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GEOCHRONOLOGY HONOURS 2006
Lecture 01
Introduction to Radioactive Decay and Dating
of Geological Materials
Revision – What is an Isotope?
Protons, Neutrons and Nuclides
 The mass of any element is determined by the protons plus
the neutrons.
 Where the element has different numbers of neutrons
these are called isotopes
 Any element can have isotopes that have the same proton
number but different numbers of neutrons and hence a
different mass number.
 The mass of any element is made up of the sum of the mass
of each isotope of that element multiplied by its atomic
abundance.
 Various combinations of N and Z are possible, although all
combinations with the same Z number are the same element.
Stable versus Unstable Nuclides
 Not all combinations of N and Z result in stable
nuclides.
 Some combinations result in stable configurations
– Relatively few combinations
– Generally N ≈ Z
– However, as A becomes larger, N > Z
 For some combinations of N+Z a nucleus forms but
is unstable with half lives of > 105 yrs to < 10-12 sec
 These unstable nuclides transform to stable
nuclides through radioactive decay
Radioactive Decay

Nuclear decay takes place at a rate that follows
the law of radioactive decay

Radioactive decay has three important features
1. The decay rate is dependent only on the energy state of
the nuclide
2. The decay rate is independent of the history of the
nucleus
3. The decay rate is independent of pressure, temperature
and chemical composition

The timing of radioactive decay is impossible to
predict but we can predict the probability of its
decay in a given time interval
Radioactive Decay
 The probability of decay in some infinitesimally
small time interval, dt, is ldt, where l is the decay
constant for the particular isotope
 The rate of decay among some number, N, of
nuclides is therefore
dN / dt = -lN
[eq. 1]
 The minus sign indicates that N decreases over
time.
 Essentially all significant equations of radiogenic
isotope geochronology can be derived from this
expression.
Types of Radioactive Decay
 Beta Decay
 Positron Decay
 Electron Capture Decay
 Branched Decay
 Alpha Decay
Beta Decay
 Beta decay is essentially the transformation of a
neutron into a proton and an electron and the
subsequent expulsion of the electron from the
nucleus as a negative beta particle.
 Beta decay can be written as an equation of the
form
40
K
19
->
40
Ca
20
+
b-
_
++Q
_
Where b- is the beta particle,  is the antineutrino and Q
stands for the maximum decay energy.
Positron Decay
 Similar to Beta decay except that now a proton in
the nucleus is transformed into a neutron, positron
and neutrino.
 Only possible when the mass of the parent is
greater than that of the daughter by at least two
electron masses.
 Positron decay can be written as an equation of
the form
18 -> O18 + b+ +  + Q
F
9
8
Where b+ is the positron,  is the neutrino and Q stands for
the maximum decay energy.
Positron VS Beta Decay
The atomic number of the
The atomic number of the
daughter isotope is decreased
daughter isotope is increased by
by 1 while the neutron number
1 while the neutron number is
is increased by 1.
decreased by 1.
Therefore in both cases the parent and daughter isotopes have the
same mass number and therefore sit on an isobar.
Electron Capture Decay
 Electron capture decay occurs when a nucleus
captures one of its extranuclear electrons and in
the process decreases its proton number by one
and increases its neutron number by one.
 This results in the same relationship between the
parent and the daughter isotope as in positron
decay whereby they both occupy the same isobar.
Alpha Emission
 Represents the spontaneous emission of alpha
particles from the nuclei of radionuclides.
 Only available to nuclides of atomic number of 58
(Cerium) or greater as well as a few of low atomic
number including He, Li and Be.
 Alpha emission can be written as:
92U
238
-> 90Th234 + 2He4 + Q
Where 2He4 is the alpha particle and Q is the
total alpha decay energy
Alpha Emission
A daughter isotope produced
by alpha emission will not
necessarily be stable and can
itself decay by either alpha
emission, or beta emission or
both.
Branched Decay
 The difference in the atomic number of two stable
isobars is greater than one, ie two adjacent
isobars cannot both be stable.
 Implication is that two stable isobars must be
separated by a radioactive isobar that can decay
by different mechanisms to produce either stable
isobar.
 Example
176 decays to
176 via negative beta decay
Lu
Hf
71
72
176 decays to
176 by positron decay or
72Hf
70Yb
electron capture.
Branched decay scheme for A=38 isobar
Branched decay scheme for A=132 isobar
Decay of 238U to 206Pb
Radiogenic Isotope Geochemistry

