the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
A simplified isotope dilution approach for the U–Pb dating of speleogenic and other low^{232}Th carbonates by multicollector ICPMS
Andrew J. Mason
Anton Vaks
Sebastian F. M. Breitenbach
John N. Hooker
Gideon M. Henderson
We describe a new method for the measurement of $\mathrm{U}/\mathrm{Pb}$ ratios by isotope dilution multicollector inductively coupled plasma mass spectrometry (MCICPMS) for the dating of geologically young clean carbonates, particularly speleothems. The method is intended for materials containing little or no initial ^{232}Th. We illustrate and validate the method with four examples ranging from 0.57 to 20 Ma. The new method is capable of applying the ^{235}U–^{207}Pb and ^{238}U–^{234}U–^{206}Pb chronometers, common Pb and quantifiable residual ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ disequilibrium permitting. These provide an alternative to the more widely used ^{238}U–^{206}Pb chronometer, which can be highly inaccurate for samples that are < ca. 20 million years old, owing to uncertainties in the excess initial ^{234}U (hence, excess radiogenic ^{206}Pb) commonly observed in speleothems.
Carbonates such as calcite and aragonite exist widely within the geological record, occurring as skeletal components of fossils such as corals, primary sedimentary deposits, secondary deposits such as speleothems, and veins and fracture fillings. Such carbonates have the capacity to capture a range of information about past sea level and climate, regional tectonics (and so on) and are of particular significance because they are often amenable to direct radiometric dating based on the decay of U (Cheng et al., 1998; Edwards et al., 2003; Nuriel et al., 2012; Rasbury and Cole, 2009). Historically, this has been achieved mainly using ^{238}U–^{234}U–^{230}Th disequilibrium dating (e.g. Scholz and Hoffmann, 2008, and references therein) or less commonly ^{235}U–^{231}Pa disequilibrium dating (Cheng et al., 1998). These radiometric clocks are inherently limited to samples younger than the timescale over which the intermediate daughter used effectively returns to secular equilibrium, i.e. roughly 600 000 years for the ^{238}U–^{234}U–^{230}Th chronometer (Scholz and Hoffmann, 2008). Uranium–lead dating, being based on the accumulation of stable radiogenic Pb, does not have this limitation, and has been applied for many decades to the dating of igneous and metamorphic accessory minerals (e.g. Heaman and Parrish, 1991). U–Pb dating has also been utilised in a more restricted way to date Mesozoic and older sedimentary carbonates (e.g. Moorbath et al., 1987; Rasbury et al., 1997; Wang et al., 1998). More recently, U–Pb dating has been adapted and applied to geologically young carbonates as a means of circumventing the ca. 600 ka limit of the ^{238}U–^{234}U–^{230}Th chronometer, opening up far more of the geological record (Bajo et al., 2012; Cliff et al., 2010; Getty et al., 2001; Li et al., 2014; Pickering et al., 2010; Richards et al., 1998; Roberts et al., 2017; Vaks et al., 2020; Woodhead et al., 2006; Woodhead and Pickering, 2012). However, the U–Pb system remains underutilised in this regard, and given the variety of sample material available and differences in laboratory setups, it is unlikely that any implementation of the U–Pb system will be universally applicable. To this end, we document in detail a novel protocol for the U–Pb dating of carbonates by isotope dilution multicollector inductively coupled plasma mass spectrometry (MCICPMS) recently used in a study of Siberian permafrost dynamics (Vaks et al., 2020).
The U–Th–Pb system is based on the twin decay chains of ^{238}U to ^{206}Pb and ^{235}U to ^{207}Pb, plus the decay chain of ^{232}Th to ^{208}Pb, together with nonradiogenic ^{204}Pb. The ^{232}Th decay chain is not of direct relevance here as we are only considering systems that have sufficiently low ^{232}Th that ^{208}Pb can also be treated as nonradiogenic; for our purposes, we consider ^{232}Th as negligible where ${}^{\mathrm{232}}\mathrm{Th}{/}^{\mathrm{238}}\mathrm{U}$ < 0.002 (Sect. 3.5). Owing to the insolubility of Th in many aqueous systems, many carbonates approximate a ^{232}Thfree system (e.g. Thomas et al., 2012; Vaks et al., 2013b).
Most previous U–Pb work on carbonates has focused on the ^{238}U–^{206}Pb system taking either a traditional solutionbased isotope dilution approach where the samples are spiked with an isotopic tracer, dissolved, and then the U and Pb purified for analysis on a multicollector MS or have utilised in situ laser ablation analysis (e.g. Getty et al., 2001; Pickering et al., 2010; Roberts et al., 2017; Woodhead et al., 2006). The former approach was initially used in our case (Mason et al., 2013) as it offers better precision, e.g. < 0.1 % uncertainty versus ca. 0.6 % or more by laser ablation on the ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratio and < 1 % by isotope dilution versus 5 %–10 % by laser ablation on the ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}\mathrm{Pb}$ ratio, as well as the ability to date younger material with lower U and Pb concentrations (Cheng et al., 2013; Lin et al., 2017; Roberts et al., 2017; Spooner et al., 2016; Woodhead et al., 2006; Woodhead and Petrus, 2019). However, because relatively large samples (> 100 mg) were required, miniaturisation of the columns to help control blanks was not an option, making the anion exchange chromatography both time consuming and challenging. Although reasonable Pb blanks (4 pg total Pb for a 2 mL resin bed) were attainable, this required secondary distillation of reagents, for example, and in some instances inconsistent purity of different anion exchange resin batches resulted in much higher Pb blanks (> 40 pg). Moreover, to avoid wasting effort and reagents on processing nonradiogenic material, separate reconnaissance analysis would be required to first identify datable material, adding to the overall time needed to obtain an age. Having a simplified procedure that simultaneously maintained acceptable precision, sidestepped the Pb blank associated with anion exchange chromatography and minimised the time penalty for processing nonradiogenic material to the point that separate reconnaissance U–Pb analyses were unnecessary, were significant motivations for developing a new method.
A caveat in U–Pb dating is that calculated U–Pb ages can strongly depend on the assumptions made regarding the initial state of the decay chains, especially initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$, ${}^{\mathrm{230}}\mathrm{Th}{/}^{\mathrm{238}}\mathrm{U}$ and ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{235}}\mathrm{U}$ ratios (Ludwig, 1977). For carbonates precipitated from fresh or sea waters, initial ^{230}Th and ^{231}Pa are likely to have been near absent owing to their insolubility in aqueous systems (Cheng et al., 1998; Edwards et al., 2003) and thus in practice do not present a major source of age uncertainty. However, initial ^{234}U can be strongly enriched with initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratios as high as 7 to 12 times equilibrium known to occur (Kronfeld et al., 1994; Plagnes et al., 2002; Vaks et al., 2013b). If unaccounted for, the initial ^{234}U excess could lead to ^{238}U–^{206}Pb age inaccuracies of upwards of 2 Myr. For samples where the initial ^{234}U disequilibrium has not yet completely decayed (typically < 2 Ma), the initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratio can be calculated from the measured ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratio as part of the age calculation (here termed the ^{238}U–^{234}U–^{206}Pb chronometer), avoiding such inaccuracies. However, for older material, the initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratio must be assumed in the age calculation (here termed the ^{238}U–^{206}Pb chronometer), potentially leading to significant inaccuracies in assessed ages. Where ages extend beyond the limit of the ^{238}U–^{234}U–^{206}Pb method, particularly where there is evidence for large variability in initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratios, the ^{235}U–^{207}Pb chronometer could prove a powerful alternative dating tool. Such a situation was found in speleothems from Siberian caves (Vaks et al., 2020), which provided an additional motivation for developing the dating approach presented here. We pursue a solutionbased method over laser ablation in order to obtain precise ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ measurements to most effectively utilise the ^{238}U–^{234}U–^{206}Pb chronometer and because it represents a better prospect for detecting the tiny quantities of radiogenic ^{207}Pb necessary to apply the ^{235}U–^{207}Pb chronometer to samples that are a few million years old.
