2.1 Grain selection and 2-D measurements

Apatite grains were picked from two samples, 97BS-CR8 (n=50) and BS95-11.3 (n=62), using a Nikon SMZ-U/100 optical microscope at a total magnification of 180×. Apatite grains were selected to include the range of grain morphologies present in the sample (e.g., broken, flat, and prismatic ends). Intentionally, several grains with visible inclusions were also selected to evaluate how well these inclusions showed up in the CT scans. All apatite grains were photographed using a Nikon digital ColorView camera connected to the microscope. The short and long axes were measured manually using AnalySIS^® imaging software (Figs. 1 and 3). We chose to measure a single width and did not flip the apatite 90^∘ because this is still common practice in many labs and would allow us to compare the “simplest” 2-D measurement approach with the 3-D CT data. For sample BS95-11.3, grains were imaged and measured on double-sided sticky tape in preparation for the CT mount (Fig. 1). However, we determined that this can cause grains to sit in upright orientations, which is fine for CT scanning but not for 2-D measurements. For sample 97BS-CR8 each apatite grain was placed on a glass slide for 2-D measurements and then transferred to the sticky tape for the CT mount to remedy this issue (Fig. 1).

Figure 1Apatite grain photos with 2-D measurements taken on an optical microscope. Dimensions are reported in micrometers and the grain aliquot name is in the top left corner of each photo. The top row is photographed on double-sided sticky tape, and the bottom row is photographed on a glass slide.

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2.2 Grain-mounting procedure for CT

Once the grains were measured optically in 2-D, they were mounted for CT scanning by orienting several tens of grains on a plastic disk and stacking multiple disks (Fig. 2). The procedure to create a single-layer mount for multi-grain scanning entails covering a flat top of a pushpin with double-sided sticky tape that can be precut using a standard hole punch. Apatite grains are then picked directly onto the tape in a grid-like pattern. The pushpin surface is ∼5 mm in diameter, which easily allows ≥50 apatite grains to be mounted in one layer, tightly spaced, without touching. Grains could be packed more densely as long as they can be reliably identified after scanning; they can even be touching, although this leads to a small increase in processing time to separate them using functions in the Blob3D software.

To utilize the total scanned volume, at least five multi-grain layers can be stacked for a single scan (up to 5 mm tall). To create stackable layers, sturdy plastic disks are made using a standard hole punch, with one side of the disk covered with double-sided sticky tape and apatite grains mounted in the procedure outlined above. Once all the layers are mounted and all excess tape is trimmed, the disks are stacked on top of the push pin. The arrangement is secured by a thin wrap of parafilm. The parafilm and sticky tape are critical to ensure the crystals and layers do not move during scanning. This mount can be easily disassembled after scanning to retrieve the grains for further analysis.

Figure 2Schematic rendering of the CT-mounting procedure. Grains are adhered to the top of a plastic disk using double-sided sticky tape, with multiple grains placed onto a 5×5 mm surface. Multiple plastic disk layers with grains may be assembled and then stacked to take full advantage of the height of the scan. These layers are held together using parafilm, and a hash mark on the pushpin enables further orientation of the scan in order to retrieve the grains afterwards for further analysis.

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2.3 X-ray CT scanning

The multi-grain mounts were scanned with a Zeiss Xradia MicroXCT scanner at the University of Texas High-Resolution X-ray CT Facility (Ketcham and Cooperdock, 2019). Optimal scanning parameters will vary with the instrument being used, with top priorities being to minimize scanning artifacts and noise, while also minimizing time and cost. Lower X-ray energies are more sensitive to compositional variations but more prone to beam-hardening artifacts. We experimented with various settings in this study. The grain mount for sample 97BS-CR8 was scanned with X-rays set at 100 kV and 10 W, with a 1.0 mm SiO₂ filter. 1153 views were gathered at 1.5 s per view, for an acquisition time of 28.9 min. Source–mount distance was 37.7 mm, and mount–detector distance was 12.8 mm. The 2048×2048 camera data were binned by two, and the lower-energy X-rays and weaker filtering necessitated the application of a beam-hardening correction during reconstruction. The reconstructed data had a voxel (3-D pixel) size of 5.03 µm.

