Download 1 Radioactive and Radiogenic Isotopes Isotopes: Same Z, different

1
Radioactive and Radiogenic Isotopes
Isotopes: Same Z, different mass numbers
Types of isotopes:
Radioactive: Decay over time into a daughter isotope (known as a radiogenic isotope) by
emitting (or even capturing)  or  particles as well as  rays. Radioactive isotopes either
occur naturally, or are produced artificially. Note that the deacy process is independent of
the bond type, T, P, ... etc.
Stable isotopes: Are those that do not decay over time.
Reasons for radioactive decay:
Most stable atoms have a subequal number of protons and electrons. Atoms which have
an excess or deficiency of neutrons or protons will be unstable, and will undergo
radioactive decay in order to reach such a stable configuration (Fig. 1).
Modes of radioactive decay:
1- Alpha decay: Occurs mostly in elements with Z > 58, although such a mode of decay
can occur in lighter elements. An alpha particle is a 4He nucleus.
2- Decay involving beta particles:
(i) Beta particle emission (electrons)
(ii) Positron emission
(iii) Electron capture
3- Fission: Could be natural or induced. In this case, the nucleus breaks into two
fragments of unequal weight. Causes damage in the host mineral and is the basis for the
method of fission track dating.
Radioactive decay law:
The principal equation governing the decay of a radioactive isotope to a more stable
daughter isotope, and which is applicable to all age dating methods can be easily derived
from the rate law equation
-dN/dt = k (N)
Which by rearranging,integrating, and taking the natural logs yields:
ln (N/N°) = -k t
(considering that the integration constant is equal to N°). Replacing k by  (the decay
constant), this equation becomes:
N = N°e-t
where N is the number of atoms of the parent isotope now present in the sample, "N°" the
original number of atoms of this radioactive parent isotope (when t = 0),  is the decay
constant, and "t" the time elapsed (since the crystallization of the mineral containing the
radioactive element), leaving behind "N" atoms of this parent isotope from the original
2
N° atoms. The decay constant  is related to the half life "T1/2" of the radioactive isotope
by the equation:
 = 0.693/T1/2
where the half life of this radioactive isotope is defined as the time necessary for one half
of a given number of radioactive atoms to decay. Therefore, when t = T1/2, N = 1/2 N°.
If the decay of a radioactive parent produces a radiogenic daughter isotope, and assuming
that our sample of interest (or mineral dated) had no atoms of this daughter isotope at
time t = 0, then the total number of atoms of the daughter isotope D* will be given by:
D* = N° - N
Substituting for N°,
D* = N(et-1).
Therefore, the age of a sample (t) can be determined if one knows the total number of
parent and daughter atoms in the mineral (or rock) dated (i.e. the concentrations of these
isotopes), and the decay constant (or half life) of the radioactive isotope, assuming that
the sample did not contain any of the daughter isotope at time t = 0, and that there was
no loss or gain of either the daughter or the parent atoms. The relationship between the
concentrations of the parent and daughter atoms as a function of time is shown in Fig. 2.
However, in nature, most of the minerals dated incorporate an amount of the daughter
element in their structure at the time of their crystallization; herein designated as D° (i.e.
before the parent isotope began to decay). Therefore, the total number of daughter atoms
in a mineral will be given by:
Dtotal = D° + D*
Dtotal = D° + N(et-1)
This necessitates knowledge of D° in order to calculate the age correctly.
Determination of D° values:
D° is "determined" by two methods:
(a) In many igneous rocks thought to have formed from a primary magma, the value of D°
for a particular system is assumed to be equal to the concentration of the daughter isotope
in standard meteorites, which are thought to represent the early composition of the earth
or primordial mantle. In other systems, D° is assumed to be equal to zero (if the daughter
isotope is geochemically different from its parent, and is not readily incorporated in the
dated minerals.
(b) The isochron technique: Involves analyzing several minerals or rock samples for
parent and radiogenic daughter isotopes, and plotting the ratios of the concentrations of
these two isotopes to the common non-radiogenic isotope of the daughter element against
one another. However, the minerals or rocks selected for such analysis should have
3
crystallized or formed at the same time (in the case of minerals, they should all be from
the same sample!). Such plots yield a straight line the slope of which is proportioanl to
the age of the samples, and the intercept yields the value of D°.
