Fission Track Dating Generally Uses Uranium-Rich Minerals

Geol. 655 Isotope Geochemistry

Lecture 10 Spring 2009

FISSON TRACK DATING & ANALYTICAL METHODS FISSION TRACKS As we have already noted, a fraction of uranium atoms undergo spontaneous fission rather than alpha 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 Figure 10.1. Fission tracks in a polished and etched zircon. atomic scale. The energy is depos- Photo courtesy J. M. Bird. 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 mag- nifications of 50,000× or greater. However, the stressed region is more readily attacked and dissolved by acid; so the tracks can be enlarged by acid etching to the point where they are visible under the opti- cal microscope. Figure 10.1 is an example. Because fission is a rare event in any case, fission track dating generally uses uranium-rich minerals. 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:

238 λα t Fs = (λ f / λα ) U(e − 1) 10.1 238 238 where Fs is the number of tracks produced by spontaneous fission, U is the number of atoms of U, 238 λα is the α decay constant for U, and λƒ 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 TABLE 10.1. ETCHING PROCEDURES FOR FISSION TRACK DATING undergo spontaneous fission for every one that undergoes α- Mineral Etching SolutionTemperature Duration decay. Equation 10.1 can be (˚ C) solved directly for t simply by Apatite 5% HNO 25 10-30 s determining the number of 3 Epidote 37.5M NaOH 159 150 min tracks and number of U atoms Muscovite 48% HF 20 20 min per volume of sample. In this Sphene Conc. HCl 90 30-90 min case, t is the time elapsed since Volcanic Glass 24% HF 25 1 min temperatures were high enough Zircon 100M NaOH 270 1.25 h for all tracks to anneal. This is the basis of fission track dating.

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The temperatures required to anneal fission damage to a crystal are lower than Removed Sample/Detector those required to isotopically homogenize the crystal. Thus fission track dating is typically used to “date” lower temperature events than conventional geochronometers. Sample NALYTICAL ROCEDURES A P Determining fission track density in- Figure 10.2. Geometry of the fission tracks in the de- volves a relatively straightforward proce- tector method of U determination. Spontaneous fission dure of polishing and etching a thin section tracks in the sample surface could have originated from or grain mount, and then counting the either the existing sample volume, or the part of the number of tracks per unit area. A number sample removed by polishing. Tracks in the detector can only originate from the existing sample volume. of etching procedures have been developed for various substances. These are listed in Table 10.1. Track densities of up to several thousand per cm2 have been recorded. A minimum density of 10 tracks per cm2 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 10.1 becomes:

238 λα t ρs = Fsq = (λ f / λα ) U(e − 1)q 10.2 238 where ρs is the track density, q is the fraction of tracks intersecting the surface, and U is now the concentration of 238U per unit area. The second step is determination 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 238U is the isotope that fissions in nature, it is actually 236U, produced by neutron capture by 235U, that undergoes neutron-induced fission. The number of 235U fission events induced by thermal neutron irradiation is: 235 Fi = Uφσ 10.3 where φ is the thermal neutron dose (neutron flux times time) and σ is the reaction cross section (about 580 barns for thermal neutrons). The induced track density is: 235 ρi = Fqi = Uφσq 10.4 Dividing equation 10.2 by 10.4 we have:

ρ λ f 137.88 s = (eλα t − 1) 10.5 ρi λα φσ In the detector method, equation 10.5 must be modified slightly to become:

ρ λ f 137.88 s = (eλα t − 1) 10.6 ρi λα 2φσ The factor of two arises because surface-intersecting tracks produced by spontaneous fission originate both from U within the sample and from that part of the sample removed from etching. However,

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tracks in the detector can obviously only originate in the remaining sample. This is illustrated in Figure 10.2. 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 radioisotope produced by neutron capture. Nevertheless, the neutron flux can be quite variable within a small space and it remains a significant source of error. We can readily solve equation 10.6 for t: 1  ρ λ 2φσ  t = ln 1+ s a  10.7 137.88 λα  ρi λ f  and thus determine the time since the tracks last annealed. Yet another alternative method is the zeta method, which involves comparison of spontaneous and induced fission track density against a standard of known age. The principle involved is no different from that used in many methods of analytical chemistry, where comparison to a standard eliminates some of the more poorly controlled variables. In the zeta method, the dose, cross section, and spontaneous fission decay constant, and U isotope ratio are combined into a single

constant: Figure 10.3. Probability density plot of fis- φσ 235U φσ sion track ages of 30 detrital zircon grains ζ = = 10.8 238U 137.88 from the reworked El Ocote tephra from λ f ρd λ f ρd Mexico. The data show a bimodal distribu-

where ρd is the density of tracks measured in a glass tion. standard. The value of ζ is determined by analyzing standards of known age in every sample batch. ζ is determined from: eλα t − 1 ζ = 10.9 λα (ρs / ρi )ρd The age is then calculated from:

1  ζλα ρsρd  t = ln1+  10.10 λα  ρi  Standards used in the zeta method include zircon from the Fish Canyon Tuff (27.9 Ma), the Tardree rhyolite of Ireland (58.7 Ma), and South African kimberlites (82 Ma). Usually, fission track ages on a number of grains must be measured for the results to be significant. The results are often presented as histograms. Alternatively, when Figure 10.4. Spontaneous track density vs. induced the errors are also considered, the results track density for the same set of zircon grains as in Fig- may be presented as a probability density ure 10.3. On this plot, the slope of the correlation is proportional to time.

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Figure 10.5. Relationship between the percentage of tracks annealed (lines la- beled 100%, 50% and 0%), temperature, and time for apatite and sphere.

diagram, such as Figure 10.3. Yet another approach is to plot the spontaneous track density (ρs) vs the induced track density (ρi), such as Figure 10.4. From equation 10.6, we see that the slope on such a diagram is proportional to time. Thus these kinds of plots are exactly analogous to conventional isochron

diagrams. There is a difference, however. On a plot of ρs vs. ρi the intercept should be 0. 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: A = ke−EA / RT 10.11 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 conventional radiometric dating, fission track dating measures 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 laboratory 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 Figure 10.6. Apparent closure (anneal- are reached. At higher temperatures, these minerals anneal ing) temperatures of fission tracks as a very quickly in nature: no fission tracks are retained. Figure function of cooling rate for a variety of 10.5 shows the experimental relationship between the percent- minerals. age of tracks annealed, temperature, and time.

