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Geochemistry of the upper part of the
solid Earth:
Lecture 1: The geochemical toolbox and first-order implications
for major earth reservoirs
Lecture 2: The geochemical toolbox (continued). Brief
introduction to the continental crust
Guest lecture: Bruno Dhuime (crustal evolution)
Lecture 3: Mid-ocean ridge magmatism
Lecture 4: Intraplate magmatism
Lecture 5: Melt generation in subduction zones
Lecture 6: The subcontinental mantle lithosphere
The Geochemical Toolbox and first-order
implications for major Earth reservoirs
• Major elements
Bulk Earth composition and how we know it
Major element composition of Earth reservoirs
• Trace elements
Factors controlling trace element partitioning
How these factors determine trace element distribution among
Earth reservoirs
• Isotopes
Radiogenic isotopes
Stable (conventional and non-conventional) isotope systems
"Mass-independant" fractionation
Goldschmidt's classification of
Elemental Behavior
Victor
Goldschmidt
(1888-1946)
White (1997)
Bulk Silicate Earth (BSE)
Bulk Earth
CaAl Ni other
Fe
Na, K,
Al other
Ca
O
Fe
Mg
Mg
O
Si
Si
Ni
First order
differentiation
of the Earth
other
Fe
Si?
Core
How do we know the bulk Earth composition?
Core: From geophysics, especially seismic and mineral physics data, and from
analogy with iron meteorites.
Bulk silicate Earth (BSE): From intersection between partial melting trend (upper
mantle peridotites) and fractional condensation trend (chondritic meteorites).
Assumptions:
• Upper mantle peridotites
are representative of whole
mantle
Ma
ntle
p
erid
otite
• Trends obtained from
chondritic meteorites are
applicable to the Earth
te
e
M
s
te
ori
BSE
s
Jagoutz et al. (1979)
Another way to estimate BSE composition
Constant chondritic
Sm/Yb ratio
Peridotite melt
extraction
trend
McDonough & Sun (1995)
Estimated BSE TiO2 content
Though different in detail, this method is also based on
comparing peridotite melt extraction trend with chondritic
meteorite trend, so same assumptions hold.
Condensation temperatures in the solar nebula
Albarede (2003)
Abundances of refractory elements are ~ 2.75 times higher in the BSE than in C1
chondrites. Ratios of refractory elements vary little in chondrites. Traditionally
Earth has been assumed to have same refractory element ratios as chondrites.
But this view has changed in the past decade with very large consequences for
our understanding of crust-mantle evolution. More on that later...
Continental crust
Continental crust extraction
overall composition: andesite
Na K
BSE (or "primitive mantle")
overall composition: lherzolite
Fe
Na, K,
Ca Al other
other
Al
Ca
Fe
O
Mg
Si
Mg
O
Si
Residual mantle
?
Composition depends on
fraction of mantle from
which crust extracted
m = mass
C = concentration of element
x = mass fraction of crust
cr = crust
rm = residual mantle
BSE = Bulk Silicate Earth
Mass Balance
mBSE = mcr + mrm
CBSE*mBSE = Ccr*mcr + Crm*mrm
CBSE = Ccr*mcr/mBSE + Crm*(mBSE-mcr)/mBSE
CBSE = Ccr*x + Crm*(1 - x)
Crm = (CBSE - Ccr*x)/(1-x)
mcr = 2.20 x 1022 kg
mBSE = 4.002 x 1024 kg (whole mantle)
x = 0.0055
mBSE = 1.96 x 1024 kg (upper mantle)
x = 0.020
Accuracy of calculated concentrations in residual mantle depends on:
1) Estimated Primitive mantle concentrations (CBSE)
2) Knowledge of crustal concentrations (Ccr)
3) Fraction of mantle from which crust is extracted
Concentrations normalized to BSE
Effect of crustal extraction on major element
composition of mantle
continental crust
residual whole
mantle
residual upper
mantle
Two endmember cases considered: crustal extraction from whole mantle and
crustal extraction uniquely from upper mantle
For most major elements, effect of crustal extraction on mantle composition is
minor.
For K, a highly incompatible element, crustal extraction has a large effect,
especially if crust extracted only from upper mantle.
