Paul F. Green

The zeta age calibration of fission-track dating.

Uranium dosimeter glasses SRM 612, CN1 and CN2 have been calibrated against Co monitors in 79 irradiations in the Herald reactor over seven years. Mean values of the calibration factors B for each glass are B612 = (5.736 ± 0.055)·109 (74 irradiations), BCN1 = (1.883 ± 0.026)·109 (21 irradiations) and BCN2 = (2.014 ± 0.0 26)·109 (21 irradiations). Comparison of relative responses of the four dosimeters reveals that unaccounted errors exist in the response of the Co monitors and, to a lesser extent, in the response of SRM 612. The errors associated with the response of the natural uranium glasses CN1 and CN2 are represented by conventional (Poisson) “counting statistics”. These results show that attempts to calibrate a uranium glass against an activation monitor in only a small number of irradiations may produce results radically discrepant from the true value. The importance of systematic errors in neutron dosimetry for fission-track dating is also discussed. An alternative zeta (ζ) calibration approach is described, which circumvents absolute φ and λf evaluation: each dosimeter glass is calibrated repeatedly against zircon age standards from the Fish Canyon and Bishop tuffs, the Tardree rhyolite and Southern African kimberlites, to obtain empirical calibration factors ζ. The weighted mean ζ-values are 339 ± 5 for SRM 612, 113.0 ± 2.6 for CN1 and 121.0 ± 3.6 for CN2. Independent K/Ar, 40Ar/39Ar and Rb/Sr calibrating ages for the standards are discussed. For two of the three glasses, the presented ζ-values derived from each of the zircon standards are consistent within error. Compatibility of the kimberlite data with that of the other samples is discussed. Age calculation by direct comparison of track density ratios in sample and standard is rejected as grossly imprecise. Examination of the reproducibility of results from repeated measurements indicates the conventional calculation of error to be reasonable, but shows the approach of Johnson et al. (1979) to give a serious over-estimate of precision.

Thermal annealing of fission tracks in apatite: 1. A qualitative description

Confined fission-track lengths have been used to study the degree of annealing of induced fission tracks in samples of a single fluorapatite crystal (Durango apatite), heated for various times (between 20 min. and 500 days) at temperatures between 95° and 400°C. In all annealed samples the mean confined track length is always less than that in unannealed control samples. As annealing progresses, the mean length is reduced and the length distribution broadens, slowly at first, and then more rapidly below a length reduction (ll0) of ∼ 0.65. In addition, the variation of track length with angle to the crystallographic c-axis becomes progressively more anisotropic. As the mean track length approaches zero, the only tracks left are aligned parallel to the c-acis. In heavily annealed samples (ll0 < 0.65) observation of individual tracks after sequential etching steps shows the presence of unetchable “gaps” in a small proportion of tracks. The existence of these gaps is borne out by annealing studies of heavy-ion tracks in apatite slices. These studies also show the anisotropy characteristic of annealing in apatite. The annealing of fission tracks in apatite appears to be characterised by two processes. For small degrees of annealing the dominant process brings about a progressive shrinking of the track from each end, with tracks perpendicular to the c-axis shortening more rapidly than those parallel to it. As annealing becomes more severe (ll0 < 0.65) the tracks begin to break up into discontinuous portions. Track length distributions in annealed apatites reflect the interplay of these processes. The effect of apatite composition on annealing has been studied using spontaneous tracks in apatites from a sample in which considerable geological annealing has occurred. Electron microprobe studies show that apatite grains rich in Cl are more resistant to annealing, while fluorapatite is more readily annealed.

Thermal annealing of fission tracks in apatite 2. A quantitative analysis

Abstract An extensive set of laboratory annealing data, relating the reduction in mean confined track length of induced fission tracks in Durango apatite (Mexico) to annealing temperature and time, has been used to construct an empirical mathematical description of the annealing process. Firstly, Laplacian smoothing splines are used to reveal the gross nature of the dependence of the length reduction, r , on logarithm of time (ln( t )) and inverse absolute temperature ( T −1 ). This suggests that contours of equal length reduction in an Arrhenius plot can be described by parallel or only slightly fanning straight lines. In seeking a more rigorous description, we construct a series of models relating some function g ( r ) and another function f {ln( t ), T −1 }, which contain most previously published relationships, as well as a number of novel forms. Within this composite model, both parallel and fanning Arrhenius plots are considered. The models are fitted and compared using formal statistical methods. None of the previously suggested relationships satisfactorily describe the data, and a novel form is proposed with g ( r )=ln(1− r ) for the parallel Arrhenius plot. The best fitting model accounts for 96.7% of the variation of g ( r ), but residual plots show some structure; suggesting that some improvement in the model is possible. The best fanning model accounts for 98.0% of the variation in g ( r ), and gives a significantly better fit than the parallel model, with residual plots showing no obvious structure. The degree of fanning is much less than in most previously published Arrhenius plots for apatite, which may be due to the presence of apatites of various compositions in those previous studies, whereas the present study relates to only a single composition. The slight amount of fanning observed in this study may be an artefact introduced by several intermediate steps between the physical processes taking place during annealing and their manifestation as the reduction in mean track length.

