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Mechanisms and kinetics of apatite fission-track annealing
Abstract
Kinetic equations derived from a physical model of the atomic-scale processes involved in apatite fission-track annealing account for the dependence of annealing rates on temperature and time over the full range of these variables investigated experimentally to date. The physical model postulates radial shrinkage of the disrupted zone surrounding the path of the fission fragments, in response to the elimination of crystalline defects by short-range atomic repositioning during thermal annealing. For the case of a disrupted zone that is cylindrical near its axial center with regions of conical taper at each end, the model predicts a two-stage annealing process in which track-length reduction is dominated initially by axial shortening, and subsequently by segmentation of tracks. The model reproduces laboratory annealing data with an accuracy nearly equal to the uncertainty of the experimental measurements. Although the dependence of annealing rates on apatite composition cannot be accurately deduced from the experimental data presently available, an analogy to rates of O diffusion in silicates suggests that the kinetic parameters of the model may vary with composition as linear functions of the total ionic porosity. Experimental indications of annealing anisotropy can be explained under this model by invoking small differences in the geometry of the disrupted zone for different crystallographic orientations. Because this kinetic model is based on explicit physical mechanisms, extrapolations of annealing rates to the lower temperatures and longer time scales required for the interpretation of natural fission-track length distributions can be made with greater confidence than is the case for purely empirical relationships fitted to the experimental annealing data.
... Annealing models continued to evolve. Carlson (1990) presented a modified version of the parallel model (Fig. 1a). Crowley et al. (1991) proposed versions of the Parallel and Fanning equations that are curved in the pseudo-Arrhenius space (Fig. 1b), implying activation energies that vary with the temperature of annealing. ...
... The annealing kinetics of fission tracks is described by empirical (Laslett et al., 1987;Crowley et al., 1991;Laslett and Galbraith, 1996;Rana et al., 2021) or semi-empirical (Carlson, 1990;Guedes et al., 2006;Guedes et al., 2013) equations relating the reduced track length, r = L/ L 0 (where L is the length of the fission track after heating and L 0 is the unannealed fission-track length), with the duration, t, of the constant temperature (T) heating. The general form of the annealing equations is: ...
... Curvilinear (PC, Eq. (PC1)) and Fanning Curvilinear (FC, Eq. (FC1)) models (Crowley et al., 1991) as well as the Carlson Model (CM, Eq. (CM1)) that mixes the Parallel Arrhenius and Parallel Curvilinear models in the same equation (Carlson, 1990), are used in this analysis. The transformation function g(r) = ln(1 − r) was chosen because it carries no fitting parameters and was shown to produce good fits to annealing data . ...
The main feature of the Fission-Track Thermochronology is its ability to infer the thermal histories of mineral samples in regions of interest for geological studies. The ingredients that make the thermal history inference possible are the annealing models, which capture the annealing kinetics of fission tracks for isothermal heating experiments, and the Principle of Equivalent Time (PET), which allows the application of the annealing models to variable temperatures. It turns out that the PET only applies to specific types of annealing models describing single activation energy annealing mechanisms (parallel models). However, the PET has been extensively applied to models related to multiple activation energy mechanisms (fanning models). This procedure is an approximation that has been overlooked due to the lack of a suitable alternative. To deal with this difficult, a formalism, based on physicochemical techniques, that allows to quantify the effects of annealing on the fission tracks for variable temperatures, is developed. It is independent of the annealing mechanism and, therefore, is applicable to any annealing model. In the cases in which the PET is valid, parallel models, the proposed method and the PET predict the same degrees of annealing. However, deviations appear when the methods are applied to the fanning models, with the PET underestimating annealing effects. The consequences for the inference of thermal histories are discussed.
... Annealing models continued to evolve. Carlson (1990) presented a modified version of the parallel model (Fig. 1a). Crowley et al. (1991) proposed versions of the Parallel and Fanning equations that are curved in the pseudo-Arrhenius space (Fig. 1b), implying activation energies that vary with the temperature of annealing. ...
... The annealing kinetics of fission tracks is described by empirical (Laslett et al., 1987;Crowley et al., 1991;Laslett and Galbraith, 1996;Rana et al., 2021) or semi-empirical (Carlson, 1990;Guedes et al., 2006Guedes et al., , 2013 equations relating the reduced track length, = ∕ 0 (where is the length of the fission track after heating and 0 is the unannealed fission-track length), with the duration, , of the constant temperature ( ) heating. The general form of the annealing equations is: ...
... in which ( ) is a transformation of and ( , ) defines the geometrical characteristics of the isoretention curves in the pseudo-Arrhenius space (ln × 1∕ , Fig. 1). The Parallel Arrhenius (PA, Eq. (PA1)) and Fanning Arrhenius (FA, Eq. (FA1)) equations (Laslett et al., 1987), the Parallel Curvilinear (PC, Eq. (PC1)) and Fanning Curvilinear (FC, Eq. (FC1)) models (Crowley et al., 1991) as well as the Carlson Model (CM, Eq. (CM1)) that mixes the Parallel Arrhenius and Parallel Curvilinear models in the same equation (Carlson, 1990), are used in this analysis. The transformation function ( ) = ln(1 − ) was chosen because it carries no fitting parameters and was shown to produce good fits to annealing data . ...
The main feature of the Fission-Track Thermochronology is its ability to infer the thermal histories of mineral samples in regions of interest for geological studies. The ingredients that make the thermal history inference possible are the annealing models, which capture the annealing kinetics of fission tracks for isothermal heating experiments, and the Principle of Equivalent Time (PET), which allows the application of the annealing models to variable temperatures. It turns out that the PET only applies to specific types of annealing models describing single activation energy annealing mechanisms (parallel models). However, the PET has been extensively applied to models related to multiple activation energy mechanisms (fanning models). This procedure is an approximation that has been overlooked due to the lack of a suitable alternative. To deal with this difficult, a formalism, based on physicochemical techniques, that allows to quantify the effects of annealing on the fission tracks for variable temperatures, is developed. It is independent of the annealing mechanism and, therefore, is applicable to any annealing model. In the cases in which the PET is valid, parallel models, the proposed method and the PET predict the same degrees of annealing. However, deviations appear when the methods are applied to the fanning models, with the PET underestimating annealing effects. The consequences for the inference of thermal histories are discussed.
... Common methods of MBT reconstruction include the maturity index of the organic matter (Héroux et al., 1979;Hackley et al., 2015;Luo et al., 2020b) and low temperature thermochronology (Carlson, 1990;Craddock and Houseknecht, 2016;Ehlers and Farley, 2003;Yamada et al., 2007). The maturity index of the organic matter is commonly characterized by the vitrinite reflectance (Mukhopadhyay, 1994;Katz and Lin, 2021), which is mainly controlled by the temperature (Hunt, 1996). ...
... For strata without vitrinite data, the bitumen reflectance and graptolite reflectance can be used to calculate the equivalent R o (Jacob, 1989;Luo et al., 2020b), but different conversion methods exist, and they have different application scopes (Schmidt et al., 2019;Katz and Lin, 2021). Low temperature thermochronology mainly uses annealing kinetic models of fission tracks in minerals (such as apatite and zircon) and (U-Th)/He thermochronology to determine the temperature evolution (Carlson, 1990;Craddock and Houseknecht, 2016;Ehlers and Farley, 2003;Yamada et al., 2007). The annealing kinetic model of apatite fission tracks is only applicable at relatively low temperatures (below 125°C; Carlson, 1990). ...
... Low temperature thermochronology mainly uses annealing kinetic models of fission tracks in minerals (such as apatite and zircon) and (U-Th)/He thermochronology to determine the temperature evolution (Carlson, 1990;Craddock and Houseknecht, 2016;Ehlers and Farley, 2003;Yamada et al., 2007). The annealing kinetic model of apatite fission tracks is only applicable at relatively low temperatures (below 125°C; Carlson, 1990). For strata that have experienced temperatures of >150°C, only the annealing of zircon fission tracks can be used (Yamada et al., 2007), but a unified annealing kinetic model of zircon has not yet been established. ...
For strata that have experienced continual burial in the early stage and uplift in the late stage, the present-day temperature is lower than the maximum burial temperature (MBT), which is a key parameter for studying the hydrocarbon generation history of source rocks in petroliferous basins. In this paper, a new method for reconstructing the MBT is proposed based on the solid-state reordering model of carbonate clumped isotopes (Δ 47). The MBT reconstructed using the Δ 47 was compared with the MBT constrained using the traditional Easy%Ro model. The clumped isotope temperature (TΔ47) of the Permian micritic limestone from the Xibeixiang outcrop (about 62°C) is much higher than its initial formation temperature (20–25°C), suggesting that the limestone experienced partial solid-state reordering during the late burial process. The MBT of the calcite obtained from the solid-state reordering model is 139–147°C, which is quite similar to the MBT determined using the Easy%Ro model (139.5–147.5°C). TΔ47 of the Permian and Triassic limestone and calcite cements in the Puguang gas field are 150–180°C, while TΔ47 of the micritic dolostone is about 70°C, suggesting that the Δ47 of the limestone and calcite cements experienced complete solid-state reordering and the dolostone only experienced partial solid-state reordering. The MBT of the dolomite determined using the solid-state reordering model is 200–220°C, which is also similar to the MBT determined using the Easy%Ro model (202–227°C). Therefore, the case studies from the Sichuan Basin suggest that Δ47 can be used to reconstruct the MBT of ancient carbonate strata lacking vitrinite and detrital zircon data. However, different types of carbonate samples should be used to reconstruct the MBT for strata that have experienced different temperature histories. Micritic limestone and very finely crystallized dolostone can be used to reconstruct the MBT of strata that have experienced MBTs of <150–200°C and >200–250°C, respectively.
