2. 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

3. 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

4. Chart of the Nuclides (1)
number of Protons
Isobar (nuclei of equal mass number)
number of Neutrons

5. Chart of the Nuclides (2)
p=n line
number of Protons
number of Neutrons

6. Solar abundance of the elements

7. 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!

8. 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)

9. 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)

10. 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!

11. 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, non-resonant nuclear reaction rates obey a law of the form:
nuclear charges
reduced mass
reaction rate
number densities
temperature
So reaction is fastest between most abundant, least charged pairs of nuclei, and increase in T is needed to make slower reactions significant

12. 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 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!

13. 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 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

14. Solar abundance of the nuclides

15. Stellar Nucleosynthesis IV : Helium Burning, etc.

16. Stellar Nucleosynthesis V: nuclear binding energy
56Fe
H-burning is by far the most effective means of converting mass into energy!
Fusion exothermic
Fusion endothermic 1H A
In principle, nuclear burning by fusion can continue only up to 56Fe, the nucleus with the greatest binding energy per nucleon

17. 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)

18. 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

19. 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:
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

20. 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

21. 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

22. Planetary Systems I: Solar Nebula

23. 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)
Ciesla (2007), Science 318(5850):

24. Planetary Systems II: Density and Size of Planets
Distance from sun, 108 km

25. 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

26. Aside: Meteorite Classification
Life on Mars!

27. 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
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 Zr

28. 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.

29. 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.

30. 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)

31. 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.

32. 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

33. Bulk composition of the Earth and Volatility

34. Bulk composition of the Earth and Volatility

35. 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):