1. Geochronology III: Other Dating Methods
Chapter 4

2. Cosmogenic Nuclides Table 4.1. Data on Cosmogenic Nuclides
Nuclide Half-life, yrs λ, yr-1
14C x 10-3
3H x 10-2
10Be 1.50 × x 10-7
26Al × x 10-5
36Cl × x 10-6
32Si x 10-2

3. Cosmic Rays
Cosmic rays are high-energy (several GeV up to 1019 eV) atomic nuclei, mainly H &, but nuclei of all the elements have been recognized.
CERN’s Large Hadron Collider, mankind’s most powerful accelerator, produces energies of ~1013 eV (10 GeV)
A significant fraction of cosmic rays originates in he Sun, although these are mainly of energies too low to generate cosmogenic nuclides. The origin of the remainder is unclear; most likely originate in supernovae or similar high-energy environments in the cosmos.
The primary reaction that occurs when cosmic rays encounter the Earth is spallation, in which a nucleus struck by a high energy particle shatters into two or more pieces, including stable and unstable nuclei, as well as protons and neutrons. Short-lived particles such as muons, pions, etc. are also created. The interaction of a cosmic ray with a nucleus sets of a chain reaction of sorts as the secondary particles and nuclear fragments, which themselves have very high energies, then strike other nuclei producing additional reactions of lower energy.

4. 14C
Carbon-14 is by far the most familiar and useful of the cosmogenic dating schemes. Its usefulness results from its relatively short half-life, a relatively high production rate, and the concentration of carbon in biological material.
14C produced primarily by reactions with secondary particles, mainly by the 14N(n,p)14C reaction involving relatively slow neutrons. The high abundance of the target nuclide is part of the reason for the high production rate.

5. Analytical Techniques
The traditional method of 14C determination is counting of the β-rays produced in its decay.
Gas proportional counter. Carbon converted to CO2 and placed in a metal tube with a negatively charged wire (the anode) running through it. The emitted beta strips electrons from atoms which drift to the wire (the anode), producing a measurable pulse of current.
In liquid scintillation counting, the carbon is converted into CO2 and then to benzene (C6H6) and mixed with a liquid scintillator (an organic liquid). β particle causes the scintillator to give off a photon, which is then detected with a photomultiplier, and the resulting electrical pulse sent to a counter. This technique is more sensitive and has largely replaced gas counters. Requires ~1g carbon.
Accelerator Mass Spectrometry. The low abundance of 14C compared to stable C isotopes (14C/12C ~ 10–12) requires very high resolution to avoid interference with those isotopes as well as others such as 14N. That requires the ions be accelerated to high energies (MeV rather than keV of conventional mass spectrometers). In the last few decades, dedicated instruments have been built for this purpose. Requires only a few milligrams C.

6. 14C Dating
Reported in units of Beq/g C (counts per minute), known as specific activity.
Equation of interest is:
where N0 is the atmospheric value of has Beq/g.
By historical convention, radiocarbon ages are reported in years before 1950 (the year the first 14C age determination; the abbreviation BP thus means not before present, but before 1950) and assuming a half-life of 5568 years (instead of the currently accepted value of 5730 years).
Partly, this is a consequence of atmospheric nuclear weapons tests in the ‘50’s, which contaminated the atmosphere with 14C.

7. Cosmic Ray Flux
Cosmogenic nuclide production affected by geomagnetic field, which deflects cosmic rays.
Cosmogenic nuclide production increases toward the poles (due to magnetic field influence on cosmic rays), but atmosphere is well mixed for CO2.
Does affect other nuclides.
Field and production rate has varied with time.
The solar wind modulates the solar magnetosphere, which deflects galactic cosmic rays at the outer edge of the solar system (the heliopause). Varies with the sunspot cycle and perhaps on longer time scales: so-called deVries Effects.

8. Reservoir Effects
Specific activity also varies because the denominator varies, .i.e., atmospheric carbon levels.
Fossil fuel burning has increased atmospheric carbon by 30% since Industrial Revolution (this carbon is 14C-free)
Shifts of CO2 between ocean and atmosphere changes atmospheric CO2 by 60% (oceanic CO2 is ‘older’ and 14C depleted).

9. Converting Radiocarbon Years to Calendar Years
As a consequence of these effect, the 14C time scale requires calibration.
Initially based on ‘dendrochronology’ – tree rings.
Further back in time, 14C has been calibrated against Th-U ages of corals.
Because the effects are non-linear, the conversion results in a probability distribution of calendar years.
Programs available such as Univ. of Belfast ( ) or Columbia U. ( LDEO.columbia.edu/ )

10. 14C Calibration based on Th-U Dating of Corals.
Calibration based on corals from Barbados Barbados, Kiritimati Atoll in the central equatorial Pacific, and from Araki Island in the southwest Pacific (Faribanks et al., 2005).