... Models presented to date are either semi-empirical, carrying some underlying physical principle (Carlson 1990;Guedes et al. 2005Guedes et al. , 2006Guedes et al. , 2013, or completely empirical (Laslett et al. 1987;Crowley et al. 1991;Ketcham et al. 1999Ketcham et al. , 2007Ketcham et al. , 2009Guedes et al. 2007). In both cases, model parameters are found by statistical fitting to laboratory annealing data (Green et al. 1986;Carlson et al. 1999; Barbarand et al. 2003;Tello et al. 2006) and the resulting model equation is extrapolated to the tenths to hundreds of million-year range of interest for geological applications. ...
... Reduced track lengths used to fit the models are all above r = 0.6 (see, for instance, Fig. 5a). Carlson (1990) postulated that etachable gaps are formed for reduced lengths less than approximately 0.6. This assumption has been criticized (Green et al. 1993) because it had been shown that segmentation is the result of fluctuation of the concentration of defects along tracks after certain degrees of annealing, mainly in tracks at higher angles to the c-axis (Green et al. 1986). ...
... This effect is at least partially corrected with the c-axis projection model . The criticism about Carlson (1990) assumption was also based on the absence of experimental evidence of track segmentation, which did not come until the experiments by Li and coworkers (Li et al. 2011(Li et al. , 2012. Latent tracks in Durango apatite samples irradiated with 2.2 GeV Au (Li et al. 2011) and 80 MeV Xe ions (Li et al. 2012) were imaged with the High Resolution Transmission Electron Microscopy technique in different stages of annealing. ...
Rana track annealing model 2007, based on an Arrhenius approach, is significantly modified, including new assumptions, fitting parameters, and analysis, to yield a new phenomenological model for annealing of fission tracks in apatite. Construction and optimization of the new six parameter model have been described in detail. The model shows a hybrid behavior. In Arrhenius plot, for higher temperatures (laboratory data included), iso-annealing lines are curved while, for low temperatures (geological time scale), iso-annealing lines become parallel straight lines. This is a new feature for any such model and has produced promising results. C-axis projected lengths from laboratory experiments on Durango apatite are employed to find model parameters. KTB borehole fission-track data are added to build the temperature function that modifies the original equation. Partial annealing zone (PAZ), closure temperature (TC) and total annealing temperature (TA) were calculated and compared to geological benchmarks. The predictions of the present model agreed well with low and high temperature benchmarks. PAZ, TC and TA predictions were also compared to the Fanning Curvilinear Arrhenius model predictions, resulting in good agreement. The present model is flexible enough to be applied to other fission-track systems, like zircon, muscovite and titanite.
... Most of these are empirical, in large part because there is no widely agreed-upon physical model for how fi ssion tracks are confi gured and how they anneal on the atomic scale. The only fully developed model with a physical basis was created by Carlson (1990), based on the assumption of fi ssion tracks consisting of vacancies and interstitials in the crystal lattice that are annealed by short translations of atoms from abnormal positions back to stable sites. The mechanism is similar to topotactic transformation, which controls the transitions between mineral polymorphs such as calcite and aragonite, except the driving force is release of strain energy rather than a chemical potential difference. ...
... In considering the relative merits of the various empirical equations, it is good to bear in mind that the Carlson (1990) ...
... The transition between linear and curvilinear Arrhenius behavior may thus be defi ned by which of these terms is dominant. Although as noted above the Carlson (1990) model as currently posed is not suitable for extrapolating laboratory data to geological time scales, it is possible that enhancements, such as using a range of activation energies rather than a single one, could bridge this gap. ...
... At least part of this acceleration is caused by the formation of slow-etching gaps, which can prevent the full etchable length of the track from being etched in standard protocols. This phenomenon suggests that track-tip annealing is augmented by annealing from the track sides (Carlson, 1990). ...
... The proper way to conceive of this zone is not straightforward, and the differing conceptions lead to different potential mechanisms for annealing. Carlson (1990) posits the disrupted zone as "laden with defects dominated by vacancies and interstitials," which are then repaired "by short translations of atoms (perhaps on the order of ~5-10 Å or less) from abnormal positions into their proper sites." This implies a partially-intact lattice whose extent of damage can be quantified as a defect density, and for which annealing consists of lowering the defect density below some threshold, and can occur throughout the damage zone (Carlson, 1990). ...
... Carlson (1990) posits the disrupted zone as "laden with defects dominated by vacancies and interstitials," which are then repaired "by short translations of atoms (perhaps on the order of ~5-10 Å or less) from abnormal positions into their proper sites." This implies a partially-intact lattice whose extent of damage can be quantified as a defect density, and for which annealing consists of lowering the defect density below some threshold, and can occur throughout the damage zone (Carlson, 1990). Alternatively, conceiving of the damage zone as partially or completely amorphous as suggested by MD simulation (Rabone et al., 2008;Trachenko et al., 2002), combined with the sharp boundaries suggested by TEM imaging, may suggest a boundarycontrolled mechanism, such as epitaxial recrystallization from the margins of the zone inwards or snapoff and migration of damaged zones by a surface energy minimization process (Li et al., 2012;Li et al., 2011). ...
This chapter reviews the evolving state of knowledge concerning fission-track (FT) annealing, primarily in apatite and zircon, based on theory, experiments, and geological observations. Multiple insights into track structure, formation, and evolution arise from transmission electron microscopy, small-angle X-ray scattering, atomic force microscopy, and molecular dynamics computer modeling. Our principal knowledge, however, comes from experiments in which spontaneous or induced tracks are annealed, etched, and measured, the results statistically fitted, and their predictions compared against geological benchmarks. This empirical approach has proven effective and resilient, though physical understanding remains an ultimate goal. The precise mechanism by which lattice damage anneals, and how it varies among minerals and damage types, remains unknown. Multiple similarities between apatite and zircon suggest equivalent underlying processes. Both minerals demonstrate annealing anisotropy, and its characterization is crucial for understanding both track shortening and density reduction. The fanning curvilinear equation, featuring curved iso-annealing lines on an Arrhenius-type diagram, has been the most successful for matching data spanning timescales from seconds to hundreds of millions of years. A super-model featuring a single set of iso-annealing lines describes all apatite experimental data to date. Annealing rates vary with both anion and cation substitutions, and more work is required to ascertain how these substitutions interact. Other areas for further research include differences between spontaneous and induced tracks, and possible additional processes affecting length and density evolution, such as seasoning. Thermal history inversion simultaneously leverages and tests our models, and accounting for kinetic variation is key for doing it soundly.
... This reparation generally results in shortening of the track length (track annealing). The dominant controls on track annealing are temperature and time (Fleischer et al., 1975) while apatite chemical composition, crystal structure and ambient pressure play lesser roles (e.g Barbarand et al., (2003a);Carlson, (1990); Green et al., (1986); Wendt et al., (2002)). The nature of this annealing/temperature relationship has been investigated at laboratory timescales Crowley et al., 1991;Duddy et al., 1988;Green et al., 1989a;Green et al., 1986;Green et al., 1989b;Laslett et al., 1987). ...
... Some models attempt to account for the kinetics of the annealing process (e.g. Carlson, 1990;Ketcham et al., 1999). There are several models in circulation (e.g. ...
... There are several models in circulation (e.g. Carlson, 1990;Crowley et al., 1991;Ketcham et al., 1999;Laslett and Galbraith, 1996;Laslett et al., 1987) and the annealing rate is slightly different in each. Generally, this difference is due to the laboratory experiments using apatites of different composition. ...
... Because the measured track density at an internal surface is directly related to the track length, the fission track age decreases correspondingly (Green 1988). If the mean track length is reduced by more than ~ 35% relative to l 0 (so below a value of ~ 10.5 µm) the 1:1 ratio between (Carlson 1990). The decrease of both track density and mean length with increasing temperatures has been confirmed by data from deep boreholes (Naeser 1979;Gleadow and Duddy 1981;Corrigan 1993;Wagner et al. 1994). ...
... F can be substituted by Cl and OH, PO 4 by CO 3 , SiO 4 , SO 4 and Ca by Na, Mn, Mg, Fe, Sr, Ba, U, Th and rare earth elements Barbarand and Pagel 2001). In the annealing experiments conducted so far (e.g. Green et al. 1986;Duddy et al. 1988;Carlson 1990;Crowley et al. 1991;Carlson et al. 1999) chemical composition appears to be the predominant cause of variation in annealing kinetics. ...
