Track Length Reduction Research Articles

Arrhenius activation energy and transitivity in fission-track annealing equations

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.

Etching of fission tracks in monazite: Further evidence from optical and focused ion beam scanning electron microscopy

Abstract A series of experiments on monazites from Victoria, Australia, is presented to further understand their fission track etching properties. Using a 6 M HCl etchant at 90 °C, SEM images on crystal (100) pinacoid faces reveal well-etched rhombic spontaneous fission track openings. Average rhombic etch pit diameters Dpc and Dpb, parallel to the crystallographic c- and b-axes are 0.81 ± 0.20 µm and 0.73 ± 0.26 µm, respectively. An angular distribution experiment on (100) faces found that spontaneous fission tracks initially etch anisotropically, being preferentially revealed at an azimuth of 90° to the crystallographic c-axis up to ~60 min of etching. As etching continues, however, the distribution becomes progressively more uniform and is essentially isotropic by 90 min. Two experimental methods determined the rate at which the etchant penetrated along the lengths of implanted 252Cf fission tracks. This involved the application of a focused ion beam scanning electron microscope (FIB-SEM) to mill progressively into slightly etched monazite crystals followed by an etch-anneal-etch approach. Results indicate that at least the greater part of the etchable ranges of the latent fission tracks were penetrated by the 6 M HCl etchant within the first few minutes. Continued etching to 5 min indicates that track etching slows down toward the ends of the tracks, but the maximum ranges are estimated to be reached after 5–15 min, which represents the longest time the latent segments of the tracks are exposed to potential annealing at the etchant temperature. Taking into account that implanted 252Cf fission tracks in monazite anneal on average ~4% of their length at 90 °C after 1 h (Jones et al. 2019), suggests that a much shorter duration for exposure to this temperature causes less than ~1% of fission track length reduction during etching.

The influence of artificial radiation damage and thermal annealing on helium diffusion kinetics in apatite

Recent work [Shuster D. L., Flowers R. M. and Farley K. A. (2006) The influence of natural radiation damage on helium diffusion kinetics in apatite. Earth Planet. Sci. Lett. 249(3–4), 148–161] revealing a correlation between radiogenic 4He concentration and He diffusivity in natural apatites suggests that helium migration is retarded by radiation-induced damage to the crystal structure. If so, the He diffusion kinetics of an apatite is an evolving function of time and the effective uranium concentration in a cooling sample, a fact which must be considered when interpreting apatite (U–Th)/He ages. Here we report the results of experiments designed to investigate and quantify this phenomenon by determining He diffusivities in apatites after systematically adding or removing radiation damage. Radiation damage was added to a suite of synthetic and natural apatites by exposure to between 1 and 100 h of neutron irradiation in a nuclear reactor. The samples were then irradiated with a 220 MeV proton beam and the resulting spallogenic 3He used as a diffusant in step-heating diffusion experiments. In every sample, irradiation increased the activation energy ( E a ) and the frequency factor ( D o / a 2) of diffusion and yielded a higher He closure temperature ( T c ) than the starting material. For example, 100 h in the reactor caused the He closure temperature to increase by as much as 36 °C. For a given neutron fluence the magnitude of increase in closure temperature scales negatively with the initial closure temperature. This is consistent with a logarithmic response in which the neutron damage is additive to the initial damage present. In detail, the irradiations introduce correlated increases in E a and ln( D o/a 2) that lie on the same array as found in natural apatites. This strongly suggests that neutron-induced damage mimics the damage produced by U and Th decay in natural apatites. To investigate the potential consequences of annealing of radiation damage, samples of Durango apatite were heated in vacuum to temperatures up to 550 °C for between 1 and 350 h. After this treatment the samples were step-heated using the remaining natural 4He as the diffusant. At temperatures above 290 °C a systematic change in T c was observed, with values becoming lower with increasing temperature and time. For example, reduction of T c from the starting value of 71 to ∼52 °C occurred in 1 h at 375 °C or 10 h at 330 °C. The observed variations in T c are strongly correlated with the fission track length reduction predicted from the initial holding time and temperature. Furthermore, like the neutron irradiated apatites, these samples plot on the same E a − ln( D o / a 2) array as natural samples, suggesting that damage annealing is simply undoing the consequences of damage accumulation in terms of He diffusivity. Taken together these data provide unequivocal evidence that at these levels, radiation damage acts to retard He diffusion in apatite, and that thermal annealing reverses the process. The data provide support for the previously described radiation damage trapping kinetic model of Shuster et al. (2006) and can be used to define a model which fully accommodates damage production and annealing.

