GEOCHRONOLOGY

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GEOCHRONOLOGY

• USE OF RADIOGENIC ISOTOPES AS DATING TOOLS AND
  GEOCHEMICAL TRACERS

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LAW OF RADIOACTIVITY

• The rate of decay of radioactive nuclide is
  proportional to the number of that nuclide
  remaining at any time, i.e.
• where -dN/dt is the rate of decay, ? is the decay
  constant, and N is the number of nuclides
  remaining at time t.
• The decay constant ? is independent of
  temperature and pressure.

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• Integrating the above expression we obtain
• where N0 is the number of nuclides at the start.
• Half-life - time required for half of a given
  number of radionuclides to decay.
• If t T1/2, then N N0/2, so

or
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DISINTEGRATION RATE

• We define the disintegration rate A as
• A can be measured with a scintillation counter.
• We can rewrite the decay equation as
• This equation tells us that a plot of ln A vs. t
  should yield a straight line with slope ?. This
  is one way to measure the decay constant.

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Decay of 24Na in ln-normal coordinates
ln A0
Slope -0.04614 ? 0.04614 hr-1 T1/2 15.0 hr
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GROWTH OF STABLE DAUGHTER

• If the decay of the parent radionuclide gives
  rise to a stable daughter isotope we can write
• where D is the number of stable, radiogenic
  daughter atoms. We can then rewrite the equation
• as
• which expresses the growth of daughter atoms as a
  function of time.

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Decay curve of a radionuclide and growth curve of
its stable daughter in linear coordinates.
Growth curve of daughter
Decay curve of parent
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GEOCHRONOMETRY EQUATION

• The last equation can also be expressed as
• This is called the geochronometry equation. It is
  more useful than the previous equation because we
  dont always know N0 for a rock, but we can
  determine N.
• We can further write D D0 D
• where D is the total number of radiogenic
  daughters, D0 is the number of radiogenic
  daughters in the rock at the time of its
  formation, and D is the number of radiogenic
  daughters present due to decay of parent.

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• To date a rock using radioactive decay, we must
  therefore know D, D0, N and ?.
• D, N - measured by analysis using a mass
  spectrometer
• ? - a constant, usually known
• How do we determine D0?
• 1) Make an assumption about D0, e.g., in the K-Ar
  method we assume D0 0.

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• 2) Analyze a series of related rocks of the same
  age and having the same D0 value but different
  N0. These data should yield a straight line on
  plotting D vs. N.
• On such a plot, D0 will be the intercept, and
  (e?t-1) is the slope.
• This is the so-called Isochron Method and will
  be discussed in more detail when we discuss the
  Rb-Sr system.

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ASSUMPTIONS INHERENT IN RADIOMETRIC DATING

• 1) The values of N and D have changed only as a
  result of radioactive decay, i.e., the system is
  closed chemically.
• 2) The isotopic composition of the parent was not
  altered by fractionation at the time of formation
  of the rock.
• 3) The decay constant is known accurately.
• 4) The isochron is not a mixing line.
• 5) The analytical data are accurate.

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Schematic gass-source mass spectrometer. It
consists of three parts 1) a source of ions 2)
an electromagnet to separate ions by mass 3) an
ion collector.
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DATING METHODS
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THE K-Ar METHOD

• Based on the decay reaction
• with a half-life
• T1/2 11.9 B.Y.
• The pertinent geochronometry equation is
• The factor ?e/? is the ratio of decay by 40K ?
  40Ar to total decay of 40K, which also includes
  40K ? 40Ca.
• It is generally assumed that 40Ar0 ? 0, because
  Ar does not usually become incorporated in
  minerals at the time of formation.

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• Why not use the decay 40K ? 40Ca as a
  geochronometer?
• 40Ca is the most common Ca isotope, and Ca
  concentrations are quite high in most rocks. The
  amount of 40Ca that forms in a rock due to decay
  of 40K is relatively small compared to the amount
  of 40Ca already present at time t 0. We cannot
  analyze the small additional amount of radiogenic
  40Ca accurately enough.
• The K-Ar method has been widely used to date
  K-bearing minerals, e.g., K-feldspar, muscovite,
  biotite and hornblende. It is used less
  frequently now because of the ease of loss of
  radiogenic Ar.

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BLOCKING TEMPERATURE

• The K-Ar method actually dates the time at which
  the mineral cooled sufficiently so that
  radiogenic 40Ar cannot diffuse out of the
  crystals.
• Blocking temperature - the temperature at which
  the mineral becomes closed with respect to Ar
  loss.
• Thus, the date obtained with the K-Ar method will
  generally be less than the true age, unless the
  rocks being dated cooled very rapidly.
• Blocking temperatures are different for different
  minerals. We can use this fact to calculate rates
  of uplift.

