Short communication concerning experimental factors affecting fission-track counts in apatite

The tools for interpreting fission-track data are evolving apace but, even so, the out5 comes cannot be better than the data. Recent studies that have again taken up the issues of etching and observation have shown that both have an effect on confined-track length measurements. We report experiments concerning the effects of grain orientation, polishing, etching and observation on fission-track counts in apatite. The results cannot be generalized to circumstances other than those of the experiments, and thus do not solve the problems of track count10 ing. Our findings nevertheless throw light on the factors affecting the track counts, and thence the sample ages, whilst raising the question: what counts as an etched surface track? This is pertinent to manual and automatic track counts and to designing training strategies for neural networks. We cannot be confident that counting prism faces and using the ζ-calibration for age calculation are adequate for dealing with all etchingand counting-related factors across all sam15 ples. Prism faces are not unproblematic for counting and other surface orientations are not per se useless. Our results suggest that a reinvestigation of the etching properties of different apatite faces could increase the range useful for dating, and so lift a severe restriction for provenance studies. Summary. Fission tracks are damage trails from uranium fission in minerals, whose thermal 20 histories are deduced from their number and length. A mineral is etched for observing the tracks with a microscope. We show that the etching and observation conditions affect the track count and explain it in the framework of a recent etch model. We conclude that established solutions do not secure that the ages and thermal histories inferred from track counts and measurements are accurate. 25 * corresponding author: Carolin.Aslanian@geo.tu-freiberg.de https://doi.org/10.5194/gchron-2021-28 Preprint. Discussion started: 29 September 2021 c © Author(s) 2021. CC BY 4.0 License.

ing. Our findings nevertheless throw light on the factors affecting the track counts, and thence the sample ages, whilst raising the question: what counts as an etched surface track? This is pertinent to manual and automatic track counts and to designing training strategies for neural networks. We cannot be confident that counting prism faces and using the ζ-calibration for age calculation are adequate for dealing with all etching-and counting-related factors across all sam-15 ples. Prism faces are not unproblematic for counting and other surface orientations are not per se useless. Our results suggest that a reinvestigation of the etching properties of different apatite faces could increase the range useful for dating, and so lift a severe restriction for provenance studies.
Summary. Fission tracks are damage trails from uranium fission in minerals, whose thermal 20 histories are deduced from their number and length. A mineral is etched for observing the tracks with a microscope. We show that the etching and observation conditions affect the track count and explain it in the framework of a recent etch model. We conclude that established solutions do not secure that the ages and thermal histories inferred from track counts and measurements are accurate.

Introduction
Fission-track dating and temperature-time-path modelling are much-used thermochronologi-30 cal tools for geological research. The fission-track method rests on counting and measuring the lattice damage trails caused by uranium fission. Fission tracks in apatite are ~20 µm long (Bhandari et al., 1971;Jonckheere, 2003) and ~10 nm wide (Paul and Fitzgerald, 1992;Paul, 1993;Li et al., 2011;2014), thus too thin to observe with a microscope. Polished grain mounts are therefore etched to make them visible. Although it is important to understand 35 etching for interpreting track data, it is often taken for granted that experimental factors related to etching and counting are inconsequential, e.g., that counting losses are negligible in slow-etching surfaces such as apatite prism faces. It is further assumed that systematic errors on the track counts cancel out if the sought ages are calibrated against those of age standards (e.g., ζ-calibration; Hurford, 1990). We believe that, from lack of investigation, there persist 40 certain misconceptions concerning these issues, which lead us to overestimate the accuracy of fission-track ages but also to impose undue practical restrictions, such as excluding all apatite grains not polished parallel to their c-axes from the track counts and the confined-track measurements.
We report experiments aimed at furthering our understanding of fission-track counts and meas-45 urements in apatite. Because there is a subjective aspect to the counts (Enkelmann et al., 2005;Jonckheere et al., 2015) and measurements (Ketcham et al., 2015;Ketcham and Tamer, 2021), our numerical results cannot be generalized. They nevertheless reveal significant trends, which we endeavour to interpret in the context of recent etching models and to relate to practical dating issues.

