Apatite Fission-Track Dating: A Comparative Study of Ages Obtained by the Automated Counting LA-ICP-MS and External Detector Methodologies

Over the last six decades, apatite fission-track (AFT) thermochronometry has been used as a reliable thermochronological tool in a wide range of geological settings [1]. Conventionally, AFT dating makes use of the crystal linear radiation damage tracks in crystals produced by the spontaneous fission of parent ²³⁸U atoms [2-4]. As in other radiometric methods, a parent–daughter isotopic ratio is required for an age determination. The most common method for fission-track dating is the external detector method (EDM) [5-7]. The EDM involves neutron irradiation in order to induce fission of ²³⁵U, and since ²³⁵U/²³⁸U ratio is a constant, the ²³⁸U concentration can be determined. More recently, studies have been made that avoid neutron irradiation and instead use laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) to directly determine the ²³⁸U content in crystals [8-15]. LA-ICP-MS is a destructive technique on a microscopic scale, destroying part of each grain such that fission-track measurements are not later possible in the area of interest. In order to overcome the consequences of grain ablation, a recent methodology, involving digital image capture, provides new capabilities for the fission-track analysis even after ablation. In this study, we refer to the digital automated counting in combination with LA-ICP-MS as the ACLA methodology, and this was used on two thermochronology apatite standard samples and in a comparative study between the EDM and the ACLA on nonstandard samples. We report the analytical and statistical treatment of data obtained by the ACLA method for AFT dating. Results for apatite standards and unknown age samples are robust statistically and are reproducible using both methodologies.

The conventional EDM is based on recording fission tracks in an external detector as a result of the induced fission of ²³⁵U atoms during thermal neutron irradiation [7]. The detector (commonly muscovite), which is in close contact with the apatite crystals, records the U distribution in the irradiated crystals. The isotopic ratio ²³⁵U/²³⁸U is constant in nature (7.2527 × 10⁻³); therefore, the ²³⁸U content can be determined. The EDM relies on counting the spontaneous and induced track densities under the microscope for an age determination.

For the EDM, the ζ-factor calibration has been the most common approach for fission-track age determinations [16]. This method has been a practical approach to calibrate problematic uncertainties, such as the thermal neutron flux received and the fission decay constant, against different age standards such as apatite from Fish Canyon Tuff (FCT), Durango, and Mt. Dromedary monzonite [5, 16-18].

The EDM has several advantages, for example: (i) its implementation is less expensive compared to the LA-ICP-MS method; (ii) the statistical aspects are well understood; and (iii) fission-track counting is performed on identical areas on a grain and its corresponding mirror image on the external detector, which represents a reliable proxy for U distribution in the mineral grains, especially with respect to zoning and zero track count data [19, 20]. On the other hand, the EDM presents two technical disadvantages: (i) it involves a laborious sample preparation procedure and (ii) the need to irradiate samples in a nuclear reactor (which is becoming increasingly difficult following the closure of many around the world) that involves considerable “cooling” time postirradiation until samples can be handled safely. This makes sample turn-around-time quite long, usually at least several weeks and often months. Furthermore, the transportation and handling of radioactive samples require specific occupational health and safety precautions, thus making the process complex and more time-consuming [15, 20]. The EDM was used in this work to determine AFT ages on samples presented as part of a comparative evaluation of methodologies.

The ACLA method involves a combination of recent advances in digital microscopy, image analysis, and computer software (designed for capturing high-resolution images). It provides an opportunity for the automated counting approach for the AFT analysis [21-23]. For this work, we have used the combination of software from the Fission Track Studio suite (TrackWorks^© and FastTracks^©), developed by the Thermochronology Group at the University of Melbourne and Autoscan Systems Pty Ltd [23]. This software suite is used for capturing high-resolution images in reflected and transmitted light, including a z-stack of images to perform the automated fission-track counting. An important advantage of this procedure is that it results in a permanent digital record of the fission tracks in the analyzed crystals. The captured images are stored and are available for the later inspection, even after grains have been partially destroyed by the laser ablation [13]. Other advantages include improved accuracy for measuring the areas over which spontaneous tracks are counted and visualization of crystals on a computer screen. Methodology and analytical procedures followed by results presented in this study are described in online Appendix A in accordance with most procedures described by Gleadow et al. [12, 13]. Pooled AFT ages were calculated according to the formulae in Hasebe et al. [8].

The practical age equation for the EDM is given by:

where R is the estimator for the ratio between N_s and N_i, $λD=1.55125×10-10yr-1$ is the total decay constant for ²³⁸U, N_s and N_i are the number of spontaneous and induced fission tracks, respectively, ζ is the calibration factor, g is the geometry correction factor, and $ρD$ is the glass monitor track density. For the pooled age:

where n is the total number of analyzed crystals and j represents an individual crystal. For the central age R is given by:

where $θ^$ is the estimate of $NsNs+Ni$⁠, obtained iteratively [19].

