G 3. AN ELECTRONIC JOURNAL OF THE EARTH SCIENCES Published by AGU and the Geochemical Society

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1 Geosystems G 3 AN ELECTRONIC JOURNAL OF THE EARTH SCIENCES Published by AGU and the Geochemical Society Article Volume March 2010 Q0AA06, doi: /2009gc ISSN: Click Here for Full Article Improved laser ablation U Pb zircon geochronology through robust downhole fractionation correction Chad Paton School of Earth Sciences, University of Melbourne, Parkville, Victoria 3010, Australia Now at Centre for Star and Planet Formation, Geological Museum, University of Copenhagen, Øster Voldgade 5 7, DK 1350 Copenhagen, Denmark. (chadpaton@gmail.com) Jon D. Woodhead, John C. Hellstrom, Janet M. Hergt, Alan Greig, and Roland Maas School of Earth Sciences, University of Melbourne, Parkville, Victoria 3010, Australia [1] Elemental fractionation effects during analysis are the most significant impediment to obtaining precise and accurate U Pb ages by laser ablation ICPMS. Several methods have been proposed to minimize the degree of downhole fractionation, typically by rastering or limiting acquisition to relatively short intervals of time, but these compromise minimum target size or the temporal resolution of data. Alternatively, other methods have been developed which attempt to correct for the effects of downhole elemental fractionation. A common feature of all these techniques, however, is that they impose an expected model of elemental fractionation behavior; thus, any variance in actual fractionation response between laboratories, mineral types, or matrix types cannot be easily accommodated. Here we investigate an alternate approach that aims to reverse the problem by first observing the elemental fractionation response and then applying an appropriate (and often unique) model to the data. This approach has the versatility to treat data from any laboratory, regardless of the expression of downhole fractionation under any given set of analytical conditions. We demonstrate that the use of more complex models of elemental fractionation such as exponential curves and smoothed cubic splines can efficiently correct complex fractionation trends, allowing detection of spatial heterogeneities, while simultaneously maintaining data quality. We present a data reduction module for use with the Iolite software package that implements this methodology and which may provide the means for simpler interlaboratory comparisons and, perhaps most importantly, enable the rapid reduction of large quantities of data with maximum feedback to the user at each stage. Components: 19,711 words, 13 figures, 3 tables. Keywords: laser ablation; geochronology; U Pb; zircon; software; fractionation. Index Terms: 1194 Geochronology: Instruments and techniques; 1115 Geochronology: Radioisotope geochronology. Received 11 May 2009; Revised 18 December 2009; Accepted 5 January 2010; Published 26 March Paton, C., J. D. Woodhead, J. C. Hellstrom, J. M. Hergt, A. Greig, and R. Maas (2010), Improved laser ablation U Pb zircon geochronology through robust downhole fractionation correction, Geochem. Geophys. Geosyst., 11, Q0AA06, doi: /2009gc Theme: EarthTime: Advances in Geochronological Technique Guest Editors: D. Condon, G. Gehrels, M. Heizler, and F. Hilgen Copyright 2010 by the American Geophysical Union 1 of 36

2 1. Introduction [2] U (Th) Pb zircon geochronology by laser ablation inductively coupled plasma mass spectrometry (LA ICPMS) has seen a dramatic rise in popularity in the last decade [Kosler and Sylvester, 2003]. While the precision of the method cannot rival that of the benchmark isotope dilution thermal ionization mass spectrometry (ID TIMS), and its spatial resolution cannot easily compete with less destructive secondary ion mass spectrometry (SIMS) techniques, for many applications these drawbacks are outweighed by the low cost and rapid sample throughput achieved by LA ICPMS, and many research facilities now have in house laser ablation capabilities. [3] A natural consequence of this rapid proliferation, combined with the relative immaturity of the technique, is an immense diversity in both the instrumentation and methodologies employed by individual facilities, producing significant differences in observed downhole elemental fractionation behavior arguably the single largest influence on the accuracy and precision of the method [e.g., Horn et al., 2000; Jackson et al., 2004; Kosler et al., 2001]. This has resulted in a large number of in house data reduction methods, with no firm consensus on how the correction for downhole fractionation should best be performed. There is also little transparency in other aspects of data reduction, notably propagation of uncertainties, making interlaboratory comparisons of data sets difficult. [4] All LA ICPMS systems inherently produce some degree of elemental and/or mass related discrimination during sampling. These so called instrumental biases are generally observed to drift over the course of days or weeks, but may also vary detectably within a single analytical session. In addition to these relatively long term effects, elemental biases occur during laser ablation which vary on a short time scale as the ablation pit deepens. In U Th Pb dating, this downhole fractionation produces readily resolvable changes in measured Pb/U and Pb/Th ratios, and hence apparent age of the ablation target. Numerous studies have investigated the underlying causes of such behavior [Eggins et al., 1998; Hergenröder, 2006a, 2006b; Kosler et al., 2005], but it remains unclear which of many possible processes dominate, and how they vary with time. What is clear is that the interaction between these is complex, and that variables such as laser wavelength, the aspect ratio of the laser pit, choice of carrier gas, and gas flow create a myriad of potential trends in elemental fractionation. [5] Although the use of rastering (which involves continuously traversing the laser across the sample surface) can effectively eliminate variations in elemental fractionation [e.g., Horstwood et al., 2003], this approach does limit the minimum possible target surface area (i.e., the 2 D spatial resolution) to several times larger than the laser spot diameter. Similarly, although fractionation can be minimized by employing short ablation times (e.g., 10 s), this approach limits the likelihood of detecting Pb loss, age zoning, etc., while also compromising data quality. For this reason, a number of researchers have proposed methods that attempt to correct for downhole fractionation effects. [6] The most popular approach is the modeling of elemental fractionation using a linear regression, in which case the slope of the fractionation versus time trend is either calculated using an empirical relationship to spot size and hole depth [Horn et al., 2000], or the fitting of separate gradients to each sample analysis [Kosler et al., 2002a]. There are assumptions required in each of the above methods but the single largest drawback to their applicability is the fact that elemental fractionation is not always linear. As such, any application of the approach to nonlinear fractionation trends will produce inaccurate results. Although a correction method using the average of the standard over an interval identical to that of the sample can be employed [Jackson et al., 2004], this approach sacrifices temporal resolution (i.e., the time resolved aspect of laser ablation data), making it more difficult to detect either regions of compromised data or true age zonation. [7] This paper investigates new methods for the correction of laser induced elemental fractionation, with the aim of establishing protocols that retain as much 2 D (ablated area) and depth (the timeresolved aspect of corrected data) resolution as possible, while still retaining sufficient flexibility to process data from any laboratory, exhibiting any degree of complexity. We also address the propagation of uncertainties during the correction procedure. 2. Analytical Methods [8] All analyses were conducted at the School of Earth Sciences, University of Melbourne, employing a prototype of the Varian 810 quadrupole 2of36