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Consider a U-bearing mineral cooling from metamorphic or igneous temperatures. At first, tracks anneal as quickly as they form. As temperature drops, tracks will be partially, but not entirely pre- served. As we discussed in the context of K-Ar dating, the apparent closure temperature is a function of cooling rate. This cooling rate dependency is summarized in Figure 10.6. 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 geochronometers, so they are particularly useful in analysis of low temperature events and in determining 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 Bo- livian Andes is 12.5 Ma. We chose 10˚C/Ma for a first order estimate of cooling rate and determine the closure temperature from Figure 10.6 to be 95˚C. Assuming an average surface temperature of 10˚C, we calculate the cooling rate to be: dT 95 − 10 = = 6.8˚C / Ma 10.12 dt 12.5 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: dz dT / dt 6.8˚C / Ma = = = 226m / Ma 10.13 dt dT / dz 0.030˚C / m 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 10.7 shows an example of the results of one such study of the Himalayas from northern India (Kashmir). A plot of ages vs. the altitude at which the samples were collected (Figure10.7) indicates an exhumation rate of 0.35 mm/a or 350 m/Ma over the last 7 million years. Interpreting Track Length As fission tracks anneal, they become shorter. Thus when a grain is subjected to elevated temperature, both the track density and the mean track length will decrease. As a result, problems of partial annealing of fission tracks can to some degree be overcome by also measuring the length of the tracks. Because (1) tracks tend to Figure 10.7. Apatite fission track ages vs. altitude for metamor- have a constant length (controlled phic rocks of the Higher Himalaya Crystalline belt of Kashmir. by the energy liberated in the fis- The correlation coefficient is 0.88. The slope indicates an uplift sion), (2) tracks become progres- rate of 350 m/Ma. From Kumar et al. (1995). sively shorter during annealing,

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and (3) each track is actually a different age and has experi- enced a different fraction of the thermal history of the sample, the length distribution records information about the thermal history of the sample. Figure 10.8 illustrates how track lengths are expected to vary for a variety of hypothetical time-temperature paths. Uni- form track lengths suggest a simple thermal history of rapid cooling and subsequent low temperatures (such as might be expected for a volcanic rock), while a broad distribution of track lengths suggests slower cooling. A skewed distribution suggests initial slow cooling and subsequent low temperatures. One problem with the approach is that both etching rates and annealing rates, and therefore track lengths, depend on crystallographic orientation. As a result, track length meas- Figure 10.8. Hypothetical time-temperature paths and the distribution of track lengths that should result from these paths. From Ravenhurst urements should be only on and Donelick (1992). tracks having the same crystallographic orientation. ANALYTICAL METHODOLOGY SAMPLE PREPARATION Isotopic analysis can be performed on minerals, rocks, and solutions. Analysis of minerals requires that they first be separated from the rocks that contain them. This begins with crushing, usually fol- lowed by some form of magnetic or density separation. The latter may involve devices such as shaking table or heavy liquids, the former usually involves a device called a “Franz”. The final step is often hand-picking under a microscope. The final step of preparation is usually to grind the sample to a powder, which greatly facilitates dissolution. Care must be excercised not contaminate the sample in this step, something even apparently “inert” grinding materials such as alumina oxide, titanium car- bide, and opal can do. In some cases, such as analysis of Pb isotope ratios in many basalts, it is better to avoid powdering and use crushed fragments (~10 mg each) instead. Water samples, of course, do not require this preparation, but they should be collected in carefully cleaned containers. In most cases, it is advisable to acidify the water sample immediately following collection to avoid absorption of particle- reactive elements, such as Pb, Hf, and the REE, on container walls.

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PREPARATIVE CHEMISTRY The techniques described below generally require that we first purify the element to be analyzed. Thus some form of preparative chemistry is usually required. The first step for solid samples is disso-

lution. For silicate rocks, this requires hydrofluoric acid (HF). Many fluorides, particularly CaF2 and MgF2 are highly insoluble, however. To insure a soluble sample once digestion is complete, a small amount of a high-boiling point acid such as perchloric acid (HClO4) is usually added to the HF. Basal- tic rocks and some minerals can be digested in Teflon beakers on hot plates, generally overnight, but rocks with more resistant minerals, such as zircons, as well as those minerals, must be digested in pres- sure vessels (“bombs”) in ovens at 200˚ C or more. Once digested, the sample is evaporated to dryness. The sample is again taken up in acid solution and the element of interest isolated by ion exchange. Pb and Sr can be isolated with a single step ion exchange process, while Hf and Nd require 2 or 3 separate ion exchange steps. With water samples, digestion is, of course skipped, and the procedure begins with ion exchange.

The separation of Os involves entirely different procedures, due to the volatility of OsO4. There are several techniques, one of which is “fire assay” in which the rock powder is mixed with a flux such as nickel sulfide, heated and fused. The platinum group metals will concentrated in the nickel sulfide, making their ultimate purification easier. As second technique is Carius tube digestion. In this tech-