I- Age Dating
Conditions necessary for successful age dating:
(1) If dating is carried out on a mineral, one must know the "age" of this mineral
relative to other coexisting minerals formed during the igneous, metamorphic,
sedimentary, or weathering history of the sample in question. For example, if the mineral
dated crystallized during weathering and/or retrogression of a metamorphic or igneous
rock, the "age" obtained will be "younger" than the age of peak metamorphism or
crystallization from a magma.
(2) The decay constants of the systems used must be well known.
(3) The concentrations of the parent and daughter isotopes must be measured
accurately and precisely
(4) The system must have remained closed to the parent and daughter isotopes
after the dated event (in our case, after metamorphism), so that the daughter/parent
isotope ratio is not changed by later events such as thermal overprinting, hydrothermal
alteration, or weathering.
(5) The dated mineral or rock should not have had any original daughter isotope in
its structure prior to crystallization. If it did, then that amount should be properly
determined or estimated, otherwise, one would get an age that is "too old".
(6) If dating is performed by the isochron technique, then the "isochron" better be
a true one, rather than a mixing line (i.e., samples or minerals used must have formed at
the same time!)
Definition: Closure Temperature: Is the temperature below which the mineral retains all
of its daughter isotope; i.e. the temperature at which the system becomes closed to that
daughter isotope.
Different minerals have different closure temperatures for different isotopic systems.
Closure temperatures depend on:
(1) Grain size
(2) Grain shape and geometry
(3) Mineral composition
(4) Rate of cooling
(5) Activation energy
Methods of age dating: (Table 1)
(1) U-Pb method
(2) Rb-Sr
(3) Sm-Nd
(4) K-Ar and 40Ar/39Ar
(5) Fission track dating
4
(6) 14C method
(7) U- Th method
The U - Pb method
Principles:
T1/2 = 4.468 .
238U  206Pb
+ 8  + 6  + 
235U  207Pb
+ 7  + 4  + 
109
T1/2 = 0.7038 .
109
232Th
 208Pb + 6  + 4  + 
T1/2 = 2.47 . 105
The common Pb isotope is 204Pb.
Applications
With these three radioactive decay series, any mineral that can accomodate U in its
structure can be used for age dating using all three series. If the system has remained
closed to U and Pb since the time of its formation, ages calculated by each one of these
decay series should be identical (concordant). The conventional way of using the U-Pb
method relies on plotting the values of 206Pb*/238U vs. 207Pb*/235U, where:
206Pb*
= 206Pb/204Pb - (206Pb/204Pb)i, and 207Pb* = 207Pb/204Pb - (207Pb/204Pb)i,
where the subscript "i" denotes the initial isotope ratio.
Since 238U and 235U have different half lives, all minerals that have remained closed to U
and Pb since their formation should plot on a curve known as the "concordia" (Fig. 3). In
practice, minerals do not plot on this curve, but usually below it, and the age obtained
from 208Pb is usually the "youngest", whereas that obtained from 207Pb measurements is
the oldest. Grains of the same mineral separated from the same sample were found to plot
along a chord known as "discordia", which plots below concordia. This phenomenon is
due to the loss of Pb after the crystallization of the mineral, usually as a result of chemical
weathering, continuous diffusion, or an episode of thermal overprinting (metamorphism),
which affect the different grains from the same sample differently (depending on the
composition of these grains, their sizes, ... etc.). Lines drawn from the origin passing
through each point intersect the concordia at points ('), each defining the "time" at
which Pb loss took place for each grain (Fig. 4). This information can be useful in
determining the age of the thermal overprint if episodic Pb loss is to be believed.
However, keep in mind that such "ages" may be meaningless, as Pb loss may take place
by continuous diffusion. On the other hand, the discordia intersects concordia in two
points that define (a) the time elapsed since the original crystallization of the mineral (
°) and (b) the time elapsed since the system became closed to U and Pb () (Fig. 4).
5
A third explanation of discordia (other than episodic Pb loss or loss of Pb by continuous
diffusion) suggests that radiation damage resulting from alpha decay of U and Th results
in the formation of microcapillary channels in the crystals that allow water to enter such
crystals, and escape with dissolved Pb upon the release of pressure. If this is the case, the
lower intercept of discordia with concordia "" would define the time at which rock
exhumation took place.