3 Table 1. Key Instrument Parameters and Operating Conditions for Laser Ablation U (Th) Pb Analysis Parameter Value Helex ablation system Lambda Physik Compex nm ArF excimer Energy density <5 J cm 2 Repetition rate 5 Hz Spot diameter 19 to 71 mm Helium gas flow rate 0.25 l min 1 Argon gas flow rate 1.06 l min 1 Effective cell volume 2 cm 2 Varian 810 Prototype ICPMS RF power 1400 W Sheath gas flow rate 0.26 l min 1 Auxiliary gas flow rate 1.85 l min 1 Cooling gas flow rate 17.5 l min 1 Points per peak 1 Isotope Dwell Time Attenuation ms none ms none ms none ms auto ms auto Total duration of one mass cycle 0.11 s (9 Hz) ICPMS coupled to a HelEx laser ablation system that utilizes a 193 nm ArF excimer laser. The laser was operated with an output energy of 70 mj per pulse, providing an estimated power density on the sample of <5 J cm 2. A full list of instrumental parameters is included in Table 1. For full details of the Helex ablation system we refer the reader to Woodhead et al. [2004] and Eggins et al. [2005], although we would note here the following key characteristics of the system: [9] 1. Although the laser cell is large in volume, ablation occurs within a nested microcell with a volume of 2 cm 3, resulting in high temporal resolution with minimal memory effects (see Woodhead et al. [2007, Figure 1] for an illustration). [10] 2. The laser optics produce well defined ablation pits with near vertical walls [Eggins et al., 1998] and an even energy distribution across the spot. [11] 3. Ablation occurs in a stratified combination of helium beneath argon within the microcell (compared to mixing of argon and helium downstream of the cell in many other systems). The helium minimizes redeposition of ejecta/condensates, while argon provides efficient sample transport to the ICPMS. [12] All data reduction was conducted off line using the freely distributed Iolite data reduction package which runs within the Wavemetrics Igor Pro data analysis software; the reader is referred to Hellstrom et al. [2008] and the Iolite website ( for further details. Backgrounds were measured prior to each ablation with the laser shutter closed and employing identical settings and gas flows to those used during ablation. Data were acquired in batches approximately 1 h in duration, consisting of multiple groups of 5 to 15 sample unknowns bracketed by pairs or triplets of primary and secondary zircon standards. Background intensities were interpolated using a smoothed cubic spline, as were changes in instrumental bias (modeled using downhole fractionation corrected ratios of the zircon standard analyses). Elapsed time since the beginning of sample ablation was used as a proxy for hole depth, with laseron events calculated by Iolite using an algorithm based on the rate of change in signal intensity, an approach that we have found to be highly reproducible. For further details of Iolite and the U Th Pb data reduction scheme we refer the reader to Hellstrom et al. [2008] and Appendix B, respectively. [13] For each selected time period (e.g., 50 s of data from a spot analysis) the mean and standard error of the measured ratios were calculated, using no outlier rejection for baselines, and a 2 standard error outlier rejection for all other data. All uncertainties are quoted at the 2 sigma level. [14] All analyzed zircons were mounted in epoxy resin blocks and polished to a 1 mm finish. Each mount was cleaned ultrasonically in ultrapure water after polishing, then cleaned again prior to analysis using AR grade methanol. Prior to each individual analysis in any batch, regions of interest were preablated using several pulses of the laser (this equates to 0.2 mm in depth) to remove potential surface contamination, a method we have found to dramatically reduce common Pb contamination that would otherwise affect the first few seconds of analyses. 235 U was calculated from 238 U using a 238 U/ 235 U ratio of [Jaffey et al., 1971]. [15] Analyses were routinely examined for spurious data caused by surface Pb contamination, cracks or fractures containing contaminants, areas of Pb loss, etc. This interrogation was achieved using a combination of baseline subtracted intensities of individual isotopes, raw ratios and corrected ratios. Useful data could not be obtained for 204 Pb due to 3of36

