# Historical Geology/Ar-Ar dating

Some of the problems of K-Ar dating can be avoided by the use of the related Ar-Ar dating method. In this article we shall explain how this method works and why it is superior to the K-Ar method. The reader should be thoroughly familiar with the K-Ar method, as explained in the previous article, before reading any further.

## The isotopes

In the previous article I introduced you to $^{40}$K, an unstable isotope of potassium which produces the daughter isotope $^{40}$Ar by electron capture or beta plus decay.
The Ar-Ar dating method relies crucially on the existence of two other isotopes. $^{39}$K is a stable isotope of potassium, which by definition means that it will not spontaneously undergo decay into another isotope. However, if you put it near the core of a nuclear reactor, so that it is bombarded by neutrons, then this will convert it into $^{39}$Ar. This isotope of argon is quite unstable, having a half-life of only 269 years. Consequently, the amount of it found in rocks is negligible — unless you subject them to an artificial neutron source.
A crucial point to note is that because $^{39}$K and $^{40}$K are isotopes of the same element, they have the same chemical properties. Therefore when the rock first forms, some of the minerals in it will have more potassium in and some less, but all the minerals will have the same initial ratio of $^{39}$K to $^{40}$K, because since they have identical chemical properties, there is no way that the $^{40}$K could preferentially end up in the hornblende and the $^{39}$K in the biotite.

## The method

First, you take your rock sample and place it near the core of a nuclear reactor. As a result, some of the $^{39}$K is converted to $^{39}$Ar as a consequence of the neutron bombardment.
Then you heat the rock sample to release the $^{39}$Ar and the $^{40}$Ar. The first of these, you will recall, is produced by our artificial neutron bombardment of the stable $^{39}$K isotope; the second is produced by the natural decay of the unstable $^{40}$K isotope in the rock.
So if all has gone well, and if there were no problems with argon loss or excess argon, then the age of the sample would be given by the following formula:
    t = h × log$_2$(1 + J × R)
where
* t is the age of the rock in years;
* h is the half-life of $^{40}$K in years;
* R is the measured ratio of $^{40}$Ar to $^{39}$Ar.
But what is J? J is a factor which depends on the nature of the neutron bombardment. J is not calculated on theoretical grounds, but is found experimentally; alongside the sample we're interested in, we irradiate and then heat a sample of known age (a standard).
Measuring the $^{39}$Ar and $^{40}$Ar emitted from the standard, and knowing the time t that it was formed, we can put these figures into the equation above and solve it for J.
So now we know J, and we have measured the R-value of the sample we're actually interested in dating, so we can use these data to solve the equation for t, giving us the age we're looking for.
You will note that this means that we have to be able to date some rocks accurately using some method other than Ar-Ar, so that we can find a standard to use for the determination of J; fortunately we can do this, and geologists have put a lot of effort into identifying rocks which can be accurately dated and used as standards.

## Advantages of the Ar-Ar method

So far, all we seem to have done is taken the K-Ar dating method and made it much more complicated for no apparent reason. However, there are advantages to this more complex method.
In the first place, recall that one of the potential problems with the K-Ar method is that it requires two different samples, one to measure the potassium and the other to measure the argon; if the two samples had different chemical compositions when they first formed then this will introduce an error. However, in Ar-Ar dating the two isotopes of argon are both measured from the same sample, and so at least one potential source of error is eliminated.
The other important advantage of Ar-Ar dating is the extra data gained from step heating: instead of heating the irradiated sample to the highest possible temperature all at once, and so releasing all the argon all at once, we can increase the temperature in steps starting at a low temperature.
What's the point of this? Well, different minerals within the rock will give up their argon at different temperatures, so each step will give us a ratio of $^{40}$Ar to $^{39}$Ar which we can use in the equation to calculate a date. Now, recall that we said that when the rock was first formed, the $^{39}$K and $^{40}$K from which these are derived must have appeared in the same ratio in each mineral, because both isotopes of potassium have the same chemical properties.
This means that if the rock cooled rapidly enough that all the minerals in it have the same date, and if there has been no argon loss, and if there is no excess argon added to the system, then the dates we calculate at each step of the heating will be the same date.
If we don't get the same date at each step, then we may be able to work out what's going on.
For example, if the date increases at each step, then we are quite possibly looking at a slow-cooling igneous rock in which different minerals crystallized out of the magma at different times, a possibility we can investigate further.
Or if we consistently get one date for the steps below (for example) 400°C, and consistently get another date in the steps above 400°C, then it seems as though argon loss occurred as a result of metamorphism at a temperature of about 400°C, with the younger date representing the date of the metamorphism, and the older date representing the formation of the rock; and we can investigate this clue further by looking for other evidence of the metamorphic event.
And if the dates we get are all over the place, then we are probably looking at excess argon. Now the bad news is that there is no way we can somehow manipulate this data to give us a correct date for the sample. But the good news is that we do know that there's a problem; whereas if we'd analyzed the same rock using the K-Ar method, then it would have supplied us with a date and there'd have been no sign in the K-Ar data of anything wrong with it.
For these reasons Ar-Ar dating has largely superseded K-Ar dating, although the simpler method is still employed in some cases where it is known to be unproblematic or where Ar-Ar is unsuitable for some technical reason.
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