## Understandable Earth Science

### How old is that rock? Part 4: ⁴⁰Ar/³⁹Ar dating diagrams

Many ⁴⁰Ar/³⁹Ar dating publications use age spectrum and isotope correlation diagrams to interpret their data and calculate ages. These can be quite confusing if you don’t know how to interpret them so I have sketched some schematic examples to explain how they work.

First up, let’s look at an Age Spectrum:

In the diagram below I have drawn 2 different age spectra. The bottom, green spectrum is what we would expect to see if we had an ideal sample that has no excess-Ar, and the top, blue spectrum is what we might expect if the sample contained excess-Ar in fluid inclusions. Both of these “experiments” involved 7 heating steps where the temperature increased for each step and the gas released from each step was analysed. The data for each of those 7 steps is represented by one of the 7 boxes on the diagram.

The Y-axis (vertical) shows the ⁴⁰Ar/³⁹Ar age calculated for each step (these are schematic diagrams, so I have not put a scale on them). On an age spectrum, the ages are plotted as boxes to show how big the errors are on each step. On the green diagram I have also drawn age data points and error bars at the end of each box to help you visualise it better. Hopefully you can see that, on the green diagram, all the ages are very similar, but on the blue diagram the first three steps give older Ar-ages.

The X-axis (horizontal) shows the cumulative percentage of ³⁹Ar released in the experiment and each step is plotted sequentially, which means, for stepped heating experiments, temperature increases to the right.  If you look at the width of the boxes you can tell which heating steps released the most ³⁹Ar (for the green diagram steps 4 and 6 are the widest, so we know these released the most ³⁹Ar). Remember that ³⁹Ar is the same as K, which is the source of ⁴⁰Ar* and should usually be evenly distributed throughout the crystal, so we can use this to understand something about where in the crystal the gas we analysed came from.

If a sample is well behaved and has no excess-Ar, all of the temperature steps should give the same ⁴⁰Ar/³⁹Ar age and this is what we see in the green diagram – all of the ages overlap within error. In this situation we can use all of the data to calculate a more precise age for the sample – that is represented by the dotted black line.

But what if there are fluid inclusions in the sample that add excess-Ar, like we discussed in the last blog? Well, it is quite common for these inclusions to break down and release their gas at relatively low temperatures.

This means that the ages we calculate from the first few temperature steps will be older than the later steps that release gas from the crystal lattice. You can see how this typically manifests in the blue age-spectrum, where the first 3 steps have older ages than the later steps. In this situation we can just discard the data from the steps contaminated with excess-Ar and calculate an age from the steps that give a nice flat, consistent spectrum. We call this part of the spectrum the plateau, because it is flat.

So, hopefully you now know a bit more about what those strange block diagrams mean. Let’s move onto isotope correlation diagrams. These are basically just data points along mixing lines between 2 or more different things. Let’s start with a non-geological example. I am going to make a creamy chocolate coconut dessert. I’m going make this by alternating layers of ganache, which is a mixture of cream and chocolate, and a pre-made coconut pudding that is a mixture of cream and coconut. Both of these ingredients contain cream. If I know what the proportion of chocolate to cream is in the ganache, and the proportion of coconut to cream in the coconut pudding, then I can calculate how much chocolate, coconut and cream there is in different mixtures of ganache and coconut pudding. I’ve done this in the table here.

So, the ganache is 70% chocolate and 30% cream. The coconut pudding is 50% coconut and 50% cream. If the final dessert has half ganache and half coconut pudding, then it will have 35% chocolate, 25% coconut and 40% cream.

If I calculate some ratios of the ingredients, and then plot them up on some graphs, we can see that the composition of the ganache – coconut pudding mixtures all lie on a straight line between the compositions of the 2 main ingredients.

The x-axis is chocolate / cream (amount of chocolate divided by the amount of cream). That means, as you move to the right of the graph, you either have more chocolate, or less cream (or both).  That also means that, if you move to the left of the graph, you have less chocolate or more cream (or both). When you reach zero on the x-axis, that basically means you have no more chocolate <sad face>.