4 Figure 1. Examples of observed variability in 206 Pb/ 238 U ratios with time (so called downhole fractionation ): (a) Approximately linear fractionation patterns which have been observed to vary systematically with spot diameter (reprinted from Horn et al. [2000], copyright 2000, with permission from Elsevier). (b) The effects of changing carrier gas on fractionation patterns. Note that even using He some nonlinear behavior is apparent (reprinted from Jackson et al. [2004], copyright 2004, with permission from Elsevier). (c) An average of 3 separate (baseline subtracted) spot analyses of the zircon standard displaying nonlinear fractionation with time. Data were acquired with a 213 nm New Wave laser coupled to an X Series quadrupole mass spectrometer using He as the carrier gas (B. Kamber, personal communication, 2008). (d) An average of 14 separate (baseline subtracted) spot analyses of the zircon standard, again showing a nonlinear change in 206 Pb/ 238 U ratio with time. Data were acquired using a 193 nm New Wave laser coupled to an Agilent 7500 quadrupole mass spectrometer using He as the carrier gas (S. Meffre, personal communication, 2008). large isobaric Hg interferences derived from the carrier gases. 3. Observations of Downhole Elemental Fractionation [16] Downhole elemental fractionation is the change in the measured ratios between different elements, and occurs during laser ablation as the hole created by the laser deepens. In general, the signal intensities of refractory elements decrease more rapidly than volatile elements [Longerich et al., 1996], although changes with time can be complex, and other factors also influence fractionation [Eggins et al., 1998]. It has been observed that downhole fractionation does not correlate well with mass, and is better predicted by chemical characteristics such as whether an element is chalcophile or lithophile [Longerich et al., 1996]. [17] The expressions of the downhole fractionation effect vary with parameters such as laser wavelength [Jackson et al., 2004], spot size (Figure 1) [Horn et al., 2000], cell volume, gas flows, and choice of ablation gas (Figure 1) to name but a few. Nevertheless, it is reasonable to assume that the underlying processes contributing to the phenom- 4of36

5 enon are common to all systems, and that variables such as those noted above simply affect the degree to which each underlying process influences results, and the time during an analysis at which it is most influential. A large number of studies have examined these underlying causes [e.g., Eggins et al., 1998; Hergenröder, 2006a, 2006b; Kosler et al., 2002b, 2005; Kroslakova and Günther, 2007; Longerich et al., 1996], and we do not intend to reiterate them here. However, we would emphasize that these studies have universally demonstrated that downhole fractionation is the result of complex interactions between multiple processes. As such, any attempt to model or predict fractionation should be undertaken with caution, and the validity of any model employed should be carefully tested. [18] Downhole fractionation typically causes an increase in observed Pb/U ratios with depth [Jackson et al., 2004; Kosler and Sylvester, 2003; Tiepolo, 2003], with minor changes in Pb/Th ratios. Although methods used to correct for these effects in U (Th) Pb geochronology typically assume that the changes with time are linear, this is not always the case. For example, Figure 1 illustrates that although 206 Pb/ 238 U can vary approximately linearly with time (i.e., depth) in some cases (Figures 1a and 1b), curved fractionation patterns often occur to varying degrees (Figures 1c and 1d). Indeed, such nonlinear trends are characteristic of our own analytical system, prompting this study. Furthermore, the steepness and absolute position of the data arrays can also vary depending on the spot size (e.g., Figure 1a) and the carrier gas employed (Figure 1b). Plots illustrating variations in fractionation pattern with spot size (Figure 2) on our own instrument Figure 2. Variations in downhole elemental fractionation with laser spot diameter. Although changes in (baseline subtracted) 206 Pb/ 238 U ratio decrease in magnitude with increasing spot size, the pattern becomes increasingly more complex: (a) Fractionation is relatively linear with a19mmdiameter spot, although the rate of change does decrease detectably with depth. (b) For a 25 mm spot the pattern of fractionation is approximately exponential and is almost flat after 60 s. (c) The pattern of a 42 mm diameter spot begins exponentially but flattens after approximately 30 s. (d) Using a 71 mm diameter spot the curve rapidly flattens and even appears to decrease slightly after 40 s. Note that surficial common Pb contamination, which will cause an increase in 206 Pb/ 238 U ratios early in the analysis, does not appear to have affected results. Each ablation lasted 60 s, consisted of 300 pulses, and created a pit approximately mm deep. 5of36

6 not only further demonstrate that curved trends occur, but that the overall pattern can vary significantly, and is strongly influenced by the aspect ratio of the pit produced. All ratios show a rapid early increase, but the degree of subsequent curvature after 10 s results in an overall exponential pattern for 25 and 42 mm spot sizes, and actually produces a negative response in values of the 71 mm spot after 40 s. As noted above, the washout/response time of our ablation system is very rapid and the fact that we observe these phenomena so clearly has led us to believe that complex fractionation patterns of this type are the norm but may be masked to some extent in systems with slow ablation cell response times (perhaps producing pseudolinear trends). [19] To understand the fractionation patterns of elemental ratios, it is worth first examining the (baseline subtracted) signal intensities used in ratio calculation. Figure 3 illustrates a combination of data from 6 ablations of the zircon standard, each of 60 s duration. The original data (pale colors) were combined to produce an average for each time segment (black line). Figures 3a 3c show the baseline subtracted beam intensities of U, Th and Pb and indicate that decay is not exponential (red line), as might be expected. Instead, more complex patterns are observed, and significant differences in response are apparent between elements. For each element, signals after 25 s appear to decay exponentially, but prior to this each maintains a steadier intensity than the exponential curve, suggesting the operation of multiple superimposed phenomena (e.g., gas flows, condensation conditions). This effect is most apparent for Pb and Th, which can deviate from the fitted exponential curve by over 10%, whereas the effect is more subtle for U (at least in our system). Correspondingly, the overall decrease in signal intensity is high for U (approximately 55%), in comparison to a 45% decrease for Th and Pb. [20] Based on these observations, it is not surprising that the resulting 206 Pb/ 238 U ratio (Figure 3d) varies substantially, and in this case appears to closely follow an exponential curve (in red). The same test conducted with 5 ablations using a 71 mm spot (Figure 3f), however, shows a more complex response that cannot be modeled by a simple exponential curve. Interestingly, although signal intensities of both Th and Pb (Figures 3b and 3c, respectively) are relatively complex at 42 mm, the resulting 208 Pb/ 232 Th ratio (Figure 3e) is relatively stable over 60 s, decreasing steadily with time. This suggests that fractionation effects are well synchronized between these elements in both timing and magnitude, despite their complex. 4. Existing Methods for the Correction of Downhole Elemental Fractionation and Their Limitations [21] Methods for the correction of downhole elemental fractionation can be subdivided according to whether standard sample bracketing is employed in modeling downhole fractionation patterns. Those that use standard sample bracketing assume that standards and unknowns will behave identically during ablation, and that the characteristics of downhole fractionation in the standard can be used to model its effects in unknowns, whereas other methods are independent of this assumption. Each of these categories is considered separately below. Note that this subdivision refers specifically to treatment of downhole fractionation, and not to the correction of long term instrumental bias, which may also be corrected using standard sample bracketing Methods Without Standard Sample Bracketing [22] Horn et al. [2000] detailed an empirical method for the correction of fractionation effects, based on the observation that elemental ratios have a linear relationship to hole depth (for a given laser spot diameter and energy density (Figure 1a)). Because these observations were highly reproducible using their system, they generated an empirical formula describing the relationship between pit diameter and the slope of the fractionation trend for a given energy density. Using this formula they individually corrected each time slice of the data for downhole fractionation (Figure 4a), then calculated the mean and standard deviation of the ratio from these corrected data points. The effects of instrumental bias were corrected separately using simultaneous nebulization of a Tl/U tracer solution. Although this approach has the potential to accurately correct downhole fractionation, it relies on the stability of fractionation patterns between analytical sessions, and thus requires highly reproducible operating conditions. [23] To avoid these constraints, Kosler et al. [2002a] proposed a method that does not require all analyses to have the same fractionation pattern. Instead, the data for each laser pit are treated separately, and are 6of36

