Fission Track Density Research Articles

Apatite fission-track dating by LA-Q-ICP-MS imaging

Obtaining accurate and precise apatite fission-track (AFT) ages depends on the availability of high-quality apatite grains from a sample, ideally with high spontaneous fission-track densities (c. >1.105 tracks.cm−2). However, many natural samples, such as bedrock samples from young orogenic belts or low-grade metamorphic samples with low U contents yield low spontaneous fission-track densities. Such apatites must be counted to avoid biasing the resultant FT age. AFT dating employing LA-Q-ICP-MS spot ablation works very well for grains with high spontaneous fission-track densities. This approach allows detection of potential U zoning, while also removing the need for an irradiation step and facilitating simultaneous acquisition of U-Pb and trace element data. The LA-Q-ICP-MS spot ablation thus offers several advantages compared to the External Detector Method (EDM). However, the spot ablation approach requires the counted area to mimic exactly the site and size of the laser spot, which for grains with low spontaneous fission-track densities (<105 tracks.cm−2), implies fewer track counts and impairs the precision of the resultant AFT age. Here we present an alternative approach to LA-Q-ICP-MS spot analysis of low fission-tracks density grains by generating a U distribution (238U/43Ca) map of the entire apatite surface by LA-Q-ICP-MS elemental mapping, which enables characterization of U zonation. The Monocle plugin for the Iolite LA-ICP-MS data reduction software is used to display elemental maps and extract mean 238U/43Ca values of the same area counted for the fission-tracks. A typical grain-mapping session takes <5 h to map 80 grains. The method was employed on the Durango and Fish Canyon Tuff apatite reference materials, six bedrock apatite samples with low fission-track densities (≤1.105 track.cm−2), and one bedrock apatite sample with high fission-track density (>1.106 track.cm−2) to assess the precision and accuracy of our approach. Most apatite samples investigated here were previously dated by the EDM or the LA-Q-ICP-MS ablation spot method. The AFT grain-mapping ages agree with previously published EDM or LA-Q-ICP-MS spot ablation ages at the 2σ level. For each apatite sample, we simultaneously acquired U-Pb age and trace element data (Mn, Sr, La, Ce, Sm, Eu, Gd, Lu); here again the data agree with literature constraints (when available) within uncertainties. The mapping approach is therefore a practical solution to low-temperature thermochronology studies facing apatite grains with low spontaneous fission-track densities, while also facilitating investigation of the spatial relationships between thermo- and geochronometric ages and grain chemistry.

The effect of chemical and physical imperfections in zircon grains in influencing the U-Pb age analyses: Insights from zircon fission track etching

Understanding the chemical etching effects in the crystalline structure of zircon grains is crucial to know their chemical composition, morphology and isotopic geochemistry. After chemical etching, the zircon grain can be classified as homogeneous heterogeneous, hybrid and anomalous depending on the surface fission-track density observed under an optical microscope. The complementary techniques such as optical microscopy, micro-Raman spectroscopy, scanning electron microscopy (imaging by cathodoluminescence and secondary electrons) and electron microprobe, were employed to characterize the zircon grain surfaces from Igneous, Metamorphic and Sedimentary rocks before and after chemical etching, except for Raman spectroscopy. Measurements of U-Pb age are concordant in areas on the grain surface with uniform fission-track density. The chemical and isotopic analyses show that the etching is capable of revealing the different layer imperfections of the zircon crystalline structure, which can be inherent in its crystallization or acquired during its geological history. Therefore, identification of crystallographic preserved areas on the zircon surface, which are associated with uniform fission-track density, helps to get highly concordant U-Pb ages. In general, the results showed that the U-Pb system depends significantly on the amorphization degree of the zircon crystalline structure, which in most cases can only be revealed by etching.

