Short-lived, relative isotopic dating

A short-lived nuclide has a short (geological) half life. ¹⁴⁶Sm, for example, has a half life of ~100 Myr. So if you generate this isotope, by way of a super nova for example, after 5 or 6 half lives there won’t be any left in measurable amounts. What will be left, however, is a corresponding concentration of what’s called a daughter isotope. So the parent isotope of ¹⁴⁶Sm will decay, through the emission of an α particle (i.e, a helium nucleus), to ¹⁴²Nd. The short-lived nature of this system, and the fact ¹⁴⁶Sm isn’t being actively produced, make the system unusual for terrestrial dating (you normally want a long-lived isotopic system such as the uranium series to get long age dates on Earth, more on that later).

As the Solar System was forming, a variety of short-lived radioactive nuclides were present, most likely due to being injected into the Solar nebula by the way of a nearby exploding super nova. The original concentration of ¹⁴⁶Sm can be measured in meteorites (which formed within a few MYr of the short-lived nuclides being introduced into the solar nebula) by measuring the surplus amount of ¹⁴²Nd in relation to other isotopes of Sm and Nd. From those measurements and through some calculations (which I won’t detail, since it can get a little hairy), you can get the original concentration of radioactive ¹⁴⁶Sm in the solar system.

In order to determine how long it’s been since the ¹⁴⁶Sm was introduced into the system until the (very ancient) rock you have solidified, you measure the concentration of the daughter isotope ¹⁴²Nd, in comparison to the solar concentration of ¹⁴²Nd today, and calculate the elevated concentration of radioactively produced ¹⁴²Nd (written as δ¹⁴²Nd* – the δ means the variation from the solar concentration while the * means the radioactively produced portion).

The rare earth elements (REE) behave as a cohesive geochemical block. This is useful since Nd and Sm are pretty much equally compatible in minerals like plagioclase or pyroxene, and have very similar melting temperatures. Therefore, you can determine how much Nd or Sm there’s likely to be in a mineral (usually very equal amounts) and the isotopes ratios thereof. So regardless of the actual Nd concentration in parts per million, there’ll be a ratio of ¹⁴²Nd/¹⁴³Nd = 2.230 for rocks or minerals which crystallised >600 Myr after the ¹⁴⁶Sm generating super nova (discounting chemical and other effects, which is what you do in your calculations and in the lab). If this ratio is higher than that, there was most likely some ¹⁴⁶Sm still lingering around when the rock formed, which has subsequently decayed into a surplus of ¹⁴²Nd.

This is reasonably straight forward. The problem is this will only give you a relative age to what is at best, an estimation of the original ¹⁴⁶Sm concentration in the solar system. That is why the errors on the dated rocks we’re talking about are between 3.8 and 4.3 billion years. Establishing the original amount of ¹⁴⁶Sm is difficult, hence the large errors.

Long-lived absolute isotopic dating

So the recently announced oldest rocks in the world maybe a little younger than expected, but the only way to know for sure is by using crystals of zircon (AKA zircons). Zircon is useful because it is a stable, durable mineral that more often than not, contained uranium and thorium when it formed. U and Th are great, because their radioactive isotopes are still alive today, and they’ve been sitting around producing daughter isotopes through the uranium decay series since the formation of the solar system 4.567 billion years ago. This is the ultimate set of isotopes insofar as dating goes. Both U and Th are long-lived and because of that, you can do absolute dating. It’s almost as easy as “Here’s the concentration of U and Th, here’s the concentration of ²⁰⁷Pb and ²⁰⁶Pb, therefore this crystal has been around for X MYr” – disregarding the extremely difficult lab work and calculations you have to do to get those precise, accurate numbers.

So, until the team from Carnegie Institution of Washington and McGill University in Montreal can get some absolute dates from zircons, this discovery should be put into the “very likely, but awaiting confirmation” pile.

*This is the problem so far as I understand it. I’ve not done any ¹⁴⁶Sm→¹⁴²Nd dating in my time, but I have done ²⁶Al→²⁶Mg dating, and I believe the concept to be similar. I’m open to correction, so correct away below if needed.