Chapter
17
The
other
isotopes
Earth
has
a spirit
of
growth.
Leonardo
do
Vinci
Background
The
various
chemical
elements
have
different
properties
and
can
therefore
be
readily
separated
from
each
other
by
igneous
processes
.
The
vari-
ous
isotopes
of
a
given
element
are
not
so
easily
separated.
The
abundances
of
the
radioactive
iso-
topes
in
the
crust
and
mantle,
and
their
decay
products,
are
not
constant
in
time.
Elemental
compositions
of
magmas
and
resid
u a l
mantle
are
complementary;
isotopic
compositions
are
iden-
tical,
but
they
diverge
with
time.
Therefore,
the
information
conveyed
by
the
study
of
isotopes
is
different
in
kind
than
that
provided
by
the
elements.
Each
isotopic
system
contains
unique
information,
and
the
radioactive
isotopes
allow
dating
of
processes
in
a
planet's
history.
The
unstable
isotopes
most
useful
in
geochemistry
have
a
wide
range
of
decay
constants,
or
half-
lives
,
and
can
be
used
to
infer
processes
occur-
ring
over
the
entire
age
of
the
Earth
(Table
17.1).
In
addition,
isotopes
can
be
used
as
tracers
and
in
this
regard
they
complement
the
major-
and
trace-element
chemistry
of
rocks
and
magmas.
Isotopes
in
magmas
and
gases,
however,
cannot
be
used
to
infer
the
depth
or
location
of
the
source
.
Studies
of
isotope
ratios
have
played
an
impor-
tant
role
in
constraining
mantle
an
d
cr
u
stal
evo-
lution,
mixing
and
the
long-time
isolation
of
mantle
components
or
reservoirs
.
Isotope
studies
derive
their
power
from
the
existence
of
suitable
pairs
of
isotopes
of
a
given
element,
one
a ' pri-
mordial'
isotope
present
in
the
Earth
since
its
for-
mation,
the
other
a
radiogenic
daughter
isotope
produced
by
radioactive
decay
at
a
known
rate
throughout
geological
time.
The
isotopic
compo-
sition
of
these
isotope
pairs
in
different
terres-
trial
reservoirs
-
for
example,
the
atmosphere
,
the
ocean,
and
the
different
parts
of
the
crust
and
mantle
-
are
a
function
of
the
transport
and
mixing
of
parent
and
daughter
elements
between
the
reservoirs.
In
some
cases
the
parent
and
daughter
have
similar
geochemical
charac-
teristics
and
are
difficult
to
separate
in
geological
processes.
In
other
cases
the
parent
and
daugh-
ter
have
quite
different
properties,
and
isotopi
c
ratios
contain
information
that
is
no
longer
avail-
able
from
studies
of
the
elements
themselves.
For
example
Sr-isotope
ratios
give
information
about
the
time-integrated
Rb
/
Sr
ratio
of
the
rock
or
its
source
.
Since
rubidium
is
a
volatile
ele-
ment
and
separates
from
strontium
both
in
pre-
accretional
and
magmatic
processes
,
the
isotope
ratios
of
strontium
in
the
products
of
mantle
dif-
ferentiation,
combined
with
mass-balance
calcu-
lations,
are
our
best
guide
to
the
rubidium
con-
tent,
and
volatile
content,
of
the
Earth.
Lead
iso-
topes
can
be
similarly
used
to
constrain
the
U/Pb
ratio,
a refractoryf(volatile,
chalcophile)
pair.
The
40
Ar
content
of
the
atmosphere
helps
constrain
the
4
°K
content
of
the
Earth;
both
Ar
and
K
are
considered
to
be
volatile
elements
in
cosmochem-
istry
.
In
other
cases,
such
as
the
neodymium-
samarium
pair,
the
elements
in
question
are
both
212
THE
OTHER
ISOTOPES
Table
17.1
/
Radioactive
nuclides
and
their
decay
products
Radioactive
D
eca
y
H
alf-
li
fe
Pare
nt
Product
(bil
li
o n
years)
23a
u
206
pb
4.468
232
Th
208
pb
14.
