A reappraisal of the principle of equivalent time based on physicochemical methods

TL;DR

This paper critically reexamines the Principle of Equivalent Time in fission-track thermochronology, proposing a physicochemical formalism that accurately models annealing effects across different mechanisms and clarifies the limitations of PET.

Contribution

It introduces a mechanism-independent formalism for modeling annealing effects, extending the applicability beyond the traditional PET's scope and highlighting its limitations.

Findings

PET applies only to single activation energy models

The new formalism is mechanism-independent and more accurate

Deviations occur when applying PET to multi-mechanism models

Abstract

The main feature of the Fission-Track Thermochronology is its ability to infer the thermal histories of mineral samples in regions of interest for geological studies. The ingredients that make the thermal history inference possible are the annealing models, which capture the annealing kinetics of fission tracks for isothermal heating experiments, and the Principle of Equivalent Time (PET), which allows the application of the annealing models to variable temperatures. It turns out that the PET only applies to specific types of annealing models describing single activation energy annealing mechanisms (parallel models). However, the PET has been extensively applied to models related to multiple activation energy mechanisms (fanning models). This procedure is an approximation that has been overlooked due to the lack of a suitable alternative. To deal with this difficult, a formalism, based on physicochemical techniques, that allows to quantify the effects of annealing on the fission tracks for variable temperatures, is developed. It is independent of the annealing mechanism and, therefore, is applicable to any annealing model. In the cases in which the PET is valid, parallel models, the proposed method and the PET predict the same degrees of annealing. However, deviations appear when the methods are applied to the fanning models, with the PET underestimating annealing effects. The consequences for the inference of thermal histories are discussed.