White (1997)
Factors controlling partitioning during melting:
ionic radius and charge
LIL
REE
HFSE
White (1997)
Contours: clinopyroxene/liquid
partition coefficients (Kd), where
Kd = Concentration in
phase/concentration in liquid
LIL= Large Ion Lithophile
REE = Rare Earth Elements
HFSE = High Field Strength Elements
LIL vs. HFSE
Large Ion Lithophile elements: Large radii and low charge (low
z/r)  highly incompatible during magmatic processes and
highly mobile in hydrothermal fluids.
High Field Strength Elements: Small radii and high charge (high
z/r)  form strong bonds that are difficult to break and are
therefore immobile in hydrothermal fluids.
Provides a first order explanation for why LIL and HFSE show
similar behavior in mid-ocean ridge magmas (dependant
essentially on magmatic processes) and divergent behavior in
arc magmas (dependant on both magmatic and hydrothermal
processes).
Rare Earth Elements (REE) - Ionic radius
3+ charge
White (1997)
Explains systematic behavior of REE in most
minerals and Eu anomalies found in certain rocks
REE Kd values
for major mantle
phases
In most mantle
phases, light REE
(LREE) are much
more incompatible
(low kd) than heavy
REE.
Positive Eu anomaly
in plagioclase
reflects substitution
of Eu2+ for Ca2+
White (1997)
Effect of partial melting on REE spectra
Albarede (2003)
Because LREE are more incompatible than HREE in most mantle phases,
melts are relatively enriched in LREE while residues are depleted.
Extraction of continental crust depleted residual
mantle in incompatible elements
continental crust
residual after extraction from
whole mantle
residual after
extraction from
upper mantle
Increasing crustal concentrations
Increasing compatibility
Crust data: Taylor and McLennan (1985); Primitive mantle (BSE) data: Hofmann (1988)
Trace element spectra of basalts from different
tectonic contexts
Ocean basins
Arcs
White (1997)
LIL
LIL
REE
HFSE
HFSE
Increasing compatibility during peridotite melting
REE
Basalts from different tectonic contexts have different trace
element spectra that reflect source composition, source
phases, pressure, mechanism and extent of melting.
Isotopic variations in the crust and mantle
Radiogenic isotopes
• Nuclear processes
• Absolute dating
• Powerful source tracers
• Not fractionated by geochemical processes (or minor
fractionation is corrected during analysis)
Stable isotope fractionation
• Physicochemical processes
• Varies in a systematic manner with isotope mass
• Sensitive to geochemical processes and temperature
• Source tracers
"Mass independant" isotope fractionation
• Sensitive to highly specific processes
Mechanisms of Radioactive decay
1) Emission of a β particle (Rb-Sr, Re-Os)
β- Electron emission from nucleus. The atomic number increases by one, the
mass remains unchanged.
β+ Positron emission from nucleus. The atomic number decreases by one, the
mass remains unchanged.
2) Electron capture (K-Ar)
Nucleus absorbs an inner shell electron. The atomic number decreases by one,
the mass remains unchanged.
3) Emission of an α particle (nucleus of He) (Sm-Nd)
The atomic number decreases by two, the atomic mass decreases by four.
4) Spontaneous fission (U-Xe)
5) Decay chains (U-Pb, Th-Pb)
The radiogenic daughters are themselves radioactive. A whole series of instable
isotopes exists between the radioactive parent (238U, 235U or 232Th) and the
stable daughter (206Pb, 207Pb, 208Pb). Nucleii of 4He atoms are produced by
emission of α particles.
Radiometric isotope systems
•
Systems with long half lives - used for dating and tracing sources of
mantle and crustal magmas
87Rb
 87Sr
147Sm  143Nd
176Lu  176Hf
187Re  187Os
40K  40Ar
•
U-Th-Pb decay series - provide time constraints for magmatic processes
238U
...  206Pb
235U ...  207Pb
232Th ...  208Pb
•
t1/2 = 4.47 Gy
t1/2 = 0.7 Gy
t1/2 = 14 Gy
by-product 4He
Cosmogenic isotopes
10Be
•
t1/2 = 48 Gy
t1/2 = 106 Gy
t1/2 = 36 Gy
t1/2 = 42 Gy
t1/2 = 1.28 Gy
(from spallation)
t1/2 = 1.4 My
Short-lived extinct isotopes - provide constraints on earliest Earth
processes and on material from which Earth formed
146Sm
 142Nd
182Hf  182W
t1/2 = 103 My
t1/2 = 9 My
Black: lithophile; Red: siderophile/chalcophile; Blue: volatile
Radioactive decay equations
The rate at which the abundance of a radioactive isotope (parent) decreases is
proportional to the number of atoms remaining (N) :
-dN/dt = λN
λ = decay constant
Solution: N = Noe-λt
No = number of atoms of the parent at t = 0.