nique, sample powder is heated with aqua regia (HCl and HNO3) in sealed glass tubes (Carius tubes). In both approaches, Os is ultimately purified by distillation of OsO4 from nitric acid solution. The ultimate product of these techniques is a small amount, picograms to micrograms, of a salt of the element of interest. THE MASS SPECTROMETER In most cases, isotopic abundances are measured by mass spectrometry. The exceptions are, as we have seen, short-lived radioactive isotopes, the abundances of which are determined by measuring their decay rate, and in fission track dating, where the abundance of 238U is measured, in effect, by in- ducing fission. (Another exception is spectroscopic measurement of isotope ratios in stars. Frequencies of electromagnetic emissions of the lightest elements are sufficiently dependent on nuclear mass that emissions from different isotopes can be resolved. We will discuss this when we consider stable isotopes.) A mass spectrometer is simply a device that can separate atoms or molecules according to their mass. There are a number of different kinds of mass spectrometers operating on different principles. Undoubtedly, the vast majority of mass spectrometers are used by chemists for qualitative or quantita- tive analysis of organic compounds. We will focus exclusively, however, on mass spectrometers used for isotope ratio determination. Most isotope ratio mass spectrometers are of a similar design, the magnetic-sector, or Nier mass spectrometer*, a schematic of which is shown in Figure 10.9. It consists of three essential parts: an ion source, a mass analyzer and a detector. There are, however, several variations on the design of the Nier mass spectrometer. Some of these modifications relate to the spe- cific task of the instrument; others are evolutionary improvements. We will first consider the Nier mass spectrometer, and then briefly consider a few other kinds of mass spectrometers.

* It was developed by Alfred Nier of the University of Minnesota in the 1930's. Nier used his instrument to determine the isotopic abundances of many of the elements. In the course of doing so, however, he observed variations in the ratios of isotopes of a number of stable isotopes as well as Pb isotopes and hence was partly responsible for the fields of stable and radiogenic isotope geochemistry. He also was the first to use a mass spectrometer for geochronology, providing the first radiometric age of the solar system. In the 1980's he was still designing mass spectrometers, this time miniature ones which could fly on spacecraft on interplanetary voyages. These instruments provided measurements of the isotopic composition of atmospheric gases of Venus and Mars. Nier died in 1994.

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Ion Source 60° Collector Array

Figure 10.9. The magnetic sector or Nier mass spectrometer. This instrument uses a 60° magnetic sector, but 90° magnetic sectors are also sometimes used. The Ion Source As its name implies, the job of the ion source is to provide a stream of energetic ions to the mass analyzer. Ions are most often produced by either thermal ionization, for solid-source mass spectrometers, electron bombardment, for gas-source mass spectrometers, or by inductively exciting a carrier gas into a plasma state in the case of inductively coupled plasma–mass spectrometers (ICP-MS). In thermal ionization, a solution containing the element(s) of interest is dried or electroplated onto a ribbon of high-temperature metal, generally Re (rhenium), Ta (tantalum), or W (tungsten), welded to two supports. The ribbon is typically 0.010" thick, 0.030" wide and 0.3" long. In the simplest situation, the ribbon is placed in the instrument and heated by passing an electric current of several amperes through it. At temperatures between about 1100° C and 1800° C the sample evaporates in the vacuum environment of the mass spectrometer. Depending on the element and its first ionization potential (i.e., the energy required to remove one electron from the atom), some or all the atoms will also ionize. The efficiency with which the sample ionizes determines the amount of sample needed. The alkali metals ionize quite easily; the ionization efficiency for Cs, for example, approaches 100%. For some other elements, it can be 0.1% or less. On top of this, modern mass spectrometers have transmission efficiencies of only 50%, which is to say only 50% of the ions produced reach the detector. In some cases, the rare earth elements, for example, there is a tendency for the element to evaporate as a molecule, most typically an oxide, rather than as a metal atom. This problem can be overcome by using two or three filaments. In this case, the sample is loaded on one or two filaments, from which it is evaporated at relatively low temperatures. The neutral atoms or molecules are then decomposed and ionized by another filament kept at much higher temperature (~1900-2000°C). In general, a double or triple filament technique will have a somewhat lower ionization efficiency than a single filament technique. Hence, for some difficult to ionize elements, such as Nd and Th, greater sensitivity can be achieved by analyzing the oxide ion, e.g., NdO+. This, however, requires extensive correction for inter- fering isobaric species, e.g., 142Nd18O+ on 144Nd16O+. Except where one wishes to measure very small samples, it is generally easier to analyze the metal ion. In some cases, for example U and Th, carbon is loaded along with the sample as a reducing agent so that the metal rather than the oxide will be evaporated. For some elements, molecular species are the only effective way in which an accurate isotopic analysis can be achieved. For example, Os isotopic composition is now determined by analyzing the mass – spectra of OsO 4 , because Os does not evaporate at temperatures achievable by thermal ionization. B isotope ratios are typically measured by measuring the mass spectra of sodium or cesium metaborate, because errors resulting from mass fractionation are much smaller for these heavy molecules than for the B ion. The same is true of Li. Ionization efficiency can sometimes be increased by using a suitable substrate with a high work function. The greater energy required to evaporate the atom results in a higher likelihood of its also being ionized. Tantalum oxide, for example, is a good substrate for analysis of Sr. Ionization efficiency can

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also be increased by altering the chemical form of the element of interest so that its evaporation temperature is increased (ionization is more likely at higher temperatures). For example, when a silica gel suspension is loaded along with Pb, the evaporation temperature of Pb is increased by several hundred degrees, and the ionization efficiency improved by orders of magnitude. Finally, the sample may be loaded in a particular chemical form in order to (1) form a positive rather than negative ion (or visa versa) and (2) provide a molecule of high mass to minimize mass fractionation, as for boron, or to promote or inhibit the formation of oxides. Electron bombardment is somewhat more straightforward. The gas is slowly leaked into the mass spectrometer through a small orifice. A beam of electrons, typically produced by a hot filament (nor- mally Re), is shot across the gas stream. Electron-molecule collisions will knock one of the outer elec-

