Expanding the Limits of Laser-Ablation U-Pb Calcite Geochronology

U-Pb geochronology of calcite by laser-ablation inductively-coupled mass spectrometry (LA5 ICMPS) is an emerging field with potential to solve a vast array of geologic problems. Because of low 6 levels of U and Pb, measurement by more sensitive instruments, such as those with multiple collectors 7 (MC), is advantageous. However, whereas measurement of traditional geochronometers (e.g., zircon) by 8 MC-ICPMS has been limited by detection of the daughter isotope, U-Pb dating of calcite can be limited 9 by detection of the parent isotope, if measured on a Faraday detector. The Nu P3D MC-ICPMS employs a 10 new detector array to measure all isotopes of interest on Daly detectors. A new method, described herein, 11 utilizes the low detection limit and high dynamic range of the Nu P3D for calcite U-Pb geochronology, 12 and compares it with traditional methods. Data from natural samples indicates that measurement of 238U 13 by Daly is advantageous at count rates <30,000; this includes samples low in U or those necessitating 14 smaller spots. Age precision for samples run in this mode are limited by 207Pb counts and the maximum 15 U/Pbc. To explore these limits—i.e., the minimum U, Pb, and U/Pb ratios that can be measured by LA16 ICPMS—a model is created and discussed; these models are meant to serve as a guide to evaluate 17 potential candidate materials for geochronology. As an example, for samples necessitating a <1 Ma 18 uncertainty, a minimum of ~10 ppb U is needed at a spot size of 100 μm and rep rate of 10 Hz; absolute 19 uncertainty scales roughly with U concentration. 20


Introduction 21
Calcite U-Pb geochronology by laser-ablation inductively-coupled mass spectrometry (LA-ICPMS) is a 22 relatively new technique with untapped potential for solving numerous geochronologic problems from the 23 timing of faulting (e.g., Roberts and Walker, 2016;Nuriel et al., 2017;Goodfellow et al., 2017), age of 24 ore deposits (Burisch et al., 2017) to paleoclimate, sedimentation, and diagenesis (e.g., Mangenot et al.,25 2018; Rasbury et al., 1997;Hoff et al., 1995;Winter and Johnson, 1995;Wang et al., 1998;Rasbury et 26 al., 1998). Early studies focused on carbonates more likely to contain high concentrations of U, such as 27 speleothems (e.g., Richards et al., 1998) because the method employed-thermal ionization mass 28 spectrometry (TIMS)-required weeks to produce reliable ratios; samples with a low likelihood of 29 success, that is, those with potentially low U contents, were ignored. With the advent of LA-ICPMS, 30 however, sample throughput and analytical costs have been greatly reduced, such that hundreds of 31 geoanalytical facilities can, at the very least, screen a large number of samples and choose those suitable 32 for geochronology in a relatively short period of time and for little cost; sample preparation is minimal, 33 several samples can be analyzed in a day, and dozens of labs worldwide have the capability to perform 34 such analyses. LA-ICPMS also has the advantage of sampling smaller volumes of material; it can thus 35 take advantage of the heterogenous nature of calcite with respect to U and Pb, using larger datasets to 36 better constrain both the initial 207 Pb/ 206 Pb compositions and the common Pb-corrected concordia ages. 37 These isochron ages are calculated with ease on a Tera-Wasserburg diagram similar to other common-Pb-38 bearing mineral chronometers like titanite and apatite (e.g., Chew et al., 2014;Spencer et al., 2013), but 39 calcite also lends itself to a 208 Pb-based correction, given that it usually contains low levels of Th (Parrish 40 et al., 2018). 41 For typical LA-ICPMS analyses, a 193 nm excimer laser is employed in conjunction with either a single-42 collector (SC-ICPMS; either a quadrupole or sector-field instrument), or multi-collector (MC-ICPMS) 43 sector-field instrument. Traditionally, an MC-ICPMS uses a series of Faraday detectors on the high-mass 44 side of the detector array to measure 238 U and 232 Th, and either Faraday cups or secondary electron 45 multipliers (SEMs) on the low-mass side of the array to concurrently measure Pb isotopes; SC-ICMPS 46 instruments measure isotope count rates sequentially with a single SEM. The SC and MC instruments 47 discarded; removing these data has little influence on the final age. The data from the unknowns are all a 126 bit scattered for geological reasons, and were culled to yield single populations for ease of comparison 127 (Though beyond the scope of this manuscript, the Paleozoic samples are interpreted to have suffered 128 partial Pb loss or new crystal growth in the Cretaceous-Tertiary, and the older Cretaceous sample likely 129 (re)crystallized over an extended period.) 130 as the fewest spots available to make an isochron; this is depicted graphically in Figure 1b as a steeper 140 negative slope for Experiment F vs Experiments D and Q. These results are consistent with a higher 141 average and median U ppb (Table 2); low U concentrations that were measured in Experiments D and Q 142 went undetected or yielded large uncertainties in Experiment F. Though samples with median 238 U count 143 rates of >10,000 cps (C273C and C304A) returned fewer viable analyses and worse average 238 U/ 206 Pb 144 uncertainties in Experiment F, the uncertainty of the final age was similar for the higher-U samples on 145 both configurations on the P3D; both yielded lower uncertainties than the Q-ICPMS, despite the 3-fold 146 volume increase in analyzed material on the Q-ICPMS (Figure 2). 147

