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.

5
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.

7
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 daughters, D0 is
  the number of 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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Rocks subject to tectonic uplift would yield a
temperature-time plot that looks like the one
below.
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A hypothetical temperature-time plot showing the
array of different thermochronometers that may be
used to constrain T-t history.
19
Temperature-time history for the Adirondack
highlands, New York. U-Pb on garnet, monazite,
rutile and sphene, Ar-Ar on hornblende and
biotite.
20
A plot of mineral age vs. blocking temperature
for the Glen Dessary syenite from Scotland. The
mineral ages define a cooling curve for the
pluton.
21
Temperature-time plot showing the cooling history
of the Quottoon Pluton, B.C.
22
Temperature-time history for the Valhalla
Complex, B.C. Note cooling rate in excess of
10C/Ma.
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THE Ar-Ar METHOD

• A major disadvantage of K-Ar dating it that Ar is
  easily lost from many minerals. Loss of 40Ar
  results in erroneously young ages. Consider a
  hornblende crystal like that drawn below

We would expect the outer portions of a crystal
to lose Ar more readily, but the centers retain
it longer. Thus, the rim will give a younger age
than the core, and the average age of the crystal
will be erroneously young.
Ar tends to be lost easily from the rim.
It takes longer for Ar to diffuse from the
center, so it retains Ar longer.
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• We can ratio the number of 40Ar atoms remaining
  to the number of some stable, non-radiogenic
  isotope that is not lost from minerals, e.g.,
  39K. This ratio, 40Ar/39K will be highest in the
  crystal core and lowest in the rim.
• To date a mineral with the Ar-Ar method, we first
  irradiate the mineral in a nuclear reactor to
  cause the transformation 39K ? 39Ar
• The number of 39Ar formed can be calculated as

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• where 39Ar is the number of 39Ar atoms produced
  during irradiation, 39K is the number of 39K
  atoms present before irradiation, tirr is the
  irradiation time, ? is the neutron flux of the
  reactor (neutrons cm-2 s-1), ? is the neutron
  capture cross section, and ? represents the
  energy of the neutrons. Because the neutrons have
  a distribution of different energies, we
  integrate over the entire energy spectrum.
• The number of 40Ar in the rock depends on the
  amount of radioactive decay according to

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• Taking the ratio of these two expressions we get
• Many of the quantities on the right hand side of
  the equation are difficult to measure. We can
  rewrite the equation as
• J can be determined by placing a sample of known
  age (flux monitor) in the reactor with the
  unknown sample.
• Thus, if we know the ratio 40Ar/39Ar coming off
  an irradiated sample when heated, we can
  calculate an age.
• In practice, the sample is heated in steps, the
  the ratio 40Ar/39Ar of the Ar released at each
  step is measured.

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40Ar-39Ar age versus cumulative 39Ar released for
mica and amphibole samples from a blueschist.
Heating started at 550C and continued in 50C
steps. If the entire sample was closed to Ar loss
throughout its history, the age calculated at
each increment would be the same. This plot shows
Ar loss from the rim, but a plateau at 185 M.Y.
age of metamorphism 185 M.Y.
28
Schematic 40Ar-39Ar age spectra (A) an
undisturbed sample yielding a plateau across the
entire gas release (B) a sample showing slight
disturbance (C) a disturbed sample yielding no
plateau (D) a reset sample yielding a plateau
corresponding to the age of overprinting (E) a
saddle-shaped spectrum reflecting the presence of
excess 40Ar.
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THE Rb-Sr METHOD

• Based on the decay reaction
• with a half-life
• T1/2 48.8 B.Y.
• We write the geochronometry equation in terms of
  the ratio 87Sr/86Sr because ratios are more
  accurately determined by mass spectrometry.

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• The Rb-Sr method is commonly used to date Rb-rich
  minerals such as muscovite, biotite and
  K-feldspar these same minerals usually do not
  incorporate much Sr at the time of their
  formation (application of Goldschmidts rules!).
• The blocking temperature for the Rb-Sr system in
  a given mineral is usually greater than that for
  K-Ar thus, Rb-Sr usually gives somewhat older
  ages than K-Ar.
• We usually use the isochron method to determine
  the age and initial 87Sr/86Sr ratio of a suite of
  rocks.

