An Historical Perspective on Fission-Track Thermochronology

Abstract

This chapter reviews the background, beginnings and early development of fission-track (FT) thermochronology. In the 1930s, it was discovered that uranium would break into two lighter products when bombarded with neutrons and, subsequently, that uranium was capable of natural, spontaneous fission. The fission process produced damage tracks in solid-state detectors, which could be revealed by chemical etching and observed by electron and, later, by optical microscopy. Fleischer, Price and Walker at the General Electric R&D laboratories developed diverse track-etching procedures, estimates of track registration and stability in different materials, track formation models, uranium determination in terrestrial, lunar and meteorite samples, neutron dosimetry and mineral dating using ²³⁸U spontaneous fission. Application to dating of natural and man-made glass was frustrated by low-uranium content and relative ease of track fading (annealing). In the 1970s–1980s, most FT analyses used apatite, zircon and titanite (sphene) to date tephra and acid intrusive rocks with the recognition of differing sensitivities of track annealing in each mineral. Studies in the Alps showed apatite with its greater susceptibility to annealing could provide estimates of the timing and rate of exhumation. The landmark 1980 Pisa FT Workshop highlighted problems with FT system calibration and emphasised the value of annealing in apatite to reveal thermal history. System calibration eventually reached a consensus agreement in 1988 at the Besançon FT Workshop with the majority of analysts adopting the zeta comparative approach. Multiple laboratory and borehole studies have determined the conditions for track annealing in apatite leading to widespread applications in exhumation, sedimentary basin, hydrocarbon exploration and other areas.

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1 FT Thermochronology: The Fundamentals

If a crystal of apatite (Ca₅(PO₄)₃(F, Cl, OH)) is immersed in dilute nitric acid at room temperature for about 20 s, minute etch figures are revealed which can be observed and counted under an optical microscope at high magnification (Fig. 1.1a). Similar etch figures are found if zircon (ZrSiO₄) and titanite (sphene) (CaTiSiO₅) are immersed in different chemical etchants for appropriate times and temperatures (Fig. 1.1b, c)—see Chap. 2, (Kohn et al. 2018) for specific conditions. These etched tracks have accumulated over time and result from the natural, spontaneous fission of ²³⁸U atoms in the crystal lattice of the minerals.¹ Each track results from the fission of a single atom. The number of these spontaneous tracks also depends upon the amount of uranium in the apatite, which is determined conventionally by irradiating the sample with low-energy neutrons. Irradiation induces a proportion of the less abundant ²³⁵U isotope to fission, giving a second generation of induced tracks that are revealed and counted in the apatite itself or, more usually, in a detector held against the mineral. The ratio of spontaneous-to-induced tracks provides a measure of the atoms decayed by fission to the total uranium remaining. Allowance has to be made in calculation for the additional decay of uranium by alpha emission. This spontaneous-to-induced track ratio, when used with the rate of spontaneous fission decay, a physical constant, yields the time during which fission tracks have been accumulating in the mineral which in some circumstances may equate to the age of the sample. This method is known as fission-track (FT) dating.

Fig. 1.1

Images courtesy of Andy Gleadow and Andy Carter

Fission tracks etched in commonly used materials (scale bars approx. 50 µm). a Spontaneous ²³⁸U tracks in apatite from Tioga ash bed, Pennsylvania, USA (Roden et al. 1990). Etched 5 M HNO₃ at 20 °C for 20 s. b Spontaneous ²³⁸U tracks in zircon from Fish Canyon Tuff. Etched in 100 N NaOH at 220 °C for 6 h (these samples predate use of the NaOH–KOH eutectic etchant). c Spontaneous ²³⁸U tracks in titanite (sphene) from the Thorr Granite in Donegal, Ireland. Etched in 1HF:2HCl:3HNO₃:6H₂O acid mixture at 20 °C for 6 min. d Induced ²³⁵U tracks in a nineteenth century man-made U-bearing glass from Robert Brill at Corning (Brill et al. 1964). Etched in 40% HF at 20 °C for 5 s.

Spontaneous tracks heal or fade naturally at temperatures above ambient values, a process known as annealing. Early applications to natural and man-made glasses found annealing of tracks (along with low-uranium contents) to be major problems. Apatite is more resistant to track fading than glass, but more susceptible than zircon or titanite, especially at temperatures typically found in the upper few kilometres of the Earth’s crust. Thus, calculated FT ages may not relate to the age of formation of a sample but to its subsequent history; measured ages should be considered alongside all available geological information.

Understanding the annealing parameters of fission tracks has provided the means for interpreting sample thermal history and interpreting the measured FT age. The particular sensitivity of apatite to annealing has made it especially useful in reconstructing thermal history, in particular by relating the reduction of the lengths of spontaneous tracks (specifically confined track lengths—see below) to temperature and time. Since each track is formed at a different time in the life of a sample, it is exposed to a different portion of that sample’s thermal history. The overall track-length distribution thus preserves the integrated temperature record of that sample. Such FT thermochronology has proved especially valuable in sedimentary basin analysis, in hydrocarbon prospection and in understanding the exhumation of crustal rocks. These applications form the basis of many of the chapters that follow.

2 The Fission-Track Story Begins

In the 1930s, Enrico Fermi (1934) and his collaborators bombarded uranium with neutrons, concluding that the resulting particles were new elements, lighter than uranium but heavier than lead. Ida Noddack (1934) criticised Fermi’s work in that he failed to analyse for elements lighter than lead, suggesting that:

“It is conceivable that the (uranium) nucleus breaks up into several large fragments, which would, of course, be isotopes of known elements but would not be neighbors of the irradiated element.”

Although her paper went largely unnoticed, Noddack effectively predicted nuclear fission. In 1939, Otto Hahn and Fritz Strassman in attempting to reproduce Fermi’s results clearly identified the reaction as a break-up of uranium into two lighter products with a range of atomic numbers. Lise Meitner and her nephew Otto Frisch (1939) confirmed these findings coining the term “fission” for the first time because of the similarity of the process to biological cell division. Having fled Germany in July 1938 first to the Netherlands and then to Stockholm (Meitner) and Copenhagen (Frisch), these authors gave the first qualitative discussion of the fission process, drawing the analogy with the liquid-droplet model and contrasting the disrupting effects of Coulomb repulsion with the stabilising influence of surface tension. On 1 September 1939, a propitious month in world history, Niels Bohr and John Wheeler presented a theoretical description which placed the recent developments firmly within the context of the liquid-droplet model. One year later, Flerov and Petrjak (1940) reported the first evidence of the natural spontaneous fission of a nuclide, namely ²³⁸U, eliminating any possible cosmic-ray-induced fission by working in an underground laboratory at the Dinamo Station of the Moscow Metro. The formal certificate of discovery stated:

“The new type of radioactivity with mother nucleus decays into two nuclei, that have kinetic energy of about 160 meV.”

The historical events of the 1940s dictated the next steps: the military implications of fission were seized upon, and the remainder of the decade saw frantic applied and basic experimentation. It was not until the 1950s and 60s that advances were made in basic theory largely due to the development of nuclear irradiation facilities.

The first positive recognition of uranium fission tracks can be attributed to D. A. Young in 1958, working at the Atomic Energy Research Establishment, Harwell, UK. Young found that if a lithium fluoride crystal was sandwiched against an uranium foil, irradiated with thermal (low energy) neutrons and then chemically etched, a series of etch pits would be produced. The number of etch pits showed close agreement with the calculated number of fission fragments originating from the uranium foil, and thus, it appeared that each etch pit related to some solid-state damage associated with the passage of the fission fragment. One year later, Silk and Barnes (1959), also working at Harwell, published the first direct transmission electron micrographs of damage tracks in mica created by the passage of ²³⁵U fission fragments. These discoveries started a chain reaction of electron microscopic observations of heavy charged-particle tracks in thin films of various materials, although the appearance of the tracks depended critically upon the structure and thickness of the film.