A second caveat in U–Pb dating is that carbonates often contain an appreciable amount of initial (common) Pb that must be accounted for, usually requiring some form of isochron technique, though the choice of isochron used varies widely (e.g. Mason et al., 2013; Pickering et al., 2010; Woodhead et al., 2006). One approach (e.g. Roberts et al., 2017) is to use the intersection of an isochron in ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}\mathrm{Pb}$ – ${}^{\mathrm{207}}\mathrm{Pb}{/}^{\mathrm{206}}\mathrm{Pb}$ (Tera–Wasserburg) space (or ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}\mathrm{Pb}$ – ${}^{\mathrm{207}}\mathrm{Pb}{/}^{\mathrm{206}}\mathrm{Pb}$ – ^{204}Pb^{206}Pb “total” Pb space, Ludwig, 1998) with concordia to determine the ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}\mathrm{Pb}$_{rad} ratio (^{20x}Pb_{rad}= radiogenic ^{20x}Pb) and, by extension, the age. However, this approach precludes an independent assessment of the ${}^{\mathrm{235}}\mathrm{U}{/}^{\mathrm{207}}\mathrm{Pb}$_{rad} ratio, inhibiting the use of the ^{235}U–^{207}Pb chronometer. This strategy is further complicated by the calculation of concordia itself being sensitive to initial disequilibrium in the ^{238}U and ^{235}U decay chains. Alternatively, separate 2D isochrons based on nonradiogenic ^{204}Pb (e.g. Rasbury and Cole, 2009) can be used to independently correct common ^{206}Pb and common ^{207}Pb, permitting the usage of both the ^{238}U–^{206}Pb and ^{235}U–^{207}Pb systems. Nevertheless, using ^{204}Pb has the practical drawbacks of it being a lowabundance isotope and having an isobaric interference on ICP systems from instrumental Hg. However, in samples with negligible ^{232}Th, the much more abundant ^{208}Pb can be used in place of ^{204}Pb as the nonradiogenic Pb isotope (e.g. Mason et al., 2013). Implementing a streamlined ^{208}Pbbased approach, which obviously requires that ^{208}Pb be measured, was a further motivation for the development work presented here.
In summary, the objective of the present work is to present a new isotopedilutionbased method that streamlines sample preparation, particularly with regard to analysing blanksensitive $\mathrm{Pb}/\mathrm{Pb}$ and $\mathrm{U}/\mathrm{Pb}$ ratios, and which allows a ^{208}Pbbased approach to common Pb correction, such that the ^{238}U–^{234}U–^{206}Pb and ^{235}U–^{207}Pb chronometers can both be utilised, where the nature of the sample permits.
3.1 Protocol overview and reagents
The protocol comprises two distinct analytical procedures carried out sequentially, which in tandem are intended to provide the information necessary to calculate ^{238}U–^{234}U–^{206}Pb, ^{238}U–^{206}Pb, and ^{235}U–^{207}Pb ages, utilising ^{208}Pb for common Pb correction. The first procedure is concerned with determining the ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}\mathrm{Pb}$, ${}^{\mathrm{235}}\mathrm{U}{/}^{\mathrm{207}}\mathrm{Pb}$, ${}^{\mathrm{208}}\mathrm{Pb}{/}^{\mathrm{206}}\mathrm{Pb}$ and ${}^{\mathrm{208}}\mathrm{Pb}{/}^{\mathrm{207}}\mathrm{Pb}$ ratios within a sample or part of a sample if more than one growth interval is present. The second procedure is concerned with analysing the same sample material to characterise residual ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ disequilibrium, where the aforementioned $\mathrm{U}/\mathrm{Pb}$ measurement indicates a ^{238}U–^{234}U–^{206}Pb age may be attainable.
The two procedures collectively require the following reagents, consumables, etc., but will otherwise be described separately:

18.2 MΩ cm water

Quartzdistilled (or equivalent highpurity) 10 M HCl and dilutions of this product;

Quartzdistilled (or equivalent highpurity) 16 M HNO_{3} and dilutions of this product;

Reagent grade 16 M HNO_{3};

BioRad AG1 X8 anion exchange resin (or equivalent) 100–200 mesh;

15 mL polypropylene bottles, acid cleaned for ∼ 1 week in 1–2 M distilled HNO_{3}, then rinsed thoroughly with 18.2 MΩ cm water;

22 mL or 27 mL PFA vials, acid cleaned in hot, concentrated reagentgrade HNO_{3} for ∼ 1 week, then refluxed in distilled 10 M HCl for at least 24 h and thoroughly rinsed with 18.2 MΩ cm water after each acid stage;

2 mL BioRad polyprep columns (or equivalent), acid cleaned for ∼ 1 week in 1–2 M distilled HNO_{3}, then rinsed thoroughly with 18.2 MΩ cm water;

CRM145 (New Brunswick Laboratory) natural U or equivalent U isotopic reference material;

Singleelement Tl standard.
The quartzdistilled acids used are comparable to commercially available ultrapure acids – i.e. parts per trillion or lower concentrations for the analytes of interest. The 18.2 MΩ cm water used is approaching absolute purity for the analytes of interest (e.g. < 20 ppq for Pb). All dilutions of distilled acids were prepared with 18.2 MΩ cm water.
3.2 U–Pb measurements
Collected samples were first sawn using a diamondcoated wire saw to reveal their internal structure and provide access to the stratigraphic horizons or growth domains of interest. Clean carbonate subsamples weighing between ca. 50 and 500 mg were then cut from specific stratigraphic horizon or growth domains using a small diamond circular saw and transferred to acidcleaned 15 mL polypropylene bottles. These subsamples were then sonicated repeatedly in 18.2 MΩ cm water until no suspended particles were visible, rinsing between each wash. The subsamples were then acid cleaned twice for a few minutes in distilled 2 % HNO_{3} with sonication to remove any residual dirt and surface contamination. Following each wash, the subsamples were thoroughly rinsed with 18.2 MΩ cm water and sonicated to ensure removal of any residual acid and dislodged surface material. Each acid wash was removed before the acid was consumed to prevent adsorption of dissolved ions back on to the surface of the sample. Where sample material was abundant, we used initial subsample masses of a few hundred milligrams for ease of handling during cleaning, but this mass was reduced where material was limited. The subsample mass after cleaning should be no smaller than ca. 10 mg. Cleaned subsamples were then stored until the day of analysis.
Subsamples were usually taken from specific sample domains without prior characterisation of the $\mathrm{U}/\mathrm{Pb}$ system. Instead, surplus subsamples were prepared from a number of different samples or sample domain to provide the flexibility to retarget the subsequent analytical session, as it became apparent which material was radiogenic and which was not.
On the day of analysis, one to two drops of a mixed ^{204}Pb–^{230}Th–^{236}U (∼ 30 µL drop volume, ca. 15 pg µL^{−1} ^{236}U, ca. 1 pg µL^{−1} ^{204}Pb, and 0.5 pg µL^{−1} ^{230}Th; full isotopic calibration is given in Mason et al., 2013) spike in ca. 2 M HNO_{3} was added directly to the acidcleaned carbonate subsample and gently agitated to mix as the spike dissolved the subsample. Cleaned subsamples were not weighed in order to minimise handling. Instead, the mass of CaCO_{3} from the subsample used was in excess of the HNO_{3} in the spike, such that the spike can dissolve sample material until the contained HNO_{3} is consumed, thereby fixing the mass of sample material dissolved (typically 3–8 mg) to ca. 10 % of the added spike mass. Although not critical to the age calculation, this allowed the absolute sample U concentration to be estimated without weighing, based on the amount of sample expected to dissolve in a given mass of spike. Once visible reaction with the spike was complete, the solution was diluted to around 15 mL with 18.2 MΩ cm water, thoroughly shaken to homogenise and then immediately analysed, with no preconcentration of U and Pb. Dilution to ca. 15 mL provides sufficient solution to check the instrument setup (see below) prior to analysis, allows replicate analyses if needed and mitigates matrix loading on the instrument.
