Thermal annealing of fission tracks in apatite 3. Variable temperature behaviour

Abstract

Despite considerable attention to isothermal behaviour in the literature, no satisfactory description of the variable temperature annealing behaviour of fission tracks in apatite has been given to date. Here, we show that our recently published constant-temperature annealing description can be adapted to temperatures which vary with time using the “principle of equivalent time”. This assumes that at any moment, a track which has been annealed to a certain degree r (= l/ l 0) behaves during further annealing in a manner which is independent of the conditions which caused the prior annealing, but which depends only on the degree of annealing that has occurred, and the prevailing conditions of temperature and time. Comparison of predictions of mean track length based on this assumption with observed values in a large number of laboratory variable-temperature annealing experiments shows good agreement, suggesting that the assumption is valid. Detailed inspection of the behaviour of tracks during heating and cooling shows that annealing is much more rapid at higher temperatures, and that temperature is the dominant factor in fission-track annealing in apatite. Extension of this treatment to geological situations is not straightforward and is left to a future paper.