The grain mount for sample BS95-11.3 was scanned with X-rays set at 150 kV and 10 W with a 1.6 mm CaF₂ beam filter, acquiring 571 views at 1.5 s per view, for an acquisition time of 14.3 min, not including calibration. Source–mount distance was 37.7 mm, and mount–detector distance was 17.8 mm. The camera data were binned by 2, and no beam-hardening correction was applied during reconstruction. The resulting data had a voxel size of 4.58 µm.

Figure 3Example CT slices (a, b) and 3-D renderings (c, d) of apatite grain mounts for BS95 (a, c) and 97BS (b, d). Arrows indicate two grains with high-attenuation mineral inclusions in BS95 and a fluid inclusion in 97BS. The CT slice for 97BS is actually an oblique slice through the original data to allow all grains to appear in the same image.

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Example images from the two datasets are shown in Fig. 3, illustrating some of the trade-offs. The scan data for BS95 are noisier, primarily due to the faster acquisition, higher X-ray energy, and more severe filtering. Even with this level of noise, high-attenuation inclusions are evident. The scan data for 97BS are less noisy, allowing for the detection of a fluid inclusion, but beam hardening due to the lower-energy X-ray spectrum has caused faint streaks to emanate from or connect some grains. These subtle artifacts have a negligible effect on measurements but may be expected to increase in severity with more or higher-density grains.

2.4 Grain size and shape, F_T, mass calculations

2.4.1 2-D measurement calculations

The microscope length and width measurements are used to calculate volume and surface area, which are then used to calculate mass, ESR, and F_T,U and F_T,Th for each apatite grain, following methods laid out in Farley et al. (1996), Farley (2002), and Farley and Stockli (2002) (Fig. 4). An equidimensional hexagonal prism geometry was assumed with the length (L) measurement for height of the prism and the half-width (r) for the radius of the prism. All equations used for calculating these parameters are included below or in the Appendix.

Volume (V):

$$\begin{array}{}\text{(1)}& V={\displaystyle \frac{\mathrm{3}\times \surd \mathrm{3}}{\mathrm{2}}}\times r^{\mathrm{2}}\times L,\end{array}$$

where L is height and r is the half-width.

Surface area (SA):

$$\begin{array}{}\text{(2)}& \mathrm{SA}=\mathrm{6}\times r\times L+\mathrm{3}\surd \mathrm{3}\times r^{\mathrm{2}},\end{array}$$

where L is height and r is the half-width.

Equivalent spherical radius (ESR):

$$\begin{array}{}\text{(3)}& \mathrm{ESR}=\mathrm{3}\times {\displaystyle \frac{V}{\mathrm{SA}}}.\end{array}$$

Mass:

$$\begin{array}{}\text{(4)}& \mathrm{mass}=\mathrm{3.2}\left({\displaystyle \frac{g}{{\mathrm{cm}}^{\mathrm{3}}}}\right)\times V\left({\mathrm{mm}}^{\mathrm{3}}\right)\times \mathrm{1000}.\end{array}$$

F_T,U and F_T,Th (2-D case; e.g., Farley, 2002):

$$\begin{array}{}\text{(5)}& \begin{array}{rl}& F_{T,U}=\mathrm{1}-\left(\mathrm{5.13}\times {\displaystyle \frac{\mathrm{SA}}{V}}\right)+\left(\mathrm{6.78}\times {{\displaystyle \frac{\mathrm{SA}}{V}}}^{\mathrm{2}}\right),\\ & F_{T,\mathrm{Th}}=\mathrm{1}-\left(\mathrm{5.9}\times {\displaystyle \frac{\mathrm{SA}}{V}}\right)+\left(\mathrm{8.99}\times {{\displaystyle \frac{\mathrm{SA}}{V}}}^{\mathrm{2}}\right).\end{array}\end{array}$$

Mean F_T (see Appendix for explanation) from Farley et al. (1996) (used here for 2-D calculations):

$$\begin{array}{}\text{(6a)}& F_T=a_{\mathrm{238}}\times F_{T,U}+(\mathrm{1}-a_{\mathrm{238}})\times F_{T,\mathrm{Th}},\end{array}$$

where $a_{\mathrm{238}}={\left(\mathrm{1.04}+\mathrm{0.245}\times \frac{\mathrm{Th}}{\mathrm{U}}\right)}^{-\mathrm{1}}$.