Results 131
When average count rates of 238 U were below ~8000 cps (near the detection limit of the Faraday detector 148 on the P3D), however, the number of viable analyses and final age precision was significantly higher in Experiment D (Table 2 and Figure 2). As an example, sample C258 yielded few viable data points (35% 150 of the 110 analyses) in Experiment F, fewer than half the number of good analyses in Experiments D and 151 Q. In addition, the resulting uncertainty in the final age calculation (~4%) is significantly larger than that 152 of Experiment D, and similar to the resulting uncertainty in Experiment Q (although the Q-ICPMS 153 yielded >2 times the number of viable spots). Samples C283A and C283C-which also contain low levels 154 of U-yielded ~50% fewer viable data, necessitated double the average count rates of 238 U, and final 155 uncertainties that were significantly greater in Experiment F than those of Experiment D. 156 A summary of the precision vs. U count rate is shown in Figure 1, which shows the precision of 238 U/ 206 Pb 157 and 238 U on a single spot vs. the count rate of 238 U. While there is considerable overlap in the precision vs. 158 238 U cps of both 238 U and 238 U/ 206 Pb at count rates above approx. 30,000 cps, data collected in Experiment 159 F yielded no better than a few kcps 2σ uncertainty on 238 U (Fig. 1a); 238 U/ 206 Pb uncertainties consequently 160 show a similar deviation from the high-count-rate trend (Fig. 1b). Finally, though the Q-ICPMS shows 161 similar gains in precision for low-U analyses, the lower sensitivity of the Q-ICPMS results in a smaller 162 window of U concentrations for which analyses have lower uncertainties than those run on the P3D 163 (vertical offset in symbols in Fig. 1b). 164

Discussion 165
While there is a clear advantage of using the new Daly-only detector setup on the P3D for LA-based 166 calcite geochronology for some samples, the extent to which this advantage obtains for all samples is still 167 somewhat ambiguous. The samples that benefit most from the new instrumentation are not only low in U, 168 but also older. For most measurements of long-lived-isotope geochronology, the analytical limit is 169 determined by the detection limit of the daughter, not the parent, isotope. However, because older 170 samples have more daughter product, they are-for samples with low U/Pbc ratios-more likely to be 171 limited by the count rate of the parent isotope. For samples run on a SC-ICPMS, this distinction is 172 unimportant because the detection limit of 238 U is in all cases lower than that for Pb. However, because the MC-ICPMS has a large sensitivity and precision advantage over the SC-ICPMS, it is important to 174 distinguish the limits of measurement between the Faraday-Daly and all-Daly configuration. 175