trons out of its orbit, ionizing the molecule or atom. Carbon and oxygen are analyzed as CO2; other species are analyzed as single atom ions. Most solid source mass spectrometers employ a turret source in which a number of samples (typically 6 to 20) can be loaded. The turret is rotated to bring each sample into position for analysis. Gas source mass spectrometers often employ automated gas inlet systems, which allow for automated analysis of many samples. Several other methods for producing ions are used in special circumstances. The first is ion sputtering. This method is somewhat like electron bombardment, except positive ions, typically O, rather than electrons are fired at the sample and it is used for solids not gases. This is the standard method of ion production in an ion probe, which is a variety of mass spectrometer. Another method of ion production is resonance ionization. In this technique, a laser, tuned to a frequency appropriate for ionization of the element of interest, is fired at the sample. Continuous emission lasers of sufficient power are not currently available, so pulsed lasers are used. Finally, an inductively coupled plasma (ICP) is also used as an ion source and is slowly replacing thermal ionization for many applications. An ICP operates by passing a carrier gas, generally Ar, through an induction coil, which heats the gas to ~7000°K, a temperature at which the gas is completely ionized. The sample is aspirated, generally as a solution, into the plasma and is ionized by the plasma. The ions flow through an orifice into mass spectrometer. Initially, quadrupole mass spectrometers were employed for these instruments, largely because they are cheaper to manufacture and do not require as high a vacuum as a magnetic sector mass spectrometer. However, quadrupoles cannot achieve the same level of accuracy as magnetic sector instruments, and the initial generation of ICP-MS instruments were not used for the high precision isotope ratio measurements needed in geochronology and isotope geochemistry. These quadrupole ICP-MS instruments are used primarily for elemental analysis, with only some limited used for isotope ratio determination. Mag- netic sector ICP-MS instruments came on the market a decade after quadrupole ICP-MS instruments and are now at the point where they achieve accuracies competitive with thermal ionization instruments. Combined with their generally higher ionization efficiency and hence higher sensitivity, they produce results that are superior to thermal instruments for several elements. As they continue to de- velop they will likely entirely replace thermal ionization instruments. After the ions are produced, they are accelerated by an electrostatic potential, typically in the range of 5-20 kV for magnetic sector mass spectrometers (in thermal ionization mass spectrometers, the filament with the sample are at this potential). The ions move through a series of slits between charged plates. The charge on the plates also serves to collimate the ions into a beam. Generally the potential on the plates can be varied somewhat; in varying the potential on the plates, one attempts to maximize the beam intensity by 'steering' as many ions as possible through the slits. Thus the source produces a narrow beam of nearly monenergetic ions. The Mass Analyzer The function of the mass analyzer is two-fold. The main purpose is to separated the ions according to their mass (strictly speaking, according the their mass/charge ratio). But as is apparent in Figure 10.9,

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the mass analyzer of a sector mass spectrometer also acts as a lens, focusing the ion beam on the detector. A charged particle moving in a magnetic experiences a force F = qv × B 10.14 where B is the magnetic field strength, v is the particle velocity, and q is its charge (bold is used to de- note vector quantities). Note that force is applied perpendicular to the direction of motion (hence it is more properly termed a torque), and it is also perpendicular to the magnetic field vector. Since the force is always directed perpendicular to the direction of motion, the particle begins to move in a circu- lar path. The motion is thus much like swinging a ball at the end of a string, and we can use equation for a centripetal force: v2 F = m 10.15 r This can be equated with the magnetic force: v2 m = qv × B 10.16 r The velocity of the particle can be determined from its energy, which is the accelerating potential, V, times the charge: 1 Vq = mv2 10.17 2 Solving 10.17 for v2, and substituting in equation 10.16 yields (in non-vector form): V 2Vq 2 = B 10.18 r m Solving 10.18 for the mass/charge ratio: m B2r2 = 10.19 q 2V relates the mass/charge ratio, the accelerating potential, the magnetic field, and the radius of curvature of the instrument. If B is in gauss, r in cm, and V in volts, this equation becomes: m B2r2 = 4.825 × 10−5 10.19a q V with m in unified atomic mass units and q in units of electronic charge. For a given set of conditions, a heavier particle will move along a curve having a longer radius than a lighter one. In other words, the lighter isotopes experience greater deflections in the mass analyzer. The radius of the Cornell mass spectrometer is 27 cm; it typically operates at 8 kV. Masses are se- lected for analysis by varying the magnetic field (note that in principle we could also vary the accelerating potential; however doing so has a second order effect on beam intensity, which is undesirable), generally in the range of a few thousand gauss. It was shown in the 1950's that if the ions entered the magnetic field at an angle of 26.5° rather than at 90°, the effective radius of the mass analyzer doubles. This design trick, employed in all modern mass spectrometers, results in higher resolution (better separation between the masses at the collector). The Cornell instrument, for example, has an effective radius of 54 cm. An additional advantage of this ‘ex- tended geometry’ is that the ion beam is focused in the ‘z’ direction (up-down) in addition to the x-y direction. This is an important effect because it allows the entire ion beam to enter the detector, which in

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turn allows the use of multiple detectors. In addition, modern mass spectrometers have further modifications to the magnet pole faces to produce a linear focal plane, which is helpful in the multiple collec- tors currently in use. Collisions of ions with ambient gas result in velocity and energy changes and cause the beam to broaden. To minimize this, the mass spectrometer is evacuated to 10-6 to 10-9 torr (mm Hg ≈ 10-3 atm). Where very high resolution is required, an energy filter is employed. This is simply an electrostatic field. The electric field force is not proportional to velocity, as it the magnetic field. Instead, ions are deflected according to their energy. The radius of curvature is given by: 2V Electrostatic Analyzer R = 10.20 V2 X-Y lens

