarian loess for IR-RF dating. The IR-RF ages of ~200 ka presented by [START_REF] Novothny | Infrared stimulated luminescence and radiofluorescence dating of aeolian sediments from Hungary[END_REF] significantly overestimated the fading-corrected IRSL ages of ~130 ka, explained due to insufficient bleaching of the coarse-grained fraction. An IR-RF age overestimation compared to quartz OSL ages of reworked aeolian sediments from Egypt was also reported by [START_REF] Buylaert | IR-RF dating of sandsized K-feldspar extracts: A test of accuracy[END_REF], which was either attributed to a preliminary determination of the bleaching level before the regenerative dose measurement or sensitivity changes between the measurement of the natural and regenerated curves.

It was recently demonstrated that the modified IRSAR-protocol, measuring the IR-RF signal at 70 °C (RF70), recovered IR-RF ages on modern aeolian samples that agreed with independent age control. [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF] have shown reasonable agreement with independent age control from polymineral (4-11 µm) fine-grain results published by [START_REF] Meszner | Late Pleistocene landscape dynamics in Saxony, Germany: Paleoenvironmental reconstruction using loess-paleosol sequences[END_REF]. However, they also observed a large scatter in their De distributions. Another age from a loess sample from the same site appeared to be underestimated. This offset was explained by the low De values resulting from low signal intensities [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF]. Kreutzer et al. (2018a) presented a dating application study on coastal dynamics from the Médoc region (south-west France), comparing coarse grain K-feldspar IR-RF ages (RF70 protocol) with quartz OSL ages and quartz multiple-centre ESR dating [START_REF] Toyoda | Bleaching of ESR signals by the sunlight: a laboratory experiment for establishing the ESR dating of sediments[END_REF]. In this study, the IR-RF ages were systematically older than the SAR quartz ages, which was believed to be a consequence of insufficient resetting of the IR-RF signal. However, this study showed reasonable agreement with the ESR ages for older sediments (200-330 ka). Similarly, [START_REF] Scerri | The expansion of later Acheulean hominins into the Arabian Peninsula[END_REF] also found that RF70 and pIRIR290 age estimates were consistent within a 2-sigma limit and in stratigraphic order. The aeolian samples from an archaeological site in Saudi Arabia resulted in age estimates of ~276 ka for the older (archaeologically sterile) layer and 197 ka for the human occupation layer.

Remarks on IR-RF age accuracy and independent age control

Figure 13 presents a non-exhaustive overview of published IR-RF data. The ages from the IR-RF dating approaches generally show good agreement with independent age control (e.g., [START_REF] Degering | Dating of interglacial sediments by luminescence methods[END_REF], whereas the IR-RF ages from [START_REF] Buylaert | IR-RF dating of sandsized K-feldspar extracts: A test of accuracy[END_REF] disagree with independently derived ages. Again, a good agreement between IR-RF and independent ages was reported using a modified IRSAR protocol (RF70) suggested by [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF].

The study by [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF] was the first to present various IR-RF dating applications with a modified IRSAR protocol (RF70), which agreed with independent age control. IR-RF dating of a Pleistocene beach deposit from Peru and colluvial deposits from France appeared to be overestimated compared to independent age information from IRSL, U/Th series or radiocarbon dating; a pattern also observed by [START_REF] Schaarschmidt | pIRIR and IR-RF dating of archaeological deposits at Badahlin and Gu Myaung Caves -First luminescence ages for Myanmar[END_REF]. However, for the Peruvian sample, IR-RF and pIRIR290 ages agreed within error limits. Similarly, Holocene beach sand from Denmark and another colluvial example from France yielded ages in good agreement with independent age information. In conclusion, published IR-RF dating results indicated that the IR-RF dating method produced correct ages in some cases, but fails for other cases. It seems that there are still methodological problems related to IR-RF dating, and further investigation is needed to overcome these challenges.

Summary and future directions of IR-RF dating

Overall, regardless of ambivalent dating results in some studies, IR-RF appears to be a promising but somewhat overlooked dating method on K-feldspars. The status quo renders a picture with several, potentially, game-changing advantages but without a significant breakthrough because those benefits are not received as significant enough by dating practitioners. On the other hand, IR-RF poses a bunch of open questions and challenges that are yet to overcome.

The status quo

The plus side of IR-RF dating has different dimensions. From a methodological perspective, IR-RF is believed to monitor the trapping of electrons in the principal trap, i.e., it is a direct measurement of the dose accumulation in the mineral. This approach is conceptionally different from conventional OSL, IRSL and TL measurements, involving secondary recombination processes to infer the signal of interest. Debated methodological issues, such as phosphorescence and sensitivity change (see Secs. 5.35.4), appear to be manageable by proper experimental and data analysis design.