Annealing experiments on induced fission tracks in apatite: Measurements of horizontal-confined track lengths and track densities in basal sections and randomly oriented grains

To improve kinetic models for apatite fission-track annealing, we present new experimental annealing data that complement previously published data. To determine the degree of annealing of induced tracks, surface density (ρ), and mean horizontal-confined track lengths (l), were measured, both for basal and randomly oriented faces. Our annealing data were obtained by submitting an apatite sample collected in Itambé, Bahia, Brazil, to 46 different isothermal treatments where temperature ranged from 150 to 600 °C (duration of 1, 10, 100, and 1000 h). To compare the behavior of Itambé to Durango apatite, the latter was also annealed for 1 h in 9 isothermal experiments at temperatures between 240 and 380 °C. Our results show that the l/l 0 values in Durango are systematically smaller than those in Itambé sample, both in basal and random faces. The curves depicting relative track density reduction, ρ/ρ 0 , and relative mean confined track length reduction, l/l 0 , as a function of time and temperature, are similar for ρ/ρ 0 > ~0.5, but different for ρ/ρ 0 < ~0.5. In this interval, ρ/ρ 0 can be measured but the measurement of l/l 0 is very difficult because the confined tracks become undetectable. Measurements of ρ/ρ 0 and l/l 0 for tracks revealed in basal surfaces are systematically lower (but this difference is <3%) than those in randomly oriented ones.

Variability of apatite fission-track annealing kinetics; II, Crystallographic orientation effects

A method is presented that permits the length of any horizontal, confined fission-track inclined at a specified angle to the crystallographic c axis in apatite to be converted to an equivalent track length parallel to the crystallographic c axis. The model is based on the results of annealing experiments for six selected apatites (five calcian fluorapatites and Durango apatite) representing a subset of the 15 total apatite specimens studied. An iterative process of calculation is required to project fission-track lengths onto the c axis and computer source code implementing the solution to this problem is presented. This method of projecting apatite fission-track lengths onto the crystallographic c axis is shown to remove effectively fission-track length variation within single fission-track populations due to anisotropic track-length reduction for all 15 apatites studied. In addition, a model is developed that offers predictions that closely reproduce published experimental data concerning the relationship between fission-track density (etched fission tracks per unit area of apatite surface) and the arithmetic mean fission-track length. Finally, it is shown that natural fission-track populations exhibit fission-track length anisotropy similar to that of fission-track populations created and annealed in the laboratory. This observation implies that the same process by which apatite fission tracks anneal in the laboratory is responsible for annealing of apatite fission tracks in the geological environment.

Optimizing time step size for apatite fission track annealing models

Empirical isothermal apatite fission track (AFT) annealing models are used to extract variable temperature histories from measured AFT parameters by forward and inverse modeling techniques. Using one such published annealing model based on Durango apatite data, a method has been developed for optimally discretizing thermal histories into isothermal steps for the evaluation of the annealing model. The equation S = (√ log( T a T m ) A 1 + A 2e − (T m − T) A 3 ) R A 4 predicts isothermal time step size ( S) as a function of maximum interval temperature ( T m in kelvins) and rate of temperature change ( R in K m.y. −1) with constants A 1 = 0.00596, A 2 = 0.043, A 3 = 34.8, and A 4 = 0.978, and with the total annealing temperature ( T a ) given as a power function of R, T a = 398.15( R 0.0157). This equation offers improved computational efficiency and accuracy for the full range of track length reduction in comparison with other methods published. Improved model performance is important particularly for inversion type models which may require the generation of thousands of model temperature histories with large variations in heating and cooling rates. For similar amounts of annealing, integration step sizes differ by two orders of magnitude for heating/cooling rates that range between 0.1 and 10 K m.y. −1, a range that encompasses most sedimentary basins. As an added advantage, users can specify the approximate degree of accuracy for track length calculations by multiplying S by the scaling factor, √10 E, where E is the approximate percent error on calculated track lengths. For E values of 0.1 and 1.0, computed thermal histories are within ⩽0.2 °C and ⩽1.0 °C, respectively, of the true numerical solution.