From Blob3D for this study (used here for 3-D calculations):

$$\begin{array}{}\text{(6b)}& \begin{array}{rl}\stackrel{\mathrm{‾}}{F_T}=& A_{\mathrm{238}}{F}_{T,\mathrm{238}}+A_{\mathrm{232}}{F}_{T,\mathrm{232}}+\left(\mathrm{1}-A_{\mathrm{238}}-A_{\mathrm{232}}\right)\\ & F_{T,\mathrm{235}},\end{array}\end{array}$$

where $A_{\mathrm{238}}={\left(\mathrm{1.04}+\mathrm{0.247}\left[\frac{\mathrm{Th}}{\mathrm{U}}\right]\right)}^{-\mathrm{1}}$ and $A_{\mathrm{232}}={\left(\mathrm{1}+\mathrm{4.21}/\left[\frac{\mathrm{Th}}{\mathrm{U}}\right]\right)}^{-\mathrm{1}}$.

Effective uranium concentration (eU) (see Appendix for explanation):

$$\begin{array}{}\text{(7)}& \mathrm{eU}=\left[U\right]+\mathrm{0.238}\left[\mathrm{Th}\right]+\mathrm{0.0012}\left[\mathrm{Sm}\right].\end{array}$$

Figure 4(a, b) Rendering of dimension data collected by 2-D and 3-D methods. Length and width are measured in 2-D using an optical microscope measuring the long and wide axis of a grain. Blob3D reports the length, width, and height (BoxA, BoxB, and BoxC) based on the best-fit rectangle for the grain dimensions. (c) Rendering of the full range of variations in grain terminations exhibited by the apatite in this study. Highlighted in gray are potential areas of overestimated volume if an ideal hexagonal prism is assumed and calculated with 2-D length and width data.

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2.5 (U–Th) ∕ He procedure

The apatite (U–Th) ∕ He ages were analyzed in the UTChron Thermochronology Laboratory at the University of Texas at Austin. Individual grains were measured, wrapped into platinum tubes, loaded into a 42-hole sample holder, and pumped to ultrahigh vacuum. Each aliquot was heated to ∼1070 ^∘C for 5 min using a Fusions Diode laser system. The released gas was spiked with a ³He tracer and purified by a Janis cryogenic cold trap at 40 K and SAES NP-10 getter prior to measurement of the ⁴He∕³He on a Blazers Prisma QMS-200 quadrupole mass spectrometer. Final ⁴He contents were calculated using a manometrically calibrated ⁴He standard of known concentration measured during the analytical run. All apatite aliquots were reheated once under the same conditions to ensure full gas release.

After degassing, the platinum packets containing the apatite grains were placed into plastic vials and dissolved in a 100 µL 30 % HNO₃ ${}^{\mathrm{235}}\mathrm{U}{-}^{\mathrm{230}}\mathrm{Th}{-}^{\mathrm{149}}\mathrm{Sm}$ spike solution for 90 min at 90 ^∘C. After acid digestion, 500 µL of Milli-Q ultrapure H₂O was added to dilute the solutions to ∼5 % HNO₃ and equilibrated for ≥ 24 h prior to analysis. The solutions were analyzed using a Thermo Element2 high-resolution inductively coupled plasma–mass spectrometer (HR-ICP-MS) equipped with a 50 µL min⁻¹ micro-concentric nebulizer. Final ²³⁸U, ²³²Th, and ¹⁴⁷Sm values were blank-corrected and calibrated using a spiked, gravimetrically calibrated ∼1 ppb standard solution. Final (uncorrected) ages were calculated by solving the He age equation by means of Taylor series expansion and reported with a 6 % standard error based on long-term intra-laboratory analysis of apatite age standards. Corrected final ages are determined by dividing the uncorrected age by the mean F_T factor (Eq. 5). U, Th, and Sm concentrations, although not used in the age calculations, were determined for reporting purposes using the grain volumes and a nominal apatite density (e.g., Fig. 4, Eq. 4).

