1. Lecture 11: Periodic table, geochemical affinity, core formation, lunar origin
Last time, we made the Earth and discussed how much of each element was incorporated and why
Today we begin to review the differentiation of the Earth into its major reservoirs and the chemical behavior of the elements during these processes
Questions:
What is the gross-scale chemical structure of the Earth (core, mantle, oceanic crust, continental crust, hydrosphere, atmosphere) and how do we know?
How did the core form, and when?
Which elements are partitioned into which gross reservoirs and why?
Where did the moon come from and how does it relate to differentiation of the Earth?
Tools
The Periodic Table of the Elements

2. Summary of Earth Differentiation
(nucleosynthesis, mixing)
Solar Nebula
(volatiles)
(gas-solid equilibria)
(refractories)
Condensation and Accretion
(late veneer)
(continuing
cometary flux?)
(siderophile & chalcophile)
(melting; gravity and geochemical affinity)
(lithophile)
(atmophile)
(lost due to impacts)
Core
Silicate Earth
Primitive Atmosphere
(freezing)
(catastrophic
impact)
Moon
Primitive Mantle
Inner
Core
Outer
Core
(partial melting;
liquid-crystal partitioning)
degassing
Upper Mantle
Lower Mantle
Continental Crust
(plate tectonics: partial melting, recycling)
(hotspot plumes)
degassing
Modern Ocean &
Atmosphere
Oceanic Crust

3. Earth Structure I: seismic evidence
• From velocity structure, density structure, and existence of refracted, reflected, and converted phases at various source-receiver distances, we know the earth has a core, a mantle, and a crust. We know the depths of the boundaries. We know the outer core is liquid, the other regions are solid.

4. Earth Structure II: chemical evidence
Relative to volatility trend, some elements are grossly depleted in silicate portion of the earth (but N.B. the most depleted elements are in chondritic relative proportions) …if our understanding of accretion is right there is a big hidden reservoir. What do the depleted elements have in common?

5. Earth Structure III: Other geophysical evidence
Moment of Inertia Ratio
For uniform density sphere, I = 0.4 M R2
For Earth, I = M R2
(For Moon, 0.394; Mars 0.365; Sun 0.06!)
Magnetic Field
Dynamo requires conducting liquid layer

6. Origin of the Moon
Before the Apollo moon landings and the direct geochemical analysis of lunar rocks, several theories of lunar origin competed, none of them especially reasonable:
Intact Capture
Co-accretion
Earth fission
Disintegrative Capture
The present favored and widely accepted hypothesis is collisional ejection from the earth during impact of a Mars-sized planetesimal after Earth core formation
The evidence bearing on the problem includes:
the very large angular momentum of the Earth-Moon system (but not big enough to fission the Earth)
the depletion of the Moon in volatile elements (much like Earth)
the depletion of the Moon in Fe (like Earth’s mantle)
the common oxygen-isotope line of the Earth-moon system
the early Lunar magma ocean

7. Core Formation: How?
Core/Mantle chemistry is explained by equilibria involving Fe liquid. Also, efficient separation of dense Fe and buoyant silicates requires at least one component to be molten
Heat necessary to melt at least Fe fraction of Earth is derived from two sources
(Fast) Impact heating…enough to vaporize earth if all retained at once
Total gravitational binding energy of uniform-density earth
(Slower) Radioactivity (including short-lived nuclides)
Relative importance of these two sources for each planet or planetesimal depends on time of accretion, rate of accretion, and size of the body…late, slow, and small bodies may not melt at all (hence primitive meteorites)
Once core formation begins, it is catastrophic and self-sustaining
gravitational energy dissipated by moving dense material downward is ~10% of total gravitational binding energy of earth, enough to heat earth 3000 K and melt it completely