0 1
1
76
Lu
1
76
Hf
35.7
147
Sm
143
Nd
106
.0
87
Rb
87
Sr
48.8
ns
u
207
pb
0.7038
40K
40
Ar.
4o
c a
1.250
1
29
1
129
Xe
0.0
16
26
AI
26
Mg
8.8
x
1
o-
4
refractory,
have
similar
geochemical
characteris-
tics
and
are
probably
in
the
Earth
in
chondritic
ratios,
or
at
least
,
in
their
original
ratios
.
The
neodymium
isotopes
can
therefore
be
used
to
infer
ages
of
mantle
components
or
reservoirs
and
to
discuss
whether
these
are
enriched
or
depleted,
in
terms
of
Nd/Sm
,
relative
to
chon-
dritic
or
undifferentiated
material.
The
Rb/Sr
and
Nd/Sm
ratios
are
changed
when
melt
is
removed
or
added
or
if
sediment,
crust
or
seawater
is
added.
With
time
,
the
isotope
ratios
of
such
com-
ponents
diverge.
The
isotope
ratios
of
the
crust
and
differ-
ent
magmas
show
that
mantle
differentiation
is
ancient
and
that
remixing
and
homogeniza-
tion
is
secondary
in
importance
to
separation
and
isolation,
at
least
until
the
magma
cham-
ber
and
eruption
stages.
Magma
mixing
is
an
ef
ficient
way
to
obtain
uniform
isotopic
ratios,
such
as
occur
in
MORB.
Although
isotopes
cannot
tell
us
where
the
components
are,
or
their
bulk
chemistry,
their
long-term
isolation
and
lack
of
homogenization
plus
the
temporal
and
spatial
proximity
of
their
products
sug
gests
that,
on
average,
they
evolved
at
different
depths
or
in
large
blobs
that
differ
in
lithology
.
This
suggests
that
the
different
components
differ
in
intrinsic
density
and
melting
point
and
therefore
in
bulk
chemistry
and
mineralogy.
Melts,
and
partially
molten
blobs,
however,
can
be
buoyant
relative
to
the
shallow
mantle
even
if
the
parent
blob
is
dense
or
neutrally
buoyant.
The
crust
is
extremely
enriched
in
many
of
the
so-called
incompatible
elements,
particularly
the
large
ionic-radius
lithophil
e
(LIL)
or
high-fi
eld
str
ength
(HFS)
elements
that
do
not
readily
fit
into
the
lattices
of
the
major
mantle
minerals,
olivine
(ol)
and
orthopyroxene
(opx)
.
These
are
also
called
the
crustal
elements,
and
they
distinguish
enrich
ed
magmas
from
depleted
magmas
.
The
crust
is
not
particularly
enriched
in
elements
of
moderate
charge
having
ionic
radii
between
the
radii
of
Ca
and
A1
ions
.
This
suggests
that
the
mantle
has
retained
elements
that
can
be
accommodated
in
the
garnet
(gt)
and
clinopyroxene
(cpx)
structures.
In
other
words,
some
of
the
so-called
LIL
elements
are
actually
compatible
in
gt
and
cpx.
The
crust
is
also
not
excessively
enriched
in
lithium,
sodium
,
lead,
bismuth
and
helium
.
Isotopes
as
fingerprints
Box
models
Radiogenic
isotopes
are
useful
for
understanding
the
chemical
evolution
of
planetary
bodies.
They
can
also
be
used
to
fingerprint
different
sources
of
magma
.
In
addition
,
they
can
constrain
timin
g
of
events.
Isotopes
are
less
useful
in
constrain-
in
g
the
locations
or
depths
of
mantle
compo-
nents
or
reservoirs.