We know that there is no chocolate in the coconut cream, so any data points that have 0 on the x-axis, must be 100% coconut cream, and the value they have on the y-axis (we call this the intercept, because it is where a line intercepts the axis) is the ratio of coconut to cream. We can see from the diagram that this ratio is 1; if you look at the table, you can see that the composition of coconut pudding is 50:50 coconut and cream; 50/50 = 1. Similarly, the value of the x-intercept is the composition of the ganache – we can see from the table that ganache is 70% chocolate and 30% cream; 70 / 30 = 2.3, which is what we can see on the graph.

Next, let’s reverse this. Pretend we don’t know the composition of our 2 basic ingredients – all we have are the compositions for 3 different mixtures of ganache and coconut pudding – they make up the 3 data points in the middle of the graph. If we draw a line through them and extrapolate it to both axes, we can calculate the compositions of our original ingredients.

OK, now let’s use this tool to help work out some ages.

Here are a couple of schematic isotope correlation diagrams that I sketched. They are both the same kind of diagram, but illustrating different types of samples.

On the x-axis, we have ³⁹Ar/⁴⁰Ar and on the Y-axis we have ³⁶Ar/⁴⁰Ar. Recall that ³⁹Ar comes from the K in the sample, ³⁶Ar comes from the atmosphere, and ⁴⁰Ar can come from radiogenic ⁴⁰Ar*, from the atmosphere, or from excess-Ar (or, in many cases, all three). Data points are usually plotted as ellipses, to represent the analytical errors on both the x and y axes. A regression line is calculated to fit through the data points and this also calculates the values on the x and y intercepts (shown as stars on this diagram ). We use this diagram for 2 things: 1) to work out the  ratio of  ⁴⁰Ar*/³⁹Ar  in the sample, so we can calculate an age, and 2) to identify the composition of any trapped Ar – is it atmospheric or is there excess-Ar present?

If we move to the left on this graph, that means we either have less ³⁹Ar or more ⁴⁰Ar. We know that ⁴⁰Ar* is always going to be associated with ³⁹Ar because K is needed to produce the ⁴⁰Ar*. So that means, when we hit the y-axis, ³⁹Ar = 0 and that must mean all ⁴⁰Ar is non-radiogenic – it is either atmospheric or excess-Ar; the value of the y-intercept is the composition of the trapped Ar in the sample. If the trapped Ar is purely atmosphere, the y-intercept should have a value of 0.0033 (this has been measured on samples of air). If the value is smaller, that means there is more ⁴⁰Ar than we would expect in the atmosphere, which means excess-Ar is present.

So, how do we get the age? ³⁶Ar only comes from the trapped, atmospheric-composition gas in the sample. Moving down the graph means we either have less ³⁶Ar or more ⁴⁰Ar (or both), and when we hit the x-axis, that means there is no ³⁶Ar, and so no trapped-Ar; All the ⁴⁰Ar on the x-intercept is radiogenic. We simply read off the ³⁹Ar/⁴⁰Ar* value and use this to calculate the age of the sample. Using this method it doesn’t matter whether excess-Ar is present or not, because the calculated age is completely independent of the trapped Ar composition.

In the sketch diagrams I have illustrated a few examples. In the left diagram I am comparing how data would look, for 2 samples that are the same age, but one has excess-Ar (red) and the other doesn’t (blue). You can see that the blue data fall on a mixing line between air (y-axis) and the radiogenic component (x-axis), while the red data fall on a mixing line between the same radiogenic component and a trapped Ar composition with more ⁴⁰Ar than in air. If you were to calculate Ar-ages from each of the individual data points, the blue data would all give the correct age, but the red data would give ages that are too old.

In the right hand diagram I am comparing two samples that do not have excess-Ar but are different ages. This might happen if a volcano erupts explosively and the ash picks up some old crystals from a previous eruption. In this case, the data fall onto 2 mixing lines between air and different radiogenic components. The yellow data have an x-intercept that is a lower value than the green data – this means the yellow data contain more ⁴⁰Ar* and so they are older.

The lines that we calculate and extrapolate between the data points represent a range of isotopic compositions that are all associated with the same age, and so these diagrams are often called “isochron diagrams” instead of isotope-correlation diagrams. There are other ways of plotting and analysing the data to make isochrons, and the example here is actually called an “inverse isochron” to distinguish it from another diagram that plots ³⁹Ar/³⁶Ar against ⁴⁰Ar/³⁶Ar. I focussed on inverse isochrons for this blog entry because they seem to be the most popular way of displaying and analysing Ar-isotope data at the moment, but the principles of mixing between 2 different components (trapped and radiogenic Ar) are the same for all isochron diagrams.