... Despite the large number of annealing studies, the role played by chemical composition in fission track annealing, is still poorly understood. Cl-content ), ionic porosity (Carlson 1990;Dahl 1997) or etch-pit diameter Dpar (Burtner et al. 1994) have been proposed as reliable indicators for annealing behavior of apatites, but appear to have limited predictive value Barbarand and Pagel, 2001). For example, the influence of Fe, Mn and Sr on annealing behavior appears to be considerable (Crowley et al. 1991;Carlson et al. 1999), but none of the proposed indicators reflect Fe, Mn or Sr concentrations in the apatite. ...
In this study, the history of cooling and denudation of the Northern Scandes range and the
adjacent Norwegian and Barents Sea margins is investigated. This is done with Fission Track
and (U-Th)/He thermochronology. Several other previously published studies have focused
at similar issues in other parts of Scandinavia. Both from the geomorphological record, as
well as from the offshore sedimentary record, it seems evident that the development of the
Northern Scandes differs in several respects from the development of its southern
counterpart, the Southern Scandes range. The history of cooling and denudation in northern
Scandinavia is presented first and is then compared to that of other North Atlantic margins,
with emphasis on the eastern North Atlantic margins.
Chapter 2 presents an overview of the Precambrian – Paleozoic evolution of the
Fennoscandian shield. The main structures and tectonic units and also the geomorphological
surfaces that are most relevant to the present study are introduced. The offshore basin
evolution of the Norwegian Sea and the Barents Sea is briefly summarized.
Chapter 3 offers an introduction to the theoretical backgrounds of Fission Track and (U-Th)/
He thermochronology. The different methods and techniques that have been applied in
the lab are outlined. The potential applications of both Fission Track and (U-Th)/He
thermochronology are discussed, as well as how one should interpret both types of data.
Electron microprobe data for a selected set of apatite samples are included in this chapter.
In Chapter 4 it is demonstrated that the pattern of Apatite Fission Track ages with respect to
distance to the northern Norwegian Atlantic margin is very similar to that of models of
passive margin evolution that represent a retreating scarp. On the margin itself the AFT ages
are as young as 90 – 100 Ma and further inland, right across the Northern Scandes mountain
range, the ages increase to more than 300 Ma on the gentle eastern flank of the range. Late
Cretaceous – Paleogene (U-Th)/He ages in a vertical profile on Kebnekaise, the highest peak
in the range, together with the observed age pattern suggest a rift shoulder origin for the
range. Nevertheless, other uplift mechanisms have played an important role in the later
development of the range. On the margin, the young AFT ages coincide spatially with a
strong, negative gravity anomaly. Inverse modeling histories here indicate an important
Neogene phase of denudation which is not recorded anywhere else in the mountain range by
the AFT or (U-Th)/He systems.
There is no clear pattern for the pattern of the AFT ages with distance to the southern
Barents Sea margin. This is discussed in Chapter 5. Only a clear difference between relatively
young ages (< 270 Ma) along the southwestern Barents Sea margin with respect to those
further east (> 270 Ma) has been identified. For the region along the southwestern Barents
Sea margin, inverse thermal histories provide a record of the Triassic and younger thermal
history, whereas samples along the eastern part of the southern Barents Sea margins reveal
the Paleozoic to Triassic thermal history only. Previously published apatite fission track and
zircon fission track ages from the Kola Super Deep Borehole are used in conjunction with
new apatite fission track data from surface samples.
In Chapter 6, differential vertical movements between, and within, the Lofoten and
Vesterålen domains are documented by the inverse thermal histories based on the new AFT
data from both domains and extrapolation of offshore sedimentary units over the archipelago.
Cooling and denudation on Vesterålen apparently was accompanied by Late Paleozoic –
Early Mesozoic sedimentation and burial in the Lofoten domain. Cooling and denudation of
the present-day Lofoten Ridge in the Jurassic and Cretaceous was contemporaneous with
deposition of a sedimentary cover in the Vesterålen area, again indicating differential vertical
movements between both domains. The boundary between both domains, which seems to be
the Vesterålen transfer zone, lines up with an oceanic fracture zone. The youngest ages in the
XII
region, ~120 Ma, in the southern part of the Lofoten domain, coincide with a strong, positive
gravity anomaly.
Different mechanisms for the uplift of the Northern Scandes mountain range are discussed
in Chapter 7. Asthenospheric diapirism has previously been proposed as an uplift mechanism
for both the Southern and Northern Scandes mountains, but the new observations from the
northern area do not satisfactorily fit the timing and pattern of cooling and denudation that is
predicted by this mechanism. The initial uplift of the Northern Scandes range seems to be
related to rift shoulder uplift, but a different mechanism must have been active as well in the
Neogene. An important factor seems to be a large, low density granitic body within the upper
crust, but the issue of what triggered the Neogene uplift in this region is not entirely clear yet.
Although the observations are clear, tectonic modeling is required to get a better
understanding of this phase.
This is a first order study and it provides clear indications for the direction that future
research into the low temperature evolution of the northern Scandinavian study area should
take. This study provides the basis on which future research on a more detailed, smaller scale,
can build further.
... Importantly, the empirical mathematical model of Laslett et al. (1987) and the physical model of Carlson (1990) offer a vantage point from which to consider the form of the mathematical model. Both of these studies yielded similar contours of fi ssion-track length in pseudo-Arrhenius space. ...
... Both of these studies yielded similar contours of fi ssion-track length in pseudo-Arrhenius space. However, the model of Carlson (1990) was predicated upon a track shape. If that track shape is allowed to vary by including an infl ection point, then this would cause an infl ection to occur among the track length contours. ...
... Rufino and coworkers (Rufino and Guedes, 2022;Rufino et al., 2023) showed that the curvilinear models exhibit physicochemical patterns characteristic of reactions, in which the activation energy changes with temperature, as previously suggested by other authors (Carlson, 1990;Ketcham, 2019). They also showed that the physicochemical patterns of the fanning models are characteristic of multiple concurring processes with different activation energies, which change at different rates with temperature and with the quantity of remaining defects compounding the track. ...
... This high-density shell, as directly observed by the Z-contrast method, is consistent with the core-shell structure of ion tracks in amorphous SiO 2 , as indirectly detected by using the small angle x-ray scattering method (Kluth et al., 2008). However, the SAXS results (Kluth et al., 2008) and our STEM results in Fig. 1 are different from the previous model of fission tracks (Carlson, 1990), which assumed a gradual decrease in defect concentration from the radial center of the track to the undamaged material in the absence of high-density shell. The molecular dynamics (MD) modeling work (Trachenko et al., 2002(Trachenko et al., , 2004 showed the depleted core and densified boundary for alpha-decay event damage (mainly for the alpha-recoil nucleus). ...
Fission events in minerals create a damage track, which provides critical information for events that occur over a wide range of time scales, ranging from nuclear fission events (10−20 to 10−12 seconds) to track formation (10−17 to 10−9 seconds) and geological processes (millions of years). However, the site where fission occurs has never been identified along a fission track, as it is long (∼20 μm), thin (diameter <10 nm), and randomly oriented in the mineral matrix. Here, we, for the first time, observe an unexpectedly narrower track diameter (∼1 nm), rather than the conventionally assumed largest diameter, near the fission-event site by a novel technique that confines fission events to the sample surface. The low-charge states of fission fragments produce the narrower track nearest the fission site due to the instantaneous partitioning of negatively charged electrons between two positively charged fission fragments, roughly scaling to their proton numbers. Because a narrower fission track is easier to anneal, the nanostructure nearest the fission site provides spatial information necessary for understanding the atomic-scale mechanisms of track formation and track annealing, with significant implications for fission track thermochronology.
... Discussion of the approach by Refs. [133][134][135][136] lead to an improved version the multikinetic model [122] that was based on a substantial annealing dataset [118,132]. The multikinetic model included mixed-composition apatites and accounted for crystallographic effects [137][138][139][140][141]. ...
... Discussion of the approach by Refs. [133][134][135][136] lead to an improved version the multikinetic model [122] that was based on a substantial annealing dataset [118,132]. The multikinetic model included mixed-composition apatites and accounted for crystallographic effects [137][138][139][140][141]. ...
Minerals are solid state nuclear track detectors - nuclear recoils in a mineral leave latent damage to the crystal structure. Depending on the mineral and its temperature, the damage features are retained in the material from minutes (in low-melting point materials such as salts at a few hundred degrees C) to timescales much larger than the 4.5 Gyr-age of the Solar System (in refractory materials at room temperature). The damage features from the O(50) MeV fission fragments left by spontaneous fission of U and other heavy unstable isotopes have long been used for fission track dating of geological samples. Laboratory studies have demonstrated the readout of defects caused by nuclear recoils with energies as small as O(1) keV. This whitepaper discusses a wide range of possible applications of minerals as detectors for keV nuclear recoils: Using natural minerals, one could use the damage features accumulated over O(10) Myr Gyr to measure astrophysical neutrino fluxes (from the Sun, supernovae, or cosmic rays interacting with the atmosphere) as well as search for Dark Matter. Using signals accumulated over months to few-years timescales in laboratory-manufactured minerals, one could measure reactor neutrinos or use them as Dark Matter detectors, potentially with directional sensitivity. Research groups in Europe, Asia, and America have started developing microscopy techniques to read out the nm damage features in crystals left by keV nuclear recoils. We report on the status and plans of these programs. The research program towards the realization of such detectors is highly interdisciplinary, combining geoscience, material science, applied and fundamental physics with techniques from quantum information and Artificial Intelligence.