A new approach for electron microprobe zircon fission track thermochronology

Fission track thermochronology (FTT) has been applied for decades to quantify rates and timing of processes in the shallow crust. The most widely used approach is the external detector method (EDM). In this conventional approach, an age is obtained by counting both the fossil (238U spontaneous fission) and the induced (235U induced fission) tracks using an optical microscope. The induced tracks are obtained through the irradiation of the sample with thermal neutrons in the nuclear reactor, which causes fission of 235U. Based on the studies carried out by Gombosi et al. (2014), we present an alternative method of dating zircons using electron probe microprobe analysis (EPMA) to measure uranium concentration [U]. The electron microprobe analysis fission track (EPMA-FT) method was applied to three samples of rapidly cooled zircons: the Fish Canyon Tuff, Poços de Caldas (syenite) and Serra Geral zircons. The analyses were performed using two approaches: 1) using the age equation described in Gombosi et al. (2014) and 2) using a new age equation calibration developed for this work. The results using the Gombosi et al. (2014) age equation were 26.7±4.1Ma, 80.6±12.8Ma and 130.9±20.1Ma, respectively, and the results using the age equation from this work were 27.8±1.9Ma, 83.8±7.7Ma and 136±12Ma, respectively. The uncertainty of the age is affected mainly by 238U concentration and ρS (the spontaneous fission track density) determinations. Other factors can affect the uncertainty of the age, but their contributions are smaller. For all samples, the yield ages found by the two methods are consistent and overlap within two standard deviations of published reference ages determined from other radiometric techniques (i.e., K/Ar, 40Ar/39Ar, and/or U/Pb) and traditional FTT by the EDM.

Distinction between the Youngest Toba Tuff and Oldest Toba Tuff from northern Sumatra based on the area density of spontaneous fission tracks in their glass shards

Determination of the area density of spontaneous fission tracks (ρs) in glass shards of Toba tephra is a reliable way to distinguish between the Youngest Toba Tuff (YTT) and the Oldest Toba Tuff (OTT). The ρs values for YTT, uncorrected for partial track fading, range from 70 to 181tracks/cm2 with a weighted mean of 108±5tracks/cm2, based on 15 samples. Corrected ρs values for YTT are in the range of 77–140tracks/cm2 with a weighted mean of 113±8tracks/cm2, within the range of uncorrected ρs values. No significant difference in ρs exists between YTT samples collected from marine and continental depositional settings. The uncorrected ρs for OTT is 1567±114tracks/cm2 so that confusion with YTT is unlikely.The ρs values of the Toba tephra at Bori, Morgaon, and Gandhigram in northwestern India indicate a YTT identity, in agreement with geochemical data on their glass shards, the presence of multiple glass populations, and a glass fission-track age determination. Therefore, the view of others that OTT is present at these sites – and thereby indicates an early Pleistocene age for the associated Acheulean artifacts – is incorrect.

Raman spectroscopy and scanning electron microscopy characterizations of fission track method datable zircon grains.

Spectroscopic and morphological studies, designed to improve our understanding of the physicochemical phenomena that occur during zircon crystallization, are presented. The zircon fission track method (ZFTM) is used routinely in various laboratories around the world; however, there are some methodological difficulties needing attention. Depending on the surface fission track density observed under an optical microscope, the zircon grain surfaces are classified as homogeneous, heterogeneous, hybrid, or anomalous. In this study, zircon grain surfaces are characterized using complementary techniques such as optical microscopy (OM), micro-Raman spectroscopy, and scanning electron microscopy (SEM), both before and after chemical etching. Our results suggest that anomalous grains have subfamilies and that etching anisotropy related to heterogeneous grains is due to different crystallographic faces within the same polished surface that cannot be observed under an optical microscope. The improved methodology was used to determine the zircon fission track ages of samples collected from the Bauru Group located in the north of Paraná Basin, Brazil. A total of 514 zircon grains were analyzed, consisting of 10% homogeneous, about 10% heterogeneous, about 20% hybrid, and 60% anomalous grains. These results show that the age distributions obtained for homogeneous, heterogeneous, and hybrid grains are both statistically and geologically compatible.

