16.7     Track length measurements

 

Because annealing initially causes shortening of tracks rather than their complete erasure, the use of etched track densities to chart the progress of annealing is an indirect approach. Under the ‘random line segment model’ of Fleischer et al. (1975) there should be a linear relationship between track density and average track length. However, when we only count track densities, we ignore information about the variation in track length on either side of the mean value. This variation in track length can yield additional information about the cooling history of a sample, because the longer the residence time of a sample in the partial annealing zone, the larger will be the variation in track length around the mean value. Therefore, fission track data can be used more effectively to study the thermal history of a sample if the apparent age determined from track density is augmented by study of the length of etched tracks.

 

            Track length studies were first made in dating micas (Maurette et al., 1964; Bigazzi, 1967), and were applied in detail to tektite glasses by Storzer and Wagner (1969). However, the etching of fission tracks in glasses tends to yield circular pits because of the smaller difference in structure, and hence etching rate, between tracks and the free surface. Consequently, the progress of annealing in glasses is accompanied by a decrease in the diameter rather than length of etched tracks. Nevertheless,  Storzer and Wagner showed that pit diameter was correlated with pit density in variably annealed tektite glasses, and were able to use the measurements of pit diameter to correct fission track ages  for the effects of annealing.

Fig. 16.23. Plot of mean pit diameter against pit density in variably annealed tektite glass samples, relative to the original pit size and density before annealing. After Storzer and Wagner (1969).

 

            In mineral samples, track length data can be collected in two different ways. One is to measure the apparent length of tracks which intersect the etched surface. These are termed ‘projected track lengths’ (e.g. Dakowski, 1978). The alternative approach is to measure ‘confined track length’ (Bhandari et al., 1971; Green, 1981; Laslett et al. 1982; 1984). These are tracks which do not break the general etched surface, but which become etched by the penetration of acid down a channel inside the mineral which intersects the track (Fig. 16.24). The two most common types are termed ‘Track-IN-Track’ (TINT) and ‘Track-IN-CLEavage’ (TINCLE) respectively (Lal et al., 1969; Fleischer et al., 1975).

Fig. 16.24. Line drawing of high-contrast features in an etched apatite grain, viewed under dry (non immersion) conditions. Four confined tracks are visible (arrowed). From a photograph by Gleadow et al. (1986).

 

            Measurement of confined tracks which are horizontal (parallel to the etched surface) leads to the minimum bias from true track length. However, confined tracks must be counted using fixed selection criteria to exclude the possibility of subjective bias. Laslett et al. (1994) recommended the ‘bright reflection’ criterion, which exploits the property of etched tracks at a low angle to the horizontal (less than about 15%) to show a bright image in reflected light. In contrast, a criterion which requires tracks to be in focus along their entire length is unsuitable because it causes a higher rejection rate for long tracks than for short tracks.

 

            Another analytical variable that must be carefully controlled is the etching time. It is necessary that some tracks become over-etched to ensure that other are not under-etched. Since tracks have effectively zero width before etching, over-etched tracks can be recognised by their non-zero width, which is almost the same as the excess length (2 H ), Fig. 16.25a). The optimum etching time is determined by experiments on incremental etching (Fig. 16.25b). The standard etching time of 20 seconds used by Laslett et al. (1984) leads on average to 1 :m of over-etching.

Fig. 16.25. Illustration of the progress of etching. a) For a single track; b) average track length in Durango apatite (Mexico) as a function of etching time in 5M HNO3 at 21 oC. After Laslett et al. (1984).

 

            Hejl (1995) identified an additional problem in recovering the true length distribution of annealed tracks from projected track lengths. This is due to the existence of unetchable gaps in the middle of tracks, a phenomenon which appears to be more widespread than previously realised. Hejl proposed that the true lengths of confined tracks could be recovered, despite unetchable gaps, by a double etching procedure. This breaks through the ‘unetchable gap’ to produce a track with a wide middle (double etched) and a narrow extension (beyond the original gap). The total track length can then be measured (Fig. 16.26). This procedure would be more difficult on projected tracks.

Fig. 16.26. Technique of double-etching to break though unetchable gaps in partially annealed tracks. After Heil (1995).