3 Fleischer, Price and Walker at GEC Schenectady

In 1961, P. Buford Price and R. M. Walker were working on nuclear tracks at the General Electric Research Laboratory at Schenectady, New York, being joined by R. L. Fleischer the following year. As reported in Fleischer (1998), together the trio were:

“Charged with doing science – with the long range expectation that some fraction of qualitatively new advances would be of practical use to society, and (crucially) to General Electric.”

They resolved to explore the use of solid-state track detectors in nuclear research and, subordinately, hoped to find fossil tracks of cosmic-ray-induced events in meteorites. Price and Walker (1962a) using an electron microscope to observe mica with zircon and apatite inclusions first identified fossil fission tracks which had resulted from the spontaneous fission of ²³⁸U. Unaware at this stage of Young’s experiments, Price and Walker (1962b) similarly found that tracks in mica could be “developed and fixed” by chemical etching giving permanent channels visible under an optical microscope, thus avoiding track fading problems common when viewing samples by electron microscopy. Anomalous etch figures which had long puzzled crystallographers (e.g. Baumhauer 1894; Honess 1927) were now identified as etched spontaneous fission tracks (Fleischer et al. 1964a). Tracks are revealed because of an accelerated etch rate (V_T) along the damaged track zone relative to the general (or bulk) etch rate (V_G) for the material. In minerals, V_T ≫ V_G for some crystallographic orientations (e.g. prismatic c-axis parallel sections of apatite and zircon) giving a linear etch figure (Fig. 1.2). In glasses, V_T approximates to V_G forming conical etch pits with circular to elliptical outlines (see Fig. 1.1d). For comprehensive descriptions of etching geometry, see Chap. 2 of each of Fleischer et al. (1975) and Wagner and van den Haute (1992).

Fig. 1.2

Fundamental track registration and etching geometry. a Latent fission tracks are revealed after time t by an accelerated etch rate (V_T) along the damaged track zone relative to the general (or bulk) etch rate (V_G) of the material. Track shape is determined by the difference in the two etch rates. Where V_T ≫ V_G as in many minerals, the track is linear (Fig. 1.1a–c). Where V_T is only slightly greater than V_G as in glasses, the track is an elliptical pit (Fig. 1.1d). b Tracks lying at an angle of incidence θ greater than a critical value θ_c are registered on the etched and viewed surface. c For tracks lying less than the critical angle θ_c, the surface of the material is removed faster during etching than the normal component of V_T and thus the track is totally removed. V_T/V_G defines a material’s etching efficiency, that is fraction of tracks intersecting a given surface that are etched on that surface under specified conditions (after Fleischer et al. 1975)

Fleischer, Price and Walker subsequently applied the nuclear track technique to a wide variety of other materials, including minerals, glasses and plastics, finding great variation in the sensitivity of materials to particles of different mass and charge. A profusion of papers from these authors and their associates during the mid- and late 1960s included track-etching recipes, estimates of the stabilities of tracks in different media, registration characteristics of different detectors, models of track formation, applications in uranium determination of terrestrial, meteoritic and lunar samples, and neutron dosimetry. A comprehensive review of their work was provided by the three scientists in their seminal volume “Nuclear Tracks in Solids” (Fleischer et al. 1975).

Pertinent to our story, Price and Walker (1963) first suggested that the spontaneous fission decay of ²³⁸U could be usefully employed as a radiometric rock and mineral dating method. FT ages of 3.5 × 10⁸ yr for muscovite from Renfrew, Canada, and of 5 × 10⁸ yr for phlogopite mica from Madagascar were taken as substantiating the concept, and suggestions were proffered for the use of other minerals. FT dating had been born!

4 Deriving a FT Age

As with other isotopic dating methods, a FT age depends on the decay of a naturally radioactive parent isotope to a stable daughter product—in our case a fission damage track. From Rutherford and Soddy’s law of radioactive decay, the rate of decay is proportional to the number of unstable parent atoms N remaining after any time t:

$${\text{d}}N/{\text{d}}t = - \lambda \,N$$

(1.1)

where λ is a constant of proportionality, the decay constant, with a specific value for each radionuclide, expressed in units of inverse time and representing the probability that a nucleus will decay within a given period of time. Integrating Eq. 1.1 with respect to time and accepting that at time t = 0 none of the original parent atoms have decayed gives:

$$N = N_{\text{o}} \exp ( - \lambda \,t)$$

(1.2)

which is the general formula for describing the number N of radioactive nuclei remaining after time t, where N_o is the initial number of atoms present. The number of decay events D_t which have occurred since time t is given by:

$$D_{t} = N_{\text{o}} {-}N$$

(1.3)

Since it is easier to deal with N, the measurable number of atoms of a radionuclide still remaining in a system, rather than estimating N_o, the original number of atoms present, Eq. 1.2 can be arranged to give an expression for N_o:

$$N_{\text{o}} = N\,(\exp \lambda \,t)$$

which, substituted into Eq. 1.3, gives:

$$D_{t} = N\,(\exp \lambda \,t - 1)$$

(1.4)

²³⁸U decays both by α-emission, eventually forming ²⁰⁶Pb, and by spontaneous nuclear fission. Each process has a specific decay constant which can be summed to give λ_D, the total constant for the decay of ²³⁸U by both mechanisms. λ_D is essentially just the α-decay constant because this is more than six orders of magnitude greater than the fission decay constant λ_f. Thus for the total decay of ²³⁸U, Eq. 1.4 reads:

$$D_{t} = N\,(\exp \lambda_{\text{D}} t - 1)$$

(1.5)

D_t includes both α-decay and spontaneous fission decay events, the small fraction due to spontaneous fission, D_s, being given by:

$$D_{\text{s}} = \lambda_{\text{f}} /\lambda_{\text{D}} N\,(\exp \lambda_{\text{D}} t - 1)$$

(1.6)

Equation 1.6 gives the number of fission events which have taken place over time t in a material now containing N atoms of ²³⁸U. Provided the material contained no fission tracks at the beginning of time t and that it has lost no fission tracks through annealing, then it will now contain D_s spontaneous fission tracks, and t will be its FT age. Equation 1.6 can be solved for t provided that D_s can be evaluated and expressed as a proportion of N.

The number of fission events, D_s, in a unit volume can be measured from the area density of etched fission tracks ρ on an internal surface of the uranium-bearing material. Only a fraction of the fission events within one fission-track range of the surface will actually intersect it to give an etchable track. This fraction can be expressed in terms of an effective distance R from the etched surface, within which every fission event can reach the surface although not all may be registered as an etchable track. R is obtained by integrating the contribution of etched tracks from all distances up to R_o, the maximum fission-fragment range. This integral can be evaluated to show that R is equivalent to the etchable range of one fission fragment, that is half a track range on either side of an internal surface. The number of fission tracks crossing an internal surface is therefore given by D_s R.

The track density ρ actually observed on any surface will also be determined by the etching efficiency η that is the fraction of tracks crossing the surface which are revealed by etching. Thus for the etched FT density on any internal surface, we can write:

$$\rho = D_{\text{s}} \,R\,\eta$$

(1.7)

For the ²³⁸U spontaneous FT density, ρ_s, resulting from D_s fissions per unit volume, Eqs. 1.6 and 1.7 combine to give:

$$\rho_{\text{s}} = \lambda_{\text{f}} /\lambda_{\text{D}} [^{238} U]\,(\exp \lambda_{\text{D}} t - 1)\,R\,\eta$$

(1.8)

where N has been replaced by [²³⁸U], the number of atoms of ²³⁸U per unit volume remaining in the uranium-bearing material. Conventional evaluation of uranium uses neutron activation, but direct determination of [²³⁸U] requires higher energy neutrons which also induce fission in other uranium and thorium isotopes. Lower-energy, thermal neutron irradiation causes ²³⁵U alone to fission, creating a second, induced track density in the host material. The number of thermal neutron-induced ²³⁵U fissions per unit volume, D_i, can be expressed as:

$$D_{i} = \left[ {^{235} U} \right]\sigma \,\phi$$

(1.9)

where [²³⁵U] is the number of ²³⁵U atoms per unit volume; σ the ²³⁵U nuclear cross section for thermal neutron-induced fission; and ϕ the neutron fluence received by the sample, in neutrons per cm².