Just
about
every
radiogenic,
nucleogenic
or
cosmogenic
isotope
has
been
used
at
one
time
or
another
to
argue
for
a
deep
mantle
or
lower
mantle
source,
or
even
a
core
source,
for
ocean
island
and
continental
flood
basalts
and
carbonatites,
but
isotopes
cannot
be
used
in
this
way.
Isotope
ratios
have
also
been
used
to
ar
g
ue
that
some
basalts
are
derived
from
unfraction-
ated
or
unde
g
assed
reservoirs,
and
that
reservoir
boundaries
coincide
with
seismological
bound-
aries
(implying
that
major
elements
and
physical
properties
correlate
with
isotopes).
Some
mantle
rocks
and
magmas
have
high
concentrations
of
incompatible
elements
and
have
isotope
ratios
that
reflect
long-term
enrich-
ment
of
an
appropriate
incompatible-element
parent
.
The
crust
may
somehow
be
involved
in
the
evolution
of
these
magmas,
either
by
c
ru
s
tal
contamination
prior
to
or
during
erup
-
tion,
by
recyclin
g
of
continent-derived
sediments
or
by
delamination
of
the
lower
continental
crust
.
Stable
isotopes
can
be
used
to
test
these
hypotheses.
Early
models
of
mantle
geochemistry
assumed
that
all
potential
crust-forming
mate-
rial
had
not
been
removed
from
the
mantle
or
that
the
crust
formation
process
was
not
100%
efficient
in
removing
the
incompatible
elements
from
the
mantle.
Recycling
was
ignored.
Later
models
assumed
that
crustal
elements
were
very
efficiently
removed
from
the
upper
mantle-
and,
importantly,
only
the
upper
mantle
-
leaving
it
depleted.
Vigorous
convection
then
homogenized
the
source
of
midocean-ridge
basalts
,
which
was
assumed
to
extend
to
the
major
mantle
disconti-
nuity
near
650
km
depth.
A
parallel
geochemical
hypothesis
at
the
time
was
that
some
magmas
represented
melts
from
a
'primitive'
mantle
reservoir
that
had
survived
from
the
accretion
of
the
Earth
without
any
degassing,
melting
or
melt
extraction.
The
assumption
underlying
this
model
was
that
the
part
of
the
mantle
that
provided
the
present
crust
did
so
with
100%
efficiency,
and
the
rest
of
the
mantle
was
iso-
lated,
albeit
leaky.
In
this
scenario,
'depleted'
magmas
were
derived
from
a
homogenized
reser-
voir,
complementary
to
the
continental
crust
that
had
experienced
a
multi-stage
history
(stage
one
involved
an
ancient
removal
of
a
small
melt
fraction,
the
crust;
stage
two
involved
vigorous
convection
and
mixing
of
the
upper
mantle;
stage
three
involved
a
recent
extensive
melt-
ing
process,
which
generated
MORB).
Non-MORB
magmas
(also
called
'primitive,'
'less
depleted,'
'hotspot'
or
'plume'
magmas)
were
assumed
to
be
single-stage
melts
from
a
'primitive'
reservoir.
There
is
no
room
in
these
models
for
ancient
enriched
mantle
components.
These
early
'box
models'
contained
three
boxes:
the
present
con-
tinental
crust,
the
'depleted
mantle'
(which
is
equated
to
the
upper
mantle
or
MORB
reser-
voir)
and
'primitive
mantle'
(which
is
equated
to
the
lower
mantle)
with
the
constraint
that
primitive
mantle
is
the
sum
of
continental
crust
and
depleted
mantle.
With
these
simple
rules
many
games
were
played
with
crustal
recycling
rates
and
mean
age
of
the
crust.
When
contra-
dictions
appeared
they
were,
and
are,
tradition-
ally
explained
by
hiding
material
in
the
lower
crust,
the
continental
lithosphere
or
the
core,
or
by
storing
material
somewhere
in
the
mantle
for
ISOTOPES
AS
CHRONOMETERS
213
long
periods
of
time.
