Radiogenic
Isotope
Geochemistry III
Lecture 31
The Rb-Sr System
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Both elements incompatible
(Rb more so than Sr).
Both soluble and therefore
mobile (Rb more so than Sr).
Range of Rb/Sr is large,
particularly in crustal rocks
(good for geochronology).
Subject to disturbance by
metamorphism and
weathering.
Both elements concentrated
in crust relative to mantle - Rb
more so than Sr.
87Sr/86Sr evolves to high values
in the crust, low ones in the
mantle.
Sr Isotope
Chronostratigraphy
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We can’t generally radiometricly
date sedimentary rocks, but there is
an exception of sorts.
87Sr/86Sr has evolved very non-linearly
in seawater. This is because the
residence time of Sr in seawater is
short compared to 87Rb half-life, so
87Sr/86Sr is controlled by the relative
fluxes of Sr to the oceans:
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Rivers and dust from the continents
The mantle, via oceanic crust and hydrothermal
systems.
Changes in these fluxes result in
changes in 87Sr/86Sr over time.
Sr is concentrated in carbonates
precipitated from seawater. By
comparing the 87Sr/86Sr of carbonates
with the evolution curve, an age can
be assigned.
This quite accurate in the Tertiary
(and widely used by oil companies),
less so in earlier times.
The Sm-Nd System
147Sm
alpha decays to 143Nd with a half-life of 106 billion years.
Both are rare earths and behave similarly.
In addition, 146Sm decays to 142Nd with a half-life of 68 million years.
As a consequence of its short half-life, 146Sm no longer exists in the
solar system or the Earth. But it once did, and this provides some
interesting insights.
Sm-Nd and εNd
• Because Sm and Nd, like all rare earths, are refractory
lithophile elements, and because their relative abundances
vary little in chondritic meteorites, it is reasonable to suppose
that the Sm/Nd ratio of the Earth is the same as chondrites.
• This leads to a notation of 143Nd/144Nd ratios relative to the
chondritic value, εNd:
e Nd
æ 143 Nd / 144 Ndsample - 143 Nd / 144 Ndchondrites ö
=ç
143
144
÷ ´10000
Nd
/
Nd
è
ø
chondrites
• While we usually use present-day values in this equation, we
can calculate εNd (t) for any time, using the appropriate values
for that time.
• There are several advantages:
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ε values are generally numbers between ~+10 and -20.
If the Earth has chondritic Sm/Nd, then the 143Nd/144Nd of the Earth is chondritic and
εNd of the bulk Earth is 0 both today and at any time in the past.
The 142Nd/144Nd of the modern observable Earth differs from chondrites slightly (by
about 20 ppm), which raises the question of whether the Earth’s Sm/Nd ratio is in fact
exactly chondritic. The notation survives, however.
Sm-Nd Evolution of the
Earth
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Sm and Nd are incompatible
elements (Nd more so that Sm).
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By converting to εNd, our
evolution diagram rotates such
that a chondritic uniform
reservoir always evolves
horizontally (εNd always 0).
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Consequently, the crust evolves to low
143Nd/144Nd while the mantle evolves to high
143Nd/144Nd.
The mantle evolves to positive εNd, the crust
to negative εNd.
Both Sm and Nd are insoluble
and not very mobile, so it is in
many ways a more robust
chronometer than Rb-Sr.
Unfortunately, the range in
Sm/Nd ratios in crustal rocks is
usually small, limiting the use of
the system for geochronology.
Sm-Nd model ages or
‘Crustal Residence Times”
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A relatively large fractionation of Sm/Nd is
involved in crust formation. But after a
crustal rock is formed, its Sm/Nd ratio tends
not to change.
This leads to another useful concept, the
model age or crustal residence time. From
143Nd/144Nd and 147Sm/144Nd, we can
estimate the “age” or crustal residence
time, i.e., the time the rock has spent in the
crust. We assume:
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We
along a line whose slope corresponds to
the measured present 147Sm/144Nd ratio until
it intersects the chondritic growth line. The
model age is this age at which these lines
intersect:
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The crustal rock or its precursor was derived from the
mantle
The 147Sm/144Nd of the crustal rock did not change.
We know how the mantle evolved.
project the 143Nd/144Nd ratio back
CHUR model age (τCHUR).
Depleted mantle model age is used (τDM).
In either case, the model age is calculated
by extrapolating the 143Nd/144Nd ratio back
to the intersection with the mantle growth
curve.
Our isochron equation was:
147
147
æ 143 Nd ö
Nd æ 143 Nd ö
Sm lt
Sm
= ç 144 ÷ + 144 (e -1) @ ç 144 ÷ + 144 l t
144
Nd è Nd ø 0
Nd
Nd
è Nd ø 0
143
If we plot the radiogenic isotope ratio
against t, then the slope is RP/Dλ.