Theoretical uncertainty of Tera-Wasserburg data 176
To explore the limits of precision for each analytical configuration, a synthetic dataset was created (using 177 an MS Excel spreadsheet; available on request) to represent different U/Pbc and 238 U cps for samples of 178 different ages. Figure 3 shows samples with ages of 440, 80, and 15 Ma with error ellipses at U/Pbc ratios 179 of 1, 2, 5, 10, 20, 100 and 200. The size of the ellipse is the maximum possible uncertainty (from 180 counting statistics only) for a 10s analysis, given the limit of detection of the instrument. For the all-Daly 181 configuration, the limit of detection is determined by 207 Pb counts, the least abundant isotope of interest. 182 For this example, 30 cps is assumed (the best achieved LODs herein; Hansman et al., 2018), but it is 183 important to recognize that the LOD of Pb is based on the background, which varies from lab to lab, and 184 is also a function of the instrumental sensitivity. For the Faraday-Daly arrangement, the LOD is limited 185 by 238 U counts for samples with lower U/Pbc and by 207 Pb for samples with high U/Pbc-and increasingly 186 so as the sample age decreases. In this case, a minimum of 30,000 cps of 238 U is considered-as opposed 187 to the actual ca. 8000 cps LOD-for the Faraday, because that is the count rate below which a distinct 188 benefit in precision is gained by using the all-Daly arrangement (see Figure 1 and discussion above). As 189 depicted in Figure 3, older samples yield the greatest range of U/Pbc ratios that could yield an advantage 190 of measurement by 238 U on an ion counter, whereas the advantage of the Daly detector disappears at 191 U/Pbc ratios greater than ca. 500 and 250 for samples that are 80 and 15 Ma, respectively. As an example 192 of the benefit of 238 U measurement by Daly, an 80 Ma sample with a maximum U/Pbc ratio of 10 yields 193 1400 cps of 238 U at the LOD of 30 cps 207 Pb. Given a limit of detection of 8000 cps for the Faraday 194 detector, the signal size would need to be 6 times higher before it could be measured by such means. 195 Furthermore, as discussed above, and shown in Figure 1, the benefit of the Daly extends to ca. 30,000 196 cps, or ~20 times the signal that can be measured by the Faraday-Daly configuration. The benefit extends to 200 times for a U/Pbc ratio of 1; but some question arises as to the ability to measure ages at such low 198 U/Pbc values. 199

Choosing Samples and Instruments 200
One intention of this manuscript is to serve as a guide to determine whether any given calcite (or any 201 other Pbc-bearing) sample is appropriate for U-Pb geochronology, and deciding which type of analytical 202 equipment to use. As such, the model above is expanded below to explore the U/Pbc ratios and count rates 203 needed to produce a reliable age from a given number of analyses. These models are then compared with 204 the natural results to determine best practices when selecting samples and instruments for analysis. 205

U and Pbc distribution in calcite 206
Calculating theoretical limits is complicated, however, because the uncertainty of an isochron depends on 207 the distribution of U, Pbc, and thus the distribution of U/Pb and Pb/Pb ratios. For example, a sample with 208 a given maximum U/Pbc will yield a final precision that increases with the number of analyses, but this and can be rather uniform (e.g., C273C). The manner by which the type of distribution affects the final 218 uncertainty is demonstrated in Figure 5. The precision of a T-W isochron is best defined by precisely 219 defined end points with maximum spread; as such, except for samples with extreme U/Pbc, a uniform 220 distribution of 238 U/ 206 Pb ratios results in better final age precision than does a normal distribution. For 221 example, a sample that is 440 Ma with normally distributed data (and ratios ± 3σ from the mean) requires nearly 2 times as many points to achieve the same precision as a sample with uniformly distributed data 223 over the same U/Pb range (Figure 5d; though this also depends on the maximum U/Pbc). For normally 224 distributed data with the same maximum U/Pbc, but only 50% of the spread (i.e., more tightly clustered; 225 Figure 5b), the number of necessary data points increases further, excepting samples with extreme U/Pbc 226 (these data would be less dependent on the precision of the upper intercept). 227

