1 lecture 11: periodic table, geochemical affinity, core formation, lunar origin last time, we made...
TRANSCRIPT
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
(refractories)
(volatiles)
(siderophile & chalcophile)
(lithophile) (atmophile)(lost due to impacts)
(late veneer)
Solar Nebula
Condensation and Accretion
Core Silicate Earth Primitive Atmosphere
InnerCore
OuterCore
Primitive Mantle Moon
Lower MantleUpper Mantle
Continental Crust
Oceanic CrustModern Ocean &
Atmosphere
(continuingcometary
flux?)
(partial melting;liquid-crystal partitioning)
(plate tectonics: partial melting, recycling)
(nucleosynthesis, mixing)
(gas-solid equilibria)
(melting; gravity and geochemical affinity)
(freezing)(catastrophic
impact)
(hotspot plumes)
degassing
degassing
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
Mo
W
Os Ir
As
Pt
Fe
Co
Ru
Ni
Re Pd
P
CrGd
V
B
S
Na
Sb
CuZn
Ge
Sn
Ag
Rb
Cs
PbHg
Br
In
Cd
Si
Mg
Rh
Au
I
Te
SeC
N
Bi
K
0.0001
0.001
0.01
0.1
1
10
Bulk Earth /CI = volatility
Silicate Earth/CI = ?
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 = 0.331 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/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
Core Formation: How?
€
ΔT =1
MCp
GMdM
r0
R
∫ uniform ρ3
5Cp
GM
R≈
3 ×107 J/kg
103 J/kg/K= 30000 K!
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 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
4.55 Ga 4.50 4.45
formation of chondrites
formation of irons and achondritesend of earth accretionage of moon
permissible range of core formation times
9
Core Formation: more How?
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
CORE MERGING EVENT (Hf-W timescale ≠ planet formation timescale
10
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
Silicate Liquid
Sulfide Liquid
Metallic Liquid
Gas Phase
Siderophile
Chalcophile
Lithophile
Atmophile 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
Cu, Zn, Ga, Ag, Cd, In, Hg, Tl, As, S, Sb, Se, Pb, Bi, Te
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)
• Melting a chondrite gives 3 immiscible liquids plus vapor:
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:
H
Li
Na
K
Rb
Cs
Fr
Be
Mg
Ca
Sr
Ba
Ra
Sc
Y
Ti
Zr
Hf
Rf
V
Nb
Ta
Db
Cr
Mo
W
Sg
Mn
Tc
Re
Bh
Fe
Ru
Os
Hs
Co
Rh
Ir
Mt
Ni
Pd
Pt
Cu
Ag
Au
Zn
Cd
Hg
Ga
In
Tl
Ge
Sn
Pb
As
Sb
Bi
Se
Te
Po
Br
I
At
Kr
Xe
Rn
B
Al
C
Si
N
P
O
S
F
Cl
Ne
Ar
He
La
Ac
Ce
Th
Pr
Pa
Nd
U
Pm
Np
Sm
Pu
Eu
Am
Gd
Cm
Tb
Bk
Dy
Cf
Ho
Es
Er
Fm
Tm
Md
Yb
No
Lu
Lr
1
2
3
4
5
6
7
IA IIA IIIA IVA VA VIA VIIA VIIIA
IIIB IVB VB VIB VIIB VIIIB IB IIB
Lanthanides
Actinides
1
3
11
19
37
55
87
4
12
20
38
56
88
21
39
22
40
72
104
23
41
73
105
24
42
74
106
25
43
75
107
26
44
76
108
27
45
77
109
28
46
78
29
47
79
30
48
80
5
13
31
49
81
6
14
32
50
82
7
15
33
51
83
8
16
34
52
84
9
17
35
53
85
10
18
36
54
86
2
57
89
58
90
59
91
60
92
61
93
62
94
63
95
64
96
65
97
66
98
67
99
68
100
69
101
70
102
71
103
Atmophile
Lithophile
Chalcophile
Siderophile
Artificial
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...
1s 2s 3s 4s 5s 6s 7s
2p 3p 4p 5p 6p 7p
3d 4d 5d 6d 7d
4f 5f 6f 7f
0
2
2
4
4
10
12
12
18
20
20
30
36
38
38
48
54
56
56
70
80
86
88
88
102
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
H
Li
Na
K
Rb
Cs
Fr
Be
Mg
Ca
Sr
Ba
Ra
Sc
Y
Ti
Zr
Hf
Rf
V
Nb
Ta
Db
Cr
Mo
W
Sg
Mn
Tc
Re
Bh
Fe
Ru
Os
Hs
Co
Rh
Ir
Mt
Ni
Pd
Pt
Cu
Ag
Au
Zn
Cd
Hg
Ga
In
Tl
Ge
Sn
Pb
As
Sb
Bi
Se
Te
Po
Br
I
At
Kr
Xe
Rn
B
Al
C
Si
N
P
O
S
F
Cl
Ne
Ar
He
La
Ac
Ce
Th
Pr
Pa
Nd
U
Pm
Np
Sm
Pu
Eu
Am
Gd
Cm
Tb
Bk
Dy
Cf
Ho
Es
Er
Fm
Tm
Md
Yb
No
Lu
Lr
1
2
3
4
5
6
7
IA IIA IIIA IVA VA VIA VIIA VIIIA
IIIB IVB VB VIB VIIB VIIIB IB IIB
Lanthanides
Actinides
1
3
11
19
37
55
87
4
12
20
38
56
88
21
39
22
40
72
104
23
41
73
105
24
42
74
106
25
43
75
107
26
44
76
108
27
45
77
109
28
46
78
29
47
79
30
48
80
5
13
31
49
81
6
14
32
50
82
7
15
33
51
83
8
16
34
52
84
9
17
35
53
85
10
18
36
54
86
2
57
89
58
90
59
91
60
92
61
93
62
94
63
95
64
96
65
97
66
98
67
99
68
100
69
101
70
102
71
103
s filling
p filling
d filling
f filling
2 10 6
14
16
Systematics of the Periodic Table: IP and electronegativityFirst Ionization Potentials of the Elements
CsRbKNaLi
Rn
Xe
Kr
Ar
Ne
He
Fr
RaPu
B
C
O
F
Mg
Al
Si
Cl
Ca
Fe
Ga
Ge
Br
Sn
IAu Hg
Lu
0
5
10
15
20
25
Noble Gases
Alkali Metals
Rare Earths
Pauling Electronegativity of the Elements
At
Lu
Hg
AuI
Sn
Br
Ge
Ga
Fe
Ca
Cl
Si
Al
Mg
F
O
C
B
Pu
AcRa
He Ne Ar Kr Xe Ra
LiNa
K RbCs Fr
U
ChalcophileSiderophileLithophileAtmophile
0
0.5
1
1.5
2
2.5
3
3.5
4
0 10 20 30 40 50 60 70 80 90 100
Z
Noble Gases
Alkali Metals
Rare Earths
Halogens
Fir
st I
oniz
atio
n P
oten
tial
(eV
)P
auli
ng E
lect
rone
gati
vity
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.