Shielding experiments for optimization of shield materials in fast reactor using SSNTDs

Neutron transport through single shield materials for fast reactor was experimentally studied using solid state nuclear track detectors (SSNTDs) and activation techniques. The single shield materials studied were stainless steel (SS-316), sodium and borated graphite. Neptunium and thorium foil in contact with Lexan track detectors were used to study neutron attenuation in the intermediate neutron energy region. Further, activation detectors using indium foil were also used to study the attenuation in the similar neutron energy region. It is shown in the present paper that SSNTDs can be used as a complimentary to activation detectors used to study deep penetration shielding experiments, where measurements were carried out to study neutron attenuation of the order of 10−4. The fission reaction rates of 237Np having effective threshold energy of 0.6 MeV and 232Th having threshold energy of 1.4 MeV were studied by counting the neutron induced fission track density on Lexan polycarbonate. The reaction rate from 115In(n,n′)In115m foils having effective threshold energy of 1.3 MeV was studied by activation techniques.

Neutron Induced Fission Track Estimation of Uranium Concentration and Its Associated Health Hazards in Drinking Water of the Faisalabad Industrial City

Drinking water plays a major role regarding quality of human life because polluted water is the main cause of many types of diseases. Besides other pollutants, high concentration of uranium above a certain level in drinking water is also hazardous. As water and food are the main sources of uranium intake, it is absolutely imperative that their level of concentrations is monitored regularly for safety of the general public. In this regard, trace amount of uranium in drinking water samples collected from different locations of Faisalabadcity has been carried out using Neutron Induced Fission Track Technique. The water samples along with the standard of known uranium concentration were poured and dried over Lexan track detectors and then irradiated with thermal neutrons in Reactor. After etching, the tracks produced in the detectors as a result of 235U (n, f) reaction were counted under an optical microscope. The uranium concentration was determined by counting and comparing the observed fission track density in the samples and the standard. The observed uranium concentration in the studied water samples varied from (1.04 ± 0.30) μg·L-1 to (21.08 ± 2. 95) μg·L-1 with an average value of (7.39 ± 1.30) μg·L-1 and is found to be within safe limits as far as uranium related health hazards are concerned.

Advantages and challenges of automated apatite fission track counting

Fission track thermochronometry data are often a core element of modern tectonic and denudation studies. Soon after the development of the fission track method, interest emerged for the development of automated counting procedures to replace the time consuming labor of counting fission tracks under the microscope. Automated track counting became feasible in recent years with increasing improvements in computer software and hardware, and the development of microscopes and stage systems. One such example examined in this study is the commercial automated fission track counting procedure from Autoscan Systems Pty. and the University of Melbourne thermochronology group. We conducted experiments that are designed to reliably and consistently test the ability of this fully automated counting system to recognize fission tracks in apatite and a muscovite external detector. Fission tracks were analyzed in a series of samples with a step-wise increase in sample complexity. In addition to the automated counting procedure, the same samples were also analyzed using conventional counting procedures. We found for all samples that the fully automated fission track counting procedure using the Autoscan System yields a larger scatter in the measured fission-track densities compared to conventional (manual) track counting. This scatter typically resulted from the false identification of tracks, regardless of the image filtering procedure used or sample coating. Large differences between track densities analyzed with the automated counting persisted between different grains analyzed in one sample as well as between different samples. As a result of these differences a manual correction of the fully automated fission track counts is necessary for each individual surface area and grain counted. This manual correction procedure significantly increases the time required to analyze a sample with the automated counting procedure compared to the conventional approach.

