# In radiometric isochron dating why is at t=0 D*/Dref=const but P/Dref not?

I am a physics graduate and trying to understand one of the assumptions made for isochron dating of rocks: at crystallization time of the rock, $$t=0$$, the ratio of the parent isotope to a stable reference daughter isotope was variable for different parts/minerals of the rock ($$P/D_{ref}\neq const$$), but the ratio of the radiogenic daughter isotope to the stable reference daughter isotope was constant ($$D*/D_{ref}=const$$). See for that the figure below taken from here :

My question: Why is the one ratio constant, but the other not? I taught $$D*/D_{ref}=const$$ holds, because just before $$t=0$$ the rock is still molten and components are well mixed, but then why shouldn't $$P$$ and $$D_{ref}$$ be also homogeneously mixed and uniformly distributed.

Additional question: In the figure below, taken from here, I get that the linear function is the isochron, but what is the logarithmic function and how does it help in the dating process/what is its contribution? Thanks

• Can you please edit the question so it contains only the first question, and ask a separate question for the second one? These are two different dating methods, and will require two different answers. Apr 21, 2020 at 10:46
• @Gimelist Ah, sorry, I forgot not to put 2 questions in 1 post. I already received a well explained answer, should I still split the question or leave it like it is now? Apr 22, 2020 at 23:27

1) D* (radiogenic isotope) and Dref (stable reference isotope) are two isotopes of the same element. P is the radioactive parent of D*, and is a different element. Chemical fractionation between P and Dref occurs as the rock solidifies because different elements are preferentially incorporated in different minerals depending on how well their ionic radii and valences are compatible with the mineral's crystalline lattice.

Although there can be some mass-fractionation of isotopes of a same element, it is usually very small (IE negligible) relative to the chemical fractionation. Often, for making such isochrons, geologists choose different mineral species with very different P concentrations (and thus varying P/Dref) to provide spread along the isochron line; this allows for more precise regression and determination of the slope / age.

2) The second diagram you show is a concordia plot, not an isochron. There is no common isotope on the ratio denominator. Rather, this plot shows two different isotope systems each with their own decay chain (238U->206Pb and 235U->207Pb), these two Uranium decay chains have different half lives. The curved line is the "concordia" curve, which is the expected result if the sample exhibits closed-system behaviour (IE Pb has not diffused out of the crystal).

In this case a mineral (probably a zircon) was formed at 2.6 Ga and had open system behaviour at around 0.4 Ga. (IE the radiometric clock was partially reset). The straight line is called a "discordia line" and is a mixing line between the two time points on the concordia curve.

• Thanks, very informative! Especially, it makes now sense why $P/D_{ref}$ has a spread along the x-axis in the isochron plot. About the concordia/discordia I am still reading through articles, if you have a link to share I would be happy to read it :) Apr 22, 2020 at 23:25
• Unfortunately most of the documentation I can come up with is behind a paywall. This one perhaps? geo.cornell.edu/geology/classes/Geo656/656notes03/… Apr 24, 2020 at 7:19