From a practical perspective, compared to post-IR IRSL dating, for instance, the measurement sequence for one aliquot is reasonably concise, less error-prone, and, depending on the aimed dose range, likely less time-consuming (depending on the chosen measurement sequence). The dose-response curve is the IR-RF curve measured during irradiation with a resolution usually in the order of a fraction of a Gy. Instead of applying different fitting equations determining the De, the data analysis using the sliding method, i.e., matching two dose-response curves (RFnat and RFreg), could not be more straightforward. Software to analyse IR-RF signals is freely available and partly open-source. The biggest obstacle for applying IR-RF dating in the past, availability of equipment, is no more. At least two commercial manufacturers offer ready-to-use IR-RF readers for research and dating applications.

From a dating perspective, the target mineral, K-feldspar, shows a high natural abundance, an acknowledged higher luminescence dating range compared to quartz, and the internal potassium concentration lowers the impact of the external dose-rate contribution. However, conventional feldspar luminescence is reported to suffer from an unwanted athermal signal loss (fading).

Contrary to IRSL, no definite evidence was provided for fading of the IR-RF signal of Kfeldspars to date. Although [START_REF] Buylaert | IR-RF dating of sandsized K-feldspar extracts: A test of accuracy[END_REF] reported age underestimations for older samples of ca 30 %, this does not appear to be a generally observed pattern. Furthermore, signal instability as a cause for this observation was considered unlikely by [START_REF] Kumar | Sediment dating using Infrared Photoluminescence[END_REF]. The thermal stability of the IR-RF signal (determining the potential age range) appears to be sufficiently high up to 700 ˚C (Sec. 5.6), though previous experiments indicated changes of the IR-RF signal shape above ~250 °C (Trautmann et al., 1999a;Erfurt and Krbetschek, 2003b;[START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF].

However, to sustain, a dating method has to show advantages over established methods, which are also perceived as significant for application studies. Supposing that the signal of choice is thermally and athermally stable, for luminescence-based chronologies such advantages are measured in terms of bleachability and temporal range.

Preprint for QG revision 4 -Infrared Radiofluorescence (IR-RF) dating: a review

Page 35 of 64

Compared to pIRIR290, which seems to suffer from no or at least less fading than IRSL, IR-RF's bleachability is comparable. In other words, in natural environments involving sediment transport processes with only short sunlight exposure, IR-RF dating seems to be as applicable as pIRIR290 and other methods may suit better. Whether the temporal range is as high as the ~1.2-3 Ma (~ 3,600 Gy) postulated by Murari et al. ( 2018) is yet to be revealed. More realistically seem values around up to 1,500 Gy measured by, e.g., [START_REF] Erfurt | Radiolumineszenzspektroskopie und -dosimetrie an Feldspäten und synthetischen Luminophoren für die geochronometrische Anwendung[END_REF], [START_REF] Frouin | Les feldspaths comme support pour la datation par luminescence de gisements archéologiques et de séquences quaternaires d'Aquitaine[END_REF], [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF] and Kreutzer et al. (2018). Here we conclude that the signal saturation limit (and thus the temporal range) appears to be significantly higher than for conventional OSL on quartz (up to 400 Gy, typically lower, for a review cf. [START_REF] Wintle | Optically stimulated luminescence signals from quartz: A review[END_REF]. This "winning margin" is less pronounced if IR-RF is compared to studies reporting post-IR IRSL (more specific: pIRIR290) or MET-pIRIR results. For instance, [START_REF] Liu | Stability of fine-grained TT-OSL and post-IR IRSL signals from a c. 1 Ma sequence of aeolian and lacustrine deposits from the Nihewan Basin (northern China)[END_REF]

Future directions

Future methodological research on IR-RF should first resolve some open debates, particularly on signal saturation and signal stability (fading). Although fading does not appear to be a generally observed pattern, this topic should be explored in more detail, along with potential sensitivity changes using samples of known and geological age. The biggest obstacle to resolving whether the signal recorded with IR-RF is stable or suffers from an athermal signal loss over geological timescales might be the experimental design. From the current perspective, it appears that short experiments over a couple of weeks to months are not sufficient to provide answers to that question. Hence, research should involve laboratories with a relatively long history and an archive of already measured, irradiated and stored feldspar specimen. The quantification of the saturation level is more of theoretical than practical relevance.

With regard to the literature, it is safe to assume a rather broad, sample dependent, saturation level range between 600 Gy and 2,000 Gy up to perhaps 4,000 Gy. However, of relevance for the

Preprint for QG revision 4 -Infrared Radiofluorescence (IR-RF) dating: a review

Page 36 of 64 dating practice is the limit of the K-feldspar sample at hand, regardless of any theoretical value.