AFT ages were calculated using the Galbraith algorithm [19]. Pooled and central ages were obtained using RadialPlotter from Vermeesch [24]. The Enkelmann et al. [25] evaluation, using an earlier version of FastTracks^©, suggested that human review to correct for miscounted features required a long time, but now with the automated counting function using FastTracks^©, this task is more time efficient for the evaluation of fission-track counts. We used FastTracks^© version 1.2.13 for calculating the fission-track density for the EDM and ACLA methods. No significant differences were observed between manual and automated counting. Nevertheless, the accuracy of automated counting is not assessed in this study since the main purpose is to compare AFT ages calculated by the two different methodologies.

A total of seventeen samples were analyzed. Thirteen samples correspond to granitic rocks from Sonora, Mexico. These intrusive rocks are related to late Cretaceous to early Cenozoic Farallon plate subduction, and the spatial distribution of these samples can be found in ref. [26, 27]. Four samples are from the eastern India peninsula; samples I-06-26 and I-06-30 correspond to a late Archaean–early Proterozoic (~2.5 Ga) gneissic complex in the eastern Dharwar craton (EDC), and samples I-06-13 and I-06-14 correspond to the Proterozoic Kurnool group. Locations of these samples are presented in ref. [28].

Apatite concentrates were obtained following conventional procedures. Samples were initially crushed and sieved, followed by mechanical separation with a Gemini table. The magnetic fraction was removed using a Frantz magnetic separator, and heavy liquids sodium polytungstate (specific gravity ~2.9 gr/cm³) and methylene iodide (specific gravity ~3.3 gr/cm³) were used to separate apatites from other minerals. Apatites were mounted in epoxy resin and polished using a Struers Rotopol equipment with sequential polishing of 6, 3, and 1 µm diamond paste. Mounts were chemically etched using HNO₃ (5M) for 20 seconds at 20°C. For mounts analyzed by the EDM, a muscovite detector was attached in close contact with the mount and then sent for neutron irradiation in the X-7 position of the High Flux Australian Reactor (now decommissioned) at Lucas Heights, New South Wales, Australia. A nominal neutron fluence of 1.6 × 10¹⁶ n/cm² was reported for each batch. After “cooling down” for about 8 weeks, sample batches were unpacked and muscovite detectors from both grain mounts and standard glasses were etched in 40% HF for 20 minutes at room temperature of 20°C. After irradiation cooling time, mounts and mica detectors were mounted on thin glass slides for counting of spontaneous and induced tracks under the microscope. In order to improve the image quality, the mounts were coated with a thin aluminum film [7]. Images of apatite crystals were captured using a Zeiss Axiotron M1 digital microscope fitted with a high-resolution camera and a motorized AutoScan^© stage controlled by the TrackWorks^© prior to laser ablation ICP-MS measurements.

The experimental procedure followed for each method is summarized in Figure 1.

We analyzed a total of 165 individual FCT grains. The pooled age using the ACLA method was 28.1 ± 1.0 Ma (Table 1). Results obtained by this method are in close agreement with an independent sanidine ⁴⁰Ar/³⁹Ar age of 28.196 ± 0.030 Ma for this standard sample [12, 29]. For Durango apatite, forty grains were analyzed by the ACLA method. The calculated AFT pooled age is slightly younger (28.8 ± 1.4 Ma) than the reference value (31.4 ± 0.2 Ma) [30] but is concordant at the 2σ uncertainty level. This difference in age can result from different factors, mainly the ζ-factor calibration variations [31]. Results for the single-grain ages for the two apatite standards are plotted in Figure 2. Track densities and average ²³⁸U content for the apatite standards are presented in Table 1.

AFT central ages were calculated using the approach of Galbraith [19]. The central age for FCT apatite yields a younger age than the pooled age (Table 1). For Durango apatite, the central age is in broad agreement with the pooled age (Table 1), but this age is probably influenced by some outliers. For the FCT sample, the calculated pooled age by the ACLA method is in close agreement with ages determined by other geochronological techniques. Based on these considerations, the ages determined by ACLA method are presented based on the pooled approach of Hasebe et al. [8].

A total of seventeen samples of unknown age were analyzed by the EDM and ACLA methods for AFT age comparison using separate aliquots from each sample (Table 2). Thirteen samples correspond to plutonic rocks from Sonora, México [26, 27], and four samples correspond to granitoids from the EDC in India [27].