Apatite fission-track analysis of Oligocene strata in South Texas, U.S.A.: Testing annealing models

Analysis of apatite fission-track data from forty-seven surface and subsurface samples of fine-grained sandstone to pebbly conglomerate from the Oligocene Catahoula (Gueydan), Frio and Vicksburg Formations documents the response of fission-track ages and track-length distributions to simple post-depositional thermal histories characterized by monotonic heating. Data from outcrop samples document that the apatite component was derived from source areas characterized by rapid cooling through the temperature range from ∼ 120° to 50°C during the early Tertiary. The apatite population is characterized by a log-normal chlorine distribution (mean = 0.3 wt%, σ = 0.3 wt%) consisting predominantly of low-Cl apatites (80% is ⩽ 0.5 wt%). Mean track lengths from core samples decrease systematically with increasing depth and temperature. The decrease in apatite fission-track ages with increasing depth and temperature is less systematic due to the scatter in inherited ages at the time of deposition. No tracks were observed in apatite from samples at temperatures above 130°C. Mean track-lengths for the South Texas data agree well with those for a similar data set from the Otway Basin, southeastern Australia, for present-day temperatures of < 70°C). At higher temperatures, mean lengths are 1 to 9 μm longer than those observed from the Otway Basin. This discrepancy is interpreted to reflect up to 40-Ma-longer residence times at maximum burial temperatures for the Otway Basin samples. Standard deviations about mean lengths are also lower than observed in the Otway Basin study, consistent with the wider variation of Cl contents (mean = 0.8 wt%, σ = 0.7 wt%) that characterize apatite from the Otway Basin. Recently published apatite fission-track annealing models predict significantly different mean track length vs. present-day temperature profiles for thermal histories believed to be representative of those experienced by sampled South Texas strata. Because of the large uncertainties attributed to present-day temperatures (± 10°C), the predicted mean length vs. temperature trends for these models essentially fall within or on the uncertainty envelope for the observed trend. Residuals of predicted minus observed mean lengths suggest that the previously published Carlson composite parameter model. using an initial mean length of 15.8 μm instead of 16.5 μm, or the Crowley et al. model for track-length reduction down to ∼ 11 μm, provide the best estimates of mean track-length reduction over geologic time scales for near end-member F-apatite populations.

L'apatite de Durango (Mexique): Analyse d'un minéral standard pour la datation par traces de fission

Durango apatite is analyzed by four analysts using three different dating techniques. Both the annealing technique and the external detector technique are applied to basal and prismatic sections cut from single crystals. The population technique is applied to mounts of randomly oriented grains. Provided an individual determination of the geometry factor is performed, all ages are indistinguishable from the reference age of 31.4 ± 0.5 Ma. There is no noticeable influence of either the dating technique or the crystallographic orientation of the dated section on the FT age. Based on the projected lengths of surface tracks, spontaneous track length reduction varies from ∼4% to ∼10% (mean ∼6%), depending on the analyst. Two simple corrections are applied to eliminate the net effect of the missing short tracks on the mean projected length. After correction the amount of shortening of the spontaneous tracks is found to be slightly larger (mean ∼8%) but is still dependent on the analyst (∼4% to ∼12%). The mean is in fairly good agreement with the value obtained from confined track length measurements (∼9%). Finally, an isochronal (1 h) plateau annealing procedure was applied to a separate set of basal and prismatic sections cut from the same single crystals. Annealing temperatures up to 300°C do not affect the FT age. Erratic ages at 350°C are ascribed to the occurrence of unetchable gaps. It is argued that the absence of a distinct plateau up to temperatures where it could be expected from theoretical considerations indicates that the FT age of Durango apatite needs no correction.