Figure 5Scatter plots for volume, surface area, eU, mass, mean F_T, ESR, and age for both samples. Both samples are plotted together unless otherwise noted. Each data point represents a single apatite aliquot. Dashed lines represent the percent difference from the 1:1 line (black line). 3-D data measurements are plotted on the y axis in all plots. 2-D measurements overestimate volume, surface area, and mass and underestimate eU and mean F_T.

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3.1 Grain factors

Grains from both samples display a range of habits typical for apatite, including two flat ends, two prismatic ends, one flat and one prismatic end, and one or two broken or chipped ends (Figs. 1 and 4). The grain morphology and the presence of any visible inclusions were recorded during handpicking (Table 2). Surprisingly, there are no clear systematic relationships between the presence of inclusions and grain age or grain shape and ESR, volume, or surface area. The 2-D length measurements are on average ∼2 % smaller than the 3-D BoxA dimension. On the other hand, the 2-D width dimension is on average ∼3 % greater than the 3-D BoxB dimension (Table 1).

Table 2(U–Th) ∕ He age results.

FL: flat, PR: prismatic, CH: chipped or broken, i: inclusion, * excluded from average, SD.

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Table 32-D vs. 3-D data comparison with other studies.

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One inevitable source of uncertainty in 2-D length and width measurements is analyst judgment and error. For example, if a grain has uneven terminations, it is at the analyst's discretion to measure the longest axis or split the difference, whereas the CT analysis always reflects the longest axis. Similarly, CT scanning is also not subject to any user error introduced by measuring the apatite grain not lying on its widest face or at an incorrect magnification. In our dataset, a couple of grains have very large deviations from the CT-derived volume, which may be caused by the microscope magnification setting being slightly off during measuring. Of course, the degree of analyst error is subject to many factors (e.g., experience of the analyst, the age and type of microscope, measuring software, etc.) and must be addressed on a lab-by-lab basis. In this study we found that human error may lead to “outliers” in the results, and therefore it is a factor that we consider.

3.2 Volume and surface area

Volumes and surface areas calculated using the 2-D microscope dimensions both average ∼20 % larger than the 3-D calculations (3-D ∕ 2-D_VOL=0.82, 3-D ∕ 2-D_SA=0.81) (Table 1, Fig. 5). Specifically, 2-D volumes and surface areas calculated from length and width data assuming a hexagonal prism shape have an absolute average difference of 23±32 % (2σ) and 22±18 % (2σ), respectively, from 3-D Blob3D-calculated volumes and surface areas.

Figure 6Workflow diagram showing the effect of volume and surface area measurements on other parameters used for (U–Th) ∕ He age calculation and interpretation. The average absolute differences between 2-D and 3-D measurements for each of the parameters are reported with their 1σ uncertainties (reported in Table 1). Note that the greatest deviations are in volume and surface area, as well as parameters that rely on volume alone. ESR, F_T, and ages deviate less because they use SA∕V, which is ∼1 between 2-D and 3-D measurements.

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3.3 ESR and mass

The 2-D ESR is calculated using the surface-area-to-volume ratio (SA∕V), which is derived assuming a hexagonal prism with the length and width dimensions measured on the microscope (Eq. 2, Fig. 6). The 3-D data had the ESR calculated based on SA∕V in three ways. First, the SA∕V for ESR_SVm is calculated using the BoxA and BoxB values provided by Blob3D and assuming a hexagonal prism, mimicking the 2-D approach. The variation between 2-D and 3-D ESR_SVm measurements has a 2σ spread of ±12 %, but the variability is fairly evenly split in overestimating and underestimating the ESR such that the average 3-D ∕ 2-D ratio is 1.02. Second, the 3-D SA∕V is calculated using the surface area and volume measurements output by Blob3D (ESR_SV3D). The variation between 2-D and 3-D ESR_SV3D is even larger at ±18 % (2σ), with an average 3-D ∕ 2-D ratio of 1.01 (Table 1, Fig. 5).