In other words, the saturation level of IR-RF dating and with it the temporal range, will itself establish circumstantially over time; with or without dedicated research. However, both research on the fading behaviour and the signal saturation might contribute to a broader understanding of the physics underpinning IR-RF. To date, Trautmann's model (Trautman et al., 2000a) remained, to our knowledge, the only comprehensible model genuinely dedicated to IR-RF. Cleary, efforts are needed to combine the old and new findings around IR-PL and combine them with established knowledge in IRSL to decipher the proposed resemblance of IR-RF and IR-PL (cf. [START_REF] Kumar | Site-selective mapping of metastable states using electron-beam induced luminescence microscopy[END_REF]. Similarly, while there seems to be extensive research to identify the defect responsible for IR-PL (most recently [START_REF] Kumar | Site-selective mapping of metastable states using electron-beam induced luminescence microscopy[END_REF], it appears that established knowledge on the role of Pb in the luminescence production in feldspar (cf. textbook by Ostrooumov, 2016) did not (yet) receive full attention.

On the application site, the next logical application step is spatially resolved IR-RF in a single grain (Mittelstrass and Kreutzer, preprint) or even sub-grain level as concluded by [START_REF] Kumar | Site-selective mapping of metastable states using electron-beam induced luminescence microscopy[END_REF].

Another direction to test, for already available multi-grain IR-RF, are fine-grain (polymineral) mineral fractions. The few attempts reported in the literature yielded promising results [START_REF] Schilles | Die Infrarot-Radiolumineszenz von Feldspäten und ihr Einsatz in der Lumineszenzdatierung[END_REF][START_REF] Coussot | Séquence de Comblement d'un Paléovallon en Contexte de Plateau (290-10 Ka)[END_REF]. However, the mixture of minerals in such samples may hamper its application. [START_REF] Meyer | Quantitative evaluation of mineral grains using automated SEM-EDS analysis and its application potential in optically stimulated luminescence dating[END_REF] used quantitative evaluation of minerals by scanning electron microscopy (QEMSCAN) for polymineral fine grain OSL samples from interglacial lacustrine units (NW11 and THG 4 from Switzerland; [START_REF] Lowick | Testing the application of post IR-IRSL dating to fine grain waterlain sediments[END_REF] and found that K-feldspar amounts only to ~2-4 %. The major component of the samples was quartz (40-50 %). [START_REF] Tsukamoto | A comparative study of the luminescence characteristics of polymineral fine grains and coarse-grained K-, and Na-rich feldspars[END_REF] confirmed similar observations for various loess samples using X-ray diffractometry (XRD) as well as scanning electron microscopy-energy dispersive X-ray (SEM-EDX). While quartz samples emit RF in the IR region, but not beyond 735 nm [START_REF] Schmidt | Radiofluorescence of quartz: A review[END_REF], quartz may not interfere with the main IR-RF emission (865 nm). However, the polymineral composition may lead to unfortunate emission spectra with, e.g., a dominating peak at 710 nm (cf. [START_REF] Heydari | Bayesian luminescence dating at Ghār-e Boof, Iran, provides a new chronology for Middle and Upper Paleolithic in the southern Zagro[END_REF], for an unsuccessful IR-RF dating attempt using polyminerals). Hence, for such an application, spectrometer measurements appear indispensable.

Besides, deploying IR-RF on polymineral fine grain samples would significantly broaden the

Preprint for QG revision 4 -Infrared Radiofluorescence (IR-RF) dating: a review

Page 37 of 64 application to environmental settings where grain sizes <90 µm dominate, and applications can be tested preferably without extensive methodological research.

In summary, the current status of IR-RF dating still leaves room for rich methodological and application studies towards a potentially bright future.

Figure captions

Figure 1 Schematic of the different luminescence transitions involved in IR-RF, IRSL and post-IR IRSL measurements, based on [START_REF] Trautmann | Investigations of feldspar radioluminescence: potential for a new dating technique[END_REF]Trautmann et al. ( , 1999aTrautmann et al. ( , 2000a) ) and [START_REF] Jain | Towards a non-fading signal in feldspar: Insight into charge transport and tunnelling from time-resolved optically stimulated luminescence[END_REF]. Colours read as follows: Black lines indicate electron transitions; blue lines indicate hole migrations. Red colours also refer to electron transitions but related to the production of IRSL.

Figure 3

The efficiencies of four different spectrometers. The overall efficiencies of spectrometers were approximated by multiplying the individual efficiencies of the grating with those of the spectrograph and the CCD chip.

Figure 4

Effective detection band for (A) the setups used by [START_REF] Schilles | Die Infrarot-Radiolumineszenz von Feldspäten und ihr Einsatz in der Lumineszenzdatierung[END_REF] and [START_REF] Erfurt | Radiolumineszenzspektroskopie und -dosimetrie an Feldspäten und synthetischen Luminophoren für die geochronometrische Anwendung[END_REF], and (B)

Risø and lexsyg research readers. The net transitions were estimated by interpolation and by multiplying the filter transmission and quantum efficiency of the PMT.