Observations of fission-tracks in zircons by atomic force microscope

Abstract The fission-track (FT) method is a dating technique based on the observation of damage (tracks) by spontaneous fission of 238 U left in a mineral. The date is calculated from the track density and the uranium concentration in the mineral. This is possible because the number of tracks is a function of uranium concentration and time since the start of track accumulation. Usually, the number of tracks is counted under an optical microscope after etching (chemical expansion of a track). However, as FT density per unit area rises, it becomes difficult to count the number of tracks. This is due to the fact that FTs overlap one another and are unable to be readily distinguished. This research examines the potential of atomic force microscope (AFM) for FT dating using zircons, which are likely to show higher FT density than other minerals due to their high U concentrations. To obtain an AFM image for a sample prepared for FT dating, removing the static electricity of the sample is essential to avoid an unexpected movement of the cantilever. A grain should be wider than about 30 μm to bring the cantilever on the mineral surface. Polishing with a fine grained compound is very important. There is not much difference in sharpness between images by AC mode (scanning with vibrating cantilever at a constant cycle) and Contact mode (scanning with the cantilever always in close contact with the surface). To confirm how tracks can be identified with the AFM, an AFM image was compared with an image obtained with the optical microscope. When change in the number of tracks and their shapes were observed through stepwise etching, the track expanded as the etching time increased. In addition, the etching rate was slower for large tracks than those for small tracks. This implied that the AFM can be used to observe etching of zircons with different degrees of nuclear fission damage. A track that could not be seen with the optical microscope due to insufficient etching could be observed by AFM methods, indicating the possibility of FT dating with high track densities using AFM after relatively short etching periods.

Effects of Etching on Zircon Grains and its Implications for the Fission Track Method

Studies of zircon grains using optical microscopy, micro-Raman spectroscopy, and scanning electron microscopy (SEM) have been carried out to characterize the surface of natural zircon as a function of etching time. According to the surface characteristics observed using an optical microscope after etching, the zircon grains were classified as: (i) homogeneous; (ii) anomalous, and (iii) hybrid. Micro-Raman results showed that, as etching time increases, the crystal lattice is slightly altered for homogeneous grains, it is completely damaged for anomalous grains, and it is altered in some areas for hybrid grains. The SEM (energy dispersive X-ray spectroscopy, EDS) results indicated that, independent of the grain types, where the crystallinity remains after etching, the chemical composition of zircon is approximately 33% SiO(2):65% ZrO(2) (standard natural zircon), and for areas where the grain does not have a crystalline structure, there are variations of ZrO(2) and, mainly, SiO(2). In addition, it is possible to observe a uniform surface density of fission tracks in grain areas where the determined crystal lattice and chemical composition are those of zircon. Regarding hybrid grains, we discuss whether the areas slightly altered by the chemical etching can be analyzed by the fission track method (FTM) or not. Results of zircon fission track and U-Pb dating show that hybrid and homogeneous grains can be used for dating, and not only homogeneous grains. More than 50 sedimentary samples from the Bauru Basin (southeast Brazil) were analyzed and show that only a small amount of grains are homogeneous (10%), questioning the validity of the rest of the grains for thermo-chronological evolution studies using zircon FTM dating.

A new approach to crystallographic orientation measurement for apatite fission track analysis: Effects of crystal morphology and implications for automation

Apatite fission track analysis and in particular, computer-assisted fission track recognition require the determination of crystallographic orientation, crystal morphology, cracks, fractures and inclusions. The selection of a crystal for fission track analysis has largely been based on its surface and track etching characteristics that, in conventional fission track dating, is performed by the analyst. This requires manual scanning of the entire mount for suitable grains, which is a very time-intensive process during manual fission track counting. Therefore, a computer-assisted grain characterisation system is of interest to allow for an automated pre-selection of suitable crystals. With the use of a fully automated Fabric Analyser, c-axis orientations can be measured inside an apatite crystal for each pixel with a spatial resolution of 5 μm. The results are represented in geometric quality and retardation maps consisting of the c-axis orientations for each pixel and two quality values evaluating each orientation. These maps allow the determination of the crystallography of the apatite grain as well as its outline. In addition, most of the crystal morphologies, fractures and impurities, which can influence automated fission track recognition techniques based on image analysis, are determinable using the quality maps. On the other hand, the method is not sensitive to smaller crystal cracks, high fission track densities or coating. The quantification of the crystal geometric properties by this method is a step forward to develop a fully automated fission track analysis process.

