Divalent cations octahedral site preference energy

Crystal chemistry of spinels. A classic example showing that transition metal ions display distinct site preferences in oxides stems from studies of spinel crystal chemistry. The spinel structure contains tetrahedral and octahedral sites normal and inverse forms exist in which divalent and trivalent ions, respectively, fill the tetrahedral sites. The type of spinel formed by a cation is related to its octahedral site preference energy (OSPE), or difference between crystal field stabilization energies in octahedral and tetrahedral coordinations in an oxide structure. Trivalent and divalent cations with large site preference energies (e.g., Cr3 and Ni2+) tend to form normal and inverse spinels, respectively. The type of spinel adopted by cations with zero CFSE (e.g., Fe3+ and Mn2+) is controlled by the preferences of the second cation in the structure. 

Several factors in addition to ionic size enter into the choice of lattice site preferred by a particular cation. For example, divalent Zn and Cd are larger than divalent Ni and trivalent Cr, yet the former show a marked preference for the tetrahedral sites, while the latter prefer an octahedral environment. The s electrons of Zn and Cd can easily form sp hybrid covalent bonds with oxygen, while the crystal field of the octahedral environment lowers the energy of Ni and Cr (crystal field stabilization). Electrostatic considerations also enter in, i.e., ions of small positive charge will be coordinated to a smaller number of negative ions. Calculations suggest that the inverse structure is favored (lowest lattice energy) when u < 0.379 and the normal structure is favored when u > 0.379. ... 

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