An event like metamorphism could heat the crystal to the point where Pb will become mobile.
Another possible scenario involves U leakage, again possibly as a result of a metamorphic event.
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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.
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.
One assumption that can be made is that all the lead in the sample was once uranium, but if there was lead there to start with, this assumption is not valid, and any date based on that assumption will be incorrect (too old).
In the case of carbon dating, it is not the initial quantity that is important, but the initial ratio of C, but the same principle otherwise applies.
Thus, if we start out with 1 gram of the parent isotope, after the passage of 1 half-life there will be 0.5 gram of the parent isotope left.
After the passage of two half-lives only 0.25 gram will remain, and after 3 half lives only 0.125 will remain etc.
Recognizing this problem, scientists try to focus on rocks that do not contain the decay product originally.
For example, in uranium-lead dating, they use rocks containing zircon (Zr Si O Zircon and baddeleyite incorporate uranium atoms into their crystalline structure as substitutes for zirconium, but strongly reject lead.
Zircon has a high hardness (7.5) which makes it resistant to mechanical weathering, and it is also very resistant to chemical weathering. Chemically, zircon usually contains high amounts of U and low amounts of Pb, so that large amounts of radiogenic Pb are produced.