# 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. – Gimelist Apr 21 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? – NeStack Apr 22 at 23:27

• 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 :) – NeStack Apr 22 at 23:25