Analyses were performed on a firstgeneration Nu Plasma MCICPMS (Belshaw et al., 1998) using the collector configuration given in Table 1 and described further below. The instrument was fitted with a set of “Btype” Ni cones reserved for very lowlevel Pb work. Sample introduction was via a DSN100 (Nu Instruments) desolvator using either a ca. 50 µL min^{−1} or 75 µL min^{−1} selfaspirating PFA nebuliser (ESI). The instrument and desolvator were slightly modified by replacing the gas and sample lines with acidcleaned PFA to lower the longterm instrumental Hg background, reducing the ^{204}Hg interference on ^{204}Pb. The “hot gas” feed to the DSN100 spray chamber was also disconnected and sealed.
At the beginning of an analytical session the instrument was prepared by cleaning the desolvator and sample lines with 10 % HNO_{3}, 2 % HNO_{3}, and 18.2 MΩ cm water. The Ni cones were also gently cleaned by rinsing with deionised water prior to use to remove excessive Ca buildup from the skimmer orifice from previous use; however, as far as possible, the surface coating on the cones was not disturbed. The instrument was then initially tuned and optimised with ca. 100 ppt Tl solution and 5 ppb CRM145 U solution (both in 2 % HNO_{3}). Pb was avoided to prevent recontamination of the instrument, and sufficient Pbblank was present in the Tl solution to identify the Pb peaks. Instrumental Pb background could then be further reduced by temporarily lowering the auxiliary gas flow (to ca. 0.5 L min^{−1}) with RF power at 1300 W, allowing the plasma to run hot to “evaporate” residual Pb from the instrument interface and then using relatively cool running conditions (auxiliary gas flow of 1.15 L min^{−1} and 1200–1250 Watts RF power). In some instances, this reduced the Pb background by a factor of > 10×, without major loss of sensitivity. The instrument was then left for several hours until Hg adsorbed on the interface had evaporated and the Hg background had stabilised.
After the initial tuning and optimisation of the instrument on the dilute Tl and U solutions, instrument settings were checked on actual samples. At the beginning of an analytical session, particularly after the cones had been cleaned, it was often necessary to refocus the zoom optics to obtain optimal flattopped peaks on the matrixheavy samples. The DSN100 membrane gas flow was also retuned to suppress a molecular interference observed to overlap the Pb peaks, particularly ^{208}Pb, but with its peak centres offset by ca. 0.15 AMU to the lowmass side of the Pb peaks. The ca. 0.15 AMU mass offset generally made the superimposed interference peaks obvious, such that the DSN100 “membrane” gas flow could be adjusted while performing a mass scan until the superimposed peak had been largely eliminated. Based on the mass offset, the interference is a molecular of a midmass element; Sr_{2}O${}_{\mathrm{2}}^{+}$ is suspected based on the group 2 elementrich matrix and the relative magnitude at masses 208, 207, 206, etc. The signal intensity of this interference varies over several orders of magnitude with the DSN100 membrane and hot gas settings, but has been observed to be largely eliminated by disabling the hot gas flow and setting the membrane gas flow slightly below the optimum value for Tl signal intensity on the pure Tl solution. Where a residual interference was seen (only apparent on ^{208}Pb and occasionally up to 10 % of the ^{208}Pb signal, but only on highly radiogenic samples with little ^{208}Pb), the mass offset between the Pb and interference beams meant the extreme highmass side of the Pb peaks was effectively resolved from the interference, proving peak shape was optimal. No correction was made for the Sr_{2}O${}_{\mathrm{2}}^{+}$ interference, and the method is based on its elimination. ^{208}Pb, although not directly used for age calculation, forms the basis of the common Pb correction (Sect. 3.5), and thus at this stage an assessment of any residual interference was made in terms of its impact on the common Pb correction. Where no residual interference on ^{208}Pb was observed or where it was considered irrelevant (e.g. for material with almost no common Pb), the instrument was set to analyse on the centre of the Pb peaks for optimum stability. Where this was not the case, particularly where ^{235}U–^{207}Pb ages were targeted (owing to the larger common Pb correction on ^{207}Pb), the instrument was set to analyse the extreme highmass side of the Pb peak flats where the interference is resolved. No evidence of interferences on U has been observed.
“DVM” collectors are Faraday collectors. “IC” collectors are electron multiplier ion counters. Step 6 is optional and can be omitted if the ^{232}Th is already known to be negligible in the sample (e.g. from a prior attempt at U–Th dating).
Analyses were carried out in a sixstep routine with the magnet switched successively between steps (Table 1) for 10 or 15 repetitions. In steps 0–3 ^{208}Pb, ^{207}Pb, ^{206}Pb, ^{204}Pb+^{204}Hg, and ^{202}Hg were measured on three ioncounters (ICx collectors in Table 1) separated by Faraday collectors (DVMx collectors in Table 1), which are not used in these steps owing to the small size of the Pb signals. The relative gains of the three ion counters were determined based on the successive measurement of the mass204^{+} beam on each ion counter during the analysis. ^{207}Pb was measured entirely dynamically owing to the ion counter spacing. Ion counter gains and dynamic ratios involving ^{207}Pb were calculated with no beam interpolation between steps assuming a steadystate measurement. ^{202}Hg was measured and used to correct for the ^{204}Hg interference (typically ca. 15 % of the total 204^{+} beam with the quantity of spike used here). In steps 4–5 ^{238}U was measured on a Faraday collector, with ^{235}U and ^{236}U measured alternately on both Faraday and ion counter; the intention being that this gives the option of using the Faraday $/$ Faraday ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{235}}\mathrm{U}$ ratio or the Faraday $/$ ion counter ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{235}}\mathrm{U}$ ratio (using the ^{236}U to calibrate the ion counter gain as needed) depending on ^{235}U signal intensity. An optional step with ^{232}Th in IC0 and ^{230}Th in IC1 (Table 1) can be added where estimation of sample ${}^{\mathrm{232}}\mathrm{Th}/\mathrm{U}$ ratio is required (as a check ^{232}Th is negligible), if this is not already known (e.g. from a prior attempt at U–Th dating). Mass fractionation for U was determined from the measured ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{235}}\mathrm{U}$ ratio of the samples and an assumed natural value of 137.75 (based on data for carbonates precipitated from surface waters summarised in Hiess et al., 2012, from Stirling et al., 2007, and Weyer et al., 2008). Mass fractionation for Pb was also estimated based on the measured ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{235}}\mathrm{U}$ ratio but with a +2 ‰/AMU offset applied based on previous characterisation of the U–Pb mass fractionation behaviour of this instrument (Mason and Henderson, 2010). In these tests, the offset between U and Pb fractionation was observed to be nearly constant over a wide range of fractionation values, including those seen for the matrixrich samples analysed here. Samples were washed out with 10 % and 2 % distilled HNO_{3} while the next sample was spiked. Analysis time was around 15 min.
Instrument settings were checked periodically during the analytical session to ensure peak centring, peak shape, and suppression of interferences was maintained. Special care was taken when highly radiogenic material capable of yielding precise ages was encountered and when the instrument was set to measure on the extreme highmass side of the Pb peak flats. The DSN100 was recleaned with 18.2 MΩ cm water as required to remove U and Pb background or when sensitivity dropped due to Caloading of the membrane.
Explicit procedural blank corrections were not made to the U–Pb analyses owing to the measured blank signals being below the instrumental detection limit. However, based on a typically observed detection limit for total Pb of ca. 20 ppq (based on ^{208}Pb), an upper limit for the total procedural Pb blank can be estimated at ca. 0.3 pg.
