Geochemists like to sort the elements in various ways … By nucleosynthetic origin and nuclear properties primordial, H burning, red giant processes, neutron capture, proton capture stable, long-lived radioactive, short-lived (extinct?) radioactive By volatility in gas-solid equilibria, i.e. by condensation temperature (50% condensation temperature : the temperature for which the equilibrium vapor pressure drops to 50% of its value at the point where the cooling trajectory initially crosses the equilibrium line) refractory, moderately volatile, highly volatile 1) Condensation T ; sensitive to C/O : if C/O>1, many elements condense as carbides or sulrfides 2) Refractory ; remain solid at high T : Al, Al 2 O 3

Geochemists like to sort the elements in various ways … By affinity during gross chemical differentiation of the earth siderophile(iron-loving : oxsides with Gibb’s energy less negative than that of FeO ), lithophile(rock-loving : oxside with Gibb’s energy more negative than that of FeO), Atmophile (N,C,O,noble gases), charcophile (literally copper-loving, is used for a positive affinity for sulfur. In meteorites associate with the mineral FeS(troilite)) 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( 예 : ionic radii for Lanthanides)

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

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

Solar abundance of the elements

General decrease in abundance with atomic number (H most abundant, U least abundant) General decrease in abundance with atomic number (H most abundant, U least abundant) Relative to this trend: Relative to this trend: Big negative anomaly at Be, B, Li Big negative anomaly at Be, B, Li Moderate positive anomaly around Fe Moderate positive anomaly around Fe Sawtooth pattern from odd-even effect 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 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 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 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! Successful model of nuclear origins needs to explain all these features in the abundance pattern! Solar abundance of the elements: things of note

Origin of atoms in the solar system Two sources of nuclei: nucleosynthesis in the Big Bang and in Stars Two sources of nuclei: nucleosynthesis in the Big Bang and in Stars The Big Bang made only H and He, Li, Be, B The Big Bang made only H and He, Li, Be, B All other nuclei are manufactured in stars, by three essential kinds of processes: 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 32 S, but no heavier Nuclear burning (fusion): PP cycles, CNO bi-cycle, He burning, C burning, O burning, Si burning … makes atoms up to 32 S, but no heavier These processes happen in normal stars and in red giants These processes happen in normal stars and in red giants Photodisintegration rearrangement: when thermal radiation reaches gamma-ray energies it drives rapid nuclear rearrangement creating everything up to 56 Fe, but nothing heavier Photodisintegration rearrangement: when thermal radiation reaches gamma-ray energies it drives rapid nuclear rearrangement creating everything up to 56 Fe, but nothing heavier Neutron irradiation: most nuclei heavier than 56 Fe are generated by neutron capture, which follows two paths depending on neutron flux: Neutron irradiation: most nuclei heavier than 56 Fe are generated by neutron capture, which follows two paths depending on neutron flux: The s-process, in which neutron addition is slow compared to  -decay The s-process, in which neutron addition is slow compared to  -decay The r-process, in which neutron addition is rapid compared to  -decay The r-process, in which neutron addition is rapid compared to  -decay r-process occurs only in supernovae 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) Proton irradiation: some low-abundance nuclei are made by an s- process-like addition of protons rather than neutrons (p-process)

The Big Bang Primary evidence for hot big bang origin of the universe: Primary evidence for hot big bang origin of the universe: Hubble expansion – Microwave background Hubble expansion – Microwave background linear relationship between distance and red-shift demonstrates uniform expansion, implying a point-source origin perfect, isotropic 2.7 K blackbody spectrum of photons created at recombination (~300 ky after big bang)

Big Bang Nucleosynthesis Universe starts at temperature (or energy) too hot for normal matter 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 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. 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 4 He (and a bit of 2 D and 3 He) nuclei consumed the free neutrons. After ~30 minutes, when p/n ~ 7, temperatures reached stability range of small nuclei and 4 He (and a bit of 2 D and 3 He) nuclei consumed the free neutrons. This predicts a mass fraction 4 He/( 4 He+H) ~ 25%, which is indeed observed … powerful evidence in favor of big bang hypothesis This predicts a mass fraction 4 He/( 4 He+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! Since there is no stable mass 5 nucleus and synthesis of He occurred on cooling (not heating), no heavy nuclei are formed!

Stellar Nucleosynthesis I Until stars form, there is nothing except H and He 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 Gravitational instabilities develop which lead to formation of galaxies and collapse of molecular clouds to form stars At sufficient temperature and density (~10 7 K), nuclear fusion begins in star cores At sufficient temperature and density (~10 7 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: Due to Coulomb repulsion between positively charged nuclei, non-resonant nuclear reaction rates obey a law of the form: reaction rate number densities nuclear chargesreduced mass temperature So reaction is fastest between most abundant, least charged pairs of nuclei, and increase in T is needed to make slower reactions significant