where V2 is the electrostatic potential of Beta Slit the energy filter and V is the energy of Alpha Slit the ions (equal to the accelerating poten- Y and Z deflectors tial). Ion sputtering produces ions of a variety of energies, hence an energy filter focus is generally required with this method of Ion Source ion production. ICP sources also produce ions that are less monoenegetic that thermal ionization or electron bombardment, so energy filters are also used with Magnetic Analyzer high precision ICP mass spectrometers. Instruments employing both mass and energy filters are sometimes called double focusing instruments. An example is shown in Figure 10.10. The Collector Defining Slits In general, ions are 'collected', or detected, at the focal plane of the mass Collector spectrometer in one of two ways. The Figure 10.10. A double focusing or Nier-Johnson mass most common method, particularly for spectrometer with both magnetic and electrostatic sec- high precision mass spectrometers, is tors. After Majer (1977). with a 'Faraday cup', which is shown schematically in Figure 10.11. As the name implies, this is a metal cup, generally a few millimeters wide and several centimeters deep (the depth is necessary to prevent ions and electrons from escaping). After passing through a narrow slit, ions strike the Faraday cup and are neutralized by electrons flow- ing to the cup from ground. The ion current into the cup is determined by measuring the voltage developed across a resistor as electrons flow to the cup to neutralize the ion current. The voltage is amplified, converted to a digital signal, and sent to a computer that controls data acquisition. (In the old days, the voltage would be sent to a chart recorder. Isotope ratios were measured by measuring the displacement of the pen trace with a ruler.) In most mass spectrometers, the resistor has a value of 1011 ohms. Since V = IΩ, an ion current of 10-11 A will produce a voltage of 1 V. Typical ion currents are on the order of 10-15 to 10-10 A. In the design of the collector, care must be exercised that ions or free electrons produced when the ion strikes the cup cannot escape from the cup. A surface coating of carbon of the cup with carbon provides a “soft landing” and aids in minimizing the generation of ions from the surface. One must also insure that stray ions or electrons cannot enter the cup. This is done by placing

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wires or plates with small negative or positive potentials in appropriate locations in front of the collector assembly, which serve to collect stray ions. Most modern mass spectrometers now employ a number of Faraday cups arrayed along the focal plane so that several isotopes can be collected simultaneously. The spacing of the Faraday cups varies from element to element. In the Cornell instrument, the positioning of cups is done using stepping motors under computer control. For accurate isotopic analysis, and “accu- Figure 10.11. Schematic drawing of a Faraday cup rate” means a few tens of ppms or better, all configured for positive ions. Electron flow would re- the ions of each isotope being measured verse for negative ions. must be completely collected. In addition, each Faraday cup is connected to its own dedicated amplifier and digital voltmeter. The gain and background characteristics of these amplifiers vary, and this must somehow be corrected for in the analysis. This is done in one of two possible ways. The first is to measure the ion current of one isotope in each of the cups in use. This allows for a normalization of the gain factors. This method will be explained in detail below. The other method is to electronically calibrate each amplifier by passing a known current through each. The resulting calibration is used by the computer to correct the observed intensities. In addition, the amplifier gains are temperature sensitive. For this reason, the amplifiers are housed in an insulated container whose temperature is controlled to within 0.01°C. The second method of detection is the use of a multiplier, either an electron multiplier or photomul- tiplier. In an electron multiplier, illustrated in Figure 10.12, the ion strikes a charged dynode. The colli- sion produces a number of free electrons, which then move down a potential gradient. Each one of the electrons strikes a second electrode, again producing a number of free electrons. This process continues through a series of 10 or so electrodes to produce a cascade or shower of electrons. The net effect is an amplification of the signal of typically 100. The Cornell instrument employs a slightly different method of signal multiplication: a Daly detector (named for its inventor), illustrated in Figure 10.13. Ions strike a charged electrode, producing electrons as in the electron multiplier. These electrons then strike a fluorescent screen producing light, which is later converted to electrical signal. The net effect is also an amplification of a factor of 100. Multipliers are used for weak signals because of their very low signal-to-noise ratio. Typically, a multiplier is useful for signals of 10-13 A or less. However, at higher beam intensities, the greater accuracy of the Faraday cup outweighs the signal-to-noise advantage of the multiplier. Multipliers may be used in either “analog” or “pulse count” mode. In analog model, the ion beam current is simply amplified and measured. In pulse count mode, rather than measuring the ion beam current, individual ions are counted. When an ion strikes the detector, an electrical “pulse” is pro-

— + Ion Beam Signal out

Electron Cascade Figure 10.12. Schematic of an electron multiplier.

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duced. In pulse count mode, these pulses are counted by specialized electronics. Pulse count mode is useful Daly Knob only at low beam intensities; at higher — ion beam intensities, an analog detector, such as the faraday cup, provides Ion Beam Secondary Electrons superior results. ACCELERATOR MASS Fluorescent Screen SPECTROMETRY Traditionally, cosmogenic nuclides have been measured by counting their Photons decays. In the past decade or two, the utility of these cosmogenic nuclides in geochemistry and geochronology has been greatly enhanced by the advent of accelerator mass spectrometers, providing both more precise results from old applications (e.g., 14C dating) and new applications (identifying subducted sediment with 10Be). Mass Photo Detector spectrometry is a much more efficient Figure 10.13. Schematic of the Daly Detector. method of detecting atoms that counting their decays in most instances. For example, the 14C/12C ratio in the atmosphere is 10-12. One gram of this carbon produces about 15 beta decays per minute. But this gram contains about 1010 atoms of 14C. Even at an efficiency of ion production and detection of only 1%, 70µg of carbon can produce an ion beam that will result in detection of 36,000 atoms 14C per hour. It would take 65 years for the same amount of carbon to produce 36,000 beta decays. However, there are some severe limitations with conventional mass spectrometry in measuring very small isotope ratios (down to 10-15). Two problems must be overcome: limitations of resolution, and isobaric interferences. Conventional mass spectrometers have resolutions of only about a ppm at ∆m of 1 u, and a fraction of a ppm at ∆m of 2 u. What this means is that for every106 or 107 12C atoms that arrived at the 12C position in the detector, about 1 12C atom will arrive at the 14C position. If the 14C/12C ratio is 10-14, some 107 more 12C would be detected at the 14C position than 14C atoms! The techniques involved in accelerator mass spectrometry vary with the element of interest, but most applications share some common features that we will briefly consider. Figure 10.14 is an illustration of the University of Rochester accelerator mass spectrometer. We will consider its application in 14C analysis as an example. A beam of C– is produced by sputtering a graphite target with Cs+ ions. There are several advantages in producing, in the initial stage, negative ions, the most important of which in this case is the instability of the negative ion of the principal atomic isobar, 14N. The ions are accelerated to 20keV (an energy somewhat higher than most conventional mass spectrometers) and separated with the first magnet, so that only ions with m/q of 14 enter the accelerator. The faraday cup FC 1 (before accelerator) is used to monitor the intensity of the 12C beam. In the accelerator, the ions are accelerated to about 8 MeV, and electrons removed (through high-energy collisions with Ar gas) to produce C4+ ions. The reason for producing multiply-charged ions is that there are no known stable molecular ions with charge greater than +2. Thus the production of multiply charged ions effectively separates 14C ions 12 from molecular isobaric ions such as CH2. The now positively charged ions are separated from residual ions through two more magnetic sectors, and an electrostatic one (which selects for ion energy E/q).