Apatite (U–Th)/He thermochronometry using a radiation damage accumulation and annealing model

Helium diffusion from apatite is a sensitive function of the volume fraction of radiation damage to the crystal, a quantity that varies over the lifetime of the apatite. Using recently published laboratory data we develop and investigate a new kinetic model, the radiation damage accumulation and annealing model (RDAAM), that adopts the effective fission-track density as a proxy for accumulated radiation damage. This proxy incorporates creation of crystal damage proportional to α-production from U and Th decay, and the elimination of that damage governed by the kinetics of fission-track annealing. The RDAAM is a version of the helium trapping model (HeTM; 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, 148–161), calibrated by helium diffusion data in natural and partially annealed apatites. The chief limitation of the HeTM, now addressed by RDAAM, is its use of He concentration as the radiation damage proxy for circumstances in which radiation damage and He are not accumulated and lost proportionately from the crystal. By incorporating the RDAAM into the HeFTy computer program, we explore its implications for apatite (U–Th)/He thermochronometry. We show how (U–Th)/He dates predicted from the model are sensitive to both effective U concentration (eU) and details of the temperature history. The RDAAM predicts an effective He closure temperature of 62 °C for a 28 ppm eU apatite of 60 μm radius that experienced a 10 °C/Ma monotonic cooling rate; this is 8 °C lower than the 70 °C effective closure temperature predicted using commonly assumed Durango diffusion kinetics. Use of the RDAAM is most important for accurate interpretation of (U–Th)/He data for apatite suites that experienced moderate to slow monotonic cooling (1–0.1 °C/Ma), prolonged residence in the helium partial retention zone, or a duration at temperatures appropriate for radiation damage accumulation followed by reheating and partial helium loss. Under common circumstances the RDAAM predicts (U–Th)/He dates that are older, sometimes much older, than corresponding fission-track dates. Nonlinear positive correlations between apatite (U–Th)/He date and eU in apatites subjected to the same temperature history are a diagnostic signature of the RDAAM for many but not all thermal histories. Observed date-eU correlations in four different localities can be explained with the RDAAM using geologically reasonable thermal histories consistent with independent fission-track datasets. The existence of date-eU correlations not only supports a radiation damage based kinetic model, but can significantly limit the range of acceptable time-temperature paths that account for the data. In contrast, these datasets are inexplicable using the Durango diffusion model. The RDAAM helps reconcile enigmatic data in which apatite (U–Th)/He dates are older than expected using the Durango model when compared with thermal histories based on apatite fission-track data or other geological constraints. It also has the potential to explain at least some cases in which (U–Th)/He dates are actually older than the corresponding fission-track dates.

Micro‐Raman spectroscopy and SEM/EDX applied to improve the zircon fission track method used for dating geological formations

AbstractThe zircon mineral is widely studied in geochronology. In the case of the fission track method (FTM), the age is determined by the density of fission tracks at the zircon surface, which can be observed with an optical microscope after an appropriate chemical treatment (etching). The etching must be isotropic at the zircon grain surface to be used in the FTM, which leads those zircon grains whose etching is anisotropic to be discarded. The only reason for this discarding is the nonuniform morphology of the surface grain seen by optical microscopy, that is, no further physicochemical analysis is performed. In this work, combining micro‐Raman and scanning electron microscopy (SEM) to study the etching anisotropy, it was shown that zircon grains that present at least one area at the surface where the density of fission track is uniform can be used in the FTM. The micro‐Raman showed characteristic spectra of the standard zircon sample either from the areas where there are tracks or from where there are not. The only difference found was in the Raman bandwidths, which were broader for the areas with higher density of fission tracks. This suggests simply a decrease in the relative percentage of the crystalline/amorphous phases at these areas. The SEM/energy dispersive spectrometry (EDX) showed that there were no significant differences in the principal chemical composition at the areas with and without fission tracks. Copyright © 2008 John Wiley &amp; Sons, Ltd.