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Rb-Sr isochron diagram for a series of meteorites
formed at the same time
32
Schematic Rb-Sr isochron diagram illustrating how
the isochron evolves as a function of time. M1
and M2 are cogenetic minerals and R1 and R2 are
cogenetic rocks, all with different initial Rb/Sr
ratios.
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EXAMPLE PROBLEM
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EXAMPLE (continued)
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EXAMPLE (continued)
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EXAMPLE PROBLEM
slope (e?t 1) 0.002591 0.002591 (e?t 1)
e?t 1.002591 (1.42x10-11 a-1)t 0.002587 t
182,183,099 a 182 Ma 0.182 Ga
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Sr ISOTOPES AS TRACERS OF ROCK ORIGIN
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The evolution of 87Sr/86Sr with time in the
continental crust and mantle.
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Sr ISOTOPES AS TRACERS OF ROCK ORIGIN

• According to the foregoing, the (87Sr/86Sr)0
  ratio can be used as a tracer to determine if a
  magma evolved directly from the mantle or if
  crust was involved.
• For mantle-derived rocks (87Sr/86Sr)0 ?
  0.699-0.706.
• For crustal involvement (87Sr/86Sr)0 ?
  0.705-0.735

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THE Sm-Nd METHOD

• Based on the decay
• 147Sm ? 143Nd T1/2 106 Ga
• Nd is slightly more compatible in the crust than
  Sm. Although the difference is small, 143Nd/144Nd
  increases faster in the mantle than in the crust.
  Thus, mantle-derived rocks have higher
  (143Nd/144Nd)0 than crustal rocks.
• Sm-Nd method is useful in Ca-bearing rocks
  because REE substitute for Ca.
• Sm-Nd method relatively resistant to alteration.

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Sm-Nd isochron diagram illustrating data from
scheelite (CaWO4) from several lode Au deposits
associated with an early shear zone system in
Zimbabwe
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MODEL AGES

• Model age - a measure of the length of time a
  sample has been separated from the mantle from
  which it was originally derived.
• Model ages are useful because they can be
  calculated for an individual rock from a single
  pair of Sm-Nd isotopic ratios.
• The basis of all such model ages is an assumption
  about the isotopic composition of the mantle
  source region from which the samples were
  originally derived.
• Care must be exercised in their interpretation.

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CHUR

• CHUR - CHondrite Uniform Reservoir
• The CHUR model assumes that the Earths primitive
  mantle had the same isotopic composition as the
  average chondritic meteorite at the formation of
  the Earth (4.6 B.Y.).
• For Nd isotopes, the CHUR composition is the same
  as the composition of the bulk Earth.
• A model age calculated relative to CHUR is the
  time in the past at which the sample suite
  separated from the mantle reservoir and acquired
  a different Sm/Nd ratio. It is also the time at
  which the sample had the same 143Nd/144Nd ratio
  as CHUR.

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CALCULATING T-CHUR
This model age is very sensitive to the
difference in the denominator. Only rocks with
Sm/Nd ratios significantly different from CHUR
will yield precise ages.
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The evolution of Nd isotopes with time in the
mantle, the continental crust and the bulk Earth
(CHUR).
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EPSILON NOTATION

• The mantle has a higher 147Sm/144Nd ratio than
  CHUR, so the mantle has been evolving values of
  143Nd/144Nd greater than CHUR with time, so
  ?Nd,CHUR gt 0 for the mantle. The crust has a
  lower 147Sm/144Nd ratio than CHUR, so the crust
  has been evolving values of 143Nd/144Nd less than
  CHUR with time, so ?Nd,CHUR lt 0 for the crust.

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The contrasting evolution of ?Nd in the
continental crust and mantle. CHUR is the
chondritic uniform reservoir and is equivalent to
the bulk Earth value. Five different estimates of
the evolution of the depleted mantle are shown.
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THE Re-Os METHOD

• This is based on the decay 187Re ? 187Os with
  T1/2 41.606 Ga.
• Originally, the following equation was employed
  to calculate dates
• However, it was later discovered that 186Os is a
  radiogenic daughter of the decay 190Pt ? 186Os.
  Although this is not a problem for young or
  Pt-poor rocks, in older, Pt-rich rocks, the
  normalization factor would not be constant.

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• Thus, it was decided to abandon 186Os as the
  normalization factor in favor of 188Os.
• Re-Os concentrations are low in many rocks, but
  both metals are concentrated in the Fe-Ni alloy
  phases of meteorites. Re is concentrated in
  sulfide, and particularly Mo-sulfide ores. Os is
  concentrated in mafic-ultramafic rocks and
  platinum-group element (Pt, Pd, Os, Ir, Ru, Rh)
  ores. Ages can be calculated using the isochron
  method.

