Assuming a closed system means that nothing on the outside of the rock affected the sample.
This means that none of the parent or daughter isotope leaked in or out.
Most radiometric daters prefer using zircon for these reasons, but it is not the only compound used for uranium-lead dating.
Some other compounds used that have zirconium are zirconolite, and badeleyite.
The reason for stopping at lead is because lead is not radioactive and will not change into a different element.
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Scientists know that there are geological events that can disturb the zircon and release the lead created from the uranium. To try to account for this, a radiometric dater will use many different samples and use the ones that fit the Concordia curve.
If they do not fit, it is assumed that it signifies a large geological event The part of the rock a dater will use to date the rock is normally the zircon in the rock.
The last of the benefits is that the zircon, itself, is very hard.
This fact helps with extracting the zircon out of the rock it was in.
This data is compared to a curve called the Concordia diagram.