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Is the fact that Iron is attracted to magnets in any way related to the fact that it is also the element occupying the singular periodic table position where the chains of nuclear fission and fusion converge?

Or is this just a coincidence?

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It is coincidence.

For example not all forms of iron are ferromagnetic, even though they all have the same nuclei. Iron exists in three slightly different crystal structures called ferritic, martensitic and austenitic. The ferritic and martensitic are ferromagnetic but the austenitic form is not. So iron can switch between a ferromagnet and paramagnet just by changing its crystal structure.

Other elements like cobalt, nickel, dysprosium and gadolinium are also ferromagnets, and there are lots of compounds that show ferromagnetism. The most obvious of these are the rare earth magnets.

Ferromagnetism is a property of unpaired electrons within the material, and is not related to the nuclear energy levels involved in nuclear reactions. There is a basic description of ferromagnetism in Why does magnet attract iron but not other metals?

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