Potassium (K) is the 7th most abundant element in the earth's crust, and is a major component of many common rock forming minerals. Very common minerals like biotite and muscovite mica and potassium feldspar contain weight percent levels of K. Naturally occurring K is made of 3 isotopes,

^{39}K (93.258%),

^{40}K (0.012%) and

^{41}K (6.730%).

^{39}K and

^{41}K are stable,

^{40}K is radioactive. Natural Ar is fairly abundant in the earth's atmosphere (~1% of the air we breathe) and is composed of three isotops,

^{40}Ar (99.600%),

^{38}Ar (0.063%), and

^{36}Ar (0.337%).

^{40}K decay is an interesting process, unlike the U and Th systems I've blogged about earlier which undergo a chain decay,

^{40}K has a branched or dual decay scheme. That means that 89.52% of the time,

^{40}K decays by beta emission to

^{40}Ca. 10.48% of time time,

^{40}K decays by extranuclear electron capture to

^{40}Ar. The

^{40}K to

^{40}Ar process is the one we will concern ourselves with in this post.

^{40}K -

^{40}Ca is rarely used as a geochronometer because Ca is so abundant in nature. It is hard to differentiate in minerals what Ca formed in the mineral from decay of K and what Ca was included in the original mineral structure. Argon, a noble gas, is rarely present in significant amounts within crystals, so we do not have to worry as much about the original

^{40}Ar component (although you will see later that the

^{40}Ar/

^{39}Ar technique lets us deal even with "inherited"

^{40}Ar).

^{40}K has a half-life of 1.25 billion years (Ga), which makes it perfect for addressing a wide range of geologic problems. The graph below shows the evolution of

^{40}K,

^{40}Ca, and

^{40}Ar abundance versus time.

Like in all graphs that show parents and daughters, the curves intersect at the half-life. Focusing on the

^{40}Ar then, we can see that the daughter to parent ratio, or

^{40}Ar/

^{40}K changes over time, like this

We can measure the

^{40}Ar and

^{40}K in a sample, and from that ratio, calculate an age. The age equation (shown below)

then relates the amount of parent (

^{40}K), daughter (

^{40}Ar) and time. Like with all geochronologic systems, actually calculating the age is fairly straightforward. The actual K-Ar age equation is a little more involved because of the branched decay I mentioned earlier, so the final form looks like thiswhere

is the

^{40}K decay constant (total)

and

are the decay constants for the two decay paths that produce

^{40}Ar, and

is the decay constant for

^{40}Ca production from

^{40}K. The term in the age equation just before the daughter to parent ratio therefore describes the fraction of

^{40}K decays that result in the formation of a

^{40}Ar atom.

The K-Ar geochronometer came into widespread use in the 1940's, once the basics of the decay scheme were worked out. There are two main issues with the technique, however, that are kind of a pain, and are the reasons that more often that not the

^{40}Ar/

^{39}Ar technique is much more popular today. First, you cannot measure K and Ar on the same machine. Typically, samples would first be heated (often using an induction furnace) to very high temperatures (~1400°C). At these temperatures the Ar trapped in the sample is liberated and can then be measured. The

^{40}Ar from the sample would be spiked with

^{38}Ar, and then measured on a mass spectrometer. The degassed sample would then be retrieved from the furnace, and analyzed separately for

^{40}K. With the amount of

^{40}Ar and

^{40}K, you culd then calculated an age.

The second problem with the K/Ar technique is determining where the Ar came from. As I mentioned earlier, Ar is fairly abundant in the atmosphere, making up about 1% of what we breathe. It is also fairly common in groundwater and geo-fluids (fluids associated with igneous intrusions and metamorphism). Some of this Ar could become trapped in the crystals, therefore rendering the calculated age kind of meaningless. We know the atmospheric

^{40}Ar/

^{36}Ar ratio very well, so by measuring the

^{36}Ar we can correct for this "trapped Ar", but we have to assume that the composition is atmospheric. In some cases this is a perfectly reasonable assumption, but with the advent of the

^{40}Ar/

^{39}Ar technique, we are actually able to evaluate that assumption.

The basis of the

^{40}Ar/

^{39}Ar technique is the fact that when K is bombarded with neutrons (in a nuclear reactor), some important reactions take place. Namely,

^{39}K is converted into

^{39}Ar. We know the natural

^{39}K/

^{40}K ratio, so if we can measure the efficiency of this transformation in the reactor, we can use

^{39}Ar as a proxy for

^{40}K. This would allow us to measure an age by simply measuring the

^{40}Ar/

^{39}Ar ratio of a sample. What is even better is that

^{39}Ar does not exist naturally, so we do not have to worry about any inheritance or atmospheric contamination.

