LA-ICP-MS U-Pb carbonate geochronology: strategies, progress, and application to fracture-fill calcite

Laser Ablation Inductively Coupled Plasma Mass Spectrometry (LA-ICP-MS) U-Pb 35 geochronology of carbonate minerals, calcite in particular, is rapidly gaining popularity as 36 an absolute dating method. The technique has proven useful for dating fracture-fill calcite, 37 which provides a powerful record of palaeohydrology, and within certain constraints, can be 38 used to bracket the timing of brittle fracture and fault development. The high spatial 39 resolution of LA-ICP-MS U-Pb carbonate geochronology is beneficial over traditional 40 Isotope Dilution methods, particularly for diagenetic and hydrothermal calcite, because 41 uranium and lead are heterogeneously distributed on the sub-mm scale. At the same time, 42 this can provide limitations to the method, as locating zones of radiogenic lead can be time- 43 consuming and ‘hit or miss’. Here, we present strategies for dating carbonates with in situ 44 techniques, through imaging and petrographic techniques to data interpretation; we focus 45 on examples of fracture-filling calcite, but most of our discussion is relevant to all carbonate 46 applications. We demonstrate these strategies through a series of case studies. We review 47 several limitations to the method, including open system behaviour, variable initial lead 48 compositions, and U-daughter disequilibrium. We also discuss two approaches to data 49 collection: traditional spot analyses guided by petrographic and elemental imaging, and 50 image-based dating that utilises LA-ICP-MS elemental and isotopic map data. 51 52 is interpreted as a zone of alteration. Further U-Pb spot analyses were placed in a domain away from this feature that exhibits high U, with the data yielding a more precise regression with an age of 287 ± 14 Ma (MSWD = 2.5). This highlights the use of trace element mapping to locate regions of highest U, to assist and refine U-Pb analyses, and shows the potential for dating calcite veins into the Palaeozoic. ± for its U, Th and Pb elemental distribution using LA-ICP- The map shows zoning of U, Th and Pb that is interpreted as growth zoning during 729 primary calcite growth. Pb is distributed similarly, but with high concentrations along narrow the Pb-bearing imperfections Pb in the regression, generation. This is 768 usually conducted after an initial inspection of the mapping data combined with prior 769 imaging and petrography; however, the screening can also employ an iterative approach 770 after generation of initial U-Pb isochrons. After this screening/filtering, the remaining data 771 are pooled into a number of pseudo-analyses (each corresponding to the same number of 772 pixels) based on a suitable isotope ratio, such as 238 U/ 208 Pb or 235 U/ 207 Pb. The pooling is 773 achieved using an empirical cumulative distribution function ECDF) to maximise the spread 774 in U/Pb ratios, and an appropriate number of pixels to produce a reasonable population of 775 data, for example twenty to forty data-points. Here, we present examples of this approach 776 applied to vein-filling calcite. nascent in geochronology, and as such has not been fully explored.


134
The biggest benefit of LA-ICP-MS comes from the spatial resolution (less than ca. 100 m) 135 at which data can be obtained, particularly given the length scales of uranium concentration 136 heterogeneity in carbonate. We find that for hydrothermal and diagenetic calcite in 137 particular, uranium is heterogeneously distributed across veins and vein phases, and within 138 individual crystals (see Figure 1). Uranium concentration heterogeneity typically spans 1 to 139 3 orders of magnitude, with the length-scale of this variation being commonly much less 140 than 1 mm. Targeting of high U domains is therefore difficult without a high spatial-141 resolution sampling method. Intracrystalline uranium distributions within calcite define 142 several patterns (see For common-lead bearing minerals such as calcite, the extreme range in parent/daughter 167 ratios encountered (quoted here as 238 U divided by initial lead as 204 Pb; a ratio known as µ), 168 means that ID does not always lead to an improvement in precision on the regressed age. 169 This is demonstrated by the schematic model in Figure 2. Sampling for ID provides an 170 average of elemental and isotopic zonation within the analytical volume, perhaps >1 mm 3 , 171 depending on the concentration of U and Pb within the crystal(s). The resulting data should 172 be precise (depending on the sample/blank ratios), but may potentially have a small spread 173 in parent/daughter ratios (i.e. 238 U/ 206 Pb) due to the averaging effect during sampling. In 174 contrast, LA sampling has the potential to target and utilise such zonation, better resolving 175 end-member µ compositions, and resulting in analyses with a greater spread in 238 U/ 206 Pb 176 ratios. This potentially improves the resolving power of a regression of the measured 177 isotopic ratios allowing definition of, ideally, the high-µ (radiogenic lead) and low-µ (initial 178 lead) end-member compositions of the data array (see Figure 2). Along with the generally 179 high-n datasets generated by the LA-ICP-MS approach, these well-constrained regressions 180 can result in similar or even greater precision age determinations than those using ID data 181 alone. However, a caveat to this, is that lower precision data points can mask true 182 geological heterogeneity.  