3.3 Choice of tracer solution
We use a mixed ^{236}U–^{230}Th–^{204}Pb tracer for isotope dilution (calibration in Mason et al., 2013). Using the nonradiogenic ^{204}Pb as tracer allows the measurement of the radiogenic ^{206}Pb and ^{207}Pb, and it is the least abundant of the four stable Pb isotopes in the samples. ^{204}Pb is also more easily obtainable than artificial ^{205}Pb and ^{202}Pb. The instrumental Hg background also makes the small nonspiked ^{204}Pb signal unsuitable as a monitor for common Pb without preconcentration, and thus spiking with ^{204}Pb does not sacrifice any sample information that would otherwise have been obtainable. Moreover, for ^{238}U–^{234}U–^{206}Pb chronology, using a tracer with ^{204}Pb paired with artificial ^{236}U means that the critical ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}\mathrm{Pb}$ ratio is determined from the ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{236}}\mathrm{U}$ and ${}^{\mathrm{206}}\mathrm{Pb}{/}^{\mathrm{204}}\mathrm{Pb}$ ratios, and thus it is relatively insensitive to instrumental mass fractionation due to the mass difference for the natural and spike isotope being the same for both U and Pb. For ^{238}U–^{234}U–^{206}Pb chronology on the instrument used, ^{204}Pb is also more favourable than ^{205}Pb because it can be collected simultaneously on the ion counters with ^{206}Pb, whereas ^{205}Pb cannot (Table 1); ^{205}Pb may, however, represent a better option for other hardware configurations. The disadvantage of using ^{204}Pb is that sample (and blank) ^{204}Pb must be corrected for, but this correction can be reduced by adding sufficient spike ^{204}Pb that the sample contribution is minor. In our case, the sample to spike weight ratio is limited to about 0.1 by the availability of the HNO_{3} in the spike to dissolve sample. For most analyses, this corresponds to > 98.5 % ^{204}Pb arising from the spike, with many of the highly radiogenic analyses (i.e. the fractions for which precise ages can be obtained) having > 99.8 % of the ^{204}Pb originating from the spike. Any age bias introduced in accounting for the sample ^{204}Pb is therefore likely to be at the ‰ level and less than the typical analytical precision on the ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}\mathrm{Pb}$ and ${}^{\mathrm{235}}\mathrm{U}{/}^{\mathrm{207}}\mathrm{Pb}$ ratios.
^{230}Th is included in the tracer to provide the option to measure ^{232}Th as a check that ^{208}Pb is nonradiogenic. ^{230}Th is preferable to artificial ^{229}Th on the instrument used because of the 2 AMU spacing of the ion counters (Table 1). Again sample ^{230}Th needs to be accounted for, but for samples in the U–Pb age range sample ^{230}Th is likely to be close to equilibrium with ^{234}U. Moreover, the ^{232}Th only needs to be measured semiquantitatively as a check of the applicability of the method, and is not used in the age calculation.
3.4 ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ measurements for ^{238}U–^{234}U–^{206}Pb chronology
Where the U–Pb data indicated a particular sample domain is radiogenic and potentially young enough to retain measurable residual ^{234}U disequilibrium, the domain was additionally analysed for the ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratio for ^{238}U–^{234}U–^{206}Pb chronology. Sample aliquots of up to about 0.2 g were dissolved and purified to obtain U cuts. As far as possible these aliquots comprised the residual solution and remaining carbonate from the U–Pb analysis so that the $\mathrm{U}/\mathrm{Pb}$ and ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ measurements were made on as close to the same material as possible. Dissolution was by addition of 0.2 mL of 10 M HCl to the residual solution + residual carbonate. After obvious reaction had ceased, the solution was transferred to clean 22 mL or 27 mL PFA vials and evaporated to dryness. The sample was then converted to chloride form by adding 1 mL 10 M HCl and again evaporating to dryness. Samples were then dissolved in 1 mL of 10 M HCl for loading onto columns for separation of U. Purification used 2 mL BioRad polyprep columns and an AG1X8 anion exchange resin bed of 2 mL. Resin was batched precleaned by suspending it in either 18.2 MΩ cm H_{2}O or dilute HCl, allowing it to settle and decanting any residual suspended fines 8–10 times. Resin was then loaded into the column and cleaned sequentially with ∼ 10 mL (column reservoir filled) 18.2 MΩ cm H_{2}O, 10 M HCl and 18.2 MΩ cm H_{2}O. The resin was then conditioned with two 4 mL aliquots of 10 M HCl, and the sample loaded and matrix Ca eluted with 2×5 mL aliquots of 10 M HCl. Sample U was eluted with 2×5 mL aliquots of 18.2 MΩ cm water and collected in the origin PFA vial (which was rinsed first with 18.2 MΩ cm H_{2}O to remove the bulk of any sample Ca residue). The purified U was measured on the same instrument, with the ^{234}U and ^{238}U measured on ion counter and Faraday collectors, respectively. Standard bracketing with CRM145 (CRM112a) was used to correct both for mass fractionation and ion counter gain.
Owing to the very small ^{234}U blank signal, the ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratio of the U blank could not be meaningfully measured, and thus no blank correction was routinely applied to the ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ measurements. The typical procedural blank for the ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratio measurement was ca. 50 pg U.
Purification of the U fraction is required because the ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratio must be measured to a higher precision than the ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}\mathrm{Pb}$ ratio. This requires preconcentration of the U to obtain a sufficiently large ^{234}U signal to ideally obtain better than 1 ‰ precision. Uranium, however, is generally less blank sensitive than Pb, and thus the ion exchange procedure is relatively straightforward. Moreover, only those samples for which a ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ measurement will be beneficial need be processed.
3.5 Nonradiogenic Pb correction and Age calculation
To obtain an accurate age, it is necessary to account for any nonradiogenic Pb (blank and sample common Pb) in an analysis. The preferred method used here is to employ a 2D isochrontype approach in which the ^{238}U–(^{234}U)–^{206}Pb and ^{235}U–^{207}Pb systems are independently corrected for common Pb, respectively in ${}^{\mathrm{208}}\mathrm{Pb}{/}^{\mathrm{206}}\mathrm{Pb}$–${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}\mathrm{Pb}$ and ${}^{\mathrm{208}}\mathrm{Pb}{/}^{\mathrm{207}}\mathrm{Pb}$–${}^{\mathrm{235}}\mathrm{U}{/}^{\mathrm{207}}\mathrm{Pb}$ isotope space; example plots are shown in Sects. 5 and 6. For a ^{232}Thfree system, subsamples of the same age should define a mixing trend between the common ^{208}Pb $/$ ^{20x}Pb composition falling on the ^{208}Pb $/$ ^{20x}Pb axis (i.e. where ^{23y}U $/$ ^{20x}Pb = 0) and the radiogenic ^{23y}U $/$ ^{20x}Pb composition falling on the ^{23y}U $/$ ^{20x}Pb axis (i.e. where ^{208}Pb $/$ ^{20x}Pb = 0, assuming all ^{208}Pb is common), where ^{20x}Pb is the daughter of ^{23y}U. The common Pb correction can then either be made by fitting a regression line through the data to estimate the ^{23y}U $/$ ^{20x}Pb_{rad} ratio (the intersection with the ^{23y}U $/$ ^{20x}Pb axis), or a regression line can be fitted to estimate the common ^{208}Pb $/$ ^{20x}Pb composition (the intersection with the ^{208}Pb $/$ ^{20x}Pb axis), which can then be used to correct each U–Pb analysis based on its measured ^{208}Pb $/$ ^{20x}Pb ratio. The latter option is preferred here because it allows ageindependent scatter in the radiogenic ^{23y}U $/$ ^{20x}Pb ratio arising from differences in initial disequilibrium state to be accommodated; the estimation of the common Pb composition is insensitive to such scatter in the radiogenic composition providing that any regression is anchored by relatively nonradiogenic analyses. Correcting measurements individually also allows for the pairing of each corrected U–Pb analysis with a corresponding ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ measurement, capturing any additional information encoded in the ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratio. For regressions we use the method of York (1969).
In practice, when dealing with a set of related material (e.g. different growth domains in the same speleothem, or different speleothems from the same cave), isochrons for every sample domain to be dated were not constructed at the outset to attempt to minimise analytical effort. Instead, data were acquired until subsets of material approximating a mixing trend between the radiogenic and common Pb endmembers could be identified (e.g. an nonradiogenic layer stratigraphically bracketed by more radiogenic layers) and regressed to estimate the common Pb composition. This estimate was then used as the basis for the common Pb correction in the wider data set for the related material under consideration. Where samples proved complex in terms of their U–Pb systematics, additional analyses were added to provide further characterisation and to allow true isochrons to be constructed if needed.