These induced fission tracks can be etched on an internal surface of the host material in exactly the same way as for the spontaneous tracks. Substituting D_i for D in Eq. 1.7 gives the induced track density, ρ_i, observed on an internal surface:

$$\rho_{i} = \left[ {^{235} U} \right]\sigma \,R\,\phi \,\eta$$

(1.10)

on the reasonable assumption that R and η are essentially identical for ²³⁸U and ²³⁵U fission-fragment tracks. By taking the ratio of the two track densities from Eqs. 1.8 and 1.10, these range and etching efficiency terms cancel, giving:

$$\rho_{\text{s}} /\rho_{i} = (\lambda_{\text{f}} \left[ {^{238} U} \right]\exp \lambda_{\text{D}} t - 1)/(\lambda_{\text{D}} [^{235} U]\sigma \,\phi )$$

(1.11)

Assuming the atomic ratio [²³⁵U]/[²³⁸U] for natural uranium is constant in nature, it may be represented by the isotopic abundance ratio I. Solving Eq. 1.11 for t gives the general form of the FT age equation (Price and Walker 1963; Naeser 1967):

$$t = 1/\lambda_{\text{D}} \ln \,[1 + (\lambda_{\text{D}} \sigma \,I\,\phi \,\rho_{\text{s}} )/(\lambda_{\text{f}} \,\rho_{i} )]$$

(1.12)

Equation 1.12 assumes that the spontaneous and induced track densities, ρ_s and ρ_i are measured on surfaces with similar geometry or else modified by a suitable factor. A useful approximation can be made by noting that ln (1+ x)= x, where x is much smaller than 1. Where FT ages are less than a few hundred million years, this approximation can be applied to Eq. 1.12 which then simplifies to:

$$t = (\sigma \,I\,\phi \,\rho_{\text{s}} )/(\lambda_{\text{f}} \,\rho_{i} )$$

(1.13)

This approximation simply means that over this period of time, which is short compared to the half-life of ²³⁸U, there is so little reduction in the total amount of ²³⁸U by radioactive decay that effectively it can be regarded as constant. The total decay constant, λ_D, therefore cancels out in the simplification.

5 Aspirations for the Infant FT Method

Price and Walker’s (1963) paper triggered a series of studies to date mica, ubiquitous in many igneous rocks (e.g. Fleischer et al. 1964a; Bigazzi 1967; Miller 1968). Much activity was also invested in determining recipes for etching tracks in a wide variety of minerals including tourmaline, epidote and garnet, the tracks being derived by implantation of heavy ions (see Fleischer et al. 1975; Wagner and van den Haute 1992 and references therein).

Volcanic and other glasses also received considerable attention in the infancy of the method. In ocean floor basalts correlation of K–Ar ages with preserved magnetic reversal signatures offered support for the then-new concept of sea-floor spreading. This prompted attempts to measure FT data on the glassy skins of pillow basalt lavas erupted from the Mid-Atlantic Ridge spreading centre (e.g. Aumento 1969; Fleischer et al. 1971). The dating of glass shards from acidic volcanic tephra was seen as a direct means of determining the age of volcanic eruption with data published from studies in Tanzania (Fleischer et al. 1965a), New Zealand (Seward 1974, 1975) and the Yukon (Briggs and Westgate 1978). FT dating was used to supplement K–Ar ages determined on tektites, those enigmatic glassy objects probably resulting from meteorite impacts (see discussion in Wagner and van den Haute 1992). In archaeometry, the infant FT dating technique prompted excitement with studies undertaken on the dating of artifacts heated in fires, glazes on ceramic bowls and man-made glasses (see Wagner 1978; Wagner and van den Haute 1992; Bigazzi et al. 1993).

Glasses have low-uranium contents and require long analysis times to search for just a few tracks, yielding very poor statistics and high analytical errors; they are also especially susceptible to track annealing at temperatures <<100 °C. Most FT studies on glasses were in the early years of the method, and this application is now generally considered to be inaccurate if used for direct dating. Similarly virtually no dating analyses have been reported since the 1970s for micas or other low-uraniferous minerals whose etching characteristics had been investigated. In contrast, in uranium ores the crystal structure becomes metamict (effectively destroyed) as a result of α-recoil damage from uranium and thorium decay, and no fission tracks can be discerned. To take the infant FT method, forward attention turned to using accessory minerals.

6 Accessorise: Apatite, Zircon and Titanite

The accessory minerals apatite, zircon and titanite (sphene) have trace amounts of uranium in the ppm range giving resolvable numbers of spontaneous tracks. They have proved the ideal material for routine FT analysis. Credit must go to Charles (Chuck) Naeser and to Günther Wagner for pioneering the use of accessory minerals to solve geological problems. Naeser, working in the Southern Methodist University, Dallas, Texas, and subsequently the US Geological Survey, Denver, established the fundamental preparation and analytical techniques and readily passed on his knowledge and expertise to the next generations of FT exponents. Initially, other workers analysed only apatite and titanite because of the simpler handling procedures (see Chap. 2, Kohn et al. 2018). Naeser (1969) had determined FT ages on zircons, but his sample handling techniques were complicated and not readily replicated by others. A revised technical approach (Gleadow et al. 1976) based on Naeser’s early experiments opened up FT dating of zircon to all workers, with zircon ages frequently equating with those of titanite. Wagner was pursuing very similar studies on apatite at the University of Pennsylvania and then at the Max-Planck Institut für Kernphysik, Heidelberg (Wagner 1968, 1969—and see references below).

The philosophy in the 1960s and 1970s was to use the FT technique as a dating tool analogous to K–Ar and Rb–Sr methods to determine the age of a sample—by implication the crystallisation age. Investigations concentrated on the dating of acid volcanic and intrusive rocks. A major study dating Tertiary ash-flow tuffs from Central Nevada (Naeser and McKee 1970) furthered the application of FT dating to tephrochronology, with many studies providing time-marker horizons in stratigraphic sequences which have served in Phanerozoic timescale calibration, e.g. zircons and apatites from tuffs and bentonites in UK Ordovician and Silurian stratotypes (Ross et al. 1982). Early studies on acid intrusive rocks yielded apatite FT (AFT) and titanite FT (TFT) ages which equated with K–Ar and Rb–Sr ages, and similarly represented the timing of crystallisation (see, e.g., Naeser 1967; Christopher 1969). However, the recognition of the different annealing characteristics of apatite and titanite (Wagner 1968; Naeser and Faul 1969) produced a tool for the detection of thermal events whereby discordant ages from pairs of co-existing minerals gave a clear indication of minor heating. Calk and Naeser (1973) studied the 10 Ma-old intrusion of a 100-m-diameter basaltic plug into the 80 Ma-old Cathedral Park quartz monzonite in Yosemite National Park, California. Their AFT ages in the country rock were totally or partially annealed up to 150 m from the contact, whilst TFT ages were unaffected just 10 m from basalt.

Clear differences between AFT and K–Ar biotite and hornblende ages were reported by Wagner (1968) for the same granite, granodiorite and gabbro samples from the Odenwald basement, Germany: apatite ages ranged between 69 and 105 Ma, whilst K–Ar spanned 315–340 Ma. Since no post-Hercynian thermal event could be presumed to have affected these rocks, Wagner argued that the AFT ages represented the approximate time of cooling through ~100 °C, thereby revealing a difference in uplift rate between the northern and southern Odenwald. This probably represents the first approach towards interpreting FT data in terms of exhumation.