So, I hope that if you now decide to pick up a paper about Ar-dating you’ll be able to understand a little bit about some of the strange diagrams in it.

### How old is that rock? Part 3: ⁴⁰Ar/³⁹Ar dating

In the previous blog I described how we measure the amount of ⁴⁰K, ⁴⁰Ar and ³⁶Ar to calculate how old a sample is.

All good yeah? Unfortunately, not quite.

While there are some samples and situations where this K-Ar dating technique works really well, it isn’t perfect. The technique uses a few key assumptions that are not always true. These assumptions are:

1. The ⁴⁰K and ⁴⁰Ar* are homogenously distributed in the sample, so it doesn’t matter that the K and Ar measurements are carried out on different aliquots (sub-sample) of the sample using different techniques.
2. When we measure the Ar content, we manage to release ALL of the Ar from the sample – we need absolute concentrations of ⁴⁰K and ⁴⁰Ar because they are measured with different techniques on different aliquots.
3. All of the ⁴⁰Ar in the sample is either from radioactive decay of ⁴⁰K (i.e. ⁴⁰Ar*) or from the atmosphere (⁴⁰Arₐ).

Assumption 1 shouldn’t cause too many problems for old rocks where the concentration of ⁴⁰Ar* is high and it is easy to analyse small samples (10s of milligrams). But the younger the rock, or the lower K-content of the rock, the less ⁴⁰Ar* there is and larger samples need to be analysed to release enough gas to measure. The larger the sample, the greater chance of sample inhomogeneity – and that means there is a bigger chance that the two aliquots analysed for K and Ar don’t quite match.

Assumption 2 can cause problems when analysing certain minerals, especially a mineral called sanidine. This is a kind of K-rich feldspar that forms at high temperatures and has a very disordered crystal lattice. This disordered crystal lattice makes it more difficult for Ar to diffuse out of the sample during analysis, and the high melting temperature makes it difficult to completely melt the sample to release the all of the gas. This means you might end up underestimating the amount of ⁴⁰Ar* and getting an age that is too young.

Assumption 3 can be a problem in various situations. Sticking with the simple volcanic eruption scenario from the last blog, if the magma chamber is quite new and forms in old continental crust, there might be a lot of ⁴⁰Ar in the magma that has come from radioactive decay of ⁴⁰K in the crust.  This might become trapped in a crystal we want to date, either just by being in equilibrium with the gas, or the crystal might trap tiny pockets of magma or hydrothermal fluid as it grows – we call these magmatic or fluid inclusions. This kind of ⁴⁰Ar did form by radioactive decay, but in a different system to the one we are trying date (it formed in the host crust, rather than in the crystals we want to date), so for ⁴⁰Ar/³⁹Ar dating we stop referring to this as ⁴⁰Ar* and start calling it excess-argon, or ⁴⁰Arₑ.

Fortunately, in the late 1960s, 2 scientists called Craig Merrihue and Grenville Turner discovered that if you put a K-bearing sample into a nuclear reactor and bombarded it with neutrons, some of the ³⁹K changed into ³⁹Ar. This meant that you could measure the ³⁹Ar on a noble gas mass spectrometer, at the same time as the usual ⁴⁰Ar and ³⁶Ar and calculate ⁴⁰K/⁴⁰Ar* from ³⁹Ar/⁴⁰Ar*.

With this new technique, the amount of ³⁹Ar produced depends on how much neutron irradiation the sample received, which is difficult to directly measure. To get around this, a sample of well-known age (an “age standard” or “fluence monitor”) is included in the irradiation and the Ar-isotopic composition of this standard is used, along with its age,  to calculate something called the J-value, which is a proxy for neutron dose. This J-value is then used to help calculate the age of our samples.

This new technique dealt with any problems associated with assumption 1 of the K-Ar technique. It also dealt with assumption 2, because it no longer mattered if you didn’t release all of the Ar from the sample – it is the ratio of the parent to daughter isotopes that is important, rather than the absolute concentrations.