In reality, ^{232}Th will be present in trace amounts, with the resulting trace ^{208}Pb_{rad} shifting the ^{208}Pb $/$ ^{20x}Pb ratio to slightly higher values than if ^{232}Th was absent, slightly biasing the calculated ^{23y}U $/$ ^{20x}Pb_{rad} ratio. We consider the bias to be acceptable without correction for ^{232}Th where ^{232}Th $/$ ^{235}U < 0.276 (equivalent to ${}^{\mathrm{232}}\mathrm{Th}{/}^{\mathrm{238}}\mathrm{U}$ < 0.002). This threshold corresponds to a maximum bias in the ${}^{\mathrm{235}}\mathrm{U}{/}^{\mathrm{207}}\mathrm{Pb}$_{rad} ratio of ca. 0.6 %, or ca. onethird of the typical analytical precision on the measured ${}^{\mathrm{235}}\mathrm{U}{/}^{\mathrm{207}}\mathrm{Pb}$ ratio; the ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}\mathrm{Pb}$_{rad} ratio is much less sensitive owing to the smaller common Pb correction on ^{206}Pb. Setting this limit on ^{232}Th in terms of the Th/U ratio has two effects in terms of ^{208}Pb $/$ ^{20x}Pb^{23y}U $/$ ^{20x}Pb space. Firstly, it constrains the ^{208}Pb_{rad} $/$ ^{20x}Pb_{rad} ratio to be close to zero by limiting the ratio of the respective parent isotopes, such that an accurate radiogenic ^{23y}U $/$ ^{20x}Pb composition can still be obtained by extrapolation to the ^{23y}U $/$ ^{20x}Pb axis (i.e. to ^{208}Pb $/$ ^{20x}Pb = 0). Secondly, it constrains compositions with a low $\mathrm{U}/\mathrm{Pb}$ ratio to also have a low $\mathrm{Th}/\mathrm{Pb}$ ratio, such that extrapolation to the ^{208}Pb $/$ ^{20x}Pb axis (^{23y}U $/$ ^{20x}Pb = 0) to obtain the common Pb composition will also correspond to a ^{232}Thfree composition free of radiogenic ^{208}Pb.
For relatively young samples in which residual initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ disequilibrium can still be quantified, model ^{238}U–^{234}U–^{206}Pb ages were calculated from each corresponding pair of U–Pb and ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ analyses, using the estimated common ${}^{\mathrm{208}}\mathrm{Pb}{/}^{\mathrm{206}}\mathrm{Pb}$ ratio to correct for the total nonradiogenic ^{206}Pb, based on the measured ${}^{\mathrm{208}}\mathrm{Pb}{/}^{\mathrm{206}}\mathrm{Pb}$ ratio. In this instance, the initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratio was calculated from the measured ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratio as part of the age calculation analogous to U–Th dating. For generally older material where the initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ cannot be directly quantified, model ^{238}U–^{206}Pb ages were calculated using an assumed initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratio (which was chosen arbitrarily in the present work for illustrative purposes only). Model ^{235}U–^{207}Pb ages were calculated in an equivalent way correcting for the total nonradiogenic ^{207}Pb in the analysis based on the measured ${}^{\mathrm{208}}\mathrm{Pb}{/}^{\mathrm{207}}\mathrm{Pb}$ ratio and the estimated common ${}^{\mathrm{208}}\mathrm{Pb}{/}^{\mathrm{207}}\mathrm{Pb}$ ratio. Where ^{235}U–^{207}Pb ages were calculated but no corresponding ^{238}U–^{234}U–^{206}Pb age could be determined, the ^{238}U→^{206}Pb system was solved for the initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratio using the calculated ${}^{\mathrm{207}}\mathrm{Pb}{/}^{\mathrm{235}}\mathrm{U}$ age.
Alternatively, Tera–Wasserburg space was used in which the age is determined without explicit common Pb correction, based on the intersection of an isochron with concordia (e.g. Roberts et al., 2017). This approach, however, is not favoured by us as it does not allow separate evaluation of the ^{238}U–(^{234}U)–^{206}Pb and ^{235}U–^{207}Pb systems (and often involves assumptions about initial disequilibrium in order to calculate concordia) but is utilised here where necessary to compare independently obtained data (e.g. when ^{208}Pb was not measured).
Model ages and concordia were calculated using an inhouse implementation of the general decay equations given by Faure (1986), in which the decay chains are simplified to ^{238}U →^{234}U →^{230}Th → ^{226}Ra →^{206}Pb and ^{235}U→^{231}Pa → ^{207}Pb. Initial ^{230}Th and ^{231}Pa were assumed to have been absent, and initial ^{226}Ra was assumed to have been at equilibrium. Decay constants used were ^{238}U: 1.55125 × 10^{−10}; ^{234}U: 2.82203 × 10^{−6}; ^{230}Th: 9.17055 × 10^{−6}; ^{226}Ra: 4.33488 × 10^{−4}; ^{235}U: 9.8485 × 10^{−10}; ^{231}Pa: 2.11583 × 10^{−5}; ^{232}Th: 4.9475 × 10^{−11} (Cheng et al., 1998, 2013; Steiger and Jäger, 1977). Age uncertainties were determined using a Monte Carlo approach to propagate analytical uncertainty and uncertainties arising from initial ratios such as the common Pb composition and initial U isotopic composition. A natural ${}^{\mathrm{208}}\mathrm{Pb}{/}^{\mathrm{204}}\mathrm{Pb}$ ratio of 37.1 ± 10 (95 % confidence level) was assumed when accounting for sample ^{204}Pb in the isotope dilution calculation; the large uncertainty is to cover reasonably foreseeable terrestrial isotopic variations. As part of the isotope dilution calculation the spike ^{204}Pb proportion is output so that analyses with an excessive sample ^{204}Pb contribution can be identified. For most analyses, > 99 % of the total ^{204}Pb originated from the tracer. Blank Pb is not separately corrected for and is dealt with as part of the total nonradiogenic Pb correction; however, given a number of analyses have yielded > 99 % radiogenic ^{206}Pb, the Pb blank can be considered a generally minor source of nonradiogenic Pb.
In the absence of suitable wellcharacterised carbonate reference materials during the period of method development, the validation of the new procedure required means other than the direct analysis of reference materials. As an alternative, we set four independent validation tests for the new method.

The new method must be able to produce data and ages consistent with measurements by a conventional isotope dilution approach with purification of U and Pb – i.e. not removing the matrix must have no appreciable impact on the resulting data and ages.

The method must be able to generate U–Pb ages that vary systematically with stratigraphic order in samples where the successive growth intervals are resolvable.

In samples where the common Pb correction permits, the method must be able to generate concordant ^{238}U–^{234}U–^{206}Pb and ^{235}U–^{207}Pb ages.

The method should replicate data obtained independently in a different laboratory.
These four tests have been performed on three samples: ASH15, SLL106, and JOHO1. A fourth sample, SB_pk142 is analysed as a case study for the application of the ^{235}U–^{207}Pb chronometer.
ASH15 is a calcite flowstone comprising a younger relatively thin brownish layer overlying an older, more massive yellowish layer (Fig. 1), and originates from Ashalim cave, Negev Desert, Israel. The massive yellow layer has previously been independently analysed at the University of Melbourne (Vaks et al., 2013a) and the University of Oxford (Mason et al., 2013) and has an age of ca. 3 Ma and a U concentration of ca. 1.5 ppm; ^{232}Th is negligible (Mason et al., 2013). The latter data set, obtained with purification of the U and Pb from the matrix, is compared to new data obtained using the new protocol (i.e. without matrix removal) as a preliminary test of not removing the matrix.