Church and Bickford (1971) related AFT ages of 45–50 Ma from a suite of igneous rocks in the Sawatch Range of Colorado (Rb–Sr whole-rock isochron age of 1650 ± 35 Ma) together with other similar AFT and TFT ages reported by Naeser and Faul (1969) to Laramide igneous activity. Stuckless and Naeser (1972) reported three time–temperature events in the evolution of the Precambrian plutonic basement around the Superstition volcanic field in Arizona. The intrusion of granite at ~1390 Ma recorded by Rb–Sr whole-rock isochron and TFT systems, completely reset the titanite and disturbed the Rb–Sr systems in a quartz diorite intruded earlier (Rb–Sr whole-rock age 1540 ± 45 Ma; TFT age 1390 ± 60 Ma). A third episode at ~50 Ma recorded by the AFT age in the granite represented cooling due to uplift and erosion subsequent to the Laramide orogeny.

In the Tatra mountains, Poland, AFT ages from 10 to 36 Ma in Hercynian granitic and metamorphic basement significantly post-dated the main nappe-style folding at ~80 Ma, leading Burchart (1972) to conclude that the AFT ages related to Miocene post-orogenic uplift and erosion.

AFT was a chronometer capable of recording “events” at temperatures much less than those detected by other mineral and isotopic systems. Publication of the seminal work “The tectonic interpretation of fission track ages” by Wagner and Reimer (1972) represented a major advance in the understanding and use of AFT ages in active mountain belts. The study showed the distribution of AFT ages in the Central and Southern European Alps to be concordant with regional tectonic elements when considered with elevation: AFT age generally increased with elevation. This was interpreted as the earlier cooling of the upper sample below the temperature at which fission tracks are retained; thus, for a limited lateral distance, the difference in sample elevation divided by the difference in AFT age may provide a direct measure of uplift. Wagner and Reimer reported an uplift rate of 0.4 mm/yr for the Monte Rosa nappe area and that the fastest uplift around the Simplon Pass had occurred in recent times. This study (and the less readily available Wagner et al. (1977)) represent the foundation of many subsequent tectonic uplift and exhumation studies in active mountain belts worldwide, although in modern thinking the trend of increasing age with elevation may often reflect an uplifted partial annealing zone (see Chap. 8, Malusà and Fitzgerald 2018, and Chap. 9, Fitzgerald and Malusà 2018).

7 Problems and Renaissance: Pisa 1980

Despite this promising beginning and the flurry of activity to use the fledgling method to determine ages, FT dating faced serious criticism in the 1970s. Some established geochronologists who measured isotope abundances using mass spectrometry underlined the low analytical precision of the FT method, with the results of a relatively small number of fissioned uranium atoms being observed and counted manually with the inherent potential for misidentification. This was contrasted with other isotopic methods using mass spectrometric automated counting of many ions of precisely known mass. The high level of sensitivity of fission tracks to annealing (especially in apatite) was viewed as rendering the method of little, if any value in determining age—remember the thinking was still dominantly of formation or crystallisation age. A third criticism was the lack of a single system of calibrating the FT system—in particular with no agreed value for the decay constant λ_f—giving little confidence to the comparison of results from different workers and laboratories. Together, these perceived failings caused one pre-eminent British isotope geologist to dismiss fission tracks as the “Cinderella of dating methods”. By the late 1970s, the earth sciences community had heard of fission tracks and they wondered if the method might provide something interesting to solve geological problems, but was suspicious as to whether the technique was fundamentally flawed.

Under this cloud of uncertainty, a group of FT workers attending the 4th ICOG² in 1978 met to discuss shared problems in methodology, in fundamental principles and in interpretation. They determined to hold a workshop specifically to deal with FT matters and hopefully resolve some of the outstanding problems. Thus in September 1980, 44 FT practitioners from 15 countries took up this proposal, meeting in Pisa,³ Italy, at the Domus Galilaeana, founded in 1942 to commemorate the tercentenary of the death of Galileo Galilei. The Pisa Workshop was a critical week in the history of FT thermochronometry and truly represented the renaissance of the method with four main issues being debated:

• Methodology: what experimental strategies are used by different laboratories?

• Calibration: how is the FT dating system calibrated?

• Statistics: what are the uncertainties of the method and how do different laboratories compare?

• Interpretation: what does track annealing mean and can lowered ages be corrected?

Each of these issues is considered below. The formal confrontation of these problems at Pisa determined the FT community to seek effective solutions. Possibly most significant was the recognition that the understanding of annealing provides a unique means to reveal thermal history (Gleadow and Duddy 1981; Green 1981a) rather than being the hitherto perceived burden. Here lies the foundation of the diversity of geoscience applications we see today including application to hydrocarbon prospection (Gleadow et al. 1983). On FT calibration, the issue was subsequently taken up by the IUGS Subcommission on Geochronology with widespread consultation leading to a recommendation and agreement on procedure (see Sect. 1.9).

8 Experimental Strategies

Ideally, the spontaneous and induced track densities measured in FT dating should be registered, revealed and counted under identical conditions over areas having exactly the same uranium content. At the Pisa Workshop Andrew Gleadow underlined that a wide variety of strategies of differing reliability were in use by FT analysts and that the sample may also impose a compromise from the ideal. Variation between strategies derives essentially from differences in registration geometry and etching efficiency of the surfaces on which the tracks are counted. Two distinct groups of procedures can be distinguished (Fig. 1.3), (Gleadow 1981; Hurford and Green 1982).

Fig. 1.3

Experimental strategies for FT dating (modified from Hurford and Green 1982). Amongst the methods described in this chapter, only the external detector (and to a much lesser extent population) methods are nowadays employed. Some laboratories now use LA-ICP-MS to determine uranium content (Hasebe et al. 2004), the equations for which are given in Chap. 6

Multi-grain Methods

use separate sample aliquots to determine spontaneous and induced tracks, the track counts from each being summed over the total grains counted (see, e.g. Price and Walker 1963; Naeser 1967, 1979). Typically, areas usually of equal size are measured in 100 grains for each track count. The population method has been widely used and requires one aliquot to be heated to anneal fully the spontaneous tracks before irradiation to induce tracks in a portion of ²³⁵U atoms. The two aliquots are then processed identically and counted sequentially, one aliquot containing only spontaneous tracks the other only induced tracks. The subtraction method omits the heating step so that the irradiated portion contains both induced and spontaneous tracks, the induced track density being calculated by subtracting the spontaneous density, inherently less precise since two uncertainties are involved in determining the induced track density.

With multi-grain methods both track counts are made on internal surfaces of the same material with identical registration and etching characteristics. However, statistically equivalent uranium concentrations are assumed in the two aliquots, which supposes a relatively homogeneous uranium distribution both within and between the sample grains, frequently not true. Multi-grain approaches also assume a single age population, probably true for a rapidly cooled volcanics but invalid for samples with multiple age populations, e.g. a contaminated volcaniclastic. Further, laboratory annealing can remove accumulated α-recoil radiation damage in the crystal lattice resulting from uranium and thorium decay. This appears to have no effect on apatite (possibly because α-recoil damage is not preserved) but for zircon and titanite the etching characteristics may be substantially altered, invalidating one of the principal advantages of the multi-grain strategy.