The
products
of
mantle
dif-
ferentiat
i
on
are
viewed
as
readily
and
efficiently
separable
but,
at
the
same
time,
storable
for
long
periods
of
time
in
a
hot,
convecting
mantle
and
accessible
when
needed.
A
l
arge
body
of
isotope
and
trace-element
analyses
of
midocean-ridge
basalts
demonstrates
that
the
upper
mantle
is
not
homogenous;
it
con-
tains
several
distinct
geochemical
domains
on
a
var
i
ety
of
length
scales.
However,
the
physi-
ca
l
properties
of
these
domains,
including
their
exact
location,
size,
temperature
and
dynamics,
remain
largely
unconstrained.
Seismic
data
indi-
cate
that
the
upper
mantle
is
heterogenous
in
physical
properties.
Plate
tectonic
processes
cre-
ate
and
remove
heterogeneities
in
the
mantle,
and
create
thermal
anomalies
.
Global
tomography
and
the
use
of
long-lived
isotopes
are
very
broad
brushes
with
which
to
paint
the
story
of
Earth
structure,
origin
and
evo-
lution.
Simple
models
such
as
the
one-
and
two-
reservoir
models,
undegassed
undifferentiated
lower-mantle
models,
and
whole-mantle
convec-
tion
models
are
the
results
of
these
broad-brush
pai
n
tings,
as
are
ideas
about
delayed
and
contin-
uous
formation
of
the
crust
and
core.
Short-lived
isotopes
and
high-resolution
and
quantitative
seismic
techniques
paint
a
comp
l
etely
different
story.
Isotopes
as
chronometers
Some
of
the
great
scientists,
carefully
ciphering
the
evidences
furnished
by
geology
,
have
arrived
at
the
conviction
that
our
world
is
prodigious
ly
old,
and
they
may
be
right,
but
Lord
Kelvin
is
not
of
their
opinion
.
Mark
Twain
Ear
lies
t
hi
st
o ry
of
t he Eart
h
The
current
best
estimate
for
the
age
of
the
Earth
Moon
meteorite
system
is
4.51
to
4.55
billion
years
(Dalrymple,
2001).
The
solar
nebula
cooled
to
the
point
at
which
solid
matter
could
con-
dense
by
~
4.566
billion
years,
after
which
the
Earth
grew
through
accretion
of
these
solid
particles;
the
Earth's
outer
core
and
the
Moon
were
in
place
by
~
4.51
billion
years.
214
THE
OTHER
ISOTOPES
Clair
Patterson
of
Cal
tech
determined
the
age
of
the
Earth
to
be
4.550
billion
years
(or
4.55
Gyr)
±7
0
million
years
from
long-lived
Pb
iso-
topes
(Patterson,
1956).
This
age
was
based
on
isotopic
dating
of
meteorites
and
samples
of
modern
Earth
lead,
all
of
which
plot
along
a
linear
isochron
on
a
plot
of
207
Pb
j
204
Pb
versus
2o6
Pb/
2o4
pb.
Numerous
other
isotopic
systems
are
used
to
determine
the
ages
of
solar
system
materials
and
ages
of
significant
events,
such
as
Moon
forma-
tion
.
The
isotopes
include
both
those
with
long
half
lives,
such
as
rubidium-87-
written
87Rb
or
87
Rb
(half
life
of
48
.8
billion
years),
which
decays
to
strontium-87-
written
87Sr
or
87
S
r-
and
those
that
have
half
lives
that
are
so
short
that
the
radioactive
isotope
no
longer
exists
in
measur-
able
quantities.
Meteorites
contain
evidence
for
decay
of
short-lived
extinct
natural
radioactivities
that
were
present
when
solids
condensed
from
the
primitive
solar
nebula.
Three
such
short-
lived
radioactivities,
53
Mn,
182
Hf
and
146
Sm,
have
half-lives
of
3.7,
9
and
103
million
years,
respec-
tively.
The
evidence
indicates
rapid
accretion
of
solid
bodies
in
the
solar
nebula
,
and
early
chem-
ical
differentiation
.