Can be used in two important ways
1. Tracer Studies


Makes use of the differences in the ratio of the
radiogenic daughter isotope to other isotopes of the
element
Can make use of the differences in radiogenic isotopes
to look at Earth Evolution and the interaction and
differentiation of different reservoirs
Radiogenic Isotope Geochemistry
2. Geochronology


Makes use of the constancy of the rate of radioactive
decay
Since a radioactive nuclide decays to its daughter at a
rate independent of everything, it is possible to
determine time simply by determining how much of the
nuclide has decayed.
Radiogenic Isotope Systems
 The radiogenic isotope systems that are of
interest in geology include the following
•
•
•
•
•
•
•
•
•
K-Ar
Ar-Ar
Fission Track
Cosmogenic Isotopes
Rb-Sr
Sm-Nd
Re-Os
U-Th-Pb
Lu-Hf
Table of the elements
Radiogenic Isotope Systems
 The radiogenic isotope systems that are of
interest in geology include the following
•
•
•
•
•
•
•
•
•
K-Ar
Ar-Ar
Fission Track
Cosmogenic Isotopes
Rb-Sr
Sm-Nd
Re-Os
U-Th-Pb
Lu-Hf
Geochronology and Tracer Studies
Isotopic variations between rocks and minerals due to
1. Daughters produced in varying proportions resulting
from previous event of chemical fractionation
•
40K