The F_T-based ESR was on average similar to the SV-based one (ESR${}_{F_T}/$ ESR_SVm=1.0), but the variation was ±9 % for the two samples, and extreme values were 9 % higher and 21 % lower. The relative variation of the ESR${}_{F_T}$ value with the 2-D data is ±14 %, similar to that for the other 3-D ESR calculations (Table 1, Fig. 5).

The grain mass is calculated from the volume data using a nominal apatite density, and therefore 2-D and 3-D mass determination directly reflect the variability in the 2-D and 3-D volume data. The 2-D approach consistently overestimates the mass, with a high degree of scatter (3-D ∕ 2-D $=\mathrm{0.82}\pm \mathrm{0.44}$ (2σ)) (Table 1, Fig. 5).

3.4 F_T corrections

F_T,U and F_T,Th correction factors calculated from the 2-D data are generally 1 %–2 % lower than the Blob3D U and Th F_T factors. To combine the F_T factors into a single term that is applied to the (U–Th) ∕ He age, a mean F_T was calculated in two ways using Eq. (6) (see Methods). This results in mean F_T factors that vary by an average of 2 % between the 2-D and 3-D datasets. The 1σ scatter in 3-D ∕ 2-D F_T factors is 1.8 %, though individual differences can reach up to 9 % (Table 1, Fig. 5).

3.5 (U–Th) ∕ He age and effective uranium

We calculated the apatite (U–Th) ∕ He-corrected age by dividing the raw (U–Th) ∕ He age by the mean F_T factor. The 2-D F_T (U–Th) ∕ He ages tend to be slightly older than the 3-D F_T (U–Th) ∕ He ages (3-D ∕ 2-D =0.99) owing to the fact that the 2-D F_T values are slightly lower, leading to a larger correction (Table 1, Fig. 5). The average difference between the 2-D and 3-D F_T-corrected ages is 2 %, mimicking that of the variation between 2-D and 3-D F_T (full range is < 1 % to 9 %). This has an insignificant impact on the mean age and uncertainty for both samples. Sample 97BS-CR8 has a 2-D F_T mean age of 56.8±2.9 Ma and a 3-D F_T mean age of 56.0±2.9 Ma (Table 2, Fig. 5). Sample BS95-11.3 has a 2-D F_T age of 12.2±4.0 Ma and a 3-D F_T mean age of 12.1±4.0 Ma (Table 2, Fig. 5).

The effective uranium concentrations (eU = [U] + [Th] $\times \mathrm{0.238}+$ [Sm] ×0.0012) for the apatite are normalized to the mass of the grain. Since 2-D and 3-D grain mass calculations varied by ∼25 %, the eU concentration measurements vary by a similar degree (3-D ∕ 2-D $=\mathrm{1.29}\pm \mathrm{0.24}$ (2σ)) (Table 1, Fig. 5). Note that not all grains were analyzed for U, Th, and Sm, so there are less data for eU comparison than mass.

4.1 Accuracy of 2-D vs. 3-D grain measurements

4.2 Reproducibility of (U–Th) ∕ He ages

In addition to assessing the accuracy of using the 2-D measurements, this study aimed to quantify the uncertainties that may be introduced by such measurements, particularly in F_T, as a means to potentially improve age accuracy, precision, and intra-sample dispersion. Previous studies have estimated that uncertainties in F_T calculation can account for 1 %–5 % of sample age uncertainty (Evans et al., 2008; Glotzbach et al., 2019). Our results are consistent with this range and suggest that uncertainties in the U and Th F_T calculation are on the order of 1 %–3 %, and mean F_T varies by 2 % (Table 1). We find the greatest deviations are likely caused by user error for our samples and not the assumed grain geometry. In samples with less euhedral apatite grains, the effects of F_T and an assumed grain geometry can increase.