Single-grain Methods

allow ages to be measured for each suitable grain even at relatively small sizes (~100 µm) and are essential for samples containing multiple populations. Historically 6–10 grains were analysed for each sample. Today, when the age structure of a sample is used to reveal source and thermal history, many more grains are examined—see Chap. 2, (Kohn et al. 2018). The re-polish and re-etch strategies are variations with a sample re-polished, re-etched and recounted after irradiation to determine the induced track density (e.g. Fleischer and Price 1963); these approaches compound uncertainties and are no longer used. In contrast, the external detector method (EDM) (Fleischer et al. 1964b; Naeser and Dodge 1969) has been used almost exclusively as the FT strategy of choice for several decades. In the EDM ²³⁸U spontaneous fission tracks are etched in the grain and ²³⁵U induced tracks recorded and etched in a detector of low-uranium muscovite held against the grain mount during irradiation. Analysis examines the etched grain and its mirror image recorded by ²³⁵U induced tracks in the detector allowing exact comparison of the identical uranium contents. The EDM records tracks with different track registration geometries. Spontaneous tracks have a 4π geometry with tracks originating from fissioned uranium atoms in the grain lying below the viewed surface, and from above in the part of the grain removed during polishing. In contrast, the detector has 2π geometry with tracks contributed only from below. A correction factor must therefore be applied to the spontaneous/induced ratio which, in the ideal circumstance, is 0.5. Deviation from this value would arise if the bulk etch rate (see Fig. 1.2) was high in either grain and/or detector, thereby possibly removing tracks lying at low angles to the etched and viewed surface. Fortunately, the minerals in common use, apatite, zircon and titanite all have high etching efficiencies for prismatic (c-axis parallel) faces, as does muscovite mica mainly used as detector, and thus, the ideal geometry of 0.5 is appropriate (Gleadow and Lovering 1977; Green and Durrani 1978). Note that etch rate is dependent upon crystal orientation and other faces may exhibit different and anisotropic etching. Some early studies used polycarbonate plastic as a detector. The track registration mechanism may be quite different for such plastics (see Fleischer et al. 1975), and a geometry factor of 0.5 may also be inappropriate. Accordingly, low-uranium muscovite is preferred as a detector by most analysts.

9 Calibration of the FT Dating System

A major problem confronting the FT method from its inception until the early 1980s was the fundamental question of system calibration and hinged, in part, upon the value of the ²³⁸U spontaneous fission decay constant λ_f. Some 45 experiments revealed a spectrum of results which centred around either 7 × 10⁻¹⁷ yr⁻¹ or 8.5 × 10⁻¹⁷ yr⁻¹, ~20% difference (see, e.g., Wagner et al. 1975; Thiel and Herr 1976; Bigazzi 1981; van den Haute et al. 1998). Four groups of experimental procedures have been used to determine λ_f:

• direct determination of fission events using ion chambers and other particle systems

• radiochemical or mass spectrometric measurement of uranium and fission products

• detection and counting of fission tracks in solid-state track detectors (SSTDs) or in photographic emulsions

• comparison of measured FT ages with independently known ages.

Most λ_f values determined using SSTDs and by comparison with minerals from rocks of known age supported a lower value. These experiments require neutron irradiation, and intuitively such methods might appear more appropriate to FT dating with calibration and sample determinations using similar procedures. However, evaluation of neutron fluence can vary according to the dosimetry system used. Thus when a λ_f value determined using specific neutron dosimetry is used to evaluate a sample, similar irradiation and dosimetry protocols should be followed. Those λ_f determinations using direct measurements and radiochemical methods tend to support the higher value. The independence of these values from any neutron dosimetry, track registration or track-etching process argues that they may be more robust when seeking an absolute calibration approach to FT analysis.

Neutron Fluence Measurement

can use either metal activation monitors or uranium-doped glass dosimeters. With a metal activation technique the neutron-induced gamma activity in foils of gold, cobalt or copper is measured using a scintillation counter and, using the mass of isotope present in the foil, the reacting neutron fluence is calculated. However, neutron beams are not mono-energetic and the response of an isotope varies according to the energy of the bombarding neutron. Different isotopes respond to neutrons of different energies in different ways: the response of one monitor compared with another, and with the ²³⁵U in a dating sample, cannot be assumed to be equivalent.

Fortunately for thermal neutrons (energies of 0–0.25 eV with the highest probability of 0.0253 eV at 20.4 °C), the responses of ²³⁵U, ¹⁹⁷Au and ⁵⁹Co are virtually parallel with a 0.5 slope denoting a 1/V behaviour (see Wagner and van den Haute 1992, their Fig. 3.3). Thus, in principle, for reactors with well-thermalised fluxes the fluences reacting with these isotopes should be equivalent. However, at higher energy levels (in the epithermal neutron energy range) this relationship breaks down with large resonance peaks in the Au capture cross section. Use of a poorly thermalised reactor facility would thus result in deviation from this 1/V relationship and would complicate the comparison of the ²³⁵U, ¹⁹⁷Au and ⁵⁹Co responses necessitating complex corrections. In addition, whilst thermal neutrons induce fission only in ²³⁵U, epithermal neutrons induce fission in both ²³⁵U and ²³⁸U. Fast neutrons induce fission in both uranium isotopes and ²³²Th, the resulting tracks being indistinguishable. Neutron dosimetry has been treated in detail by Green and Hurford (1984) who also recommend minimum specifications for thermalisation of reactor facilities used for FT work expressed in terms of cadmium ratios of 3 for Au, 24 for Co and 48 for Cu.⁴

Uranium-Doped Glasses

can be used to monitor neutron-induced ²³⁵U fission events by counting the resulting tracks in the glass or, more usually, in a detector held against the glass during irradiation. Detectors of low-uranium mica are preferable in that they preserve a permanent record of the irradiation whilst leaving the dosimeter glass undamaged and reusable for multiple irradiations (see, e.g., Hurford and Green 1983). As a dosimetry method it is appealing in that neutron-induced ²³⁵U fission is used in both standard glass and unknown sample. However, quantitative determination of fluence is complicated by the need for evaluation of the detection and etching efficiencies of the system. Nevertheless, if identical dosimeter and experimental conditions are always used, the fluence ϕ is related to the measured induced track density ρ_d in the dosimeter (or its detector) by:

$$\phi = B\rho_{\text{d}}$$

(1.14)

where B is a constant specific to the dosimeter (Fleischer et al. 1975; Hurford and Green 1981a).

To avoid the difficult empirical evaluation of fission-fragment ranges and etching efficiencies (see, e.g., Wagner and van den Haute 1992), some workers have used metal activation monitors to evaluate B, often over multiple irradiations: Hurford and Green (1983) showed values of B for two dosimeter glasses measured over a 5-year period. B may then be used to derive fluence values in subsequent irradiations which, in turn, are substituted into the age equation to calculate sample ages.

A comprehensive listing of uranium-doped glasses used as neutron dosimeters is given in Hurford (1998, Table 1). The two sets of glasses used most extensively are the NIST (NBS) SRM 600 series and six glasses subsequently denoted CN1–CN6 prepared by Jan Schreurs at the Corning Glass Works. A subset of SRM 600, numbered SRM 961–964 was issued as pre-irradiated glasses with neutron fluences measured at NBS by activation monitors (Carpenter and Reimer 1974). These pre-irradiated glasses offered a common baseline for all workers, whereby a virgin SRM glass wafer of the same series could be irradiated in an unknown reactor facility and then etched simultaneously with the equivalent NBS-irradiated glass. After counting the track densities in the two glasses, the fluence in the unknown reactor ϕ_UNK could be calculated directly by comparison with the cited NBS fluence value ϕ_NBS:

$$\phi_{\text{UNK}} = \phi_{\text{NBS}} \,\rho_{{{\text{d}}2}} /\rho_{{{\text{d}}1}}$$

(1.15)

where ρ_d1 is the ²³⁵U induced track density measured in the NBS pre-irradiated glass, and ρ_d2 is the ²³⁵U induced track density measured in the equivalent glass irradiated in the unknown reactor.

Despite the conceptual excellence of this calibration experiment, its effectiveness was marred by differences of up to 11% in the fluences measured by gold and copper activation monitors for the same NBS irradiation. Unlike the SRM 600 series, the Corning glasses were prepared:

• using an uranium salt with natural uranium isotopic ratios—the salt was prepared before 1939, that is before depletion of ²³⁵U was initiated

• without the addition of other trace elements which can produce unwanted additional activity after irradiation and/or disturb the neutron fluence, e.g. Gd, can absorb neutrons.

Repeated analysis has shown an homogeneous distribution of uranium both within and between the Corning glass wafers. Thus for most analysts, CN1, CN2 and CN5 have become the dosimeter glasses of choice with, respectively 39.81 ± 0.69, 36.5 ± 1.4 and 12.17 ± 0.62 uranium ppm by weight (see Hurford 1990; Bellemans et al. 1995).