7 Figure 3. Data for six separate (baseline subtracted) ablations of the zircon standard (pale shades) and the average (black lines). Model exponential curves are shown in red. The baseline subtracted beam intensities for (a) U, (b) Th, and (c) Pb. (d) The complex changes in intensity observed for Pb and U generate 206 Pb/ 238 U ratios that are nonlinear, perhaps exponential although some sinusoidal behavior is apparent. (e) Despite the variations illustrated in Figures 3b and 3c, calculated 208 Pb/ 232 Th ratios appear to decrease linearly with time. (f) A repeat of the experiment, with five separate ablations using a spot diameter of 71 mm, illustrates the complex changes in fractionation patterns with this change in spot diameter. The 206 Pb/ 238 U ratios produced here decrease after 45 s, and the variations are not well modeled by an exponential curve. 7of36

8 Figure 4. A schematic illustration of various existing methods of downhole fractionation correction. (a) An empirically derived linear equation is used to correct fractionation in each time slice of the analysis [Horn et al., 2000], producing time resolved downhole corrected ratios. (b) A least squares fit is applied to the data of a single spot analysis to estimate the rate of downhole fractionation with depth, with the y intercept and uncertainty in the fit providing the average and uncertainty, respectively. This method produces a different gradient for each spot analysis and is thus independent of changes in fractionation caused by spot size or matrix effects between analyses [Kosler et al., 2002a]. (c) Individual time slices of each analysis are corrected using corresponding time slices of the standard(s) [Jackson et al., 2004]. Depending on the duration of each time slice, some or all of the temporal resolution may be sacrificed. 8of36

9 corrected using a least squares linear fit (Figure 4b) of the elemental ratio over time. Using this approach, the derived y intercept and its uncertainty provide the corrected ratio and its precision, respectively. Like Horn et al. [2000], instrumental bias was corrected separately via simultaneous nebulization of a Tl/U tracer solution, although other studies have demonstrated that instrumental bias can be accounted for by normalization to standard zircons analyzed in the same analytical session [Chang et al., 2006; Gehrels et al., 2008], or by a combination of these two methods [Klotzli et al., 2009]. The method allows for differences in elemental fractionation behavior between analytical sessions, or between individual analyses due, for example, to matrix related effects. However, this flexibility also means that it may not distinguish between some cases of real sample variability (e.g., gradual transition into a growth zone of different age) and the effects of fractionation. In addition, the lack of time resolved corrected ratios can make it difficult to detect the effects of fractures, inclusions, etc. on results Methods Employing Standard Sample Bracketing [24] The most common method of standard sample bracketing is to correct the sample analysis using a corresponding time interval (for example, relative to laser on ) from a neighboring standard analysis, or the pooled data of multiple standards [e.g., Jackson et al., 2004; Van Achterberg et al., 2001]. In this way, the effects of downhole fractionation are accounted for (Figure 4c), without any requirement to observe or model fractionation behavior. However, because this method takes the average ratio of a time interval in the standard(s) to correct unknowns, the method often reduces the temporal resolution of the data and thus also reduces feedback regarding the validity of the correction, lowering the probability of detecting heterogeneities such as growth zoning, fractures, or inclusions. [25] A similar alternative is the total counts approach, in which all ions measured during an ablation are treated together [Johnston et al., 2009]. Although this approach, which was developed specifically for small volume sampling, is capable of modeling nonlinear fractionation patterns it does assume that fractionation is identical in standards and unknowns, and cannot generate time resolved corrected ratios. As such, it may be difficult to assess the validity of the correction used, or to detect downhole age variability, inclusions, etc. 5. Modeling Complex Downhole Elemental Fractionation [26] Each of the methods outlined above clearly have positive and negative aspects, but they generally rely upon linear variations in elemental ratios with time, which as illustrated above (Figures 2 and 3) may not always be the case. So how can we best retain spatial and temporal resolution, while accommodating more complex fractionation patterns? [27] Philosophically, we believe this can best be achieved by moving away from the tendency of existing methods to rely on fitting data to a presupposed model of fractionation, and instead to first observe the effects of downhole fractionation, then fit an appropriate model to the data, whatever form it may take. To do this, it is not necessary to understand the causes of elemental fractionation, which are clearly both multiple and complex, but only to model their combined effects on elemental ratios. In taking this approach, we implement a standard sample bracketing methodology, using observations of the group of standard analyses within an analytical session to model the fractionation pattern in unknowns. Although this method is free from the extreme reliance on stability of the empirical approach of Horn et al. [2000], it does require careful verification of the assumption that standards and unknowns behave identically. Evidence for the validity of this assumption is provided in Appendix A. We do not employ the simultaneous nebulization of a Tl/U tracer solution, and as such do not discriminate between instrumental bias generated within the mass spectrometer and the laser sampling system. We correct for instrumental bias by normalization to standard zircons analyzed in the same analytical session. Like Gehrels et al. [2008], we use all standard analyses of the session to determine variations in the degree of instrumental bias. We model this variability using a smoothed cubic spline, although a number of other options are available in Iolite (e.g., linear interpolation, average of the session). [28] As a starting point for this study, and as a result of our observations of curved fractionation trends under a range of different analytical conditions (Figures 1c, 1d, and 2d), we employ a model fitting an exponential curve (with the equation y = a + b.exp cx ) to the changes in elemental 9of36