 

            A third cause of bias in confined track lengths is the effect of crystallographic orientation (Green and Durrani, 1977). Compared to un-annealed apatite grains, in which track length is effectively equal in all directions, annealed apatites demonstrate less shortening of tracks parallel to the c axis than in other orientations. Therefore, in order to see the whole range of track lengths in an annealed apatite (and thus gain the maximum information), the prismatic section is observed, containing tracks at all angles to the c axis (Gleadow et al., 1986).

 

            Laslett et al. (1982) and Gleadow et al. (1986) compared the results of projected and confined track length in samples with different thermal histories. They argued that while projected track lengths yield only subtle indications of different thermal histories, confined tracks gave clear diagnostic indicators of thermal history. These can be divided into five types (Fig. 16.27a)e).

 

            Induced tracks (Fig. 16.27a) are the longest and most uniform type (16 " 1 :m, based on several different sample types). Tracks in undisturbed volcanics and rapidly-cooled shallow intrusions are also uniform within a single sample (Fig. 16.27b), but there is some variation between sample means (ca. 14 ) 15.5 :m). This can be attributed to limited annealing at near-ambient temperatures over periods of tens of Myr. Tracks in undisturbed basement apatite (Fig. 16.27c) are somewhat shorter (means of 12 ) 14 :m), with a skewed distribution attributed to slow cooling from regional metamorphism. Finally, bimodal and mixed distributions (Fig. 16.27 d and e) are attributed to various types of two-stage thermal history, in which pre-existing tracks were partially erased by a thermal event between initial cooling and the present.

Fig. 16.27. Histograms of track length (as a percentage of total sample) for apatites with different types of thermal history (see text). Top row: horizontal confined tracks; bottom row: projected tracks. After Gleadow et al. (1986).

 

 

16.7.1  Projected tracks

 

The apparent length of these tracks is biassed from the true length distribution by three factors. Firstly, truncation by the surface reduces apparent length. Secondly, tracks undergo visual fore-shortening to an extent which depends on their angle to the surface. Thirdly, more frequent intersection of long tracks with the surface biasses apparent length upwards. Together, these biasses cause the projected track length distributions in Fig. 16.27 to be severely obscured. However, useful information can be extracted from these distributions if projected lengths of spontaneous tracks are ratioed against the length of projected induced tracks (in a population experiment). In this case the biasses are cancelled out.

 

            Wagner (1988) performed this analysis by comparing the percentage of spontaneous tracks which exceeded a certain length with the percentage of induced tracks over this length, to yield the ratio ‘cs/ci’. A value of 10 :m was initially chosen as a convenient length cut-off for this analysis. However, Wagner and Hejl (1991) generalised the above approach by calculating an apparent fission track age for all projected track lengths exceeding a series of cut-off lengths (x) from zero to 15 :m (at 1 :m-intervals). Relative to the conventional fission track age (x = 0), the normalised age (t) at different values of x is given as:

 

     t   =  cs Ds / ci Di                                                                  [16.9]

 

These apparent ages can then be plotted as an ‘age-spectrum’ diagram. The significant thing about this diagram is that the cut-off for preservation of fission tracks of different lengths is related to temperature, although probably not as a linear function. Hence, the apparent-age diagram is itself a plot of temperature against time, if we can calibrate the cut-off length against temperature. As a preliminary calibration we can adopt the following points:

  1. A track length of zero should correspond to the conventional blocking temperature of ca. 120             oC which marks the upper temperature limit of the PAZ.

  2. Wagner (1988) assigned a cut-off length of 10 :m to the blocking temperature of 60 oC at the lower temperature limit of the PAZ.

  3. A track length of 15 :m represents the case of zero annealing, which may be sustained at ambient temperatures of ca. 30 oC.