... For apatite, tracks segment for higher degrees of annealing. The segmentation process would be more important for r<0.6 (Carlson, 1990), and is observed as an accelerated rate of track shortening. The segmentation process is anisotropic with respect to track orientation. ...
Fission-track annealing models aim to extrapolate laboratory annealing kinetics to the geological timescale for application to geological studies. Model trends empirically capture the mechanisms of track length reduction. To facilitate the interpretation of the fission-track annealing trends, a formalism, based on quantities already in use for the study of physicochemical processes, is developed and allows for the calculation of rate constants, Arrhenius activation energies, and transitivity functions for the fission-track annealing models. These quantities are then obtained for the parallel Arrhenius, parallel curvilinear, fanning Arrhenius, and fanning curvilinear models, and fitted with Durango apatite data. Parallel models showed to be consistent with a single activation energy mechanism and a reaction-order model of order ≈ − 4. However, the fanning curvilinear model is the one that results in better fits laboratory data and predictions in better agreement with geological evidence. Fanning models seem to describe a more complex picture, with concurrent recombination mechanisms presenting activation energies varying with time and temperature, and the reaction-order model seems not to be the most appropriate. It is apparent from the transitivity analysis that the dominant mechanisms described by the fanning models are classical (not quantum) energy barrier transitions.
... As a consequence, annealing decreases the apparent age of the sample as each track is shortened to a degree reflecting the maximum temperature experienced during its history before being totally annealed at approximately 100-120 • C (Gleadow & Duddy, 1981;Green and others, 1986;Gleadow and others, 1986a). Laboratory experiments have also demonstrated that resistance to thermal annealing is influenced by apatite composition, primarily Cl and various elemental substitutions that enhance track retentivity compared to common fluorapatite, such as: Fe, Mg, Mn, Na, OH, Si, and Sr (Green and others, 1985;Carlson, 1990;Crowley and others, 1990;Carlson and Fig. 1. A) Hypothetical thermal history scenarios and the corresponding c-axis projected track length distributions produced from each t-T path. ...
Understanding the long-term erosion and burial history of cratons is challenging due to the incompleteness of the rock record. Low-temperature thermochronology is used to elucidate these surface histories by inverting thermochronological data for the time-temperature history and incorporating sparse constraints and other assumptions about the regional geologic evolution. However, imposing certain assumptions will influence the form of the inferred thermal histories, and in some cases this step may limit impartial assessment of the unknown history in terms of what features are required by the data and those that the data are consistent with (or at least do not contradict). Here we present a study involving laser ablation apatite fission-track data from three central Canadian Shield basement samples collected adjacent to the Hudson Platform Ordovician nonconformity in northern Manitoba and Ontario. Compared to a conventional fission-track analysis, our samples are characterized by up to ~3x the number of dated age grains and > 6–8x the number of track length measurements. The additional data improve inferences that are conditional on the data in Bayesian QTQt inversions, which in turn provide guidance on the potential conditions necessary for informing classical Frequentist inversions using the AFTINV software. Thermal history modeling is thus guided by a heuristic philosophy regarding the use of explicit constraints, which allows us to (i) examine the ability of the Bayesian model to independently infer geologically plausible time-temperature paths from the data (that is, assess sensitivity), (ii) compare the results with the known geology, and (iii) recursively parameterize models with respect to the previous results. QTQt models without time-temperature constraint boxes suggest two reheating events better explain the fission-track data (compared to a monotonic-cooling scenario) and indirectly imply periods at cooler, near-surface conditions in the latest Neoproterozoic to early Paleozoic, and in the Jurassic to early Cretaceous. The timing of such periods are consistent with major Hudson Platform unconformities. Collectively, best-fitting inverse thermal histories establish that the presently exposed basement near the Hudson Bay Basin experienced peak Paleozoic burial at ca. 317 ± 36 Ma (2σ). Burial could have occurred as early as Famennian or as late as Carnian time. A second burial event occurred in the latest Mesozoic to Tertiary at ca. 46 ± 30 Ma, but could have been as early as Aptian and as late as Chattian time. The sample furthest to the east nearer to the Moose River Basin may have experienced peak burial conditions earlier at 83 ± 14 Ma (within uncertainty of other models), synchronous with late Cretaceous sea-level rise. These estimates are in broad agreement with the preserved regional geology and previous thermochronology studies. However, our models support peak burial during Pennsylvanian and Eocene times, which could suggest a more extensive sedimentary cover than implied from preserved Hudson Bay Basin rocks (of well-known depositional age). Such histories are broadly consistent with Williston Basin and Slave craton burial history reconstructions to the west. Sedimentary rocks are estimated to have been ~1.4 ± 0.7 km (2σ) thick in the Paleozoic and ~1.5 ± 0.9 km thick in the latest Mesozoic to middle Cenozoic.
... For apatite, tracks segment for higher degrees of annealing. This segmentation process would be more important for < 0.6 (Carlson, 1990), and is observed as an accelerated rate of track shortening. In spite of the differences between recombination rate and etched track shortening rate, their trends are similar. ...
Fission-track annealing models aim to extrapolate laboratory annealing kinetics to the geological timescale for application to geological studies. Model trends empirically capture the mechanisms of track length reduction. To facilitate the interpretation of the fission-track annealing trends, a formalism, based on quantities already in use for the study of physicochemical processes, is developed and allows for the calculation of rate constants, Arrhenius activation energies, and transitivity functions for the fission-track annealing models. These quantities are then obtained for the parallel Arrhenius, parallel curvilinear, fanning Arrhenius, and fanning curvilinear models, fitted with Durango apatite data. Parallel models showed to be consistent with a single activation energy mechanism and a reaction order model of order ~ -4. However, the fanning curvilinear model is the one that results in better fits laboratory data and predictions in better agreement with geological evidence. Fanning models seem to describe a more complex picture, with concurrent recombination mechanisms presenting activation energies varying with time and temperature, and the reaction order model seems not to be the most appropriate. It is apparent from the transitivity analysis that the dominant mechanisms described by the fanning models are classical (not quantum) energy barrier transitions.
... These tracks anneal (i.e., heal and shorten) as a function of temperature and time such that they eventually disappear (e.g., Green et al., 1985Green et al., , 1986Ketcham et al., 1999;Laslett et al., 1987). The temperature range over which the annealing rate significantly varies is called the partial annealing zone and occurs between ∼110 and 60 °C (e.g., Carlson, 1990;Gleadow et al., 1986;Ketcham et al., 2007Ketcham et al., , 1999Laslett et al., 1987). The complementary apatite helium system is a radiometric dating technique predicated upon alpha decay of U, Th, and Sm. ...
... Chlorine content has been identified as a primary control on fission-track retentivity [28]. Subsequent experiments found that other hydroxyl and cation substituents such as OH − , Fe 2 +, Na + , Si, and REE are also important in regulating FT retention [31,32,33,34,35,36,37]. ...
The geological history of the Canadian Shield is difficult to constrain because the sedimentary record is missing in those areas where Precambrian basement is exposed at the surface. This study presents preliminary results and interpretations of new apatite fission-track (AFT) analyses to elucidate the low-temperature (< 120 °C) history across Canada. The AFT modelling of samples from Southampton Island, in Nunavut, indicate that maximum temperatures varied between 62–93 °C during the Phanerozoic. Maximum burial occurred in the Devonian, but a second phase of Mesozoic burial is proposed, especially in the case for the sample recovered closest to the northern island-bounding normal faults. The AFT modelling of a sample from northern Ontario indicates that a maximum burial temperature of approximately 75 °C was reached during the Late Devonian. Overall, these results demonstrate that the Hudson Bay sedimentary succession is the remnant of a more extensive and thicker sedimentary cover than is preserved. This study also provides the opportunity to discuss innovative methodology and modelling approaches for low-temperature thermochronology.
... More recently other annealing models have been proposed. Carlson (1990) invokes a two stage annealing process for apatite, with an initial axial shortening followed by segmentation. The kinetics of this process are derived using a physical model that postulates that shrinkage of the disrupted crystal lattice in response to the elimination of crystal defects during heating. ...