Age variations from EDM to ACLA methods are as low as 2% for a particular sample. Based on the concordance of ages between methods and within error limits of less than 3%, samples CY-08-05, SV-08-10, SC-08-17, and SC-08-18 show the best agreement of the analyzed samples. The youngest calculated ages correspond to sample LM-08-26 with an ACLA age of 11.1 ± 1.1 Ma and the oldest to sample TI-09-27 with an EDM age of 42.2 ± 3.6 Ma. All calculated ages are concordant between the two methods (ACLA and EDM) within analytical errors at the ±2σ uncertainty level. At the ±1σ uncertainty level, three samples (TI-09-27, RY-08-43, and MZ-08-66) are not concordant, with sample TI-09-27 showing the greatest difference (Figure 3). This level of discordance is within what would be expected from random variations at the 1σ level. Since the ACLA method typically determines U content from a single ablation spot, this approach could be prone to overestimation and underestimation (as well as dispersion) of age due to U zonation, which could result in discordance between ages obtained via the two methods used. However, these random grain-by-grain errors are likely to at least partly cancel when considering the pooled or central ages for a complete sample analysis.

Finally, three different statistical tests were carried out. The first, a Student’s t-test where we compared if the two methods ACLA and EDM provided identical mean (μ) ages. The second, a two-sample t-test, this is also known as the independent samples t-test, in these last individual ages for each method was compared. Third, we applied a Kolmogorov–Smirnov test for two samples and compared cumulative density functions of individual ages obtained by the ACLA and EDM methods. For the first test, using a significance level of 0.05, the t-test suggests that ACLA ages are as reliable as EDM ages (see online Appendix B1). By contrast for the second two-sample test using a significance level of 0.01, almost all samples pass the test with the exception of three samples (RY-08-43, PS-08-45, and I-06-26; Table B2 in online Appendix B2). In the third test, these observations for the three samples were also corroborated using the Kolmogorov–Smirnov test (see online Appendix B2).

Samples analyzed using ACLA methodology demonstrate the viability of using LA-ICP-MS for determining the U content for AFT age determinations. Development and improvements of correction parameters and different protocols for the laser ablation approach for fission-track age determination are undergoing continuous revision. This is not the case for the EDM, where the parameters have long been agreed upon and standardized [16]. Further assessments should consider the following parameters.

Under ACLA conditions described here, the depth of the laser ablation pits is approximately 8 µm (Figure 4). Excavating to approximately this depth is important, considering that the mean confined induced fission-track length reported previously for standard apatites is ~16.2 μm [32]. The dimensions of representative pits were measured with high precision, using a Zeiss Confocal Laser Scanning Microscope in topographic imaging mode. A correlation between U content and pit dimensions is expected, and therefore, it is assumed that the pits ablated contain a representative portion of the U source of the etched fission tracks counted on the polished surface.

High uranium heterogeneity was detected occasionally in apatite grains from the analyzed samples (Figure 5). As such grains that could potentially bias, the results were not considered for the age calculation. We used two criteria to exclude grains for the age calculation: (i) those which following visual inspection of their etched surface exhibit a range of spontaneous track distributions and (ii) where a high degree of U heterogeneity is detected during the ablation time excavating to increasing depth on the z-axis. The ideal case is to have a bandwidth with low dispersion indicating no variation in uranium with depth. A statistical test can be applied to reject or accept bandwidths for the crystals analyzed.

Because the U content is averaged through the entire depth of an ablation pit, the effect of chemical etching to reveal spontaneous tracks prior to carrying out the ICP-MS determinations can be neglected. Also, systematic changes in U concentration near the crystal surface were not detected. This confirms, as reported previously by Hasebe et al. [33], that chemical etching does not introduce significant changes to the U concentration when determined by LA-ICP-MS. In terms of the ²³⁸U content of the analyzed samples, the average values between the two methods are in good agreement for each sample (Figure 3). Minor differences in the U content can be attributed to measurements carried out on different aliquots of the relatively small number of crystals. Therefore, minor content variations can be expected within apatite grains from the same sample, and as also shown in Figure 5, the ²³⁸U content may vary between grains and also within the same grain. However, taking into account the dimensions of the error frame for ²³⁸U and ²³²Th, grains 3 and 6 in sample SV-08-10 were rejected. Generally, the pattern of trace and major element measurements have a flat shape or generally vary within narrow error limits and are considered in grain selection for age calculation criteria. Another approach, not used here, for high U zonation grains is to use a multispot ablation approach to reduce intragrain age dispersion [34, 35].

The Zeta calibration approach for the EDM was introduced to overcome difficulties in the calibration of the neutron dosimeters and uncertainty in the spontaneous fission decay constant [6, 18].

