Kinetic model for the annealing of fission tracks in minerals and its application to apatite

Fission tracks are formed in apatite and other minerals after the passage of fission fragments, which deliver locally intense amounts of energy to the crystal lattice. It is well known that the observable mean track lengths are reduced due to thermal treatment. If the annealing kinetics are known, it is sometimes possible to infer the thermal history a given sample experienced. Given the present lack of appropriate information on track formation, annealing and etching, researchers have used empirical models fitted to laboratory data on annealing to describe the annealing kinetics. In this work, a kinetic model is presented to describe the annealing process. It is based upon some experimental evidence. Instead of furnishing a complete and detailed description, it is intended to relate the observable quantities, namely, etched confined fission tracks, time and temperature based on simple hypotheses using a simplified view of the track.A kinetic model equation for the reduced mean track length, L/L0L/L0, as a function of temperature, T, and heating duration, t, which fits quite well the available literature, has been derived and is given by(L/L0)=exp{-nexp[-w′(U0-A1ln(t)+A2ln2(t)-kBT)1/2]}in which n   is a parameter related to etching and track geometry, w′w′ and U0U0 are the width and the energy of a newly hypothesized potential barrier, respectively. A1A1 and A2A2 account for the dependence of the energy barrier on the duration of heating. Correlations with cell parameters of compositionally different apatites show that the barrier energy is the principal model descriptor for annealing.