It has long been noted that during spot ablation of zircon, time resolved analytical (TRA) measurements of 206Pb/238U are found to increase especially for relatively narrow spots. The bias increases as a function of the aspect ratio of the pit with an early rapid rise changing to a slower linear rise, eventually levelling off and then dropping as emission becomes much weaker (Paton et al., 2010; Eggins et al., 1998). Downhole fractionation appears to be reduced with shorter pulse duration, the femtosecond laser showing less fractionation than nanosecond lasers (Kimura et al., 2015).

Ablation bias still appears to be poorly understood. It depends on interaction of the sample with the laser, rather than plasma conditions, and is the most limiting for accuracy. Eggins et al. (1998) measured the fractionation of volatile Pb and Bi over refractory U and Th as a function of ablation pit depth in NIST612, as well as the geometry of the pit. They showed that Bi/Th increases with pit depth (downhole fractionation) until an aspect ratio (depth/surface diameter) of about 3:1 where the bottom of the pit had tapered to a diameter of about 1/3 of that at the surface and signal intensity was reduced by an order of magnitude. Subsequently, downhole fractionation reversed with Bi/Th decreasing. They concluded that the principal mechanism for elemental fractionation is condensation of the more refractory elements on the walls of the pit. In contrast, Kroslakova and Günther (2007), after aerosol dilution experiments, concluded that elemental fractionation is at least partly a result of interaction of the ablated material with the plasma.

The ZrO2–SiO2 phase diagram determined by Butterman and Foster (1967) shows the appearance of a melt, consisting of ZrO2 and an SiO2-rich liquid, at about 2250 °C for the zircon composition with a single liquid above 2400 °C. As shown by Davis (2008), zircon decomposes leaving these two phases below 1500 °C in the presence of excess silica. Kosler et al. (2005) concluded that during ablation of zircon the retention of U in the dissociated ZrO2 phase with release of volatile Pb is the reason for increasing Pb/U implying that fractionation in zircon is an effect of mineralogical changes in the target. However, this does not explain why the least ablation bias is seen at the start of a 206Pb/238U time resolved analytical (TRA) profile for zircon.

It is instructive to carry out a rough calculation of the expected temperature increase of the target during ablation. This should be a function of the laser energy flux, expected absorption volume and specific heat of the mineral. A typical laser configuration delivers about 30 µJ per pulse to a 30 µm diameter target. Assuming that the energy is absorbed in a 0.1 µm layer, roughly consistent with observed ablation rates, a target with a heat capacity typical of zircon (0.75 Jg-1C-1), would be exposed to energy an order of magnitude greater than that required for melting (estimated temperature increase of about 10 000 °C assuming constant specific heat). At this energy flux, it is likely that all minerals boil and produce a transient ablation cloud.

A thorough study of ablated particle composition and size distributions determined using time of flight mass spectrometry is given in Adamson et al. (2026). For the purpose of modelling the Pb/U fractionation process, we consider four components: a melt pool at the base of the pit, an ablation cloud whose composition reflects measured laser induced elemental fractionation (LIEF; Adamson et al., 2026), fallback material that accumulates around the pit, and deposit within the pit. The cloud consists of melt droplets with a range of sizes and compositions. One might expect that fallback material would accumulate a relatively high proportion of large particle sizes and that the finer particles would be preferentially entrained into the plasma. Adamson et al. (2026) selectively ablated fallback material using low laser fluence (dusting) and found that it delivered a higher proportion of fine material into the plasma than that from the pit. However, since the fallback material was re-ablated, this may not represent its original particle distribution. Both Adamson et al. (2026) and Kaser et al. (2025) show that average fallback material is enriched in volatile elements including Pb, but this does not rule out the possibility that fallback could contain a dominant fraction of depleted material during part of the ablation process.

Melt, along with Pb vapour, should boil off during irradiation down to a depth at the base of the pit where temperature falls below the boiling point, then be quenched by rapid loss of heat to the mount leaving a Pb-depleted layer. Zircon ablation pits typically show a layer of what appears to be solidified melt at the base and along the walls (Fig. 2). Although this relies on morphology rather than high-resolution analytical techniques, we assume that it is mostly glass. The glass layer may not be visibly obvious with relatively undamaged zircon but it can be made obvious by rotating the laser beam around a circle within the pit as shown in Fig. 2B, which has the effect of creating flow-like structures.