The 207Pb/204Pb vs 206Pb/204Pb isochron technique:
Plots of 207Pb/204Pb vs 206Pb/204Pb for a suite of "cogenetic" samples allows for the
determination of the age of these samples (which is then equal to the slope of the
isochron; Fig. 5). This method reduces errors arising from recent losses of Pb or U by
such methods as chemical weathering, and yields the oldest ages, which are often
considered the most reliable ages.
Single grain dating:
With the advent of the ion microprobe, it has become possible to date single grains. This
is particularly useful because some samples contain several different populations of
zircon that formed at different times (e.g. inherited igneous zircons and metamorphic
zircons), whereas in other samples, the zircon crystals may be zoned. By focussing an ion
beam on specific parts of a zircon crystal, one may be able to determine the ages of the
cores vs. rims,.. etc., which will in turn help understand the history of the sample.
Minerals suitable for U-Pb dating:
The mineral that is most suited for the U-Pb dating is zircon. Since zircon does not
accomodate much Pb in its structure during crystallization, but incorporates a significant
amount of U, Pb occurring in zircon will be almost entirely the product of radioactive
decay. Zircon is a refractory mineral, that recrystallizes only at high temperatures. Hence,
ages obtained by U-Pb dating of zircon from a metamorphic rock may not reflect the age
of metamorphism, but rather the age of original crystallization of these zircons. Other
minerals suitable for U-Pb dating include monazite and sphene.
6
The Sm-Nd method of dating
Principle:
147Sm
 143Nd +  + 
T1/2 = 1.06 . 1011
Geochemistry and minerals dated:
Nd+3 has the larger radius of these two isotopes, and therefore tends to concentrate in
minerals that crystallize later in the magmatic sequence (i.e. with increasing
differentiation). Because of the long half life of 147Sm and the high closure temperature
of this system, this method is more suited for dating old mafic and ultramafic igneous or
high temperature metamorphic rocks (as, gabbros, peridotites, eclogites and granulites).
Dating is performed by determining the slopes of whole rock isochrons (plots of
143Nd/144Nd vs. 147Sm/144Nd) for a cogenetic suite of rocks, or determining ages for
such minerals as garnets, clinopyroxenes and plagioclase feldspars.
The Rb-Sr method
Principle:
87Rb
 87Sr +  +  + 
T1/2 = 4.89 . 1010
Geochemistry and dated minerals:
Sr replaces Ca (especially in eight-fold coordinated sites) in such minerals as aragonite,
plagioclase and apatite. Rb replaces K in micas, feldspars and clay minerals. Because
these minerals are common rock-forming ones, this method is quite powerful.
Method:
The common (non-radiogenic) isotope of Sr is 86Sr, and is used to express the
concentrations of these two isotopes in minerals and rocks as 87Rb/86Sr, and 87Sr/86Sr
(because mass spectrometers measure isotopic ratios, not absolute concentrations). An
age may be assigned for a mineral or whole rock from the relationship:
87Sr/86Sr = (87Sr/86Sr) + 87Rb/86Sr (et-1)
i
provided that the term: (87Sr/86Sr)i (the initial ratio before decay) is known.
Alternatively, the isochron method can be used, where one plots 87Sr/86Sr vs. 87Rb/86Sr
for minerals and whole rocks (Fig. 6). The slope of such curve would be proportional to
the age of the mineral or rock, and the intercept with the ordinate yields the (87Sr/86Sr)i
value. Rocks that are cogenetic or minerals from the same rock should therefore all fall
on this isochron, as they are all of the same age (Fig. 6).
