On the viability of detrital biotite Rb–Sr geochronology

. Re-examination of International Ocean Discovery Program (IODP) sediment samples collected from the Bay of Bengal via laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) Rb–Sr geochronology demonstrates the viability of the biotite Rb–Sr system for use as a detrital chronometer. The age population deﬁned by the Rb–Sr dates essentially reproduces that previously published for detrital 40 Ar / 39 Ar dates. The effect of unknown/assumed initial 87 Sr / 86 Sr on the calculated population can be ameliorated by ﬁltering for higher 87 Rb / 86 Sr ratios. Such ﬁltering, however, could introduce bias toward more radiogenic populations, especially in younger material that has not had time to accumulate radiogenic product (e.g. limiting the effect of initial 87 Sr / 86 Sr to ∼ < 5 % requires ﬁltering of 87 Rb / 86 Sr > 500 at 250 Ma and 87 Rb / 86 Sr > 50 at 2500 Ma). Finally, Ti-in-biotite temperatures calculated based on element concentration data collected during LA-ICP-MS overlap with those calculated for the same material based


Introduction
Detrital geochronology is a commonly used approach to assess a wide variety of geological questions.For example, detrital zircon can provide information about the maximum depositional age for a sedimentary unit, likely sediment sources, and timescales of exhumation and sediment transport (e.g.Gehrels, 2014;Thomas, 2011;Malusà and Fitzgerald, 2020).Moreover, detrital zircon chemistry can provide additional insight into the nature of the source rocks, such as crystallization depth and degree of fractional crystallization (e.g.Stevenson and Patchett, 1990;Iizuka et al., 2010;Howard et al., 2009;Mueller et al., 2008).Detrital geochronology (or thermochronology) of mineral phases dated via radio decay systems that may record cooling rather than crystallization, such as 40 Ar/ 39 Ar on mica or fission track and U-Th-He dating of U-bearing minerals, can be used to quantify rates of exhumation and/or burial in active orogenic systems (e.g.Ruiz et al., 2004;Najman et al., 1997Najman et al., , 2001;;Reiners et al., 2005).
Critical to detrital geochronology, in all forms, is analyzing sufficient material to characterize the statistical variation in the age data.Prior to the development of spot geochronology analytical techniques, analyzing enough material (e.g.Vermeesch, 2004) to characterize a specimen was timeconsuming and expensive.The proliferation of geochronology based on laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) has enabled the rapid acquisition of large datasets.While this is especially true for detrital U-Pb zircon geochronology, limitations still exist for other methods.For example, 40 Ar/ 39 Ar LA-ICP-MS geochronology still requires irradiation of samples prior to analysis, which increases the expense and time it takes to generate data.
The development of in situ beta decay geochronology techniques (e.g.Zack and Hogmalm, 2016;Simpson et al., 2021) now allows additional detrital geochronometer options, with the critical caveat that these are typically isochron-based methods.As such, quantifying an initial isotope composition can be an integral part of calculating a date.In the absence of a measured cogenetic non-radiogenic phase to constrain that intercept, multiple radiogenic data points, which typically have varying initial isotopic reservoirs, can be regressed to define a date.Such isochrons (regressions) rely on all analyses comprising a single closed isotopic system, which is incompatible with detrital geochronology.It is possible, however, to assume an initial intercept for isochronbased data and calculate two-point regressions through that intercept and each data point to calculate a spot date.For both Rb-Sr and Lu-Hf, the possible/expected terrestrial initial ratios typically span a rather narrow range of values (e.g.0.699-0.780and 0.281-0.283;Rösel and Zack, 2022;Fisher and Vervoort, 2018).Moreover, the more radiogenic the spot analyses are, the less control the initial ratio exerts on the final two-point isochron date.This dependence is demonstrated in Larson et al. (2023a), who show that correcting Rb-Sr data for common 87 Sr based on the current 87 Sr/ 88 Sr, which effectively mimics the result of a two-point isochron through 0.71, effectively reproduces the isochron regression dates for samples with high Rb/Sr.The coincidence of the isochron and spot dates derived independently of the measured initial 87 Sr/ 86 Sr indicates that detrital Rb-Sr geochronology may be a viable alternative or addition to detrital 40 Ar/ 39 Ar geochronology (e.g.Crossingham et al., 2024), eliminating the potentially time-consuming step of irradiation and facilitating increased numbers of analyses.
This study presents the results of in situ Rb-Sr analysis of biotite mica grains picked from sand samples collected from the Bay of Bengal that have either previously been dated via 40 Ar/ 39 Ar detrital geochronology or are directly adjacent to dated samples (see Najman et al., 2019).The potential viability of Rb-Sr as a detrital chronometer is compared against the published 40 Ar/ 39 Ar data.Moreover, the derivation of additional information (i.e.Ti-in-biotite temperature) from the mica grain via LA-ICP-MS is also investigated to determine if it can be used to help further quantify source characteristics.