To test the hypothesis of a Pb depleted melt, a wide (130 µm) pit was ablated into KL zircon with 200 pulses at 10 Hz, 3.5 Jcm-2. It was hoped to form a melt layer around the wall that was thick enough to sample (10 µm or greater). However, the wall layer proved to be only a few microns wide. Examination of the pit shows that the sides are smooth and somewhat wavy in shape whereas the base is partly floored by an irregular layer of what appears to be solidified congealed melt lying on top of a smooth surface (Fig. 3A). Material in the pit was analyzed by passing a 30 µm beam across it under standard conditions (see Fig. 3A for scan footprint). The scan shows an order of magnitude reduction in 238U signal intensity within the pit, (Fig. 3B) which is partly due to defocusing but may also be because of limited coupling of the laser to the highly uneven surface. Most importantly, there is a decrease in 206Pb/238U ratio of up to 40 % (Fig. 3C, Supplementary Data File 2) with wall-adjacent material showing the lowest values in both emission and ratios. It is therefore clear that the basal melt is depleted in Pb and might represent at least part of the reservoir that balanced emitted Pb-enriched material.

A potential approach to correcting ablation bias might be to measure the ratio of another pair of elements of different volatility, besides Pb and U, on the same grain. A possible candidate is Yb since it is the most volatile of the rare earth elements. HREE are enriched in zircon and are easily measured in most cases. If one could detect Yb/Yb* significantly higher than 1 (Yb* is the interpolated value of measurements of chondrite-normalized Tm and Lu, the adjacent REE below and above Yb) and could demonstrate a proportional relationship with Pb/U bias, the latter could be corrected. Unfortunately, no significant Yb anomaly was detected in zircon within the percent resolution of our data (Fig. 3D), indicating that Yb is insufficiently volatile compared to Pb.

The usual way to correct for all biases is to measure a standard of similar composition (matrix-matched) under the same conditions as the sample, fit all or part of the 206Pb/238U time resolved analysis (TRA) profile for the standard to a curve, extrapolate it to zero time to determine the total bias correction, and apply this to the unknown using a similar extrapolation of its data (Paton et al., 2010; Gehrels et al., 2008). A complication with zircon is that, although most natural zircon is of similar composition, the crystal structure can be damaged by alpha recoil associated with the decay of isotopes in the U and Th decay series. In cases of old high-U zircon the crystal structure can be reduced to a disordered (metamict) state, which should reduce the melting temperature, increase the amount of ablated material and modulate the profile. Zircon commonly shows oscillatory zoning of U, which can cause variability in damage and degree of melting by the laser. A mitigating factor is that highly damaged zircon is likely to be Precambrian in age where, because of the shape of the U–Pb concordia curve, ages determined from 207Pb/206Pb ratios are much more accurate and precise than those based on 206Pb/238U measurements. Isotope ratios from a single element are much less biased by ablation than those involving Pb and U so the TRA profiles for 207Pb/206Pb are usually constant over the course of an analysis. As the sample age becomes younger, 207Pb/206Pb age precision is increasingly degraded because of the shallow angle of the concordia curve relative to the Pb isotope ratio measurement line. For Phanerozoic ages the 206Pb/238U system must be relied on but younger zircon should generally have less damage, especially if samples are annealed before being ablated. Taking data from scan lines rather than spots is one approach to mitigating this problem but may also be affected by some degree of ablation bias (Fig. 1). In any case scans are not possible with most zircon, which consists of grains no more than a few hundred microns in size, which may have complex structures that need to be analyzed with spots.

The mechanism of progressive Pb/U fractionation must be understood for there to be any possibility of using complete data sets to accurately constrain the unbiased value of the 206Pb/238U ratio. Potentially useful information can be inferred about the ablation process from the cross-sections of actual pits documented by Eggins et al. (1998) using NIST612. The 300 pulse pit (Fig. 6 in Eggins et al., 1998) is most comparable in dimensions to a typical analytical pit in zircon. Although the NIST612 glass has a much lower melting point than zircon, we assume that ablation produces zircon pits that are at least qualitatively similar.