Stellar Nucleosynthesis II : Hydrogen Burning None of the two-particle reactions between the major species in juvenile H+He matter produce a stable product: None of the two-particle reactions between the major species in juvenile H+He matter produce a stable product: 1 H + 1 H = 2 He (unstable) = 1 H + 1 H 1 H + 1 H = 2 He (unstable) = 1 H + 1 H 1 H + 4 He = 5 Li (unstable) = 1 H + 4 He 1 H + 4 He = 5 Li (unstable) = 1 H + 4 He 4 He + 4 He = 8 Be (unstable) = 4 He + 4 He 4 He + 4 He = 8 Be (unstable) = 4 He + 4 He However, Hans Bethe (1939) showed how hydrogen burning can begin with the exothermic formation of deuterium: However, Hans Bethe (1939) showed how hydrogen burning can begin with the exothermic formation of deuterium: 1 H + 1 H = 2 D +  MeV 1 H + 1 H = 2 D +  MeV This reaction initiates the PPI chain: This reaction initiates the PPI chain: 2 ( 1 H + 1 H = 2 D +  + +  1 H + 2 D = 3 He +  1 H + 2 D = 3 He +  3 He + 3 He = 4 He + 2   3 He + 3 He = 4 He + 2   Net: 4 1 H = 4 He  Net: 4 1 H = 4 He  2 D/ 1 H quickly approaches equilibrium value, but this is times smaller than the terrestrial value … terrestrial 2 D is made elsewhere! 2 D/ 1 H quickly approaches equilibrium value, but this is times smaller than the terrestrial value … terrestrial 2 D is made elsewhere!

Stellar Nucleosynthesis III : Helium Burning, etc. If 1 H becomes so depleted that 1 H+ 1 H collisions become too rare to drive PPI chain fast enough to maintain thermal pressure (after ~10 6 y in a red giant star), the core collapses, temperature rises, and at ~2 x 10 8 K, He burning becomes possible If 1 H becomes so depleted that 1 H+ 1 H collisions become too rare to drive PPI chain fast enough to maintain thermal pressure (after ~10 6 y in a red giant star), the core collapses, temperature rises, and at ~2 x 10 8 K, He burning becomes possible This requires particle velocities fast enough that the reaction rate This requires particle velocities fast enough that the reaction rate 4 He + 8 Be = 12 C +  exceeds the decay rate of 8 Be (half-life 2.6 x s!), despite the large Coulomb repulsion: Z 1 2 Z 2 2 = 1024 Likewise, when 4 He runs out, another core collapse heats up the core enough to initiate C-burning Likewise, when 4 He runs out, another core collapse heats up the core enough to initiate C-burning This continues up through Si-burning This continues up through Si-burning This type of nuclear burning produces all the alpha-particle nuclides: 4 He, 12 C, 16 O, 20 Ne, 24 Mg, 28 Si, 32 S This type of nuclear burning produces all the alpha-particle nuclides: 4 He, 12 C, 16 O, 20 Ne, 24 Mg, 28 Si, 32 S Smaller quantities of 14 N, 15 N, 13 C, Na, P also result Smaller quantities of 14 N, 15 N, 13 C, Na, P also result Explains excesses of  -particle nuclei up to 40 Ca, if solar system contains matter expelled from red giants Explains excesses of  -particle nuclei up to 40 Ca, if solar system contains matter expelled from red giants

Solar abundance of the nuclides

Stellar Nucleosynthesis IV : Helium Burning, etc.

Stellar Nucleosynthesis V: nuclear binding energy In principle, nuclear burning by fusion can continue only up to 56 Fe, the nucleus with the greatest binding energy per nucleon A 56 Fe 1H1H Fusion exothermic Fusion endothermic H-burning is by far the most effective means of converting mass into energy!

Stellar Nucleosynthesis VI : nuclear statistical equilibrium By the time temperature reaches the Si-burning stage, ~3 x 10 9 K, thermal radiation reaches gamma-ray energy By the time temperature reaches the Si-burning stage, ~3 x 10 9 K, thermal radiation reaches gamma-ray energy by Wien ’ s displacement law, the peak radiance is at photon energy by Wien ’ s displacement law, the peak radiance is at photon energy E ~ 5kT ~ 4 x 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 56 Fe, 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)

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 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 10 9 K the lines connect isotopes of the same element overall agreement is not bad

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 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 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  N is a smoothly varying function, as observed and modeled with fair accuracy

Stellar Nucleosynthesis VIII : neutron capture processes If neutron flux is slow compared to  -decay times, nuclei follow the valley of stability and make s-process nuclei If neutron flux is slow compared to  -decay times, nuclei follow the valley of stability and make s-process nuclei If neutron flux is so fast that repeated captures occur before  -decay, nuclei on the neutron dripline (where  goes to zero) are made, which subsequently decay back to first stable nuclide on each isobar If neutron flux is so fast that repeated captures occur before  -decay, nuclei on the neutron dripline (where  goes to zero) are made, which subsequently decay back to first stable nuclide on each isobar

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 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) 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: 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, 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) size of the body (i.e., effect of gravity and energy of impacts towards end of accretion)

Planetary Systems II: Density and Size of Planets Distance from sun, 10 8 km

Planetary Systems III: Condensation sequence Mercury Venus Earth Mars Jupiter Saturn Condensing the ices is what gave the giant planets the mass to gravitationally capture H and He from nebula Bulk oxidation state of a planet is set by how much O is condensed as FeO and how much H is retained as H 2 O

Aside: Meteorite Classification Life on Mars!

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

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.

Bulk composition of the Earth and Volatility