Kinetic model for the relationship between confined fission-track length shortening and fission-track age reduction in minerals

Abstract

As a consequence of thermal treatment, fission tracks are shortened and a reduction of the surface density is expected, implying in a reduction of the fission-track age. Geometric considerations predict a linear relationship between track shortening and surface density reduction. However, experimental results for apatite, zircon and titanite found in literature, show a deviation from this relationship. Observation efficiency, crystallographic orientation, track segmentation and biases in length measurements have been invoked in order to explain the experiments, but do not succeeded in this aim. In this work, a model relating etching efficiency (via critical angle) with the amount of lattice defect (via mean track length) is proposed. It is assumed that the chemical etching obeys a rate law and that the observable means of densities and lengths are the net result from the mean actions of the orientation-dependent track and bulk etching velocities. The result is a two-parameter kinetic model described by the equation (ρ/ρ 0)=(l/l 0){1−[1+(kl 0(l/l 0)) n] −2}/{1−[1+(kl 0) n] −2}, where k and n are parameters related to the particular characteristics of the minerals. The model fits quite well the experimental data, showing that the general model principles (hypotheses and simplifications), provide a good general description of the processes causing the deviation detected by the experiments. The presented model does not discard, but embrace the previous attempts of explaining the relationship between fission-track lengths and densities.