Methods
To test the viability of detrital biotite Rb-Sr geochronology, four samples (1450-24-25F, 1450-100-104-108F, 1451-47-49F, and 1451-86F), collected from Late Miocene to Middle or Late Pleistocene sediments during the Bengal Fan International Ocean Discovery Program (IODP) Expedition 354, were examined.For simplicity, the sample names have been shortened here to 25F, 108F, 49F, and 86F, respectively.These same samples, or closely adjacent ones, have been previously investigated for detrital white mica 40 Ar/ 39 Ar, zircon fission track, apatite U-Pb, and/or rutile U-Pb geochronology (Najman et al., 2019).Given the propensity for biotite (sensu lato) to be more radiogenic than white mica (e.g.Fournier et al., 2016) and the sensitivity of low radiogenic material to the initial value of an isochron, only biotite was targeted in this study.The biotite grains were either manually picked from sediment separates (see Najman et al., 2019) and mounted in epoxy, or the sediments were poured directly into an epoxy mount.Grains were not mounted with a preferred orientation, resulting in a semi-random c-axis orientation (the natural shape of a mica lath favours a c axis normal to the mounting surface).Mixed c-axis orientations may help avoid less optimal signal stability ablating parallel to the mica c axis (Rösel and Zack, 2022), which may affect the final Rb-Sr date calculated (Lloyd et al., 2023).After polishing, targets were verified (i.e. the presence of K and Fe and the lack of visible inclusions) via micro-XRF elemental mapping of each mount prior to analysis.