For rocks that were affected by some thermal event during their history, the Rb-Sr age
obtained for their minerals may differ from that obtained for the whole rock, as Sr in the
minerals tends to be isotopically homogenized by metamorphic events. This results in two
isochrons with two different intercepts (i.e. different (87Sr/86Sr)i values) and different
7
ages (Fig. 7). The slope of the mineral isochron is proportional to the age of
metamorphsim; the intercept yielding the new (87Sr/86Sr)i value after Sr homogenization
(due to metamorphism), whereas the whole rock isochron yields the original age of
formation of these rocks prior to metamorphism (Fig. 7). This is merely because some
minerals incorporate Sr in their structure and almost no Rb (e.g. apatite), whereas others
preferentially incorporate Rb rather than Sr (e.g. biotite). Thus, during metamorphism, Bt
that recryatllizes loses 87Sr that had accumulated in its structure by the decay of Rb,
whereas apatite takes up that amount of 87Sr, increasing its (87Sr/86Sr)i ratio to a new
value (the new intercept with the ordinate; cf Figs. 7 & 8). Note that the closure
temperature for the Rb/Sr method is lower than that for the Sm-Nd one, making it more
useful for dating metamorphic rocks metamorphosed under crustal conditions. However,
keep in mind that different minerals have different closure temperatures (Table 2).
The K-Ar and 40Ar/39Ar methods
This is one of the most popular techniques of dating metamorphic rocks, since K is one of
the most common elements and enters in the structures of several major rock-forming
minerals.
Principles:
40K
40K
+   40Ar + 
+ +1  40Ca + 
Only 11.2% of the 40K atoms decay to 40Ar, the rest decaying to 40Ca, which is of no use
in geochronology because 40Ca is the most common isotope of Ca. Accordingly, the
following equation applies:
40Ar + 40Ca = 40K(et -1),
where  is the combined decay constant for the two series (i.e. K to Ca and K to Ar),
and is equal to 5.543 . 10-10 y-1. The combined half life T1/2 of 40K is therefore equal to
1.25 . 109 years.
Method:
This method can be used to date micas, feldspars, hornblende and whole rocks, provided
that all of the 40Ar in these minerals (or rocks) was formed by radioactive decay, i.e. the
rock did not contain any 40Ar prior to the crystallization of these minerals, and if it did, it
was not incorporated in their structures. On the other hand, if such minerals do
incorporate inherited 40Ar in their structures, the ages will be "too old", and the mineral is
said to contain "excess Ar". Because Ar diffuses out of the crytstal structure if the
mineral is heated, and is generally difficult to retain at high T, the K-Ar method is most
successful in dating relatively young, volcanic rocks that cooled rapidly and were not later
affected by some thermal event.
8
The minerals to be dated are separated, and the K concentration is determined by some
chemical method, whereas the concentrations of the different Ar isotopes are measured
using a mass spectrometer. The ages are then determined from the relation:

i + (e/) 40K/36Ar (e t -1)
40Ar/36Ar = (40Ar/36Ar)
where e is the decay constant of K to 40Ar and  is the combined decay constant.
The isotopic composition of Ar in the atmosphere of the earth is: 40Ar = 99.6%, 38Ar =
0.063%, 36Ar = 0.337%, and the atmospheric 40Ar/36Ar is therefore 295.5. Therefore, on
an isochron diagram of 40Ar/36Ar vs. K/36Ar (or 39Ar/36Ar in the case of 40Ar/39Ar
dating), the intercept with the ordinate should be equal to 295.5 if the dated sample
contained no inherited or excess 40Ar.
To avoid errors that may arise from determining K and Ar separately by two different
techniques, the sample is irradiated in a nuclear reactor to convert all 40K into 39Ar. The
produced 39Ar can therefore be measured directly with 40Ar in the same sample in a mass
spectrometer, and will be directly proportional to the amount of K in the sample. This is
the basis for the 40Ar/39Ar technique. By heating the sample in increments (steps), the
gas incorporated in the structure of the minerals is released in stages. Analyzing the
isotopic ratio of the gas released in each step yields an "apparent age" calculated from the
39Ar/40Ar ratio determined for that gas fraction. Plotting the "apparent age" of each step
against the percentage of 39Ar released yields a spectrum (see figures). If all apparent
ages determined for the different increments coincided within error, the spectrum would
have the shape of a "plateau" that may represent the age of crystallization of the mineral
dated (Fig. 9), and would have a well defined isochron (on a 40Ar/36Ar vs. 39Ar/36Ar
diagram; Fig. 10) with an intercept of 295.5. Alternatively, some of the low temperature
steps may yield "older" or "younger" ages, compared to the rest of the plateau, which in
turn yield a different intercept on the isochron diagram and may therefore be a good way
of telling if the sample contained "excess Ar" or if it lost Ar after its crystallization (e.g.
