# Historical Geology/U-Pb, Pb-Pb, and fission track dating

In this article we shall discuss the basis of the U-Pb and Pb-Pb methods, and also fission track dating. The reader will find this article much easier to grasp if s/he has already mastered the material in the articles on K-Ar dating, Ar-Ar dating, and Rb-Sr dating.

## The isotopes

There are a number of isotopes of interest in U-Pb dating.
$^{238}$U (uranium-238) decays to $^{206}$Pb (lead-206) by a complex decay chain. It has a half-life of 4.5 billion years. $^{235}$U (uranium-235) decays to $^{207}$Pb (lead-207) by an equally complex decay chain, and has a half-life of 0.7 billion years.
It is also useful to know of the existence of $^{204}$Pb (lead-204), which is neither unstable nor radiogenic.

## Isochron dating and U-Pb

We can always try U-Pb dating using the isochron method, but this often doesn't work: the compositions of the minerals involved, when plotted on an isochron diagram, fail to lie on a straight line.
There seem to be two reasons for this. First of all, the straight-line property of the isochron diagram is destroyed when the isotopes involved get shuffled between minerals. Now lead and uranium are particularly susceptible to such shuffling in the event of even mild metamorphism. The other problem is that uranium is particularly susceptible to weathering. Now since all rocks are somewhat porous, and since we are pretty much obliged to date rocks from near the surface, it's hard to find instances in which uranium has not been lost.

## Zircons

Zircon is the mineral ZrSiO$_4$; as you can see from its chemical formula, it is one of the silicate minerals. Although it is not abundant in igneous rocks, it is sufficiently common to be used for the purposes of radiometric dating.
It has two properties which make it useful for this purpose.
First of all, uranium will readily substitute for the zirconium (Zr) in the mineral, whereas lead is strongly rejected. For this reason we expect zircons, when formed, to contain some uranium, but virtually no lead.
Second, zircons are durable and chemically inert, able to resist chemical weathering and even high-grade metamorphism up to about 900 °C.
Zircons, then, are relatively immune to the problems that make isochron U-Pb dating so difficult. But of course for isochron dating we need more than one mineral; zircons alone would not be enough.
However, these facts about zircons, combined with what we know about uranium, suggest an alternative method of dating.

## The method

If there is no lead in the zircon originally, and if no lead or uranium has been added or subtracted to the zircon since its formation, then the following formula will hold:
    t$_{238}$ = h$_{238}$ × log$_2$(1 + R$_{238}$)
where t$_{238}$ is the age of the zircon, h$_{238}$ is the half-life of $^{238}$U and R$_{238}$ is the ratio of $^{206}$Pb to $^{238}$U.
Not only that, but since we have two uranium isotopes to work with, we will also have
    t$_{235}$ = h$_{235}$ × log$_2$(1 + R$_{235}$)
where t$_{235}$ is the age of the zircon, h$_{235}$ is the half-life of $^{235}$U and R$_{235}$ is the ratio of $^{207}$Pb to $^{235}$U.
Now because the zircon has only one age, it follows that if no lead or uranium has been added or subtracted from the zircon since its formation, we will have t$_{238}$ = t$_{235}$, in which case the two t values are said to be concordant; whereas if lead and/or uranium has been added or subtracted, then it would require some sort of statistical fluke for the two t values to end up identical. So analysis of both the $^{206}$Pb/$^{238}$U ratio and the $^{207}$Pb/$^{235}$U ratio acts as a check on the correctness of the date we come up with in the same way that step heating does in the Ar-Ar method and the plotting of several minerals on an isochron diagram does for the Rb-Sr and related methods: it allows us to find out if the isotope ratios have been affected by something other than the passage of time, and to reject any "dates" calculated from the isotope ratios if this turns out to be the case.
It is possible to refine this date still further. If we suspect that the zircon, despite its chemical properties, still managed to incorporate a little lead at or after its formation, then since all lead isotopes are chemically the same, we can measure the amount of $^{204}$Pb the zircon contains. Since we know the ratios in which the various lead isotopes are usually found, we can then apply the same sort of correction we used to account for atmospheric argon in the K-Ar method.
While zircon has been the most popular mineral for U-Pb dating, other minerals have been employed, including apatite, monazite, titanite, allanite and, most interesting of all, xenotime.

## Xenotime

There is a difficulty in using radiometric dating to put an age on sedimentary rock. The problem is that sediment is made up of clasts of some parent rock, and when we date these clasts, we are in effect dating the parent rock rather than the sediment as such. If, for example, we apply U-Pb dating to a grain of zircon found in sandstone, we aren't dating the formation of the sandstone, we're dating the formation of the granite that the zircon came from; all we could say about the sandstone is that it must be younger than that.
However, it is possible to put a date on some sedimentary rocks using the mineral xenotime (YPO$_4$). Uranium can and often does substitute for the element yttrium, whereas lead cannot, making xenotime suitable for radiometric dating.
The key fact about xenotime is that since it has the same crystal structure as zircon, it can grow on zircon crystals, forming a crust; and this process, of course, cannot begin to take place while the zircon crystal is still locked inside its parent rock. The zircon will only start acquiring its xenotime crust after weathering and erosion have freed it from its parent rock and it becomes sediment.
So by dating the xenotime crust, we can find out when the zircon it's growing on became sediment; dating the zircon itself would tell you the age of the parent rock.