SLL106 is a highU (6 to 43 ppm) calcite stalagmite from Ledyanaya Lenskaya cave, Siberia, Russia (Vaks et al., 2020). The sample comprises several distinct layers designated from A to G, in order of increasing stratigraphic age and mostly separated by visible hiatuses (Fig. 1). All seven stratigraphic layers have been analysed using the new protocol. Five subsamples each from the F and G layers have also been purified and analysed using the method of Mason et al. (2013). This provides control data, such that the reproducibility of the F and G ages, with and without matrix separation, can be tested. The multilayer nature of the sample is additionally used to test the ability of the new method to produce ages in stratigraphic order, while the highU nature of the sample makes it suitable for testing concordance of ^{238}U–^{234}U–^{206}Pb ages and ^{235}U–^{207}Pb ages. Previous ${}^{\mathrm{232}}\mathrm{Th}{/}^{\mathrm{238}}\mathrm{U}$ measurements from this sample and other samples from the same cave (Vaks et al., 2013b) give a maximum ${}^{\mathrm{232}}\mathrm{Th}{/}^{\mathrm{238}}\mathrm{U}$ ratio of 1.6 × 10^{−3} and indicate that the radiogenic ^{208}Pb contribution is insignificant.
JOHO1 (Fig. 1) is a fault vein calcite from the Middle East with a relatively low bulk U concentration of 0.3–0.5 ppm. The fault vein has been analysed independently at the University of Oxford using the new protocol described and at the NERC Isotope Geoscience Laboratory (NIGL), Keyworth, UK, by laser ablation ICPMS, following the methods of Roberts et al. (2017). The laser ablation analyses targeted a domain that included material with a much higher U concentration (up to 25 ppm). The sample is used to test the new protocol via interlaboratory comparison.
SB_pk142 (Fig. 1) is an aragonite speleothem from Botovskaya cave, Siberia, Russia. The sample consists of part of a stalactite that has merged into flowstone, the remains of a second smaller stalactite (now encased by the flowstone portion of the sample) on one corner of the sample, and traces of reddishbrown clay on the stratigraphic base of the flowstone. The sample contains two stratigraphic domains separated by a prominent iron oxide stained lamina, possibly representing a hiatus. Multiple subsamples from both stratigraphic domains have been analysed using the new method. A notable feature of speleothems from this cave is the large and variable ^{234}U excess, with known initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratios ranging between 3.4 and 8.1 times equilibrium (Vaks et al., 2013b, 2020). This sample is used as an example application of the ^{235}U–^{207}Pb chronometer to a cave system where the ^{238}U–^{206}Pb chronometer is problematic. Aragonite samples from Botovskaya cave show consistently low ${}^{\mathrm{232}}\mathrm{Th}{/}^{\mathrm{238}}\mathrm{U}$ ratios (< 2 × 10^{−4}, Vaks et al., 2013b), such that the radiogenic ^{208}Pb contribution is insignificant.
Detailed representative sample petrography for samples from Ledyanaya Lenskaya and Botovskaya caves, as well as details of the caves themselves, are given in Vaks et al. (2013b, 2020).
5.1 ASH15
Results for ASH15 are given in Table 2 and Fig. 2. These analyses were intended as a preliminary test that the new U–Pb measurement procedure without matrix separation produces data consistent with published data (Mason et al., 2013) obtained using the same spike but with purification of U and Pb from the matrix. The new analyses are slightly less radiogenic than the analyses of Mason et al. (2013); however, they are not exact replicates of the same subsamples, so some variation in the proportion of common Pb can be expected. The critical feature is that the data with and without matrix separation are colinear defining a common isochron (Fig. 2) and are therefore consistent.
5.2 SLL106
Control data for the F and G layers obtained with purification of U and Pb from the matrix following the method of Mason et al. (2013) are given in Table 2 and Fig. 3. Data and ages obtained using the new analytical methodology for all layers of SLL106 are also given in Table 2 and Fig. 4. Blanks for the control data were 4.1 pg Pb, 24.8 pg U for the F layer and 42.0 pg Pb, 18.8 pg U for the G layer. Control data are blank corrected.
In terms of the measured ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}\mathrm{Pb}$ ratio, for the F layer, the control data are markedly more precise than the data obtained using the new protocol (typical relative uncertainty of ±0.075 % versus ±0.9 %; Table 2), but the precision is more similar for the G layer (0.8 % versus 1.2 %) owing to the larger Pb blank correction in the G layer control data. The control data yield ^{238}U–^{234}U–^{206}Pb isochron ages of 1073.6 ± 6.7 and 949.9 ± 5.4 ka (95 % conf.) for the G layer and the upper part of the F layer, respectively. The corresponding ages for the G layer and the upper part of the F layer obtained using the new protocol are 1076.2 + 8.5$/$8.8 ka and 944.7 + 5.6$/$5.6 ka, respectively. The ^{238}U–^{234}U–^{206}Pb ages therefore replicate with an uncertainty of better than 1 %, irrespective of whether the matrix is removed or not. Moreover, the precision of the ages is not greatly degraded by applying the simplified protocol, and interestingly the higher analytical precision of the control data for the F layer does not translate to higher age precision because of scatter in the data.
^{238}U–^{234}U–^{206}Pb ages for SLL106 obtained using the new protocol vary systematically from 1076.2 + 8.5$/$8.8 ka near the stratigraphic base of the sample to 571.4 + 13.7$/$14.4 ka near the stratigraphic top of the sample, with no age reversals. Treating replicate and overlapping ages as single values, five distinct age values are observed. The likelihood of these ages falling in stratigraphic order as the consequence of a fluke result is thus 1 in 5! or less than 1 %.
^{235}U–^{207}Pb ages obtained for SLL106 using the new method are less precise than the ^{238}U–^{234}U–^{206}Pb ages owing mainly to the proportionally larger common Pb correction on ^{207}Pb. Nevertheless, the most radiogenic analyses, layer G and F_{top}, yield fairly precise (ca. ±5 %) ^{235}U–^{207}Pb ages of 1060 + 46$/$48 ka and 960 + 47$/\mathrm{54}$ ka respectively, in agreement with the corresponding ^{238}U–^{234}U–^{206}Pb ages of 1076.2 + $\mathrm{8.5}/\mathrm{8.8}$ ka and 944.7 + $\mathrm{5.6}/\mathrm{5.6}$ ka. All other obtained ^{235}U–^{207}Pb ages are also concordant with their corresponding ^{238}U–^{234}U–^{206}Pb ages.
5.3 JOHO1
Results for JOHO1 are given in Table 2 and Fig. 5. The results are intended as an interlaboratory comparison of isotopic measurements made using the new protocol at the University of Oxford with those obtained independently at NIGL by laser ablation. Results are given in terms of ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}\mathrm{Pb}$–${}^{\mathrm{207}}\mathrm{Pb}{/}^{\mathrm{206}}\mathrm{Pb}$ ratios for compatibility with the NIGL laser ablation measurements. In terms of the measured ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}\mathrm{Pb}$ ratio, the precision of the two data sets is comparable (with typical ±2 % uncertainties for the Oxford solution data versus ±3 % for the NIGL data; Table 2). However, the NIGL data targeted a small domain with up to 25 ppm U, whereas the solution measurements were made on material with a bulk U concentration of 0.3–0.5 ppm.
The NIGL data define a mixing trend from highly radiogenic compositions (with a ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}\mathrm{Pb}$ ratio of ca. 340 and a ${}^{\mathrm{207}}\mathrm{Pb}{/}^{\mathrm{206}}\mathrm{Pb}$ ratio of ca. 0.05) falling just above concordia, towards a common Pb ${}^{\mathrm{207}}\mathrm{Pb}{/}^{\mathrm{206}}\mathrm{Pb}$ ratio of ca. 0.65, but with the majority of the analyses clustering towards the radiogenic end of the trend. The Oxford data fall towards the radiogenic end of the same trend and are thus consistent with the NIGL analyses and yield a comparable age if common assumptions are used. Thus, for example, regression of each data set through a common ${}^{\mathrm{207}}\mathrm{Pb}{/}^{\mathrm{206}}\mathrm{Pb}$ ratio of 0.65 ± 0.1 yields concordia intercepts at 19.34 ± 0.30 and 19.19 ± 0.15 Ma, respectively, for the Oxford solution data and NIGL laser ablation data (concordia assumes no initial ^{230}Th or ^{231}Pa and equilibrium initial ^{234}U and ^{226}Ra). Less spread towards nonradiogenic compositions is seen in the Oxford data, but this is unsurprising given that fewer analyses were made.