Ti-in-biotite thermometry
In addition to Rb-Sr isotopes, Ti, Mg, and Fe concentrations were measured for each analytical spot via LA-ICP-MS with dwell times of 1, 0.5, and 1 ms, respectively.Concentrations were normalized to repeated measurements of the NIST SRM 610 glass reference material (Jochum et al., 2011) assuming stoichiometric Si (16.36 weight (wt.) % Si or 35 wt % SiO 2 ), typical of metamorphic biotite from greenschist through granulite facies (e.g.Dyck et al., 2021).Titanium concentrations (ppm) were converted to molar-weightper-oxide TiO 2 equivalents and then normalized to calculated Si content based on an assumed 5.4 atoms per formula unit (a.p.f.u.) Si per 22 O as detailed in Eq. ( 1): Ti a.p.f.u.= ( C Ti/ WT TiO 2 /10 000/ M TiO 2 ) × (5.4/A Si), ( 1) where C Ti is the concentration of Ti in ppm, WT TiO 2 is the weight proportion of Ti in TiO 2 , M TiO 2 is the molar weight per oxide, and A Si is the molar weight per cation Si assuming 35 wt % SiO 2 .Ti-in-biotite temperatures were calculated using the equation of Henry et al. (2005), which requires Ti a.p.f.u and Mg# (Mg/(Mg + Fe)) for each analysis.The values for Mg# were calculated using parts-per-million (ppm) concentrations of Fe and Mg.The 1σ uncertainty of the Tiin-biotite temperatures is <24 °C at 480 °C decreasing to 12 °C at 800 °C (Henry et al., 2005).
To verify the LA-ICP-MS-derived Ti-in-biotite temperatures, the chemistries of the same mica grains were analyzed using the CAMECA SXFiveFE electron probe microanalyzer (EPMA), also housed in the FiLTER facility.Quantitative spot analyses were carried out with an acceleration voltage of 15 kV, a regulated beam current of 20 nA, and a spot size of 5 µm.Elemental x-ray data were collected using a dwell time of 30 s on peak and 15 s on background and were calibrated to the known composition of synthetic and natural mineral reference standards from Micro-Analysis Consultants Ltd.The standards used for calibration were spessartine for Si and Mn, titanite for Ti, almandine for Al and Fe, wollastonite for Ca, albite for Na, diopside for Mg, orthoclase for K, and apatite for P. The crystals used were LTAP for Si and Al; LPET for Ti, Ca, K, and P; LLIF for Fe and Mn; and TAP for Na, Mg.The EPMA data were converted to atomsper-formula-unit biotite on the basis of 22 oxygen whereby cation (a.p.f.u.) = cation proportion × no.oxygen (a.p.f.u.) / sum of oxygen proportions, (2) oxygen proportion = cation proportion × (1/2) cation charge, (3) cation proportion = oxide wt %/oxide molecular wt. (4) Given that the biotite analyzed was collected as detritus from the Bengal Fan and given the tendency of biotite to weather (e.g.Wilson, 2004), alteration was expected.To avoid the most altered material, EPMA data were filtered for totals >88 wt % and K concentrations >1.1 a.p.f.u.Plotting K a.p.f.u against Mg# or calculated temperature shows that analyses with K a.p.f.u.>1.1 rarely form outliers (Fig. 3).While it is recognized that an a.p.f.u of 1.1 K is significantly lower than that expected of unaltered biotite, K is expected to leave the mineral via hydrated cation exchange as part of the initial weathering stage/vermiculitization (Price and Velbel, 2014;Gilkes and Suddhiprakarn, 1979).In contrast, Fe, Mg, and Ti are relatively immobile until more advanced alteration of biotite to goethite or kaolinite (Gilkes and Suddhiprakarn, 1979).Exchange of hydrated cations with interlayer K will result in lower-oxide EPMA wt % totals, which, upon normalization (for a biotite with an XMg of 0.44), increases the temperature calculated using the Ti-in-biotite thermometer by ∼ 2.2 °C per 1 wt % oxide deficit.The sensitivity of Tiin-biotite temperatures to EPMA oxide wt % totals, using the Henry et al. (2005) calibration, is shown in Fig. S1.To illustrate the effect of weathering on our data we plot all analyses, coloured by oxide wt % totals, in Fig. 3a and b.In general, filtering analyses with K concentrations >1.1 a.p.f.u rather than filtering solely on oxide wt % totals is the more robust approach to removing outliers with anomalously low Mg# (e.g.<0.15) and Ti-in-biotite temperatures (e.g.<400 °C).
Full EPMA data are provided in Table S3.
For each specimen, spot dates were calculated as twopoint dates based on a regression between each analysis and a specified initial 87 Sr/ 86 Sr value (see Tables S4-S7).The initial 87 Sr/ 86 Sr values used (0.71, 0.72, 0.73, 0.74, 0.75, and 0.76) cover the range of expected values for most plutonic and metamorphic sources (Rösel and Zack, 2022).The dates calculated for each specimen are depicted in Fig. 2 as kernel density estimations (KDEs; bandwidth = 3).In general, the KDEs have a single peak for >0 Ma dates (if a spot analysis has an 87 Sr/ 86 Sr < the initial 87 Sr/ 86 Sr, a negative date will be calculated, a situation exacerbated in young material that has not had time to accumulate radiogenic 87 Sr; see Tahttps://doi.org/10.5194/gchron-6-303-2024 Geochronology, 6, 303-312, 2024 bles S4-S7).The KDE peaks for each specimen generally increase in width, decrease in height, and move to slightly younger positions with two-point dates calculated with progressively higher initial 87 Sr/ 86 Sr (Fig. 2).

Ti-in-biotite thermometry
Ti-in-biotite temperatures calculated via LA-ICP-MS data generally range between ∼ 650 and 725 °C for most samples (Fig. 3b, c).The SiO 2 content used in the calculations has little effect on temperature.Increasing the SiO 2 from 35 wt % to 40 wt % results in only an ∼ 5 °C temperature change (Fig. S2), well within the expected uncertainty of the method (Henry et al., 2005).While the precision of Ti data generated by LA-ICP-MS is lower than EPMA data, the second-and third-quartile temperatures overlap (within un-certainty) with those calculated using EPMA data for each specimen (Fig. 3c).