Estimation of trace levels of plutonium in urine samples by fission track technique

Individual monitoring of radiation workers handling Pu in various nuclear installations requires the detection of trace levels of plutonium in bioassay samples. It is necessary to develop methods that can detect urinary excretion of Pu in fraction of mBq range. Therefore, a sensitive method such as fission track analysis has been developed for the measurement of trace levels of Pu in bioassay samples. In this technique, chemically separated plutonium from the sample and a Pu standard were electrodeposited on planchettes and covered with Lexan solid state nuclear track detector (SSNTD) and irradiated with thermal neutrons in APSARA reactor of Bhabha Atomic Research Centre, India. The fission track densities in the Lexan films of the sample and the standard were used to calculate the amount of Pu in the sample. The minimum amount of Pu that can be analyzed by this method using doubly distilled electronic grade (E. G.) reagents is about 12 μBq/L.

Determination of uranium fission rate in an arbitrary neutron field using fission track detectors

In accelerator driven systems, particularly near the spallation target, the neutron spectrum covers a very wide range of energies and has a complex angular distribution. It is possible to determine the fission rate of fissionable nuclei in such neutron fields using fission track technique. We use the mean density of fission tracks in the two track detectors in contact with two faces of a fission foil (radiator). A calibration factor, w , relating the number of fission events to the track density is needed and was determined in a very well-known neutron field. It was used to estimate the fission rate in a uranium–lead assembly when the lead target was irradiated with protons of energy 1 GeV. Experimental results are compared with Monte Carlo predictions using MCNPX code.

Measurements of fossil confined fission tracks in ion-irradiated apatite samples with low track densities

This investigation looks into the potential and consequences of combined ion-irradiation and sequential etching as means for increasing the number of measurable horizontal confined tracks in geological apatite samples with low fission-track densities. The gain is substantial but varies between samples depending on the size and aspect of the grains and the fraction of prismatic sections. The average maximum gain (ρion≈2×06cm−2; lion≈30μm; θion=15°; 35s etching in 4M HNO3 at 25°C) is ∼200 times. Greater gains are achieved in some cases but there are indications of saturation. For maximum effect, the beam parameters should be tailored to the properties of the sample. The effectiveness of sequential etching is much greater than expected from the ratio of the etching times or of the track cross-sections at successive etching times. The number of confined tracks increases ∼3.5 times between te=15s and 25s and a further ∼2 times between te=25s and 35s. The total increase due to etching (∼7 times) is still much lower than that from ion-irradiation alone, estimated at ∼30 times. Ion-irradiation has no significant effect on the etchable lengths of individual confined tracks and no pronounced effect on their angular distribution. Sequential etching has no apparent effect on their angular distribution; its effects on the lengths of individual tracks, mean confined-track length, length distribution and anisotropy are less clear. Overall, our results document a quasi-isotropic increase of the mean confined-track length between te=15s and 25s and an according quasi-uniform shift of the track-length distribution towards longer lengths but no significant further increase nor shift between te=25s and 35s. This trend varies between samples because the relationship between the mean track length and that of individual confined tracks is affected by complex sampling issues that require detailed investigation.

Calibration of track detectors for fission rate determination: An experimental and theoretical study

The calibration factor w, for the determination of fission rate in fissionable materials using the track detectors (mica, Lavsan and soda glass) was studied experimentally and by the Monte Carlo method. The calibration factor relates the fission track density to the number of fission-inducing particles. It is shown that a w obtained via low-energy particle-induced fission, can be used for the determination of fission rate in a particle (neutron) field with an unknown energy spectrum and angular distribution, if in the determination of w and in its subsequent use, the mean density of the tracks in the track detectors on either side of the fission foil is used.

