A Monte-Carlo calculation of the size distribution of latent alpha-recoil tracks in phlogopite: Implications for the recoil-track dating method

We used a Monte-Carlo method to calculate the size distribution of alpha-recoil tracks in phlogopite. The calculations span the age range 0–1 Ma and the range of Th/U-ratios encountered in phlogopites of different origin. The track-size distribution is bimodal, with a narrow maximum centred on ∼30nm and a broader maximum centred on ∼110nm. The bimodal distribution is a consequence of the long half-lives of the daughters of 238U and, to a lesser extent, 234U, and the fraction of small-sized tracks, therefore, decreases with increasing age and Th/U-ratio. The fact that the recoil-track population cannot be characterised by a single average size complicates the relationship between the number of tracks intersecting a unit area of mineral surface, ρARTρART, and the number of recoil tracks per unit volume of the mineral, NARTNART.On the other hand, the present results offer the prospect of an alternative recoil-track dating method, based on the ratio r of small-sized tracks to that of larger-sized tracks. It is shown that, if r can be measured and the Th/U-ratio of the sample is known, then its recoil-track age can be calculated. There exists a less than straightforward relationship between the size distribution of latent and the maximum-diameter distribution of etched recoil tracks, so that r can, in principle, be calculated after deconvolution of the etched-track diameter distribution. The Monte-Carlo calculation can be extended to minerals doped with known amounts of other radioactive isotopes.