Confined fission track revelation: how it works and why it matters

Since the advent of particle-track methods, it has been understood that the energy loss rate of an ion changes continuously along the particle trajectory, and that energy loss rate in turn affects etching rate. As fission particles slow down and stop, their energy loss rate also drops, which in turn reduces their along-track etching velocity. Conversely, the conceptual model that underlies the way we interpret track length data is based on a more simplified paradigm of a constant along-track etching velocity, vT, with the track tip marking the transition to bulk crystal etching, vB, at its maximum etchable extent. We present a new model for the etching and revelation of confined fission tracks that incorporates and attempts to quantify variable along-track etching velocity, vT(x). The model attempts to fully represent the track-in-track (TINT) revelation process, consisting of etchant penetration along semi-tracks intersecting the polished grain surface, expansion of etchant channels to intersect latent confined tracks, etching of confined tracks, and finally selection by the analyst of tracks suitable for measurement. We successfully use the model to fit step-etching data for spontaneous and unannealed and annealed induced confined tracks in Durango apatite. All model fits support a continuous decrease in etching velocity toward track tips, and lead to a series of insights concerning the theory and practice of fission-track thermochronology. Etching rates for annealed induced tracks in Durango apatite are much faster than those for unannealed induced and spontaneous tracks, impacting the relative efficiency of both confined track length and density measurements, and suggesting that high-temperature laboratory annealing may induce a transformation in track cores that does not occur at geological conditions of partial annealing. However, we are still investigating to what degree that pattern holds for other apatite varieties. The model also quantifies how variation in track selection criteria by analysts, which we approximate as the ratio of along-track to bulk etching velocity at the etched track tip (vT/vB), is likely to play a first-order role in the reproducibility of confined length measurements, and may explain the bulk of the variability observed in inter-laboratory calibration exercises. The concept of a “fully etched track” is subjective. Finally, the model illustrates how a substantial proportion of tracks that are intersected are not measured, which in turn indicates that length biasing is likely to be an insufficient mathematical basis for predicting the relative probability of detection of different track populations.