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Lecture 10: Cosmochemistry: origin of nuclei, solar system,
and earth
Questions
• What is the bulk composition of the solar system?
• Where/when/how did the atoms of the solar system originate?
• How did bulk solar system stuff condense into solids and
eventually planets, and how did this process sort the elements?
• What evidence of all this is available from meteorites?
Tools
• The Chart of the Nuclides
Reading
• Albarède, Chapter 9
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Geochemists like to sort the elements in various ways…
useful to keep in mind what category scheme we are using in each lecture
• By nucleosynthetic origin and nuclear properties
• primordial, H burning, red giant processes, neutron capture
• stable, long-lived radioactive, short-lived (extinct?) radioactive
• By volatility in gas-solid equilibria, i.e. by condensation temperature
• refractory, moderately volatile, highly volatile
• By affinity during gross chemical differentiation of the earth
• siderophile, lithophile, atmophile
• By compatibility (solid/melt concentration ratio) in igneous processes
• compatible, incompatible, very incompatible; generally functions
of charge and ionic radius…related to position in periodic table in
systematic ways
• By abundance here, there, or anywhere
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number of Protons
Chart of the Nuclides (1)
Isobar (nuclei
of equal mass
number)
number of Neutrons
4
number of Protons
Chart of the Nuclides (2)
number of Neutrons
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Solar abundance of the elements
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Solar abundance of the elements: things of note
• General decrease in abundance with atomic number (H most abundant,
U least abundant)
• Relative to this trend:
– Big negative anomaly at Be, B, Li
– Moderate positive anomaly around Fe
– Sawtooth pattern from odd-even effect
• This data is obtained from observation of atomic absorption lines in the
solar spectrum, from light passing through solar atmosphere
– 99% of solar system mass is in the sun, so solar composition is good
approximation to bulk solar system composition
– Some elements, for which spectroscopy is difficult, are filled in using
meteorite data
• Successful model of nuclear origins needs to explain all these features
in the abundance pattern!
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Origin of atoms in the solar system
• Two sources of nuclei: nucleosynthesis in the Big Bang and in Stars
• The Big Bang made only H and He
• All other nuclei are manufactured in stars, by three essential kinds of processes:
– Nuclear burning (fusion): PP cycles, CNO bi-cycle, He burning, C burning, O
burning, Si burning…makes atoms up to 40Ca, but no heavier
• These processes happen in main sequence stars and in red giants
– Photodisintegration rearrangement: when thermal radiation reaches gamma-ray
energies it drives rapid nuclear rearrangement creating everything up to 56Fe, but
nothing heavier
– Neutron irradiation: most nuclei heavier than 56Fe are generated by neutron capture,
which follows two paths depending on neutron flux:
• The s-process, in which neutron addition is slow compared to b-decay
• The r-process, in which neutron addition is rapid compared to b-decay
• r-process occurs only in supernovae
– Proton irradiation: some low-abundance nuclei are made by an s-process-like
addition of protons rather than neutrons (p-process)
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The Big Bang
• Primary evidence for hot big bang origin of the universe:
– Hubble expansion
– Microwave background
Kirshner R P PNAS 2004;101:8-13
• linear relationship between distance
and red-shift demonstrates uniform
expansion, implying a point-source
origin
• almost perfect, isotropic 2.7 K
blackbody spectrum of photons created
at recombination (~300 ky after big
bang)
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Big Bang Nucleosynthesis
• Universe starts at temperature (or energy) too hot for normal matter
• At about 1 second, the universe was a hot and dense mixture of free
electrons, protons, neutrons, neutrinos and photons. The ratio of
protons to neutrons is kept at unity as long as energy is high enough
for matter to interact strongly with neutrinos.
• At about 2 seconds, neutrino mediation ends. Since free neutrons
decay with half life of 900 seconds, the proton-to-neutron (p/n) ratio
began to increase.
• After ~30 minutes, when p/n ~ 7, temperatures reached stability range
of small nuclei and 4He (and a bit of 2D and 3He) nuclei consumed the
free neutrons.
• This predicts a mass fraction 4He/(4He+H) ~ 25%, which is indeed
observed…powerful evidence in favor of big bang hypothesis
• Since there is no stable mass 5 nucleus and synthesis of He occurred
on cooling (not heating), no heavy nuclei are formed!