10 ratios with time. To evaluate this model we chose an analytical session of approximately 1 h duration, containing a number of 42 mm diameter spot analyses each of 50 s length. Nine analyses of the zircon standard spaced throughout the run were included for standard sample bracketing purposes. To test the efficacy of an exponential curve fit we combined all standard analyses for the session to produce an average 206 Pb/ 238 U ratio versus ablation time plot (Figure 5a). This average is more representative of the effects of fractionation than any single standard and has the additional benefits of reducing scatter in the pattern, and thus allowing the calculation of an uncertainty for each time slice of the average. Because we are only interested in the relative change in the ratio with ablation depth, longer term instrumental drift does not affect the result, and can be corrected separately after downhole fractionation correction (provided, of course, that no drift in the pattern of downhole fractionation occurs). The exponential equation was fit to this average pattern using Igor Pro s built in curve fitting function, which incorporates calculated uncertainties on each time slice of the average, and iteratively produces a fit that minimizes chi square using the Levenberg Marquardt algorithm. Figure 5b, which illustrates 206 Pb/ 238 U ratios of the zircon after correction using the exponential equation derived in Figure 5a, demonstrates the effectiveness of the model, with corrected ratios showing no observable variability with ablation time. [29] In order to objectively test the applicability of the fractionation model, three Temora 2 zircon grains analyzed in the same session were used as secondary standards. Again, 206 Pb/ 238 U ratios corrected using the same model exhibit no discernable variation with time (Figure 5c), and the weighted average of the ratios (corrected for instrumental drift using the zircon analyses) of ± is indistinguishable from the true 206 Pb/ 238 U ratio of [Black et al., 2004]. A detailed comparison of the effectiveness of linear and exponential models, including tabulated data, is provided in Appendix A. [30] The success of a model incorporating an exponential curve fit is encouraging, but there is no a priori reason for downhole fractionation to follow Figure 5. Data for nine 60 s ablations of the zircon standard using a 42 mm diameter spot. Individual baseline subtracted data (pale colors) are combined to produce an average ratio for each time segment (black line), which were then used to fit model curves (red line). (a) Raw 206 Pb/ 238 U variations and an exponential curve fit. (b) Corrected 206 Pb/ 238 U ratios show no variability with time, indicating that the fitted exponential curve is a suitable model for downhole elemental fractionation. (c) The 206 Pb/ 238 U ratios of three Temora 2 analyses from the same analytical session corrected using the same exponential curve equation. The weighted average of the analyses (calculated using Isoplot [Ludwig, 2001]) of ± is well within error of the accepted value of [Black et al., 2004]. 10 of 36

11 a simple pattern (such as linear, or exponential, changes with ablation time). Indeed, the data in Figure 2d and Figure 3f cannot be satisfactorily modeled using an exponential curve, and are excellent examples of cases that would benefit from a more versatile approach. To this end, we extended the above method by using a smoothed cubic spline fit, which should be capable of reproducing any observed downhole fractionation trend. The approach is essentially the same as that described above, but instead of an exponential curve a smoothed cubic spline was fit to the data using a built in Igor Pro function called Interpolate2. [31] Although long ablation times are uncommon in routine U Pb zircon dating by laser ablation, since drill rates are generally relatively fast, we employed 55 mm diameter spot analyses of 2 min duration in order to exhaustively test the potential of this approach. As with the exponential curve modeling described above, pairs or triplets of the zircon standard were spaced evenly throughout the experiment, and data from these multiple analyses were combined to produce an average pattern of downhole fractionation (Figure 6a) for the session. Clearly, changes in fractionation pattern with ablation time are complex, and simple models employing a linear or exponential fit would be incapable of effectively modeling these variations. To produce a more appropriate model, a smoothed cubic spline was calculated from the average pattern of the standards. This spline accurately models the fractionation response observed in the standard analyses and, when used to correct fractionation in the standards (Figure 6b), produces corrected ratios that do not vary with ablation time (in contrast, if a simple linear model is employed the average of the standards varies by up to 8% with ablation time). [32] The applicability of the model to other zircons was then tested using analyses of the Temora 2 zircon as a secondary standard. Despite the long (2 min) duration of analyses, the six spot analyses for the session have a fractionation pattern (Figure 6c) very similar to When corrected using the smoothed cubic spline calculated from the average pattern (Figure 6a), 206 Pb/ 238 U ratios of the Temora 2 analyses do not vary with hole depth (Figure 6d), indicating the validity of the fractionation correction employed. When combined to generate a concordia age, the six Temora 2 analyses yield a concordant result of ± 2.7 Ma (Figure 6e), which is statistically indistinguishable from the accepted TIMS age for Temora 2 of ± 0.3 Ma [Black et al., 2004]. [33] This experiment was repeated using a spot size of 42 mm, with a total of 8 Temora 2 analyses for the session, bracketed by 12 ablations of the calibration zircon (all analyses were again of 2 min duration). A similar downhole fractionation pattern was observed (illustrated in Figure 7b), although the overall change in elemental ratio was 30%, in comparison to a variation of 20% in the earlier experiment (Figure 6a). Once again, a smoothed cubic spline, calculated from the average downhole pattern of the zircon standard, was used to correct all analyses. After correction of downhole fractionation and instrumental drift, the 8 spot analyses of the Temora 2 standard yielded a concordia age of ± 2.4 Ma, which is within 1% of the accepted age. We therefore conclude that even the more complex patterns of downhole fractionation remain relatively constant throughout an analytical session (and at a given spot size), and that this behavior can be modeled and then applied to unknowns in the same session providing a robust correction for downhole effects. 6. Depth Profiling as an Example Application of the Method [34] One immediate benefit resulting from accurate correction of downhole elemental fractionation is the potential to resolve downhole age variation in complex zircons. To investigate this possibility we simulated the effects of age zoning within a natural zircon grain by bonding together polished wafers of the Plesovice zircon standard ( 337 Ma [Slama et al., 2008]) and the zircon standard ( 1063 [Wiedenbeck et al., 1995]). We then created a depth profile of this zoned sample by ablating through the 10 mm thick Plesovice layer into the underlying grain (Figure 7a). By employing a spot ablation of 2 min duration the laser drilled to a total depth of 40 mm, sufficient to sample both of the zircon standards. This experiment can be considered a worst case scenario because the Plesovice zircon has a U concentration more than 5 times greater than the zircon (465 ppm, compared to 81 ppm), so any contamination of the portion of the signal by Plesovice (due to memory effects or ablation of the pit walls) would be amplified by the greater U concentration of the latter. [35] The depth profiling test was conducted within the same analytical session as the second batch of Temora 2 standards described above (see Figure 6f), using a 42 mm laser spot, and a duration of 2 min per ablation (equating to pit depths of 40 mm). The 11 of 36

