Spinel lattice energy

Glidewell, C. (1976) Cation distribution in spinels Lattice energy versus crystal field stabilization energy. Inorg. Chim. Acta, 19, L45-7. 

Table 1.19 Lattice energy and CFSE for selected spinel compounds. Values of U, E, and from Ottonello (1986). CFSE values calculated with values proposed by McClure (1957). Data in kJ/mole x = degree of inversion.

O Neill, H. St C. Navrotsky, A. (1983) Simple spinels crystallographic parameters, cation radii, lattice energies, and cation distribution. Amer. Mineral., 68,181-94. 

With these energies, it is possible to calculate not only the preferred cation distribution over two types of available anion interstice, as in the spinel lattice, but also the valency distribution given two atoms on the same site, each with multiple-valence alternatives. This point... 

Many spinel compounds adopt an alternative structure where half the B cations occupy the tetrahedral sites while the remaining B cations and A cations occupy the octahedral sites. These are known as inverse spinels. The occupancy of the latter sites may be random or ordered. The adoption of an inverse spinel versus a spinel structure depends on a variety of factors the relative size of the A and B cations, the relative lattice energies, ligand-field stabilization, energies of octahedral versus tetrahedral coordination, and polarization or covalency effects. For example, in MgABOq one might expect the small... 

Calculations of the lattice energy on the simple electrostatic theory, without allowance for crystal field effects, indicate that while the inverse structure should be more stable for 4 2 spinels, the preferrred structure for 2 3 spinels should be the normal structure. In fact a number of the latter have the inverse structure, as... 

Binding energies of the different metals contained in the catalyst after calcination at 773 or 873 K results are presented in Table 1. No fundamental differences were found at either temperature. The values of B.E. obtained for Ni and Co are those typically reported for Ni0-t-NiAl204 and well-defined C0AI2O4 structmes, respectively [7,8]. Nevertheless, the results shown in Table 2 (first and fourth rows) clearly indicate that an increase in the calcination temperature preferentially favors the incorporation of Co cations into the spinel lattice, increasing the relative amount of nickel in the catalyst surface. This can be related to the greater tendency of cobalt to form a well-defined bulk spinel phase [5]. 

These findings are quite interesting since they are different with respect to what has been reported for the pure spinels where Co exhibits a tendency (of the order of 13 kJ/mole, difference between the octahedral and tetrahedral coordination lattice energies) to assume a tetrahedral coordination and Ni even a more marked tendency (of the order of 50kJ/mole, difference between the tetrahedral and octahedral coordination lattice energies) to assume an octahedral coordination [8]. 

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. 

Attempted lattice energy calculations, as well as the experimental observation of different cation distributions in spinels containing ions of similar charge and size, suggest that the difference in electrostatic lattice energy between normal and inverse spinel is small in common 2-3 and 2-4 spinels. Other factors, such as the site preference of individual cations, will then determine the cation distribution. The crystal structure of magnetite is shown in Figure 9.2. 

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