## Speleothems

A speleothem, more colloquially known as a cave formation, is formed when minerals dissolved in water precipitate out of the water as it drips, seeps, or flows into a cave. The reader will probably be familiar with stalagmites and stalagtites; more speleothems are shown in the photograph to the right.
Now, compounds of uranium are often highly soluble in water (this, indeed, is one of the major problems with U-Pb isochron dating) whereas compounds of lead are stubbornly insoluble. As a result, we expect speleothems when they are first formed to contain some uranium but little or no lead — just like zircons. So we can apply the same technique to speleothems as we do to zircons.

## Pb-Pb dating

We can exploit our double system of $^{238}$U-$^{206}$Pb and $^{235}$U-$^{207}$Pb in another way. Suppose we separate the minerals in a rock, and plot a graph showing their $^{206}$Pb/$^{204}$Pb ratios on one axis and their $^{207}$Pb/$^{204}$Pb ratios on another (similar, though not identical, to what we did when constructing isochron diagrams). It can be shown mathematically that if the rock has been undisturbed, so that the isotope ratios reflect nothing but the passage of time, then just as with the isochron diagrams we've already discussed (though for a different reason) the minerals so plotted will lie on a straight line on the graph; and the age of the rock can be calculated from the slope of the line.
Unlike the ordinary isochron methods such as Rb-Sr, the Pb-Pb method does not allow us to deduce the original proportions of the various lead isotopes from the data acquired from the sample. Instead, we need to find this out some other way.
We can do this by finding minerals that contain lead but never contained any uranium, or only ever contained it in negligible quantities. Troilite (FeS) from iron-rich meteorites fits the bill: its present ratio of uranium to lead is so tiny that either the solar system and indeed the universe is many many times older than cosmologists think, or, given the long half-life (4.5 billion years) of $^{238}$U, there can hardly have been any uranium in the meteorites to start with, and so its decay can hardly have affected the lead isotope ratios of these meteorites.
You might perhaps doubt that meteorites would have the same initial lead isotope ratios as the Earth. Planetary scientists maintain that they should, for reasons which are somewhat beyond the scope of this textbook. Another reason for believing it is that if we calculate Pb-Pb dates on this basis, the dates we get are in agreement with dates produced by other methods where they can be applied: this would hardly be possible if we were using the wrong figures for the initial lead isotope ratios. So taking the figure derived from the troilite as an "anchor" for our calculations, we can then go ahead and apply the Pb-Pb method to rocks which do contain significant quantities of uranium.
Now, recalling that I began this article by explaining that the isochron method is no use for U-Pb, you may wonder why this Pb-Pb isochron should be any better. However, recall that one of the major problems with the U-Pb isochron is that uranium compounds are highly soluble and are easily removed from the rock by weathering. But when that occurs, the lead will still remain and can be used for Pb-Pb dating. What's more, even if some lead is also removed, then since all the lead isotopes are the same element, having the same merely chemical properties, there will be no tendency for one isotope to be lost in a greater proportion to the others, and so the isotope ratios will remain the same.
It is true, of course, that the removal of the uranium by weathering will slow down and even, if all the uranium is removed, completely stop the radiometric clock, so that we will not have an accurate measurement of the time after the weathering began, and Pb-Pb dating will therefore tell us that the rock is a little younger than it is. But only a little younger, because a typical chunk of igneous rock will only have spent a relatively short amount of time being exposed to chemical weathering compared to the time when it was not.
As with the isochron methods we've already met, the Pb-Pb isochron method carries its own built-in check on its correctness: if the rock has been seriously disturbed, so that the isotope ratios depend on something other than the passage of time, then when we plot the minerals on our graph, they will almost certainly not lie on a straight line, and we will not obtain a date.

## Fission track dating

Finally, I should mention fission track dating. The decay chain by which uranium decays involves the emission of alpha particles, and as these particles travel through the rock they produce microscopic scars (fission tracks) in the minerals they pass through, which can be revealed by cutting and polishing the minerals and inspecting them through a microscope. A number of minerals are suitable for this process, including apatite, zircon, and titanite.
The number of fission tracks in the minerals will depend on the quantity of uranium and the amount of time it's had to do damage. So, conversely, if we count the fission tracks and we measure the amount of uranium, then we can figure out how much time it must have taken to produce the fission tracks.
One weakness of this method is that the fission tracks will heal over if the rock is heated to about 200 °C, so the fission track clock will be reset even by the mildest metamorphism.
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