The amount of U needed to generate an age is dependent on two factors: (1) the age of the 255 material and (2) the initial µ ratio of the material. The younger a sample is, the less time 256 there is for the growth of radiogenic daughter Pb from parent U. With a higher µ, the ratio of 257 measured radiogenic Pb to common (initial) Pb will be higher, giving greater confidence and 258 (in general) precision and accuracy to the resulting age determination. 259

260
The effect of these factors is shown in Figure 4. Two Tera-Wasserburg plots are shown, 261 with isochrons for samples of different ages (100 to 10 Ma on the left, 1000 to 100 Ma on 262 the right). The most accurate and precise age determinations, i.e. those that can be 263 interpreted with most confidence, are generated when the sample comprises abundant 264 radiogenic lead, i.e. gets close to the lower part of the concordia curve where the 265 regression intercepts. Each plot shows regressions for individual samples between a 266 common-lead composition (~0.8) and a radiogenic end-member (with the age labelled). The 267 colour-coded points along each regression reflect the amount of radiogenic lead that will be 268 created by decay of 238  When absent of concordant analyses, both high µ and a significant spread in initial µ values 287 are required to generate the most robust ages, as these will pin the isochron at the 288 radiogenic end-member with greater confidence. Some calcite exhibits sufficiently high µ to 289 generate concordant data (e.g. Richards et al., 1998;Roberts & Walker, 2016;Nuriel et al., 290 2017). Such robust ages are rare with a material that so commonly exhibits high initial lead 291 abundances. Ages can be derived from isochrons with low amounts of radiogenic lead, i.e. 292 those with low µ. Such isochrons can be regressed to provide lower intercept ages, but the 293 confidence in these ages is subject to having well-behaved data conforming to a single 294 population, requiring precise data-point uncertainties (e.g. Figure 5G). Such low µ 295 isochrons can potentially give inaccurate lower intercept ages if the material is very young, 296 and thus confirmation through multiple samples and/or alternative age constraints are 297 In Figure 5, we present a selection of 'real-world' data to highlight the potential complexity 300 of carbonate U-Pb data. These data from natural samples broadly range from undesirable 301 to most desirable from A to I, with the following notable characteristics: 302 A) Dominated by common lead with large data-point uncertainties ( Reeder, 1995;Reeder, 1996). and we note the following salient features: 1) Pb is both particle reactive and relatively 353 insoluble; 2) Pb is found at very low levels in most fluids (ppt-ppb), providing high Ca/Pb 354 ratios; 3) Pb can substitute for Ca in the crystal lattice, although the Pb cation is larger -355 ionic radii of Ca 2+ and Pb 2+ in six-fold coordination are 114 and 133 pm, respectively; 4) U 356 exists in multiple oxidation states, and its solubility is strongly affected by Eh and pH; and 5) 357 both U(VI) and U(IV) have been found in calcite, but with the latter being interpreted as the 358 most likely and most stable form. determinations that were performed in oxic conditions, and interpreted this high uranium 372 uptake as due to incorporation of U(IV) and thus that the partition coefficient for U(IV) is 373 orders of magnitude larger than for U(VI). It is evident that more data from natural 374 carbonates in different settings are needed to more fully understand the controls on U and 375 Pb incorporation. 376

377