 

            Wagner and Hejl presented fission track age-spectrum diagrams for three rocks with different thermal histories in order to explore the usefulness of this diagram (Fig. 16.28). The Fish Canyon Tuff from Colorado (Fig. 16.28a) shows the effects of rapid cooling through the PAZ, with minimal loss of short tracks, but does shows some loss of long tracks. Therefore, it has either suffered a mild thermal pulse since eruption (for which there is little evidence), or else ambient temperatures are sufficient to cause some annealing. The Gotthard Pass granite from the Alps (Fig. 16.28b) shows the effect of slower cooling through the PAZ, due to a uniform but rapid uplift rate. Finally, a paragneiss from the Continental Deep Drill hole in Bavaria (Fig. 16.28c) shows the behaviour of a sample which is undergoing slow uplift, but is still buried. The sample came from 2353 m depth, with an ambient temperature of 70 oC, near the low-temperature limit (= upper depth limit) of the PAZ.

Fig. 16.28. Projected track length age-spectrum diagrams for three geological examples: a) Fish Canyon Tuff; b) Alpine (Gotthard Pass) granite; c) paragneiss from 2353 m depth in the Continental Deep Drill hole, Bavaria. For discussion, see text. Modified after Wagner and Hejl (1991).

 

 

16.7.2  Confined tracks

 

Although useful information can be extracted from projected track lengths, correction of the biasses involved in this method has the effect of degrading the statistic quality of the data. This was demonstrated by Laslett et al. (1994) in a comparison of the usefulness of confined and projected track lengths for thermal history analysis.

 

            Confined track lengths bear a simpler relationship to the true track length distribution, but projected tracks (also referred to as semi-tracks) are more numerous. Therefore, Laslett et al. performed simulations to test the ability of 2000 projected tracks and 100 confined tracks to recover the true track length variation in a mixed population with lengths of 14.5 and 10 um. The proportion of shorter tracks (p) was varied in different simulations from 20% to 80%. Results showed that when the shorter tracks made up 60 to 80% of the population, both methods could recover the length of these tracks and the correct value of p with similar error bars (Fig. 16.29). However, when the proportion of short tracks fell below 50%, the projected track data were seriously compromised.

Fig. 16.29. Comparison of the success of projected and confined tacks to recover the length and the proportion of a population of short tracks amongst a population of longer tracks. Error bars indicate 95% confidence limits, except where they are truncated by the edge of the diagram. After Laslett et al. (1994).

 

            Laslett et al. concluded from this experiment that a relatively small number of confined track measurements can more reliably recover the true track length distribution than a large number of projected track lengths. Hence, it is now generally agreed that confined tracks are superior to projected tracks for thermal history analysis.

 

            In order to use track length analysis to make quantitative interpretations of thermal histories, Laslett et al. (1987) developed a model to predict the degree of track shortening after heating episodes of different intensity. This model was based on isothermal laboratory annealing experiments on large gem-quality apatite samples from Durango, Mexico (Green et al., 1986). Arrhenius (temperature–time) relationships were observed for given fractions of track shortening. These are analogous to the Arrhenius relationships for track density (e.g. Fig. 16.18).

 

            The isothermal model was extended to more complex thermal histories involving variable temperature conditions by Duddy et al. (1988), and applied to geological time-scales by Green et al. (1989). In their approach, a predicted temperature–time curve is divided into intervals (e.g. 1 Myr each), and after each interval the degree of shortening of existing tracks is calculated. At a constant elevated temperature, track shortening occurs rapidly at first, because the track ends are least energetically stable, but the rate subsequently slows considerably. In addition to the annealing of old tracks, new track formation is simulated at 10 Myr intervals. Tracks formed at each of these intervals define an evolution path of reduced track length against time (Fig. 16.30a). The sum of these evolution paths at the present day forms a histogram of track length distribution (Fig. 16.30b).

Fig. 16.30. Model for fission track formation and annealing in a subsiding sedimentary basin. a) Progress of track formation and shortening; b) resulting distribution of track length data. After Green et al. (1989).

 

            Green et al. (1989) modelled the track length distribution expected from several different types of thermal history. This process, of predicting track lengths distributions from thermal history data, is termed forward modelling. They tested the model results against data from the Otway basin, SE Australia. In the Otway basin case, the thermal history problem is over-constrained because Green et al. had access to full track length distributions for a suite of borehole samples from different depths. Therefore, they were able to simplify their analysis by discarding the information on track length variation, and comparing only predicted and measured mean track lengths. This is really a waste of the track length method, since it throws away the useful information about track length variation. However, in this case it serves to verify the model. The result is shown in Fig. 16.31, compared with average measured track lengths from Otway Basin boreholes.