8. Core Formation: When?
We can distinguish whether (a) impact and short-lived nuclides or (b) long-lived radionuclides raised T to melting and allowed core formation by determining how quickly it occurred
Moon postdates core formation and age of moon is no more than ~60 Ma after formation of meteorites; moon formation is part of earth accretion
182Hf-182W (extinct siderophile-lithophile pair): Earth and moon are not chondritic, so core formation ≤ 30 Ma after iron meteorite formation
Xe isotopes requires that accretion completed Ma after meteorites
Pb segregation into core or by volatile loss altered U/Pb ratio of mantle affecting subsequent evolution of Pb isotopes; implies t < 100 Ma
Conclusion: Core formation before the end of accretion, too late for short-lived nuclide heating, too fast for long-lived nuclide heating…impact driven
formation of irons and achondrites
age of moon
end of earth accretion
formation of chondrites
4.55 Ga
4.50
4.45
permissible range of core formation times

9. Core Formation: more How?
CORE MERGING EVENT
(Hf-W timescale ≠ planet formation timescale
Early differentiation in Moon-sized bodies
collision
EMULSIFICATION DURING IMPACT (Hf-W timescale ~ planet formation timescale if emulsification is sufficiently small scale
Early differentiation in Moon-sized bodies
collision

10. Geochemical Affinity Atmophile Lithophile Chalcophile Siderophile
• In the classification scheme of Goldschmidt, elements are divided according to how they partition between coexisting silicate liquid, sulfide liquid, metallic liquid, and gas phase…defined by examining ore smelting slags and meteorites
• Melting a chondrite gives 3 immiscible liquids plus vapor:
Atmophile
Gas Phase
H, He, N, Noble gases
Alkalis, Alkaline Earths, Halogens, B, O, Al, Si, Sc, Ti, V, Cr, Mn, Y, Zr, Nb, Lanthanides, Hf, Ta, Th, U
Lithophile
Silicate Liquid
Sulfide Liquid
Chalcophile
Cu, Zn, Ga, Ag, Cd, In, Hg, Tl, As, S, Sb, Se, Pb, Bi, Te
Metallic Liquid
Siderophile
Fe, Co, Ni, Ru, Rh, Pd, Os, Ir, Pt, Mo, Re, Au, C, P, Ge, Sn
• To first order, the distribution of elements between core and mantle resembles equilibrium partitioning between metal liquid and silicates…confirmed by iron and achondrite meteorites (but at high P, no separate sulfide phase)

11. Geochemical Affinity and Electronic Chemistry
• OK, but what makes an element siderophile or lithophile? Notably, the Goldschmidt categories are well-grouped in the periodic table of the elements:

12. Electronic Chemistry and the Periodic Table
• OK, but what is the periodic table? A graph of the shell-structure of electrons in neutral atoms. This is a useful predictor of chemical behavior because only outer-shell electrons participate in ordinary chemical reactions
Quantum mechanics describes the energy-levels or orbitals that the electron can occupy, each described by four quantum numbers n, l, m, s
n, the energy level, any + integer (for H it is the energy:
l, the angular momentum, is allowed values 0, 1, …, n–1
m, the magnetic moment, is allowed values –l, …, l
s, the spin, is +1/2 or –1/2 for electrons
The periodic table results from two more rules. A neutral atom with Z protons also has Z electrons and:
The Pauli Exclusion Principle: no two electrons in the same atom can have the same set of quantum numbers
The Aufbau Principle: the ground state of an atom is found by filling the orbitals from the lowest energy level upwards
Energy levels of H atom

13. Electronic Chemistry and the Periodic Table II
• Allowed quantum states (n,l,m,s):
n=1: 1,0,0,±1/2 1s (2 electrons) [2 electrons]
n=2: 2,0,0 ,±1/2 2s (2 electrons)
2,1,(–1,0,1),±1/2 2p (6 electrons) [8 electrons]
n=3: 3,0,0 ,±1/2 3s (2 electrons)
3,1,(–1,0,1),±1/2 3p (6 electrons)
3,2,(0,±1,±2),±1/2 3d (10 electrons) [18 electrons]
n=4: 4,0,0 ,±1/2 4s (2 electrons)
4,1,(–1,0,1),±1/2 4p (6 electrons)
4,2,(0,±1,±2),±1/2 4d (10 electrons)
4,3,(0,±1,±2,±3),±1/2 4f (14 electrons) [32 electrons]