Confined fission track lengths in apatite: a diagnostic tool for thermal history analysis

Fission-track ages in apatite are generally accepted as giving a measure of the time over which a sample has been exposed to temperatures below approximately 100° C. A compilation of the lengths of confined fission tracks in a wide variety of apatites from different geological environments has shown that the distribution of confined track lengths can provide unique thermal history information in the temperature range below about 150° C over times of the order of 106 to 109 years. The distribution of confined lengths of freshly produced induced tracks is characterised by a narrow, symmetrical distribution with a mean length of around 16.3 μm and a standard deviation of the distribution of approximately 0.9 μm. In volcanic and related rocks which have cooled very rapidly, and never been reheated above about 50° C, the distribution is also narrow and symmetric, but with a shorter mean of 14.5 to 15 μm, and a standard deviation of the distribution of approximately 1.0 μm. In granitic basement terrains which are thought never to have been significantly disturbed thermally, since their original post-emplacement cooling, the distribution becomes negatively skewed, with a mean around 12 or 13 μm and a standard deviation between 1.2 and 2 μm.This distribution is thought to characterise slow continuous cooling from temperatures in excess of 120° C, to ambient surface temperatures. More complex thermal histories produce correspondingly complex distributions of confined tracks. The continuous production of tracks through time, coupled with the fact that the length of each track shrinks to a value characteristic of the maximum temperature it has experienced, gives a final length distribution which directly reflects the nature of the variation of temperature with time. Most distinctive of the myriad possible forms of the final distribution are the bimodal distributions, which give clear evidence of a two-stage history, including high and low temperature phases. The study of confined length distributions therefore offers invaluable evidence on the meaning of any fission-track age, and bears the potential of providing rigorous constraints on thermal history in the temperature regime below about 150° C. The results of this study strongly suggest that any apatite fission-track age determination should be supported by a confined track length distribution.

Thermal annealing of fission tracks in apatite 4. Quantitative modelling techniques and extension to geological timescales

Abstract A methodology is presented for the prediction of fission-track parameters in geological situations from a laboratory-based description of annealing kinetics. To test the validity of extrapolation from laboratory to geological timescales, the approach is applied to a number of geological situations for which apatite fission-track analysis (AFTA) data are available and where thermal history is known with some confidence. Predicted fission-track parameters agree well with observation in all cases, giving confidence in the validity of the extrapolation, and suggesting that fission-track annealing takes place by a single pathway in both laboratory and geological conditions. The precision of predicted track lengths is considered in some detail. Typical levels of precision are ∼ ±0.5 μm for mean lengths ⪷ 10 μm, and ∼ ±0.3 μm for length ⪆ 10 μm. Precision is largely independent of thermal history for any reasonable geological thermal history. Accuracy of prediction is limited principally by the effect of apatite composition on annealing kinetics. The development of fission-track parameters is illustrated through a series of notional thermal histories to emphasise various key aspects of the response of the system. Temperature dominates over time in determining final fission-track parameters, with an order of magnitude increase in time being equivalent to a ∼ 10°C increase in temperature. The final length of a track is determined predominantly by the maximum temperature to which it is subjected. Aspects of AFTA response are further highlighted by prediction of patterns of AFTA parameters as a function of depth and temperature from a series of notional burial histories embodying a variety of thermal history styles. The quantitative understanding of AFTA response not only affords the basis of rigorous paleotemperature estimation, but also allows a better understanding of the situations in which AFTA can be applied to yield useful information.

A new look at statistics in fission-track dating

Abstract Poissonian errors, as routinely applied in fission-track dating, represent a limiting case, which may not always be attainable in practice. Other experimental factors may introduce additional non-Poissonian errors, which must be taken into account. In the population method, sampling of non-homogeneous uranium distributions introduces experimental error. In the external detector method (EDM), many factors exist to introduce such error. Simply quoting total numbers of spontaneous and induced fission tracks obtained by the EDM may disguise the possible influence of experimental variation. The present work concentrates on the EDM, and describes a test which has recently been proposed to detect the presence of experimental error in EDM analyses. The question of an alternative analysis for cases where such error is present is also considered. A method of presenting EDM data is suggeted, which allows assessment of the importance of experimental errors.