Fig. 16.31. Predicted curve for mean fission track length against temperature in the Otway Basin, compared with measured data points from bore-holes. After Green et al. (1989).

 

            A suite of samples at different depths is not always available from one locality, but by using the complete track length distribution (rather than just the mean) it should be possible to test alternative thermal histories using a single sample. However, several different model thermal histories might generate track length distributions which fit the observed data set. Therefore, it is desirable to test many different solutions in order to see what range of possible histories can generate the observed data. The final objective of this process, to determine which thermal history best explains the observed track length distribution, is termed inversion modelling (e.g. Corrigan, 1991; Gallagher, 1995).

 

            Because initial track development and subsequent track shortening are processes subject to random noise, thermal histories cannot be uniquely determined, but must be based on probabilities. In practice, thermal histories chosen at random (the Monte Carlo method) are used to calculate track length distributions by forward modelling. The results are then tested against the observed (or simulated) track length data. After a few hundred iterations it is possible to map out a range of possible thermal histories which are consistent with the data set. Within this range of possibilities, the highest probability density defines an optimum, but not necessarily unique, thermal history (Fig. 16.32). Relatively well constrained thermal histories can be projected back to the last temperature maximum, but beyond this time the thermal history is very poorly constrained (as indicated by the fanning of the probability contours at ages over 60 Myr).

Fig. 16.32. Plot of probability density for modelled thermal histories of a sedimentary basin, based on fission track data. In this test case the actual thermal history is known, and is shown for reference (dashed line). After Corrigan (1991).

 

            A continuing source of uncertainty in such modelling is the extrapolation of laboratory experiments to geological time-scales. Gallagher compared three alternative annealing models which have been proposed over the past ten years. The first of these uses the laboratory data of Green et al. (1986), extrapolated by Laslett (1987). The second model (Carlson, 1990) uses the same data set, coupled with an ad hoc geometrical model, but has been criticised as non-realistic in crystallographic terms (e.g. Green et al., 1993). The third model is based on new laboratory data by Crowley et al. (1991). Since the models of Carlson and Crowley et al., diverge on opposite sides of the Laslett et al. model, the latter still appears to be the most useful for thermal history modelling.

 

 

16.8     Pressure effects

 

Recently, Wendt et al. (2000) introduced a further twist to fission track analysis by suggesting that the process of thermal track annealing in apatite is also pressure dependant. They performed annealing experiments at 250 oC for a variety of different times and pressures on apatite from four geological occurrences. It was felt that experiments on spontaneous tracks in natural materials would be less likely to introduce artifacts into the experiments.

 

            The results of these experiments for two of the sample types used by Wendt et al. are presented both in terms of track length variations and track densities in Fig. 16.33 (a & b). These two samples were from Canada and Siberia, and both displayed evidence of slight prior annealing over their geological history. The results showed that pressures of 100 MPa and 300 MPa had a dramatic effect on the extent of thermal annealing, compared with the behaviour at 0.1 MPA (ambient pressure). The effects were observed on both average track length (Fig. 16.33a) and track density (Fig. 16.33b), and the effect was to reduce the extent of annealing at higher pressure.

Fig. 16.33. Affects of pressure on the annealing of two natural apatites, expressed in terms of, (a) track length; and (b) track density. Each ellipse defines the range of properties of the two different apatites. All experiments were carried out at 250 oC. Modified after Wendt et al. (2002).

 

            The pressures of 100 and 300 MPA used in these experiments correspond to 1 kbar and 3 kbar respectively, equivalent to depths of ca. 3.5 km and 10 km in the crust. Comparison of these numbers with the 3.5 km depth of the Otway Basin, Australia, suggests that these pressure effects are occurring within the depth range where apatite fission track data have been applied to geological problems. Hence, the evidence suggests that pressure effects could have a significant effect on calculated cooling histories. However, Wendt et al. did not observe any pressure effect on the annealing behaviour of zircon. The controversial nature of this proposal is demonstrated by the scientific discussion that ensued (Chem. Geol. 215, p. 299)316, 2003).

 

 

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