This study uses fission track analysis to provide temperature and time constraints on the cooling and exhumation history of the basement rocks of the Calabrian Arc of southern Italy. Fission track analysis also provides information on the provenance and burial history of the terrigenous Oligo-Miocene Stilo-Capo d'Orlando Formation. 65 samples from the basement rocks have yielded 57 apatite fission track ages, 54 zircon fission track ages and 25 apatite track length distributions. 9 samples from the Stilo- Capo d'Orlando Formation have yielded 8 apatite fission track ages, 8 zircon fission track ages and 6 apatite track length distributions. Qualitative and quantitative analysis of the fission track data reveals that the majority of the basement rocks underwent a phase of increased cooling related to exhumation between about 35 Ma (Early Oligocene) and 15 Ma (Middle Miocene). Evidence from the local sedimentary record indicates that erosion played an important role in the exhumation process. Extensional tectonism also contributes to some of the increased exhumation. Analysis of the fission track results obtained from the Stilo-Capo d'Orlando Formation confirm a Calabrian basement provenance for the sediments. The previously debated origin of volcanic conglomerate clasts from the formation is also resolved. Finally apatite fission track analysis indicates post-depositional burial at the base of the formation to temperatures greater than 80° C. The final part of this thesis uses the fission track age and temperature constraints to produce an improved tectonic model for the Oligo-Miocene tectonic evolution of the Calabrian Arc. This model proposes that increased exhumation is a consequence of the dynamics of an overthickened orogenic wedge. The model is related to the overall plate dynamics of the western Mediterranean orogeny.
... The curvature in the predicted annealing contours essentially posit more geological-time-scale annealing than the fanning linear forms that more closely reflect standard kinetics based on the Arrhenius equation. This curvature may be ascribable to temperature dependence in the kinetic frequency factor (Carlson, 1990;Ketcham, 2019), but superposition of multiple mechanisms may be a reasonable alternative. For example, molecular dynamics modeling suggests that there are multiple damage types and states within a track, ranging from slightly distorted lattice to amorphous or glassy material (Rabone et al., 2008), and different components of damage may anneal at different rates or by different mechanisms. ...
We report a new series of experiments to explore the phenomenon of low‐temperature annealing of fission tracks in apatite that feature a number of improvements over previous work. Grain mounts were preirradiated using ²⁵²Cf to increase confined track detection and allow briefer thermal neutron irradiation. We coirradiated and etched four apatite varieties (Durango, Fish Canyon, Renfrew, and Tioga) over five time steps equally spaced from 3.66 to 15 ln(s). A length standard was coetched with all experiments to ensure that subtle differences are within detection limits. Finally, we used a standard etching protocol, allowing the data to be comodeled with extensive high‐temperature data sets and recent analyses of induced tracks that underwent ambient‐temperature annealing over year‐to‐decade time scales. Ambient‐temperature annealing occurs at two different rates, with faster annealing at early stages that decreases to a slower rate that converges with empirical fanning linear or curvilinear models. The nature of this decrease varies among the apatite species examined, but no patterns could be determined. The fitted models make geological time‐scale predictions consistent with those based on high‐temperature data only and also make predictions consistent with reasonable inferred low‐temperature histories for all four apatite varieties. The empirical fanning curvilinear equation encompasses low‐temperature annealing at month‐to‐decade time scales, but low‐temperature annealing at shorter time scales may occur by a distinct mechanism. We consider but rule out annealing by radiation from short‐lived activated isotopes. We also reconsider the notion of the initial track length, and the appropriate length for normalizing confined track length measurements.
... It may also reveal a complex cooling process for longer track length <14 μm (Danišik, Dunkl, Putiš, Frisch, & Kráľ', 2004;Fayon & Whitney, 2007). assumed to be of no effect, though it may have a large influence on the mechanisms of FT annealing (Carlson, 1990;Tello et al., 2006). ...
Analysis of apatite fission‐track and vitrinite reflectance combined with 1‐D basin modelling was used to reconstruct the thermo‐tectonic history of the northeast Sichuan Basin, China. The study indicates that the basin has evolved through multi‐phase tectonic regimes involving a series of subsidence and tectonic uplift phases exerting significant control on the thermal history. Heating and cooling processes were largely related to deep burial and intense exhumation, respectively. Exhumation that extended from 122 to 2.5 Ma has resulted in at least 4 km of sedimentary removal. The rate of exhumation and removal (denudation) was found to have reached 58 and 35 m/Myr, respectively. The results show that the denudation magnitude is significantly higher in the eastern part reaching 5.5 km, compared with 2.2 km in the western part of the study area. The fission‐track ages demonstrate the occurrence of three cooling phases: initial‐gradually increasing (~120–70 Ma), stagnant (70–15 Ma), and rapid (15 Ma to present). This suggests that cooling was associated with different compressive thermo‐structural events that began in the mid‐Lower Cretaceous (~122 Ma) marking the subsidence climax period. With the sedimentary section approximating 8‐km thickness by the time of maximum burial, the modelled average maximum temperature and vitrinite reflectivity coefficient reached roughly 232°C, and 3.5% for the Lower Triassic Feixianguan Formation (T1f1), thus indicating the conditions of dry gas generation. The Meso‐Cenozoic thermo‐structural evolution that postdated the onset of hydrocarbon generation has been critical for the evolution of the petroleum play, including the Feixianguan Formation in the marine carbonates of the Early Triassic and the Xujiahe Formation in the non‐marine sandstones of the Upper Triassic. This resulted in the modification of primary hydrocarbon accumulations, mostly in the lower petroleum play, and development of secondary accumulation in the newly formed structural traps in the upper petroleum play. Therefore, accurate thermo‐tectonic history reconstruction is valuable for understanding the geological history and hydrocarbon prospectivity.
... The curvature in the predicted annealing contours essentially posit more 521 geological-time-scale annealing than the fanning linear forms that more closely reflect standard 522 kinetics based on the Arrhenius equation. This curvature may be ascribable to temperature 523 dependence in the kinetic frequency factor (Carlson, 1990;Ketcham, 2019) The data of our study indicate that mean "unannealed" track lengths decrease over therefore any track we observe is annealed to some degree. ...
... However, difficulties remain in fully characterizing the thermally-activated annealing behaviour of fission tracks and the temperature of complete track annealing, as these factors are influenced by duration of heating e.g. (Green et al., 1986;Green, 1988;Green et al., 1989), variable apatite composition (i.e. common fluorapatite vs. chlorapatite; Carlson, 1990;Carlson et al., 1999;Barbarand et al., 2003), and crystal anisotropy e.g. Ketcham et al., 2007;Nadzri et al., 2017). ...
... Gleadow and Duddy, 1981;Green, 1988). However, difficulties remain in fully characterizing the thermally-activated annealing behaviour of fission tracks and the temperature of complete track annealing, as these factors are influenced by duration of heating (e.g. Green et al., 1986;Green, 1988;Green et al., 1989), variable apatite composition (i.e. common fluorapatite vs. chlorapatite; Carlson, 1990;Carlson et al., 1999;Barbarand et al., 2003), and crystal anisotropy (e.g. Donelick et al., 1999;Ketcham et al., 2007;Nadzri et al., 2017). ...
... Little or no track shortening will be detected below about 70°C over the same period. For further discussion of the apatite fission-track technique, see Green et al. (1986), Laslett et al. (1987), Carlson (1990), Crowley et al. (1991), Carlson et al. (1999), , and Ketcham et al. (1999). ...
... Chlorine content has been identified as a primary control on fission-track retentivity (Green et al., 1985). Subsequent experiments found that other hydroxyl and cation substituents such as OH − , Fe 2+ , Na + , Si, and REE are also important in regulating FT retention (Carlson, 1990;Crowley et al., 1990;Ravenhurst et al., 1993;Carlson et al., 1999;Barbarand et al., 2003;Ravenhurst et al., 2003;Tello et al., 2006). ...
The geologic history of the Canadian Shield is difficult to constrain because the sedimentary record is missing where Precambrian basement is exposed at the surface. This study presents preliminary results and interpretations of new apatite fission-track (AFT) analyses to elucidate the low-temperature (<110°C) history across Canada. AFT modeling of samples from Southampton Island indicate that maximum temperatures vary between 62-93°C during the Phanerozoic. Maximum burial occurred in the Devonian, but a second phase of Mesozoic burial is proposed, especially for the sample closest to the northern island-bounding normal faults. AFT modeling of a sample from northern Ontario indicates a maximum burial temperature of ~75°C was reached during the Late Devonian. Overall, these results demonstrate that the Hudson Bay sedimentary succession is the remnant of a more extensive and thicker sedimentary cover than is preserved. This study also provides the opportunity to discuss innovative methodology and modelling approaches for low-temperature thermochronology.
... A variety of different laboratory calibrated annealing models have been published (Laslett et al., 1987;Crowley et al., 1991;Carlson, 1990;Ketcham et al., 1999). These differ in detail, but given the uncertainties on the data and the models themselves (Barbarand et al., 2003), they produce broadly similar solutions when extrapolated to geological time scales. ...