Parts Per Billion Doping and Characterization of Uranium Distribution in an Epoxy Polymer Matrix

Formulating an epoxy polymer provides a broadly applicable method for homogeneously doping a chemically stable, particulate-resistant, and radiation-hardened matrix with virtually any trace elements of interest. In the example reported, control of uranium levels over the range, 15 microg/g-15 ng/g, is demonstrated. Fission track density determinations, referenced to NIST SRMs, indicate +/-5% variations in lateral uranium distributions. Determinations of levels of uranium impurities in commercially available high-purity samples of graphite, fused silica, and aluminum show respective nanogram per gram ranges of 3 +/- 0.1-5 +/- 0.3, 3 +/- 0.8-27 +/- 2, and 113 +/- 11-546 +/- 11. The prepared polymer materials cover 3 orders of magnitude of uranium levels in an ideal matrix. This accomplishes the prerequisite for subsequent investigations of the chemistry occurring at fission fragment-induced damage sites of selected track registering materials as a function of controlled reactive site densities. The matrix also serves as a source of swift heavy ions for creating nanoscale features in dielectric materials.

Detection efficiency of fission tracks in apatite related to mica external detectors by the spike irradiation technique

Detection efficiency of fission tracks in non-annealed and annealed Durango apatite crystals related to mica external detectors for fission track dating was estimated experimentally using the spike irradiation technique [Suzuki, 2002a. Abstracts of 21st International Conference on Nuclear Tracks in Solids, p. 22]. The relation of the fission track density between apatite samples and mica external detectors is an important parameter for the determination of fission track ages using an absolute approach especially for crystalline minerals. Spike irradiation of uranium-235-induced fission fragments was carried out using a high uranium content glass, GE1497, fixed firmly on the sample surface. Experimental works were carried out for sections parallel and perpendicular to the crystallographic c -axis of apatite. The detection efficiency of fission tracks in non-annealed apatite related to the mica external detectors was estimated to be 0.90 for the prism face and 0.99 for the basal face. The fission track age of Durango apatite averaged for the prism and basal faces was estimated to be 30.6 ( ± 2.5 ) Ma, which is concordant with reference values reported previously, using the detection efficiency data with a B 0 value of the CN5 monitor glass and a U-238 spontaneous decay constant value of 8.46 × 10 - 17 a - 1 . The results also indicate that the B 0 age calibration method can be used effectively for the absolute evaluation of fission track ages of apatite.

Kinetic model for the relationship between mean diameter shortening and age reduction in glass samples

Fission tracks in glass samples are shortened when they experience thermal treatment. Consequently, the observable dimensions associated with track length also diminish. The dimension normally used to characterize track size is the mean diameter of the etched track at the surface, D. Another consequence of length shortening is the reduction of surface density, ρ , implying a reduction of the fission-track age. In this work, a kinetic model is developed to describe the relationship between fission-track mean diameter shortening and surface fission-track density reduction in glass samples, based on geometrical and etching hypotheses. The result is a two-parameter equation given by (1) ρ ρ 0 = D D 0 2 ( 1 + 1 / n ) 4 h 2 + D 0 2 4 h 2 + D 0 2 ( D / D 0 ) 2 2 4 h 2 - D 0 2 4 h 2 - D 0 2 ( D / D 0 ) 2 1 / n in which h is the thickness of the layer removed during etching and n is a parameter related to the latent track geometry and etching reaction rate. The equation was compared with experimental data on Australite glass found in the literature and with fresh data on Macusanite glass presented in this work. The model fits the experimental curves quite well, showing that it describes the etching effects correctly (within its limitations). In addition, the model equation derived in this work can be very useful in age correction of partially annealed glass samples.