The mixed-valence oxide Fe O can be regarded stoichiometrically as FeO·Fe O

CHEMISTRY · Multi-part · AP · Chemistry · Compound Structure and Properties · Compound Structure and Properties

Problem

The mixed-valence oxide Fe3_3O4_4 can be regarded stoichiometrically as FeO·Fe2_2O3_3. In the spinel lattice, oxide ions approximate a cubic close-packed arrangement, while Fe2+^{2+} and Fe3+^{3+} ions occupy both tetrahedral (T) and octahedral (O) interstitial sites. Ionic radii (high-spin): rFe2+=92 pmr_{\text{Fe}^{2+}}=92\,\text{pm}; rFe3+=78 pmr_{\text{Fe}^{3+}}=78\,\text{pm}. (a) A full spinel unit cell contains 32 O2−^{2-} ions. Determine the total numbers of Fe2+^{2+} and Fe3+^{3+} ions that must be distributed among the 64 T sites and 32 O sites to satisfy overall stoichiometry. (b) Using the radii provided, rationalize which oxidation state preferentially occupies tetrahedral sites and which occupies octahedral sites. Support your answer with quantitative or qualitative arguments involving ion size and electrostatic considerations. (c) Demonstrate that the cation distribution proposed in part (b) preserves local charge neutrality around both tetrahedral and octahedral sites while maximizing attractions and minimizing repulsions. (d) Suppose 10\% of the Fe2+^{2+} ions are replaced by Mn2+^{2+} (radius 97 pm97\,\text{pm}). Predict how this substitution would be expected to shift the relative occupancies of T and O sites, and explain your reasoning.

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