The role of provenance and inherited information in the inference and resolution of thermal histories from fission-track data from detrital apatite is examined in a set of synthetic samples with variable predepositional (provenance) and postdepositional (burial) components in the total thermal history. The models and data are used to show how partially reset samples with protracted provenance history lead to under-prediction of the maximum burial temperature. Neglect of provenance effects can therefore lead to misinterpretation of postdepositional thermal histories. To avoid this problem, the sample depositional (stratigraphic) age should be routinely used where available to constrain the modeling procedure. We also show how provenance thermal histories can be recovered over a greater temperature range than previously considered. In practice, this will depend on the annealing model appropriate for a given apatite composition. For common fluorapatite samples with a protracted but simple provenance thermal history, this can be as high as 100 °C, rather than just up to 60 °C, as is often inferred
... The first published apatite annealing model using track-length data (Laslett et al., 1987) was based on laboratory-timescale heating experiments by Green et al. (1986) using the Durango apatite, a widely available gem quality apatite from Cerro de Mercado, Durango City, in Mexico (Young et al., 1969). Carlson (1990) used the results of earlier annealing studies to develop a physical model in which track-length reduction is dominated initially by axial shortening and subsequently by segmentation of tracks. Soon after Crowley et al. (1991) explored compositional variations using F-and Sr-rich apatites, previous studies having monitored the behaviour of single apatite compositions. ...
Compositional control on the annealing kinetics of fission-tracks (FT) in apatite requires routine measurement of sample grain composition. However, for practical reasons the bulk composition of analysed grains is not routinely measured and instead grain chlorine content or etch-pit dimensions are used to characterise a samples annealing behaviour. A more desirable approach is to measure crystallographic parameters (i.e. unit cell dimension) of a grain as these represent the summed effect of all substitutions and crystal defects. We show how Raman microspectrometry can be used as a routine non-destructive tool to obtain rapid measurement of the crystallographic structure of apatite grains etched for FT analysis. Variations of unit cell parameter a are found to correspond to a systematic variation of Raman shift in the range of 452–440 cm− 1 for measurements made on c-parallel sections of apatite where the direction of the polarized incident beam is parallel to the c axis.
... Gleadow and Duddy, 1981;Green, 1988). However, difficulties remain in fully characterizing the thermally-activated annealing behaviour of fission tracks at geologic timescales and the temperature of complete track annealing, as these factors are influenced by duration of heating (Duddy et al., 1988;Green et al., 1986;Green, 1988;Green et al., 1989), variable apatite composition (i.e. common fluorapatite vs. chlorapatite; Carlson, 1990; Barbarand et al., 2003;Carlson et al., 1999), and crystal anisotropy (e.g. Donelick et al., 1999;Ketcham et al., 2007;Nadzri et al., 2017). ...
Apatite fission track (AFT) analyses for granitoid and metamorphic bedrock samples from the Western Superior Province (Ontario), the Churchill-Rae Province (Melville Peninsula and Southampton Island, Nunavut), and the Slave Province (Northwest Territories) show a broad
range of single grain effective uranium concentrations (eU) (<1 to ~300 ppm) and some of the oldest reported AFT ages in North America. Although most of our samples are characterized by near-endmember fluorapatite composition with implied low track retentivity (<0.1 apfu Cl, rmr0 ~0.85-0.82), single-grain AFT ages are statistically overdispersed and ages decrease with increasing eU content. This eU-age relationship is resonant of the Hendriks and Redfield (2005) Earth Planet. Sci. Lett. 236 (443-458) argument for α-radiation enhanced fission track annealing (REA) and is analogous to the negative age-eU correlations observed in published zircon and titanite (U-Th)/He data from slowly-cooled cratonic rocks. In all cases, the samples fail the
canonical χ2 test (<5%), generally considered to indicate that the ages are unlikely to be drawn from a single Poissonian distribution with a discrete mean value and may represent multiple populations. The high intra-sample age variability for low-Cl bedrock apatites with protracted
histories (>200-500 m.y.) at <100°C since the Precambrian suggests strong REA control on AFT ages. Conversely, some low Cl AFT samples with a narrower eU range show less age dispersion and a weak apparent age-eU correlation. A complex trade-off between radiation damage, chemical composition (e.g. low Cl and REE enrichment), and thermal history is implied when eU and rmr0 are positively correlated. Previous assessments of the influence of REA on AFT age were based on evaluating central age and mean track length, which potentially mask high single grain age scatter and REA effects due to the modal nature of central age determination. REA is also supported by and compatible with materials science and nuclear waste studies of radiation damage in different apatite groups, therefore it is crucial that bedrock samples exhibiting high age scatter are evaluated in terms of intra-sample compositional heterogeneity. AFT samples with relatively low Cl concentrations are especially prone to greater REA control of cooling ages and this underscores the need for routine acquisition of compositional data for AFT datasets. Our broad range in single-grain AFT ages (with no other clear, strong compositional controls) supports the notion that radiation damage affects both the AFT and (U-Th)/He thermochronometers in slowly-cooled settings and must be accounted for during thermal history
modeling and interpretation.
... The model codes and forms are: 0: Fanning linear, based on Laslett et al. (1987) and Crowley et al. (1991). 2: Model of Carlson (1990). ...
... These closure temperature ranges are generally accurate, but they can change depending on apatite composition in the AFT system (e.g., Green et al., 1986) and on the accumulated radiation damage in the AHe system (e.g., Flowers et al., 2009). The fact that tracks shorten (anneal) in a certain temperature range allows extraction of important information about their cooling paths, as rapidly cooled rocks would display mostly long tracks >14 μm, contrary to slowly cooled rocks that would exhibit shortened tracks <14 μm (Green et al., 1986, Carlson, 1990Crowley, 1993;Crowley et al., 1991). Importantly, it is widely known that apatites can present different annealing behaviors that are usually linked to compositional variations, with chlorine-rich apatites presenting more resistance to annealing than fluorine-rich apatites (e.g., ...
New thermochronometric data provide evidence for an along-strike diachronous building of the Andes in north-central Chile (28.5–32°S). Geochronological (U-Pb zircon) and thermochronological (apatite fission track and (U-Th)/He) analyses of rock units were obtained in west-to-east transects across the western topographic front. Thermal models indicate that the area west of the topographic front was little exhumed since approximately 45 Ma. To the east of the western topographic front, the Main Cordillera shows both latitudinal and longitudinal differences in exhumation patterns. North of 31.5°S, Cenozoic exhumation began before approximately 40–30 Ma at the western and eastern limits of the Main Cordillera, building the Incaic Range. Later, accelerated exhumation focused on the core of the Main Cordillera and in the Frontal Cordillera at approximately 22–14 Ma and approximately 7 Ma, respectively. South of 31.5°S, accelerated exhumation in the Main Cordillera occurred mainly around 22–14 Ma, after an initial Eocene phase, and the locus of exhumation moved eastward by the late Miocene. Whereas accelerated exhumation in the early to mid-Miocene correlates with the breakup of the Farallon Plate, late Miocene accelerated exhumation correlates with the onset of flat subduction. Latitudinal differences on the exhumation timing along the western topographic front of the Main Cordillera may be due to the absence of the Paleozoic crystalline core south of 31.5°S, which seems to have acted as a buttress for shortening during the Eocene.
... FT thermochronology is founded on the concept that tracks are partially or entirely erased at elevated temperatures, resulting in readily measured reductions in both track lengths and track densities. For apatite, kinetic models for thermally activated annealing of the fission tracks are well developed (e.g., Naeser 1979;Gleadow et al. 1986;Green et al. 1989a, b;Carlson 1990;Corrigan 1991;Crowley et al. 1991;Ketcham et al. 1999). Fluorapatite is the most common form of apatite (e.g., Pan and Fleet 2002) and is generally the least resistant to thermal annealing (see Chap. 3, Ketcham 2018). ...
The maturation of organic material into petroleum in a sedimentary basin is controlled by the maximum temperatures attained by the source rock and the thermal history of the basin. A cycle of continuous deposition into the basin (burial) and regional basin inversions represented by unconformities (unroofing) may complicate the simple thermal development of the basin. Applications of low-temperature thermochronology via fission-track (FT) and (U–Th)/He dating coupled with independent measurements (vitrinite reflectance, Rock-Eval) resolving the paleothermal maximum are the ideal approach to illuminate the relationship between time and temperature. In this contribution, we review the basics of low-temperature thermochronology in the context of a project workflow, from sampling to modeling, for resolving the thermal evolution of a hydrocarbon-bearing sedimentary basin. We specifically highlight the application of multi-kinetic apatite FT dating, emphasizing the usefulness of the rmr0 parameter for interpreting complex apatite age populations that are often present in sedimentary rocks. Still a rapidly advancing science, thermochronology can yield a rich and effective dataset when the minerals are carefully and properly characterized, particularly with regard to mineral chemistry and radiation damage.
... Gleadow and Duddy, 1981;Green, 1988). However, difficulties remain in fully characterizing the thermally-activated annealing behaviour of fission tracks at geologic timescales and the temperature of complete track annealing, as these factors are influenced by duration of heating ( Duddy et al., 1988;Green et al., 1986;Green, 1988;Green et al., 1989), variable apatite composition (i.e. common fluorapatite vs. chlorapatite; Carlson, 1990;Barbarand et al., 2003;Carlson et al., 1999), and crystal anisotropy (e.g. Donelick et al., 1999;Ketcham et al., 2007;Nadzri et al., 2017). ...
