A closed system is one in which there is no free exchange of elements in a material with the outside environment.
Because these elements (and their isotopes) all have different half-lives, elements with longer half-lives will be present in greater quantities than those with shorter half-lives.
Accurate dating by measurement of ionium alone requires that the rate of sedimentation of ionium be constant with time, an assumption that does not hold for many sediments; any thorium-232 present in seawater will also precipitate, and the decay of the ratio of ionium to thorium-232 can be used as a measure of time.
This method does not require a constant rate of sedimentation of ionium but simply that the two isotopes are precipitated in a constant proportion.
The lead incorporated within the of uranium and thorium isotopes.
Thus, the lead isotopic composition of any mineral or rock depends upon its age and the environment from which it was formed; that is, it would depend upon the ratio of uranium plus thorium to lead in the parent material.
Primordial lead is thought to have been formed by stellar nuclear reactions, released to space by supernovae explosions, and incorporated within the dust cloud that constituted the primordial solar system; the troilite (iron sulfide) phase of iron meteorites contains lead that approximates the primordial composition.The Earth can be assumed to be a very large sample containing lead evolving from primordial lead by radiogenic increments.If modern lead, for example, from marine sediments or modern basalts has the composition of lead in the Earth and if the lead in the troilite phase of iron meteorites has the composition of primordial lead, then a simple model yields about 4.6 billion years for the age of the Earth.The sample age is based on the difference between the initial ratio of U with the environment (i.e., that it is a closed system.) The method is used for samples that can retain Uranium and Thorium, such as carbonate sediments, bones and teeth. Ages between 1000 and 300,000 years have been reported.