Ian R. Duddy

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 natural long-term track annealing experiment for apatite

Abstract Fission track ages of apatites from volcaniclastic sandstones in several deep drill-holes in southern Victoria, Australia, decrease from 120 Myr near the surface to zero near the bottom of the deepest holes. Track fading occurs between 60 and 125°C, a narrower temperature interval than predicted from laboratory annealing studies, but the 50% track-loss temperature (98°C) is very close to earlier predictions for the estimated heating time in the drill-holes of 10 to 40 Myr. Average track lengths, measured on confined tracks (TINTS, etc.), also decrease with increasing down-hole temperature. Track-length reduction relative to fresh, induced tracks was found in apatites from all depths and even outcrop samples which show no reduction in their fission track ages.

Bias in measurement of fission-track length distributions

Abstract Problems in the measurement of fission-track length distributions include biases in various methods of sampling and the amount of information about the true lenght distribution that can be recovered. It is concluded that all length measurements are biased and that this bias must be corrected before meaningful geological interpretations can be made. It is recommended that track-length measurements in minerals be restricted to horizontal confined fission tracks, because the length bias is then simple and easy to correct. Projected track-length measurements are not recommended because of complicated bias and insensitivity to important features of the true length distribution. These points are illustrated by length measurements on two Australian apatite 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.

Fission-track annealing in apatite: Track length measurements and the form of the Arrhenius plot

Abstract Previous fission-track annealing studies have described the reduction in fission-track density in terms of a series of fanning lines on an Arrhenius plot. This has been interpreted in terms of a range of activation energies corresponding to different degrees of annealing, with activation energies varying by a factor of 2 or 3 from complete retention to total erasure. New High precision measurements of confined track lengths in annealed Durango apatite, however, seem to be described by a single activation energy or only a very narrow range of energies (about 30%), implying a near parallelism of lines for various degrees of length reduction in an Arrhenius plot. Borehole studies have shown that different apatite grains respond to the same annealing conditions to differing degrees. Electron microprobe analyses of these apatites indicate that the annealing properties of individual grains are strongly controlled by their Cl/F ratio. The interpretation of laboratory annealing studies, and to a lesser extent borehole studies, in terms of fanning Arrhenius plots may be understood as the result of the superposition of a series of near parallel Arrhenius plots corresponding to the range of compositions present, each characterised by different activation energies.

Apatite Fission-Track Analysis as a Paleotemperature Indicator for Hydrocarbon Exploration

Apatite Fission-Track Analysis (AFTA) is emerging as an important new tool for thermal history analysis in sedimentary basins. At temperatures between approximately 20°C and 150°C over times of the order of 1 to 100 my, fission tracks in apatite are annealed. This is due to a rearrangement of the damage present in unetched tracks, with the result that less of a track is etchable than in fresh, newly created tracks. Because of this, the length of an etched fission track reduces with increasing annealing, and in turn, the track density (and hence the fission-track age) is also decreased. In selected boreholes in the Otway basin, southeastern Australia, apatites from the Otway Group show reduction in confined fission-track length and apparent fission-track age, in a fashion characteristic of a simple thermal history in which samples are at or near their maximum temperatures at the present day. Track lengths show a steady decrease from lengths of approximately 15 µm in outcrop or near surface samples, to zero at about 125°C. Fission-track ages, however, show little or no decrease in age until temperatures exceed about 70°C. Above this temperature, ages rapidly reduce to zero at about 125°C.

Thermal annealing of fission tracks in apatite 3. Variable temperature behaviour

Abstract Despite considerable attention to isothermal behaviour in the literature, no satisfactory description of the variable temperature annealing behaviour of fission tracks in apatite has been given to date. Here, we show that our recently published constant-temperature annealing description can be adapted to temperatures which vary with time using the “principle of equivalent time”. This assumes that at any moment, a track which has been annealed to a certain degree r (= l/l0) behaves during further annealing in a manner which is independent of the conditions which caused the prior annealing, but which depends only on the degree of annealing that has occurred, and the prevailing conditions of temperature and time. Comparison of predictions of mean track length based on this assumption with observed values in a large number of laboratory variable-temperature annealing experiments shows good agreement, suggesting that the assumption is valid. Detailed inspection of the behaviour of tracks during heating and cooling shows that annealing is much more rapid at higher temperatures, and that temperature is the dominant factor in fission-track annealing in apatite. Extension of this treatment to geological situations is not straightforward and is left to a future paper.