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Here is the crystal structure of soluble Prussian Blue $\ce{KFe[Fe(CN)6]}$. The Fe(II) and F(III) are spaced alternatively like NaCl with cyanides in between. You can see that the places of Fe(II) and Fe(III) are not equivalent because one is attached to carbon while the other attached to nitrogen. This leaves some ambiguities because the places of Fe(II) and Fe(III) can be swapped without causing charge imbalance. Historically it was believed that Prussian Blue and Turnbull’s Blue are two different materials of the same atomic structure, but more rigorous studies confirmed that they are actually the same thing. enter image description here My question is whether it applies to other crystals containing transition metal elements. My guess is that there are unlikely counter examples because electrons are not confined to single atoms but shared among multiple atoms in solids, which makes it very easy for electrons to move among atoms to reach the most stable configuration. In another word, there should be only one stable orbital configuration which is either configuration A or B or somewhere in between like the orbital resonance in organic chemistry.

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  • $\begingroup$ It is the default norm for any crystal to only have one possible configuration. Then again, there are things like the non-stoichiometric $\rm Fe_{0.95}O$; does that count? $\endgroup$ Jul 23, 2023 at 19:14

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This leaves some ambiguities because the places of Fe(II) and Fe(III) can be swapped without causing charge imbalance.

It sounds like iron Fe(II) and Fe(III) are free chemical species, they are just emergent species in the most stable configuration. The oxidation state is sometimes relevant, but remain hypothetical, the fluctuation of charge of an atom depends mainly on the neighboring environment. The ground state of Prussian Blue has an iron atom between two carbons and therefore loses less charge $\ce{Fe^2+}$ and the other is between two nitrogens more electronegative and loses more charge $\ce{Fe^3+}$, if the electronic structure of this crystal is analyzed carefully, the exact charge at each iron atom will never be $+2$ or $+3$, swapping iron atoms will not affect much the crystal, the charge will remain the same as there is only one stable configuration.

Here is an academic example that has important magnetic properties: lanthanum manganite : $\ce{LaMnO3}$, the crystal structure is peroskite and the manganese has the oxidation state $+3$. When it is doped with Sr, the structure becomes $\ce{La_{1-x}Sr_xMnO3}$, the environment changes and the manganese has either an oxidation state $+3$ or $+4$ depending on the presence of Sr. The exchange of two manganese atoms even with the partial charge will not always converge to the same structure with the same charge configuration. There is a double exchange in $\ce{La_{1-x}Sr_xMnO3}$, a very important effect of these oxidation states.

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