We have compiled uranium and lead concentration data from carbonates analysed in the 378 ratios for speleothems are ~500, whereas median values for Mid-Ocean Ridge (MOR) and 380 continental vein calcite are 8.2 and 2.6, respectively. Note that these are total Pb contents, 381 and include radiogenic Pb as well as initial Pb, which causes the short linear trends that 382 represent individual samples. Samples in Figure 6 are mostly younger than 200 Ma, or < 4 383 Ma for the speleothems. The concentration data and U/Pb ratios demonstrate that 384 speleothems in general are much more amenable to U-Pb geochronology, which is why 385 they have been the main focus for this method until the last few years. Dating vein calcite, 386 with more variable and lower contents of U, and higher contents of Pb, has a lower chance 387 of success than speleothems (although it should be noted that the speleothems in general 388 have already been visually pre-screened during sampling).  In addition to the microscopy-based methods listed above, a lower resolution but potentially 477 useful technique is provided by storage-phosphor imaging-plate (IP) autoradiography using 478 a plastic support film coated with a photostimulated phosphor (BaFBr:Eu 2+ ) (Hareyama et 479 al., 2000). This technique records an image of the spatial distribution and intensity of total 480 radioactivity (from alpha, beta and gamma emitters) from a flat sample surface. In natural 481 geological materials, IP radiography records radioactivity from U, Th (and their radioactive 482 daughters), 87 Rb, and 40 K (Hareyama et al., 2000;Cole et al., 2003). Although U is not 483 specifically discriminated, it has been shown to be a useful screening tool for finding U-484 bearing domains in carbonate materials (Cole et al., 2005). The method has been 485 particularly applied to speleothem studies where its large sample-size capabilities (up to at 486 least 40 cm) are beneficial. Spatial resolution is a few tens of micrometres, depending on 487 the pixel size of the laser scanner. However, the detection limit depends on the exposure 488 time of the IP in direct contact with the sample surface: routinely this is around 14-28 days 489 giving a detection limit of a few ppm U, which is typically higher than many carbonate 490 samples. Whilst this may be suitable for speleothems, which typically have higher uranium 491 concentrations, we do not regularly adopt the method for very low U contents in vein-filling 492 or diagenetic carbonates.  Several approaches for destructive sample screening using LA-ICP-MS are available. 520 These can include either systematic or non-systematic (random) spot traverses across 521 carbonate samples, and can include full analyses (i.e. a 30 second ablation following a pre-522 ablation) or a much shorter analysis time (with or without pre-ablation). We commonly adopt 523 systematic traverses across samples utilising shorter ablation times but including a pre-524 ablation, so as to avoid common Pb from the surface. This is a quick way to determine with 525 reasonable precision and accuracy whether a sample is a single age population that 526 represents a closed isotopic system with a suitable range in µ. For some samples, this 527 provides potentially useable age information that does not require any further refinement 528 (e.g. Figure 5H-5I). Conversely, this may provide a population of data that exhibits no 529 potential, i.e. dominated by common-lead (e.g. Figure 5A-5B), open-system behaviour (e.g. 530 Figure 5D), or mixed analyses (e.g. Figure 5C). Screening in this way allows us to analyse 531 several samples or sample-aliquots in a single LA-ICP-MS session, and thus identify the 532 material most likely to provide an accurate and precise age. 533 534 Either as an alternative to spot traverses, or subsequent to spot traverses, we use LA-ICP-535 MS mapping to determine both the location and nature of U and Pb zonation in the 536 carbonate material. Whereas spot traverses provide rapid screening of multiple 537 samples/aliquots, mapping provides fairly rapid (5 x 5 mm in < 2 hours) screening across 538 complexly zoned samples. Different approaches can be adopted, a suite of major and trace 539 elements can be analysed alone, a suite of elements for age determination (i.e. Pb to U ± 540 Hg) can be measured, or, depending on ICP-MS instrumentation, these can be combined, An alternative approach is to produce maps that generate U-Pb data directly (see Section 556 5.5). These have obvious utility in determining suitable domains of calcite; however, for 557 common-lead bearing minerals they can be difficult to interpret by visual inspection. Pb-Pb 558 or Pb-U isotope maps can be created with ease; however, because of the inherent inclusion 559 of common lead, more useful is a map of common lead-corrected 206 Pb/ 238 U ages or ratios. 