^{39}Ar production can be described by this equation

where

is the neutron flux at energy Eis the neutron capture cross section at energy E for the reaction

^{39}K(n,p)

^{39}Ar, and

is the duration of the irradiation. In practice, instead of measuring these values directly we figure them out using well defined age standards, producing this equation

where

^{40}Ar

^{*}is the

^{40}Ar derived from radioactive decay,

^{39}Ar

_{K}is the

^{39}Ar produced in the reactor from

^{39}K, and J is a term that incorporates all of the irradiation variables but can be calculated from standards of known age (determined with other methods), whereThe advent and refinement of the

^{40}Ar/

^{39}Ar method solved some of the larger problems with the K/Ar technique. First, sample analysis became much more straightforward, measuring different isotopes of the same element is much easier that measuring different elements. Measuring a ratio of two isotopes is also easier that measuring abundances of two elements. The

^{40}Ar/

^{39}Ar frees us from uncertainty in the spikes used during analysis.

Second, it allows the geochronologist to evaluate the assumption that the "extraneous Ar" in the sample is atmospheric in composition. This is done by progressively degassing the sample at higher and higher temperatures (called step-heating experiments). The first temperature steps are at low temperatures, and tend only to liberate very loosely bound Ar from the crystal, perhaps Ar adsorbed to the surface of the crystal, or held near the surface. With increasing temperature we access and analyze gas that is more tightly bound up in the crystal structure. In the end we then have a series of steps, each with separate isotopic values. If the gas came only from the atmosphere, and was not related to any K, then

^{39}Ar/

^{40}Ar would equal 0. If the gas was entirely radiogenic, and had no atmospheric input, then

^{36}Ar/

^{40}Ar would equal 0. In truth, we typically have some mixture of inherited (or atmospheric) Ar and radiogenic Ar. If we plot up these values on an inverse isochron diagram we can determine what the composition of the extraneous Ar reservoir is, and therefore correct our values to determine the real age.

as shown above. If your sample is a mixture of inherited Ar from a single reservoir and radiogenic Ar of a single age, then your individual temperature steps will define a mixing line between those two compositions. We can use the inherited Ar composition to correct our

^{40}Ar values, and get the real age. It is also common to see the data displayed as an age spectra, shown below. Here, each box represents an indivual temperature step from a single sample. The y-axis is the age (here in Ma), corrected for extraneous Ar. The height of the box is proportional to the uncertainty of the measurements. The x-axis is the cumulative percent of Ar released. The steps are in order, so the first low temperature steps are on the left, and progressively higher temperatures towards the right. The width of the box is proportional to the amount of radiogenic Ar (

^{40}Ar

^{*}) released during that step. The large flat area in the middle of the graph is called a plateau and indicates that ages from different temperature steps agree. There is no real physical basis for the definitions of a plateau, and variations abound. Realistically, if our measurement precision was high enough, we would never see plateaus, because natural volume diffusion should round out the profile and make the early temperature steps slightly younger. But, age spectra are very common in literature, so it is important to know how to read them.

The inverse isochron diagram is much more powerful, and I am suspect of Ar papers that do not include inverse isochron diagrams. If the sample is very radiogenic, and there is little

^{36}Ar, then the corrections aren't significant, but still that information should be included. Plateaus and age spectra diagrams are interesting on their own, almost from a Psychology of Science perspective. Even though they are not the most powerful Ar/Ar tool, they are visually pleasing, and telling someone you got a nice plateau usually convinces them of your data quality faster than discussing inverse isochron diagrams. The definitions of a proper plateau usually involve some minimum number of consecutive steps representing some fraction of the total gas that are within error of each other for age and have no statistically discernible slope. You can imagine that if your measurements were kind of crappy, and the age uncertainty on each step high, then getting consecutive steps to agree isn't very difficult. As labs drive for higher and higher precision, and individual step ages have uncertainties less than 1% and official plateau get tougher and tougher to create, even when the age and sample are perfectly acceptable.

^{40}Ar/

^{39}Ar thermochronology is a very common and useful tool for geologists, and is particulary interesting because it allows the direct examination of a number of the assumptions involved with radiogenic isotope geochronology. Later posts will examine the power of the technique in more detail.

Note - the inverse isochron diagram I used is one I made up just as a teaching tool, the age spectra is real data I collected a few years ago.

## 11 comments:

about half of your pictures / equations give a graphic not found symbol.

must be something with blogger or your connection, they all seem to work from my home and work computers...hmmm, I'll investigate more. Anyone else having issues with the images?

The ones with green backgrounds at home don't show up at all at work.

Very weird, I am still having no problems with them. Which ones have green backgrounds? Perhaps I can try to reload them.

OK, just tried it on a PC at work (I am a Mac man myself), and the images all look fine. Anyone else having problems?

i can see all the figures fine...

nice post, I still haven't fully grasped some of the first posts along these lines!

Thanks, I am thinking this is the first draft of what will eventually become a GeoWiki post. Any comments/suggestions are most welcome. I'd especially like suggestions that relate to interpreting published data.

Yep the images all work for me too. Interesting post, thank you!

"I'd especially like suggestions that relate to interpreting published data."

Most of those issues don't really relate to the decay equations, they relate to geologic context, diffusion, thermal history, deformation, etc.

I suppose I mean questions dealing with the two primary diagrams, irradiation corrections, etc, anything is fair game.

Thank you dude... nice work. Can this method be applied for dating Precambrian deformed &/or igneous gneisses rocks..?

Post a Comment