Figure 5

Simulated Gaussian IR-RF peaks from K-feldspar at 710 nm, 865 nm and 910 nm (similar to Erfurt and Krbetschek, 2003b). The main IR-RF peak is centred at 865 nm. A) Simulated IR-RF spectrum with a high 865 nm peak, simulating a bleached sample. B) Simulated IR-RF spectrum with a high 710 nm peak, a situation appearing when the sample is dosed. C) A typical spectrum from K-feldspar for a sediment sample (redrawn after [START_REF] Schilles | Die Infrarot-Radiolumineszenz von Feldspäten und ihr Einsatz in der Lumineszenzdatierung[END_REF].

Figure 6

IR-RF bleaching using different bleaching sources. A) Sunlight bleaching (redrawn after Trautmann et al., 1999a). Full signal resetting is reached within 4-6 h. B) Monochromatic bleaching for wavelengths <500 nm; a bleaching plateau seems to be reached within ca. 0.3 h (redrawn after Trautmann et al., 2000a). C) Solar simulator (200 W high-pressure Hg-lamp, 5

mm Schott KG3 heat absorbing filter at a distance 20 cm) allows full signal resetting within 0.7 h (redrawn after Krbetschek et al., 2000). D) A bleaching comparison of IR-RF measured at elevated temperature (RF70) with IR50, pIRIR225 and pIRIR290 (redrawn after [START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF].

Resetting of the IR-RF signal is much slower compared to IR50 and pIRIR225, but it is similar or slightly faster than pIRIR290 ad needs ~3 h bleaching time. The x-axis scale is similar for all subplots.

Figure 7

IR phosphorescence of a K-feldspar sample after bleaching as observed by Erfurt and Krbetschek (2003b) (redrawn after Erfurt and Krbetschek, 2003b).

Figure 8

A schematic representation to explain the sensitivity change monitored by various authors using different methods. A) Derived sensitivity correction factor (s) by fitting exponential functions to two bleached regenerated IR-RF (RFreg) curves [START_REF] Schilles | Die Infrarot-Radiolumineszenz von Feldspäten und ihr Einsatz in der Lumineszenzdatierung[END_REF]. B) Sensitivity correction factor (Fs) estimation using spline fitting and extrapolation [START_REF] Varma | Aspects of infrared radioluminescence dosimetry in K-feldspar[END_REF]. C) Sensitivity correction of IR-RF data by sliding the natural IR-RF (RFnat) curve vertically up or down along with horizontal sliding to find the best match with the RFreg curve (see main text for detail).

Figure 9

A) A typical behaviour of the initial rise of IR-RF from a natural sample. The first few channels of the measured data show an initial rise in IR-RF intensity before decaying monotonically. B) IR-RF signal dynamic range measured while irradiating the sample with a cumulative dose of 3,900 Gy. The typical dynamic range of IR-RF signals is ~2, as reported by [START_REF] Schilles | Die Infrarot-Radiolumineszenz von Feldspäten und ihr Einsatz in der Lumineszenzdatierung[END_REF] and [START_REF] Erfurt | Radiolumineszenzspektroskopie und -dosimetrie an Feldspäten und synthetischen Luminophoren für die geochronometrische Anwendung[END_REF].

Figure 12

Simulated IR-RF curves for different equations reported in the literature, with Φ0 the initial IR-RF photon flux, ∆Φ the dose-dependent change of the IR-RF flux, λ the decay parameter, ß the dispersion factor and D the dose. For similar parameter values, the curve shapes differ markedly.

Values chosen for the figure: Φ0 = 1, ∆Φ = 1, λ = 2.274e-03, ß = 7.6e-01.

Figure 13

A) Independent age control vs IR-RF age (redrawn after [START_REF] Degering | Dating of interglacial sediments by luminescence methods[END_REF] The instrumental setup differs considerably across the studies and should be considered before protocol application. If no measurement temperature is listed, such value was not reported by the study or no additional heating above ambient temperature was applied. Please note that the table lists only general treatments, for further details the reader is referred to the respective publication.

Figure 1

 1 Figure 1 illustrates the different electronic transitions associated with IRSL and IR-RF production in one plot. Please note: Although we compiled different ideas in one figure, our graphical representation should not be considered a new model. In Fig. 1, continuous exposure to ionizing radiation leads to a constant flow of electrons from the valence band to the conduction band [a], from which electrons can either recombine radiatively [b] or non-radiatively (not shown for clarity), or become trapped [c]. As irradiation persists, the IRSL trap [c] becomes filled, resulting in more electrons recombining radiatively [b], accounting for the observed rise in

  summarize the details of various instruments concerning signal detection and sample bleaching parameters. Figures 2 A-D provide different technical realizations for measuring the RF signal from K-feldspar samples.