Being able to measure both the parent and daughter isotope at the same time also opened up a whole new level of gas-release technique that helped to address any problems associated with assumption 3. Ar could be released from samples by stepwise heating (heat the sample a little bit and analyse the gas released, and then increase the temperature – repeat until there is no more gas left)- this helps in two ways. Firstly, any separate reservoirs of ⁴⁰Arₑ, like the fluid inclusions I mentioned above, tend to be released from crystals at lower temperatures than the ⁴⁰Ar* stored in the crystal lattice. That means that stepwise heating can identify different reservoirs of Ar in a sample, and we can use this information to identify which heating steps can be used to calculate an age.  Secondly, multiple measurements from the same sample (either stepped heating, or multiple analyses of single crystals) can be plotted on isotope correlation diagrams and these can be used to calculate mixing lines between different end-member isotopic compositions, making it possible to interpret complex data.

In the next blog I will explain how some of these diagrams and data-analysis techniques work. But I want to finish this post with a brief summary of the capabilities and challenges of ⁴⁰Ar/³⁹Ar dating.

• The ⁴⁰Ar/³⁹Ar technique can potentially date rocks and minerals between a few thousand, and a few billion years old;
• The first ⁴⁰Ar/³⁹Ar dates produced in the late 1960s and early 1970s were on meteorites and lunar rocks recovered from the Apollo missions, which are all between 3 and 4.5 billion years old. The technique is still routinely used to date old, extra-terrestrial material.
• With the right samples, it is also possible to date relatively young rocks – back in 1997 the ⁴⁰Ar/³⁹Ar lab at the Berkeley Geochronology Centre successfully dated the 79AD eruption of Vesuvius that wiped out the town of Pompeii.
• The easiest samples to work on contain a lot of K (typically between 5 and 15% K₂O), but with increased sensitivity of mass spectrometers, changes to the gas extraction systems and improvements in sample preparation, it is now possible to date samples that have a K-content of less than 0.5%, even for quite young samples. This means that the range of material that can be analysed to give an ⁴⁰Ar/³⁹Ar age is massive.
• ⁴⁰Ar/³⁹Ar dating gives cooling ages, so it can date not just volcanic eruptions, but igneous intrusions and metamorphism. It can even been used to date fault movement and meteorite impacts.
• ⁴⁰Ar/³⁹Ar dates need to be calibrated against a standard of known age. This means that the accuracy and precision of the ages it produces is always going to be limited by the accuracy and precision of the age of the standards. This is being addressed as part of an international project called EARTHTIME that aims to improve the precision of various dating techniques.

So, in short, the technique covers a massive date range and it can date a wide range of materials to give age information on lots of different kinds of geological events.

I was fortunate enough to do my PhD in the Ar-dating lab at The University of Manchester, using the MS-1 – the mass spectrometer that was built by Grenville Turner and produced the first Ar-dates. Grenville retired the year I started at Manchester, and the lab is now run by Prof. Ray Burgess, who was my PhD supervisor.  But here is a cheesy photo of me and Grenville at my graduation in 2005.

Grenville recently wrote an article giving a bit of the history of the MS-1 mass spectrometer, which you can read here.

And here are a couple of other interesting articles about Grenville and this history of his research:

Todmorden news

Floreat Domus (pdf – go to p. 34)

### How old is that rock? part 2: K-Ar dating

In the previous blog I talked about radioactivity and how we can use radioactive decay as a kind of clock. In this blog I am going to talk about a specific dating technique called potassium-argon (K-Ar) dating. This is a geological dating technique that has been in use since the 1950s and is the basis of a more versatile technique called argon-argon (⁴⁰Ar/³⁹Ar) dating, that I will talk about later.

• Potassium (K) is an alkali metal that has 3 naturally occurring isotopes –³⁹K, ⁴⁰K and ⁴¹K. It is relatively common in the earth’s crust, especially in continental crust.
• Argon (Ar) is a noble gas that has 3 naturally occurring isotopes – ⁴⁰Ar, ³⁸Ar and ³⁶Ar.
• ⁴⁰K is radioactive and this radioactively decays to form ⁴⁰Ca (calcium) and ⁴⁰Ar. As discussed in the last blog, we call ⁴⁰K the parent isotope and radiogenic (made by radioactive decay) ⁴⁰Ca* and ⁴⁰Ar* daughter isotopes, because ⁴⁰Ca and ⁴⁰Ar are produced by ⁴⁰K. The star on daughter isotopes is a common notation that means “this isotope was formed by radioactive decay”.