An additional series of unirradiated and irradiated uranium-doped glasses IRMM-540 has been produced at the Institute for Reference Materials and Measurements of the European Commission, Geel, Belgium, with fluence measurement using both ⁹⁷Au and ⁵⁹Co monitors (De Corte et al. 1998; Roebben et al. 2006).

Interdependence of λ_f and ϕ

In the 1970s and early 1980s, analysts were publishing FT ages using different λ_f values and neutron dosimetry schemes. In the age equation (Eq. 1.13), a change in either λ_f or ϕ could be compensated for by a change in the other. Such changes were not a matter of artifice but resulted from the selection by the analyst of a λ_f value and neutron irradiation scheme which gave the right ages on standard material (see below). This interrelation of λ_f and neutron dosimetry has been discussed by Khan and Durrani (1973), Wagner et al. (1975), Thiel and Herr (1976), Hurford and Green (1981a, 1982 and 1983). It was the ratio ϕ/λ_f which was effective in giving these concordant results, indicating that simple agreement with an independent age cannot be taken to validate individually either the neutron dosimetry or the value of λ_f. Correct calculation of a sample age cannot be made by casual selection of λ_f and a neutron fluence dosimetry scheme, but Eq. 1.13 can be used to discern which combination of parameters gives the right answers on age standards of known age.

Standards are critical for all analytical procedures, providing baselines to assess the reproducibility of measurement, comparison of analysts, equipment and laboratories, and to compare different methodological approaches. Age standards have long been used in geochronology to provide confidence in the data to the geological end-user and should meet strict criteria:

• come from an accessible, geologically well-documented horizon

• be sufficient to fulfil immediate and future needs

• be homogeneous in age; if a mineral is separated it should be a single generation and free from older, derived crystals

• have unambiguous, precise independent calibrating ages (e.g. ⁴⁰Ar–³⁹Ar, K–Ar, U–Pb and Rb–Sr), preferably determined in more than one laboratory and compatible with known stratigraphy

• require no correction to the FT density based on track-size measurement (see G. A. Wagner in Hurford and Green 1981b, 1983).

Although a prospective standard may conform to these criteria, if the FT and independent ages were inequal, a systematic error would be introduced into the FT calibration. Such a difference could exist if a sample had been heated sufficiently to cause partial track loss, but insufficiently to affect the independent (e.g. argon) system: such an FT calibration would subsequently yield sample ages which were too old. Conversely, inclusion of older derived crystals in an FT calibration analysis would give an FT value disproportionately high when compared with the calibrating age, resulting in the subsequent calculation of sample ages that are too young. The self-consistency of results obtained on a series of putative age standards from wide geographical, temporal and uranium concentration ranges safeguards against the introduction of such a systematic error since it is inconceivable that such an error could be of constant proportion for each of a widespread group of samples. Ideal age standards are sub-aerial volcanic rocks or minor high-level intrusives, which have cooled quickly and which show no evidence of post-formational disturbance. Few samples completely fulfil the conditions demanded of an age standard. Table 1.1 lists those samples most widely used in FT analysis.

Table 1.1 Age standards used most frequently in FT dating

Zeta and the Besançon Agreement

An alternative approach to FT calibration which circumvented the need for explicit evaluation of λ_f and an absolute determination of thermal neutron fluence was proposed by Fleischer and Hart in 1972—and then ignored. They suggested that the simplified age equation (Eq. 1.13) may be rewritten in terms of three track densities and a proportionality factor zeta $\zeta$:

$$t = \zeta (\rho_{\text{s}} /\rho_{i} )\,\rho_{\text{d}}$$

(1.16)

Note that neutron fluence ϕ is represented by ρ_d the track density in a specific dosimeter glass or adjacent mica detector. Zeta for the dosimeter glass may be evaluated against a mineral standard whose age t_std is known (or reasonably inferred) from independent age determinations:

$$\zeta = (t_{\text{std}} \,\rho_{i} )/(\rho_{\text{s}} \,\rho_{\text{d}} )$$

(1.17)

Substituting ζ into the full FT age Eq. 1.12, and introducing an appropriate geometry factor G, gives:

$$t = 1/\lambda_{\text{D}} \ln \,(1 + G\,\lambda_{\text{D}} \zeta \,\rho_{\text{d}} \,\rho_{\text{s}} /\rho_{i} )$$

(1.18)

where ζ for a given glass dosimeter is evaluated from age standards according to:

$$\zeta = \left[ {\exp \,(\lambda_{\text{D}} t_{\text{std}} ) - 1} \right]/\left[ {\lambda_{\text{D}} (\rho_{\text{s}} /\rho_{i} )_{\text{std}} \,\rho_{\text{d}} } \right]$$

(1.19)

and where G = 0.5 for the external detector method, and G = 1 for the population method.

The first zeta values were published by Paul Green and myself for dosimeter glasses SRM 612, CN1 and CN2 measured using zircons from four sources over a seven-year period (Hurford and Green 1983). Green (1985) extended this initial zeta study to a larger number of zircon samples and, for the first time, to apatite and titanite. Three dosimeter glasses were used in his study although the results were recalculated to a common baseline for glass SRM 612 and showed overall weighted mean zetas of 381.8 ± 10.3 for zircon, 353.5 ± 7.8 for apatite and 320.0 ± 12.4 for titanite. Green notes that the study illustrates the need for all FT age determinations to be derived from a calibration scale based on the use of age standards and that consistent FT counting must be achieved in controlled experiments before reliable ages may be determined on unknown samples. In contrast to Green’s results, Takahiro Tagami (1987) found no difference within analytical uncertainties between zetas which he measured for glass SRM 612 using zircon, apatite and titanite age standards: 348.4 ± 8.3 (2σ) zircon; 330.1 ± 15.2 apatite; and 335.7 ± 11.5 titanite.

During the 1980s, the FT community recognised that the zeta approach circumvented the uncertainties of FT calibration, with age standards providing a common baseline for all analysts. More zeta values were published and the long-forgotten proposal of Fleischer and Hart (1972) took root. Under the auspices of the IUGS Subcommission on Geochronology, all known FT workers were questioned about their approach to calibration, following the IUGS precedent of agreeing decay constants for other geochronological methods (Steiger and Jäger 1977). Long discussions and extensive consultations culminated in 1988 at the 6th International FT Workshop in Besançon, France, in the consensus recommendation of two approaches to calibration (Hurford 1986a, 1990):

• the zeta approach was recommended for all minerals and techniques using the age standards listed in Table 1.1.

• the absolute approach with selection of λ_f and measurement of neutron fluence was recommended for population method analyses of apatite only.

Since 1988, FT workers have almost exclusively followed the IUGS recommendation with the vast majority opting for the zeta calibration approach publishing their zeta values or referencing their data in doctoral theses. The FT method has burgeoned in the subsequent decades and problems that beset the method during the 1970s have been overcome, securing widespread acceptance of the method throughout the geoscience community. Zeta has enabled the FT community to produce results which are comparable between analysts and which relate directly to other radiometric ages. To counter the 1970s comment from the eminent British isotope geologist: “Cinderella had gone to the ball!”

However, zeta combines physical constants with empirically determinable factors. As Peter van den Haute and his colleagues have eloquently pointed out, precision neutron metrology is today practicable and an exact determination of λ_f achievable (van den Haute et al. 1998). Perhaps future deconvolution of zeta might be possible with an agreed λ_f value and a defined activation monitor protocol. However, for the present the zeta approach remains the preferred calibration method for most laboratories.

10 Uncertainties and Data Reporting

All analytical methods need to define experimental uncertainty to provide the user with the limitations placed on the measured result. FT thermochronometry is dependent in part upon personal technique and experience, and so reproducibility of analysis needs to be demonstrated; the Besançon agreement recommended that analysts make a minimum of 5 measurements per mineral phase over at least 3 irradiations to establish their calibration (Hurford 1990). In most laboratories, new workers are more likely to analyse at least 30 age standard mounts to establish their mean zeta value, whilst age standard mounts are regularly included in irradiation packages as a control of irradiation and experimental conditions.