40Ar
by radioactive decay
• Basalt  rhyolite by FX (a chemical fractionation
process)
• Rhyolite has more K than basalt
•
40K
 more 40Ar over time in rhyolite than in basalt
• 40Ar/39Ar ratio will be different in each
2. Time: the longer 40K  40Ar decay takes place, the
greater the difference between the basalt and rhyolite
will be
The Decay Constant
 Over time the amount of the daughter (radiogenic) isotope
in a system increases and the amount of the parent
(radioactive) isotope decreases as it decays away. If the
rate of radioactive decay is known we can use the increase
in the amount of radiogenic isotopes to measure time.
 The rate of decay of a radioactive (parent) isotope is
directly proportional to the number of atoms of that
isotope that are present in a system, ie Equation 1 that we
have seen previously.
– dN/dt = -lN,
[eq. 1]
– where N = the number of parent atoms and l is the decay
constant
– The -ve sign means that the rate decreases over time
The Half Life
 The half life of a radioactive
isotope is the time it takes
for the number of parent
isotopes to decay away to half
their original value. It is
related to the decay constant
by the expression
– T1/2 = ln2/l
 For 87Rb, the decay constant
is 1.42 x 10-11y-1, hence, t1/2
87Rb = 4.88 x 1010years. In
other words after 4.88 x
1010years a system will contain
half as many atoms of 87Rb as
it started off with.
Geologically Important Isotopes and their Decay
Constants
Using the Decay Constant
The number of radiogenic daughter atoms (D*)
produced from the decay of the parent since date
of formation of the sample is given by
D* = No - N
[eq. 2]
Where D* is the number of daughter atoms
produced by decay of the parent atom and No is
the number of original parent atoms
Therefore the total number of daughter atoms, D,
in a sample is given by
D = Do + D*
[eq. 3]
Using the Decay Constant
The two equations can be combined to give
D = Do + No – N
[eq. 4]
Generally, when rocks or minerals first form they
contain a greater or lesser amount of the
daughter atoms of a particular isotope system, i.e.,
not all the daughter atoms that we measure in a
sample today were formed by decay of the parent
isotope since the rock first formed.
Dating of Rocks from Radioactive Decay
Recalling that
-dN/dt = lN
[eq. 1]
Integration of the above yields
N=Noe-lt
[eq. 5]
We can substitute this into equation 4 to get
D=Do + Nelt – N [eq. 6]
which simplifies to
D=Do + N(elt – 1) [eq. 7]
The Radiogenic Decay Equation
 Equation 7 is the basic decay equation and is used
extensively in radiogenic isotope geochemistry.
 In principle, D and N are measurable quantities,
while Do is a constant whose value can be either
assumed or calculated from data for cogenetic
samples of the same age.
 If these three variables are known then the above
equation can be solved for t to give an “age” for
the rock or mineral in question.
Plotting Geochron Data
 There are two methods for graphically illustrating
geochron data
 1. The Isochron Technique
– Used when the decay scheme has one parent isotope
decaying to a daughter isotope.
– Results in a straight line plot
 2. The Concordia Diagram
– Used when more than one decay scheme results in the
formation of the daughter isotopes
– Results in a curved diagram (we’ll talk more about this
later when we look at U-Th-Pb)
The Isochron Technique
 The Isochron Technique
– Requires 3 or more cogenetic samples with a range of
Rb/Sr
• 3 cogenetic rocks derived from a single source by
partial melting, FX, etc.
• 3 coexisting minerals with different K/Ca ratios in a
single rock
 Let’s look at an example in the Rb/Sr system
The Rb-Sr system
 Strontium has four naturally occurring isotopes all
of which are stable
– 38Sr88, 38Sr87, 38Sr86, 38Sr84
 Their isotopic abundances are approximately
– 82.53%, 7.04%, 9.87%, and 0.56%
 However the isotopic abundances of strontium
isotopes varies because of the formation of
radiogenic Sr87 from the decay of naturally
occurring Rb87
 Therefore the precise isotopic composition of
strontium in a rock or mineral depends on the age
and Rb/Sr ratio of that rock or mineral.
Rb-Sr Isochrons
 If we are trying to date a rock using the Rb/Sr
system then the basic decay equation we derived
earlier has the form
Sr87 = Sr87i + Rb87(elt –1)
 In practice, it is a lot easier to measure the ratio
of isotopes in a sample of rock or a mineral, rather
than their absolute abundances. Therefore we can
divide the above equation through by the number
of Sr86 atoms which is constant because this
isotope is stable and not produced by decay of a
naturally occurring isotope of another element.
Rb-Sr Isochrons
 This gives us the equation
87Sr/86Sr
= (87Sr/86Sr)i +
87Rb/86Sr(elt
– 1)
 To solve this equation, the concentrations of Rb
and Sr and the 87Sr/86Sr ratio must be measured.
 The Sr isotope ratio is measured on a mass
spectrometer whilst the concentrations of Rb and
Sr are normally determined by XRF or ICPMS.
Rb-Sr Isochrons
 The concentrations of Rb and Sr are converted to
the 87Rb/86Sr ratio by the following equation.
= (Rb/Sr) x (Ab87Rb x WSr)/(Ab86Sr x WRb),
where Ab is the isotopic abundance and W is the atomic
weight.
87Rb/86Sr
 The abundance of 86Sr (Ab86Sr) and the atomic
weight of Sr (WSr) depend on the abundance of
87Sr and therefore must be calculated for each
sample.
What can we learn from this?
1. After each period of time, the 87Rb in each rock
decays to 87Sr producing a new line
2. This line is still linear but is steeper than the
previous line.
3. We can use this to tell us two important things
• The age of the rock
• The initial 87Sr/86Sr isotope ratio
Determining the Age of a Rock
Determining the Age of a Rock
Let’s look now at the initial ratio
The Fitting of Isochrons
 After the 87Sr/86Sr and 87Rb/86Sr ratios of
