A quantitative description of fission-track etching in apatite

Abstract

We measured the apatite etch rate vR in 5.5 M HNO3 at 21 °C as a function of orientation. Results for Durango apatite evidence that vR varies by a factor >5 with angle to the c-axis. Our measurements also provided track etch rates vT and surface etch rates vS. However, these cannot be combined for calculating track etching or counting efficiencies. By inserting the measured etch rates in a recent model, we calculate the geometries and dimensions of surface tracks in different apatite faces. The proposed model must be recalibrated for different etching protocols and adapted for other minerals. We submit that the new model justifies reviewing track counting efficiencies based on the existing (vB-vT) etch model. We anticipate that this will have an effect on practical aspects of fission track dating. Single-track step-etch data show that the confined track lengths increase with etch time at a decreasing average rate vL that differs from the track etch rate vT and the apatite etch rate vR. Both vT and vL exhibit large track-to-track differences that produce irreducible length variation related to the latent-track structure resulting from formation and annealing. Step etching and track width measurements are effective for reducing or eliminating procedure-related artifacts from track length data, and so for accessing more fundamental track properties.

Fission-track etching in apatite: A model and some implications

“…The midsection has straight sides (βγ and εη), without the least curvature resulting from a decreasing or increasing track-etch rate vT (Fleischer et al 1969;1975); (βγ) and (εη) converge away from (ι); the enclosed angle (4.4°) corresponds to a ratio vT/vR = arctan (4.4/2) ≈ 25. For vR ≈ 3.0 µm min -1 at 69° to c (Aslanian et al 2021), this gives vT ≈ 75 µm min -1 , within the vT range of Aslanian et al (2021). At this rate, it took 10 s to etch the 12.6 µm from (ι) to the end (αβ) and under 3 s from (ι) to (δ).…”

“…The track-length increase is thus difficult to predict, whichever track-etch (vT) model one favours (Masumoto 1992;Jonckheere et al 2017;Tamer et al 2019;Tamer and Ketcham 2020;Aslanian et al 2021). A better understanding of track etching nevertheless permits a fuller characterization of confined tracks than just their measured lengths and orientations.…”

“…Figure 8b shows a track at a low angle to c, with straight sides which join onto short sections parallel to c (αβ and γδ) towards both ends. Its slender form makes it difficult to estimate vT but it is possible to calculate tE from its width (0.6 µm) and the widening rate at 8.6° to c (0.75 µm min -1 ; Aslanian et al 2021). This gives tE = ½ × 0.6 µm/0.75 µm min -1 = 24 s. The confined track in Figure 8c illustrates the characteristic shape of tracks almost perpendicular to the c-axis.…”

“…It is difficult to determine tE from the channel width; tE can instead be calculated from the distances between parallel edges bounding the funnels on both sides of the host track: 3.6 µm between (βγ) and (εη), and 3.7 µm between (γδ) and (κη). For the maximum etch rate (3.05 µm min -1 ; Aslanian et al 2021) this corresponds to 35 -36 s. The surviving channel section is too short and thin for estimating vT.…”

“…Beginning before, but for the most part after the ζ-watershed, etching experiments were aimed at defining suitable protocols for etching confined fission tracks in advance of comprehensive annealing experiments, e.g., Laslett et al (1984), Green et al (1986), Crowley et al (1991), Carlson et al (1999), Barbarand et al (2003), Ravenhurst et al (2003), and Tello et al (2006). Other studies addressed certain fundamental aspects of fission-track etching in apatite (Hejl 1995;Jonckheere and Van den haute 1996;Jonckheere et al 2005;2017;2019;Murrell et al 2009;Moreira et al 2010;Sobel and Seward 2010;Tamer et al 2019;Tamer and Ketcham 2020;Aslanian et al 2021).…”