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COSMOGENIC NUCLIDES

• Examples 3H, 10Be, 14C, 26Al, 32Si, 35Mn, 36Cl,
  39Ar.
• These radionuclides are produced by nuclear
  reactions between cosmic rays and stable atoms in
  the atmosphere and at the Earths surface
  (SPALLATION ? turns a larger ion into several
  smaller ones)
• The radionuclides are removed from the atmosphere
  by precipitation, and if prevented from contact
  with cosmic rays, radioactive decay will be the
  dominant process controlling their concentration.
• Once removed from contact with cosmic rays, the
  concentration of these nuclides decreases with
  time, i.e., a clock starts ticking.

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CARBON-14

• 14N neutron ? 14C 1H
• The 14C produced in the atmosphere is
  incorporated into CO2 and is rapidly mixed
  throughout the atmosphere.
• The CO2 is then absorbed by plants during
  photosynthesis. Animals take up 14C by eating
  plants, etc. As long as the plant or animal is
  alive, a steady state exists. That is, the rate
  of production of 14C by cosmic rays is just
  balanced by the rate of radioactive decay.
• When the organism dies, uptake of 14C ceases and
  the activity of 14C declines with time, i.e., the
  clock starts ticking.

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• Decay reaction 14C ? 14N ?- energy
• T1/2 ? 5730 a
• A activity, as measured by a scintillation
  counter.
• A present-day activity A0 initial activity
  (usually assumed to be equal to 14C activity in
  atmosphere.
• This method is used to date C-bearing materials
  such as charcoal, wood, peat, and CaCO3 in
  fossils and sediment.

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• After 7 half-lives, the activity decays to
  immeasurably low values. Thus, the limit for 14C
  dates is 35,000-45,000 a.
• OTHER COMPLICATIONS
• 1) Variations in 14C production rate
• - fluctuations in cosmic-ray flux
• - changes in magnetic field
• 2) Variations in 14C content due to chemical and
  physical fractionation
• 3) Dilution of 14C by low-14C CO2 from fossil
  fuel burning.

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10Be, 26Al

• Both of these isotopes are formed by spallation
  reactions between cosmic rays and O and N in
  atmosphere.
• Both isotopes are removed by rain and snow.
• Upon entering oceans or lakes, the isotopes are
  scavenged by adsorption onto sediment particles
  and carried to the bottom.
• After deposition and removal from contact with
  cosmic rays, their concentrations decrease owing
  to decay.
• 10Be T1/2 1.5 Ma 26Al T1/2 0.716 Ma

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• Similar processes occur during the formation of
  ice sheets in Greenland and Antarctica, and in
  successive lava flow.
• Decay occurs according to the following two
  reactions
• With knowledge of the thickness of the sequence
  (sediment column, ice sheet, lava layers) and t,
  the rate of accumulation of sediment/ice/lava can
  be calculated.

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THE K-Ar METHOD

• Based on the decay reaction
• with a half-life
• T1/2 11.9 B.Y.
• The pertinent geochronometry equation is
• The factor ?e/? is the ratio of decay by 40K ?
  40Ar to total decay of 40K, which also includes
  40K ? 40Ca.
• It is generally assumed that 40Ar0 ? 0, because
  Ar does not usually become incorporated in
  minerals at the time of formation.

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• Why not use the decay 40K ? 40Ca as a
  geochronometer?
• 40Ca is the most common Ca isotope, and Ca
  concentrations are quite high in most rocks. The
  amount of 40Ca that forms in a rock due to decay
  of 40K is relatively small compared to the amount
  of 40Ca already present at time t 0. We cannot
  analyze the small additional amount of radiogenic
  40Ca accurately enough.
• The K-Ar method has been widely used to date
  K-bearing minerals, e.g., K-feldspar, muscovite,
  biotite and hornblende. It is used less
  frequently now because of the ease of loss of
  radiogenic Ar.

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BLOCKING TEMPERATURE

• The K-Ar method actually dates the time at which
  the mineral cooled sufficiently so that
  radiogenic 40Ar cannot diffuse out of the
  crystals.
• Blocking temperature - the temperature at which
  the mineral becomes closed with respect to Ar
  loss.
• Thus, the date obtained with the K-Ar method will
  generally be less than the true age, unless the
  rocks being dated cooled very rapidly.
• Blocking temperatures are different for different
  minerals. We can use this fact to calculate rates
  of uplift.