560 Common lead-corrected age maps require: 1) precise knowledge of the initial lead 561 composition (or upper intercept in Tera-Wasserburg space); and 2) knowledge that the 562 initial Pb composition is homogeneous across the mapped region, something that is not 563 always the case (see Section 5.4). However, with the recent advent of more advanced data 564 processing software, such as the Monocle plug-in for Iolite (Petrus et al., 2017), complex 565 age determination from maps is becoming more amenable (see Section 5.5). The caveat 566 with such data processing packages is that non-related domains defining a single age with 567 a good precision can potentially be selected with subjectivity, and without relation to actual 568 geological/mineralogical process. For this reason, we suggest that it is imperative that users 569 relate domains they have selected for U-Pb age determination to specific mineralogical 570 domains that can be identified independently with other means, whether these be entire 571 crystals, domains of crystals, growth bands, or specific veinlets. As suggested by Drost et 572 al. (2018), who demonstrate the method for carbonate sediments, it is also useful to 573 compare conventional spot ablation analyses with the map-generated dates to verify the 574 accuracy of the latter. 575 California Santa Barbara (Santa Barbara, USA). There are two key points of the method we 587 feel are worth highlighting that differ from 'standard' methods based on silicate minerals 588 such as zircon. Firstly, the heterogeneous nature of the Pb isotope composition of matrix-589 matched, i.e. calcite/dolomite, minerals (due to variable common Pb incorporation), means 590 that normalisation of the Pb-Pb isotope ratios is currently achieved using a synthetic glass 591 rather than a carbonate, typically NIST612 or NIST614. At present, there is no evidence to 592 suggest that the Pb/Pb mass bias is variable across different matrices. Secondly, 593 calculation of the reproducibility of the primary and secondary matrix-matched reference 594 materials, which is required for uncertainty propagation (Horstwood et al., 2016) and 595 determination of the true method accuracy and precision, is hindered by the fact that the 596 carbonate reference materials currently employed have U/Pb heterogeneity that is equal to 597 or much larger than the analytical uncertainties (Roberts et al., 2017). This means there will 598 typically be a significant excess variance of the reference material U/Pb isotope 599 measurements in any one session (including after correction for common lead), which does 600 not describe the reproducibility of the analytical system but instead reflects the natural 601 variation in the reference material. If propagated onto the sample data-point uncertainties 602 as a within-session excess variance as recommended for zircon in Horstwood et al (2016), 603 these data point uncertainties will be overestimated masking any smaller scale, real 604 geological scatter in the sample isochron and result in meaningless ages with erroneously 605 high precision. For this reason, it is suggested that calculation of the session-based 606 reproducibility is best estimated using a more homogenous material such as NIST glass or 607 zircon. However, it should be noted that through this practice results can only be compared 608 in a relative sense within session, or between sessions if validation materials are compiled 609 and used. To compare data in an absolute sense, i.e. to assign an age and total uncertainty 610 to a material for comparison between laboratories and/or with other methods, the 611 uncertainty from the primary reference material must be included to reflect the accuracy 612 with which the matrix-matched normalisation is known. In this way, the uncertainty of the 613 primary reference material constitutes a limiting uncertainty on any sample age. Improved 614 reference materials with less scatter around the U/Pb isochron are therefore a pre-requisite 615 for improving this method. 616

Generating U-Pb data and interpreting ages 618
Generating ages and relating these to geological processes requires the marriage of 619 spatially-resolved variations in composition (elemental and isotopic) and U-Pb isotopic 620 concentrations. In this section, we present several case studies to highlight our approach to 621 dating vein-filling calcite, the potential applications to dating faulting and fluid-flow, and the 622 type of material commonly encountered. First we present the standard approach, which 623 used independent imagery and analysis to target, refine, and interpret the U-Pb analyses 624 that are based on static spot ablations. This is the same approach as using CL imagery to 625 help interpret zircon dates, and that can be further refined with information such as 626 companion trace element data. A second approach (age mapping) is to use mapping tools 627 not just to image the sample and its composition, but to extract age data from the map itself 628  We have demonstrated that elemental mapping data are useful for refining and interpreting 751 U-Pb isotopic data. For example, in Example B above, we manually located the spots in a 752 high U zone, and in Example C, we manually removed the data with high Pb 753 concentrations. An alternative approach to using the maps to 'manually' locate spots or 754 refine spot data, is to generate