14. Electronic Chemistry and the Periodic Table III
• Filling sequence: 1s22s22p63s23p64s23d104p65s24d104p66s24f145d106p67s25f146d10...
A mnemonic for the filling sequence…follow the gray arrows:
• Examples:
C (Z=6) 1s22s22p2
Si (Z=14) 1s22s22p63s23p2 = [Ne]3s23p2
Ge (Z=32) 1s22s22p63s23p64s23d104p2 =
[Ar]4s23d104p2
(These elements have same number of valence (outer-shell) electrons, hence related chemical behavior
Energy of orbitals with different l split for Z>1 due to differential shielding and penetration near nucleus

15. Electronic Chemistry and the Periodic Table IV

16. Systematics of the Periodic Table: IP and electronegativity
First Ionization Potential (eV)
Pauling Electronegativity

17. Systematics of the Periodic Table: columns and valence
A filled shell of 8 s and p electrons is especially stable; half-filled p or d shells also have extra stability. Hence the ions that an element forms are largely governed by column in the periodic table (i.e., the number of electrons in the outer shell of the neutral atom)
Elements with small electronegativity easily achieve filled outer shell by giving up valence electrons and becoming positively-charged cations. Elements with large electronegativity easily achieve filled outer shell by accepting extra electrons and becoming negatively-charged anions.

18. Geochemical significance of electronegatvity
Pairs of atoms with very different electronegativity achieve greatest stability by trading electrons completely and forming ionic bonds. This is the dominant bonding environment in nearly all minerals. Elements with very high or low electronegativity therefore tend to be lithophile.
Pairs of atoms with nearly equal electronegativity share electrons in covalent bonds. This is the dominant bonding process in organic compounds, sulfides, and compound anions (CO32-, SO42-, etc.). Elements with intermediate electronegativity and full or empty d-shells are happiest in covalent bonds with S and are therefore chalcophile.
Elements with intermediate electronegativity and ~4 to ~8 d electrons are stabilized in neutral metallic bonding environments and tend to be siderophile.
Delocalized conduction electrons
NaCl, ionic
CCl4, covalent
Cr, metallic

19. Systematics of the Periodic Table: valence and ionic radii
• geochemical behavior of an element is largely governed by valence (what charge ion it tends to form) and ionic radius (what size site the ion will fit into)…both are systematically related to column and period in the periodic table

20. Systematics of the Periodic Table: valence and ionic radii
• Lithophiles have ionic radii that allow charge-balanced formation of oxides [r(O2-)=1.4Å)]
• Chalcophiles have ionic radii that allow charge-balanced formation of sulfides [r(S2-)~1.8Å)]
• e.g., Hg2+, r=1.1Å: r(Hg2+)/r(S2-)=0.6, allows octahedral coordination in HgS. r(Hg2+)/r(O2-)=0.85, requires 8-coordination, a much more open structure, unfavorable except at very low pressure.

21. Valence, ionic radii, and Goldschmidt’s rules
• Except in the rare case of complete melting, geochemical behavior of elements is usually related to whether they “fit” in the structure of solid minerals.
• Which minerals are present is controlled by the major elements, which we discuss in Lecture 4.
• The behavior of minor and trace elements is then controlled by whether they can substitute for a major constituent of a mineral. The ease of substitution obeys Goldschmidt’s rules:
Ions whose radii differ by less than 15% readily substitute each other
Ions whose charge differ by one unit can substitute if coupled to a suitable charge-balancing substitution; ions differing by more than one charge do not substitute extensively.
In any substitution the ion with the higher ionic potential (charge/radius) forms a stronger bond and a more stable mineral
Ions with very different electronegativity will not substitute much even if charge and radius match