U and Pbc distribution in calcite 228
To compare theoretical data with that obtained from this study-i.e., in order to best represent a natural 229 dataset-we present and discuss models (using the same Excel sheet as that in Section 4.1) with 100 230 uniformly distributed 238 U/ 206 Pb data points acquired for 10 s at 10 Hz, recognizing that, as stated above, 231 this is likely a best-case scenario. We explore the implications of varying maximum U/Pbc ratios rather 232 than 238 U/ 206 Pb ratios because the former are independent of sample age. The results of the model are 233 shown in Figure 6. Because the precision of analyses in an ion-counter-only configuration is limited by 234 the count rate of 207 Pb, we calculate the maximum U/Pbc ratio that can be achieved for different 235 concentrations of U. For example, a 440 Ma sample with 10 ppb U run with a 65 µm spot size will yield 236 ~1500-2000 cps of U (star symbol in Figures 6a, 6b, 6c). The maximum U/Pbc that could be achieved 237 with this count rate will be ~13, because any higher values will yield too few counts of 207 Pb to be 238 measured. Assuming constant U concentration and normally distributed 238 U/ 206 Pb ratios, the best 239 precision on the age of this sample is 0.6%-considerably better than expected for LA-ICPMS (e.g., 240 Horstwood et al., 2016). As a comparison, sample C283A contains an average of 10 ppb U (and 241 maximum of 40 ppb) and thus yields a similar average count rate of 238 U. Its maximum U/Pbc of 26 is 242 considerably less than the maximum theoretical value based on the concentration of that particular 243 analysis because its Pb concentration is well above detection. It should be no surprise then, that the age 244 uncertainty is higher than the theoretical value at that count rate, but it is also higher than the theoretical 245 value for a U/Pbc of 26. Several factors may explain this: 1) though 100 analyses were measured, 32 were 246 imprecise and rejected; 2) the distribution of 238 U/ 206 Pb ratios is not uniform; 3) laser instability, detector 247 response time, laser-induced elemental fractionation (LIEF), signal instability, etc. add uncertainty 248 beyond that based on counting statistics; and 4) low U/Pbc values likely have less U and Pb than in the 249

model. 250
Although optimistic, this model serves as a guide for the limitation of analyses of calcite by LA-ICPMS, 251 given U concentration, maximum U/Pbc, and spot size. First, for all but the youngest samples (<<15 Ma), 252 measurement with the P3D can be advantageous for samples with lower U or those necessitating small 253 spot sizes (e.g., <150 ppb U and <70 µm, or <50 ppb U and <125 µm; symbols in Figure 6a); this is 254 shown as the light-and dark grey areas in Figure 6 (i.e., the area below the "no Daly benefit line" in 255 Figure 6e). However, if, for example, the sample contains concentrations >100 ppb U and the spot can be 256 >100 µm, there is no advantage to using the all-Daly configuration, and if there is significant material 257 (i.e., spot size can be >200 µm), any LA-ICPMS will provide the best possible results (that is, the 258 precision will be limited not by the count rate, but rather other factors such as differences in LIEF, matrix 259 effects etc.). Second, it is highly unlikely that even with extreme spot sizes and rep rates, that samples The theoretical models discussed above use a 10 sec integration time to compare the models to the 275 empirical data. As discussed above, precision can be improved by increasing the number of analytical 276 spots, but each spot can also be ablated for longer or at a higher rep rate (i.e., making deeper pits rather 277 than more pits). One might imagine that these methods might be equally effective, however, there are two 278 important points to consider. First, individual spot precision is limited to the long-term reproducibility of 279 down-hole measurements, and is generally no better than 2%; this precision is more difficult to assess in 280 calcite because most known reference materials exhibit moderate isotopic heterogeneity (e.g., Roberts et 281 al., 2017). Thus, if increasing the depth of the pit yields analytical uncertainties <2%, then the excess pit 282 depth is wasted and overall uncertainty fails to improve. Second, whereas increasing the number of spots 283 leads to a linear increase in the total number of counts (and thus an increase in precision by √ ), an 284 increase in pit depth does not lead to a linear increase in counts because ablation yields decrease with pit 285 depth. Thus, if an increase in total counts could yield better precision, that increase should come from 286 more, shallower laser pits, rather than fewer, deeper pits. 287 It is also possible to increase precision by increasing the spot size. In fact, an argument could be made 288 that a SC-ICPMS that measures 250 µm spots is just as effective as a MC-ICPMS that measures 100 µm 289 spots. Though this argument has merit, the downside is twofold; 1) some regions of interest are simply 290 not large enough to permit a spot 2.5X as wide, and 2) U and/or Pb (i.e., U/Pbc) may be heterogeneous at 291 scales smaller than the spot size, mixing calcite of different age or reducing the range of isotopic ratios 292 that are used to construct an isochron. Figure 7 demonstrates that even though larger spots can yield a 293 better per-spot precision, analyzing the same volume of material with smaller spots can yield better age 294 precision because it can take advantage of the heterogeneous U and Pb concentrations typical of calcite. 295

