Normal and inverse spinels cation distribution

In the spinel MgAl204, A1 and Mg cations occupy the octahedral and tetrahedral sites, respectively. This cation distribution is usually indicated 

The physical properties of spinels depend not only on the kinds of cation in the lattice, but also on their distribution over the available crystal 

O atoms (large circles) are displaced along the 111 directions due to the presence of tetrahedral cations. In the ideal, undeformed case, u = 0.375. (Adapted from Smit Wijn, 1961.) 

The factors that contribute to the total lattice energy in spinels are  

The first two energies are usually sufficient to determine the total lattice energy in ionic, non-transition-metal oxides. Elastic energy refers to the degree of distortion of the crystal structure due to the difference in ionic radii assuming that ions adopt a spherical shape. Smaller cations, with ionic radii of 0.225-0.4 A, should occupy tetrahedral sites, while cations of radii 0.4-0.73 A should enter octahedral ones. This distribution leads to a minimum in lattice strain. Since trivalent cations are usually smaller than divalent ones, a tendency toward the inverse arrangement would be expected in 2, 3 spinels. 

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