Now let’s think about the geological processes we want to date. In terms of dating, one of the simplest geological events is a volcanic eruption, because these happen instantaneously on geological timescales.

Volcanoes exist because of pockets of magma (molten rock) stored in the crust. As magma cools (or changes pressure) it starts to grow crystals. Some of these crystals contain K. If the volcano erupts explosively (e.g. Mount Pinatubo, The Philippines) we call the deposits “tephra”, which is a catch-all term for “broken bits of rock, pumice and ash that come out of the volcano” (in volcanology, “ash” is a kind of tephra that specifically has a grain size of < 2 mm).  When the volcano erupts, the molten rock forces its way out of the ground, becomes solid and no more crystals form. This is when our geological clock starts. Over time, the ⁴⁰K in these new crystals starts turning into ⁴⁰Ar (and ⁴⁰Ca). Eventually, a geologist might come along and take a sample of the tephra to analyse.

For K-Ar dating, we take a rock sample and measure the amount of ⁴⁰K and the amount of ⁴⁰Ar in the rock and from this we calculate the age.  Measuring K is quite straightforward, but things are a little more complicated for Ar.

Ar makes up nearly 1% of the earth’s atmosphere, and ⁴⁰Ar is the most abundant Ar-isotope. 1% doesn’t sound like much, but it is enough to guarantee that the vast majority of samples will contain a little bit of Ar from the atmosphere. If we were to measure the amount of ⁴⁰Ar in a sample and use that to calculate a radiometric age, our age would be too old, because some of that ⁴⁰Ar would be from the atmosphere (let’s call that “⁴⁰Arₐ”), instead of being the ⁴⁰Ar*produced by decay of ⁴⁰K.

The first way to deal with this is to measure Ar using a special noble gas mass spectrometer. These  use ultra-high-vacuum (UHV) extraction lines. This means that the Ar is released from the sample and passed to the mass spectrometer along a tube that is under vacuum – it is completely empty, meaning the gas we measure is only the gas released from the sample and we don’t have to worry about Ar from the atmosphere in the lab contaminating the sample.

But, as I previously said, most *samples* contain at least some atmospheric contamination, and that needs to be removed for our age calculation. Fortunately, the Ar-isotopic composition of air is consistent and well known. ³⁶Ar, is the second most abundant isotope of Ar in the atmosphere and it ONLY occurs in the atmosphere. We know what the ratio of ⁴⁰Ar/³⁶Ar is in air, so if we measure the amount of ³⁶Ar in a sample we can calculate how much ⁴⁰Arₐ is in our sample and simply subtract it to get the ⁴⁰Ar*.

So, in summary, we measure the amount of ⁴⁰K in a sample to get a value for the parent isotope. Then we measure the amount of ⁴⁰Ar and ³⁶Ar in a sample and use those to calculate the amount of the daughter isotope ( ⁴⁰Ar*). We then use these values of ⁴⁰K and ⁴⁰Ar* to calculate how old the sample is.

Hang on a minute!! What if the crystals grow a long time before the volcano erupts? When does the clock start? – This is a question at the cutting edge of dating research at the moment. Fortunately, Ar is an inert gas. This means that it doesn’t form bonds with any parts of the crystal lattice and it is free to diffuse through the crystal. How fast something diffuses is controlled by temperature.  At magmatic temperatures (often between 800 °C and 1300 °C) the Ar is able to diffuse so quickly that it doesn’t build up in the crystal. The radiometric clock starts when the temperature drops (immediately after eruption) and the Ar is no longer able to diffuse out of the crystal. This means that the K-Ar technique dates geological *cooling* events, rather than *crystallisation* events, which makes it very useful for dating volcanic eruptions. There are other isotope systems (e.g. Rb-Sr, U-Th-Pb) that can be used to date crystallisation, instead of cooling.

In the next blog, I will talk about some of the problems with K-Ar dating, and how these can be solved using the ⁴⁰Ar/³⁹Ar technique.

### How old is that rock? Part 1: Radioactivity

Radioactive decay is a process that is well understood and has been studied by physicists (and earth scientists) for over 100 years.  Nowadays radioactivity is used for a wide range of things, including power generation, specialist medical investigations and even making your smoke alarm work (don’t worry – smoke alarms are not dangerous!).