Figure

  Figure 2 A B C D

Figure

  Figure 4 A B (PMT efficiency and filter combinations)

Figure

  Figure 6 A B C D

  Figure 7

  also showed a shape mismatch and change in intensity for multiple measurements but demonstrated that this sensitivity change would only affect the dose estimation by 3 % (cf. Fig 4 inErfurt and Krbetschek, 2003b). In addition to these studies,[START_REF] Buylaert | IR-RF dating of sandsized K-feldspar extracts: A test of accuracy[END_REF] mentioned the possibility of a significant sensitivity change, either induced by bleaching or by the IR-RF measurement itself.[START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF] reported on a curve shape mismatch between the natural IR-RF (RFnat) and the regenerated IR-RF (RFreg) curve (cf. Fig.2in[START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF], and rejected the measured aliquots (Fig.8C). In the literature, two attempts have been made to explain this behaviour:[START_REF] Kreutzer | Always remain suspicious: a case study on tracking down a technical artefact while measuring IR-RF[END_REF] gave evidence that a technical artefact with the measurement equipment caused an unwanted geometry change.[START_REF] Murari | Further investigations on IR-RF: Dose recovery and correction[END_REF] investigated the possible reason for this shape mismatch using three modern bleached samples in a dose recovery study. For these samples, a given dose was recovered using the RFnat and RFreg signals. In their study, RFnat refers to IR-RF curves from the naturally bleached modern sample, and RFreg refers to IR-RF curves measured after bleaching with the solar simulator. As samples are bleached in both cases, both IR-RF curves, RFnat and RFreg, can act as regenerated IR-RF curves. An offset of 23 % was observed when the dose was recovered from the RFnat signal (cf. Fig.2in[START_REF] Murari | Further investigations on IR-RF: Dose recovery and correction[END_REF]

  Krbetschek et al. (2000) presented experimental results supporting the hypothesis of long-term stability of the IR-RF signal. For instance, short-term (days to months) fading tests with storage of samples for several months at room temperature showed no sign of signal increase (i.e., no emptying of traps) which seems to confirm signal stability over short periods (at room temperature). Furthermore, based on the dating of sediment samples using IR-RF, e.g.,[START_REF] Wagner | Radiometric dating of the type-site for Homo heidelbergensis at Mauer, Germany[END_REF] and[START_REF] Novothny | Infrared stimulated luminescence and radiofluorescence dating of aeolian sediments from Hungary[END_REF] claimed that the IR-RF signal exhibited no indication of fading for ages in the range ca 420-700 ka[START_REF] Wagner | Radiometric dating of the type-site for Homo heidelbergensis at Mauer, Germany[END_REF] and 148-250 ka[START_REF] Novothny | Infrared stimulated luminescence and radiofluorescence dating of aeolian sediments from Hungary[END_REF]. Likewise,[START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF] andKreutzer et al. (2018a) reported a good agreement with the independent age control of even older ages. By contrast,[START_REF] Buylaert | IR-RF dating of sandsized K-feldspar extracts: A test of accuracy[END_REF] showed age underestimation for older samples (>100 ka) and overestimation for younger samples (< 50 ka). They speculated whether the offset could be explained by signal instability (fading), bleachability and sensitivity change during measurement. They also showed the natural IR-RF signal from an infinitely old sample was only 84 % of the saturation, suggesting the signal might fade. However, the measurement setup by[START_REF] Buylaert | IR-RF dating of sandsized K-feldspar extracts: A test of accuracy[END_REF] did not match the suggestions byErfurt and Krbetschek (2003b), e.g., regarding the detection window, and should be read cautiously. Recently,[START_REF] Kumar | Sediment dating using Infrared Photoluminescence[END_REF] reinterpreted the findings by[START_REF] Buylaert | IR-RF dating of sandsized K-feldspar extracts: A test of accuracy[END_REF].

Figure

  Figure10 A B

  if polymineral fine grain (4-11 µm) or other grain size fractions untreated with HF are used. So far, only a single study exists determining the α-efficiency of Kfeldspar using IR-RF. Kreutzer et al. (2018b) used an α-flux calibrated 241 Am source. The central Preprint for QG revision 4 -Infrared Radiofluorescence (IR-RF) dating: a review Page 24 of 64

  Bleaching duration: All published protocols include an optical bleaching step to reset the natural IR-RF signal. The bleaching is either carried out by using an artificial light source or by natural sunlight. To mimic natural sunlight conditions,[START_REF] Frouin | The issue of laboratory bleaching in the infrared-radiofluorescence dating method[END_REF] proposed a bleaching spectrum consisting of six different wavelengths ranging from UV-A (365 nm) to NIR (850 nm), while[START_REF] Buylaert | IR-RF dating of sandsized K-feldspar extracts: A test of accuracy[END_REF] used only a single wavelength (UV-violet LED, 395 nm) to reset the IR-RF signal. The bleaching duration is sample dependent and linked to the technical specification of the equipment, the available wavelengths, and power. Using a similar measurement setup,[START_REF] Varma | Aspects of infrared radioluminescence dosimetry in K-feldspar[END_REF] and[START_REF] Buylaert | IR-RF dating of sandsized K-feldspar extracts: A test of accuracy[END_REF] found bleaching for 800 s and 1,500 s respectively, to be sufficient for most cases,[START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF] suggested solar simulator bleaching for at least 10,800 s.Kreutzer et al. (2018a) suggested a bleaching test using the internal solar simulator of their lexsyg system. The test applied consecutive bleaching steps of 1,000 s each. A stable signal plateau indicates sufficient bleaching. Generally, it appears that longer bleaching times should be preferred to ensure the resetting of the natural IR-RF signal.

