Why does zircon hate lead? How do these tiny crystals so effectively exclude lead atoms during formation enabling accurate uranium-lead (U-Pb) dating?

### Background


From the December 29, 2022 NPR article [To peer into Earth's deep time, meet a hardy mineral known as the Time Lord](https://www.npr.org/2022/12/29/1139782011/to-peer-into-earths-deep-time-meet-a-hardy-mineral-known-as-the-time-lord):



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> "(Zircons) are really the best markers of Earth's time, or the history of the Earth," says [Michael Ackerson](https://naturalhistory.si.edu/staff/michael-ackerson), a geologist with the Smithsonian's National Museum of Natural History.)
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From the podcast linked on the same page after 01:00:



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> He tells me that one of the crystals I'm looking at is 4.32 billion years old. Zircons are the oldest known pieces of Earth that still exist on the surface today; the oldest go back as far as 4.37 billion years.
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> "They are the best markers of Earth's time, (for) the history of the Earth.
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> Ackerson says a zircon crystal originally forms in magma - hot molten rock. Other minerals do too; together they'll make up say, a granite mountain, that slowly weathers away.
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> "Most of the minerals don't survive, they slowly weather away. Quartz, feldspar, they're chemically or physically weathered or eroded, to a point where they're no longer quartz and feldspar. Zircon, and one of the reasons that zircons are so useful, is that zircon is very resilient.
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> The hearty crystals persist, and eventually get incorporated into another rock as it's forming. That means scientists can crush up the Earth's oldest rocks and pick through the debris, to find little grains of zircon, that are even older.
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> To know a zircon's age, they zap it with a laser.
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Discussion of the use of lasers, argon plasma and detectors to count uranium and lead atoms.



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> The important atoms are uranium and lead. A growing crystal of zircon ***loves uranium*** and will take it in, but ***zircon hates lead,*** so if you find lead inside, it pretty surely came from the decay of uranium, which happens at a steady rate, like the ticking of a clock.
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### Question:


Why does zircon hate lead? How do these tiny crystals so effectively exclude lead atoms during formation enabling accurate uranium-lead (U-Pb) dating?


I'm interested in a basic understand of the chemistry that allows a growing crystal of zircon in magma to so effectively prevent uranium from being incorporated while allowing so many other metals in.


Besides uranium and obviously zirconium and silicon, Wikipedia's [zircon](https://en.wikipedia.org/wiki/Zircon) gives the formula for zirconium silicate as $\ce{(Zr\_{1–y}, REE\_y)(SiO4)\_{1–x}(OH)\_{4x–y}}$ where $\ce{REE}$ stands for [rare earth element](https://en.wikipedia.org/wiki/Rare-earth_element):



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> ...a set of 17 nearly-indistinguishable lustrous silvery-white soft heavy metals.
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The Wikipedia zircon page also says:



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> Zircon precipitates from silicate melts and has relatively high concentrations of high field strength incompatible elements. For example, hafnium is almost always present in quantities ranging from 1 to 4%.
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This seems potentially relevant: [Chapter Six - Computer modeling of Zircon (ZrSiO4)—Coffinite (USiO4) solid solutions and lead incorporation: Geological implications](https://www.sciencedirect.com/science/article/abs/pii/S246851781930005X)



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> The structure of zircon, ZrSiO4 is modeled using interatomic potentials. The uranium end-member, coffinite (USiO4) and intermediate solid solutions of zircon and coffinite (UxZr1–xSiO4) are then modeled, allowing the prediction of lattice parameters as a function of uranium concentration. Finally, possible structures resulting from the radioactive decay of uranium to lead in coffinite are considered.
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Zircon is rather picky because of its rather unusual composition. It has the composition $\ce{MSiO4}$ where $\ce{M}$ is predominantly zirconium (which is of course named after the mineral) but generally includes other elements in solid solution. Bevause the $\ce{SiO4}$ group with the normal oxidation states of silicon and oxygen takes four negative charges, the metal $\ce{M}$ must match the $+4$ oxidation state of the zirconium, at least on average. The metal must also have relatively large atoms in this oxidation state to substitute comfortably for the zirconium. Only lanthanides, actinides, and a few early-group transition elements in the fifth or later period fit these criteria. [Wikipedia](https://en.wikipedia.org/wiki/Zircon) specifically mentions "[high field strength incompatible elements"](https://en.wikipedia.org/wiki/Incompatible_element) including $\ce{Zr, Nb, Hf, Ta, Th, U}$ and rare earth elements.


Uranium, which commonly adopts the $+4$ oxidation state, works well, but lead does not. Lead is too difficult to achieve the $+4$ oxidation state because of the relativistic impact that emerges in heavy late-group elements. Wikipedia discusses this relativistic effect:



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> Lead shows two main oxidation states: +4 and +2. The tetravalent state is common for the carbon group. The divalent state is rare for carbon and silicon, minor for germanium, important (but not prevailing) for tin, and is the more important of the two oxidation states for lead.[1] This is attributable to relativistic effects, specifically the inert pair effect, which manifests itself when there is a large difference in electronegativity between lead and oxide, halide, or nitride anions, leading to a significant partial positive charge on lead. The result is a stronger contraction of the lead 6s orbital than is the case for the 6p orbital, making it rather inert in ionic compounds.
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**Cited Reference**


1. Greenwood, N. N.; Earnshaw, A. (1998), *Chemistry of the Elements* (2nd ed.), Butterworth-Heinemann, ISBN 978-0-7506-3365-9, p. 373.


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