D* = No- N = N(eλt - 1)
D* = number of atoms of the daughter produced by radioactive decay
D = Do + D* = Do + N(eλt - 1)
Do = number of atoms of the daughter t = 0
D = total number of atoms of the daughter
Radioactive decay equations (cont.)
Example of Rb-Sr couple : 87Rb (parent) 87Sr (daughter) (t1/2 ~ 49 Gy)
D = Do + N(eλt - 1)
87Sr
= 87Sro + 87Rb(eλt - 1)
Normalized to a non-radiogenic isotope (here 86Sr) because:
• not all phases will have same 87Sro, but all should have same 87Sr/86Sr
• it is much easier to precisely determine an isotopic ratio than the absolute
quantity of a given isotope
87Sr/86Sr
= (87Sr/86Sr)o + (87Rb/86Sr)(eλt - 1)
Linear equation
y-intercept (initial
ratio)
Slope (depends
on age)
Isochron method
Example of Rb-Sr system
87Sr/86Sr
t2
t1
sample
1
sample
2
t0
sample
3
87Rb/86Sr
Evolution of
87Sr/86Sr
over time
to 86Sr, a non-radiogenic isotope.)
(87Sr and
87Rb
are normalized
Conditions required to produce an isochron
87Sr/86Sr
t2
t1
t0
87Rb/86Sr
1) At t0, all phases must have the same isotopic ratio
2) The range of parent/daughter ratios must be substantial
3) The system must remain closed since its formation
87Sr/86Sr
= 87Sr/86Sri + 87Rb/86Sr (eλt - 1)
87Sr/86Sr
t = age
λ= decay constant of 87Rb = 1.42 x 10-11 years-1
87Sr/86Sr = initial isotopic ratio
i
Initial isotopic ratio =
87Sr/86Sr
i
Provides information
about the source
Isochron
equation
Slope = eλt - 1
The age is determined from
the slope of the isochron
87Rb/86Sr
How do radiogenic isotope compositions of major Earth
reservoirs evolve through time?
continental crust
residual after extraction from
whole mantle
residual after
extraction from
upper mantle
Increasing crustal concentrations
Rb, Sr, Sm, Nd, Lu, H are all incompatible during mantle melting. But:
DRb < DSr (Rb more incompatible than Sr)
D= bulk partition coefficient
DSm > DNd
DLu > DHf
Sr isotopic evolution of Continental Crust and Mantle
(?)
Since DRb< DSr
Rb/Sr crust >
Rb/Sr BSE >
Rb/Sr residual
mantle
White (1997)
BABI (Basaltic Achondrite Best Initial) =
estimate of solar system initial 87Sr/86Sr
Over time, the crust has developed a radiogenic signature relative to BSE
while the residual mantle has developed an unradiogenic signature. Exact
87Sr/86Sr values of each reservoir depend on crustal extraction history.
Nd isotopic evolution
of Crust and Mantle
Since DSm> DNd
Sm/Nd crust
< Sm/Nd BSE
< Sm/Nd mantle
(?)
chondritic Sm/Nd
As a result, residual mantle
Nd becomes radiogenic while
crustal Nd becomes relatively
unradiogenic over time.
" Nd
!
$ 143 Nd
'
sample
) )
& 144 (
Nd
= 10000 * & 143
#1)
Nd
&
chondrite) )
(
144
% Nd
(
CHUR = chondritic
uniform reservoir
What fraction of the
mantle was depleted
by formation of the
Continental Crust?
Can be calculated from the mean Nd isotopic compositions and
concentrations of the continental crust, the depleted mantle (known
from MORB) and the Bulk Silicate Earth.
But our knowledge of each of these parameters, particularly for the
BSE, is limited. (We'll come back to this...)
