Simple spinels; crystallographic parameters, cation radii, lattice energies, and cation distribution

Electrostatic lattice energy calculations and consideration of the structure of the spinel group of minerals show that the size of a cation is important in determining its site preference. In oxide spinels containing 2⁺ and 3⁺ ions (2-3 spinels) there is a tendency for the larger ion to prefer the tetrahedral site; the reverse holds for 2-4 spinels. A set of cation radii optimized to best fit spinel lattice parameters is presented. Based on lattice energy calculations, the enthalpy change accompanying cation disordering is not a linear function of the degree of cation disorder, but a quadratic, with the two parameters approximately equal in magnitude and opposite in sign. Most published data on the change of cation arrangement with temperature fit a thermodynamic model with this non-linear change in enthalpy, but those for Fe₃O₄ may require an additional non-configurational entropy as well, and the data for MgAl₂O₄ cannot be described adequately by any simple model.