All pits are slightly flared at the mount surface with diameter decreasing as the base is approached. The walls of the pit appear to be covered by a uniform thickness (about 5 µm) of brighter material, which consists of two thinner (about 0.2 of the total wall thickness) relatively bright sub-layers on the outside and inside, with a greyer layer in between. The available SEM images do not permit ruling out the possibility that at least one of the layers represents an imaging artifact. If so, this is most likely to be the inner layer. The outer layer has the highest and most consistent brightness. Both bright layers merge into a single convex-shaped layer over the base.

The inside exposed surface of the pit can be seen in Fig. 3b of Eggins et al. (1998) to consist of flow banded material, which could represent deposit or wall melt from the ablation plume. The brightness of secondary electron images is usually a result of electrons being emitted from surfaces at high angle. This suggests that the thin bright layers or layer, if only one, enclose numerous surfaces left from fracturing or boiling.

The pit sections in Eggins et al. (1998) were exposed by ablating between two pieces of NIST610 glass fitted together along polished surfaces. It is therefore conceivable that the exposed wall features might have resulted from penetration of the ablation cloud along the connecting surface but they seem much too regular to be explained this way.

Based on Fig. 2 of Eggins et al. (1998), the diameter of the laser beam is about equal to the opening of the pit. The sheath of glass observed at the edges of pits in zircon (Fig. 2, this work), approximately corresponds in thickness to the pit wall layers seen in Fig. 6 of Eggins et al. (1998). Their thickness remains constant with depth in pits over a wide range of aspect ratios.

The volume of the inner layers on the walls is roughly comparable to what might be expected from deposits left inside during excavation of the pit based on the assumption that deposit is proportional to wall area relative to the area of the pit opening as well as the observed drop in signal intensity. Wall area increases as the pit deepens, sequestering more deposit, but its thickness should not change rapidly and the fluted shape of the wall near the surface may have been eroded out by expansion of the ablation cloud.

Wall deposits may be represented by the 2 inner layers while the outer bright layer represents the edges of the basal layer at previous depths, covered with semi-liquid deposit. The photos of cross sections in Eggins et al. (1998) also show the buildup of fallback deposit, which continues to accumulate past aspect ratios well above those used for zircon analysis.

To summarize, three reservoirs are recognized as possible contributors to Pb/U signal fractionation: basal melt, wall deposit and fallback. Volatilization of melt at the base (bright outer layer in Fig. 6 of Eggins et al., 1998) is probably the main if not the only contributor to the signal and may be the only reservoir affected by recycling. Pb is considerably more volatile than U and significant evaporation should occur from boiling melt at the base. Ignoring the effect of fallback, melt from the first pulse should be relatively depleted in Pb, producing a complimentary high 206Pb/238U signal. Re-ablation of the Pb depleted melt by the second pulse should produce a signal with lower 206Pb/238U bias and so forth until the melt fractionation reaches isotopic equilibrium with the sample and there is no signal fractionation. This by itself would predict an initial high and decreasing Pb/U fractionation but observed signal fractionation profiles are increasing, at least past the first few pulses, is so the effect of melt fractionation must be offset by other factors, most likely recycling.

Experiments collecting the ablated fraction show that it consists of solidified micro-droplets (Kosler et al., 2005), which would have an enormous surface area. Although their interiors should be Pb-depleted, they provide the main surface onto which Pb vapour is likely to condense and therefore should provide a Pb-enriched signal. The strong positive relationship between ablation bias and aspect ratio of the pit suggests that deposition of part of the ablation cloud either on the pit wall and/or as fallback plays a major role. Larger melt droplets should be less depleted in Pb and should be preferentially deposited as fallback. Smaller droplets may be deposited against the walls of the pit and if not recycled would contribute to fractionation of the signal.

A simple conceptual sketch of one possible excavation process is shown in Fig. 4A. The first laser pulse leaves a shallow (∼0.1µm) pit with a Pb-depleted layer on the base and a small amount of possibly Pb-enriched material along the rim wall as well as fallback material deposited outside the pit, which cannot be recycled. As mentioned above, fallback is visually seen to accumulate throughout an analysis. This complicates modelling if fallback contains significant fractionated material. An argument against this would be that the coarsest particles are likely to contribute to fallback whereas the finest are most likely to have lost Pb and should be entrained in the He flow. Fallback should not increase with pit depth so it is difficult to see it as a primary cause of increasing fractionation. We therefore choose to ignore fallback in the modelling and assume that it is constant after the first few pulses.