Fig. 10). This makes the 40Ar/39Ar method more useful than the conventional K-Ar
method in understanding the thermal history of the mineral separate. This technique also
has the advantage of identifying more than one generation or population of a mineral in
the dated separate.
Closure temperatures:
The closure temperatures of amphiboles, plagiocalse, biotite and muscovite are lower for
the 40Ar/39Ar system compared to the U-Pb and Rb-Sr systems. Tc of hornblende is 
500°C, for biotite  370-400°C, for muscovite  350°C, and for microcline  132°C
(all estimates based on a cooling rate of 5°C/Ma for fine-- to medium grained crystals).
Dating Hb, Bt and muscovite from the same sample by the 40Ar/39Ar method would yield
valuable information on the cooling history and exhumation rate of this sample (Fig. 11).
Similarly, cooling rates and cooling curves can be derived by dating several minerals
using different methods (Fig. 12).
9
Fission track dating
Principle
The spontaneous fission of 238U causes defects in the crystals in which it is contained.
Such defects take the form of tracks (Fig. 13) known as fission tracks. The density of
fission tracks is proportional to the amount of 238U in the mineral, and by proper
standardization and calibration, may be used to determine the time elapsed since these
tracks were produced. However, with increasing temperature, these tracks fade (or are
annealed), until a specific temperature is reached beyond which all tracks disappear. The
fission track method can therefore be used to determine the time elapsed since the mineral
cooled through that temperature.
Method:
The minerals most commonly used for fission track dating are apatite, sphene and zircon.
Epidote can also be used, but the behaviour of its fission tracks is poorly understood. So
far, apatite is the most widely used mineral for fission track dating. Annealing of fission
tracks in apatite begins at a T of  50°C and is completed at T  of 175°C. The
annealing T of sphene ranges from 250 to 420°C (Fig. 14).
For age determination, the mineral is irradiated for a specific time period, and the original
fission tracks are calibrated against the secondary tracks resulting from irradiation. The
mineral is etched by an acid to enhance the tracks, which are then counted within a
known area. The track lengths are also measured, as such lengths reflect the cooling rate
(shorter tracks indicate partial annealing, whereas longer tracks suggest rapid cooling and
uplift). A bimodal distribution of track lengths indicates that the mineral evidenced some
thermal event that led to the incomplete or partial annealing of tracks.
Due to the relatively low temperatures of track annealing of apatite, sphene and zircon,
the fission track method is most useful in determining the uplift rates of metamorphic
rocks, and the thermal histories of sedimentary basins.
The U-Th method
This method is based on the fractionation of 234U and its daughter 230Th, and therefore
their separation. this happens because U is commonly hexavalent, whereas Th is
tetravalent. 230Th has a short half life (relative to 232Th), and can therefore be used to
date young sediments and calcite (< 150,000 yrs old), as well as sedimentation rates,
particularly where the depth below the sediment water interface is known.
10
14C
method of dating
Part of the 14N in the atmosphere is converted to 14C by reaction with neutrons from
cosmic rays. 14C is radioactive, and decays to 14N by emission of an electron with a half
life of 5730 yrs. 14C is also oxidized to CO2, which is absorbed by living organisms.
Such 14C is in equilibrium with the one in the atmosphere. When the organisms die, the
amount of 14C in the dead body decreases by decay. Ages of the "dead body since its
death" are determined by measuring the radioactivity resulting from the 14C decay (in #
of disintegrations per minute per gm of C) in that body "A", and comparing it to the
radioactivity resulting from a C compound (or organic matter) in equilibrium with the
atmosphere "A°". The age is then determined using the relation:
A = A°e-t
This method is useful only for determining ages of organic material that is < 70,000 yrs
"old".
Precautions:
14C dates are affected by:
(i) Changes in the cosmic ray intensity over time (hence making A° not a real
constant!)
(ii) Changes in the amount of organic activity on the earth's surface
(iii) Changes in the amount of inert CO2 added to the atmosphere
(iv) Changes in the 14C of the atmosphere by nuclear explosions.
II- The Use of Radiogenic isotopes as tracers
In igneous petrogenesis, radiogenic isotopes are useful for identifying the source of the
magma from which the igneous rock crystallized, as well as some of the processes that
contributed to its formation (e.g. assimilation, magma mixing, ... etc.). The basic principle
beehind this application is that the parent and daughter isotopes have different
geochemical characteristics, and are therefore fractionated among crystallizing phases.
