GEOCHRONOLOGY HONOURS 2006

Lecture 01Introduction 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 dt, where is the decay constant for the particular isotope

The rate of decay among some number, N, of nuclides is therefore

dN / dt = -N [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

19K40 -> 20Ca40 + - + + Q

Where - is the beta particle, is the antineutrino and Q stands for the maximum decay energy.

_

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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

9F18 -> 8O18 + + + + QWhere + is the positron, is the neutrino and Q stands

for the maximum decay energy.

Positron VS Beta Decay

The atomic number of the daughter isotope is decreased by 1 while the neutron number is increased by 1.

The atomic number of the daughter isotope is increased by 1 while the neutron number is 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:

92U238 -> 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

71Lu176 decays to 72Hf176 via negative beta decay

72Hf176 decays to 70Yb176 by positron decay or 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 each2. 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 = -N, [eq. 1]– where N = the number of parent atoms and 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/

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 = N [eq. 1]

Integration of the above yields

N=Noe-t [eq. 5]

We can substitute this into equation 4 to get

D=Do + Net – N [eq. 6]

which simplifies to

D=Do + N(et – 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(et –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(et – 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.

87Rb/86Sr = (Rb/Sr) x (Ab87Rb x WSr)/(Ab86Sr x WRb), where Ab is the isotopic abundance and W is the atomic weight.

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 co-

genetic?

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(et – 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:

Nd(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 K ppm Sr ppm Ca ppm

Ultrabasic 0.2 40 1 25,000Basaltic 30 8,300 465 76,000High Ca granite 110 25,200 440 25,300Low Ca granite 170 42,000 100 5,100Syenite 110 48,000 200 18,000Shale 140 26,600 300 22,100Sandstone 60 10,700 20 39,100Carbonate 3 2,700 610 302,300Deep sea carbonate 10 2,900 2000312,400 Deep sea clay 110 25,000 180 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/NdOlivine 0.07 0.36 0.19Garnet 1.17 2.17 0.539Apatite 223 718 0.311Monazite 15,000 88,000 0.17MORB Thol 3.30 10.3 0.320Rhyolite 4.65 21.6 0.215Eclogite 2.61 8.64 0.302Granulite 4.96 31.8 0.156Sandstone 8.93 39.4 0.227Chondrites 0.199 0.620 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