Experiments and Results
We cut plane sections from Durango apatite crystals at 0° (prism face; sample P00), 30° (B60) and 90° (basal face; B00) to their c-axes and mounted them in resin. We ground and polished them with 6, 3, and 1 µm diamond suspensions and a 0.04 µm silica suspension, and etched them in 10-s steps for 10, 20 and 30 s in 5.5 M HNO3 at 21 °C. Reference points on the mounts allowed us to register the position of each investigated field and to return to it after each etch 55 step. Each step, we counted the tracks at the exact same locations with a motorized Zeiss Z2m microscope and Märzhäuser stage controlled from a desktop computer running the Autoscan software.      tracks. The individual deviations are random: a track is lost in one field while one is added in a 95 different field of the same sample. In general, however, track loss dominates in the basal face (B00), while tracks are gained in P00 an B60. The overall changes between 10 and 30 s amount to ~10% of the initial values. The changes are smaller from 20 to 30 s etching than from 10 to 20 s, but consistent with the initial trend. We interpret this as an indication, but not proof, of a decreasing surface etch rate, linked to decreasing polishing damage with increasing depth (Ku-  Table 2 lists the intercepts and slopes of geometric mean regression lines fitted to the plots in ference that the loss is proportional to the track count is not obvious since higher track counts are not associated with higher uranium concentrations but due to random Poisson variation. We propose that the track loss is due to the growth and merger of the surface etch pits, which consume the shorter track channels causing losses proportional to the initial number of tracks in each field. For P00 and B60, the slopes remain constant at ~1 while the intercepts increase persist after the surface has overtaken the latent track. This phenomenon is more pronounced at low etchant concentrations (Jonckheere and Van den haute, 1996). This reconciles our new observations with the new etch model, while also explaining the fact that the net rate of addition is not much greater for B60 than for P00 despite its more than twice higher etch rate (Aslanian et al., 2021).    For the second experiment, we cut fourteen prism sections from a crystal of Durango apatite.
We   under TL decreases faster than the RL features. We counted these features on the assumption that they represent the surface intersections of long (with channel) or short (without channel) etched segments of intermittent latent fission tracks (Gleadow et al., 1983;Green et al., 1986;Paul and Fitzgerald, 1992;Paul, 1993;Li et al., 2011;2014;Wauschkuhn et al., 2015). Table 3 and Figure 6 compare the RL and TL counts of the same areas. There is a close correla-185 tion between the RL and TL counts up to 271 °C, with the former 5-10 % higher for both fossil and induced tracks and across the investigated range of track densities (TL: 0.127-2.923 10 6 cm -2 ; RL: 0.134-3.016 10 6 cm -2 ). The TL counts collapse at higher temperatures while the RL counts remain almost constant in comparison. The transition from consistent to inconsistent RL-and TL counts occurs at the point (ρ/ρ0 ≈ 0.70) at which tracks at high angles to the c-axis 190 break up in shorter etchable segments separated by unetchable gaps (Watt et al., 1984;Green et al., 1986) or are subject to accelerated length reduction (Donelick et al., 1999). It is worth noting that, with few exceptions, the RL and TL counts have standard deviations close to those of the Poisson distribution (σ/σP ≈ 1), irrespective of the ratio of the RL to TL track counts, as expected for the products of a radioactive process. It is improbable that defect swarms pos-

Discussion and Conclusions
We submit this contribution from a concern that, while the tools for interpreting fission-track lead to reduced grain counts, which is a particular problem for distinguishing age components in a mixture. Grain selection based on shape can also cause an age component to be missed.
The drawbacks of the ζ-calibration are of a different nature (Hurford, 1998;Enkelmann et al., 2005;Jonckheere et al., 2015;Iwano et al., 2018;: ζ is an efficient workaround for the calibration problem, but it is just that: it circumvents difficulties without eliminating them. It 215 has to be taken on trust that it deals with all etching-and counting-related factors under all circumstances.
Our findings provide no solution. It is doubtful that here is a single solution for all polishing, etching and counting protocols, or for all samples. Our results do illustrate how simple experiments throw light on the factors affecting the track counts, and, thence, the sample ages. This