Effect of initial 87 Sr/ 86 Sr
As with any isochron method, the value of the intercept can have a significant impact on the results when calculating two-point isochron Rb-Sr dates.That effect, however, is less significant with older material (higher radiogenic Sr) and more radiogenic analyses.As shown in Fig. 4, the effect of initial intercept selection can be demonstrated by generating three artificial datasets with one analysis every 500 87 Rb/ 86 Sr increments between 10 and 4510.One dataset defines a 25 Ma isochron, one defines a 250 Ma isochron, and one defines a 2500 Ma isochron, each with an initial  (Vermeesch, 2018).The data plotted below the median line represent the results of applying different 87 Rb/ 86 Sr filters, as noted.
The effect of initial 87 Sr/ 86 Sr relative to 87 Rb/ 86 Sr can be further investigated using the real-world data presented herein.Filtering the two-point isochron dates calculated based on 87 Rb/ 86 Sr demonstrates that the position of the main population of the data remains relatively invariant for different 87 Rb/ 86 Sr but that the half-width decreases and the density of the main population increases with higher 87 Rb/ 86 Sr cut-offs (bottom curves Fig. 2).These results indicate that filtering detrital data by 87 Rb/ 86 Sr may help ameliorate the complication of unknown initial 87 Sr/ 86 Sr values, though it should be noted that doing so would introduce bias https://doi.org/10.5194/gchron-6-303-2024 Geochronology, 6, 303-312, 2024 toward more radiogenic populations and, as such, should not be done in isolation.ner et al., 2017;Larson et al., 2023a) in the Himalayan system from which these samples were collected (i.e.Himalayan detritus shed into the Bay of Bengal) and because of the resilience of white mica, relative to biotite, to weathering (Wilson, 2004).Given the differences in child product retention between white mica 40 Ar/ 39 Ar geochronology and biotite Rb-Sr geochronology, it may not be expected that the data from the two systems would overlap.White mica has an estimated nominal closure temperature of ∼ 425-400 °C for Ar diffusion (100 µm radius grain, 10°C Ma −1 cooling rate, 5-10 kbar; Harrison et al., 2009), whereas closure to diffusion of Sr out of biotite is more varied, with estimates ranging from ∼ 300 °C (Jager et al., 1967;Armstrong et al., 1966) to ∼ 400 °C (Verschure et al., 1980;Del Moro et al., 1982)  or even in excess of 400 °C depending on the specifics of the mineralogy and chemistries of the samples (Jenkin et al., 1995(Jenkin et al., , 2001)).This variability in chronometer "closure temperatures" (e.g.Dodson, 1973) may be reflected in variable offsets between the Rb-Sr and 40 Ar/ 39 Ar dates (Fig. 2).

Comparison with detrital
The various two-point isochron Rb-Sr dates calculated for 108F and 86F define density peaks with a slightly younger (∼ 1 Ma) offset than the 40 Ar/ 39 Ar dates (initial 87 Sr/ 86 Sr = 0.71), whereas for 49F and 25F two-point isochron dates essentially reproduce the density peak of the 40 Ar/ 39 Ar dates (Fig. 2).Overall, the total Rb-Sr dataset, regardless of initial 87 Sr/ 86 Sr used, defines a similar dominant population of Early to Middle Miocene age (Fig. 5) to that noted by Najman et al. (2019).That peak was interpreted to demonstrate rapid exhumation of the eastern and central Himalaya with an ∼ <4 Myr lag time between exhumation through mica closure to child product diffusion and sedimentation (Najman et al., 2019).Given the similarities between the datasets, the detrital Rb-Sr geochronology would have led to the same conclusions as the 40 Ar/ 39 Ar data generated by Najman et al. (2019).

Ti-in-biotite thermometry
Comparison of EPMA and LA-ICP-MS thermometry results demonstrates that LA-ICP-MS data can yield results comparable with traditional methods (Fig. 3).The temperatures calculated for the spot data are consistent with derivation from amphibolite facies metamorphic rocks or from associated leucogranites (e.g.Waters, 2019), which dominate the inferred exhuming Himalayan midcrustal source (Najman et al., 2019).The temperatures also broadly overlap with Zr-inrutile temperature derived from detrital rutile from the same samples (∼ 650-780 °C; Najman et al., 2019).Direct comparison of LA-ICP-MS-and EPMA-derived temperatures for the same grains from 25F and 86F defines mean Euclidean distances of 13.6 and 15.9 °C, respectively (Fig. 3d).Because this approximately 15 °C uncertainty likely reflects the analytical precision of LA-ICP-MS rather than being solely due to the uncertainties stemming from natural variations in biotite chemistry or the thermometer calibration, it should be regarded as additive to the ±12-24 °C 1σ uncertainty of Henry et al. (2005).The precision on the Ti-in-biotite temperature estimates, whether EPMA-or LA-ICP-MS-derived, does not facilitate quantifying a change across the sampled strata, as data from all samples overlap (Fig. 3c).
The viability of quantifying Ti-in-biotite temperatures via LA-ICP-MS allows each Rb-Sr spot analyzed to be associated with a unique temperature.This kind of petrochronologic association opens the possibility of many different types of studies, not unlike the linking of chemistry to spot dates did for U(-Th)-Pb geochronology in the early 2000s (e.g.Foster et al., 2004;Gibson et al., 2004;Rubatto, 2002).

