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
1
Summary of Earth Differentiation
(nucleosynthesis, mixing)
Solar Nebula
(volatiles)
(gas-solid equilibria)
(refractories)
(late veneer)
(siderophile &
chalcophile)
Condensation and Accretion
(melting; gravity and geochemical affinity)
(lithophile)
Core
Silicate Earth
(atmophile)
Primitive Atmosphere
(freezing)
Inner
Core
(continuing
cometary
flux?)
Primitive Mantle
Outer
Core
Lower Mantle
(hotspot plumes)
(lost due to
impacts)
(catastrophic
impact)
(partial melting;
liquid-crystal partitioning)
Upper Mantle
Moon
degassing
Continental Crust
(plate tectonics: partial
melting, recycling)
Oceanic Crust
degassing
Modern Ocean &
Atmosphere 2
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.
3
Earth Structure II: chemical evidence
10
Bulk Earth /CI = volatility
Silicate Earth/CI = ?
Mg
1
V
Cr
Si
Gd
Na
0.1
K
B
Fe
W
Co
Cu
Ni
Rb
Zn
In
Cs
Sn
P
Mo
Sb
As
0.0 1
Ge
Pb
Ag
I
Au
Rh
Os
Ir
Pt
Ru
Re
Pd
Cd
Hg
Br
Bi
Te
S
C
Se
0.0 01
N
0.0 001
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?
4
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
5
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
6

