PowerPoint Presentation
Geochronometry-Isotope tracing-Age of the EarthGeochronometry
(methods)Nuclear synthesisMeteoritesAge of the Earth accretionPb
Formation of the core Formation of the core (energy
considerations)Formation of crustPlate tectonics
startsGeochronometryRadiogenic isotopes Decay mechanisms ( decay,
decay, electron capture) Main isotopic systems for dating
Rb-SrK-ArU-Pb Th-Pb Other isotopes used mainly for tracing (Sm-Nd,
Re-Os, )
Geochronometry (hypotheses)Parent -> daughter decay
probability Mineral closes at temperature (depends on type: zircons
800 deg, feldspars 350, )No daughter present at closure (or it can
be accounted for)No loss or gain of parent or daughter after
mineral closes
Counting P/D gives the time that elapsed since the system
closedGeochronometry (particulars)K->Ar is a branching decay K40
-> Ar 40 or Ca 40U -> Pb two different isotopes of same
element give two independent age estimates (must be
concordant)Rb/Sr requires different minerals with variable Rb/Sr
ratios (same for Sm-Nd). Methods yield initial isotopic ratio of
Sr87/Sr86 (important for tracing)
Same equations and method for other systems (U-Pb, Sm-Nd)
K-ArNo Ar initiallyBut problem of atmospheric contamination
Correction based on Ar36Also Ar is easily lost Retrace loss by step
heating of samples and Ar-Ar ages
Dating the synthesis of elements
Meteorite samples
chondriteachondriteIron
Xe129Xe129 product of short half life I129Meteorites formed
shortly after nucleosynthesis. Xe129 in earth atmosphere (I129 in
primitive earth) comes from degasing of mantleEarth and meteorites
have ~ same age
MeteoritesAll meteorites have about the same age 4.55 Ga Some
meteorites that have younger ages come from the moon. They were
ejected after impact.A few are much younger (1.1 Ga). They are
assumed to have been ejected by Mars after a large impact
Martian meteorites (?)
Moon samples Nasa has collected samples for dating Ages range
between 3.0 and 4.5 Ga(see PDF document)Time series of a
Moon-forming impact simulation. Results are shown looking down onto
the plane of the impact at times t = 0.3, 0.7, 1.4, 1.9, 3, 3.9, 5,
7.1, 11.6, 17 and 23 hours (from left to right); the last frame is
t = 23 hours viewed on-edge. Colour scales with internal energy
(shown on the colour bar in units of 6.67 times 108 erg g-1), so
that blue and dark green represents condensed matter, and red
particles signify either the expanded phase or a hot, high-pressure
condensed phase; pressures at intermediate energies are computed by
an interpolation between the Tillotson15 condensed and expanded
phases. We form initial impactors and targets in hydrostatic
equilibrium by pre-colliding smaller bodies together at zero
incidence, resulting in realistically evolved internal energies,
stratified densities (basalt mantle + iron core) and consistent
pressures. Each particle's internal energy is evolved due to the
effects of expansion/compression and shock dissipation, with the
latter represented by artificial viscosity terms that are linear
and quadratic in the velocity divergence of converging particles;
effects of mechanical strength and radiative transfer are ignored.
The momentum of each particle is evolved due to pressure, viscous
dissipation and gravity. Gravity is computed using a binary tree
algorithm, reducing the N2 calculation of particleparticle
attractions into an NlogN calculation25. We use a beta spine kernel
to define the spatial distribution of material represented by each
SPH particle. The scale of each particle, h, is automatically
adjusted to cause overlap with a minimum of 40 other particles,
ensuring a 'smoothed' distribution of material even in low-density
regions. The code is explicit, requiring a Courant-limited timestep
Deltat < (c/h) where c is the sound speed. For a full
description of the technique, see ref. 26, from whose efforts our
present algorithm derives.
Rappel
Geochronometry hypotheses
Nucleosynthesis (6 to 4.6 Ga)Age of meteorites 4.55 GaMeteorites
follow shortly end of nucleosynthesisEarth followed shortly end of
nucleosynthesisMoon samples 3.2 to 4.5 GaOldest rock on Earth 4
GaAge of Earth from Pb 4.55 Ga
Dating core formationHafnium Hf and Tungsten W Hf182 -> W182
(half life 9 Myears)Hf180 reference Hf stays in mantleW goes in
coreInitial ratio Hf182/Hf180 in solar system different from that
of mantle
w values of carbonaceous chondrites compared with those of the
Toluca iron meteorite and terrestrial samples analysed in this
study. The values for Toluca, Allende, G1-RF and IGDL-GD are the
weighted averages of four or more independent analyses. Also
included are data from ref. 16 (indicated by a), ref. 30 (b), and
ref. 2 (c). For the definition of w see Table 1. The vertical
shaded bar refers to the uncertainty in the W isotope composition
of chondrites. Terrestrial samples include IGDL-GD (greywacke),
G1-RF (granite) and BB and BE-N (basalts).
w versus 180Hf/184W for different fractions of the H chondrites
Ste Marguerite (a) and Forest Vale (b). NM-1, NM-2 and NM-3 refer
to different nonmagnetic fractions, M is the magnetic fraction. We
interpret the positive correlation of w with 180Hf/184W as an
internal HfW isochron whose slope corresponds to the initial
182Hf/180Hf ratio at the time of closure of the HfW system.
Time of core formation in Myr after CAI condensation for Vesta,
Mars, Earth and Moon versus planet radius as deduced from HfW
systematics. For the Moon, the two data points refer to the
endmember model ages. The Moon plots distinctly to the left of the
correlation line defined by Vesta, Mars and Earth, suggesting a
different formation process.
Timing of core formation. The Earth formed through accretion,
absorbing planetesimals (lumps of rock and ice) through collisions.
Did the Earth accrete undifferentiated material that then separated
into shell and core in which case, did the planet reach its present
mass before differentiating, or was it a more gradual process?
Alternatively, core formation might have happened rapidly inside
growing planetesimals, so that the Earth's core is a combination of
these previously formed cores. Isotopic evidence supports the
latter model, and now Yoshino et al.1 demonstrate a mechanism for
the physical process.
Core formation (conservation laws)Gravitational potential energy
decreases when core formsMoment of inertia decreases Angular
velocity of rotation increasesRotational energy increases Increase
in energy of rotation < Decrease in gravitational potential
energyTotal energy must be conservedDifference goes into heat
Estimates: Core formation -> 1000-2000K temperature increase
He It is assumed that volatiles were lost during accretionVery
little He in atmosphere (too light, lost to space)He in mantle He3
is primitive, He4 primitive + decay of radioelements He4/He3 ratio
(initial ratio same as that of universe)He4/He3 ratio grows with
time Some degasingShows mantle is not well mixed
Tracing with isotopesCrust Rb/Sr highSm/Nd low
Sr87/Sr86 increasesNd143/Nd144 decreases compared with
mantle
MantleRb/Sr lowSm/Nd high