(note that x-axis label should be ‘age’,
not t, in the sense of the equation).
Model Age Calculations
• To calculate the model
age, we note that the
point where the lines
intersect is the point
where (143Nd/144Nd)0 of
both the crustal rock and
the mantle (CHUR or DM)
are equal.
• We write both growth
equations and set the
(143Nd/144Nd)0 values
equal, then solve for t.
• See Example 8.3.
Sr-Nd Systematics of the
Earth
Lu-Hf System
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176Lu
decays to 176Hf with a half-life of 37
billion years. Lu is the heaviest rare earth, Hf
in the next heavier element.
The Lu-Hf system is in many respects similar to
the Sm-Nd system:
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(1) in both cases the elements are relatively immobile;
(2) in both cases they are refractory lithophile elements;
and
(3) in both cases the daughter is preferentially enriched in
the crust, so both 143Nd/144Nd and 176Hf/177Hf ratios are
lower in the crust than in the mantle.
Lu-Hf has two advantages: the half-life is
shorter and the Lu/Hf ratio is much more
variable. It has (had) one big disadvantage:
before the advent of MC-ICP-MS, Hf isotope
ratio measurements were very difficult to
make. As a consequence, widespread use in
geochemistry and geochronology really only
began about 15 years ago.
We can define a εHf notation by exact
analogy to εNd: the relative difference from
the chondritic value times 10000.
εHf and εNd are usually strongly correlated.
Lu concentrated in garnets, Hf excluded, so
this system is particularly good for dating
garnet-bearing rocks.
Hf is very similar to Zr and concentrated in
zircon; Lu/Hf ratios are quite low. Zircon is
widely used in Pb geochronology. Ages and
initial εHf can be obtained from zircon
analyses - this has been particularly
interesting in very old crustal rocks.
The Re-Os System
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187Re
decays to 187Os by β– decay with a half-life of 42 billion
years.
Unlike the other decay systems of geological interest, Re and
Os are both siderophile elements: they are depleted in the
silicate Earth and presumably concentrated in the core. The
resulting very low concentration levels (sub-ppb) make analysis
extremely difficult. Interest blossomed when a technique was
developed to analyze OsO4– with great sensitivity. It remains
very difficult to measure in many rocks, however. Peridotites
have higher concentrations.
The siderophile/chalcophile nature of these elements, making
this a useful system to address questions of core formation and
ore genesis.
Os is a highly compatible element (bulk D ~ 10) while Re is
moderately incompatible and is enriched in melts. For
example, mantle peridotites have average Re/Os close to the
chondritic value of 0.08 whereas the average Re/Os in basalts
is ~10. Thus partial melting appears to produce an increase in
the Re/Os ratio by a factor of >102. As a consequence, the
range of Os isotope ratios in the Earth is very large. The mantle
has a 187Os/188Os ratio close to the chondritic value of, whereas
the crust appears to have a a 187Os/188Os > 1. By contrast, the
difference in 143Nd/144Nd ratios between crust and mantle is
only about 0.5%.
The near chondritic a 187Os/188Os of the mantle is surprising,
given that Os and Re should have partitioned into the core
very differently. This suggests most of the noble metals in the
silicate Earth are derived from a late accretionary veneer
added after the core formed.
In addition, 190Pt decays to 186Os with a half-life of 650 billion
years. The resulting variations in 186Os/188Os are small.
Os Isotopes in the SCLM
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Since the silicate Earth appears to have a nearchondritic 187Os/188Os ratio, it is useful to define a
parameter analogous to εNd and εHf that measures
the deviation from chondritic. γOs is defined as:
- ( Os
Os )
Os )
g
´100
Os
( Os)
Studies of pieces of subcontinental lithospheric
Os
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(
=
187
Os 188
187
sample
187
188
188
Chond
Chond
mantle xenoliths show that much of this mantle is
poor in clinopyroxene and garnet and hence
depleted in its basaltic component. Surprisingly,
these xenoliths often show evidence of
incompatible element enrichment, including high
87Sr/86Sr and low ε . This latter feature is often
Nd
attributed to reaction of the mantle lithosphere with
very small degree melts percolating upward
through it (a process termed “mantle
metasomatism”).
This process, however, apparently leaves the Re-Os
system unaffected, so that 187Re/188Os and
187Os/188Os remain low.
Low γOs is a signature of lithospheric mantle.
Os Isotopes in Seawater
• Os isotopes in seawater
(tracked by measuring Os in
Mn nodules and black
shales) reveals a variation
much like that of 87Sr/86Sr.
• The reflects a balance of
mantle and crustal inputs.