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
1
T 
MC p
R

0
GMdM
3 GM 3 107 J/kg
uniform 
 3
 30000 K!
r
5C p R
10 J/kg/K
• (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
7
3000 K and melt it completely
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 < 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
formation of chondrites
4.55 Ga
end of earth accretion
4.50
permissible range of core formation times
4.45
8
Core Formation: more How?
Early differentiation in
Moon-sized bodies
Early differentiation in
Moon-sized bodies
collision
collision
CORE MERGING EVENT
(Hf-W timescale ≠ planet formation timescale
EMULSIFICATION DURING IMPACT
(Hf-W timescale ~ planet formation
timescale if emulsification is sufficiently
small scale
9
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 phase…defined by examining ore smelting slags and meteorites
• Melting a chondrite gives 3 immiscible liquids plus vapor:
Atmophile
H, He, N, Noble gases
Silicate Liquid
Lithophile
Alkalis, Alkaline Earths,
Halogens, B, O, Al, Si, Sc, Ti,
V, Cr, Mn, Y, Zr, Nb,
Lanthanides, Hf, Ta, Th, U
Sulfide Liquid
Chalcophile
Cu, Zn, Ga, Ag, Cd, In, Hg,
Tl, As, S, Sb, Se, Pb, Bi, Te
Siderophile
Fe, Co, Ni, Ru, Rh, Pd, Os, Ir,
Pt, Mo, Re, Au, C, P, Ge, Sn
Gas Phase
Metallic Liquid
• To first order, the distribution of elements between core and mantle resembles
equilibrium partitioning between metal liquid and silicates…confirmed by iron
10
and achondrite meteorites (but at high P, no separate sulfide phase)
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:
IA
Atmophile
IIA
IIIA IVA VA
Siderophile
VIA VIIA VIIIA
1
2
H
1
3
Li
11
20
K
37
38
B
13
IIIB IVB
22
21
VB
23
40
39
Y
26
27
IB
28
29
IIB
30
C
14
Al
31
8
7
N
Si
32
O
16
15
P
F Ne
S
Cl Ar
44
43
74
105
36
35
Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br
42
73
18
17
34
33
10
9
45
47
46
48
49
50
51
52
53
Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te
104
Fr Ra
75
76
77
78
106
108
107
79
80
82
81
Pt Au Hg Tl
83
84
Kr
54
I
Xe
85
86
Pb Bi Po At
Rn
109
Rf Db Sg Bh Hs Mt
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
89
Actinides
25
Hf Ta W Re Os Ir
88
Lanthanides
V
VIIIB
VIB VIIB
24
41
72
56
Cs Ba
87
6
Chalcophile
Ca Sc Ti
Rb Sr
55
7
Be
Na Mg
4
6
5
12
19
5
He
Artificial
4
2
3
Lithophile
90
91
92
93
94
95
96
97
98
99
100
101
102
103
Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr
11
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:
Energy levels of
H atom
• 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
12
Electronic Chemistry and the Periodic Table II
• Allowed quantum states (n,l,m,s):
n=1:
1,0,0,±1/2
n=2:
2,0,0 ,±1/2
2,1,(–1,0,1),±1/2
n=3:
3,0,0 ,±1/2
3,1,(–1,0,1),±1/2
3,2,(0,±1,±2),±1/2
n=4:
4,0,0 ,±1/2
4,1,(–1,0,1),±1/2
4,2,(0,±1,±2),±1/2
4,3,(0,±1,±2,±3),±1/2
1s (2 electrons)
2s (2 electrons)
2p (6 electrons)
3s (2 electrons)
3p (6 electrons)
3d (10 electrons)
4s (2 electrons)
4p (6 electrons)
4d (10 electrons)
4f (14 electrons)
[2 electrons]
[8 electrons]
[18 electrons]
[32 electrons]
13
Electronic Chemistry and the Periodic Table III
• Filling sequence: 1s22s22p63s23p64s23d104p65s24d104p66s24f145d106p67s25f146d10...
A mnemonic for the filling
sequence…follow the gray arrows:
56
88
4f
20
38
5f
70
6f
7f
102
3d 4d 5d 6d 7d
4
12
30
48
80
2p 3p 4p 5p 6p 7p
0
2
1s
2s
2
Energy of orbitals with
different l split for Z>1
due to differential
shielding and penetration
near nucleus
10
18
3s
4
36
4s
12
54
86
5s 6s
20
38
7s
56
88
• 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
14
related chemical behavior
Electronic Chemistry and the Periodic Table IV
10
2
IA
IIIA IVA VA
IIA
1
3
4
Li
2
11
3
Na Mg
37
He
Rb Sr
IIIB IVB
22
21
VB
23
40
39
Y
56
f filling
B
27
IB
29
28
IIB
30
C
14
Al
31
8
7
N
Si
32
O
16
15
P
F
18
S
Cl Ar
44
43
74
105
36
35
Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br
42
73
Ne
17
34
33
10
9
45
47
46
48
49
50
51
52
53
Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te
104
Fr Ra
75
76
77
106
107
108
78
Ir
79
80
81
82
Pt Au Hg Tl
84
83
Kr
54
I
Xe
86
85
Pb Bi Po At
Rn
109
Rf Db Sg Bh Hs Mt
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
89
Actinides
V
26
25
Hf Ta W Re Os
88
Lanthanides
VIIIB
VIB VIIB
24
41
72
Cs Ba
87
6
13
Ca Sc Ti
38
55
7
20
K
4
6
2
5
p filling
Be
VIA VIIA VIIIA
d filling
12
19
5
s filling
H
1
6
90
91
Ac Th Pa
92
93
94
95
96
97
98
99
100
101
102
U Np Pu Am Cm Bk Cf Es Fm Md No
103
Lr
14
15
Pauling Electronegativity
First Ionization Potential (eV)
Systematics of the Periodic Table: IP and electronegativity
16
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.
IA
IIIA IVA VA
IIA
VIA VIIA VIIIA
1
1
3
2
2
4
22
21
38
VB
23
40
39
25
26
27
IB
28
29
44
42
74
45
47
46
75
76
77
+4
78
79
7
-3,+3
-4,+4
+5
14
+3 +4
31
32
49
80
-2,+6
52
83
+3,+4 +2,+4 +1,+3 +1,+2 +1,+3 +2,+4
+3
-1
84
0
18
17
+2,+4 +3,+5 +4,+6
82
81
-2
34
51
10
9
+3,+5 -2,+6
33
50
+2 +3
8
16
15
+2 +3 +4 +5
48
+3,+4 +3,+4 +1,+2 +1,+3
+3,+4
+3,+4 +4,+6 +4,+5
+5
+6,+7
IIB
30
+3,+6 +2,+7 +2,+3 +2,+3 +2,+3 +1,+2
+3,+4 +3,+4
+5 +5,+6
73
+4
VIIIB
VIB VIIB
24
41
72
56
+1 +2
87
7
IIIB IVB
+1 +2 +3 +4
55
6
13
+1 +2 +3 +4 +5
37
5
20
6
+3
12
+1 +2
19
4
5
+1 +2
11
3
0
+1,-1
-1
0
35
36
53
54
-1
0
-1
85
+4,+6
-1
70
71
0
86
0
88
+1 +2
57
Lanthanides
+3
89
Actinides
58
+3,+4
90
+3 +4
59
60
61
62
+3 +3 +3 +3
91
63
64
65
+2,+3
+3
+3,+4
66
67
68
69
+3 +3 +3 +3 +3 +3
92
+3,+4 +3,+4
+5 +5,+6
17
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.
Cl– Cl– Cl– Cl–
N a+
N a+
Delocalized conduction electrons
Cl
N a+
Cl– Cl– Cl– Cl–
N a+
N a+
N a+
Cl– Cl– Cl– Cl–
N a+
N a+
N a+
Cr3+
Cl
C
Cl
Cl– Cl– Cl– Cl–
Cl
NaCl, ionic
CCl4, covalent
Cr3+
Cr3+
Cr3+
Cr3+
Cr3+
Cr3+
Cr3+
Cr3+
Cr3+
Cr, metallic
Cr3+
Cr3+
18
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
19
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 8coordination, a much more open structure,
unfavorable except at very low pressure.
20
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
21
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
imineral
mineral/melt
Di

i melt

• 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:
Di   f j Di j / melt
j
• If the bulk partition coefficient < 1, the trace element is termed incompatible.
If the bulk partition coefficient > 1, the trace element is compatible
22
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+.
23
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: C o  FC m  (1  F)C s
(2.1)
i
i
i
Substituting the definition of Di = Cis/Cim and rearranging, we get
Cio
Cio
m
Ci 

(2.2)
Di  (1  Di )F F  (1  F)Di
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.
24
25
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)
dCio  dFCim  FdCim  (1 F)dCis  dFCis
Solids are removed from the system without reacting so dCis = 0:
dF dCim
(D 1)
 m
F
Ci
Integrating subject to Cim = Cio at F = 1, the solution is
Cim  Cio F D1
(2.4)
26
27
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:
dF
dCis

(1  F) C s ( 1  1)
i
D
Integrating subject to Cis = Cio at F = 0, the solution is
1
( 1)
Cis  Cio (1  F) D
And since the instantaneous increment of fractional melt is in
equilibrium with this residue, we can use Cim = Cis/D to obtain
Cim 
1
o
(
1)
Ci
(1 F) D
D
28
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:
Continental crust
Mid-ocean ridge basalt
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.
29
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
30
Partition coefficients and Earth differentiation
F~Cresidue/Cliquid @D~0
D=Cliquid/Cresidue
31