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• Re is more compatible in the crust and Os in the
  mantle. Therefore, crustal rocks have high Re/Os
  7-30, and crust therefore has higher 187Os/188Os
  ratios than the mantle.
• Upper continental crust Re/Os 7.8 187Os/188Os
  1.7.
• Lower continental crust (Lewisian Complex,
  Scotland) Re/Os 9.6-22.3 187Os/188Os
  2.3-28.2.
• Mantle Re/Os lt 0.4 187Os/188Os 0.1-0.3.
• Thus, there is a strong contrast in Os isotope
  composition between mantle and crust. So Os
  isotopes are a very sensitive tracer of crustal
  contamination of magmas and ore deposits.

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GAMMA NOTATION

• The reference for Os isotopes is also CHUR, and
  the deviation of the isotope composition from
  CHUR is given by
• For mantle rocks, ?Os lt 0, whereas for crustal
  rocks ?Os gt 0.
• Model ages TCHUROs can be calculated in analogy
  to TCHURNd ages.

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THE U, Th-Pb METHOD

• Based on the following three decay reactions
• 238U ? 206Pb T1/2 4.468 Ga
• 235U ? 207Pb T1/2 0.704 Ga
• 232Th ? 208Pb T1/2 14.01 Ga
• 204Pb is a non-radiogenic, stable isotope. We can
  therefore write

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• With this geochronometer, we can get three
  independent age determinations of minerals or
  rocks containing both U and Th.
• All three equations will give the same ages,
  provided no gain or loss of U, Th or Pb occurred
  after the rock formed. The ages are then said to
  be concordant.
• Often, the three dates do not agree, i.e., they
  are discordant. Discordancy often results from
  loss of Pb or intermediate daughters caused by
  radiation damage during ?-decay.

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THE Pb-Pb METHOD

• One way to lessen the effect of open-system
  behavior is to combine the two U-Pb
  geochronometers.
• A plot of 207Pb/204Pb vs. 206Pb/204Pb for a
  series of related rocks of the same age should
  yield a family of straight lines intersecting at
  a point giving the initial ratio. These straight
  lines are Pb-Pb isochrons.

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• Often, the left-hand side of the previous
  equation is written as
• The Pb-Pb method often yields older dates than
  the individual geochronometers because the ratio
  of Pb isotopes is not as sensitive to recent Pb
  loss.

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Numerical Values of e?1t - 1, e?2t - 1, and of
the Radiogenic 207Pb/206Pb Ratio as a Function of
Age (t).
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ZIRCON

• Only a few minerals are suitable for dating by
  the U,Th-Pb methods. The mineral must retain
  radiogenic Pb and be common.
• Zircon (ZrSiO4) is most often used. Zircon
  permits substitution of U and Th for Zr.
• rZr4 0.80 Å rU4 0.97 Å rTh4 1.08 Å
• However, on initial formation, zircon excludes
  Pb rPb2 1.26 Å.
• During radioactive decay, Pb becomes trapped in
  the zircon and cannot escape except under special
  circumstances.
• Zircon is relatively resistant to mechanical and
  chemical weathering.

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CONCORDIA DIAGRAM

• On a plot of 206Pb/238U vs. 207Pb/235U, the
  locus of all points yielding concordant dates is
  called the concordia curve.
• Rocks experiencing no Pb or U mobility move along
  the concordia as they age. Any rock or mineral
  that does not plot on the concordia is said to
  yield discordant dates.
• The concordia curve bends over because 235U
  decays much faster than 238U this causes 207Pb
  to be produced faster than 206Pb.

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Concordia diagram. During episodic Pb loss or U
gain, minerals are displaced from the concordia
and move along the discordia line.
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DISCORDIA LINE

• If Pb loss occurred, the rocks would plot along a
  line below the concordia.
• If U loss occurred, the rocks would plot along a
  line above the concordia.
• The line or chord that results from discordant
  samples is called a discordia line. The upper
  intercept of the chord may represent the age of
  formation of the rock. The lower intercept may
  represent the date of Pb loss, if this loss
  occurred in a single stage, and not continuously.

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Concordia-discordia diagram for zircon grains in
granulite facies metasediments from Sri Lanka.
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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.
• 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 so-called
  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.