Post-intrusive thermal and uplift histories of mount ascutney and mount royal, eastern North America: Modelling based on heat flow and fission track length reduction calculations

s-6th International FTD Workshop inclusions have a typical feature. Thus for a bulk polished geological sample it is possible to establish an age succession of the constituent minerals in functions of the track cluster patterns. Also it is shown that, knowing the migration speed of the uranium in a mineral, it will be possible to estimate the age of this mineral. The age estimation procedure was verified using samples of mica-muscovite mineral dated by the K-Ar method. POST-INTRUSIVE THERMAL AND UPLIFT HISTORIES OF MOUNT ASCUTNEY AND MOUNT ROYAL, EASTERN NORTH AMERICA: MODELLING BASED ON HEAT FLOW AND FISSION TRACK LENGTH REDUCTION CALCULATIONS RAYMOND A. DONELICK,* MARY K. RODEN,* DONALD S. MILLER* and G. NELSON EByt *Department of Geology, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, U.S.A. and tDepartment of Earth Sciences, Umverslty of Lowell, Lowell, MA 01854, U.S.A. APATITE fission track age and confined length measurements for 125 Ma intrusive rocks from Mount Ascutney (Vermont, U.S.A.) and Mount Royal (Quebec, Canada) were used to obtain time-temperature paths for temperatures ~ approximately 120CC. The apatite data obtained in this study are summarized as follows: (a) Mount Ascutney: fission track age 95.1 ± 9.8 Ma, mean confined track length 13.6 ± 1.4 microns and (b) Mount Royal: fission track age 116 ±5.2 Ma, mean confined track length 13.8 ± 1.2 microns. This information, combined With published and unpublished Rb--Sr and Ar-Ar data for these rocks, permits construction of the complete time-temperature paths for these two intrusive bodies. Collectively, these data indicate that both intrusions cooled very rapidly to below 3OQ°C (consistent with their epizonal nature and small size) but they display variable and somewhat protracted cooling in the temperature range of ~ _120°C. An attempt was made to explain the different low temperature cooling histories for these two intrusions using a two-dimensional conductive heat flow model. Results for both Mount Ascutney and Mount Royal indicate that uplift plays a dominant role in determining the low-temperature cooling histories. Cumulative post-intrusive uplift of about 3--4 km in the vicinity of Mount Ascutney and 2-3 km in the vicinity of Mount Royal has occurred. GEOCHRONOLOGY OF CARBONATITE COMPLEXES AND ASSOCIATED ALKALINE ROCKS: A COMPARISON OF FISSION-TRACK AND OTHER

Fission-track analysis of basement apatites at the western margin of the Gulf of Suez rift, Egypt: evidence for synchroneity of uplift and subsidence

Fifty-six apatite fission-track ages and 52 horizontal confined track-length measurements are reported from Precambrian crystalline rocks along the western margin of the Gulf of Suez, Egypt. Ages fall in the range of ca. 11–385 m.y. and older ages often occur within very close geographic proximity to younger ones, indicating non-uniform uplift. The wide range in ages is accompanied by a systematic variation in the distribution of horizontal confined fission track lengths. On the basis of apatite fission track ages and their length distributions, data fall into three distinct groups. Group I: ages ranging from 43 to 385 m.y. Length distributions are all positively skewed and with decreasing age become progressively broader with shorter mean track length. Group II: ages ranging from 23 to 31 m.y. Length distributions are negatively skewed with either a distinct tail or a small peak of short tracks. Group III: ages ranging from 11 to 20.5 m.y. Length distributions are al unimodal, narrow, negatively skewed and have the longest mean lengths among samples studied. Apatite ages from groups I and II are interpreted as “mixed ages” as a result of cooling during uplift from different levels within the apatite partial track annealing zone. Ages from Group III are interpreted as “cooling ages” due to uplift from the apatite total track annealing zone with minor partial annealing. Correcting the ages of the two oldest samples in this group for track-length reduction yields ages of 21 ± 2.2and23 ± 1.5m.y. It is proposed that the onset of rift-flank uplift in the Gulf of Suez—northern Red Sea area occurred between 21 and 23 m.y. ago. Fission-track analysis in combination with subsidence data from the Gulf of Suez basin, indicate that commencement of basement uplift postdate the start of rifting and is interpreted as evidence for passive rifting at the Gulf of Suez. Furthermore, this uplift is contemporaneous with, and is directly related to, the process of extension and subsidence at the Gulf of Suez.