In Fig. 4A the second laser pulse ablates much of the depleted material in the base of the pit while material previously deposited on the walls absorbs energy from the beam while being re-ablated, which results in the diameter of the flat base decreasing with depth. This exact process is unrealistic since it implies total recycling of deposit in the pit and recursive modelling results in a pit that narrows much too fast, with the base disappearing at an aspect ratio (depth/diameter) of about 0.2. However, recycling might be limited by the steep angle of the wall. The schematic process shows that narrowing of the pit could in part be an effect of sculpting the target material rather than just the buildup of deposit. Since Pb/U ablation bias rises with pit depth, it is likely that fractionated ablated material is progressively deposited against the pit wall and not recycled. In Fig. 4A, this implies that the beam does not efficiently couple to the steep surface of the deposit.

As shown schematically in Fig. 4B, successive laser pulses will form clouds of ablated target material, some of which may include a proportion of previously fractionated deposits, which would impose a Pb-depleted fractionation on the cloud. Formation of new deposit from the cloud, either within the pit or as fallback, will impose a net Pb-enrichment, which is what is measured. As mentioned above, most pit deposit might also not be recycled because of the steep angle of its surface relative to the laser beam. The relative amount of material deposited on the wall and as fallback, possibly modified by variable Pb/U fractionation and degrees of re-ablation of previous deposits, should be proportional to the difference between the measured signal attenuation curve and what the signal would be if there was no deposition, assuming that equal amounts of material are ablated by each pulse. The conceptual model suggests that emission might be lowered as the basal area of the pit becomes smaller. This would be partly offset if the outer beam rim is reflected off the sloping wall onto the base. Eggins et al. (1998) noted that the excavation rate of pits increased with pit depth, although their measured rate of increase was not sufficient to maintain the same ablation volume with each pulse.

238U could be used to represent the ablation signal if its concentration were uniform. However, U is typically zoned in zircon. Hf was also found to be zoned, following a similar pattern to U. A Zr or Si oxide species must be used so as not to overload the detector. Si-oxides have a high background due to the use of a silica plasma torch. 90Zr16O typically produces a signal 106(ZrO+) comparable to that from 238U and is therefore ideal. The suggestion that the 206Pb/238U profile is controlled by increasing sequestration of depleted material is supported by the fact that the ZrO signal loss (1 minus the signal normalized to an assumed zero-loss value), has a similar (inverted) shape to the 206Pb/238U profile at least for undamaged zircon. This is illustrated below with data on zircon grains from samples KL and DD91-1.

To acquire useful data from the earliest pulses, measurements were carried out in which single laser pulses were fired at the sample spot each 5 s (0.2 Hz) and the signals continuously measured on 106ZrO (10 ms), 206Pb (20 ms) and 238U (10 ms). A similar single-pulse approach was suggested by Cottle et al. (2009) for routine dating of zircon. To assure stable emission, the laser was left running at 10 Hz with the beam blocked, and a 5 s warm-up time assigned between single pulses. One spot was programmed with 300 passes (pulse plus warmup), which required 1500 s to fully analyze. Software to remove baseline noise and integrate each pulse is given in Supplementary Data File 3 along with results. The pulse profiles were averaged to give the instrument response functions for each mass signal, which are found to be indistinguishable after normalization (Fig. 5). If Pb continuously evaporated from a melt phase within the pit, the average 206Pb curve should appear broader than the others, which is not the case. Similar measurements were carried out at 10 Hz on the same samples and gave similar 206Pb/238U profiles after signal stabilization.

Analytical profiles for 106ZrO and 238U from KL and DD91-1 are shown in Fig. 6A, B and C, D, respectively. Data are presented in Supplementary Data File 3. The assumed zero-loss signal intensities used for normalization of ZrO and U are taken as the maximum recorded signals (Fig. 6A and C). For both samples the ZrO intensity is found to increase to a maximum at around 10 pulses and then decrease. It is common with data taken at 10 Hz to see a rapid signal rise over the first half-second followed by a more gradual rise that peaks over 1–2 s and then begins to decrease as with the 0.2 Hz data. The 0.2 Hz data show that this peak is not just a property of the transfer function but of the actual signal. This might be a result of increasing coupling of the laser but it more likely suggests that fallback is the largest component of loss when the pit is shallow and ablation cloud expansion has a large lateral component. Successively larger proportions of ablated material might remain in the deepening pit, while the fraction of material contributing to fallback might be expected to decrease as the pit deepens and the ablation cloud is directed more strongly upward. Since the pit always has an opening equal to the beam diameter, some material will always escape. Therefore, the pit must continuously deepen and, with successive pulses, an increasing proportion of the ablated material might be deposited on the walls. This requires that the base of the pit become progressively narrower as confirmed by Eggins et al. (1998).