Consistency in reporting of results and data enables other workers to review the techniques and parameters used, and to permit comparison of data from different laboratories (see Hurford 1990 after Naeser et al. 1979). It was also recommended that data for the calibration analyses be included or referenced and that some measure of the dispersion of the count data should be reported. It is normally assumed that FT counts can be described by a Poissonian distribution, an assumption supported by the work of Gold et al. (1968) who counted 4053 tracks in over 345 mica detector strips in contact with a uranium foil source. The standard deviation, σ, of a track count, N, is approximated by:

$$\sigma (N) = N^{0.5}$$

(1.20)

which can be applied to both the spontaneous and induced track densities. As most analysts monitor neutron fluence using a uranium dosimeter glass, Eq. 1.20 can also be applied to the dosimeter track density. For practical purposes, an error for the calculated age, t, can be written as:

$$\sigma (t) = t\left( {1/N_{\text{s}} + 1/N_{i} + 1/N_{\text{d}} } \right)^{0.5}$$

(1.21)

where N_s is the sum of spontaneous tracks counted in all grains, N_i is the sum of all induced tracks counted in all grains, and N_d sum of all tracks counted in the dosimeter glass detector (or glass).

This error estimation (frequently termed the conventional error analysis after the terminology of Green 1981b) has been that used by most workers for EDM analyses. However, extra-Poissonian error can be present in an analysis resulting from a multiplicity of sources, e.g. track misidentification, use of a mica detector with significant uranium content, inappropriate etching, microscope or irradiation preparation technique, or reactor flux gradients (Burchart 1981, Green 1981b). The analysis of different populations of FT ages within sediment can provide important information about sediment provenance. The use of probability density curves (Clarke and Carter 1987) and peak fitting programs such as BinonomFit (Brandon 1996) have enabled the discrimination of different age modes (e.g. Hurford et al. 1984).

In 1981, Rex Galbraith suggested using a χ² test to detect the presence of uncertainty additional to that allowed for by Poissonian variation in track counts, and this has become standard in reporting results. An additional measure of data dispersion results from construction of a radial plot, a graphical means of displaying single-grain age estimates, taking into account the different standard error of each age (Galbraith 1988, 1990). Alongside the radial plot, Galbraith and Laslett (1993) developed the central age estimate for the population of single-grain ages measured for a sample, each age being weighted according to the numbers of track counted.

11 FT Annealing and Steps Towards Data Interpretation

Annealing of tracks presents a problem in the recovery of formation age since it violates the requirement, common to all isotopic dating systems, for retention of the daughter product. Annealing is essentially a function of time and temperature although other mechanisms have been considered.⁵ Accumulation of the radiogenic daughter product below a certain temperature range is the concept of closure temperature, above which temperature the system is open and radiogenic products are lost (after Dodson 1973). Such closure cannot be instantaneous, and there exists a transitional temperature range, the partial stability zone, in which daughter products are partially lost and partially retained. Wagner (1972) proposed four schematic thermal histories applicable equally to all mineral-isotopic systems where samples pass variously between temperature zones of varying stability (Fig. 1.4a). The setting of time and temperature boundaries for partial track stability (usually now referred to as the partial annealing zone) represents the beginning of a numerical description of the annealing process which may be used to interpret measured FT ages in terms of a sample’s thermal history.

Fig. 1.4

a Schematic cooling curves for rock and mineral systems considered in terms of fission-track accumulation (redrawn after Wagner 1972). Curve 1 rapid cooling (e.g. Fish Canyon Tuff): all tracks stable and measured age approximates to formation age. Curve 2 slow cooling (e.g. an Alpine gneiss): stability reached some time after formation; tracks formed during residence in partial stability (or partial annealing) zone are partially annealed. Curves 1 and 2 only consider differences in initial accumulation of tracks. Curves 3 and 4 show reheating of already cooled samples. Curve 3 gives a mixed age: earlier-formed tracks partially annealed to a level dependent upon time and temperature experienced in partial stability zone; second family of tracks are stored on re-entry into stability zone. Intrusion of a dyke into granite could cause such partial resetting in granite samples near the contact. Curve 4 indicates a reset age: initial cooling into stability field is followed by reheating back into unstable zone. FT age would relate only to the time of re-emergence into the track stability zone. b Comparison of horizontal confined track-length distributions in apatite (after Gleadow et al. 1986). Undisturbed volcanic distributions characterise rapid cooling (Curve 1) with a dominance of long lengths, a narrow distribution and a mean track length ~14 µm. Undisturbed basement distributions are broader, with mean track lengths ~12–13 µm and would be found in samples following cooling curve 2. Partially reset samples (cooling curve 3) will also show a broad track-length mixed distribution, sometimes resolving into bimodality. Total annealing (cooling curve 4) may show volcanic or basement-type distributions depending on the rate of cooling in the stability zone

Laboratory Annealing Experiments

artificially heat different aliquots of sample at comparatively high temperatures over short annealing times. The measured FT parameters are compared with those in an unannealed sample to determine the percentage reduction at each temperature step, the laboratory data being plotted on Arrhenius-type plots (Fig. 1.5). For a single sample, points denoting similar annealing levels and thus similar percentages of track loss define straight lines forming a fanning array, with the increase in slope indicating increase in track loss. The earliest laboratory experiments by Fleischer et al. (1965b) examined annealing of tracks in zircon, olivine, micas and glass, whilst Wagner (1968) and Naeser and Faul (1969) reported the first annealing data for apatite. Listings of other early annealing studies can be found in Green (1980, Fig. 3) and Wagner and van den Haute (1992, Appendix B). Apatite has been the focus of most annealing studies (e.g. Green et al. 1986; Carlson et al. 1999; Barbarand et al. 2003), and this is considered in detail in Chap. 3 Ketcham 2018.

Fig. 1.5

Arrhenius plot of AFT annealing data, which combines the results of the laboratory studies of Naeser and Faul (1969) with data from the Eielson and Los Alamos boreholes (Naeser 1979) and the Otway Group (after Gleadow and Duddy 1981). The dashed lines represent the 0 and 100% track loss lines extrapolated from the laboratory data. Good agreement is found for the 50% annealing curves

The linearity of empirical annealing data enables their extrapolation to geological time, albeit over many orders of magnitude. For apatite extrapolation a “closure temperature” of between 70 and 125 °C for cooling rates of between 1 and 100 Ma was proposed by Wagner and Reimer (1972); Haack (1977); Gleadow and Lovering (1978). Note that whilst offering a first approximation for the stability of tracks over time, the closure temperature concept is of little value in many samples that have experienced complex thermal histories: multiple periods of burial and residence in the upper crust, magmatic activity, contact metamorphism or the passage of hot fluids all may occur at temperatures where tracks in apatite are partially stable.

Tracks in zircon and titanite are more resistant to annealing. Extrapolation of more limited laboratory studies has estimated the zircon partial annealing zone as (rather broadly) 390–170 °C (Yamada et al. 1995) or ~300–200 °C (Tagami 2005)—assuming heating for 10⁶ years or more.

Borehole Samples

As tracks in apatite are affected by very low geological temperatures, significant annealing effects should be observable in deep boreholes. Naeser (1979) reported apatite ages from a 2.9 km drill hole (and associated wells) in a metamorphic complex at the Eielson US Airforce Base, Alaska, uplifted slowly since the Mesozoic. Extrapolation of the decreasing age trend showed a zero age at a present-day temperature of ~105 °C, giving an estimate of the 100% apatite annealing temperature for a heating period of ~10⁸ years.

Geothermal test wells GT1 and GT2 at Los Alamos, New Mexico, lie on the flank of a Pleistocene volcanic centre, with the lower 2.2 km of the 2.9 km deep wells penetrating a Precambrian crystalline complex. A zero AFT age was reached where the present-day temperature is 135 °C, although TFT ages were unaffected until the temperature exceeded 177 °C. Samples here have been heated recently, and thus, 135 °C represents an estimate for 100% track loss temperature in apatite for a heating period of just 10⁶ years.