Our data also show that the 3-D F_T correction does not increase the overall sample age precision for the samples in this study. For sample 97BS-CR8, 24 apatite grains were analyzed, two of which are outliers. Of the two outliers, one (97BS-CR8-1) was clearly caused by a user error during microscope measurement, leading to an incorrect F_T correction (0.55) and old age (78.8 Ma). This was discovered during 3-D image processing, in which the same grain was identified, measured correctly, and produced an F_T of 0.76 and a more congruent corrected age of 57.2 Ma. In contrast, for a second outlier (97BS-CR8-24), the 2-D and 3-D F_T-corrected ages both produced anomalous ages of 101.2 and 98.4 Ma, respectively. An unusually high He concentration is the likely culprit for the old age for this grain, but its cause is not evident from our data. Excluding these two outliers, the average age and uncertainty for the sample population (n=22 grains) calculated based on the 2-D and 3-D measurements are indistinguishable (56.8±2.9 and 56.0±2.9 Ma); relative errors are 5.1 % in both cases.

Similarly, the sample ages calculated with 3-D and 2-D data for 95BS-11.3 (n=59 aliquots) are indistinguishable at 12.2±4.0 and 12.1±4.0 Ma, respectively. Unlike sample 97BS-CR8, there was no clear-cut evidence of user error, and the relatively high age uncertainty (33 %) is reproducible between the 2-D and 3-D F_T-corrected ages. Five aliquots produced ages > 20 Ma, which skews the mean age older (the median age is 10.2 Ma, within the error of the previous reported age in Stockli et al., 2002). The apatite ages do not correlate with factors such as ESR (grain size) or eU. The > 20 Ma aliquots all have high He concentrations (nmol g⁻¹) compared with the bulk of the sample, suggesting excess He, possibly due to implantation from high U–Th neighbors, or the presence of undetected and insoluble high eU inclusions.

Figure 7Histograms showing the 3-D ∕ 2-D mean F_T and 2-D and 3-D (U–Th) ∕ He age. Histograms show the results of randomly subsampling four grains from each sample 1000 times. For mean F_T and sample age, the subsampling is indistinguishable from the mean of the whole population analyzed. Note: numbers on x axis refer to the bars (bins) and not the tick marks.

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In addition to the above calculations, we randomly subsampled four grains 1000 times to assess the variability in F_T-corrected age for a number of grains that is more comparable to other studies. The results are plotted in Fig. 7 and reported in Table 2. The mean of the 1000 trials is indistinguishable from the entire analyzed population.

Overall, these data suggest that although the 3-D F_T can provide a more accurate F_T correction and varies from 2-D estimations by ∼2 %, it has a minimal effect on the calculated sample age (1 %–2 %) and no effect on the reproducibility for these two samples. This is not surprising, as a ∼2 % error would constitute a negligible proportion of the often-cited 6 % dispersion derived from analyzing age standards; error propagation indicates that removing a source of 2 % error would only reduce an overall 6 % error to 5.7 %. This points to the importance of other factors in intra-sample dispersion, such as U–Th zonation, and/or excess He from nano-inclusions or high U–Th neighbors.

4.3 Effects of inclusions or broken grains

It is widely accepted that inclusions and broken grains are both contributors to intra-sample dispersion and inaccurate He ages, particularly anomalously old ages. Inclusions in apatite can act as He traps or a source for excess He, particularly mineral inclusions that do not dissolve during apatite HNO₃ digestion (e.g., Ehlers and Farley, 2003). Both apatite samples had multiple grains with high-density and low-density inclusions detectable by microscope during picking and/or the CT scan (Fig. 2). In both samples, the presence of inclusions did not have any discernable effect on the (U–Th) ∕ He age (Table 2). While inclusions are certainly a source for error and dispersion in many samples and should be avoided, at least the easily visible ones do not appear to be relevant in these samples, which suggests they are likely also not U–Th-bearing inclusions. For future studies, an added benefit of CT is the detection of high- and low-density mineral and fluid inclusions.

