Geochronology
=======================

Theory for geochronology
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.. figure:: U-Pb_concordia_line.png
   :align: center

   Concordia diagram and discordant line in U-Pb dating (credit: https://www.ucl.ac.uk/~ucfbpve/geotopes/indexch5.html)


Why discordant line is straight?
------------------------------------

A question bothers me many years is that why the discordant line is a straight line. :math:`T_1` is the time when Pb-loss occurred. 

In the figure presented above, the leakage event occurred in :math:`T_1`. 
If all previous lead (:math:`Pb^{206}` and :math:`Pb^{207}`) lossed during this event, the current lead contents inside the zircon sample are all decayed results since :math:`T_1`. 
For a zircon sample which suffered no lead-leakage during the event in :math:`T_1`, then its location will be in :math:`T_0`, the time when these samples formed blocked environment.

The leakage scenario assumes that the :math:`Pb^{206}` and the :math:`Pb^{207}` present no difference. Therefore, they have the same leakage percentage, and the zircon samples with different leakage degree will be in a straight line.