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Geochronology x and fission track dating, introduction, detector, method, relationship, interpreting, fission track age
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As we have already noted, a frac- tion of uranium atoms undergo spontaneous fission rather than al- pha decay. The sum of the masses of the fragments is less than that of the parent U atom: this difference re- flects the greater binding energy of the fragments. The missing mass has been converted to kinetic energy of the fission fragments. Typically, this energy totals about 200 MeV, a con- siderable amount of energy on the atomic scale. The energy is depos- ited in the crystal lattice through which the fission fragments pass by stripping electrons from atoms in the crystal lattice. The ionized atoms repel each other, disordering the lattice and producing a small channel and a wider stressed region in the crystal. The damage is visible as tracks seen with an electron microscope operating at magnifications of 50,000¥ or greater. However, the stressed region is more readily attacked and dissolved by acid; so by acid etching the tracks can be enlarged to the point where they are visible under the optical microscope. Figure 14.1 is an example. Because fission is a rare event in any case, fission track dating generally uses uranium rich miner- als. Most work has been done on apatites, but sphene and zircon are also commonly used. Fission tracks will anneal , or self-repair, over time. The rate of annealing is vanishingly small at room temperature, but increases with temperature and becomes significant at geologically low to moderate temperatures. In the absence of such annealing, the number of tracks is a simple function of time and the uranium content of the sample:
where Fs is the number of tracks produced by spontaneous fission, 238 U is the number of atoms of (^238) U, l a is^ the^ a^ decay^ constant^ for^ (^238) U, and l ƒ is^ the^ spontaneous^ fission^ decay^ constant,^ the^ best estimate for which is 8.46 ± 0.06 ¥ 10 -17^ yr-1. Thus about 5 ¥ 10 -7^ U atoms undergo spontaneous fis- sion for every one that undergoes a-decay. Equation 14.1 can be solved directly for t simply by de- termining the number of tracks and number of U atoms per volume of sample. In this case, t is the time elapsed since temperatures were high enough for all tracks to anneal. This is the basis of fis- sion track dating. The temperatures required to anneal fission damage to a crystal are lower than those required to isotopically homogenize one. Thus fission track dating is typically used to “date” lower temperature events than conventional geochronometers.
Determining fission track density involves a relatively straightforward procedure of polishing and etching a thin section or grain mount, and then counting the number of tracks per unit area. A number of etching procedures have been developed for various substances. These are listed in Ta- ble 14.1. Track densities of up to several thousand per cm^2 have been recorded. A minimum den- sity of 10 tracks per cm^2 is required for the results to be statistically meaningful. A fission track, which is typically 10 μ long, must intersect the surface to be counted. Thus equation 14.1 becomes:
Figure 14.1. Fission tracks in a polished and etched zircon. Photo courtesy J. M. Bird.
Lecture 14 Spring 2003 where rs is the track density, q is the fraction of tracks inter- secting the surface, and 238 U is now the concentration of 238 U per unit area. The second step is determina- tion of the U concentration of the sample. This is usually done by neutron irradiation and counting of the tracks resulting from neutron-induced fission. There are variations to this procedure. In one method, spontaneous fission tracks are counted, then the sample is heated to anneal the tracks, irradiated and recounted (this is necessary because irradiation heats the sample and results in partial annealing). Alternatively, a ‘detector’, either a U- free muscovite sample or a plastic sheet, is place over the surface of the polished surface that has previously been etched and counted. The sample together with the detector is irradiated, and the tracks in the detector counted. This avoids having to heat and anneal the sample. This latter method is more commonly employed. Whereas 238 U is the isotope that fis- sions in nature, it is actually 236 U, produced by neutron capture by 235 U, that undergoes neutron-in- duced fission. The number of 235 U fission events induced by thermal neutron irradiation is:
where f is the thermal neutron dose (neutron flux times time) and s is the reaction cross section (about 580 barns for thermal neutrons). The induced track density is:
Dividing equation 14.2 by 14.4 we have:
In the detector method, equation 14.5 must be modified slightly to become:
The factor of two arises because surface-intersecting tracks produced by spontaneous fission origi- nate both from U within the sample and from that part of the sample removed from etching. How- ever, tracks in the detector can obviously only originate in the remaining sample. This is illustrated in Figure 14.2. One of the most difficult problems in this procedure is correctly measuring the neutron dose. This is usually done by including a gold or aluminum foil and counting the decays of the radioiso- tope produced by neutron capture. Nevertheless, the neutron flux can be quite variable within a small space and it remains a significant source of error.