The main difference between the signal profiles for KL and DD91-1 is that U zoning in DD91-1 creates fluctuations relative to the ZrO curve (Fig. 6B vs. D). The ZrO curve from DD91-1 also shows an increase between pulse numbers 30 and 70. This corresponds to an increase in U concentration so it might reflect higher radiation damage leading to evaporation of more sample by each pulse or fluctuations in the proportion of fallback, the effect of which is discussed below.

Assuming that the total amount of ablated material with each pulse is constant, the drop in ZrO signals with pulse number should reflect sequestration of material within the pit and as fallback. If this material were melted, it may have lost some Pb due to volatilization, which would be reflected as an increase in measured 206Pb/238U, as observed in the ratio profiles for the KL and DD91-1 samples (orange dots in Fig. 7). These show a rapid increase in bias early in the analysis followed by a more gradual quasi-linear increase, which is characteristic of most profiles for zircon.

The measured 206Pb/238U profiles are compared to a function based on 1 minus the normalized ZrO signals shown in Fig. 9B and D (blue dots in Fig. 7). Calculations are shown in Supplementary Data File 3. There are 3 free parameters that can be varied to optimize the fit between the measured and calculated profiles, assuming they are constant over the course of the ablation. One is the normalization factor (Nz0) which is set at the maximum count rate and represents a minimum estimate. The two others are the proportion of Pb vapourized from deposited material and the proportion of recycling of previous deposits. A higher value for Nz0 would uniformly elevate the curve. This is unlikely because the early parts of the two curves fit quite closely using minimum estimates for Nz0. The choice of higher values for Nz0 cannot be offset by decreasing the proportion of vapourized Pb. The presence of Pb-enriched fallback (Adamson et al., 2026; Kaser et al., 2025) would not modify the ablation bias profile if fallback sampled equal proportions of ablated material. This is least likely to be the case during the early part of ablation when the proportion of fallback should be decreasing, as argued above from early increasing signal strength. Assuming that the maximum signal is approximately the time at which fallback becomes a constant proportion of the emitted material, it should have no subsequent effect on the fractionation profile.

Multiplying the normalized ZrO depletion curve for KL by 0.78 results in a good fit over most of the measured profile, while a factor of 0.90 optimizes the fit for the DD91-1 curve (blue dots in Fig. 7). These factors could represent the fraction of Pb lost from the deposits assuming that there is no recycling.

Both curves are inconsistent with the inference that emission is proportional to the exposed area of the base and therefore decreases. As discussed above, ablation pits are normally seen to taper with depth (Eggins et al., 1998). The green dots in Fig. 7 show the effect of progressively reducing the diameter of the base of the pit down to 0.8 of that at the surface. This would result in progressive decrease of the normalization factor (the total amount of material ablated per pulse), which would result in lower rates of deposition in the equations in SD File 3, causing the latter half of the 206Pb/238U profiles to turn over and begin decreasing. Even if Pb loss were total, the ratio profile would turn over and would rise too fast near the beginning. Recycling would have the effect of further suppressing rise in the profile.

The above data show that in general if not always in detail there appears to be a consistent relationship between the observed 206Pb/238U profiles and signal decay curves for zircon. This suggests the possibility of modelling 206Pb/238U bias. The mathematical expression of a general model for progressive fractionation of 206Pb/238U from zircon using the observed signal decay as a proxy for sequestration of fractionated deposit is developed in Appendix 1 and formulated in Excel in Supplementary Data File 3 as a series of recursive equations. These calculate the Pb fractionation of an ablation cloud after absorbing a previously fractionated target, and the measured value after sequestration of material as pit deposit and fallback. The Pb loss factor Li per pulse is 0 if there is no Pb loss and 1 if Pb loss is total. The proportion of recycling per laser pulse, Ci, in the equations can vary from no (0) to complete (1) recycling where each successive pulse completely ablates the previous deposit. Recycling can only occur within the pit.

