Transcript Document

Geochronometry-Isotope tracing-Age of the Earth
 Geochronometry (methods)
 Nuclear synthesis
 Meteorites
 Age of the Earth accretion
 Pb
 Formation of the core
 Formation of the core (energy considerations)
 Formation of crust
 Plate tectonics starts
Geochronometry
 Radiogenic isotopes
 Decay mechanisms (α decay, β decay, electron capture)
 Main isotopic systems for dating
 Rb-Sr
 K-Ar
 U-Pb
 Th-Pb
 Other isotopes used mainly for “tracing” (Sm-Nd, Re-Os, …)

Geochronometry (hypotheses)
 Parent -> daughter decay probability λ
 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 closed
Geochronometry (particulars)
 K->Ar is a branching decay K40 -> Ar 40 or Ca 40
 U -> 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 SmNd). Methods yield initial isotopic ratio of Sr87/Sr86 (important for tracing)
Same equations and method for other systems (U-Pb, Sm-Nd)
K-Ar
 No Ar initially
 But problem of atmospheric contamination
 Correction based on Ar36
 Also Ar is easily lost
 Retrace loss by step heating of samples and Ar-Ar ages
Dating the synthesis of elements
Meteorite samples
chondrite
Iron
achondrite
Xe129
 Xe129 product of short half life I129
 Meteorites formed shortly after nucleosynthesis.
 Xe129 in earth atmosphere (I129 in primitive earth) comes from degasing of
mantle
 Earth and meteorites have ~ same age
Meteorites
 All 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 particle–
particle 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 Ga
Meteorites follow shortly end of nucleosynthesis
Earth followed shortly end of nucleosynthesis
Moon samples 3.2 to 4.5 Ga
Oldest rock on Earth 4 Ga
Age of Earth from Pb 4.55 Ga
Dating core formation
 Hafnium Hf and Tungsten W
 Hf182 -> W182 (half life 9 Myears)
 Hf180 reference
 Hf stays in mantle
 W goes in core
 Initial ratio Hf182/Hf180 in solar system different from that of mantle
 εw 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 εw
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).
 εw 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 εw
with 180Hf/184W as an internal
Hf–W isochron whose slope
corresponds to the initial
182Hf/180Hf ratio at the time of
closure of the Hf–W system.
 Time of core formation in Myr
after CAI condensation for
Vesta, Mars, Earth and Moon
versus planet radius as deduced
from Hf–W 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 forms
 Moment of inertia decreases
 Angular velocity of rotation increases
 Rotational energy increases
 Increase in energy of rotation < Decrease in gravitational potential energy
 Total energy must be conserved
 Difference goes into heat
 Estimates: Core formation -> 1000-2000K temperature increase
He
 It is assumed that volatiles were lost during accretion
 Very 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 degasing
 Shows mantle is not well mixed
Tracing with isotopes
 Crust
 Mantle
 Rb/Sr high
 Rb/Sr low
 Sm/Nd low
 Sm/Nd high
 Sr87/Sr86 increases
 Nd143/Nd144 decreases compared
with mantle