Isotope Geochemistry
 In isotope geochemistry, our primary interest is not in
dating, but using the time-dependent nature of isotope
ratios to make inferences about the nature of reservoirs
in the Earth and their evolution.
 Radiogenic isotope ratios, such as 87Sr/86Sr record the
time-integrated parent daughter ratios in a reservoir or
reservoirs.
Paul Gast
Sr æ 87 Sr ö
=
+
86
Sr çè 86 Sr ÷ø 0
87
Rb lt
( e -1)
86
Sr
87
 Paul Gast was arguably the father of radiogenic mantle isotope geochemistry,
being among the first to recognize its potential. Thinking of the above
equation, he explained it as follows:
In a given chemical system the isotopic abundance of 87Sr is determined by four
parameters: the isotopic abundance at a given initial time, the Rb/Sr ratio of the system, the
decay constant of 87Rb, and the time elapsed since the initial time. The isotopic composition
of a particular sample of strontium, whose history may or may not be known, may be the
result of time spent in a number of such systems or environments. In any case the isotopic
composition is the time-integrated result of the Rb/Sr ratios in all the past environments.
Local differences in the Rb/Sr will, in time, result in local differences in the abundance of
87Sr. Mixing of material during processes will tend to homogenize these local variations.
Once homogenization occurs, the isotopic composition is not further affected by these
processes. Because of this property and because of the time-integrating effect, isotopic
compositions lead to useful inferences concerning the Rb/Sr ratio of the crust and of the
upper mantle. It should be noted that similar arguments can be made for the radiogenic
isotopes of lead, which are related to the U/Pb ratio and time.
Time-Integrated Rb/Sr
87Sr/86Sr
and εNd in the Earth
87Sr/86Sr
and εNd in Oceanic Basalts
Comparing OIB & MORB
εHf &εNd in Oceanic Basalts
Summary: Sr, Nd, & Hf Isotope Ratios
in Oceanic Basalts
 Sr, Nd, and Hf isotope ratios in MORB indicate timeintegrated low Rb/Sr and high Sm/Nd and Lu/Hf.
 These indicate time-integrated incompatible element-depletion
in the MORB source – a result of partial melt extraction.
 The ratios in OIB indicate less incompatible elementdepleted sources – ranging to incompatible elementenriched sources.
 OIB and MORB overlap.
 Far more dispersion in the OIB ratios.
Pb Isotope Geochemistry
Pb Isotope Evolution
Pb isotopes in the silicate
Earth
Pb Paradox
 Pb mass balance in the Earth is difficult and suggest
the Earth is significantly younger (by 100 Ma) than the
solar system.
 Continental crust does not have higher 206Pb/204Pb than
the mantle (which it should if U is more incompatible
than Pb).
 MORB have, on average, time-integrated U/Pb ratios
greater than the silicate Earth
Pb in oceanic basalts
208Pb/204Pb
vs 206Pb/204Pb
208Pb*/206Pb*

and 208Pb/204Pb don’t correlate well with
other isotope ratios globally.
206Pb/204Pb, 207Pb/204Pb,
 This implies the fractionation of U/Pb and Th/Pb is “decoupled” from
Rb/Sr, Sm/Nd, and Lu/Hf fractionation.
 Which element is the outlier? Pb, or U and Th?
 We can to some degree eliminate Pb and focus on U/Th fractionation
by examining the ratio of urogenic Pb to thorogenic Pb:
208
Pb *
=
206
Pb *
Th (el232t -1)
(el232t -1)
= k l238t
238
U (el238t -1)
(e -1)
232
 To calculate just the radiogenic component, we subtract our the solar
system initial values (206Pb/204Pbi =9.306; 206Pb/204Pbi = 29.532:
208
Pb *
=
206
Pb *
Pb / 204 Pb - ( 208 Pb / 204 Pb)i
206
Pb / 204 Pb - ( 206 Pb / 204 Pb)i
208
Mass Balance
 From how much of the mantle would we have to extract a partial
melt to form the incompatible element-enriched continental crust?
This is a mass balance problem. REE geochemistry well
understood, so perhaps best addressed with Nd isotope ratios.
 We consider 3 reservoirs: continental crust, depleted mantle,
undepleted mantle.
 We write a series of mass balance equations:
 for all mass:
åM =1
 for element i:
åM C = C
 for isotope ratio:
j
j
i
j
j
i
0
j
åM C R
j
j
i
j
i
j
= C0i R0i
Mass Balance
 Considerations:



We know the isotopic ratio of DM, but not concentration
We know concentration of Nd and Sm/Nd in crust, but not isotope ratio
We know mass fraction of continental crust
 We simultaneously solve for ratio of mass of 2 reservoirs:
i
i
Rcci - RDM
(
) -1
M DM CCC
= i
i
M CC
C0 R0i - RDM
 We express isotope ratio in crust in terms of Sm/Nd and T – average age of
crust.
 First linearize growth equation:
143
Nd /144 Nd =143 Nd /144 Nd0 +147 Sm /144 Ndlt
 Now express isotope ratio in crust as function of Sm/Nd and T
(143 Nd /144 Nd)CC = (143 Nd /144 Nd)PM + éë(147 Sm /144 Nd)CC - (147 Sm /144 Nd)PM ùû lT
Nd isotope mass balance
Depleted Mantle as an Open
System
Geoneutrinos



β– decay produces neutrinos,
specifically, electron anti-neutrinos,
νe. 6 are produced by 238U decay
and 4 by 235U and 232Th.
We could determine U and Th in the
Earth by detecting their neutinos.
Neutrinos can induce nuclear
reactions such as:


KAMLAND neutrino detector. 1000
tons of scintillator and 1,879
photdetectors.
However,
cross
for this
1
H +the
ne ®
e+ +nsection
–44
reaction is ~10
cm2. Flux of
geoneutrinos through Earth’s surface
is 106 cm-2sec-1
Detectors, consisting of large
volumes of hydrocarbon scintillator
and many photodetectors capable of
detection geoneutrinos have been
built in Japan, Italy, and Canada.
Summary of geoneutrino results
MODELS
Cosmochemical: uses meteorites – O’Neill & Palme (’08); Javoy et al (‘10); Warren (‘11)
Geochemical: uses terrestrial rocks – McD & Sun ’95; Allegre et al ‘95; Palme O’Neil ‘03
Geodynamical: parameterized convection – Schubert et al; Turcotte et al; Anderson
OIB and Mantle Plumes
Lower Mantle Structure
Heterogeneous Plumes
Heterogeneous Plumes
Galapagos
Continental Basalts &
Subcontinental Lithosphere
U-decay series & Melt
Generation
Th & U Geochemistry
 Th and U are two highly incompatible elements
 strongly concentrate in the melt and ultimately in the
crust.
 Th is slightly more incompatible that U.
 Generally similar geochemical behavior, except under
oxidizing conditions where U is in the +6 valance state.
 Overall, because both are strongly incompatible,
fractionation between the two should be small.
Th-U Isotopes
equiline
Th enrichment
Amount of U/Th
fractionation is surprising
given similarity of partition
coefficients
U and Th Disequilibria in
Melting

For mantle at equilibrium:
(230Th) = (238U)

When melting begins, we can write the following mass balance equation:
cio = cis (1- F) + ciℓF

The partition coefficient is defined as:
s/ℓ
Di = cis / ciℓ
cio = Di ciℓ (1- F) + ciℓF

Substituting:

Rearranging and noting that activities are proportional to concentration:
aiℓ
1
=
Di (1-F )+F
aio

Concentration (or activity) is inversely proportional to partition coefficient and melt fraction
U and Th Disequilibria in
Melting
 Assuming parent and daughter were in radioactive equilibrium
before melting, the activity ratio in the melt will be:
aDℓ DP (1- F) + F
=
aPℓ DD (1- F) + F
 For a multiphase system, the distribution coefficient is the
weighted average of individual mineral partition coefficients:
Di =
å mc Dic /ℓ
c
 Partition coefficients similar, but U is slightly more compatible in
garnet.
 To produce 38% disequilibrium would require F be ~0.2% implausibly low.
Mantle Melting
Spiegelman and Elliot Model
 Spiegelman and Elliot (1993) showed that large
isotopic disequilibrium can result from differences in
transport velocities of the elements, that results from
continued solid-melt exchange as melt percolates
upward through the melting column.
 In a one-dimension steady-state system, with a
constant amount of melt, the melt flux is simply the melt
density, ρ, times porosity (we assume melt fills the
pores), φ, times velocity, v:
rmfv
Mathematically
 conservation equation for each parent-daughter pair:
¶[fr m + (1- f )r s Di ] m
ci + Ñ × [ r mf v + r s (1- f )DiV ] cim =
¶t
m
li-1 [ r mf + r s (1- f )Di-1 ] ci-1
- li [ r mf + r s (1- f )Di ] cim
!
 subscript i denotes the element, cm is the concentration of the
element of interest in the melt, ∇ is the gradient, ρm is the density of
the melt, ρs is the density of the solid, v is the velocity of the melt, V is
the velocity of the solid, D is the partition coefficient, φ is the melt
volume fraction, and λ is the decay constant.
Whew!
 In English:
[change in parent conc. with time] + [transport parent] = [decay of
daughter] – [production of daughter]
Add in Melting
 We assume the extent of melting increases linearly with the height, z,
above the base of the melting layer of thickness d:
F = Fmax
 Melting rate:
z
d
 (note Fmax and d depend on Tφ and lithospheric thickness
 Flux of solid is:
 the melt flux as a function of height is:
 Velocity of melt:
v = V0
rsF
r mf
The Usercalc Model
 Need to make assumptions about relation between porosity
and permeability and melt viscosity.
 Then think about transport of an element through the
column rather than bulk melt or solid.
 Since an element is partitioned between solid and melt, its
effective velocity depends on how much is in the melt and
how much in the solid:
i
veff
=
r mfv + r s (1- f )DiV
v -V
»V +
r mf + r s (1- f )Di
1+ Di / f
 Very incompatible elements travel up through the melting
column at near the velocity of the melt; very compatible
elements travel upward at velocities near the solid velocity.

An example in which Fmax =
20% melting begins at 4 GPa
(123.56 km) and ends at 0
GPa. Bulk partition
coefficients for U and Th are
0.0011 and 0.00024
respectively in the garnet
peridotite facies, and both are
0.00033 in the spinel
peridotite facies.

The phase transition occurs
at 2 GPa. We set the
remaining parameters to their
default values (V = 3 cm/yr,
fmax = 0.008, n = 2).

Kinks in the curves reflect the
phase change from garnet to
spinel peridotite at 20 kb.
230Th/238U of the melt flowing
out the top is 1.113.
Melt and Solid Evolution
 Contour plots illustrating
the sensitivity of U-series
disequilibria to porosity
and upwelling velocity (the
latter is in cm/yr). Colored
lines show the
combination of porosity
and upwelling velocity
needed to reproduce the
“target values”, which are
(230Th/238U)=1.15,
(226Ra/230Th)=1.15, and
(231Pa/235U)=1.5.