Mineral Etching Solution Temperature Duration (˚ C) Apatite 5% HNO 3 25 10-30 s Epidote 37.5M NaOH 159 150 min Muscovite 48% HF 20 20 min Sphene Conc. HCl 90 30-90 min Volcanic Glass 24% HF 25 1 min Zircon 100M NaOH 270 1.25 h Removed Sample/Detector Sample Figure 14.2. Geometry of the fission tracks in the de- tector method of U determination. Spontaneous fis- sion tracks in the sample surface could have origi- nated from either the existing sample volume, or the part of the sample removed by polishing. Tracks in the detector can only originate from the existing sam- ple volume.
Lecture 14 Spring 2003 INTERPRETING FISSION TRACK AGES Fission tracks will anneal at elevated temperatures. As is the case for all chemical reaction rates, the annealing rate depends exponentially on temperature:
where T is thermodynamic temperature (kelvins), k is a constant, R is the gas constant (some equations use k, Boltzmann’s constant, which is proportional to R), and EA is the activation energy. Thus, as is the case for con- ventional radiometric dating, fission track dating meas- ures the time elapsed since some high temperature event. The constants k and EA will vary from mineral to mineral, so that each mineral will close at different rates. In labo- ratory experiments, apatite begins to anneal around 70˚ C and anneals entirely on geologically short times at 175˚C. Sphene, on the other hand, only begins to anneal at 275˚C and does not entirely anneal until temperatures of 420˚C are reached. At higher temperatures, these minerals an- neal very quickly in nature: no fission tracks are retained. Figure 14.5 shows the experimental relationship between the percentage of tracks annealed, temperature, and time. Consider a U-bearing mineral cooling from metamor- phic or igneous temperatures. At first, tracks anneal as quickly as they form. As temperature drops, tracks will be partially, but not entirely preserved. As we discussed in the context of K-Ar dating, the apparent closure temperature is a function of cooling rate. This cooling Figure 14.5. Relationship between the percentage of tracks annealed (lines labeled 100%, 50% and 0%), temperature, and time for apatite and sphere. Figure 14.6. Apparent closure (annealing) temperatures of fission tracks as a function of cooling rate for a variety of minerals.
Lecture 14 Spring 2003 rate dependency is summarized in Figure 14.6. Because different methods of etching attack partially annealed tracks to different degrees, etching must be done in the same way for closure temperature determination. In general, closure temperatures for fission tracks are below those of conventional isotope geo- chronometers, so they are particularly useful in analysis of low temperature events and in determin- ing cooling histories. When combined with estimates of geothermal gradients, fission track ages, particularly if ages for a variety of minerals are determined, are a useful tool in studying uplift and erosion rates. For example, the average fission track age for 3 apatites from the Huayna Potosi batholith in the Bolivian Andes is 12.5 Ma. We chose 10˚C/Ma for a first order estimate of cooling rate and deter- mine the closure temperature from Figure 14.6 to be 95˚C. Assuming an average surface tempera- ture of 10˚C, we calculate the cooling rate to be:
We could refine this value by re-estimating the closure temperature based on our result of 6.8˚C/Ma. If we assume the geothermal gradient to be 30˚C/km, we can calculate the exhumation rate to be:
Using this approach, exhumation rates have been estimated as 500 m/Ma over the past 10 Ma for the Alps and 800 m/Ma for the Himalayas. Figure 14.7 shows an example of the results of one such study of the Himalayas from northern India (Kashmir). Fission track ages of apatites from high grade metamorphic rocks of the Higher Himalaya Crystalline complex. A plot of ages vs. the alti- tude at which the samples were collected (Figure14.7) indicates an exhumation rate of 0.35 mm/a or 350 m/Ma over the last 7 million years. As fission tracks anneal, they become shorter. Thus when a grain is subjected to elevated temperature, both the track den- sity and the mean track length will decrease. As a result, prob- lems of partial annealing of fis- sion tracks can to some degree be overcome by also measuring the length of the tracks. Because (1) tracks tend to have a constant length (controlled by the energy liberated in the fission), (2) be- come progressively shorter dur- ing annealing, and (3) each track is actually a different age and has experienced a different fraction of the thermal history of the sample, the length distribution records information about the thermal history of the sample. Uniform track lengths suggest a simple thermal history of rapid cooling and subsequent low temperature (such as might be expected for a volcanic rock), while a broad distribution of track lengths suggests a reheating event. A skewed distribution suggests initial slow cooling and subsequent low Figure 14.7. Apatite fission track ages vs. altitude for metamorphic rocks of the Higher Himalaya Crystalline belt of Kashmir. The correlation coefficient is 0.88. The slope indicates an uplift rate of 350 m/Ma. From Kumar et al. (1995).