22. Trace elements and partition coefficients
• Definition: a trace element is an element present at concentration too low to significantly affect the phase relations; hence it is a passive agent in the processes determined by the major and minor elements. In particular the behavior of the trace element does not depend on its own concentration (Henry’s Law).
To use trace elements, we need to know how they are distributed, or partitioned, among phases. Most often this is expressed by looking at the ratio of concentration in a solid phase to concentration in the liquid phase, the partition coefficient
• When several minerals are present in the rock, then we can find the bulk partition coefficient by a suitable weighted average of mineral partition coefficients:
• If the bulk partition coefficient < 1, the trace element is termed incompatible. If the bulk partition coefficient > 1, the trace element is compatible

23. Trace elements and partition coefficients
• Partition coefficients are most useful when they are constant. They are indeed independent of the concentration of the trace element, but they do vary somewhat with pressure, temperature, and the compositions of the minerals and melts.
• The values of partition coefficients can often be rationalized in terms of the ionic radius of the trace element and the strain associated with inserting an anomalous size (and sometimes charge) ion into a crystallographic site.
The figure shows Dplagioclase/melt for a variety of +1, +2, and +3 ions, showing the parabolic relationship between log D and ionic radius that results from lattice strain.
Since the essential minerals during mantle melting processes are olivine, pyroxenes, spinel, and garnet, bulk D for each element is determined by its charge and size similarities to the major cations in the sites of these minerals: tetrahedral Si4+ and Al3+, and octahedral Mg2+, Fe2+, and Ca2+.

24. Equations for trace element behavior
• Let Cio be the original concentration of element i in the source.
• Cis is the concentration in the solid residue.
• Cim is the concentration in the melt phase.
• The extent of melting by mass is F.
Batch melting is a closed system process where all melt remains in contact and equilibrium with the residue.
Conservation of mass gives:
(2.1)
Substituting the definition of Di = Cis/Cim and rearranging, we get
(2.2)
Limiting behaviors:
• for a perfectly incompatible element Di = 0 and Cim = Cio/F.
• For the first increment of melting, F = 0 and Cim = Cio/D.
• When melting is complete, F = 1 and Cim = Cio.
This equation also describes equilibrium crystallization.

26. Equations for trace element behavior
Fractional Crystallization is an open system process in which each increment of solid is immediately removed from the system as if forms. There can be no reaction between fractionated solids and remaining liquids. This is an example of a Rayleigh distillation process.
Differentiation of (2.1) gives:
(2.3)
Solids are removed from the system without reacting so dCis = 0:
Integrating subject to Cim = Cio at F = 1, the solution is
(2.4)

28. Equations for trace element behavior
Fractional Melting is not the reverse of fractional crystallization, since it is the melt that is immediately removed from the system as if forms.
Now melt is removed without reacting so dCim = 0:
Integrating subject to Cis = Cio at F = 0, the solution is
And since the instantaneous increment of fractional melt is in equilibrium with this residue, we can use Cim = Cis/D to obtain

29. Partition coefficients and Earth differentiation
Partition coefficients can be measured experimentally at particular conditions, or inferred from natural samples. The partition coefficients that obtained during melting of the primitive mantle to form the continents can be obtained (on the assumption of batch melting) from the bulk composition of the continental crust:
Here elements are ordered by enrichment in the continental crust over bulk silicate earth, a sort of qualitative partition coefficient. If we assume DRb=0, then F=1.6% and we may assign D to all the other elements.
Continental crust
Mid-ocean ridge basalt

30. Partition coefficients and Earth differentiation
The humped pattern of mid-ocean ridge basalts in these figures can be modeled as resulting from 8% melting of the source previously depleted of incompatible elements by 1.6% melting to form the continental crust. This demonstrates that the upper mantle is the complementary depleted reservoir to the continents.
Continental crust
Mid-ocean ridge basalt

31. Partition coefficients and Earth differentiation
D=Cliquid/Cresidue