a combined elemental and U-Pb isotopic 2D dataset (i.e. 755 map); the benefit of this method is that software tools can be used to both discriminate 756 specific isotopic data based upon chosen criteria, and also to show regions within these 757 First, pixels are removed, using user-defined selection criteria that are believed to be 767 related to alteration, secondary material, or a younger or older carbonate generation. This is 768 usually conducted after an initial inspection of the mapping data combined with prior 769 imaging and petrography; however, the screening can also employ an iterative approach 770 after generation of initial U-Pb isochrons. After this screening/filtering, the remaining data 771 are pooled into a number of pseudo-analyses (each corresponding to the same number of 772 pixels) based on a suitable isotope ratio, such as 238 U/ 208 Pb or 235 U/ 207 Pb. The pooling is 773 achieved using an empirical cumulative distribution function ECDF) to maximise the spread 774 in U/Pb ratios, and an appropriate number of pixels to produce a reasonable population of 775 data, for example twenty to forty data-points. Here, we present examples of this approach 776 applied to vein-filling calcite.  between the common and radiogenic end-members, and ideally will have enough spread in 851 U/Pb ratios to yield a precise regression with low uncertainties at both the lower (radiogenic 852 lead) and upper (common lead) intercepts. However, many samples will exhibit a lack of 853 spread in U/Pb ratios, or will be dominated by radiogenic compositions (e.g. Figure 5F). 854 Although a best-fit line may be calculated for such data, the slope, and thus age, may be 855 inaccurate. Thus, it is useful for such samples to have an estimation of the common lead 856 composition through other means, such as from nearby cogenetic samples formed at the 857 same age, or from different minerals also believed to have been formed at the same age. carbonate however, we find this is not always such a suitable approach. Our experience 866 from hydrothermal carbonate in particular, is that common lead compositions are often 867 more radiogenic (lower 207 Pb/ 206 Pb ratios) than the terrestrial lead model (Stacey and 868 Kramers, 1975) for age of carbonate crystallisation. This can occur if the carbonate has 869 incorporated lead during its formation that is derived from ancient sources. Figure 14 shows  Figure 15). The data exhibit a high level of common/initial lead, with 915 limited spread in radiogenic lead contents, but still forming a scattered regression to a lower 916 intercept value. Using different colours to discriminate different sections of vein, it is clear 917 that they have subtly different initial lead compositions, as indicated by the upper intercept 918 ( 207 Pb/ 206 Pb value) of the data arrays. These lead compositions are different from that 919 predicted by the Stacey & Kramers (1975) terrestrial composition, which we find is a 920 common feature of many vein-filling carbonates. This is likely due to the hydrothermal fluids 921 that are precipitating the carbonate comprising unsupported radiogenic lead components 922 derived from leaching of older uraniferous minerals or rocks. 923

924
The existence of variable Pb compositions on small length-scales (<1 mm) means that 925 careful attention is required to interpret complex data. However, the spatial resolution of LA-926 ICP-MS means that these details can potentially be teased out. This case study also shows 927 the potential of the method for measuring veinlets that are only ~150 µm wide (see Figure  928 15), a task that would be difficult for ID analyses. Mixed ages and atypical lead compositions can also make age mapping problematic. 945 946 9. Dating young materialdealing with disequilibria 947 As described in Section 3, the younger the age of the sample analysed, the lower the 948 potential for precise and accurate age determination due to the lack of radiogenic ingrowth 949 of lead. However, young carbonates are a high priority in many applications, because they 950 can date events more relevant to the Earth system at present, and because U-Pb can precision, i.e. for the Quaternary, of much less than ± 100 ka, and potentially even less than 958 ± 10 ka or < 1000 years for the Holocene. Achieving such precision requires very high U to 959 achieve abundant radiogenic lead and higher µ values (see Figure 4). products, like 230 Th, relative to secular equilibrium will bias the age with a smaller 972 magnitude but in the same direction, whereas a deficit will result in dates that are too 973 young. 974 975 Carbonates are commonly precipitated from fluids containing 234 U/ 238 U out of secular 976 equilibrium. Thus, this initial disequilibrium must be considered in any age determination. 