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Stellar Nucleosynthesis I
• Until stars form, there is nothing except H and He
• Gravitational instabilities develop which lead to formation of galaxies
and collapse of molecular clouds to form stars
• At sufficient temperature and density (~107 K), nuclear fusion begins in
star cores
• Due to Coulomb repulsion between positively charged nuclei, nonresonant nuclear reaction rates obey a law of the form:
nuclear charges
reaction rate
number densities
reduced mass
1ù
é
ê æ Z 2 Z 2 Aö 3 ú
r12 µ N1N2 exp ê-z çç 1 2 ÷÷ ú
ê è T ø ú
ê
ú
ë
û
temperature
• So reaction is fastest between most abundant, least charged pairs of nuclei,
and increase in T is needed to make slower reactions significant
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Stellar Nucleosynthesis II : Hydrogen Burning
• None of the two-particle reactions between the major species in
juvenile H+He matter produce a stable product:
–
–
–
1H
+ 1H = 2He (unstable) = 1H + 1H
1H + 4He = 5Li (unstable) = 1H + 4He
4He + 4He = 8Be (unstable) = 4He + 4He
• However, Hans Bethe (1939) showed how hydrogen burning can
begin with the exothermic formation of deuterium:
–
1H
+ 1H = 2D + b+ + n + 1.442 MeV
• This reaction initiates the PPI chain:
2 (1H + 1H = 2D + b+ + n)
2 ( 1H + 2D = 3He + g)
3He + 3He = 4He + 2 1H
Net: 4 1H = 4He + 2 n + g
•
2D/1H
quickly approaches equilibrium value, but this is 1013 times
smaller than the terrestrial value…terrestrial 2D is made elsewhere!
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Stellar Nucleosynthesis III : Helium Burning, etc.
• If 1H becomes so depleted that 1H+1H collisions become too rare to
drive PPI chain fast enough to maintain thermal pressure (after ~106 y
in a red giant star), the core collapses, temperature rises, and at ~2 x
108 K, He burning becomes possible
• This requires particle velocities fast enough that the reaction rate
4He + 8Be = 12C + g
exceeds the decay rate of 8Be (half-life 2.6 x 10-16 s!), despite the
large Coulomb repulsion: Z12Z22 = 64
• Likewise, when 4He runs out, another core collapse heats up the core
enough to initiate C-burning
• This continues up through Si-burning
• This type of nuclear burning produces all the alpha-particle nuclides:
4He, 12C, 16O, 20Ne, 24Mg, 28Si, 32S, 36Ar, 40Ca
• Smaller quantities of 14N, 15N, 13C, Na, P also result
• Explains excesses of a-particle nuclei up to 40Ca, if solar system
contains matter expelled from red giants
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Solar abundance of the nuclides
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Stellar Nucleosynthesis IV : Helium Burning, etc.
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Stellar Nucleosynthesis V: nuclear binding energy
56Fe
H-burning is by far the
most effective means
of converting mass into
energy!
1H
A
• In principle, nuclear burning by fusion can continue only up to 56Fe, the
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nucleus with the greatest binding energy per nucleon
Stellar Nucleosynthesis VI : nuclear statistical equilibrium
• By the time temperature reaches the Si-burning stage, ~3 x 109 K,
thermal radiation reaches gamma-ray energy
– by Wien’s displacement law, the peak radiance is at photon energy
E ~ 5kT ~ 4 x 10-9 T MeV
1 MeV photons have energy
comparable to nuclear binding
energies and allow continued
energy production by a maze of
transmutation reactions.