The value of D°, determined using the isochron technique for a group of comagmatic
samples would therefore always be characteristic of the original magma from which these
rocks crystallized, and will be unaffected by the degree of fractional crystallization or
partial metling, but would be highly sensitive to assimilation or magma mixing. Specific
examples follow.
Rb-Sr and 87Sr/86Sr systematics:
Returning to the isochron equation for this system:
87Sr/86Sr = (87Sr/86Sr) + 87Rb/86Sr (et-1)
i
The term: (87Sr/86Sr)i is the initial 87Sr/86Sr ratio before decay of any Rb in the
crystallizing rock or mineral (i.e. at the time of crystallization of this igneous mineral or
rock). This equation shows that the 87Sr/86Sr ratio of a rock depends on three factors: (a)
the initial 87Sr/86Sr of the magmatic reservoir from which the rock formed (87Sr/86Sr)i
and (b) the age of this rock; the older the rock the higher its 87Sr/86Sr ratio, and (c) the
87Rb/86Sr value.
11
If this rock crystallized from the primordial mantle, then a reasonable value for
(87Sr/86Sr)i will be 0.699, which is the value determined for 4.6 billion year old
meteorites with the lowest Rb/Sr ratios (known as basaltic achondrites with best initial
ratios, or BABI). The present - day 87Sr/86Sr value of this rock will therefore be ~ 0.703,
as dictated by the isochron equation. Alternatively, if the rock did not form from such a
primitive magma, its (87Sr/86Sr)i can be determined by the isochron method.
Sr replaces Ca (especially in eight-fold coordinated sites) in such minerals as plagioclase
and apatite. Rb replaces K in micas and K-feldspars. Rb is in almost all cases more
incompatible than Sr (except when we are dealing with crustal melts fractionating K-spar
and micas). Accordingly, partial melting almost always results in the concentration of Rb
in the melt, whereas Sr will preferentially reside in plagioclase. The Rb/Sr ratio in this
partial melt will therefore be high (especially if the degree of partial melting is low).
Migration of these partial melts from the mantle to the crust will enrich the crust in Rb,
and the 87Sr/86Sr ratio of the continental crust will gradually increase over time (Fig. 15).
If the age of the rock forming from the crystallization of this partial melt is known, then
its 87Sr/86Sr will be related to the original Rb/Sr ratio of the partial melt by the isochron
equation, and the (87Sr/86Sr)i value can be easily determined. This value will therefore be
the 87Sr/86Sr ratio of the original partial melt. If we are dealing with a young volcanic
rock, then (87Sr/86Sr)i = 87Sr/86Sr (because t ~ 0), and there is no need for knowing the
exact age of the rock. It can therefore be seen that the 87Sr/86Sr ratio of an igneous rock
will be a "signature" of the particular magma reservoir from which it formed, as it will be
unaffected by later processes of partial melting or fractional crystallization (only the
Rb/Sr or absolute Sr concentrations are affected by such processes, but not the 87Sr/86Sr
ratio).
Magmas resulting from the partial melting of mantle rocks will therefore have low
87Sr/86Sr ratios (0.703). On the other hand, magmas resulting from the partial melting of
highly evolved (Rb - rich) crustal rocks will crystallize igneous rocks characterized by
much higher 87Sr/86Sr ratios (0.740). Rocks with intermediate values may have therefore
formed from the assimilation of some crustal material. This technique is therefore very
powerful for identifying the magmatic source of an igneous rock, and identifying whether
the magma has been contaminated by crustal rocks. It has therefore been used
successfully in identifying the origin of many granites. Some 87Sr/86Sr values for some
common igneous rocks from different tectonic settings are listed in Table 3.
Sm-Nd Systematics
The common isotope of Nd is 144Nd, and the concentrations of both 147Sm and 143Nd are
compared to 144Nd. An isochron equation written for this system will therefore be:
143Nd/144Nd
= (143Nd/144Nd)i + 147Sm/144Nd (et-1)
Both Sm and Nd are rare earth elements with trivalent cations. However, Nd+3 has the
larger radius of these two isotopes, and therefore tends to concentrate in minerals that
12
crystallize later in the magmatic sequence (i.e. it is more incompatible than the parent
isotope 147Sm).