  suggested enhancing the technique by combining vertical and horizontal sliding to account for an observed IR-RF light level change encountered for a particular technical setup, presented in[START_REF] Murari | Further investigations on IR-RF: Dose recovery and correction[END_REF]. The sliding method requires a long natural IR-RF measurement to match the regenerative IR-RF, e.g.,[START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF] (their supplement) recommended a minimum of 40 channels for robust De estimation for the horizontal sliding method. In the case of the vertical and horizontal sliding methods,Murari et al. (

  used IR-RF to date fluvial deposits collected from sediment-cores drilled into the northern Upper Rhine Graben (Germany). They deduced several fluvial aggradation periods and phases of increased tectonic subsidence between ~300 ka and ~650 ka based on these IR-RF ages. Li et al. (2017) compared the data reported by Lauer et al. (2011) with their chronology based on fading corrected pIRIR225 ages obtained for the core Heidelberg UniNord 1. Except for the lowermost sample (below the B/M boundary) both chronologies were broadly consistent. For the lowest sample, Li et al.

  [a] Exposure to ionizing radiation results in a constant flux of electrons from the valence band to the conduction band. These electrons may recombine radiatively [b], non-radiatively (not-shown for clarity), drop immediately back to the valence band (not-shown for clarity) or populate the IRSL trap [c]. Electrons that populate the IRSL trap pass through the excited state, resulting in infrared radiofluorescence (1.43 eV). Electrons within the IRSL trap are sensitive to infrared light and preferentially recombine with proximal holes. Additionally, the electrons may tunnel directly from the ground-state of the trap [d] (anomalous fading). Alternatively, Trautmann (2000) and Trautmann et al. (2000a) proposed hole production by allowing a direct transition of electrons into the valence band. This facilitates new possibilities for the recombination of electrons in the IRSL trap [e]. Note that each electron stimulated from the valence band will result in the production of a hole. However, these are not shown for clarity. If the electrons are stimulated with infrared light, they reach the excited state of the trap, from which they can migrate locally [f] before recombining. Higher temperature stimulations provide phononassistance (dashed black arrows), allowing post-IR IRSL signals to be measured from electrons that have diffused through the band-tail states to more distal holes [g], which are thermally and athermally more stable.

Figure 2

 2 Figure 2Schematic representation of self-made and commercially available measurement devices. A) The device used by Erfurt (redrawn afterErfurt et al., 2003). B) The device used by Schilles (redrawn after[START_REF] Schilles | Die Infrarot-Radiolumineszenz von Feldspäten und ihr Einsatz in der Lumineszenzdatierung[END_REF]. C) The device manufactured by Risø laboratories (redrawn after[START_REF] Lapp | New luminescence measurement facilities in retrospective dosimetry[END_REF]. D) The device manufactured by Freiberg Instruments (redrawn after[START_REF] Richter | lexsyg -a new system for luminescence research[END_REF]

Figure 10 IR-

 10 Figure 10IR-RF signal stability with respect to pulse annealing temperature. A) All natural IR-RF (RFnat) signals measured for a fixed short duration at different annealing temperatures. All samples show an increase in IR-RF up to 150 ˚C. For samples Gro8 and Es1 the signal decrease for temperatures > 250 ˚C, but remains stable for sample Ook1, a >1 Ma old sample (redrawn afterTrautmann et al., 1999a). B) The signal remains stable until ca 250 ˚C for RFnat and regenerated IR-RF (RFreg) for sample TH8 and changes its intensity for temperatures >250 °C (redrawn after[START_REF] Frouin | An improved radiofluorescence single-aliquot regenerative dose protocol for K-feldspars[END_REF].

Figure 11

 11 Figure 11Graphical representation of IR-RF data analysis techniques used to determine the De. A) The De is obtained by extrapolation using the fitted natural IR-RF signal. B) The natural IR-RF signal is

Frouin

  measurement before and after each IR-RF measurement; Repeat step #3 and #6 to monitor sensitivity changes 1

2

  The authors used their protocol for dose recovery tests only; distinct De determinations are not mentioned.