As this population of reactions
approaches equilibrium ratios of
all nuclear products up to 56Fe,
energy production approaches zero
and total collapse of the stellar
core is inevitable…star ends up a
white dwarf, neutron star, or black
hole (depending on mass)
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Stellar Nucleosynthesis VII : nuclear statistical equilibrium
• Approach to nuclear statistical equilibrium makes definite predictions
about abundance of species in the Si-to-Fe range, and provides a
natural mechanism for the high nuclear binding energy of the Fe
group to be translated into the peak in the solar abundance pattern
This particular model shows a
prediction of abundance after 10
seconds of Si-burning at a
temperature of 4.2 x 109 K
• the lines connect isotopes of
the same element
• overall agreement is not bad
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Stellar Nucleosynthesis VII : neutron capture
• Although Coulomb repulsion prevents reactions between massive
charged nuclei at solar temperatures, neutrons have no charge and
neutron capture reactions can proceed even at room temperature
• When nuclear reactions in stars liberate a flux of neutrons, they are
captured by nuclei in proportion to their neutron capture cross-section
Evidence that stellar material
subjected to neutron flux was
ejected and incorporated into
solar system comes from
correlation of abundance with
neutron capture cross-section:
dN A
= -s A N A + s A-1 N A-1
dt
Tends towards a solution where
the product of abundance and
cross-section sN is a smoothly
varying function, as observed
and modeled with fair accuracy
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Stellar Nucleosynthesis VIII : neutron capture processes
• If neutron flux is slow compared to b-decay times, nuclei follow the
valley of stability and make s-process nuclei
• If neutron flux is so fast that repeated captures occur before b-decay,
nuclei on the neutron dripline (where s goes to zero) are made, which
subsequently decay back to first stable nuclide on each isobar
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Planetary Systems I: Solar Nebula
• The solar system formed from interstellar material already processed by
short-lived early stars (several generations?)…otherwise there would be
no material from which to form rocky planets
• Solar nebula begins hot…few pre-solar solids survive; solids condensed
from vapor of solar composition, as temperature decreased…hence the
key to understanding the distribution of elements in the solar system is
the idea of volatility…the preference of an element for gaseous species
over solids, quantified by the 50% condensation temperature (e.g., 1650
K for Al, 970 K for Na, 3 K for He)
• We can explain final composition and sizes of objects at various
distances from the sun (terrestrial planets, asteroids [meteorite parent
bodies], giant planets, comets) by considering:
– position in the solar nebula (i.e., temperature is >1000 K at
Mercury, <100 K at Jupiter)
– size of the body (i.e., effect of gravity and energy of impacts
towards end of accretion), related to surface density of nebula,
which also decreases away from the sun
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Planetary Systems I: Solar Nebula
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Planetary Systems I: Solar Nebula
• One particular solar nebula model has the
following radial density and temperature structure:
– Surface density S(r) = 6300/r g/cm2 (r in AU)
– Temperature T(r) = 1500/r0.5 K (r in AU)
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Ciesla (2007), Science 318(5850): 613-615
Planetary Systems II: Density and Size of Planets
Distance from sun, 108 km
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Planetary Systems III: Condensation sequence
Mercury
Venus
Earth
Mars
Condensing the ices is what
gave the giant planets the
mass to gravitationally
capture H and He from nebula
Jupiter
Saturn
Bulk oxidation state of a
planet is set by how much O
is condensed as FeO and how
much H is retained as H2O
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Life on Mars!
Aside: Meteorite Classification
Planetary Systems IV: Carbonaceous Chondrites
Except for the most
volatile elements (i.e.,
more volatile than
nitrogen), CI
carbonaceous chondrites
are excellent models of
bulk solar system
composition and hence
may be close to bulk
earth composition
Zr
While the sun is basically
H+He, the Earth is
dominated by O, Si, Mg,
Fe. Much Fe is in core,
leaving rocky earth
dominated by O, Si, Mg
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Planetary Systems IV: Carbonaceous Chondrites
Among the several classes of carbonaceous chondrites, relative abundance of all elements are
controlled by volatility; this plot shows the CV chondrites versus CI. Presumably similar
volatility control was active during accretion of the Earth or its source materials.
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Planetary Systems IV: Carbonaceous Chondrites
Laboratory quantification of volatility by condensation temperature shows that relative
abundance in carbonaceous chondrites is controlled by pure vapor-solid equilibrium down to
~900 K, then adsorption must become significant for retaining many highly volatile elements.
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Bulk composition of the Earth
• Primitive Upper Mantle (PUM) composition is determined from intersection of
chondritic meteorite array with mantle xenolith array
• PUM is not equal to any class of meteorites, so if bulk earth is, e.g., CI chondrite
in composition, then lower mantle must be compositionally distinct (or Si is a
major constituent of core)
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Bulk composition of the Earth
• More recent work shows pervasive volatility control even among moderately
refractory elements; the Earth is on the Carbonaceous chondrite line, but ordinary
chondrites are different except for the very most refractory elements.
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Bulk composition of the Earth
• Carbonaceous chondrites plot on simple volatility
control lines in consistent order; Earth is on the line but in
different positions for differently volatile elements 32
Bulk composition of the Earth and Volatility
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Bulk composition of the Earth and Volatility
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Aside: pre-solar grains (aka stardust)
Not quite everything
was vaporized at solar
nebula stage – we have
pre-solar grains of:
Diamond, Graphite,
SiC, Si3N4, Al2O3, TiO2,
MgAl2O4, FeCr2O4,
CaAl12O19, and recently
a few silicates.
Recognized by extreme
isotopic anomalies due
to different
nucleosynthetic sources.
A. M. Davis (2011) PNAS
108(48):19142-19146
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