Similarly, broken grains can be a source of dispersion if they were broken after the sample passed through the He partial retention zone, e.g., after the grain began to accumulate He (see Beucher et al., 2013; Brown et al., 2013). Typically, this may occur during erosional transport or during mineral separations. Brown et al. (2013) estimate that broken grains can contribute 7 to > 50 % dispersion from the sample age, depending on cooling history. In our samples, grain terminations varied from doubly prismatic to flat and in some cases appeared chipped or broken. However, there is no clear correlation between the chipped or broken grains and He age (see Table 2). One possibility is that the grains broke prior to cooling through the He retention zone. This seems somewhat unlikely, given that both samples come from crystalline rocks. Alternatively, and perhaps more plausibly, the variety of crystal habits may reflect how the crystals grew in the host rock. In any case, the grains in these samples that appear to be chipped or broken are not obvious sources for the age dispersion observed in the samples.

4.4 Benefits and limitations of X-ray CT over microscope measurements

This study purposefully selected “high-quality” apatite from fast-cooled plutonic samples to quantify the base uncertainty introduced by 2-D measurements and grain shape assumptions on F_T and (U–Th) ∕ He age factors. Although we found that 3-D grain characterization techniques did not reduce intra-sample age dispersion in our samples, it is still highly probable that the 3-D approach can improve dispersion in samples with less euhedral apatite and more complicated geologic histories. Furthermore, CT scanning mineral grains for (U–Th) ∕ He chronometry has both analytical and practical benefits that go beyond grain measurement. CT provides more accurate grain volume measurements, which becomes increasingly important as grain shapes deviate from idealized forms (e.g., abraded or broken grains). CT data are able to highlight inclusions or other internal heterogeneities based on contrasts in density in the X-ray data, which may not be visible by the naked eye. Furthermore, the CT-mounting method and scanning conditions outlined in this study allow for the scanning of up to 250 grains in a single session, and potentially many more, making it cost and time effective. Different mineral phases can be scanned together, and data can be processed in a batch so that from a single scan, one can gather volume, surface area, caliper dimensions, F_T, mass, and ESR at once for several samples and phases. Furthermore, the 3-D F_T and F_T-based ESR capabilities of the Blob3D software introduced in this study make batch processing the CT data straightforward. Thus, an analyst will be able to image, characterize, and quantify hundreds of mineral grains in significantly less time than conventional microscope measuring. We anticipate that more volume-based shape measurements can and will be developed to automatically and quantitatively evaluate grains for euhedrality, rounding, broken faces, and a wealth of other potentially informative data.

CT scanning mineral grains used for (U–Th) ∕ He dating also has the benefit of removing many possible sources of user error during the grain measurement step. Unlike with microscope measurements, the orientation of the apatite grain on the CT mount does not matter, and there is no need to set a magnification or trace the dimensions of the grain by hand, reducing the potential for mistakes. CT also eliminates variability that may arise from different microscopes, lighting conditions, and imaging software, and it creates a digital archive of 3-D grain shapes, densities, and internal structures that a microscope photo cannot capture.

The one required user input to our method is specifying the threshold CT number for grain measurement, for which we recommend using the midpoint value between the mineral and the surrounding medium (e.g., air, epoxy). When scan resolution is low in terms of both voxel size and sharpness, additional care is required; if edge blurring approaches the center of a grain, an alternative thresholding or segmentation procedure may be necessary to obtain accurate volumes (Ketcham and Mote, 2019). We thus do not recommend pushing resolution limits too far; voxel sizes generally should not exceed 1∕8 to 1∕10 of the shortest dimension of a grain. CT measurement accuracy also requires that the scans be as free as possible from artifacts that cause local changes in CT numbers, such as beam hardening, photon starvation, or rings. We further note that software artifact corrections can sometimes introduce secondary artifacts that may be harder to recognize but still affect calculations (Ketcham and Carlson, 2001), so care is required in the scanning process.

The main limitation of using CT is access to the instrumentation and cost for sample analysis. However, CT scanners are becoming more common as desktop instruments in earth science departments, and many universities have imaging facilities that include micro-CT. As CT instruments continue to proliferate and costs continue to fall, we anticipate that measuring, screening, and documenting grains used for thermogeochronology will become a widely used practice.