First, some definitions.

An atom is a basic unit of matter and consists of a nucleus of protons and neutrons surrounded by a cloud of electrons. Protons and neutrons both have mass. Protons have a positive charge and eletrons have a negative charge. The number of protons in the atom (the atomic number) defines what the element is (e.g. helium -He, carbon –C, argon – Ar, potassium – K, calcium – Ca, uranium – U….etc…).

Isotopes are atoms of a given element with different masses. They have different masses because they have different numbers of neutrons. For example, the element carbon (C ) has 6 protons but it can have 6, 7 or 8 neutrons, meaning that an atom of C could have a mass of 12, 13 or 14. We refer to different isotopes of an element by writing the mass in superscript in front of the element symbol – e.g. ¹²C, ¹³C, ¹⁴C.

 Element Carbon Carbon Carbon Argon Potassium Number of protons 6 6 6 18 19 Number of electrons 6 6 6 18 19 Number of neutrons 6 7 8 22 21 Total mass 12 13 14 40 40 Isotope ¹²C ¹³C ¹⁴C ⁴⁰Ar ⁴⁰K

Not all isotopes are stable – if there are too many or too few neutrons in a nucleus it can start to fall apart and / or change. Protons can change into neutrons and vice-versa, which involves the release of electrons or gamma-radiation, or sometimes neutrons are expelled from the nucleus to change the mass of the atom. When the number of protons in an atom changes, the atom becomes a different element. For example, the isotope of potassium ⁴⁰K (19 protons, 21 neutrons) radioactively decays to the isotope of argon ⁴⁰Ar (18 protons, 22 neutrons) by capturing an extra electron and converting a proton to a neutron. We call the original radioactive material (⁴⁰K) the parent isotope and the new material (⁴⁰Ar) the daughter isotope.

Radioactivity can be used as a kind of clock, because radioactive decay happens at a precise rate. Each radioactive isotope has a specific probability of decaying in a certain amount of time.  We can use that probability to predict how many parent isotopes will decay to daughter isotopes in a given time period. Or, turning that around, we can measure how many parent and daughter isotopes we have in a sample and use that to calculate how old the sample is.

The picture above gives a simplified explanation of how radiometric dating works. Parent isotopes are red circles and daughter isotopes are blue. We start off at time zero (t=0 mins) with 20 atoms of the parent isotope.  In this system, the radioactive parent isotope has a 50% chance of radioactively decaying within 10 minutes. That means that after 10 minutes (t=10 mins), 50% of the parent atoms have decayed and changed into the daughter isotope. That means that, at t=10 minutes, our sample now contains 10 atoms of parent and 10 atoms of daughter. 10 minutes later (t=20 mins) 50% of the atoms of parent isotope at t=10 mins (there were 10 atoms left) have decayed, adding an extra 5 daughter isotopes; at t=20 minutes there are 5 parent isotopes and 15 daughter isotopes.

Notice that the number of radioactive decays (parent changing to daughter) is not a set number for a given time period – there were 10 decays in the first 10 minutes, and only 5 decays in the next 10 minutes. The rate of radioactive decay is proportional to the amount of parent isotope, so the more parent isotopes you have, the greater the rate of change from parent to daughter. This means that radioactive decay is an exponential process.

This is shown in the next diagram which shows a sketch graph plotting the number of parent (red) and daughter (blue) isotopes over time.

An atom of the parent isotope always produces an atom of the daughter isotope when it decays, so you can see that the curve for the number of parent atoms is just the mirror image of the daughter isotope curve.

Where the parent and daughter isotope curves cross is the point in time where the number of parent and daughter atoms are equal. This means that half of the original parent isotopes have now decayed. We call this time-interval the half-life of the isotope system. So in the example I described above, the half life is 10 minutes, because that is how long it takes for half of the parent isotopes to decay.

To be able to date rocks using this theory, we need to know:

• how many atoms of parent and atoms of daughter isotope were present at the event we want to date (t=0),
• how many atoms of parent and atoms of daughter isotope are present now
• the rate of radioactive decay (for calculations we use the decay constant, which can be calculated from the half-life).

In the next blog I will show you how this is used in a dating technique called K-Ar dating.