The early part of measured profiles is discussed in detail in the next section. Bias does not show the initial decreasing trend expected from fractionation of basal melt. This is most likely due to high recycling of melt when the pit is shallow. Pb/U ratios from the first ten pulses, during which Pb-depletion in the basal melt approaches an equilibrium value such that the vapour is unfractionated, are simulated in the model by decreasing the recycling factor progressively from 0.9–0, which removes what would otherwise be a downward trend in modelled ratios (Fig. 8, Supplementary Data File 3).

Measured ratios are affected by instrument bias, which is constant, and ablation bias, which varies with pulse count. In the model (Fig. 8), 1 means no ablation bias. The measured ratios must be normalized to a number that is adjusted to provide an optimum fit to the model. The optimum normalization factor should be the product of the unbiased 206Pb/238U ratio (a function of age) with the instrument bias. The instrument bias can be removed and the unknown age determined after dividing by the optimum normalization factor found from measurements of a standard of known age measured during the same session.

As expected from the match between deposit retention and ratio profiles, the model for KL data in Fig. 8A can be made to fit the normalized ratio profile quite well with a loss factor of 0.78 and zero recycling of deposits while the best fit for DD91-1 data in Fig. 8B requires a loss factor of 0.90 with zero recycling. Increasing the recycling factor suppresses the fractionation profile similarly to decreasing the loss factor, but there is reason to suspect that the beam cannot couple to the steep wall of the pit, hence cannot re-ablate fractionated deposits, and that deposited material is quite fractionated in Pb/U.

The model for DD91-1 data shows an anomaly between pulses 25–50 where both ZrO and U signals begin to increase, but this is not reflected in the measured ratio profile. The increase in ZrO emission between pulses 30–60 (Fig. 6D) suggests that this zone is more damaged resulting in the pulses ablating more material. This would effectively raise the normalization factor which, if included in the calculations, would reduce or nullify change in the trend of the ratios. ZrO and U profiles from both samples (Fig. 6C and 6D) show a discontinuity in slope at about 60 pulses, following a short (40–60 pulse) period of stasis. This corresponds to the beginning of a short rapid increase in measured ratios, which subsequently slows to follow an extended linear trend.

The rapid increase in 206Pb/238U at the end of the measured profile for DD91-1 (Fig. 8B) cannot be explained by the model. This is associated with a drop in U signal but no change in the ZrO trend (Fig. 6D). The best explanation may be beam intersection with a significantly older core. Even though cores have never previously been noted in this sample, it is from an intrusion in metasedimentary rock which contains abundant older detrital zircon (Davis, 2002).

The aim of fitting data to a curve, whether empirical in conventional calibration or model-dependent, is to remove biases on all data, allowing them to be averaged to determine a more precise value for the 206Pb/238U ratio. Elaborating on the previous description, it is necessary to normalize each measurement in the ratio profile by a factor, R0, that provides the closest match (minimum MSWD) between data and model. R0 should then be the 206Pb/238U ratio corrected for ablation bias (although still affected by instrument bias). An error on R0 could be determined from all the data by dividing the measured ratio values by the corresponding model value as shown by the “linearized” points in Supplementary Data File 3. A realistic model should result in a randomly scattered distribution of adjusted measured data that fits a horizontal line. The weighted mean of this distribution should then give the best estimate of unbiased 206Pb/238U ratio and error based on all data. Unfortunately, this approach is not practical because there are too many degrees of freedom. In addition to uncertainty about the choice of a normalizing factor for the ZrO signal, fitting a model to the data also requires choosing Li and Ci factors (i is the pulse number). For example, a theoretical ablation model could be forced to exactly match data points by adjusting Li, and Ci for each laser pulse using an arbitrary R0 value but this would be meaningless. Similarly, adjusting one or two constant model parameters can produce acceptable fits with variable estimates of the unbiased ratio so this is also meaningless without independent knowledge of the parameters. Despite the apparent effectiveness of modelling in this case, it cannot by itself provide accurate correction of ablation bias. However, it provides a mathematical platform for testing ideas against observed data so might help improve understanding of the ablation process.