Andrew Gleadow and Ian Duddy (1981) reported a study of outcrop and borehole samples in the Otway Basin, southern Victoria, Australia, one of a series of graben formed during early continental rifting between Australia and Antarctica. Early Cretaceous sedimentation produced 3 km of non-marine sandstones, with the Otway Group, a prominent formation of lithic sandstones, having abundant volcanic rock fragments, fresh phenocryst phases and some glassy clasts. The Otway Group outcrops in two broad areas of the basin, elsewhere being covered by flat-lying late Cretaceous and early Tertiary marine deposits. Outcrop samples yielded indistinguishable apatite, titanite and zircon FT ages ~120 Ma, indicating a cooling history similar to curve 1 of Fig. 1.4a, ~120 Ma representing the age of volcanism immediately prior to deposition. The similarity of FT ages from different minerals also indicated that outcrop samples had not been significantly heated since deposition. Similar ages ~120 Ma were found for titanites from borehole samples at all depths down to 3.4 km (124 °C), demonstrating the Otway Group sandstones had an homogeneous FT age prior to burial in the deeper parts of the basin. AFT ages of ~120 Ma were found for near-surface borehole samples, but age reduction began at about 60 °C, with a zero age determined where the temperature was 120 °C. The decrease in apparent age between 60 and 120 °C delineates the apatite annealing zone (roughly equating with Wagner’s partial stability zone of Fig. 1.4a) resulting from gradual temperature increase over 120 Ma due to progressive burial. Stratigraphic evidence suggests that sediments reached their maximum burial depths ~30 Ma ago and have essentially remained at constant depth since that time: the effective duration of heating of these samples is thus of the order of 10–40 Ma. Figure 1.5 (after Gleadow and Duddy 1981) combines the results of the Otway Group, Eielson and Los Alamos borehole studies with the laboratory annealing results of Naeser and Faul (1969).

Borehole studies of annealing in zircon have also been attempted but temperatures sufficient to cause complete annealing of tracks (>300 °C) are seldom encountered, unless tectonic inversion has uplifted a fossil partial annealing zone; some zircon results have been reported from boreholes in the Vienna Basin (Tagami et al. 1996) and KTB Bavaria (Coyle and Wagner 1996). Rahn et al. (2004) have considered the affect of accumulated α-damage from uranium and thorium decay on the stability of fission tracks. Comparison of measured FT ages with ages from other mineral-isotopic systems in exhuming orogens has also provided constraints for zircon track stability (e.g. Harrison et al. 1979; Hurford 1986b).

FT Size

Thus far we have mainly considered track density: the number of tracks stored, revealed and counted for a sample as measure of time. However, early workers recognised that a fission track may shrink in size with temperature, giving a second parameter for detecting annealing. Bigazzi (1967) and Mehta and Rama (1969) showed that spontaneous tracks were shorter than induced tracks in a range of muscovite samples. Similar size reductions were found for apatites (Wagner and Storzer 1970; Bhandari et al. 1971; Märk et al. 1973) and for natural glasses (Storzer and Wagner 1969; Durrani and Khan 1970).

What is meant by track size? We need to differentiate between two types of tracks (Fig. 1.6a). Surface tracks outcrop on the viewed plane and are those tracks counted in determining an age. These are sometimes called semi-tracks because the upper part of the track has been removed during polishing and etching. Length is measured either from the 2D image projected onto the viewed surface (projected length) or by including the z-dimension by careful focusing of the microscope and use of a calibrated micrometer. In contrast, confined tracks occur totally within the mineral grain and are revealed because they cross a surface track or a crack or cleavage plane which allows a pathway for the etchant. Bhandari et al. (1971) termed these “TINTs” (track-in-track—Fig. 1.6b) or “TINCLEs” (track-in-cleavage). Unlike surface tracks, confined tracks are full length and provide a more complete record of any track annealing. Note that all track-length measurements are subject to bias although for horizontal confined tracks the bias can be determined (Laslett et al. 1982). Annealing can also be anisotropic. Green and Durrani (1977) found a marked anisotropy of projected track lengths in apatite, with tracks parallel to the c-crystallographic axis the most resistant to annealing; subsequent measurement of confined tracks in apatite confirmed this finding (Green 1981a) with a more detailed study showing that anisotropy increases directly with annealing level (Green et al. 1986).

Fig. 1.6

Photomicrograph courtesy of Paul Green

a Schematic diagram comparing semi- and confined tracks in an apatite crystal. Projected lengths of semi-tracks (or surface tracks) do not reflect their true length and are subject to complex bias. Measurement of horizontal confined tracks (parallel or near parallel to the viewed surface) gives an accurate measurement of length whose bias can be described. TINCLE is a confined track which intersects a crack or cleavage; TINT is a confined track which intersects a surface track. b Photomicrograph of an apatite showing a near horizontal confined track (a TINT) amongst surface tracks. The surface tracks are counted to determine FT age; horizontal confined tracks are measured to determine track length.

Of historical curiosity, two approaches have attempted to use reduction in track size or length to see beyond a “partial overprinting event” (e.g. curve 3 in Fig. 1.4a) and recover the original FT age—although each method is very time-consuming. The track-size correction compared spontaneous track size with that of freshly induced tracks, using the degree of size reduction to correct the measured age. Reduction is not a 1:1 relationship and requires construction of empirical calibration curves for each type of material derived from the reduction in track size and track density measured over a series of laboratory annealing experiments. Such curves have been applied to ages measured on glass, mica and apatite (e.g. Durrani and Khan 1970; Selo and Storzer 1981; Wagner and Storzer 1970). Some concordance of corrected FT age with independent age constraints was found for glasses where the heating event was in the recent past but the approach was not able to resolve older “events” or more complex thermal histories. The plateau correction method endeavoured to mimic the annealing experienced by spontaneous tracks by artificially heating the induced tracks. Pairs of sample aliquots (one with spontaneous and the other induced tracks) were heated in several steps at increasing temperature or duration. The spontaneous-to-induced track density ratio ρ_s/ρ_i increases until the level of experimental annealing in the induced aliquot equates to that experienced by the partially annealed spontaneous tracks. From this point, the annealing rates are assumed to be equal and a plateau value for ρ_s/ρ_i is reached and used to calculate an age corrected for the partial track loss. Plateau-corrected ages have been reported for glasses (e.g. Storzer and Poupeau 1973; Seward et al. 1980) and apatite (Poupeau et al. 1980). Separate measurement of spontaneous and induced track densities requires a multi-grain strategy which imposes constraints of variation in uranium content and anisotropy of track etching. Both the so-called correction methods are fraught with unresolved problems, and neither approach has any relevance to modern FT analysis.

In direct contrast to projected lengths, horizontal confined track lengths in apatite are diagnostic of a sample’s thermal history. Each track is formed with approximately identical length—all freshly induced tracks are ~16–16.5 µm—and is then shortened to a length dependent upon the maximum temperature it has experienced. Since the fission of uranium atoms in a sample is a continuing process, each track is of a different age and thus experiences a different record of temperature change, the combined track-length distribution recording the overall sample thermal history. Spontaneous lengths show a definite relationship to geological setting with clear differences between rapidly cooled volcanic samples, slowly exhumed crystalline basement samples and bimodal samples which have been reheated with the earlier-formed tracks partially annealed (Fig. 1.4b after Gleadow et al. 1986). More recent annealing studies in apatite have used confined track length as a quantitative measure of track fading. The quartet of papers from Melbourne (Annealing 1 to 4—Green et al. 1986; Laslett et al. 1987; Duddy et al. 1988; Green et al. 1989) represented a landmark in our understanding of annealing of tracks in apatite, codifying the annealing parameters, underlining the influence of composition on annealing and using the annealing model to simulate track annealing for specific time–temperature pathways to predict age and length parameters and hence thermal history (Ketcham et al. 1999, 2007). Chapter 3 (Ketcham 2018) looks at annealing and modelling in much greater detail.