A
hot
origin
of
the
Earth
is
indicated
.
The
energetics
of
terrestrial
accretion
imply
that
the
Earth
was
extensively
molten
in
its
early
history;
giant
impacts
would
have
raised
temperatures
in
the
Earth
to
about
5000-10
000
K.
The
rates
and
timing
of
the
early
processes
of
Earth
accretion
and
differentiation
are
stud-
ied
using
isotopes
such
as
129
I-
129
Xe,
182
Hf-
182
W,
146Sm-142Nd,
23S
/
23s
0
_
207
/
206p
b
and
244p
u_1
36X
e
and
simple
assumptions
about
how
parent
and
daughter
isotopes
distribute
themselves
between
components
or
geochemical
reservoirs.
The
Hf-W
and
U-Pb
chronometers
are
thought
to
yield
the
time
of
formation
of
the
core,
assuming
that
it
is
a
unique
event.
The
parent
elements
(Hf
and
U)
are
assumed
to
be
retained
in
silicates
during
accretion
and
the
daughters
(W
and
Pb)
to
be
partitioned
into
the
core.
The
partition-
ing
of
W
and
Pb
between
metals
and
silicates
-
mantle
and
core
-
also
depends
on
the
oxygen
fugacity
and
the
sulfur
content
of
the
metal
and
the
mantle.
Under
some
conditions,
W
is
a
siderophile
element
while
Pb
is a
chalcophile
par-
t
it
ioning
only
slightly
into
the
metal
phase.
Cur-
rently,
the
upper
mantle
is
oxidized
and
the
main
'metallic'
phases
are
Fe-Ni
sulfides.
146
Sm-
142
Nd
and
182
Hf-
182
W
chronometry
indicate
that
core
formation
and
mantle
differentiation
took
place
during
accretion,
producing
a
chemically
differentiated
and
depleted
mantle
.
The
decay
of
182
Hf
into
1
82
W
occurs
in
the
silicate
mantle
and
crust.
Tungsten
is
then
partitioned
into
the
metal.
The
hafnium-tungsten
pair
shows
that
most
of
Earth
formed
within
~
10
million
years
after
the
formation
of
the
first
solid
grains
in
the
solar
nebula
.
A
plausible
model
for
the
origin
of
the
Moon
is
that
a
Mars-sized
object
collided
with
the
Earth
at
the
end
of
its
accretion,
generating
the
observed
angular
momentum
and
an
Fe-depleted
Moon
from
the
resulting
debris
disc.
This
may
have
occurred
40-50
Myr
after
the
beginning
of
the
solar
system.
The
Moon-forming
impact
[Google
images]
contributed
the
final
10
%
of
the
Earth's
mass,
causing
complete
melting
and
major
degassing.
Core
formation
occurred
before,
during
and
after
the
giant
Moon-forming
impact,
within
tens
of
millions
of
years
after
the
formation
of
the
solar
system.
Some
of
the
terrestrial
core
was
probably
from
the
impactor.
Giant
impacts
melt
a
large
fraction
of
the
Earth
and
reset
or
partially
reset
isotopic
clocks.
Mass
balance
calculations
show
that
>
70%
of
the
mantle
was
processed
in
order
to
form
the
crust
and
upper
mantle.
Parts
of
the
upper
mantle
are
enriched
but
most
of
the
mantle
is
either
depleted
and
fertile
(the
MORB
reser-
voir)
or
depleted
and
infertile
or
barren.
Enriched
regions
(crust)
or
components
(kimberlites,
car-
bonatites
...
)
typically
are
so
enriched
that
a
small
volume
can
balance
the
depleted
regions.
Short-lived
radioactivities
can,
in
principle,
deter-
mine
when
this
fractionation
occurred.
Some
was
contemporaneous
with
accretion
and
some
may
have
happened
during
Moon
formation.
Elementary
isotopology
Pb
Isotopes
are
usually
expressed
as
ratios
involving
a
parent
and
a
daughter,
or
a
decay
product
and