Thermal fading of fission tracks at variable temperature: Applications to geochronology

Abstract

The Arrhenius law is extended to the case when the fading temperature varies over time. The proposed equation [equation (2)] is induced from the Arrhenius equation, independently of any representative function of some track-fading parameter, and without taking into account any of the usual track-annealing models. This extension is only based on the Arrhenius equation, regarded as basic law of the observable track-fading phenomenon in that is meaningful in itself. The following conclusions are deduced from equation (2): (a) For a given previous track-density reduction r, track-behaviour under a new annealing regime depends on the thermal conditions of the previous fading. It means that, given r, the degree by which latent tracks have been affected varies according to the thermal conditions which they have experienced, and that r does not imply by itself this process, while equation (2), of which r is a variable, implies it. (b) When the calculated age curve presents a plateau, the laboratory heating temperature at the beginning of the plateau is necessarily significantly higher than the highest previous (observable) fading temperature. It is, therefore, the required condition to obtain such a plateau. (c) Moreover, when the calculated age curve presents a plateau, which occurs with low geological temperatures, the plateau age is the ‘corrected age’, i.e. the fission-track age corrected for previous partial fading. (d) Otherwise, the calculated age curve only presents a maximum which is lower than the ‘corrected age’, the discrepancy increasing with the previous fading rate and temperature. (e) The fact that plateau ages exist implies that the Arrhenius parameter A( r) increases with r. (f) The fading process which leads to a plateau in the above-defined conditions can be described in terms of the function Γ on which equation (2) is based. By adopting the proposed ‘ r i -diagrams’ to plot plateau-age curves, any heating mode requiring no constant healing parameter can be used, and the plateau can be more surely differentiated from a simple maximum of the calculated age curve. A simple method is deduced from equation (2) to discriminate between previously affected and unaffected fossil-track populations, by using track-density data of the plateau-age technique. The onset of the last fission-track storage and the end of the last partial track-fading, and therefore the average track-fading rate corresponding to this time interval, can thus be determined by this procedure. Values of affected and unaffected fossil-track populations are compared with those which have been obtained by other methods.