(?)
εNd and 87Sr/86Sr
are anti-correlated
among main Earth
reservoirs
White (1997)
The opposing behavior of Nd and Sr isotopes is due to the fact the parent is more
incompatible than the daughter in one case (Rb/Sr) and less incompatible in the
other (Sm/Nd)
Nd and Hf
systematics
in oceanic
basalts
Continental
Crust
Dickin (2000)
In both the Sm/Nd and Lu/Hf systems the parent isotope is less
incompatible than the daughter. Produces with time a positive
correlation.
Calculating Nd model ages for extraction of a
crustal sample from the mantle
Geologic significance of model age depends on validity of the model. Based on
two questionable assumptions:
1) The mantle evolution curve is well defined.
2) The Sm/Nd ratio of the sample has remained unchanged since time of
extraction from the mantle.
Nevertheless, can provide approximate indication of age of crustal extracton.
Calculating Model ages
At the time of crustal extraction from the mantle, the sample will have the same
Nd isotopic ratio (143Nd/144Ndi) as the mantle evolution curve at that time (here
assumed to be the depleted mantle curve, DM). So:
crustal sample
depleted mantle
" 143 Nd %
" 143 Nd % " 147 Sm %
(T
$ 144 ' = $ 144 ' + $ 144 ' (e M )1)
# Nd & DM # Nd & i # Nd & DM
and
" 143 Nd %
" 143 Nd % " 147 Sm %
(T
$ 144 ' = $ 144 ' + $ 144 ' (e M )1)
# Nd & DM # Nd & i # Nd & DM
Combining equations:
!
! " 143 %
" 143 Nd %
" 147 Sm %
" 147 Sm %
Nd
)T DM
( $ 144 '
(e
(1) = $ 144 ' ( $ 144 ' (e )TDM (1)
$ 144 '
# Nd & sample # Nd & sample
# Nd & DM # Nd & DM
After a little algebra:
!
TDM
" " 143 Nd %
%
" 143 Nd %
$ $ 144 ' ( $ 144 '
'
Nd
Nd
#
&
#
&
$
'
DM
sample
ln$ 147
+1'
147
" Sm %
" Sm %
$$ $ 144 ' ( $ 144 '
''
Nd
Nd
#
&
#
&
#
DM
sample
&
=
)
where λ = 6.54 x 10-12 yr-1
(decay constant of 147Sm)
U-Th-Pb decay
systems
235U, 238U
and 232Th decay
to Pb through a series of
short-lived radioactive
daughter isotopes.
235U
 ...  207Pb
t1/2= 0.70 Gy
238U
 ...  206Pb
t1/2= 4.47 Gy
232Th
 ...  208Pb
t1/2= 14.0 Gy
For long-term processes (e.g. evolution of mantle reservoirs), can be
approximated as a direct decay from the parent (U or Th) to Pb.
For relatively rapid processes (e.g. magma generation) intermediate
daughters can be very useful for constraining rates
238U
Decay chain
• Several intermediate daughters with half-lives
appropriate for studying magmatism (234U, 230Th, 226Ra)
• Each α particle is a 4He nucleus
Pb isotopes
204Pb, 206Pb, 207Pb, 208Pb
235U
 ...  207Pb
t1/2= 0.70 Gy
238U
 ...  206Pb
t1/2= 4.47 Gy
Two isotope systems in which parent is
an isotope of U and daughter is an
isotope of Pb. Therefore can write an
isochron equation which does not
involve the U/Pb ratio.
232Th
 ...  208Pb
t1/2= 14.0 Gy
204Pb,
the only non-radiogenic Pb isotope, is used for
normalization (206Pb/204Pb, 207Pb/204Pb and 208Pb/204Pb)
Pb-Pb isochrons
207Pb/204Pb
- (207Pb/204Pb)T = ( 235U/204Pb)(eλ235T - 1)
206Pb/204Pb
- (206Pb/204Pb)T = ( 238U/204Pb)(eλ238T - 1)
where T is age of event to be dated
Dividing the two equations and replacing the ratio 235U/238U by its current value
(1/137.88), uniform (or nearly so) in the solar system:
207Pb/204Pb
- (207Pb/204Pb)T
206Pb/204Pb
(206Pb/204Pb)
-
T
=
(eλ235T - l)
137.88 (eλ238T - l)
Nevertheless, even if U doesn't appear in the equation, a substantial
range of U/Pb is needed to generate an isochron.
