How does argon-argon dating work - need a simple but not-wrong explanation

The Washington Post article Scientists discover hundreds of footprints left at the dawn of modern humanity describes the geological dating of stratified layers of mud by analyzing and dating minerals within each layer.

But since floods jumble materials of different origins and ages together, that meant the scientists had to date dozens of different minerals. The youngest crystal in the footprint layer would represent the oldest possible age for the prints; the oldest crystal in the layer above it would represent the youngest they could be.

Using the argon-argon dating technique, by which scientists measure the decay of an isotope called Argon-40 into Argon-39 in order to find the age of crystals, they came up with a rough approximation of the footprints' age: 19,000 years at the oldest, 10,000 or 12,000 years at the youngest.

I can't exactly follow the logic, but I'm asking here about the dating process itself. How does argon-argon dating work?

I do not think that Argon-40 decays into Argon-39 as the article states, at least not all by itself. And when I look at the Wikipedia article, the discussion is so technical and defensive that I can't actually picture what is going on.

How does argon-argon dating work?

• You are right: there is no decay of 40-Ar into 39-Ar. But, I am not sure how the procedure works. 40-Ar, 39-Ar and 36-Ar are measured. Based on the atmospheric 40-Ar/36-Ar ratio and the 36-concentration, the 40-Ar concentration at the time of formation is calculated. The difference between measured 40-Ar and 40-Ar at formation is used in the procedure. But then, different passages in the Wikipedia article contradict each other (first section: 39-K is converted into 39-Ar by neutron bombardment; but "age equation" section: 40-K is bombarded; I think it should be 39-Ar). – daniel.neumann Oct 16 '16 at 8:41
• @daniel.neumann Thanks - I'm still thinking about what you've said. The Wiki article looks like there's well-intentioned effort, but it needs some attention from an expert. – uhoh Oct 16 '16 at 12:03
• There's a more basic explanation here: books.google.com/… Argon-Argon dating is similar to Potassium-Argon dating, but it requires less material. The Potassium 39 in the sample is irradiated to become Argon 39, then the ratio of the gas is compared. 39 will outnumber 40, but the variance in the outnumbering is what gives the answer. – userLTK Oct 16 '16 at 19:10
• @userLTK I think the problem that this addresses is not necessarily the amount of material, but that two physically separate samples are needed, one for potassium measurement and one for argon measurement, so you have to assume that the two samples are identical. The argon-argon method applies to a single sample (but you need a 2nd sample of known age in this case). – uhoh Oct 17 '16 at 0:06

As noted in the comments the wikipedia articles (at the time this question was submitted) are contradictory. There are quite a few steps to the logic of how argon-argon dating works but none are too complicated, although I won't go into all of the possible interferences. One thing to keep in mind is that high-precision isotope measurements always measure ratios between isotopes, not absolute concentrations.

To understand argon-argon dating, you need to understand potassium-argon dating.

The isotope potassium-39 makes up about 93% of natural potassium. Potassium-40 is radioactive but has such a long half-life that it is primordial - it has been around since the earth was being formed. Because of this, we can assume that the potassium-40:potassium-39 ratio in minerals at any time is a constant. Potassium-40 decays in 2 different ways. Most decays by beta decay to calcium-40. About 10.7% decays to Argon-40 by emitting a positron.

If the argon-40 stays trapped in the crystal and you can measure the ratio of potassium-40 to argon-40, then you know how long it has been since the mineral formed. This also assumes that there is no other source of argon like trapped air. A problem is that it takes two separate measurements to get the potassium concentration and the argon isotope ratios, increasing the uncertainty. Argon-argon dating gets around many of the issues by measuring only multiple isotopes of argon.

The trick is to irradiate the sample with neutrons along with samples of known age. Some of the potassium-39 forms argon-39 by an n,p reaction. By converting potassium-39 to argon-39 then measuring the argon-39:argon-40 ratio, you can calculate the sample's potassium-40:argon-40 ratio, remembering potassium-40:potassium-39 is fixed. The standards of known age are used to account for differences in the neutron flux during irradiation. Argon-36 in the sample accounts for any air contamination.

Argon-argon dating, ideally assumes that:

• all argon-40 in the sample comes from either atmospheric argon or from decay of potassium-40 in the sample
• all argon-39 in the sample comes from irradiation of potassium-39 in the sample and as noted above, if you know potassium-39:argon-40 ratio then you know the potassium-40:argon-40 ratio because the potassium-40:potassium-39 is constant (at this point in time)
• all argon-36 is the sample is from atmospheric argon

The actual calculations are pretty simple algebra, combining all the pieces.

• Thanks. I edited it to say argon-39 is formed by an n,p reaction. – haresfur Oct 16 '16 at 23:33
• OK I think I see! Instead of measuring 40K/40Ar, you assume a fixed 39K/40K ratio, convert a fraction $f$ of 39K to 39Ar by (n,p), then measure 39Ar/40Ar. If you simultaneously irradiate and measure a 2nd sample of known age, you can infer the fraction $f$. To account for any 40Ar already present (not from 40K decay) you also measure 36Ar and assume a 36Ar/40Ar ratio. Is that about right? – uhoh Oct 17 '16 at 0:01