Lecture 11: Periodic table, geochemical affinity, core formation, lunar origin

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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

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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)
(atmophile)
(lithophile)
(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
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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.
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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?
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Earth Structure III Other geophysical evidence

• Moment of Inertia Ratio
• For uniform density sphere, I 0.4 M R2
• For Earth, I 0.331 M R2
• (For Moon, 0.394 Mars 0.365 Sun 0.06!)
• Magnetic Field
• Dynamo requires conducting liquid layer

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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 Earths
  mantle)
• the common oxygen-isotope line of the Earth-moon
  system
• the early Lunar magma ocean

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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 heatingenough 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
  bodylate, 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

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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
  50-70 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 lt 100 Ma
• Conclusion Core formation before the end of
  accretion, too late for short-lived nuclide
  heating, too fast for long-lived nuclide
  heatingimpact 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
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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
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Geochemical Affinity
In the classification scheme of Goldschmidt,
elements are divided according to how they
partition between coexisting silicate liquid,
sulfide liquid, metallic liquid, and gas
phasedefined 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
silicatesconfirmed by iron and achondrite
meteorites (but at high P, no separate sulfide
phase)
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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
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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,
  , n1
• 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
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Electronic Chemistry and the Periodic Table II
Allowed quantum states (n,l,m,s) n1 1,0,0,1
/2 1s (2 electrons) 2 electrons n2 2,0,0
,1/2 2s (2 electrons) 2,1,(1,0,1),1/2 2p
(6 electrons) 8 electrons n3 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 n4 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
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Electronic Chemistry and the Periodic Table III
Filling sequence 1s22s22p63s23p64s23d104p65s24d
104p66s24f145d106p67s25f146d10...
A mnemonic for the filling sequencefollow the
gray arrows
Examples C (Z6) 1s22s22p2 Si (Z14)
1s22s22p63s23p2 Ne3s23p2 Ge (Z32)
1s22s22p63s23p64s23d104p2
Ar4s23d104p2 (These elements have same number
of valence (outer-shell) electrons, hence related
chemical behavior
Energy of orbitals with different l split for Zgt1
due to differential shielding and penetration
near nucleus
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Electronic Chemistry and the Periodic Table IV
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Systematics of the Periodic Table IP and
electronegativity
First Ionization Potential (eV)
Pauling Electronegativity
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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.

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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
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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
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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, r1.1Å
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.
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Valence, ionic radii, and Goldschmidts 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 Goldschmidts 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

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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 (Henrys 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 lt 1, the
trace element is termed incompatible. If the bulk
partition coefficient gt 1, the trace element is
compatible
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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.
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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.
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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. Differentiatio
n 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)
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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
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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 DRb0, then F1.6 and we may assign D to
all the other elements.
Continental crust
Mid-ocean ridge basalt
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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.
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Partition coefficients and Earth differentiation
FCresidue/Cliquid _at_D0
DCliquid/Cresidue