In the case of the ACLA methodology, such an empirical calibration factor has not been implemented, although a proposal for a similar approach using the term epsilon (ε) was suggested by Hasebe et al. [8]. For the ACLA method, an absolute calibration is used based on explicit values for all the individual constants in the pooled age equation. The least well known of these constants is the etching and registration efficiency factor k, which represents the fraction of all tracks crossing a polished surface that are actually observed and counted. In this work, an intermediate k value of 0.93 was adopted based on results presented by Iwano and Danhara [36] for FCT and Durango apatite standards. For λ_f, the value of 8.46 × 10⁻¹⁷yr⁻¹ [37] was used for the set of seventeen samples analyzed by the two techniques (EDM and ACLA); the age variation was significantly different for only two of those samples (see Table 2) and then only at the 1σ level.

A major consideration for ages calculated by ACLA methodology is to evaluate where intragrain U heterogeneity at depth or laterally across the surface was significant in resulting in discordant ages compared to their corresponding EDM ages. This bias is minimized when the grain selection criteria outlined previously are considered. This also requires the analysis of a relatively large number of grains, as this will reduce the influence of nonrepresentative ages within a sample as observed in the FCT analyses (Table 1). Comparing results between central and pooled ages and EDM ages demonstrates that the P(χ2) values for the pooled ages are >5%, implying that grains correspond to a single population, for example ref. [38]. This finding is supported by the fact that the samples analyzed were from plutonic rocks, and all grains within a sample experienced a similar cooling history and had a limited range of compositional variation. Some plutons have multiple composition apatites [39], which could be similar to deal with multiple population samples; for this case, we suggest using a method to discriminate different U contents in the grains or the p-pooled method [31].

AFT ages determined using ACLA methodology are generally concordant with the EDM ages for the studied samples. Central age calculations for ACLA methodology represent an acceptable approach for age determinations, but based on the results presented for FCT, the best approach for calculating the fission-track age when using the ACLA approach is to use the pooled age, as also noted by Seiler et al. [15].

The ACLA method for the AFT analysis combining automated track counting and LA-ICP-MS was tested on established apatite age standards, yielding satisfactory results. A comparative study of AFT ages was also carried out on the same set of samples using the conventional EDM and ACLA methods, and these mostly yielded concordant ages within the ±2σ analytical uncertainties. The ACLA methodology is therefore considered a broadly reliable and time convenient approach for AFT dating.

AFT age calculations using the pooled age approach reduce the influence of single grain ages, which show a larger error on the calculated sample age. This calculation is comparable with the central age calculations presented by Galbraith [19], where single grain ages with a greater uncertainty have a lower influence on the sample age. An attempt to avoid single grain ages that may yield a larger error is that from the outset grains are chosen for the analysis, following microscopic examination, based on an apparent homogeneous spontaneous track distribution. This procedure may reduce the effect of intragrain U heterogeneities substantially as determined by the LA-ICP-MS analysis. Further investigations should focus on improving the accuracy of registration factors that are included in the k parameter.

The analytical procedure for ACLA method is presented in Appendix A, and the statistical tests are presented in the Appendices B1 and B2. Data tables for Fish Canyon Tuff and Durango apatite standards are available in the data repository (file name: Data tables FCT and DUR standards). Single grain fission-track ages for nonstandard samples are also available in the data repository (file name: Nonstandard samples grain by grain ft age data).

We have no conflicts of interest to disclose. All authors declare that they have no conflicts of interest.

Funding was provided by CONACYT and International Research and Fee Remission Scholarships from the University of Melbourne and also from the Australian Research Council under grants A10020308 and DP1092861. The University of Melbourne thermochronology laboratory receives funding under Project A3.51 of the AuScope program (www.auscope.org.au) of the Australian National Collaborative Research Infrastructure Strategy (NCRIS). Mauricio Bermúdez acknowledges the support of Minciencias and the Agencia Nacional de Hidrocarburos (ANH) for project 1109-931-94496 (CT: 80740-038-2023).

Scholarship support for the PhD studies of RELZ from the University of Melbourne and CONACYT, and project funding and laboratory infrastructure support from the Australian Research Council and AuScope are all gratefully acknowledged. The Melbourne thermochronology laboratory operates under the University of Melbourne TrACEES Research Platform. Thanks to Abaz Alimanović, Ling Chung, and Alan Greig for assistance with the acquisition of thermochronology data.

Data tables for the Fish Canyon Tuff and Durango apatite fission-track ages are available in the supplementary materials as an Excel spreadsheet (file name: Data_Tables_FCT_and_DUR_standards). Further, the single grain fission-track ages for nonstandard samples compared in this study are provided (file name: Non_standard_Samples_Grain_by_grain_ft_age_data). Appendix A contains details of the Automated Counting Laser Ablation ICP-MS analytical procedure used in this study. Appendix B.1 describes the statistical test for mean FT ages, and Appendix B.2 describes the statistical t-test for two samples. These three appendices are included in the MS Word file: Appendices A_B.1_B.2.