12 Figure 6. Ten 2 min spot analyses (colored lines) of the zircon standard using a 55 mm diameter spot, combined to produce an average (black line). (a) The 206 Pb/ 238 U ratios with a model of the fractionation pattern generated by fitting a smoothed cubic spline to this average wave (red line). (b) Corrected 206 Pb/ 238 U ratios illustrating the appropriateness of the chosen model. (c) Six analyses of the Temora 2 zircon analyzed in the same session in order to independently assess the approach. Raw 206 Pb/ 238 U ratios show very similar fractionation patterns to the zircon. (d) Corrected data using the smoothed cubic spline generated from analyses. (e) When combined, the six Temora 2 analyses yield a concordia age well within 1% of the accepted age of Ma [Black et al., 2004]. (f) Repeat of the experiment using a 42 mm diameter spot. A total of eight Temora 2 analyses, bracketed by 12 ablations of the zircon standard, produces a concordia age of ± 2.7 Ma, again well within 1% of the accepted age. 12 of 36

13 Figure 7. (a) Schematic illustration of a zircon sandwich employing polished slices of the (blue) and Plesovice (green, 10 mm thick) zircon standards. Ages and U concentrations for the Plesovice and standards are from Slama et al. [2008] and Wiedenbeck et al. [1995], respectively. (b) Uncorrected (but baseline subtracted) 206 Pb/ 238 U ratios plotted against time. A total of 12 spot analyses of the zircon (pale colored lines) was combined to produce an average pattern of downhole fractionation (black line). This average was used to model downhole fractionation for the session using a smoothed cubic spline (red). (c) Results of a 2 min spot ablation of the zircon sandwich, plotted against time (in seconds). The red trace shows 206 Pb/ 238 U ratios corrected for downhole fractionation and instrumental drift, and the blue, orange, and green traces show changes in baseline subtracted intensities of 238 U, 206 Pb, and 208 Pb (linear scaling). See section 6 for details. smoothed cubic spline fit to the average of 12 analyses of the zircon (Figure 7b) described above was used to correct all analyses for downhole fractionation. Figure 7c illustrates the 206 Pb/ 238 U ratios in the depth profile after correction for downhole fractionation and instrumental drift, together with relevant baseline subtracted beam intensities. The first 30 s of the analysis samples only the Plesovice wafer, and yields a concordia age of ± 8.7 Ma, statistically indistinguishable from the accepted age. The following 20 s of the analysis represent ablation through the wafer boundary/epoxy, and coincides with a noticeable increase in 208 Pb due to unavoidable common Pb contamination in the boundary layer. By 70 s the elemental ratio reaches a plateau, and a concordia age of the following 40 s yields an apparent age of ± 9.1 Ma. We attribute the offset between this apparent age and the accepted 206 Pb/ 238 U age for of 1065 Ma to minor sampling of the Plesovice wafer at the pit walls (note that the rapid wash out of the Helex cell means that memory effects are unlikely to have affected the result). Based on the published U concentrations and 206 Pb/ 238 U ratios of each zircon, we calculate this offset to represent a 0.3% contamination of the result by Plesovice. Given that this is well within the normal reported uncertainties of U Pb zircon dating of 1 to 4% [Jackson et al., 2004; Klotzli et al., 2009; Kosler and Sylvester, 2003], such contamination is unlikely to significantly perturb depth profiling results for natural samples. [36] The success of this depth profiling example clearly demonstrates the benefit of employing versatile downhole fractionation models, which 13 of 36