Example: Pb-Pb isochron of 3 Gy
16.0
t=2 Gy
15.8
t=1 Gy
µ=10
15.6
207Pb/204Pb
t=0
µ=9
15.4
µ=8
15.2
15.0
14.8
14.6
14.4
µ = 238U/204Pb
14.2
12
13
14
15
16
17
18
19
20
206Pb/204Pb
To calculate Pb composition at a time t, following an event of age T:
207Pb/204Pb
t
- (207Pb/204Pb)T = (µ/137.88)∗(eλ235T - eλ235t)
206Pb/204Pb
t
- (206Pb/204Pb)T = µ∗(eλ238T - eλ238t)
(µ/137.88 = 235U/204Pb)
Holmes-Houtermans
model (1946)
4 b
20 P
µ=
207Pb/204Pb
t
- (207Pb/204Pb)T
206Pb/204Pb
t
- (206Pb/204Pb)T
8 /
23 U
(eλ235T - eλ235t)
=
137.88 (eλ238T - eλ238t)
T= age of the Earth
t = age of galena sample
Determination of age of Earth with Pb-Pb isochron
after Patterson (1956)
Ocean sediments (which average large volumes of material) plot on
isochron defined by meteorites.
Lead
Paradox
White (1997)
Pb isotopic compositions of most accessible Earth reservoirs, including
MORB, plot to the enriched side of the Geochron.
But average Bulk Silicate Earth is expected to plot on the Geochron.
Where is the "missing" unradiogenic Pb? Core? Lower crust?
Subducted slabs? Still not resolved.
Another use of Pb
isotopes: U-Pb
dating of zircons
Concordia diagram
Extremely powerful tool
for dating crustal rocks
• Zircon: very common crustal phase containing almost no Pb but a lot of U
• All Pb of radiogenic origin
• Highly resistant phase
• in situ techniques allow determination of different ages from different
portions of zoned zircons
In situ U-Pb dating of zircons
bar = 50 µm
numbers = age in My
Fornelli et al. (2014)
Allows different ages to be found for different portions of zircon grains
(e.g., old xenocrystic cores and later metamorphic overgrowths).
In situ U-Pb dating often accompanied by Hf isotopic measurements.
In situ Hf isotopic measurements in zircon have
become very common - Why?
• Hf, like Zr, is a High Field Strength Element (HFSE), and so can
substitute for Zr in zircon structure
• As a result, Hf concentrations in zircon are very high (1% or
more) and Lu/Hf ratios are very low.
• Hf isotopes in zircon are excellent source tracers because low
Lu/Hf ratios minimize radiogenic ingrowth of 176Hf after zircon
crystallization
• Hf isotope data can be coupled with U/Pb ages in zircon
• Measurements by laser ablation ICPMS are rapid and "easy"
(though several pitfalls).
De
p le
176Hf/177Hf
BS
E
C ru s
0
te d
ma
n tl
e
Hf crustal model
ages of zircons
("two stage" ages)
t
zircon
crystallization age
Hf Model age
time (Gy)
4.5
stage 1: Evolution of Hf isotope composition of source rocks with an average crustal
176Lu/176Hf ratio (an assumed value often used)
stage 2: Hf residence in zircon using measured 176Lu/176Hf ratio (~0)
Major assumptions:
• Crustal precursor from which zircon parental magma formed had an "average
crustal" 176Lu/177Hf ratio.
• Crust derived from a mantle with a well-defined "depleted" Hf isotopic signature.
De
176Hf/177Hf
BS
p le
E
C ru s
0
te d
ma
n tl
e
Hf crustal model
ages of zircons
("two stage" ages)
t
zircon
Hf Model age
crystallization age
4.5
D ep
$
'
Hf
& 177 ( sample)
)
Hf
= 10000 * & 176
#1)
& Hf
)
& 177 (chondrite) )
% Hf
(
!
a n tl
e
BSE
C ru s
176
" Hf
dm
εHf
Same idea, but in
εHf notation
le te
0
t
zircon
Hf Model age
crystallization age
4.5