• And, perhaps, meteoritic
ones. Very low ratios occur
at the K-T boundary. Ratio
was already decreasing
before then: Deccan traps
volcanism? (supports the hit
‘em while their down theory
of the K-T extinction).
U-Th-Pb
• In the U-Th-Pb system there are three decay schemes
producing 3 isotopes of Pb. Two U isotopes decay to 2
Pb isotopes, and since the parent and daughter isotopes
are chemically identical, we get a particularly powerful
tool.
• Following convention, we will designate the 238U/204Pb
ratio as μ, and the 232Th/238U ratio as κ. We can write two
versions of our isochron equation:
Pb æ
=
204
Pb çè
206
Pb æ
=
204
Pb çè
206
206
204
Pb ö
+ µ(el238t -1)
÷
Pb ø 0
235
Pb ö
U
+ µ 238 (el238t -1)
204
÷
Pb ø 0
U
206
o Conventionally, the 235U/238U was assumed to have a constant, uniform value
of 1/137.88. Recent studies, however, have demonstrated that this ratio varies
slightly due to kinetic chemical fractionation. Consequently, for highest
precision, it should be measured. In most cases, however, we can use the
revised apparent average value of 1/137.82.
Pb-Pb isochrons
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These equations can be
rearranged by subtracting the
initial ratio from both sides. For
example:
206
Pb
∆ 204 = µ(el238t -1)
Pb
Dividing the two:
∆ 207 Pb / 204 Pb
=
∆ 206 Pb / 204 Pb
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U (el238t -1)
238
U (el235t -1)
235
the 235U/238U is the present day ratio and
assumed constant.
The left is a slope on a plot of
207Pb/204Pb vs 206Pb/204Pb. Slope is
proportional to time, and so is an
isochron.
The value is that we need not
know or measure the U/Pb ratio
(which is subject to change
during weathering).
Pb Isotopic Evolution
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Because the half-life of 235U is much shorter than
that of 238U, 235U decays more rapidly and Pb
isotopic evolution follows curved paths on this plot.
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All systems that begin with a common initial
isotopic composition at time t0 lie along a straight
line at some later time t. This line is the Pb-Pb
isochron.
When the solar system formed 4.57 billion years
ago, it had a single, uniform Pb isotope
composition.
We assume that bodies such as the Earth have
remained closed since their formation.
Pb in each planetary body would evolve along a
separate path that depends on µ of that body.
At any later time t, the 207Pb/204Pb and 206Pb/204Pb
ratios of all bodies plot on a unique line, called the
Geochron, which has a slope corresponding to the
age of the solar system, and passing through
‘primordial Pb’.
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The exact path depends upon µ.
True only for the planet as a whole, not individual rock formations.
The Earth as a whole must fall on this line if it
formed at the same time as the solar system with
the solar system initial Pb isotopic composition.
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The problem is that Earth may be 100 Ma younger than the ‘solar
system’ - because it took a long time to form large terrestrial
planets.
There is some flexibility in the exact position of the geochron
because the age is not exactly known.
232Th-208Pb
• We can combine the growth equations for
208Pb/204Pb and 206Pb/204Pb in a way similar to our
207Pb-206Pb isochron equation We end up with:
∆ 208 Pb / 204 Pb
(el238t -1)
= k l235t
∆ 206 Pb / 204 Pb
(e -1)
o where κ is the 232Th/238U ratio.
• The left is a slope on a plot of 208Pb/204Pb vs
206Pb/204Pb and is proportional to t and κ.
o assuming κ has been constant (except for radioactive decay).
Pb Isotope Ratios in the Earth
Pb Isotope Ratios in the Earth
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Major terrestrial reservoirs, such as the upper mantle
(represented by MORB), upper and lower
continental crust, plot near the Geochron between
growth curves for µ = 8 and µ = 8.8, suggesting µ of
the Earth ≈ 8.5.
If a system has experienced a decrease in U/Pb at
some point in the past, its Pb isotopic composition
will lie to the left of the Geochron; if its U/Pb ratio
increased, its present Pb isotopic composition will lie
to the right of the Geochron.
U is more incompatible than Pb, so incompatible
element depleted reservoirs should plot to the left
of the Geochron, enriched ones to the right.
From the other isotopic ratios, we would have
predicted that continental crust should lie to the
right of the Geochron and the mantle to the left.
Surprisingly, Pb isotope ratios of mantle-derived
rocks also plot mostly to the right of the Geochron.
This indicates the U/Pb ratio in the mantle has
increased, not decreased as expected.
This phenomenon is known as the Pb paradox and
it implies that a simple model of crust–mantle
evolution that involves only transfer of incompatible
elements from crust to mantle through magmatism
is inadequate.
There is also perhaps something of a mass balance
problem - since everything should average out to
plot on the Geochron.