14 produced accurate ages, despite long ablation times and an unusually complex fractionation pattern. 7. Quantifying the Uncertainty of Complex Fractionation Models [37] Although the methods that we have described here for the modeling and correction of downhole elemental fractionation do not readily lend themselves to a strict arithmetic propagation of uncertainties, we suggest here an alternative and robust methodology employing analyses of the primary standard within the session to estimate the propagated uncertainty of individual analyses. This approach has the advantage of being independent of the downhole fractionation model employed, and inherently propagates most sources of analytical uncertainty for the session. However, because it assumes that the primary standard has identical behavior to unknowns it cannot be used to determine whether differences in zircon matrix, age or U content can affect the ages produced. As such, secondary zircon standards are still required to assess the overall accuracy and reproducibility of analyses. [38] Our method for the estimation of analytical uncertainties is similar to the approach conventionally used to assess external reproducibility using secondary standards, with two significant differences: [39] 1. In lieu of a secondary standard, we remove each primary standard ablation in turn from the pool of primary standard analyses and recalculate its corrected ratios independently of the primary standard pool. By removing this analysis from the standard data used to normalize results, it is corrected for downhole elemental fractionation and instrumental drift in a manner identical to the treatment of unknowns (Figures 8a 8f). After sequentially treating each standard analysis as an unknown in this way, a pool of pseudosecondary standards can be generated, and these can be used to assess the analytical uncertainty. [40] 2. Instead of estimating a global uncertainty for the entire method, which is then assigned uniformly to all analyses, we generate an excess uncertainty for each analytical session that is intended to account for all unquantified sources of analytical uncertainty, then combine this with the internal precision derived for each spot analysis. To estimate the magnitude of this excess analytical uncertainty, we calculate the degree of scatter in the pool of pseudosecondary standards (Figures 8g and 8h). If the internal uncertainties of the pseudosecondary standards are insufficient to account for the scatter between analyses, the group will have an MSWD (mean of the squared weighted deviates) of greater than 1, indicating that an additional source of uncertainty exists in the population. This excess error (predominantly associated with downhole fractionation correction and drift correction) can be estimated by calculating the additional uncertainty for each analysis required to produce an MSWD of 1 for the pseudosecondary standards (Figures 8g and 8h). By combining in quadrature this excess uncertainty with the internal error of individual spot analyses, a total error for each analysis is generated. This approach then takes into account differences in internal error between samples, and thus best reflects the actual uncertainty of individual spot analyses. [41] The uncertainties generated in this manner will reflect the limitations of downhole fractionation correction, as any variation in fractionation between spot ablations will be reflected in the scatter of corrected ratios. Likewise, the use of an inappropriate model for changes in the ratio with hole Figure 8. Illustration of the error propagation procedure. (a f) The basis of the method, using five fictitious standard analyses as an example. Figures 8a and 8d show calculated values for the five standards prior to treatment, and instrumental drift modeled by cubic splines with and without smoothing. In Figures 8b and 8e, an individual standard analysis is removed from the group of standards, allowing it to be treated as an unknown (the second standard analysis in this case), after recalculation of instrumental drift using the remaining standards. In this way, a pool of pseudosecondary standards is generated (Figures 8c and 8f), with the scatter in this pool reflecting uncertainties in both drift correction and downhole fractionation correction. In this case, the smoother cubic spline employed in case 2 produces less scatter and is thus a better model of instrumental drift. (g and h) Calculation of excess uncertainty for a session. Figure 8g shows a pool of 15 pseudosecondary standards, with associated internal errors. An MSWD of 3.2 for the pool indicates that additional sources of uncertainty exist. To estimate this excess uncertainty, an increasingly larger value (dashed error bar in Figure 8h) is combined (in quadrature) with the internal uncertainty of each analysis, until the population has an MSWD of 1. The combined uncertainties account for all scatter in the population, meaning that all sources of excess uncertainty (represented by the calculated value) have been accounted for. This value is then propagated with the internal uncertainties of all analyses for the session. The 3rd and 4th values illustrate how excess uncertainty has less impact on imprecise results and that total uncertainties vary between individual spots, reflecting both internal and excess uncertainties. 14 of 36

15 Figure 8 15 of 36

16 depth will contribute additional scatter to the pseudosecondary standard pool, and will result in a larger calculated excess uncertainty. In a similar manner, any error in the modeling of instrumental drift will be reflected by a larger scatter in corrected ratios of the pseudosecondary standards, again increasing the excess uncertainty required to produce an MSWD of 1. [42] Although this method has a significant processing burden, the capabilities of current computers are more than sufficient for the automatic calculation of uncertainties in this fashion, and errors for all corrected elemental and isotopic ratios in Iolite s U (Th) Pb dating module are treated in this way. The uncertainties of all corrected ratios reported here were calculated using this method, including the Temora 2 concordia ages of Figures 6e and 6f. [43] Despite the capacity of this method to produce accurate estimates of analytical uncertainty, however, we note the following caveats: [44] 1. Any differences in U concentration and/or age between the primary standard and sample unknowns may alter the relative impact of uncertainties in the subtraction of background noise (i.e., signal to noise ratio), and counting statistics. [45] 2. Analyses of the reference standard should be evenly spaced throughout the run to best reflect the effects of instrumental drift correction on unknowns. [46] 3. To reliably quantify the excess uncertainty for a session, a suitable number of analyses of the primary standard are required. In Iolite s U Pb package, if too few standard analyses are available the potential for underestimation of the excess uncertainty is catered for by increasing the calculated value gradually, from no increase for 15 or more standards, to a factor of two for 6 standards. If less than 6 standards are used, the software will still allow the user to produce results, but a conservatively large excess uncertainty will be applied to each corrected ratio. [47] 4. The user is of course always encouraged to employ a number of secondary standards during analytical routines, as this is the only way to assess the external reproducibility of results. The method described here is simply intended to estimate realistic uncertainties for individual spot analysis in a robust, reproducible and objective way A Note on Internal Versus Systematic Uncertainties [48] In considering uncertainties and their propagation it is important to distinguish between random and systematic sources of uncertainty. Any systematic uncertainty is one which generates a bias in a data set, an obvious example for U Th Pb geochronology is the uncertainty in the known age of a reference standard. Such systematic uncertainties must be treated differently when generating a weighted average from a group of individual analyses (e.g., a group of unknown zircons from a single igneous rock sample). If the systematic component is propagated into each individual uncertainty prior to the generation of the weighted average the result will have an unrealistically small estimated uncertainty. This is because the systematic uncertainty has been treated as though it were random, and will have been reduced in the weighted average process (by the square root of the number of analyses in the weighted average). Instead, such systematic errors must be kept separate from the weighted average calculation, then propagated into the uncertainty afterward. Differences in the U concentration or age of zircon standards and unknowns will also contribute a systematic uncertainty to analyses. [49] The excess uncertainty generated using the pseudosecondary standard approach described above is unable to detect systematic uncertainties, which would bias the group of analyses without introducing any additional scatter to the population. Because the pseudosecondary standard approach only considers data scatter, and not accuracy, such biases will not affect the MSWD, and thus will not be incorporated into excess uncertainty calculations. As such, any excess uncertainty generated using the method must be random, and can therefore be propagated with other uncertainties (e.g., internal precision) prior to any weighted average calculation Correlation in Uncertainties [50] In addition to the magnitude of uncertainties, the accurate estimation of error correlation is also of importance. Although equations exist for the calculation of error correlations based on the uncertainties of bulk analyses, which are often used to great effect in single zircon TIMS dating [see, e.g., Schmitz and Schoene, 2007], the availability of large numbers of individual integrations ( scans ) in laser ablation methods offers the opportunity to employ calculations based upon the raw data populations themselves. To calculate error correlations from the data, all individual time slices for the chosen interval of the sample are combined (for example, if 40 s of data were chosen for a spot analysis, with a data acquisition rate of 16 of 36