977 Age corrections for initial U daughter deficits are at maximum ~1.44 times the half life of the 978 daughter isotope for zero initial abundance. But for initial excesses, the age difference can 979 be many times larger (see Figure 17). For most older samples dated by U-Pb, the effect of 980 disequilibrium is deemed to be insignificant compared to larger measurement uncertainties. 981 For this reason, initial disequilibrium has thus far not been mentioned in any publication 982 concerning LA-ICP-MS U-Pb dating except for those dealing with young speleothems (e.g. with only a small degree of initial disequilibrium, 234 U/ 238 Unow is likely to have reached 999 secular equilibrium. This means that 234 U/ 238 U0 cannot be estimated from the measured 1000 data alone. One approach to alleviate this problem is to take known initial ratios from 1001 younger samples (<600 ka) formed in approximately the same geologic setting, and apply 1002 these corrections to the older samples from the same setting (e.g. Woodhead et al., 2006Woodhead et al., , 1003Woodhead et al., 2019 carbonates is sparse and potentially more variable. Carbonates precipitated in the shallow 1038 crust may arise from percolating groundwater, seawater, deep brines, formation waters, or 1039 a mixture of these sources. We can use existing data on these fluid sources to make an 1040 initial estimate of what range may exist in terrestrial carbonates. Groundwater is well known 1041 to have highly variable and significant 234 U excess (e.g. Osmond and Cowart, 1976). Figure  1042 16 shows a compilation of 234 U/ 238 U activity ratios taken from a range of literature sources 1043 (see supplementary file for sources). The population of data for groundwater ( Figure 16A  To demonstrate the effect of initial activity ratios out of secular equilibrium, we have 1072 modelled synthetic data in Figure 17. This figure shows curves representing samples of ten 1073 different ages, which would range from 500 ka to 9 Ma if 234 U/ 238 U0 was in secular 1074 equilibrium (~1) during formation. The true age of the samples get younger as 234 U/ 238 U0 1075 increases. The effect does not decrease in significance as we look at older ages, i.e. the 1076 age offset on a sample with a measured age of 8 Ma is similar to that on a sample of 4 Ma. 1077 The curves are shown on a log scale, because in many systems, the variation in activity 1078 ratio is going to vary a small amount, close to secular equilibrium (~1). For example, in the 1079 Nullarbor plain cave systems, the variation is likely to be within 30% of 1 (Woodhead et al., isotope 230 Th is a potential consideration in the accuracy of 238 U-206 Pb ages. In general, 1112 most speleothem-dating studies assume no initial 230 Th in the system, as Th is very 1113 insoluble in water compared to U. Any excess initial 230 Th during formation would also result 1114 in artificially old measured ages. 231 Pa is another daughter product in the decay chain, 1115 which again, is considered very insoluble, and does not form part of the disequilibrium 1116 corrections at present. 226 Ra, another intermediate product, may co-precipitate with U, but 1117 its short half-life of 1.6 ka means it is likely to have little impact on U-Pb ages (Richards et 1118(Richards et al., 1998. A final concern is the gas 222 Rn, as this may be lost from the system by diffusive 1119 processes. A study into the effect of this showed negligible impact on the 238 U-206 Pb ages of 1120 a Quaternary speleothem (Richards et al., 1998). In summary, initial disequilibrium is clearly a major issue for the accuracy of U-Pb dating of 1140 carbonates. The effect is significant for material of any age, but as we get to older 1141 carbonates, the analytical uncertainty contributions will begin to swamp the uncertainties 1142 and Archaean (e.g. Moorbath et al., 1987;Jahn, 1998;Taylor and Kalsbeek, 1990;1155 Whitehouse and Russell, 1997); these mostly utilised Pb-Pb dating. A major issue of the 1156 Pb-Pb method, is that Pb contents of crustal fluids are much higher than that of the primary 1157 carbonates, and therefore, even small amounts of fluid-related alteration can dominate the 1158 measured Pb-Pb composition and lead to an age that is not representative of primary 1159 carbonate precipitation (e.g. Sumner & Bowring, 1996) can generally be distilled down to open-system behaviour, i.e. dating material that has 1165 remained a closed isotopic system since its formation is increasingly difficult with 1166 increasingly older material. This is simply because thermal-and/or fluid-induced mobility of 1167 parent and daughter isotopes becomes increasingly likely if the material has been exposed 1168 to multiple deformation-, burial-, uplift-, glaciation-, weathering-or fracture-related events. 1169 1170 Early studies documented various transformative processes and their impact on Pb-Pb/U-1171