Generalization of the Fission-Track Arrhenius Annealing Equations

Fission-track annealing models describe the recovery kinetics of a crystalline structure damaged by the interaction with fission fragments during the geological thermal history of a mineral sample. Arrhenius type equations have been successfully applied to model annealing and are at the core of thermal history (temperature, T, as a function of time, t, paths) reconstruction programs for fission-track thermochronology. In this work, the Arrhenius equations are generalized and synthesized in a composite equation that allows for the generation of Arrhenius-type equations by turning on/off parameters and by appropriately choosing functions of ln t and T-1. Geometrical features of the Arrhenius-type equations in the Arrhenius pseudo-space (T-1, ln t) are explored. Three examples of new models for annealing of fission tracks in apatite, obtained from the composite model, are presented, and their extrapolation to the geological timescale is discussed. The presented composite model can be applied to other studies involving annealing experiments, such as the annealing of alpha recoil damage in minerals.

Automated summary

In this study, the Arrhenius equations are generalized and synthesized to create a composite equation that allows for the generation of Arrhenius-type equations by manipulating parameters and functions. Three new models for annealing of fission tracks in apatite are presented, and their extrapolation to the geological timescale is discussed.