Abstract Despite the conceptual elegance and simplicity of the External Detector Method EDM for fission track dating, an increasing number of laboratories are switching to LA-ICP-MS as a means of measuring the uranium content of apatite, zircon and sphene.
This paper aims to bring the statistical treatment of LAFT data on an equal footing with the EDM by formulating four different analytical protocols, depending on the accuracy and reproducibility of the uranium measurements.
Uranium zoning has a detrimental effect on the accuracy of LAFT ages. This effect can be removed by counting only those fission tracks located within the laser ablation pit.
Alternatively, the uranium heterogeneity may be quantified by fitting multiple ablation spots in some or all the analysed grains, using Fission track dating reliability testing lognormal distributional assumption for the uranium concentration. LAFT dating is arguably less well suited than the EDM to young and U-poor samples that lack sufficient spontaneous fission tracks to reveal visual evidence for uranium zoning.
Such samples occasionally contain no fission tracks at all, resulting in infinite analytical uncertainties. With the age equation and zero-track strategy in place, LAFT ages can be subjected to more sophisticated statistical analysis. Using a logarithmic transformation, these ages can be visualised on radial plots and deconvolved into finite and continuous mixtures.
The methods proposed in this paper have been implemented in a software package called IsoplotR that is available free of charge at http: In a series of seminal papers published during the s, Robert Fleischer, Paul B. In its most basic form, the fundamental age equation of Fission track dating reliability testing fission track method can be written as follows: During most of the 20 th century, the only way to reliably estimate [ U ] was by proxy, via induced tracks produced by neutron irradiation.
The EDM emerged as the dominant method because it offers significant advantages over the other approaches. First, the EDM was recognised as the first geochronological method capable of routinely producing single grain age estimates, leading to the development of detrital geochronology.
Second, it is least affected by the presence of uranium zoning. Using these measurements, the apparent fission track age is given by 4 where is obtained by applying Equation 4 to an age standard and rearranging. By counting the spontaneous and induced tracks over exactly the same area, the age calculation reduces to a simple comparison of two Poisson-distributed variables N s and N i.
As a result, it is fair to say that the fission track method represents the gold standard among geochronometers in terms of statistical rigour. Unfortunately, the EDM also has a number of practical shortcomings: It requires irradiation with thermal neutrons.
This greatly increases sample turnaround times and poses administrative and safety headaches. These problems are only getting worse with time as research reactors are becoming increasingly rare. Etching the external mica detectors requires handling hazardous hydrofluoric acid. The method is tedious and time consuming, as it requires counting three different track densities spontaneous, induced and dosimeter. The late s and s saw the emergence and maturation of ion "Fission track dating reliability testing" and laser LA-ICP-MS microprobe technology allowing geoscientists, for the first time, to determine ppm-level U-concentrations of solid samples with microscopic resolution directly, rather by proxy via induced fission of U.
This limits the applicability of the method to young samples, and potentially compromises data quality in compositionally zoned crystals. The present paper addresses these issues by defining four different strategies towards LAFT dating, using either an absolute dating Section 2 or a zeta calibration Section 3 approach and using either a single or multiple laser spots per grain to account for uranium heterogeneity Section 4.
Section 5 introduces a method to calculate meaningful ages and uncertainties for very young and uranium-poor samples lacking any spontaneous fission tracks.
With the age equation in place, we can redefine the pooled age and visualise LAFT data on radial plots, allowing us to assess whether Fission track dating reliability testing single grain ages are consistent within the analytical uncertainties Section 6.
Using a logarithmic transformation, this qualitative assessment can be formalised with a Chi-square test for age homogeneity.
The methods described in this paper were implemented in a software package called IsoplotR. Section 7 applies IsoplotR to two real fission track datasets, providing practical examples of the absolute and zeta calibration approach using single and multiple laser spots per grain, and including zero track grains and finite mixtures. This opens up the possibility to use Equation 1 to calculate fission track ages: Please note that uranium sitting near the counting surface of the grain will contribute more to the spontaneous track budget than more deeply seated uranium.
For the remainder of this paper, we will assume that this depth weighting has either been done, or that the grains are not significantly zoned perpendicular to the etched surface. The effect of lateral zoning is covered in Section 4. Error propagation of Equation 5 follows the usual first order Taylor expansion neglecting the systematic uncertainties in A sL and q: Such concentration measurements are typically done by monitoring the isotope of interest i. However, glass interacts very differently with UV laser light than most minerals, and therefore the accuracy of LA-ICP-MS based U-concentration measurements often leaves "Fission track dating reliability testing" to be desired.
To avoid these problems and remove the need to measure absolute concentrations, all the poorly constrained factors that relate the raw mass spectrometer measurements i. As long as the spontaneous and induced track densities are counted over the same area, the presence of U-rich or U-poor zones has no effect on the resulting age.
Unfortunately, things are not so straightforward for LAFT data. Suppose, for example, that the analyst has placed a round laser spot in the top half of the strongly zoned grain shown in Figure 1. This would result in a high uranium Fission track dating reliability testing or isotopic ratio measurement and a small analytical uncertainty, but would be completely unrepresentative of the average composition of the grain.
Blindly combining such a single spot measurement with the number of spontaneous fission tracks counted over the entire crystal would produce a precise but grossly inaccurate age. For old and uranium-rich samples, it is often possible to detect and avoid the problems caused by uranium zoning by carefully observing the spatial distribution of the spontaneous tracks. In this old sample, the effect of an order of magnitude difference in uranium concentration is visible in both the spontaneous left and induced right track distribution.
For LAFT data, it Fission track dating reliability testing not be visible at all. A first approach is to only count the spontaneous fission tracks contained within the area occupied by the laser ablation spot Figure 2 a.