Results for SB_pk142 from Botovskaya cave are shown in Table 2 and Fig. 6. On a ${}^{\mathrm{208}}\mathrm{Pb}{/}^{\mathrm{206}}\mathrm{Pb}$–${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}\mathrm{Pb}$ plot data from SB_pk142 fall on two distinct trends corresponding to the stratigraphically older and younger sections of the sample. The stratigraphically older part of the sample has a consistently lower ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}\mathrm{Pb}$ ratio for a given ${}^{\mathrm{208}}\mathrm{Pb}{/}^{\mathrm{206}}\mathrm{Pb}$ ratio than the stratigraphically younger section. The intercept ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}\mathrm{Pb}$ values of the two trends at ca. 685 and ca. 910, respectively, for the older and younger sections of the sample correspond to apparent ^{238}U–^{206}Pb ages of ca. 9.5 and 7.2 Ma, assuming equilibrium initial ^{234}U and no initial ^{230}Th. The assumption that initial ^{234}U was in equilibrium is likely incorrect (see below) but demonstrates the point that there is an noticeable apparent age difference between the older and younger sections of the sample, which appears consistent with the apparent hiatus, and the age order superficially agrees with the stratigraphy of the sample. The common ${}^{\mathrm{208}}\mathrm{Pb}{/}^{\mathrm{206}}\mathrm{Pb}$ ratios suggested by the upper and lower sections of the sample are not appreciably different.
On a ${}^{\mathrm{208}}\mathrm{Pb}{/}^{\mathrm{207}}\mathrm{Pb}$–${}^{\mathrm{235}}\mathrm{U}{/}^{\mathrm{207}}\mathrm{Pb}$ plot data from SB_pk142 show a different pattern, and the data from both the stratigraphically older and younger portions of the sample define a single trend with an intercept of ca. 171.2. This corresponds to a ${}^{\mathrm{235}}\mathrm{U}{/}^{\mathrm{207}}\mathrm{Pb}$ age of ca. 6 Ma, and suggests the stratigraphically older and younger portions of the sample are not, in fact, appreciably different in age, and that the sample is younger than the ^{238}U–^{206}Pb system suggests.
The data show basically coherent mixing lines between a radiogenic endmember and common Pb. Thus, the discrepancy between the ^{238}U–^{206}Pb system and ^{235}U–^{207}Pb system cannot be easily attributed to open system behaviour. Moreover, such an explanation would require U or Pb isotopes from the two systems to have behaved differently. Extreme ^{234}U disequilibrium is, however, known to occur in samples from Botovskaya cave, with initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratios between 3.4 and 8.1 times equilibrium reported for samples from the last 0.5 Ma based on $\mathrm{U}/\mathrm{Th}$ dating (Vaks et al., 2013b, 2020). Excess ^{206}Pb from the decay of excess initial ^{234}U will make the ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}\mathrm{Pb}$_{rad} ratio appear low (old) compared to the corresponding ${}^{\mathrm{235}}\mathrm{U}{/}^{\mathrm{207}}\mathrm{Pb}$_{rad} ratio, with the discrepancy depending on the initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratio; in other words, it allows timeindependent variation of the ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}\mathrm{Pb}$_{rad} ratio not seen in the ${}^{\mathrm{235}}\mathrm{U}{/}^{\mathrm{207}}\mathrm{Pb}$ ratio. This could account for older apparent ^{238}U–^{206}Pb ages and the difference between the ${}^{\mathrm{208}}\mathrm{Pb}{/}^{\mathrm{206}}\mathrm{Pb}$–${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}\mathrm{Pb}$ and ${}^{\mathrm{208}}\mathrm{Pb}{/}^{\mathrm{207}}\mathrm{Pb}$–${}^{\mathrm{235}}\mathrm{U}{/}^{\mathrm{207}}\mathrm{Pb}$ plots. Excluding subsamples 15–17, which are nonradiogenic, the upper section of the sample gives a mean ^{235}U–^{207}Pb model age of 5.9 Ma with typical uncertainties on individual ${}^{\mathrm{235}}\mathrm{U}{/}^{\mathrm{207}}\mathrm{Pb}$ model ages of ±0.2 to 0.3 Myr, and suggests an initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratio varying between 3.8 and 5.8 times equilibrium (Table 2). This initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ is typical of that already documented from Botovskaya cave. The lower section of the sample is generally slightly less radiogenic, but where subsamples yield ${}^{\mathrm{235}}\mathrm{U}{/}^{\mathrm{207}}\mathrm{Pb}$ ages they are indistinguishable from the upper section of the sample. Calculated initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratios for the lower part of the sample are higher than those previously reported but not particularly unexpected for this cave, at between 10 and 11.6 times equilibrium. It is uncertain why the initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ changed between the two sections of the sample, though the fact that a prominent iron oxide stained lamina separates the two portions of the sample seems to indicate a change in growth conditions occurred.
^{a} Correlation coefficient for the uncertainties on the specified ratio pairs. ^{b} The assumed composition and uncertainty used to make corrections for the Pb initially in the samples. ^{c} The initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratio is arbitrarily chosen to allow ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}\mathrm{Pb}$ ages to be calculated to show the apparent age differences between the different sections of SB_PK 142. The ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}\mathrm{Pb}$ ages should not be taken as an accurate estimate of the true age. The assigned initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ uncertainty assumes a normal distribution. ^{d} The initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratio estimated from the ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}{\mathrm{Pb}}_{\mathrm{rad}}$ ratio using the ^{235}U–^{207}Pb age.
7.1 Method validation
The results from the samples used for method validation indicate that the new protocol passes all four method validation tests. This in turn implicitly demonstrates that matrix effects such as molecular interferences or decoupling of U and Pb mass fractionation during analysis are either unimportant or can be adequately controlled with proper setup of the instrument. Similarly, significant biases introduced during sample preparation, such as preferential leaching of U or Pb during partial sample dissolution by the spike, can also be excluded.
Not separating the matrix does not lead to inconsistent data in the preliminary test using ASH15, that is to say the data with and without matrix separation are colinear, i.e. they define a common isochron, and therefore would yield the same ${}^{\mathrm{238}}\mathrm{U}{/}^{\mathrm{206}}\mathrm{Pb}$ age. Replication of ^{238}U–^{234}U–^{206}Pb ages with and without matrix separation is demonstrated to a high precision for the F and G layers of SLL106, again demonstrating that matrix separation via anion exchange chemistry is not necessary for $\mathrm{U}/\mathrm{Pb}$ measurements. This finding is in line with the fact that laser ablation techniques have allowed measurements for a number of years without matrix separation (e.g. Roberts et al., 2017).
For SLL106, ^{238}U–^{234}U–^{206}Pb ages obtained with the new protocol from all stratigraphic layers vary systematically with stratigraphic order, without age reversals. Moreover, for sample layers that are sufficiently radiogenic to allow ^{235}U–^{207}Pb ages to be calculated, these are concordant with the ^{238}U–^{234}U–^{206}Pb ages, demonstrating the ability of the new protocol to exploit the ^{235}U–^{207}Pb system where the nature of the sample permits, even on material as young as ca. 1 Ma. This is significant because it demonstrates the ability to have a continuity of dating between young samples where the initial ^{234}U can be directly constrained via the ^{238}U–^{234}U–^{206}Pb chronometer and old material (i.e. > 20 Ma) where ^{238}U–^{206}Pb age inaccuracies associated with assuming the initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratio will be proportionally small compared to the age.
Analysis of JOHO1 using the new protocol replicates independently obtained laser ablation data, demonstrating interlaboratory consistency of the new method. Additional data quality tests of the new method are presented in the larger data set of Vaks et al. (2020) in the form of comparison with UTh ages and the testing of age reproducibility between different speleothems from a single location.