+1,-1
+1
+1
+1
+1
+1
+1
+2
+2
+2
+2
+2
+2
+3
+3 +4
+4
+5
+3,+4+5
+3,+4+5
+3,+6
+3,+4+5,+6
+4,+6
+2,+7
+4,+5+6,+7
+2,+3
+3,+4
+4
+2,+3
+3,+4
+2,+3
+1,+2+3,+4
+1,+2 +2
+2
+1,+2
+3
+3
+1,+3
+4
+2,+4
+5
+3
-2,+6
+4,+6
-1
-1
-1
0
0
0
+3
+3
-4,+4
+4
-3,+3+5
+3,+5
-2
-2,+6
-1
-1
0
0
0
+3
+3
+3,+4
+4
+3
+3,+4+5
+3
+3,+4+5,+6
+3 +3 +2,+3+3 +3,+4+3 +3 +3 +3 +3 +3
1
2
3
4
5
6
7
IA IIA IIIA IVA VA VIA VIIA VIIIA
IIIB IVB VB VIB VIIB VIIIB IB IIB
Lanthanides
Actinides
1
3
11
19
37
55
87
4
12
20
38
56
88
21
39
22
40
72
23
41
73
24
42
74
25
75
26
44
76
27
45
77
28
46
78
29
47
79
30
48
80
5
13
31
49
81
6
14
32
50
82
7
15
33
51
83
8
16
34
52
84
9
17
35
53
85
10
18
36
54
86
2
57
89
58
90
59
91
60
92
61 62 63 64 65 66 67 68 69 70 71
+4
+4,+6+3,+5+2,+4+1,+3
+1,+3+2,+4+3,+4
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 (CO3
2-, 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–
Cl– Cl– Cl– Cl–
Cl– Cl– Cl– Cl–
Cl– Cl– Cl– Cl–
Na+
Na+
Na+
Na+
Na+
Na+
Na+
Na+
Na+
NaCl, ionic
C ClCl
Cl
Cl
CCl4, covalent
Cr3+ Cr3+ Cr3+ Cr3+
Cr3+ Cr3+ Cr3+ Cr3+
Cr3+ Cr3+ Cr3+ Cr3+
Cr, metallic
Delocalized conduction electrons
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
Dimineral/melt=
i[ ]mineral
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
j∑ Di
j /melt
• 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: Cio=FCi
m+(1−F)Cis
Substituting the definition of Di = Cis/Ci
m and rearranging, we get
Cim=
Cio
Di +(1−Di)F=
Cio
F +(1−F)DiLimiting behaviors:
• for a perfectly incompatible element Di = 0 and Cim = Ci
o/F.• For the first increment of melting, F = 0 and Ci
m = Cio/D.
• When melting is complete, F = 1 and Cim = Ci
o.
This equation also describes equilibrium crystallization.
(2.1)
(2.2)
25
Batch Melting/Crystallization
0.1
1
10
0 0.2 0.4 0.6 0.8 1
F
Liquid (D=0.1)
Residue (D=0.1)
Liquid (D=10)
Residue (D=10)
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:dCi
o =dFCim+FdCi
m+(1−F)dCis−dFCi
s
Solids are removed from the system without reacting so dCis = 0:
(D−1)dFF
=dCi
m
Cim
Integrating subject to Cim = Ci
o at F = 1, the solution is
Cim=Ci
oFD−1
(2.3)
(2.4)
27
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 = Ci
o at F = 0, the solution is
dF(1−F)
=dCi
s
Cis(
1D
−1)
Cis =Ci
o(1−F)(1D
−1)
And since the instantaneous increment of fractional melt is in equilibrium with this residue, we can use Ci
m = Cis/D to obtain
Cim=
Cio
D(1−F)
(1D
−1)
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:
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.
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
Two-stage batch melting model
0.00001
0.0001
0.001
0.01
0.1
1
10
100
0.0001 0.001 0.01 0.1 1 10 100bulk partition coefficient D
Primitive Source
First Stage Liquid, F=1.6%
First Stage Residue
Second Stage Liquid, F=8.3%
Second Stage Residue
D=Cliquid/Cresidue
F~Cresidue/Cliquid @D~0