Thermal annealing of heavy ion tracks in muscovite mica

Abstract Thermal annealing of latent tracks caused by the passage of heavy ions, viz. Pb208 (13.8 MeV/n) and Ni58 (15.37 MeV/n), in muscovite mica is investigated. The activation energy for track annealing, determined using different annealing models, is compared. The effect of thermal annealing on size and energy resolution of heavy ions in mica, based on the track etch rate and track length reduction, is discussed.

Apatite fission-track dating applied to Precambrian terranes

Fission-track (FT) dating has not commonly been applied to Precambrian rocks. Although it is possible to obtain formation ages on orthosilicates, it is apatite that is dated most frequently because of its specific characteristics with regard to track annealing, which makes it especially suited for reconstructing the final thermal history of the investigated area. With this respect apatite FT ages are often interpreted in terms of uplift and age variations registered on samples from different topographic altitudes are used to calculate uplift rates. In the older part of the Earth's crust this practice may lead to very slow rates in the order of 10 m Ma −1. It is argued that these rates may have no geological meaning and that the apatite FT ages can be more probably related to a long period of complete crustal stability that has been disturbed by relatively recent tectonic uplift and erosion. In this way apatites that resided in the partial track stability zone during the period of continental stability were brought at the surface and a correlated decrease of the FT ages with topographic altitude simply reflects the greater depth at which the samples resided in that zone. The importance of track length measurements in the search for a correct age interpretation is also emphasized. With this respect old ages obtained on apatites that do not show a distinct spontaneous track length reduction are thought to plead in favor of crustal stability. The late Precambrian alkaline pluton in northern Burundi (Central Africa) offers a good case study yielding apatite FT ages that can better be interpreted using this alternative approach.

A natural long-term track annealing experiment for apatite

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

Fission track annealing characteristics and dating of vermiculite

Fission track annealing experiments for vermiculite mineral have been performed under optimised etching conditions and a correction curve translating track length reduction to track density reduction has been constructed. The blocking/closing temperature of the fission track system in the mineral has been calculated to be 125°±30° C. The corrected fission track age of vermiculite from Kasipatnam (Visakhapatnam), South India, has been calculated as 544±14 Ma. The activation energy and average uranium concentration of the mineral are 1.7 eV and 9.9×10−8 gg−1 respectively.

Annealing studies on radiation damages in biotite, apatite and sphene and corrections to fission track ages

Fission track ages need to be corrected for the loss of fossil tracks due to geological and thermal annealing. The range distribution of full-length tracks can yield such corrections if calibration curves translating length reductions into density reductions are available. The study of the annealing characteristics of the three terrestrial minerals, i.e. biotite, apatite and sphene, as functions of temperature and time, has been completed from this point of view. A linear relation has been observed between etchable track length and track density, but slopes and intercepts of the curves tend to vary from mineral to mineral. Over-etching shows significant effect in retrieving partially faded tracks in the case of biotite only, and track density reduction always lags behind track length reduction. In apatite and sphene track density is reduced in the same proportion as track length when length reduction is ∼30 to 50%. For length reductions 50% the density reduction progressively outweighs the former. The possible reasons for such variations and the usefulness of the calibration curves are briefly discussed.