Estimating the component ages in a finite mixture

A common problem in fission track dating is to estimate the component ages, particularly the youngest age, when a sample contains grains of different true ages. In this situation it is sometimes reasonable to suppose that the grains are a random sample from a population in which a proportion π1 have age τ1 and a proportion π2 have age τ2, where π1 + π2 = 1 and where π1, τ1, π2, τ2 are all unknown. We give formulae for estimating these parameters along with their relative standard errors, confidence intervals and appropriate diagnostics when the grains are dated by the external detector method. The generalisation to three or more component ages is indicated. The calculations are experimentally tested using data obtained from synthetic mixtures of grains, so that the estimates can be compared with known values and also in order to demonstrate the applicability of the method.

A users' guide to fission track dating calibration

Abstract Misconceptions regarding the fission track dating method prompt the description of five handling procedures and the derivation of commonly used system calibrations. Problems of registration geometry, inhomogeneous uranium distribution, accumulated radiation damage and anisotropic etching largely invalidate all but the population and external detector methods, and impose strict limitations upon even their routine application. Complexities of unique, absolute thermal neutron dosimetry are illustrated by the calibration and use of the NBS pre-irradiated glass SRM 962. The 20% disparity in measured λ f decay constant values cannot be isolated from neutron fluence (φ) measurement and calibration. Frequently a calibration ratio (φ/λ f ) is evaluated against an age standard and then split into its component parts. To illustrate this interdependence of λ f and φ, zircon fission track ages, in agreement with independent K Ar ages, are obtained by calculating the same track count data with each of the preferred values of λ f (λ f = 7.03 × 10 −17 yr −1 and8.46 × 10 −17 yr −1 ) together with appropriate, selected neutron dosimetry schemes. An alternative approach is presented, formally relating unknown ages of samples to known ages of standards, either by direct comparison of standard and sample track densities, or by the repeated calibration of a glass against age standards. Practical recommendations are given for the reporting and critical assessment of fission track data.

Comparison of zeta calibration baselines for fission track dating of apatite, zircon and sphene

Abstract A.J. Hurford and P.F. Green gave a description of the “zeta” method of calibrating fission-track dating against other radiometric dating techniques. In the study reported here, the work is extended to a large number of zircon samples, and applied for the first time to apatite and sphene. Values of ζ for the three minerals are determined with respect to three different uranium glass dosimeters, and reduced to a common scale using precisely determined conversion factors for the relative fission-track response of each glass dosimeter. All determinations show a high level of consistency. On a scale appropriate to SRM612, overall weighted mean zeta (OWMZ) values of 381.8 ± 10.3 for zircon, 353.5 ± 7.8 for apatite and 320.0 ±12.4 for sphene are determined, showing unexpected differences between the three minerals. Some factors which might introduce such differences are considered but none seems to produce effects of the observed magnitude, and they remain unexplained. An equivalent range of values are in common use by different workers. Further work is necessary to resolve these differences. The results are discussed in terms of the suitability of fission-track dating for placing numerical constraints on the geologic time scale. The study illustrates the need for all fission-track age determinations to be derived from a calibration scale based on the use of age standards. Some recommendations are made for newcomers to the technique. Consistent fission-track counting must be achieved in controlled experiments before reliable ages may be determined on unknown samples.

Fission track lengths in the apatite annealing zone and the interpretation of mixed ages

Abstract Measurements of confined fission tracks in apatites from deep boreholes show that their mean length is reduced, and the length distribution becomes progressively broader through the fission track annealing zone. At subsurface temperatures of around 100°C and above, the length distribution characteristically becomes very broad without a pronounced peak. The lengths of the longest tracks remain essentially constant at all stages of natural annealing observed in the boreholes. This pattern is similar to that found in laboratory annealing of spontaneous fission tracks in apatite from an outcrop sample of the same formation. These observations show that confined track lengths can be used as important indicators of the type of thermal history that a sample has experienced in the temperature zone of increasing track stability. The length distributions reported here provide a basis for interpretation of fission track ages that might otherwise be ambiguous. An apatite age which results from a uniform slow-cooling history will have a broad, negatively-skewed length distribution, while a bimodal distribution provides clear evidence of a two-stage history involving partial annealing by a discrete thermal event. The apparent fission track age associated with a bimodal length distribution will be a “mixed” age intermediate between the original age and that of the later event.