Table 2 (Irradiation units)

 2

  Nevertheless, beyond the research summarized above, further studies should be carried out to investigate the thermal and athermal stability in the context of IR-RF as a luminescence dating method. For IR-PL,[START_REF] Kumar | Sediment dating using Infrared Photoluminescence[END_REF] suggested tests on geological samples (~ Ma), i.e.Page 22 of 64 samples in apparent dose saturation, which might also provide a good test for the IR-RF signal stability in future studies.

They reported IR-PL age results in agreement with independent age control. These findings indicate that IR-PL does not suffer from athermal fading or signal instability. However, since

[START_REF] Kumar | Towards direct measurement of electrons in metastable states in K-feldspar: Do infrared-photoluminescence and radioluminescence probe the same trap?[END_REF]

hypothesised a similar trap for the IR-PL and the IR-RF, they concluded that IR-RF does not suffer from signal instability. Hence, without presenting new IR-RF data,

Kumar et al. (2021, p. 14

) concluded: "[…] that the under-estimation in IR-RF [meant are the results reported by

[START_REF] Buylaert | IR-RF dating of sandsized K-feldspar extracts: A test of accuracy[END_REF]

is likely because of sensitivity changes rather than signal stability."

  reported doses up to ca. 1,240 Gy, however, ages were reported to underestimate the independent age control above ca. 600-900 Gy (cf.Lieu et al., 2016; their Table2and Fig.3). For MET-pIRIR,[START_REF] Li | A single-aliquot luminescence dating procedure for K-feldspar based on the dose-dependent MET-pIRIR signal sensitivity[END_REF] reported potential natural dose measurements up to ca. 1,500 Gy, however, it remains unclear whether such values can be met regularly in routine dating studies (cf. Zhang and Li, 2020 for a discussion).

Table captions Table 1 :

 captions1 The main emission bands and possible defects observed in feldspar (copyright by Prasad 2017, permission granted by the author).

Table 2 :

 2 Irradiation source parameters for various devices used for IR-RF stimulation.

Table 3 :

 3 The relevant parameters for different spectrometer configurations.

Table 4 :

 4 Detection parameters for various devices used for IR-RF detection.

Table 5 :

 5 Bleaching source parameters for various devices used for IR-RF bleaching.

Table 6 :

 6 Overview of published IR-RF measurement protocols used for De determination.et al.,

	Preprint for QG revision 4 -Infrared Radiofluorescence (IR-RF) dating: a review

Table 1 :

 1 [START_REF] Finch | The causes and petrological significance of cathodoluminescence emissions from alkali feldspars[END_REF] reported the peak maximum at 430 nm related to Al 3+ -O 2-Al 3+ "Löwenstein" bridges.

	Emission band	Excitation	Possible origin	Reference
		TL	Strain and/or ionic diffusion	Garcia-Guinea et al. (1999)
	~3.8-4.4 eV	PL	Tl +	Gorobets et al. (1995)
	(280-320 nm)	IRSL		Baril and Huntley (2003a)
		TR-OSL		Clark and Bailiff (1998)
		CL	Paramagnetic defect	*Finch and Klein (1999)
	~3.1 eV (400 nm)	IRSL	?	Rieser et al. (1999)
		IRSL	?	Baril and Huntley (2003a)
		IRSL	Mn 2+	Rieser et al. (1997)
	~2.2 eV (560 nm)	IRSL CL		Baril and Huntley (2003a) Geake et al. (1977)
		TR-OSL		Clark and Bailiff (1998)
		Absorption	Fe 3+	White et al. (1986)
	~1.7 eV (730 nm)	PL IRSL		Telfer and Walker (1975) Krbetschek et al. (1997)
		PL		Poolton et al. (1996, 2006)
	~1.45 eV (855 nm)	RL or RF	IRSL dating trap	Trautmann et al. (1998)
	~1.41-1.3 eV (900 nm)	CL (at 7 K)	IRCL trap with two sites and Fe 4+	Kumar et al. (2020)
	(~880 nm and ~955 nm)		as a competitor
		RL or RF	Pb +	Erfurt (2003b)
	~1.3-1.36 eV (910 nm)	Post IR phosphorescence	IRSL dating trap	Baril and Huntley (2003a)
		TL	?	Krbetschek and Rieser (1995)

TL: Thermoluminescence, IRSL: Infrared stimulated luminescence, CL: Cathodoluminescence, RF: Radiofluorescence, RL: Radioluminescence, PL: Photoluminescence TR-OSL: Time-resolved optically stimulated luminescence, IRCL: Infrared Cathodoluminescence *

Table 2 :

 2

	Laboratory / Manufacturer	Radiation source	Activity	Radiation Type	Source type	Dose rate	Active area	Reference
			[GBq]			[Gy min -1 ]	[mm 2 ]
	Freiberg	137 Cs/ 137 Ba	0.0037	β and γ	Planar	0.050	19.6	Trautmann (1999)
	Freiberg	137 Cs/ 137 Ba	0.0050	β and γ	Planar	0.080	50.3	Erfurt (2003b)
	Heidelberg	137 Cs/ 137 Ba	0.0037	β and γ	Planar	0.034	28.3	Schilles (2002)
	Risø	90 Sr/ 90 Y	1.48	β	Planar	2.640	50.3	Buylaert et al. (2012)
	Freiberg Instruments	90 Sr/ 90 Y	1.6-2	β	Ring	2.250	n.a.	Richter et al. (2012)

# Erfurt calibrated the radiation source with Al2O3:C while the other readers were calibrated with natural (calibration) quartz.

