GEOCHRONOLOGY HONOURS 2008

Lecture 01Introduction to Radioactive Decay and Dating of Geological Materials

The Age of the Earth

The currently accepted age of the Earth is 4.54 Billion years, ie 4.54 x 109 years

How do we know this?

Let’s go back and look at what the early estimates of the age of the Earth were and why these ages under-estimated the age by quite a long way.

The Debate about the Age of the Earth

Prior to Geology becoming an accepted field of science, the age of the Earth was a matter for Theology.

Bishop Usher proclaimed in 1650 that the creation of the world took place in 4004 BC, a view that was unchallenged for over 100 years.

The official position of the church was that all the surface features of the Earth were related to catastrophic events such as the Great Flood which occurred intermittently.

Catastrophism versus Uniformitarianism So what changed?

James Hutton arrived on the scene to shake up the establishment

Hutton argued that very slow but continuously acting processes were what accounted for the surface features of the Earth

He cemented this idea, which became known as uniformitarianism, in his book Theory of the Earth which was published in 1785.

Although initially greeted with horror by many, his ideas gradually became accepted, including the conviction that very long periods of time are required for the deposition of sedimentary rocks

Early Estimates

Early estimates were based on the principle of superposition

– In the late 1790’s early 1800’s, William Smith’s nephew calculated using this principle that the Earth was 96 million years old

Estimates where also based on the rate of cooling of the Earth

– In 1779 the French naturalist Comte du Buffon did an experiment where he created a minature Earth and measured it’s rate of cooling. Doing this he estimated the Earth as being 75,000 years old.

William Thompson

In 1862 the Scottish physicist William Thompson calculated that the Earth was between 24 and 400 million years old.

He assumed that the Earth had started life as a ball of molten rock and calculated the time it would take to cool to its current temperature.

However, Charles Darwin, who had published his theory of Evolution by Natural Selection did not feel that this was enough time to account for biological changes he had observed. Other biologists agreed

William Thompson

However, Thompson’s ages were supported by independent calculations by others

– The German Physicist Herman von Helmholtz in 1856 calculated an age of 22 million years

– The Canadian astronomer Simon Newcomb in 1892 calculated an age of 18 million years

– Charles Darwin’s son, the astronomer George Darwin calculated an age of 56 million years based on the amount of time he thought was needed for Earth to develop a 24 hour day from tidal friction

– In 1899-1900, John Joly, from the University of Dublin, calculated an age of 80 to 100 million years based on the amount of time needed to accumulate all the salt in the oceans from erosion

– All these calculations tended to support William Thompson’s ideas and calculations. So where did William Thompson go from here?

Lord Kelvin

In 1869 William Thompson was involved in a very famous debate with a certain Thomas H Huxley…

In 1892 he was rasied to the peerage and became Lord Kelvin in recognition for his many scientific achievements.

In 1897 he delivered his famous lecture “The Age of the Earth as an Abode Fitted for Life” in which he reduced his previous estimate to between 20 and 40 million years.

But had he missed something…?

Mantle Currents

Lord Kelvin has assumed that the cooling of the Earth was governed only by thermal gradients and did not take into account convective currents within the mantle which threw his age out

In 1895, John Perry produced an estimate for the age of Earth of 2 to 3 billions years old using a model of a convective mantle and thin crust

Still a bit young but certainly better than 100 million years

Refinement of this model would only be possible some 60 years later with the advent of plate tectonic theory

The next big thing..

In 1896, the French chemist Henri Becquerel discovered radioactivity.

In 1898, two other French researchers, Marie and Pierre Curie, discovered the radioactive elements polonium and radium.

In 1903 Pierre Curie and his associate Albert Laborde announced that radium produces enough heat to melt its own weight in ice in less than an hour.

What did this mean?

– The Earth produced it own internal heat– Calculations on the age of the Earth based on cooling

underestimated the age of the Earth– Lot’s of scientists died of cancer

Radioactivity

In 1903 Marie and Pierre Curie and Henri Becquerel shared the Nobel Prize for Physics for the discovery of radioactivity

By now scientists including JJ Thompson and Ernest Rutherford working at the Cavendish Laboratory at Cambridge University had started to unravel the internal structure of the atom.

In 1898 Rutherford moved to MacGill University in Montreal as professor of physics where he reported that radiation consisted of three different components which he named alpha, beta and gamma.

In 1900 Frederick Soddy came to MacGill as a demonstrator in Chemistry. Together, he and Rutherford formulated the theory of radioactive decay and growth which they expressed as –dN/dt = N where is the decay constant, representing the probability that an atom will decay in unit time and N is the number of radioactive atoms present.

Radioactivity and Dating

The postulation that radioactive decay could be measured opened the door to radioactive dating.

This possibility was recognised by Rutherford and Boltwood around 1905 and in a series of lectures at Yale University that year Rutherford proposed that the age of uranium minerals could be measured by the amount of helium that had accumulated in them, helium being the product of the radioactive decay. He carried out age determinations on several uranium minerals and obtained an age of 500 million years.

The state of radioactive dating was reviewed by Arthur Holmes in 1913 in his book “The Age of the Earth” which he wrote when he was just 23.

Radioactive Dating and Isotopes

Problems soon began to arise.

The development of radioactivity and the formula for the rate of disintegration was based on assumed simple decay of one element to another.

As decay systems began to be worked out it seemed that there were different types of radioactive elements and that the atomic weight of elements was not whole numbers but fractions.

Soddy suggested a solution in which he proposed that the place occupied by an element in the periodic table could accommodate more than one kind of atom.

A young scientist, F.W Aston, working at the Cavendish Laboratory at the time, set out to examine this and eventually identified 212 of the 287 naturally occurring isotopes.

The presence of isotopes and their additional complication to the radioactive decay schemes lead many scientists to abandon the idea of radioactive dating.

Arthur Holmes

Arthur Holmes work was generally ignored until the 1920s, though in 1917 Joseph Barrell, a professor of geology at Yale, redrew geological history as it was understood at the time to conform to Holmes's findings in radiometric dating.

Barrell's research determined that the layers of strata had not all been laid down at the same rate, and so current rates of geological change could not be used to provide accurate timelines of the history of Earth.

Holmes's persistence finally began to pay off in 1921, when the speakers at the yearly meeting of the British Association for the Advancement of Science came to a rough consensus that Earth was a few billion years old, and that radiometric dating was credible.

Holmes published The Age of the Earth, an Introduction to Geological Ideas in 1927 in which he presented a range of 1.6 to 3.0 billion years, although this was still largely ignored by the geological community.

The growing weight of evidence finally tilted the balance in 1931, when the National Research Council of the US National Academy of Sciences finally decided to resolve the question of the age of Earth by appointing a committee to investigate.

Holmes, being one of the few people on Earth who was trained in radiometric dating techniques, was a committee member, and in fact wrote most of the final report.

The age of the Earth as it is accepted today was determined by CC Patterson in 1956 (more about that later…)

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

Time for lecture 2!