Apatite fission track (AFT) analyses for granitoid and metamorphic bedrock samples from the Western Superior Province (Ontario), the Churchill-Rae Province (Melville Peninsula and Southampton Island, Nunavut), and the Slave Province (Northwest Territories) show a broad range of single grain effective uranium concentrations (eU) (<1 to ~300 ppm) and some of the oldest reported AFT ages in North America. Although most of our samples are characterized by near-endmember fluorapatite composition with implied low track retentivity (<0.1 apfu Cl, rmr0 ~0.85-0.82), single-grain AFT ages are statistically overdispersed and ages decrease with increasing eU content. This eU-age relationship is resonant of the Hendriks and Redfield (2005) Earth Planet. Sci. Lett. 236 (443-458) argument for α-radiation enhanced fission track annealing (REA) and is analogous to the negative age-eU correlations observed in published zircon and titanite (U-Th)/He data from slowly-cooled cratonic rocks. In all cases, the samples fail the canonical χ2 test (<5%), generally considered to indicate that the ages are unlikely to be drawn from a single Poissonian distribution with a discrete mean value and may represent multiple populations. The high intra-sample age variability for low-Cl bedrock apatites with protracted histories (>200-500 m.y.) at <100°C since the Precambrian suggests strong REA control on AFT ages. Conversely, some low Cl AFT samples with a narrower eU range show less age dispersion and a weak apparent age-eU correlation. A complex trade-off between radiation damage, chemical composition (e.g. low Cl and REE enrichment), and thermal history is implied when eU and rmr0 are positively correlated. Previous assessments of the influence of REA on AFT age were based on evaluating central age and mean track length, which potentially mask high single-grain age scatter and REA effects due to the modal nature of central age determination. REA is also supported by and compatible with materials science and nuclear waste studies of radiation damage in different apatite groups, therefore it is crucial that bedrock samples exhibiting high age scatter are evaluated in terms of intra-sample compositional heterogeneity. AFT samples with relatively low Cl concentrations are especially prone to greater REA control of cooling ages and this underscores the need for routine acquisition of compositional data for AFT datasets. Our broad range in single-grain AFT ages (with no other clear, strong compositional controls) supports the notion that radiation damage affects both the AFT and (U-Th)/He thermochronometers in slowly-cooled settings and must be accounted for during thermal history modeling and interpretation.
... Because 8 Barbarand et al., 14 and Schmidt et al. 31 b Read in Figure 1 in Guedes et al. 32 T, annealing temperature (heated in the muffle furnace for 10 h); L, mean track length; L 0 , original length; L/L 0 ¼ 0, the sample is totally annealed; r/r 0 , the current/original track density, respectively. the kinetic prediction of ellipsoidal symmetry is equivalent to that of cylindrical symmetry, 34 an ellipsoid is used to simulate the etched track in the TVFM. Therefore, the single track volume (V s ) can be calculated by ...
Apatite fission-track (AFT) analysis, a widely used low-temperature thermochronology method, can provide details of the hydrocarbon generation history of source rocks for use in hydrocarbon exploration. The AFT method is based on the annealing behavior of fission tracks generated by ²³⁸U fission in apatite particles during geological history. Due to the cumbersome experimental steps and high expense, it is imperative to find an efficient and inexpensive technique to determinate the annealing degree of AFT. In this study, on the basis of the ellipsoid configuration of tracks, the track volume fraction model (TVFM) is established and the fission-track volume index is proposed. Furthermore, terahertz time domain spectroscopy (THz-TDS) is used for the first time to identify the variation of the AFT annealing degree of Durango apatite particles heated at 20, 275, 300, 325, 450, and 500 ℃ for 10 h. The THz absorbance of the sample increases with the degree of annealing. In addition, the THz absorption index is exponentially related to annealing temperature and can be used to characterize the fission-track volume index. Terahertz time domain spectroscopy can be an ancillary technique for AFT thermochronological research. More work is urgently needed to extrapolate experimental data to geological conditions.
... In fact, in earlier works, it has been established that the apatite fission track data depend on the burial history of the studied sample. As a rigorous mathematical description of the apatite FT shortening, under the influence of temperature and time, is not well known, many empirical models were proposed [2,3,4,5]. These models predict the resulting FT parameters from a given thermal history. ...
This paper propose an optimization algorithm for modeling thermal histories with apatite fission tracks. In fact, thermal evolution of sedimentary basins and their margins is of major importance for petroleum exploration, as it controls the timing of hydrocarbon generation. This kind of problems is characterized by their nonlinear and multi-parameter aspects. For this purpose we have used genetic algorithms (GA). The adopted GA, which is in other respects perfectly adapted to the problem’s requirements (encoding scheme, genetic operations, etc.) provide satisfactory results for both synthetic and real data. The re-examination of some samples studied earlier, from the French western Alps, confirm the obtained results.
Keywords : Thermal histories, Optimization, Genetic algorithms.
... The irregular length increments of individual tracks past the break in slope favor a discontinuous (Dartyge et al. 1981;Pellas and Perron 1984;Dartyge and Sigmund 1985;Green et al. 1986;Paul and Fitzgerald 1992;Hejl 1995;Villa et al. 1999;Jaskierowicz et al. 2004;Li et al. 2011Li et al. , 2012Li et al. , 2014) over a continuous (Carlson 1990;Afra et al. 2011;Kluth et al. 2012;) damage model. The high etch rate before the break in slope (40-50 μm/min) in the length vs. etch-strength plot (Fig. 1) suggests a more continuous central track section. ...
Fossil and induced confined fission-tracks in the Durango apatite do not etch to their full etchable lengths with the current protocols. Their mean lengths continue to increase at a diminished rate past the break in slope in a length vs. etch-time plot. The mean length of the fossil tracks increases from 14.5(1) to 16.2(1) μm and that of the induced tracks from 15.7(1) to 17.9(1) μm between 20 and 60 s etching (5.5 M HNO3; 21 °C); both are projected to converge toward ~18 μm after ~180 s. This increase is due to track etching, not bulk etching. The irregular length increments of individual tracks reveal a discontinuous track structure in the investigated length intervals. The mean lengths of the fossil and induced tracks for the standard etch time (20 s) for the (5.5 M HNO3; 21 °C) etch are thus not the result of a shortening of the latent fission tracks but instead of a lowering of the effective track-etch rate νT. The rate of length increase of individual fossil confined tracks correlates with their length: older tracks are shorter because they etch slower. Step etching thus makes it possible to some extent to distinguish between older and younger fossil fission tracks. Along-track νT measurements could reveal further useful paleo-temperature information. Because the etched length of a track at standard etch conditions is not its full etchable length, geometrical statistics based on continuous line segments of fixed length are less secure than hitherto held.
... Recently, both Carlson (1990) and Crowley et al. (1991) have published alternative kinetic models for 1175 fission track annealing in apatite. Carlson's model is based on our laboratory annealing data for 1176 Durango apatite and other (unpublished) data. ...
Latest Mesozoic to earliest Cenozoic deformation affected SE Asia's Sundaland core. The deformation event bridges the Mesozoic SE Asian fusion with the Cenozoic era of rifting, translation, basin formation, and the creation of modern SE Asian oceans. Southern Cambodia and Vietnam are central to this shift, but geological investigations of the region are in their infancy. Based on apatite and zircon fission track analyses (AFTA and ZFTA), stratigraphic and structural observations, seismic data, thermal maturity, and igneous rock dating, the geological evolution of southern Cambodia and Vietnam is investigated. Diverse depositional styles, igneous activity, structural deformation and subsurface unconformities testify to a highly variable Phanerozoic tectonic setting. Major latest Cretaceous to Paleocene thrusting and uplift affected the Kampot Fold Belt and surrounding regions and the associated up to ~11 km exhumation probably exceeds earlier denudation events since at least Permian time. The present relief of the Bokor Mountains rising high above the Kampot Fold Belt represents an artifact after differential erosion and only 2.5–4.5 km of erosion affected this area. The latest Cretaceous to Paleocene orogenesis affected much of greater Indochina probably owing to plate collision along eastern Sundaland or a combination of collisions along both east and west Sundaland. AFTA and ZFTA data document protracted cooling of Cretaceous granites and locally elevated thermal gradients persisting a few tens of million years after their emplacement. The thermal gradient had stabilized by early Miocene time, and Miocene cooling probably reflects a renewed denudation pulse driven by either regional tectonism or climate-enhanced erosion.
... Nous pensons que ceci est dfi fl une fragmentation du parcours r6v61able des traces affect6es thermiquement qui pourrait 6tre reli6 fl une structure discontinue de la trace latente (Dartyge et al., 1981;Green et al., 1986). Bien que la structure des traces de fission latentes ait 6t6 remise en question (Albrecht et al., 1985(Albrecht et al., , 1986, Carlson (1990) a sugg6r6 qu'une fragmentation des traces de fission se produit lors d'un recuit intense, m6me si ces traces poss6dent initialement une structure essentiellement continue. Une interruption de la conti-nuit6 des traces r6v616es est en effet apparente dans nos 6chantillons recuits fl 350°C. ...
... Fission track annealing i n apatite by track length reduction is a thermally controlled process. The kinetics of this process have been studied experimentally and several annealing models have been developed (i.e., Laslcu et al., 1987;Carlson 1990). Willett ( 1992). ...