7.2 Limitations of ^{238}U–^{206}Pb dating and the of utility of the ^{235}U–^{207}Pb system
One of the major limitations to applying the ^{238}U–^{206}Pb system to geologically young materials just beyond the limit of the ^{238}U–^{234}U–^{206}Pb chronometer (ca. 2 Ma, depending on initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$) is that while ages can be highly precise (e.g. Woodhead et al., 2006), an age calculated assuming equilibrium initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ and one calculated using the most extreme known initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratio differ by > 2 Myr, which is proportionally a massive difference for ages of a few million years. While it is possible to try to characterise initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ for a particular cave using younger material (e.g. Woodhead et al., 2006), it is difficult to test whether such younger material is representative, and in some instances younger material may not exist. Consequently, ^{238}U–^{206}Pb dating beyond the limit of the ^{238}U–^{234}U–^{206}Pb chronometer is something of a game of Russian roulette in terms of age accuracy, with SB_pk142 from Botovskaya cave being an example of where the “bullet” of extreme initial ^{234}U disequilibrium is in the chamber. The ^{235}U–^{207}Pb chronometer provides an alternative option for highly radiogenic samples. Moreover, because decay of excess ^{234}U leads to a permanent excess of radiogenic ^{206}Pb relative to radiogenic ^{207}Pb, comparison of the ^{238}U–^{206}Pb and ^{235}U–^{207}Pb systems can be used to constrain initial ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ after any residual disequilibrium has decayed (e.g. Mason et al., 2013). This is potentially very useful for testing assumed initial ^{238}U/^{234}U ratios used for other samples in a set where these can only be dated by the ^{238}U–^{206}Pb chronometer because of common Pb.
7.3 Applicability of the new protocol and potential future development
The present method is only applicable to samples in which ^{232}Th is near absent. The method is not intended as a blanket replacement for prior implementations of the U–Pb system, but rather as a complementary technique that can be applied where it is best suited.
The new protocol has significant advantages over a traditional solutionbased approach in terms of the simplicity of sample preparation for U–Pb analysis. Sample preparation is fast to the point that prior reconnaissance characterisation of the U–Pb system is unnecessary as the time penalty for preparing an undatable sample is minimal. Moreover, redundant sample material can be prepared with little extra effort, such that an analytical session can be retargeted in real time, as it becomes apparent which material is most favourable for dating. The greatly reduced sample preparation also eliminates stages at which contamination could occur (column chemistry, sample drydowns), reducing the need for an optimal lab and column setup. The more traditional solutionbased approach with purification of U and Pb retains an advantage in terms of analytical precision (at least under ideal conditions, e.g. the SLL106 F control data; Table 2) and is therefore likely to remain the preferred approach for the calibration of reference materials (e.g. Roberts et al., 2017). However, high analytical precision may not translate to high age precision if other limiting factors, such as scatter in the data, are present (as in the SLL106 F control data; see also the compilation of Woodhead and Petrus, 2019) – i.e. the lower analytical precision of the new procedure need not be a significant limitation in terms of age precision. Indeed, the utilisation of the new approach by us (Vaks et al., 2020) to obtain ca. 50 ^{238}U–^{234}U–^{206}Pb ages, many with corresponding concordant ^{235}U–^{207}Pb ages, on material < 1.6 Ma old, demonstrates that it can be applied effectively to generate fairly large data sets. In this case, the reduction in analytical effort achieved with the new approach allowed replication of growth ages between different stalagmites, providing additional quality control that would not otherwise have been available.
The new protocol does not provide an alternative for in situ techniques where high spatial resolution is required, e.g. on samples that are very small or have a complex morphology (e.g. Li et al., 2014). However, the results from JOHO1 indicate the new method can be applied to carbonates with < 1 ppm U. Although not investigated in detail, the comparable precision of the JOHO1 solution and laser ablation data, despite the latter being acquired on a domain with > 10 × the U concentration, suggests the new protocol would outperform laser ablation in terms of the lower U and Pb concentration limit at which ages could be obtained. Moreover, the higherprecision ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ measurements obtained with the new method relative to laser ablation (< ± 1 ‰ attained here versus ±5 ‰–6 ‰ obtained by Lin et al. (2017) by laser ablation) makes the former generally more suitable for ^{238}U–^{234}U–^{206}Pb dating, where quantifying slight residual disequilibrium in the ${}^{\mathrm{234}}\mathrm{U}{/}^{\mathrm{238}}\mathrm{U}$ ratio can be critical.
The new protocol was developed on a firstgeneration Nu plasma, an instrument ca. 20 years old at the time of writing. Hardware advancements, notably the Isotopx ATONA amplifier, which can greatly expand the dynamic range of Faraday collectors into the range traditionally belonging to the ion counter (Szymanowski and Schoene, 2020), offer future potential to refine the present methodology. While the small ^{206}Pb, ^{207}Pb and ^{208}Pb signals from radiogenic samples would still likely require measurement on ion counters, with suitable spike design, it may be possible to shift measurement of the Pb spike isotope and also ^{202}Hg onto Faraday collectors, providing more flexibility in the collector configurations that could be used. In particular, it may be a means to measure ^{207}Pb simultaneously with the spike isotope to help improve the precision of the ${}^{\mathrm{235}}\mathrm{U}{/}^{\mathrm{207}}\mathrm{Pb}$ ratio. Similarly, it may be possible to avoid the use of ion counting for small ^{235}U signals, simplifying the analysis.
Demonstrating the ability to make U–Pb measurements by directly dissolving samples with an isotopic tracer and analysing with no further preparation other than dilution, opens another intriguing possibility for future method development; the prospect of some form of quasiin situ isotope dilution analysis. If an acidcleaned subsample can be dissolved directly with the tracer and analysed, there is no reason, in principle, why an entire sample could not be acid cleaned and small domains then dissolved with the tracer for analysis while still in situ. Obviously, there would be practical hurdles to overcome, and this would not be a substitute for high spatial resolution techniques, but it could substantially streamline isotope dilution analysis and make it less destructive to the sample.
A new isotope dilution method for the U–Pb dating of carbonate samples is presented that removes the need for preconcentration of Pb. The new method produces data consistent with those obtained by isotope dilution with preconcentration of U and Pb, and with data obtained independently by another laboratory using laser ablation ICPMS. The new method also generates selfconsistent data; specifically, ages that vary systematically with growth direction without age reversals and which are concordant between the ^{238}U–^{234}U–^{206}Pb and the ^{235}U–^{207}Pb chronometers. The new method thus satisfies reasonable data quality control criteria.
The new method is capable of utilising both the ^{238}U–^{234}U–^{206}Pb chronometer and the ^{235}U–^{207}Pb chronometers, subject to inherent limitations imposed by sample age and isotopic composition.
All data used are contained within Table 2.
AJM carried out the isotope dilution method development, analyses and age interpretation. AV, GMH and SFMB obtained funding supporting this work. AV, SFMB and JNH obtained samples and assisted with sample preparation. JNH provided reference laser ablation data. AJM wrote the manuscript with input from all coauthors.
The authors declare that they have no conflict of interest.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Speleoclub Arabika Irkutsk is thanked for invaluable assistance in obtaining speleothem samples from Siberia. Nick Roberts (NIGL) is thanked for assistance in obtaining reference laser ablation data for JOHO1. Shell is thanked for providing sample JOHO1.
This research has been supported by the Natural Environment Research Council (grant nos. NE/K005057/1 and NE/G013829/1) and the Deutsche Forschungsgemeinschaft (grant no. BR 3437/21).
This paper was edited by Norbert Frank and reviewed by Robert Cliff and Ryan Ickert.
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 Abstract
 Introduction
 Overview of the U–(Th)–Pb system and the motivation for a new method
 Protocol description
 Protocol validation methodology and sampling
 Protocol validation results
 SB_pk142 results
 Discussion
 Conclusions
 Data availability
 Author contributions
 Competing interests
 Disclaimer
 Acknowledgements
 Financial support
 Review statement
 References
 Abstract
 Introduction
 Overview of the U–(Th)–Pb system and the motivation for a new method
 Protocol description
 Protocol validation methodology and sampling
 Protocol validation results
 SB_pk142 results
 Discussion
 Conclusions
 Data availability
 Author contributions
 Competing interests
 Disclaimer
 Acknowledgements
 Financial support
 Review statement
 References