A new phenomenological model for annealing of fission tracks in apatite: laboratory data fitting and geological benchmarking

Abstract

Rana track annealing model 2007, based on an Arrhenius approach, is significantly modified, including new assumptions, fitting parameters, and analysis, to yield a new phenomenological model for annealing of fission tracks in apatite. Construction and optimization of the new six parameter model have been described in detail. The model shows a hybrid behavior. In Arrhenius plot, for higher temperatures (laboratory data included), iso-annealing lines are curved while, for low temperatures (geological time scale), iso-annealing lines become parallel straight lines. This is a new feature for any such model and has produced promising results. C-axis projected lengths from laboratory experiments on Durango apatite are employed to find model parameters. KTB borehole fission-track data are added to build the temperature function that modifies the original equation. Partial annealing zone (PAZ), closure temperature ( $$T_{\mathrm{C}}$$ ) and total annealing temperature ( $$T_{\mathrm{A}}$$ ) were calculated and compared to geological benchmarks. The predictions of the present model agreed well with low and high temperature benchmarks. PAZ, $$T_{\mathrm{C}}$$ and $$T_{\mathrm{A}}$$ predictions were also compared to the Fanning Curvilinear Arrhenius model predictions, resulting in good agreement. The present model is flexible enough to be applied to other fission-track systems, like zircon, muscovite and titanite.