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NEGATIVE ION ANALYSIS MOLECULAR DISINTEGRATOR NEGATIVE ION SOURCE MP TANDEM ACCELERATOR F.C. 1 POSITIVE ION 30° MAGNET ANALYSIS ELECTROSTATIC 90° LENS MAGNET

F. C. 2

10° ELECTROSTATIC 45° MAGNET ANALYZER (DEFLECTS DOWN)

T of F DETECTORS F. C. PARTICLE 3 IDENTIFICATION

HEAVY ION COUNTER Figure 10.14. The accelerator mass spectrometer at the University of Rochester. F.C. 1, 2, & 3 are faraday cups, T of F detectors are time of flight detectors. After Litherland (1980). The final detector distinguishes 14C from residual 14N, 12C, and 14C by the rate at which they lose energy through interaction with a gas (range, effectively). ANALYTICAL STRATEGIES Isotopic variations in nature are very often quite small. For example, variations in Nd (neodymium) isotope ratios are measured in parts in 10,000. There are exceptions, of course. He and Os isotope ratios, as well as Ar isotope ratios, can vary by orders of magnitude, as can Pb in exceptional circumstances (minerals rich in uranium). These small variations necessitate great efforts in precise measurements (in the Cornell laboratory, for example, we can reproduce measurements of our Nd isotope standard to about 30 ppm, 2σ). In this section we will briefly discuss some of the methods employed in isotope geochemistry to reduce analytical error. We will exclude, for the moment, the problem of contamination. We will also exclude, for the most part, a discussion of instrument and electronics design, though these are obviously important. One technique used universally to reduce analytical errors is to make a large number of measurements. Thus a value for the 3He/4He ratio reported in a paper will actually be the mean of perhaps 100 individual ratios measured during a 'run' or analysis. Any short-term drift or noise in the instrument and its electronics, as well as in the ion beam intensity, will tend to average out. The use of multiple collec- tors and simultaneous measurement of several isotopes essentially eliminates errors resulting from fluctuations in ion beam intensity. This, however, introduces other errors related to the relative gains of the amplifiers. A final way to minimize errors is to measure a large signal. It can be shown that the uncertainty in measuring x number of counts is x . Thus the uncertainty in measuring 100 atoms is 10%, but the uncertainty in measuring 1,000,000 atoms is only 0.1%. These 'counting statistics' are the ultimate limit in analytical precision, but they come into play only for very small sample sizes.

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In mass spectrometry of gaseous elements such as H, O, N, S, and C (the latter does not, of course,

always occur as a gas; however, it is always converted to CO2 for analysis), the instruments are designed to switch quickly between samples and standards. In other words, a number of ratios of a sample will be measured, then the inlet valve will be switched to allow a standard gas into the machine and a number of ratios of the standard will be measured. This process can be repeated several times during an analysis. The measurement of standards thus calibrates the instrument and any drift in instrument response can be corrected. However, this is not practical for solid source instruments because switch- ing between sample and standard cannot be done quickly. It is also impractical for noble gas analysis because of the small quantities involved, and the difficulty of completely purging a standard gas from the instrument. Mass Fractionation One of the most important sources of error in solid source mass spectrometry results from the tendency of the lighter isotopes of an element to evaporate more readily than the heavier isotopes (we will discuss the reasons for this later in the course when we deal with stable isotope fractionations). This means that the ion beam will be richer in light isotopes than the sample remaining on the filament. As the analysis proceeds, the solid will become increasingly depleted in light isotopes and the ratio of a light isotope to a heavy one will continually decrease. This effect can produce variations up to a percent or so per mass unit (though it is generally much less). This would be fatal for Nd, for example, where natural isotopic variations are much less than a percent, if there were no way to correct for this effect. Fortunately, a correction can be made. The trick is to measure the ratio of two isotopes that are not radiogenic; that is a ratio that should not vary in nature. For Sr, for example, we measure the ratio of 86Sr/88Sr. By convention, we assume that the value of this ratio is equal to 0.11940. Any deviation from the value is assumed to result from mass fractionation in the mass spectrometer. The simplest assumption about mass fractionation is that it is linearly dependent on the difference in mass of the isotopes we are measuring. In other words, the fractionation between 87Sr and 86Sr should be half that between 88Sr and 86Sr. So if we know how much the 86Sr/88Sr has fractionated from the 'true' ratio, we can calculate the amount of fractionation between 87Sr and 86Sr. Formally, we can write the linear mass fractionation law as:  RN  uv − 1  RM  α(u,v) =  uv  10.21 Δmuv where α is the fractionation factor between two isotopes u and v, ∆m is the mass difference between u and v (e.g., 2 for 86 and 88), RN is the 'true' or 'normal' isotope ratio (e.g., 0.11940 for 86/88), and RM is the measured ratio. The correction to the ratio of two other isotopes (e.g., 87Sr/86Sr) is then calculated as: C M Rij = Rij (1+α(i, j)Δmij ) 10.22 where RC is the corrected ratio and RM is the measured ratio of i to j and α(u,v) α(i, j) = 10.23 € 1−α(u,v)ΔMvj 86 If we choose isotopes v and j to be the same (e.g., to both be Sr), then ∆mvj = 0 and α(i,j) = α(u,v). A convention that is unfortunate in terms of the above equations, however, is that we speak of the 86/88 ratio, when we should speak of the 88/86 ratio (= 8.37521). Using the 88/86 ratio, the 'normalization' equation for Sr becomes:€

