Abstract
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.