11. 10Be, 26Al, 36Cl
These nuclides have much longer half-lives than 14C and thus are be applied to longer time-scale problems, such as Pleistocene chronology and dating of groundwater.
10Be is created by spallation reactions between cosmic rays and N and O nuclei.
26Al is produced by spallation of 40Ar
36Cl is produced by 40Ar(p,α)36Cl reactions (probably mainly with secondary protons).
Production Rates
10Be 10-2 – 10-3 atoms/cm2/sec
26Al and 36Cl 10-5–10-6 atoms/cm2/sec
Unlike 14C, all are quickly washed out of the atmosphere. There are latitudinal variations in production and abundance.
Abundance of 10Be in marine sedimentation is, however, uniform due to mixing in oceans.

12. 10Be Dating
10Be mainly used for dating sediments (some tectonic/high-T application as well - later).
Begin with the equation:
assuming a constant flux, ƒ, to the sediment:
where brackets denote concentration
Sedimentation rate, s, however, may vary, so:
sedimentation rate is related to time and depth as z = s ×t

13. 10Be Dating
Taking the log of the previous equation,
log of 10Be is a linear function of z if sedimentation rate is constant (and no compaction).
If sedimentation rate is not constant:
Better to think of 10Be as a function of depth, not time (which we do not know):
Sedimentation rate is
10Be data in a sediment core from the western tropical Pacific.

14. 10Be Dating substituting for s and integrating: Solving for t(z):
The integral term is simply the sum of all 10Be above depth z.
(Some similarity to constant flux model of 210Pb)
This assumes a constant production rate (it is not constant). If we know the production rate, we can substitute ƒ(t) for ƒ in the above equation.

15. 36Cl Dating in Hydrology
14C can be used for groundwater dating, but C is not conservative (respiration, dissolution, precipitation of carbonate).
36Cl by contrast is nearly conservative in groundwater.
Stable isotopes of Cl are 35Cl and 37Cl.
36Cl produced by cosmogenic reactions on Ar in the atmosphere, hence there is a latitudinal dependence. Quickly washed out by rain, unlike C.
Activity usually ratioed to total Cl.

16. Nucleogenic Production
Complicating matters, there is some production of 36Cl in the Earth by 35Cl capture of fission-derived neutrons.
This nucleogenic 36Cl will build up over time:
where Φn is the neutron flux, ƒ is the capture cross section and [35Cl] is the concentration of 35Cl.
So how will 36Cl vary with time according to this equation?

17. 36Cl Dating “Age” of groundwater can be determined from
But groundwater in a given location could have multiple sources of multiple ages.
So we need to know the initial ratio and secular equilibrium ratios as well.
Evaporation, mixing with formation brines, dissolution of salt, etc. can all complicate age.

18. Great Artesian Aquifer of Australia

19. Great Artesian Aquifer of Australia

20. 4He dating of groundwater
4He produced by α-decay in rock
Assuming water flows by piston-flow, accumulation of 4He will be:
where Rα is the production rate, and ϕ is porosity.
Complication: high diffusivity of He

21. 4He in Great Artesian Aquifer
4He appears to be diffusing into the aquifer from below

22. In Situ Produced Cosmogenic Nuclides
Cosmic-ray spallation produces both stable and unstable nuclides.
Of the stable ones, only those that are very rare are of interest

23. In Situ Production
Some cosmic rays manage to penetrate to the Earth’s the surface. Flux then decreases exponentially as:
where z is depth, ρ is density and l is a constant that depends on the nature of the particles, their energy, and nature (composition) of materials.
l is ~160g/cm2, most rock has ρ~2.5g/cc, so flux would decrease to 1/e or 0.36 at a depth of 64 cm.
Muons penetrate more effectively (l~1000 g/cm2, but interact weakly with matter).

24. 3He dating of surfaces and erosion rates
Production of a stable nuclide at the surface will be
N = Pt
(Abundance increases linearly with time, assuming constant production rate). 3He accumulation has been used to date lava flow surfaces.
P is a function of both latitude and altitude.
The concentration as a function of time and depth will be
Of course if depth is constant, this integrates simply to:
Now suppose that depth varies as a result of erosion occurring at rate ε. Depth is then a function of time:

25. 3He dating of surfaces and erosion rates
Substituting for z:
Now substituting z0 = z + εt, at the surface (z=0) this reduces to
Neither can be solved directly. However, if the age of the rock, t, is known from some other method, one can measure a series of values, C, as function of depth and make a series of guesses of the erosion rate until a curve based on 4.28 fits the data.
Using this procedure, Kurz estimated an erosion rate of 10 m/Ma for Haleakala (for higher erosion rates, it would be necessary to take account of the muon-produced 3He).