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87 c 87 M      Sr  Sr   8.37521     =   1+  M −1 2 10.24  86 Sr  86 Sr  88 86    ( Sr / Sr)   A more accurate description of mass fractionation is the power law. The fractionation factor is:

N 1/Δmuv  Ruv  α =  M  − 1 10.25 €  Ruv 

C M Δmi, j The corrected ratio is computed as: Ri, j = Ri, j [1+ α ] 10.26

C M  1 2  or: Ri, j = Ri, j 1 + αΔmi, j + Δmi, j (Δmi, j −1)α +… 10.27  2  Since α is a small number, higher order terms may be dropped. Finally, it is claimed that the power law correction is not accurate and that the actual fractionation is described by an exponential law, from which the fractionation factor may be computed as: € N M ln[Ruv /Ruv ] and the correction is: α = 10.28 m j ln(mu /mv ) m   α j  2 2  C M mi M mi, j 2 mi, j Ri, j = Ri, j   = Ri, j 1 + αΔmi, j −α + α +… 10.29  m j   2m j 2  € The exponential law appears to provide the most accurate correction for mass fractionation. However, all of the above laws are empirical rather than theoretical. The processes of evaporation and ionization are complex, and there is yet no definitive theoretical treatment of mass fractionation during this process. € Simultaneous Correction of Mass Fractionation and Gain Bias in Multi- ple Collection We can now return to the question of correcting for the differing gains of amplifiers when more than one collector is used. I mentioned we could calibrate the gains electronically, or that we could measure one isotope in each cup and use this intensity as a calibration. A simplistic approach to the latter method would put us at the mercy of fluctuations in the ion beam intensity, whereas eliminating fluctuations in ion beam intensity is one principal advantage of multiple collection (the other advantage is speed). An alternative approach would be to measure ratios of intensities. If we could measure the intensities of two isotopes whose ratio is known, we could use these intensities to correct for gain differences. An example of a known ratio would be 86Sr/88Sr. The only difficulty is that this ratio will vary due to mass fractionation. Fortunately, there is a way to simultaneously correct for both mass fractionation and gain differences. Taking a simple case of measuring three strontium isotopes in two col- lectors, we proceed by first measuring 87Sr in cup 1 and 86Sr in cup 2. By changing the magnetic field, we then measure 88Sr in cup 1 and 87Sr in cup 2. The corrected 87Sr/86Sr ratio is then given by: 87" 87' ( 87Sr / 86Sr) = × 8.37521 10.30 true 86' 88" where ' indicates an intensity measured in cup 1, " an intensity in cup 2, and 8.37521 is the 'true' 88Sr/86Sr ratio. I will leave it as an exercise for you to demonstrate that this equation does in fact correct

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for both fractionation and gain differences. The sole disadvantage is its reliance on the linear mass fractionation law, which is the least accurate. ISOTOPE DILUTION ANALYSIS Determining precise ages generally requires that we not only determine isotope ratios precisely, but that we also determine parent-daughter ratios precisely. In essence, this means we need to determine the concentrations of the parent and daughter elements. The mass spectrometer is designed for isotope ratio analysis, but with a technique called isotope dilution, we can use it for determining concentrations of elements. It is easiest to explain the technique by taking a concrete example. We can start with the simplest possible example, that of a mono-isotopic element such as Cs. All natural Cs is 133Cs. How- ever, 135Cs is a U fission product with a half-life of 2.3 million years; on the scale of laboratory time, we can consider it to be stable. We take a known amount of rock containing an unknown amount of Cs in it and add a known amount of pure 135Cs 'spike' to it. If we separate the Cs from the rock and analyze it in the mass spectrometer, the ratio of 135Cs to 133Cs we observe will be directly proportional to the ratio of the amount of 135Cs we add to the rock to the amount of 133Cs in the rock to begin with. In other words: 135 135 133 moles Cs added Cs / Cs = 133 10.31 moles Csinrock Since we know how much 135Cs we added, we can easily calculate the moles of 133Cs in the rock. We can calculate the Cs concentration in ppm from this simply by multiplying by the atomic weight and dividing by the weight of rock we used in our analysis. This is the isotope dilution technique. The general case is slightly more complex because neither the natural element nor the ‘spike’ will be mono-isotopic. Let's take a second concrete example. Suppose we want to know the concentration of Rb is a rock. Rb has two isotopes, 85Rb and 87Rb. We make the reasonable assumption that the propor- tion of these two isotopes will not vary in nature. 85Rb constitutes 72.165% and 87Rb 27.835% of all Rb; the 87Rb/85Rb ratio is thus 0.3857. Now assume we have available a 'spike' containing 99% 87Rb and 1% 85Rb. Adding a known amount of spike to the rock, and analyzing the isotopic composition, the measured 87Rb/85Rb will be equal to:  87 Rb [ 87 Rb] + [ 87 Rb] N S 10.32  85  = 85 85  Rb [ Rb] + [ Rb] M N S 87 85 87 87 87 where ( Rb/ Rb)M is the measured ratio and [ Rb]N is the moles of 'natural' Rb in the rock, [ Rb]S is the moles of 87Rb in the spike we added, etc. 87 87 86 If our interest is geochronology and we wish to know [ Rb]N to form the Rb/ Sr ratio, we can rearrange equation 10.32 as: [ 85Rb] R 85Rb / 87 Rb − 1 87 s { M ( )S } [ Rb]N = 10.33 1− R 85Rb / 87 Rb M ( )N 87 85 85 87 85 87 where RM is ( Rb/ Rb)M and ( Rb/ Rb)N is the natural isotope ratio and ( Rb/ Rb)S is the ratio in the 87 spike. Note that [ Rb]S would more conveniently be expressed as the (molar) concentration times the weight of spike added. To find the concentration of 87Rb, we would simply divide by the weight of the sample. To form the 87Rb/86Sr ratio, we would carry out an isotope dilution analysis for Sr, and calculate the amount of 86Sr using an equation similar to 10.33. If our spike is a solution containing both Rb and Sr (which is the usual case), when we divide the equation for 87Sr by the equation from 86Sr, the terms for the weight of spike and weight of sample cancel; that is, weighing error is eliminated.