As mentioned, melting and partial volatilization of basal melt at the beginning of an analysis should result in a high, decreasing ablation bias of signals from the earliest pulses as the basal melt reservoir becomes more negatively fractionated (Fig. 3C). Eventually, negative fractionation of the melt reaches an equilibrium value where it offsets fractionation of the signal, which should result in an unfractionated signal, except that the early downward melt fractionation trend is opposed by deposition of fractionated fallback, forcing signal fractionation upward. Given these opposing factors it is surprising that fractionation usually seems to increase most rapidly near the beginning.

In fact, there is a notable mismatch to the main fractionation profile over the first 10 pulses from both of the above standard samples in which the ratio measurements show no consistent increase (Fig. 9). For KL, the average of the first 10 absolute 206Pb/238U measurements is 0.1231±0.0038, which corresponds to a instrument bias of -31.5%. while for DD91-1 it is 0.3549±0.0091, corresponding to a instrument bias is -31.2%, showing that results in this case are consistent. The first 10 pulses correspond to an anomalous period of increasing emission, which might be explained by rapidly decreasing fallback, but this does not explain the quasi-constant ratios. This may reflect an unstable balance between upward fractionation due to fallback deposition of Pb-depleted deposit and entrainment of Pb-depleted material from a shallow melt pool.

To evaluate fractionation before the reduction in slope of the 206Pb/238U profile, measurements of the first 60 pulses were conducted on KL, DD91-1 and a relatively low-U but zoned Archean standard, DD85-17, using laser frequencies of 0.2 and 10 Hz. Results from the first 5 pulses of the 10 Hz runs are omitted because the signals have not stabilized. The data set shown in Fig. 10A was acquired during a different session from that in Fig. 10B so instrument biases (Y-intercept) cannot be compared between them but should be similar for data from a single session. The number of pulses analyzed was between 50 and 60. Spot sizes are given in the “Summary” sheet of Supplementary Data File 4.

Data in Fig. 10 are averages of 4–6 runs for each sample. Data from individual runs are shown in Supplementary Data Files 4 and 5 for runs carried out at 0.2 and 10 Hz, respectively. Although the average ratios show a linear increase, about half the individual 0.2 Hz runs show 206Pb/238U ratios in the first ten pulses that do not obviously increase or increase more slowly than ratios from subsequent pulses. The y axis intercept of the average regression line from DD91-1 is distinctly (∼5%) higher than intercepts from the average KL and DD85-17 data (Fig. 10A and B). One might expect a higher slope from a more damaged zircon such as DD91-1. KL should be the least damaged because of its relative age and U concentration but DD85-17 shows the lowest intercept and slope. The variability of intercepts within a single session suggests that apparent ablation bias from the earliest pulses can be chaotic and may be affected by radiation damage. Therefore, this approach cannot be used to precisely remove instrument biases by comparing to a zircon standard.

Based on limited experimental evidence, a possible theory to explain a typical ablation bias profile might be as follows. 206Pb/238U measurements from the first ten or so laser pulses are dominated by an initial positive and decreasing bias as well as a relatively large proportion of fallback. Because fallback should be dominated by larger melt droplets, it should be depleted in Pb, forcing the signal toward positive fractionation in opposition to the effect of the basal melt. As negative fractionation of the basal melt increases, positive fractionation of its vapour decreases. The effect of depositing negatively fractionated fallback then dominates, driving the profile rapidly upward. As the pit becomes deeper, directing the ablation plume upward, fallback may decrease and its fractionation may become positive if its composition becomes more similar to that of the average plume. From this point changes in fractionation may be dominated by deposition of depleted ablated material on the wall of the deepening pit resulting in a linear trend for the measured profile.

The Y-intercept of data from the early (rapidly increasing) phase of a ratio profile appears to be affected by the structural state of the zircon and so does not appear to provide a well-constrained estimate of instrument bias. It is notable that both ratio profiles show a linear increase from about 100 to at least 250 pulses corresponding to a linear decrease in ZrO signal. Gehrels et al. (2008) proposed regressing the later linear section of profile data and using the Y-intersections of a standard and a sample to determine the unknown age. If both are affected by the same biases these will cancel, giving the ratio between unknown and known values of 206Pb/238U. In this case, the ratio calculated from the intercepts is +0.9% (higher) than the true ratio, which is accurate within measurement errors although our ablation pits are probably much deeper than those of Gehrels et al. (2008).