17 8 cycles per second, this would represent a population of 320 individual data points). When the two ratios of interest (e.g., corrected 206 Pb/ 238 U versus corrected 207 Pb/ 235 U) are plotted on an X Y diagram, the degree of correlation in the data is identical to the error correlation between the ratios. When calculated in this way, error correlations between individual analyses of a single sample can vary significantly (e.g., error correlations of spot analyses in Figure 6e vary from 0.13 to 0.31, and from 0.09 to 0.29 in Figure 6f), and error correlations themselves vary dramatically with changes in U concentration and age. 8. Conclusions [51] U (Th) Pb zircon geochronology by laser ablation ICPMS is both rapid and relatively inexpensive, and has already become an extremely popular and widespread method. At present, the single largest constraint on the accuracy and precision of the technique is the correction of downhole elemental fractionation. Patterns of fractionation with hole depth can vary dramatically both between laboratories, and with changes in operating conditions, and there is no a priori reason for them to be linear. In fact, nonlinear patterns of varying complexity have been observed in multiple laboratories. [52] We suggest that as a general approach, users should attempt to develop an appropriate model of downhole fractionation based upon observations of their own data during each analytical session, instead of attempting to fit the data to a preconceived fractionation model. Employing this strategy, we have demonstrated that models of nonlinear fractionation, such as an exponential curve, or smoothed cubic splines, can be used to efficiently correct for the effects of complex downhole fractionation. These models are capable of producing high quality ages, accurate to within 1% of accepted values, and can be used for demanding applications, such as depth profiling, without compromising data quality. [53] Careful attention should be given to the propagation of analytical uncertainties, particularly in relation to downhole fractionation and instrumental drift correction. We provide a method that allows the estimation of analytical uncertainties, using only a single reference standard, in a manner that best reflects the actual uncertainties of individual spot analyses. [54] The methodology employed here, including uncertainty propagation, error correlation, is incorporated into the U (Th) Pb dating module of the Iolite software package. Further information for Iolite, a freeware program designed for the reduction of time resolved data, is available from iolite.earthsci.unimelb.edu.au/. Appendix A: A Comparison of Linear and Exponential Models of Downhole Fractionation [55] In Appendix A, we attempt to address in greater detail the potential age effects of using different models of downhole elemental fractionation on zircon data generated by LA ICPMS. [56] In theory, if identical sampling conditions are used for matrix matched standards and unknowns, the use of a standard bracketing approach should always produce accurate ages, inherently corrected for all sources of bias, including downhole fractionation. There are several reasons why this is not the case in practice, but the most significant is that the user is often unable to sample exactly the same period of data for each analysis. Thus, any variations in corrected elemental ratios with ablation time (as a proxy for hole depth) have an impact on the final calculated age. Common reasons for wishing to use only a portion of the entire analysis include (1) contamination of the grain surface by common Pb; (2) insufficient grain thickness, meaning that the laser drills through the back of the zircon grain and begins sampling epoxy/other minerals in a thin section; and (3) penetrating through one zone of a grain into a region of different age. [57] Here we compare linear and exponential fractionation models on a group of 10 Temora 2 grains, analyzed as a secondary standard during a normal analytical session. The downhole fractionation was modeled using 13 analyses of the zircon, grouped in pairs or triplets throughout the session which also included unknowns in addition to the Temora secondary standard. The normal data reduction methods of Iolite s U Th Pb DRS (described in Appendix B) were used, but in order to assess variability between analyses the propagation of excess uncertainties was avoided. As such, all uncertainties quoted are likely to be approximately half of their propagated values. [58] When fitted to the average of the analyses, there are clear differences between the linear and exponential models of fractionation (Figures A1 and A2). This is well illustrated by the residuals to the fit, which are a proxy for the effect of 17 of 36

18 Figure A1. Linear fractionation model (screen capture from Iolite su Th Pb DRS). The model was generated using a least squares linear fit through the average (black) values of the zircon. The resulting fit (red line) is not an accurate model of changes in the ratio with ablation time (x axis) and generates significant bias in the resulting corrected ratios, illustrated here using the residuals of the fit to the average. The first and last 10 s of analyses are undercorrected by up to 15%, while the range between 10 and 40 s since shutter open are overcorrected by 5%. When the residuals to the fit are plotted as a histogram, it can also be seen that the model results in a skewed data distribution that may affect statistical methods that rely on normally distributed data (e.g., mean and standard deviation). Figure A2. Exponential fractionation model (screen capture from Iolite s U Th Pb DRS). The model was generated by fitting an exponential curve (equation in blue) through the average (black) values of the zircon. The resulting fit (red line) effectively models changes in the ratio with ablation time (x axis), producing corrected ratios with no detectable bias with ablation time and a normal bell curve distribution when plotted as a histogram. 18 of 36