26. Erosion Ages from Unstable Cosmogenic Nuclides
For a nuclide such as 26Al or 36Cl, need to take account of its decay. The concentration as a function of time and depth will be:
After many half-lives the concentration at the surface of eroding rock will be:
While the concentration is steady-state, it does depend on the erosion rate, which we can easily solve for.

27. Exposure Ages with Cosmogenic Nuclides
Concentration of unstable cosmogenic nuclide at the surface will change with time as:
Integrating
What happens eventually?

28. 36Cl Dating of Moraine Boulders in the Sierra Nevada

29. Comparison with Marine O isotope chronology

30. Fission-Track Dating

31. Fission Track Dating
A small fraction of 238U decay through fission rather than α-decay.
λƒ = 8.46 x yr-1.
Fission produces two unequal nuclear fragments (plus some neutrons). Some of the decay energy converted to kinetic energy of the fragments, which then fly through the crystal lattice, damaging it.
The lattice damage can be enhanced by acid leaching so it is visible under the microscope.
Number fission tracks is a function of time:
where λƒ/λα = 5 x 10–7. Note that λƒ+λα ≈ λα
Tracks anneal at a temperature-dependent rate, with “closure T” being fairly low, depending on mineral.

32. Analytical
Tracks must intersect surface to be counted so the track density, so density will be:
U concentration is typically determined by irradiating the sample with neutrons and inducing fission of 235U; number of induced tracks is
where ϕ is thermal neutron dose and σ is reaction cross section.

33. Zeta Method
In practice, sample is etched, tracks counted, then a “detector” placed on sample and package is irradiated. Induced tracks counted in detector. Age is related to track density as:
In practice, we irradiate a standard of known age, and pile the various constants into the zeta-factor, ζ:
where ρd is the track density in a U- doped standard.
(similar to 40Ar/39Ar)
Rearranging and solving for t:

34. Assessing Results
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 the errors are also considered, the results may be presented as a probability density diagram, such as Figure 4.16.

35. Assessing Results
Yet another approach is to plot the spontaneous track density (ρs) vs the induced track density (ρi), such as Figure From equation 4.39, 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.
Figure 4.17

36. Interpreting Ages

37. Closure Temperatures
Same dependence of closure temperature on cooling rate applies to fission tracks (and U-Th-He ages).
Figure shows comparison of apparent closure temperatures of fission tracks, U-Th-He, and K-Ar as a function of cooling rate for a variety of minerals. From Reiners & Brandon (2006).

38. Uplift Rates
As mountains respond to erosion by uplift, underlying rock cools as it approaches the surface so that temperature at depth z will be:
where Ts is the surface temperature and TL is the temperature of the base of a layer of thickness L, HT is the radiogenic heating (˚C/Ma), κ is thermal conductivity and ε is erosion rate.
If erosion rates are high, geothermal gradient can be non- linear.

39. Erosion Rates, Geothermal Gradients, and Closure Temperatures

40. Example of Apatite Fission Track Ages in the Himalaya

41. Fission Track Lengths
Additional information may be contained in the length of fission tracks (resulting from partial annealing).
When a grain is subjected to elevated tempera­ture, both the track density and the mean track length decrease. Because (1) tracks tend to have a constant length (controlled by the energy lib­erated in the fission), (2) tracks be­come progressively shorter during 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.

42. Mass Spectrometry
Quick Overview

43. Magnetic Sector Mass Spec
Consists of 3 parts
A ion source – to produce & accelerate ions
mass analyzer – deflects ions in proportion to mass
collector/detector – to detect or count ions

44. Ion Source Ions can be produced by thermal ionization
collisions with electrons produced by a hot filament
plasma
secondary ionization
laser ionization

45. Mass Analyzer
A charged particle moving in a magnetic experiences a force
F = qv × B A.1
Since the force is always di­rect­ed perpendicular to the direction of motion, the particle begins to move in a circular 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
Equating:
The velocity of the particle can be determined from its energy, which is the accelerating potential, V, times the charge:
Substituting:
We select for mass by adjusting B
Typical value of r for a thermal ionization mass spec is 54 cm.

46. Energy Filtration
If ions are not mono- energetic or to improve abundance sensitivity, some elements are fitted with an electrostatic analyzer, which selects for ion energy.

47. Faraday Cup

48. Electron Multiplier
Ion beam strikes a charged surface producing a cascade of electrons.
Can be used in either analog or ion counting modes.

49. Daly Detector

50. Quadrapole Mass Spec.
Quadrapole operates by rapidly varying charge between + and – on 4 cylinders at R.F..
Ion spirals through the analyzer.
By tuning the rate of variation, only one m/q value will arrive at the detector.
Most common kind of mass spec, but less accurate for isotope ratios.
Can be combinedwith a variety of ion sources and detectors.

51. Accelerator Mass Spec.