A more conservative estimate might to compare the averages of all, or most of, the 206Pb/238U profiles. Despite profiles for the KL and DD91-1 standards not being identical, the ratio of the averages is only 0.2 % different from the ratio based on the accepted ages of the standards when the profiles are terminated at 260 pulses before the anomalous increase for DD91-1.

The most comprehensive way to calibrate a sample of unknown age using a standard should be to directly compare the fractionation profiles. This is done by multiplying each of the 206Pb/238U data in the fractionation curve from the standard by a factor that gives a minimum MSWD between the two data sets. This approach is shown on Fig. 11. Calculations are shown in Supplementary Data File 3, KL Data sheet, columns BJ-BQ. Since this requires direct comparison between the two fractionation profiles, it reveals whether or to what extent standard and sample are an appropriate match. The normalized profile for DD91-1 is a remarkably close visual match for that of KL before the rapid increase in ratios in the last 30 pulses of the DD91-1 profile. Omitting this part, gives a calculated ratio 0.8437, which is +0.15% different from the true ratio. Given the differences between the normalized ZrO profiles found for KL and DD91-1 (Fig. 8), it seems surprising that the shapes of the measured ratio profiles for both zircon samples fit so well (Fig. 11), which suggests that we still have a limited picture of the ablation process.

A program has been written to easily process U–Pb data according to the above method of matching 206Pb/238U profiles between sample and standard. Data are entered into an Excel spreadsheet and processed using Visual Basic for Applications (VBA). The program, called UTILAZ (University of Toronto Isotopes Laser Ablation of Zircon) along with instructions, is given in Supplementary Data File 6. The program allows editing of data. The average 206Pb/238U profile from standard measurements before and after a sample measurement is adjusted by a calibration factor calculated so that the sum of squares of the differences between sample and standard data is minimized between chosen limits of the profile. The approach proposed by Paton et al. (2010) and used in Iolite is similar except that it involves smoothing profiles using cubic splines. Matching sample and normalized standard profiles gives results that are very similar, but not identical, to just dividing the averages of the two profiles, but the comparison approach provides a better way to calculate errors from dispersion of the data as the square root of the mean of squares of differences between sample and standard data divided by their number.

The program is applied to Precambrian zircon in Supplementary Data File 6, which includes raw data. KL is chosen as the standard and, as mentioned, should be the least damaged, while JG-diorite, DD85-17 and DD91-1 are Archean with DD91-1 having significantly higher U. Sample 21CB1242 has the highest U concentration and appears to be completely metamict. Alteration is clearly visible in BSE images and was avoided at the surface. 88Sr was measured as a proxy for alteration at depth. “Standard” analytical conditions were applied with beam diameter of 30 µm.

Results are summarized in Table 1 (Supplementary Data File 7) and Fig. 12. Discordance is calculated as the percent difference between the 206Pb/238U ratio of a concordant point with the measured 207Pb/206Pb ratio, and the 206Pb/238U ratio of the datum (positive if below the concordia curve). The shapes of 206Pb/238U profiles for non-metamict samples generally match well with their adjusted standard profiles. Although their calibrated 206Pb/238U data scatter somewhat outside of errors, the averages are all within ±1% even though these grains should have been affected by a range of radiation damage. 206Pb/238U profiles from the metamict zircon are somewhat flatter than those from the standard and the calibrated data show reverse discordance from -6% to -19%.

Metamict zircon might be expected to ablate more rapidly, resulting in a deeper pit and more fractionation than the relatively undamaged standard. This should result in a larger and more rapidly decaying ZrO signal, which is generally the case (Supplementary Data File 6). The UTILAZ program includes the ability to adjust calibration factors according to ZrO signal profiles, which were fitted to exponential functions to calculate normalized decay signal profiles as in the previous models. Adjusting the standard calibration results in an over-correction for the data from the metamict zircon and makes the non-metamict zircon data more discordant. These results are not shown but can be replicated using the software. The average ZrO signals from all measurements are roughly constant (Supplementary Data File 6). They show no correlation with U concentration and damage, which seems surprising if metamictization results in greater ablation volumes. Higher fallback could be an explanation, but this is contradicted by the fact that data from the metamict zircon show a correlation between reverse discordance and U concentration (Fig. 12B). This might serve as a first-order correction to 206Pb/238U bias even though its cause remains unclear.