the samples or minerals have been determined and
have been plotted on an isochron, the problem
arises of fitting the ‘best’ straight line to the data
points.
 The fit of data points to a straight line is
complicated by the errors that are associated
with each of the analyses
The Fitting of Isochrons
Equations for Calculating the Best Slope and
Intercepts of a Straight Line
The initial ratio
 How do we know if a series of rocks are cogenetic?
 For rocks to be co-genetic, implies that they are
derived from the same parent material.
 This parent material would have had a single
87Sr/86Sr isotope value, ie the initial isotope ratio
 Therefore, all samples derived from the same
parent magma should all have the same 87Sr/86Sr
isotope ratio
 If they don’t, it implies that they are derived
from a different parent source.
Errorchrons and MSWD Values
 A line fitted to a set of data that display a scatter
about this line in excess of the experimental error is
not an isochron.
 The sum of the squares of miss-fits of each point to
the regression line, may be divided by the number of
degrees of freedom (number of data points minus
two) to yield the Mean Squared Weighted Deviates
(MSWD).
 MSWD values give an indication of scatter and can
therefore be used to indicate whether an errorchron
or isochron is indicated by the data.
 MSWD values should be near unity to be indicative of
an isochron. Values over 2.5 are definitely errochrons.
Sm-Nd Isotope System
 Sm has seven naturally occurring isotopes
 Of these 147Sm, 148Sm and 149Sm are radioactive
but only 147Sm has a half life that impacts on the
abundance of 143Nd.
 The decay equation for Sm/Nd is
–
143Nd/144Nd
= (143Nd/144Nd)i +
147Sm/144Nd(elt
– 1)
Epsilon Notation
 Archean plutons have initial 143Nd/144Nd ratios
that are very similar to that of the Chondritic
Uniform Reservoir (CHUR) predicted from
meterorites.
 Because of the similar chemical behaviour of Sm
and Nd, departures in 143Nd/144Nd isotopic ratios
from the CHUR evolution line are very small in
comparison to the slope of the line.
 Therefore Epsilon notation for Sm/Nd system is:
 eNd(t) = ((143Nd/144Nd)sample (t)/(143Nd/144Nd)CHUR(t) – 1) x
104
Behaviour of Rb and Sr in Rocks and Minerals
 Rb behaves like K  micas and alkali feldspar
 Sr behaves like Ca  plagioclase and apatite (but
not clinopyroxene)
Rock Type
Rb ppm
Ultrabasic
Basaltic
High Ca granite
Low Ca granite
Syenite
Shale
Sandstone
Carbonate
Deep sea carbonate
Deep sea clay
0.2
30
110
170
110
140
60
3
10
110
K ppm
40
8,300
25,200
42,000
48,000
26,600
10,700
2,700
2,900
25,000
Sr ppm
Ca ppm
1
25,000
465 76,000
440 25,300
100 5,100
200 18,000
300 22,100
20 39,100
610 302,300
2000 312,400
180 29,000
Behaviour of Sm and Nd in Rocks and Minerals
 Both Sm and Nd are LREE
 Because Sm and Nd have very similar chemical properties
that are not fractionated very much by igneous processes
such as fractional crystallisation.
 Useful for looking at metamorphic processes not igneous
processes
Rock / Min
Sm ppm Nd ppm Sm/Nd
Olivine
Garnet
Apatite
Monazite
MORB Thol
Rhyolite
Eclogite
Granulite
Sandstone
Chondrites
0.07
1.17
223
15,000
3.30
4.65
2.61
4.96
8.93
0.199
0.36
2.17
718
88,000
10.3
21.6
8.64
31.8
39.4
0.620
0.19
0.539
0.311
0.17
0.320
0.215
0.302
0.156
0.227
0.320
Rb-Sr vs Sm-Nd
 Sm-Nd
– Mafic and Ultramafic igneous rocks
– Metamorphic Events
– Rocks that have lost Rb-Sr
 Rb-Sr
– Acidic and Intermediate igneous rocks
– Rocks enriched in rubidium and depleted in strontiu,
Model Ages
 The isotopic evolution of Nd in the Earth is described
in terms of a model called CHUR, which stands for
“Chondritic Uniform Reservoir”.
 CHUR was defined by DePaolo and Wasserburg in 1976.
 The initial (or primordial) 143Nd/144Nd ratio and
present 147Sm/144Nd ratio and the age of the Earth
have been determined by dating achondrite and
chondrite meteorites
 The model assumes that terrestrial Nd has evolved in a
uniform reservoir whose Sm/Nd ratio is equal to that
of chondritic meteorites.
CHUR and the Isotopic Evolution of Nd
 We can calculate the value of CHUR at any time, t, in the
past using the following equation and values
Implications
 Partial melting of CHUR gives rise to magmas
having lower Sm/Nd ratios than CHUR
 Igneous rocks that form from such a melt
therefore have lower present day 143Nd/144Nd
ratios than CHUR
 The residual solids that remain behind therefore
have higher Sm/Nd ratios than CHUR
 Consequently, these regions (referred to as
“depleted regions” of the reservoir) have higher
143Nd/144Nd ratios than CHUR at the present time
Nd-Isotope Evolution of Earth
Model Dates
 CHUR can be used to calculate the date at which the Nd in a
crustal rock separated from the chondritic reservoir.
 This is done by determining the time in the past when the
143Nd/144Nd ratio of the rock equaled that of CHUR
 Skipping lots of in between steps the equation becomes
Model Dates
 Dates calculated in the above manner make one
very big assumption
– The Sm/Nd ratio of the rock has not changed since the
time of separation of Nd from the Chondritic Reservoir
 If there was a disturbance in the Sm/Nd ratio
then the date calculated would not have any
geological meaning.
 This criteria is better met by Sm/Nd than by
Rb/Sr because of the similar behaviour of Sm/Nd.
Model Dates and Sr-Isotope Evolution
 The isotopic evolution of Nd and Sr in the mantle
are strongly correlated.
 This correlation gives rise to the “mantle array”
 The mantle array (defined from uncontaminated
basalts in oceanic basins) arises through the
negative correlation of 143Nd/144Nd and 87Sr/86Sr
ratios
 This indicates that oceanic basalts are derived
from rocks whose Rb/Sr ratios were lowered but
whose Sm/Nd ratios were increased in the past
Sr-Isotope Evolution of Earth
Epsilon Sr Calculations