Geological Dating
Clocks and Calendars
Clocks in General
• Clocks define time intervals. They tick.
• We count ticks to measure elapsed time and
to define our time scale
• Ticks can be generated accurately using
pendulums, oscillating balance wheels,
oscillating crystals and oscillating electrons in
an atom.
• Longer ticks are derived from Earths rotation
and orbit.
Geological Clocks
• An ideal geological clock:
– Must run for many millions of years
– Should not need calibration or re-setting
– Must have a tick that is not affected by
temperature, pressure, mechanical movement or
chemical environment
– Must count number of ticks over a long interval
Radioactive decay, a signal from an atomic
nucleus, meets these requirements.
Measurement of the number of stable decay
product atoms integrates the ticks.
Geological Column
• The study of fossil plants and animals and
their associated strata, acceptance that the
most recent sedimentary strata will be on top
and appreciation of evolution allowed
geological columns to be constructed.
• The steps in the geological column
represented ill-defined events, not time steps.
• The origin was missing. No life, no fossils, no
biological calibration ar bottom of column.
Geologic Column Timescale
The lowest segment was called
pre-cambrian.
There was no origin.
The boundaries between periods
are still argued over. A worldwide
standard is probably impossible
since temperature and climate
histories vary.
Old igneous rocks could not be
dated and the mechanics of their
formation can invalidate
arguments based on
stratification.
Radioactive Decay 1
• For a given atom, the probability of decay is
constant.
• A large assembly of atoms exhibits a constant
decay rate λNt where
– λ is a constant for an atom, Nt is the number of
atoms of that atom present at time t
• Radioactive decay is therefore exponential
Nt = N0e – and the time required for half to
decay is 0.693/λ. Half life is more easily
visualised than a reciprocal unit.
Radioactive Dating
Typically one measures the number of active
parent and stable daughter atoms present in a
mineral at a time t, the present.
Since the number of stable daughter atoms, D*,
is always the same as the number of parent
decays, one can write an expression for the
number of parent atoms when t = 0, the date we
seek. This leads us to:
D* = Nt(eλt – 1) where D* and Nt are
measurable. This is the geochronometry
equation.
Measured Quantities
• Mass spectrometry is favoured analytical
method as sensitivity improves.
• Mass spectrometers measure ratios of
similar masse most accurately.
• So geochronometry equation looks like
this in practice. 86Sr is stable, natural
reference isotope.
87
𝑆𝑟
86
𝑆𝑟
=
87
𝑆𝑟0
86
𝑆𝑟
+
87
𝑅𝑏
86
𝑆𝑟
(𝑒
𝜆𝑡
- 1)
Radiometric dating:
• Radiometric dating is
most successful when
the number of parent
and daughter isotopes
are changing rapidly
with time. The graph
shows that after 4 half
lives the method
becomes very much less
sensitive as growth and
decay curves flatten.
Hence need for a
toolbox of isotope pairs.
Sources of Natural Radioactivity
• The creation of heavy atoms during stellar
explosions that release many neutrons.
• The heaviest atoms, and a few lighter
isotopes, are unstable, so radioactive. Some
survive in the universe.
• Secondary cosmic ray packets contain
neutrons that can react with earthbound
nuclei to produce unstable atoms e.g. 14C.
14
7𝑁
+ 10𝑛
14
6𝐶
+ 11𝐻
nuclear mass
nuclear charge (protons)
Atom
Long lived naturally occurring
Isotopes used in Dating (a = years)
238 Uranium Decay Chain
Cosmogenic Radionuclides
When can one use Radiogenic Dating
• To date compounds of radioactive elements
eg: Uranium minerals, thorium deposits etc.
• To date any undisturbed mineral that contains
a radioactive atom as an embedded impurity.
• Uranium and thorium are widely distributed.
• Zircon is a widely distributed, but insoluble,
impurity present in many igneous rocks able
to sequester uranium and thorium. It’s a tight,
easily recognised and removed box. A good
marker, but it can leak lead.
Dating with Long lived isotopes
What is T0 ?
• Date of supernova explosion that created the
heavy atoms used in dating?
• Date the explosion debris solidified?
• Date Earth formed, whatever that means?
• Date this particular crystal formed from a
solution or a melt and excluded daughters?
Caveats and Assumptions
• Number of parent and daughter atoms in
specimen changed only by decay of parent to
daughter. No loss by ejection, evaporation or
solution. No gain by contamination from
environment.
• Isotope ratios in parent were not affected by
fractionation at the time of mineral formation.
• No metamorphosis that affects composition of
rock specimens.
Problems with Reality
• D0 not zero at time of specimen formation
• Loss of Lead from chemical reaction and
solution
• Zeolite lattice does not like lead, so loses
some.
• Specimen histories easily vary over a few
million years
• Metamorphism causes re-distribution of
materials in rocks. Restarts clock at best.
• You do not choose available markers
D0 not Zero
• Non-zero D0 can be dealt with if several
samples believed to be of same age are
analysed for remaining parent and daughter.
• A plot of Daughter atoms (y) versus Parent
atoms (x) has a slope of (𝑒 𝜆𝑡 - 1) and intercept
D0.
• Variation of D0 yields information about
history.
• Scope for argument
Cosmogenic Dating
The measured quantity is the radioactivity (λNt)
of an isotope whose accumulation in a mineral
or organic material has ceased due to chemical
isolation or death of the organism.
For dating to work:
The rate of production of the isotope must
have been constant for a long time for
radioactive equilibrium to be established.
The composition and intensity of cosmic
ray incidence must have been constant .
No interfering sources or fractionation.
Carbon Dating
• Sources of interference:
– Solar flares
– Neutrons from nuclear bomb testing that react
with nitrogen in air to enhance 14C
– Combustion of carbon of various ages
• Sources of fractionation:
– Mass difference 12C and 14C so
– All chemical reactions from photosynthesis to
cellulose and tissue production.
– Dissolution of CO2 and CH4 in water
Radio-carbon dating:
Validation of Carbon Dating
• Many sources of error make calibration and
validation necessary.
• One method is tree or coral ring analysis, since
age of ring is known from the ring count.
• Another is use of other short lived cosmogenic
nuclide pairs whose environment is different
or parts of a longer sequence 234U/230Th/226Ra
• Counting 16O/18O switches
Dendro-chronology:
• Tree rings are normally
formed annually and
indicate growth of trees
over many years
sometimes, hundreds
or even thousands – up
to 9000 years especially
using Britstlecone Pines.
Radiocarbon Dating Calibration Curve
Radiometric dating - Summary