Conclusions 296
1) Unlike geochronometers with high U and little to no common Pb-such as zircon and monazite-U-Pb 297 dates of minerals with low U and significant common Pb can be limited by the count rates of the parent 298 U, rather than the daughter Pb. 299 2) Given a limit of detection of ~8000 cps for on a Faraday, and the sensitivity of the Nu P3D, samples 300 with as low as 20 ppb U can be analyzed with a 100 µm spot at 10 Hz, and as low as 5 ppb for a 200 µm 301 spot. Even so, the Faraday is less precise than the Daly at count rates of <30,000 cps, corresponding to U 302 concentrations of ca. 75 and 20 ppb, with the same respective spot sizes and rep rates. 303 3) When 238 U is analyzed on a Daly, the limit of detection drops by a factor of >1000, and the analytical 304 capability is thus limited by the LOD of Pb-207 Pb in almost all cases-and the ratio required for 305 optimum precision. The typical LOD of 206 Pb and 207 Pb is ca. 50 cps; it is greater for higher sensitivity 306 instruments, and those with a higher background of common Pb. For a desired U/Pbc ratio of ca. 5-10 for 307 old and young samples, respectively, the required count rate of 238 U would be 500-1000 cps or ca. 5-10 308 times smaller than can be analyzed on a Faraday detector. The analysis of 238 U on a Daly, therefore 309 increases the analytical capability to ca. 0.5-2 ppb U for a 100-200 µm spot, respectively. 310 4) Although the % uncertainty that can be achieved with limited concentrations of U is considerably 311 different among samples with different ages, the absolute uncertainty is approximately the same. For 312 example, samples with 1500 cps 238 U yield a maximum possible uncertainty of ca. 2 Ma, nearly 313 independent of age (older samples yield slightly higher absolute uncertainties). However, because most 314 LA-ICPMS facilities can achieve up to 2% precision on final age calculations, younger samples can yield 315 better absolute uncertainties; these can only be achieved at high U concentrations, which limits the 316 advantage of the Nu P3D for young samples. However, because of their lower cycle times and inability to make concurrent measurements, SC-ICPMS 320 instruments likely require considerably higher concentrations of U to obtain comparable date precision. 321

Code Availability 322
The code described in this manuscript is available on request from the author 323

Data Availability 324
All data described herein is contained within the data supplement 325

Sample Availability 326
These samples were limited to 1 in. epoxy mounts. If necessary, the author can inquire with the provider 327 should one like access to the sample(s). 328

Competing Interests 329
The author declares that he has no conflicts of interest. 330

Acknowledgements 331
This paper was greatly improved by the reviews of D. Chew and R. Parrish. 332      of ~1 J/cm2 and 10 Hz. 6B, D, F show the maximum U/Pbc that can be achieved with the given U 368 concentration and spot size (colored contours); the star symbol in 6B illustrates an example that a 65 µm 369 spot with 10 ppb U can yield a U/Pbc no better than ~13, otherwise 207 Pb will be below detection (i.e., <30 370 cps; example explained in text). Colored circles indicate analyses of unknowns in Experiment F ( 238 U on 371 the Faraday; Table 2; 65 µm, average U ppb); color represents the maximum U/Pbc ratio-taken from 372 Table 2 Figure 5. A-C shows an example of the di ering randomly generated distributions of 100 analyses with the same maximum U/Pbc. 5A shows a normal distribution for the entire range of U/Pbc; 5B is a normal distribution over the upper 50% of the same range. The uniform distribution, shown in 5C, yields the lowest uncertainties because there are more analyses at both the upper and lower intercepts. D shows how the percent uncertainty decreases with number of analyses, depending on the type of 238U/206Pb distribution depicted in A-C; data in D assumed the best case scenario of 2% uncertainty per data point and a U/Pbc ratio of 10 for samples of 440 Figure 6. 6A shows the count rate expected with the Nu P3D given for a given spot size at a laser energy of ~1 J/cm2 and 10 Hz. 6B, D, F show the maximum U/Pbc that can be achieved with the given U concentration and spot size (colored contours); the star symbol in 6B illustrates an example that a 65 µm spot with 10 ppb U can yield a U/Pbc no better than ~13, otherwise 207Pb will be below detection (i.e., <30 cps; example explained in text). Colored circles indicate analyses of unknowns in Experiment F (238U on the Faraday; Table 2; 65 µm, average U ppb); color represents the maximum U/Pbc ratio-taken from   Figure 7. Tera-Wasserburg diagram represen�ng the analysis of a heterogeneous medium using different spot sizes. Though the bigger spot sizes yield smaller individual uncertain�es, the smaller spots take advantage of the spread in U/Pbc ra�os and thus yield a be�er overall uncertainty on the lower intercept age.