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If we are primarily interested in the concentration of an element such as Rb, rather than the 87Rb/86Sr 87 87 ratio, we can rewrite equation 10.33 in an alternative form if we let [ Rb]N = N Rb where N is the total number of atoms ( or moles) of Rb in the rock and 87Rb is now the relative abundance of 87Rb in 'natural' 87 87 Rb, i.e., 0.27835. Similarly, [ Rb]S = S Rb where S is the total number of moles of 'spike' Rb added to the sample. Equation 10.33 then becomes:  87 Rb N 87 Rb + S 87 Rb N S 10.34  85  = 85 85  Rb N Rb + S Rb M N S which we can rearrange as:  87 Rb − 85Rb R  N = S  S S M  10.35 85Rb R − 87 Rb  N M N  To convert to moles to weight in grams, we multiply the right side by the atomic weight of natural Rb. If our spike concentration is in grams, we would divide by the atomic weight of Rb in the spike:  85Rb − 87 Rb R  AW N = S  S S M  N 10.36 87 Rb R − 85Rb AW  N M N  S Once again, it is convenient to express S, the amount spike Rb added, as the concentration times the weight. And to obtain the concentration of Rb in the rock rather than the weight, we would divide by the weight of the sample:  85Rb − 87 Rb R  AW spike wt × spikeconc Rbconc = S  S S M  N 10.37 87 Rb R − 85Rb AW sample wt  N M N  S Isotope dilution has some very significant advantages over other analytical methods. We have already mentioned one: when we are interested in the ratio of two elements (or isotopes of those elements), weighing error cancel if the spike solution contains both elements. Perhaps the biggest advantage is the high accuracy with which modern mass spectrometers can measure isotope ratios: accuracies approaching 10 ppm, where as many other analytical methods have errors in percent. Another advantage is the sensitivity of the measurement: generally a few 10's of nanograms or less (depending on the ionization efficiency of the element) will suffice for an accurate ratio determination. This means we can measure very low concentrations in larger samples or moderate concentrations in very small samples with good precision. An additional advantage is that it is independent of yield. Once we obtain equilibration between sample and spike (equilibration means mixing on a scale finer than we can divide the sample), the information on the concentration of the element can be derived entirely from the isotope ratio of any aliquot of our sample. We could, for instance, loose 90% of the sample is chemical process- ing and still determine an accurate analysis. This all sounds very wonderful. Unfortunately, there are a number of disadvantages to isotope dilution as well. Foremost, perhaps, is that it is labor-intensive. It is also destructive; that is, we could not use the sample for some other analysis as we could, for example, with XRF. This is not generally a serious disadvantage, however, because very little sample is necessary for an analysis. A more serious problem is error magnification. As we can see from the above equations, the concentration we calculate is not a linear function of the isotope ratio. In particular, if the measured ratio of the sample-spike mix- ture is close to either the ratio in the spike or the ratio in the sample, errors will tend to magnify; i.e., a 87 85 0.5% error in the ( Rb/ Rb)M ratio could lead to a 5% error in Rb concentration under unfavorable circumstances. For this reason, one attempts to avoid either 'underspiking' or 'overspiking'. In addition, isotope dilution will be more sensitive to 'blank' (i.e., contamination) than methods where the measured

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parameter is linearly related to concentration. Finally, we should note that while mass spectrometers can measure ratios with accuracies approaching 10 ppm, mass fractionation will produce variations in isotope ratios which are larger than this. We can correct for this effect in spiked samples if we measure two isotope ratios (i.e., measure at least 3 isotopes), though the mathematics is slightly more complex. However, for elements have only two isotopes, such as Rb, we cannot correct for fractionation, which generally limits the precision achievable. Finally, we cannot use isotope dilution at all for mono- isotopic elements unless, as is the case for Cs, we can obtain a reasonably stable man-made isotope. REFERENCES AND SUGGESTIONS FOR FURTHER READING Dickin, A. 1995. Radiogenic Isotope Geochemistry. Cambridge: Cambridge University Press. Elmore, D. and F. M. Phillips. 1987. Accelerator mass spectrometry measurements of long-lived radioi- sotopes. Science. 236: 543-550. Kumar, A., N. Lal, A. K. Jain and R. B. Sorkhabi. 1995. Late Cenozoic-Quarternary thermo-tectonic history of Higher Himalaya Crystalline (HHC) in Kishtwar-Padar-Zanskar region, NW Himalaya: evi- dence from fission track ages. J. Geol. Soc. India. 45: 375-391. Litherland, A. E. 1980. Ultrasensitive mass spectrometry with accelerators. Ann. Rev. Nucl. Part. Sci. 30: 437-473. Majer, J. R. 1977. The mass spectrometer. London: Wykeham Publications. Ravenhurst, C. E. and R. A. Donelick.1992. Fission Track Thermochronology. in Short Course Handbook on Low Temperature Thermochronology, ed. M. Zentilli and P. H. Reynolds. 21-42. Nepean, Ontario: Mineral. Soc. Canada. Wasserburg, G. J., S. B. Jacobsen, D. J. DePaolo, M. T. McCulloch and T. Wen. 1981. Precise determination of Sm/Nd ratios, Sm and Nd isotopic abundances in standard solutions. Geochim. Cosmochim. Acta. 45: 2311-2324. Wunderlich, R. K., I. D. Hutcheon, G. J. Wasserburg and G. A. Blake. 1992. Laser-induced isotopic se- lectivity in the resonance ionization of Os. Intern. J. Mass Spec. Ion Proc. 115: 123-155. Zentilli, M. and P. H. Reynolds (ed.), 1992, Short Course Handbook on Low Temperature Thermochronology, Nepean, Ontario: Mineral. Soc. Canada.

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