Table 3 :

 3

	Laboratory / Manufacturer	Spectrograph	Spectrograph/Grating Grating Blazed	Dispersion [nm] Company	CCD Camera Camera type Active Pixels	Cooling Type	Reference
	Freiberg	Jobin Yvon CP200	Holographic	Not applicable	300-1000	Marconi	NA	1152x298	-100 ℃ (Liquid nitrogen)	Rieser et al. (1994)
	Freiberg	Jobin-Yvon CP200	Holographic	Not applicable	250-1152	Marconi	Front-illuminated	1152x352	-100 ℃ (Liquid nitrogen)	Erfurt (2003b), Rieser et al. (1994)
	Heidelberg	Acton SP150	150 lines/mm	300 nm	200-1100	Princeton Instruments	Back-illuminated	1100x330	-100 ℃ (Liquid nitrogen)	Rieser et al. (1999)
	Freiberg Instruments	Andor Shamrock 163	300 lines/mm	500 nm	200-1050	Andor Newton 920-BU/iDus 420 OE	Back-illuminated / Open Electrode	1024x255	-80 ℃ (TE Cooled)	Richter et al. (2013)
	TE Cooled: Thermoelectric cooling

Table 5 :

 5 density of the bleaching units refers to approximate power at the sample position. It can vary from device to device.

	Laboratory/	Bleaching source	Spectrum	Max Power *	Connection	Reference
	Manufacturer			[mW cm -2 ]
	Freiberg	Hg-Lamp	UV-VIS	--	Optical Guide	# Trautmann (1999)
	Freiberg	250W OSRAM LAMP	UV-VIS	100	Optical Guide	+ Erfurt (2003b)
	Heidelberg	150W QTH	UV-VIS	80	Optical Guide	+ Schilles (2002)
	Risø	UV LED	UV	700	Direct	Buylaert et al. (2012)
	Freiberg Instruments	6 LED solar simulator	UV-IR	700	Direct	Richter et al. (2013)

*

Maximum power #

[START_REF] Trautmann | Radiolumineszenzuntersuchungen an Feldspat[END_REF]

used an interference filter in front of the solar lamp for monochromatic bleaching.

+ Schilles (2002)

and

[START_REF] Erfurt | Radiolumineszenzspektroskopie und -dosimetrie an Feldspäten und synthetischen Luminophoren für die geochronometrische Anwendung[END_REF]

both used an IR cut-off filter.

Table 6 :

 6

	Reference	Protocol Abbr.	#1	#2	Treatments and observations 1 #3 #4	#5	#6	Data analysis	Comments
	Buylaert et al. (2012)	NA (based on IRSAR)	-	IR-RF [RFnat]	Bleaching (≥ 1,800 s) (ca. 395 nm)	Pause (≥ 3,600 s)	-	IR-RF [RFreg]	Sliding	-
	Erfurt and Krbetschek (2003b)	IRSAR	-	IR-RF [RFnat]	Bleaching (≥ 1,800 s) (artificial solar spectrum)	Pause (≥ 3,600 s)	-	IR-RF [RFreg]	Fitting (interp.)	RFnat is represented by only a few channels

920 nm inErfurt and Krbetschek (2003b), however, henceforth termed '910 nm' emission.

InFig. 22.3 (Wünnemann et al., 2007) the IR-RF results were erroneously presented as OSL dates.

Acknowledgements

We are grateful to Sébastien Huot, Frank Preusser and two anonymous reviewers for their patience, constructive comments, and strong support for this manuscript. M.K. Murari and M. Fuchs were supported by the German Research Foundation (DFG FU417/19-1). S. Kreutzer and N. Mercier received financial support by the LaScArBx. LaScArBx is a research programme supported by the ANR (ANR-10-LABX-52). The contribution of S. Kreutzer in 2020 received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 844457 (CREDit). M. Frouin was supported by the John Fell Fund (161/067 and 171/006) University of Oxford. N. Klasen received funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) -Project number

Page 46 of 64 Trautmann's research was based on spectrometer measurements using a 200-800 nm detection range. Later, the spectrometer was modified for detecting 300-1,000 nm. The integrated counts of IR-RF peak were used to estimate the De.

Laboratory/ Manufacturer