Conclusions
LA-ICP-MS Rb-Sr geochronology appears to be a viable method to efficiently generate detrital biotite geochronological datasets.The effect of unknown initial 87 Sr/ 86 Sr values can be mitigated for young (Cenozoic) material by filterhttps://doi.org/10.5194/gchron-6-303-2024 Geochronology, 6, 303-312, 2024 ing for significantly radiogenic analyses ( 87 Rb/ 86 Sr >2500), though such filtering may introduce bias.Filtering can be less aggressive for older material (i.e.>500 at 250 Ma) in which significant radiogenic child product has accumulated.Finally, the benefits of biotite Rb-Sr geochronology can be further extended by calculating a Ti-in-biotite temperature for each spot.Such information may allow the identification of multiple sources in detrital samples with complex provenance.
Data availability.All data related to this study are available on the Open Science Framework website: https://osf.io/vgjh6/?view_ only=52b27e0d000c4f2ea6b9ab665744e43c (OSF, 2024).
Author contributions.KPL: conceptualization, funding acquisition, methodology, investigation, visualization, and writing (original draft preparation).BD: methodology, investigation, and writing (review and editing).SS: investigation and writing (review and editing).MB: investigation and writing (review and editing).YN: resources and writing (review and editing).
Competing interests.The contact author has declared that none of the authors has any competing interests.
Disclaimer.Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper.While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

Figure 2 .
Figure 2. Kernel density estimation (KDE) plots of Rb-Sr data from samples analyzed and 40 Ar/ 39 Ar of the same or spatially adjacent samples.The kernel bandwidth was 3 Ma for all plots.Each diagram shows two different datasets.The data plotted above the median line include40 Ar/ 39 Ar white mica dates and unfiltered Rb-Sr two-point isochron dates based on initial 87 Sr/ 86 Sr as marked.Dates were calculated using IsoplotR(Vermeesch, 2018).The data plotted below the median line represent the results of applying different 87 Rb/ 86 Sr filters, as noted.

Figure 3 .
Figure 3. (a) Plot of K atoms per formula unit (a.p.f.u; based on 22O) as calculated from electron probe microanalyzer (EPMA) data versus Mg# (,Mg/(Fe + Mg)).A horizontal line is drawn at K a.p.f.u = 1.1.(b) Plot of K a.p.f.u.versus derived Ti-in-biotite temperature.A horizontal line is drawn at K a.p.f.u = 1.1.(c) Box-and-whisker plots of calculated Ti-in-biotite temperatures calculated for each sample via EPMA data (grey fill) and laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) data (blue fill).(d) Plot of EPMA versus LA-ICP-MS temperatures for adjacent spot analyses on the same grains in samples 25F and 86F.Calculated mean Euclidean distances between the EPMA versus LA-ICP-MS data points for each sample are shown.

Figure 4 .
Figure 4. Plot of modelled data demonstrating the related effects of initial 87 Sr/ 86 Sr on calculated two-point isochron dates as a function of 87 Rb/ 86 Sr. See text for discussion.

Figure 5 .
Figure 5. Kernel density estimations (bandwidth = 2) of all 40 Ar/ 39 Ar data reported by Najman et al. (2019) and Rb-Sr spot dates calculated in the present study assuming various initial 87 Sr/ 86 Sr (as denoted).The date (Ma) corresponding to each KDE peak is shown.
Najman et al. (2019)ologyNajman et al. (2019)presented the results of various detrital geochronology methods employed on the samples examined in the current study and/or other proximal samples. Thesemethods include 40 Ar/ 39 Ar geochronology on white mica.White mica was targeted in that study both because of the common problem of excess Ar associated with biotite (Stüb-