The Sm/Nd technique can therefore be used to identify the source of the magma from
which an igneous rock crystallized. Like the 87Sr/86Sr ratio, the 143Nd/144Nd ratio for an
igneous rock will not be affected by the number of times of partial melting or fractional
crystallization which this rock has undergone, and will only depend on the age of the rock
and the original 143Nd/144Nd ratio of the magma from which it has crystallized.
However, unlike the case of Rb and Sr, the daughter element Nd is more incompatible
than Sm. Therefore, increased degrees of partial melting of a rock will result in the
decrease of the Rb/Sr ratio and the simultaneous increase of the Sm/Nd ratio in the melt
(Fig. 16). On the other hand, progressive fractional crystallization of a magma depletes
the remaining melt in Sm relative to Nd, while enriching it in Rb (i.e. Sm/Nd decreases,
whereas Rb/Sr increases in the liquid).
One of the best ways of detecting the source of a magma is to plot 143Nd/144Nd of the
rock vs. its 87Sr/86Sr ratio. If all magmas formed at the same time by partial melting of a
single unique reservoir in the mantle, then all rocks would plot at the same point as that
of the mantle. However, we have already seen that different rocks have different
87Sr/86Sr ratios (reflecting different sources) and will therefore also have different
143Nd/144Nd ratios. Because of the geochemical differences between both systems
outlined above, it is clear that different rocks crystallizing from a magma produced in the
mantle will plot on a straight line with a negative slope that passes through the values of
the primordial mantle (again represented by ratios measured for meteorites with the
lowest Rb/Sr and highest Sm/Nd values; Fig. 17). This line is known as the mantle array
or mantle correlation line (Fig. 17).
Rocks that plot on the mantle array but in the upper left hand corner of this diagram (i.e.
those which have lower 87Sr/86Sr and higher 143Nd/144Nd ratios compared to the
primordial mantle) must have formed by partial melting of a depleted mantle (i.e. a
mantle that has undergone one or more stages of partial melting earlier). On the other
hand, rocks that plot in the lower right corner of the diagram but fall on the mantle array
must have formed from an enriched mantle. Samples which plot off the mantle array are
probably ones that have been contaminated to some extent. Because of the enrichment of
Rb in the crust, and because the major contaminant of a magma will be continental crust,
most of these samples will plot above the mantle array in the lower right hand corner of
the diagram (Fig. 17).
Figure 17 shows that MORBs represent products of partial melting of a strongly depleted
mantle, plotting in the upper left hand corner of the diagram. Ocean island basalts (OIV)
and AOBs also plot in the depleted mantle area on the mantle array, but fall closer to the
chondrite (or primordial mantle) values, indicating that they result from smaller degrees
of partial melting. (Kimberlites, not shown on Fig. 17, also plot close to the primordial
mantle values within the depleted area). Continental flood basalts are characterized by a
wide range of 87Sr/86Sr values resulting from various degrees of contamination of their
13
magmas with crustal material, and therefore plot off the mantle array usually in the
bottom right hand corner of the diagram (Fig. 17).
Figure 18 therefore illustrates that there are different magma reservoirs in the mantle, and
that the mantle is heterogeneous. If this heterogeneity of the mantle had been established
at the time of formation of the earth, then all parts of the mantle, each with its
characteristic 87Sr/86Sr ratio, should lie on the same isochron yielding an age equivalent
to that of the earth (i.e. 4.6 billion years). However, on an isochron diagram, different
rocks were found to lie significantly off this 4.6 billion year isochron (known as the
"Geochron"; Fig. 18). Although there is considerable scatter on this diagram, suggesting
that heterogeneity was established over a long period of time, many rocks fall on a
straight line which yields an age of 1500 Ma (Fig. 18). This suggests that a significant
event which contributed to mantle heterogeneity took place ~ 1500 Ma. Many models
have been proposed to account for this event, the most popular of which suggests that
parts of the mantle have been metasomatised (and enriched in LILE) by fluids derived
from the dehydration of subducted slabs. This selective metasomatism seems to be
reasonable since major elements seem to be more or less homogeneously distributed in
the mantle (unlike trace elements).