If a zircon crystal originally crystallizes from a magma and remains a closed system (no loss or gain of U or Pb) from the time of crystallization to the present, then the Discordant dates will not fall on the Concordia curve.
Sometimes, however, numerous discordant dates from the same rock will plot along a line representing a chord on the Concordia diagram. is then interpreted to be the date that the system became closed, and the younger date, t*, the age of an event (such as metamorphism) that was responsible for Pb leakage.
In a rock twice as old there will be one 235U atom left for every three 207Pb atoms (Pb/U = 3), and so forth.
Nd ratios on several minerals with a mass spectrometer and then from the slope determine the age of the rock. If a magma cools quickly on the surface of the Earth, some of the Ar may be trapped.
The initial ratio has particular importance for studying the chemical evolution of the Earth's mantle and crust, as we discussed in the section on igneous rocks. If this happens, then the date obtained will be older than the date at which the magma erupted.
Pb leakage is the most likely cause of discordant dates, since Pb will be occupying a site in the crystal that has suffered radiation damage as a result of U decay.
U would have been stable in the crystallographic site, but the site is now occupied by by Pb.
If nothing disturbs the grain to release any of this radiogenic lead, dating it is straightforward in concept.
In a 704-million-year-old rock, 235U is at its half-life and there will be an equal number of 235U and 207Pb atoms (the Pb/U ratio is 1).
To see how we actually use this information to date rocks, consider the following: Usually, we know the amount, N, of an isotope present today, and the amount of a daughter element produced by decay, D*.
By definition, D* = N-1) (2) Now we can calculate the age if we know the number of daughter atoms produced by decay, D* and the number of parent atoms now present, N.
We can also construct a Concordia diagram, which shows the values of Pb isotopes that would give concordant dates.