Sandstone drill core and/or cuttings from six wells in the Gulf of St Lawrence and Cabot Strait have been analyzed using the apatite fission track (AFT) method. The AFT data indicate that most Maritimes Basin strata were heated to temperatures in excess of 100-150°C very soon after their deposition. The strata also attained significant vitrinite reflectant (Ro) levels early in the burial history. These findings imply the generation of hydrocarbons and coalbed methane in the early basin history (pre-250 Ma). Thermal model of the AFT data demonstrate that they are consistent with a history of exhumation of basin strata since late Permian time. -from Authors
... A variety of different laboratory calibrated annealing models have been published (Laslett et al., 1987;Crowley et al., 1991;Carlson, 1990;Ketcham et al., 1999). These differ in detail, but given the uncertainties on the data and the models themselves (Barbarand et al., 2003), they produce broadly similar solutions when extrapolated to geological time scales. ...
The role of provenance and inherited information in the inference and resolution of thermal histories from fission-track data from detrital apatite is examined in a set of synthetic samples with variable predepositional (provenance) and postdepositional (burial) components in the total thermal history. The models and data are used to show how partially reset samples with protracted provenance history lead to underprediction of the maximum burial temperature. Neglect of provenance effects can therefore lead to misinterpretation of postdepositional thermal histories. To avoid this problem, the sample depositional (stratigraphic) age should be routinely used where available to constrain the modeling procedure. We also show how provenance thermal histories can be recovered over a greater temperature range than previously considered. In practice, this will depend on the annealing model appropriate for a given apatite composition. For common fluorapatite samples with a protracted but simple provenance thermal history, this can be as high as 100 °C, rather than just up to 60 °C, as is often inferred.
Oil and gas accumulations are the smallest and most basic units in petroleum exploration and development, and for calculating oil and gas reserves. There are numerous types of trapped reservoirs, so their classification must reflect their origins and those of the formations that host them.
Fission-track annealing models describe the recovery kinetics of a crystalline structure damaged by the interaction with fission fragments during the geological thermal history of a mineral sample. Arrhenius type equations have been successfully applied to model annealing and are at the core of thermal history (temperature, T, as a function of time, t, paths) reconstruction programs for fission-track thermochronology. In this work, the Arrhenius equations are generalized and synthesized in a composite equation that allows for the generation of Arrhenius-type equations by turning on/off parameters and by appropriately choosing functions of lnt and T-1. Geometrical features of the Arrhenius-type equations in the Arrhenius pseudo-space (T-1,lnt) are explored. Three examples of new models for annealing of fission tracks in apatite, obtained from the composite model, are presented, and their extrapolation to the geological timescale is discussed. The presented composite model can be applied to other studies involving annealing experiments, such as the annealing of alpha recoil damage in minerals.
It has been proposed that Oligo-Miocene regional uplift of Madagascar was generated and is maintained by mantle dynamical processes. Expressions of regional uplift include flat-lying Upper Cretaceous-Paleogene marine limestones that crop out at elevations of hundreds of meters along the western seaboard and emergent Quaternary coral-rich terraces that rim the coastline. Here, we explore the history of subcrustal topographic support through a combined analysis of four sets of observational constraints. First, we exploit published receiver function estimates of crustal thickness and spectral admittance between gravity and topography. An admittance value of ∼+40 ± 10 mGal km⁻¹ at wavelengths >500 km implies that ∼1 km of topography is supported by subcrustal processes. Secondly, new apatite fission-track and helium measurements from 18 basement samples are inverted, constraining temperature and denudation histories. Results suggest that 0.5–1.6 km of regional uplift occurred after ∼30 Ma. Thirdly, we calculate a history of regional uplift by minimizing the misfit between observed and calculated longitudinal river profiles. Results suggest that topography was generated during Neogene times. Finally, inverse modeling of rare earth element concentrations in Neogene mafic rocks indicates that melting of the asthenospheric source occurred at depths of ≤65 km with potential temperatures of 1300–1370 °C. Melting occurred at higher temperatures beneath Réunion Island and northern Madagascar and at lower temperatures beneath the Comores and southern Madagascar. These inferences are consistent with shear wave velocities obtained from tomographic models. We conclude that Madagascar is underlain by thinned lithospheric mantle and that a thermal anomaly lies within an asthenospheric layer beneath northern Madagascar.
Age dispersion is a common feature of apatite fission track (AFT) and apatite (U–Th)/He (AHe) thermochronological data and it can be attributed to multiple factors. One underappreciated and underreported cause for dispersion is variability in apatite composition and its influence on thermal annealing of fission tracks. Using synthetic data we investigate how multikinetic AFT annealing behaviour, defined using the rmr0 parameter, can be exploited to recover more accurate, higher resolution thermal histories than are possible using conventional interpretation and modelling approaches. Our forward model simulation spans a 2 Gyr time interval with two separate heating and cooling cycles and was used to generate synthetic AFT and AHe data for three different apatite populations with significantly different annealing kinetics. The synthetic data were then used as input for inverse modelling in the Bayesian QTQt software to recover thermal history information under various scenarios. Results show that essential features of the dual peak thermal history are captured using the multikinetic AFT data alone, with or without imposed constraints. Best results are achieved when the multikinetic AFT data are combined with the AHe data and geologic constraint boxes are included. In contrast, a more conventional monokinetic interpretation that ignores multikinetic AFT behaviour reproduces all the input data but yields incorrect thermal solutions. Under these conditions, incorporation of constraints can be misleading and fail to improve model results. In general, a close fit between observed and modelled parameters is no guarantee of a robust thermal-history solution if data are incorrectly interpreted. For the case of overdispersed AFT data, it is strongly recommended that elemental data be acquired to investigate if multikinetic annealing is the cause of the AFT apparent age scatter. Elemental analyses can also be similarly useful for broadly assessing AHe data. A future companion paper will explore multikinetic AFT methodology and application to detrital apatite samples from Yukon, Canada.
As one of the major tectonic belts in the southeastern Tibetan plateau, the Gaoligong tectonic belt plays important roles in accommodating the Indian-Eurasian plate collision. In this belt, medium-high-grade metamorphic rocks are preserved. In this study, we selected three cross-sections from the northern to the southern segment of the Gaoligong tectonic belt for detailed structural (macro- and micro-) observations and quartz fabric analysis. Quartz c-axis fabrics reflect three ranges of metamorphic temperature in the metamorphic rocks: Range 1 (>650–700 °C, corresponding to granulite facies), Range 2 (550–650 °C, amphibolite facies), and Range 3 (400–500 °C, greenschist facies). Mineral separates (amphibole, muscovite, and biotite) from five samples taken from the Lushui-Pianma section were selected for ⁴⁰Ar/³⁹Ar study, yielding plateau ages of ~30 Ma (amphibole), ~17 Ma (biotite), and ~15 Ma (muscovite), respectively. Combined with the previous geochronological data, it is suggested that there are three stages of metamorphism-deformation of the Gaoligong tectonic belt during Cenozoic. The early stage of metamorphism occurred at high temperature conditions (>650–700 °C, corresponding to granulite facies) during 50–34 Ma, coeval with the Cenozoic collision of the Indian Plate and Tengchong Block. The subsequent stage of metamorphism occurred at medium to low temperatures (550–650 °C, 400–500 °C, respectively) during 34–10 Ma and is the result of a non-coaxial progressive deformation showing dextral shear along the Gaoligong strike-slip fault. The latest stage represents rapid exhumation and cooling during 10–3 Ma.
Radiation-damage-based methods of geochronology rely on the same principles as other radioisotopic techniques except that daughter products are not nuclides but physical or electronic damage within a crystal. Of the various damage dating approaches, the fission-track technique stands out in the extensive knowledge of annealing kinetics and wide thermochronometric applications, but other approaches have also been used in analogous ways. It should be mentioned that quantification of the extent of cumulative crystallographic radiation damage by macroscopic or spectroscopic properties. Luminescence dating has been used for many decades, particularly in archeological and geomorphological applications, but has also been used as a thermochronometer for a variety of planetary and tectonic applications. State of the art approaches include higher precision and accuracy techniques, such as single aliquot regenerative (SAR) dose protocol, and calibration and detailed understanding of kinetic behaviors of discrete types of luminescence in particular minerals.
Picture yourself to be an atom in a crystal. Life would be monotonous and claustrophobic, with constant jostling by your neighbors, just enough to keep you as warm as they are. Occasionally, something really exciting would occur if you happen to be near a uranium atom that spontaneously fissions, so that you and many of your neighbors are given sudden short-distance rides like those of the atoms sketched in Figure l–8a. Between such events monotony takes over again.
Apatite Fission-Track low-temperature thermochronology of the evaporite, base metal and coal rich Maritimes Basin suggests that after rapid sedimentation from 320 to 290 Ma (Pennsylvanians) there was basin-wide exhumation from 280 to 150 Ma, which removed 1-3 km of strata. Most of the bsain experienced slow unroofing from the Jurassic to early Cretaceous. The paleogeothermal gradient was approx 25 degrees C per km, less than half of that suggested by other workers.
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