Normal spinel structure

Many of the spinel-type compounds mentioned above do not have the normal structure in which A are in tetrahedral sites (t) and B are in octahedral sites (o) instead they adopt the inverse spinel structure in which half the B cations occupy the tetrahedral sites whilst the other half of the B cations and all the A cations are distributed on the octahedral sites, i.e. (B)t[AB]o04. The occupancy of the octahedral sites may be random or ordered. Several factors influence whether a given spinel will adopt the normal or inverse structure, including (a) the relative sizes of A and B, (b) the Madelung constants for the normal and inverse structures, (c) ligand-field stabilization energies (p. 1131) of cations on tetrahedral and octahedral sites, and (d) polarization or covalency effects. ... 

Although Fc304 is an inverse spinel it will be recalled that Mn304 (pp. 1048-9) is normal. This contrast can be explained on the basis of crystal field stabilization. Manganese(II) and Fe" are both d ions and, when high-spin, have zero CFSE whether octahedral or tetrahedral. On the other hand, Mn" is a d and Fe" a d ion, both of which have greater CFSEs in the octahedral rather than the tetrahedral case. The preference of Mn" for the octahedral sites therefore favours the spinel structure, whereas the preference of Fe" for these octahedral sites favours the inverse structure. 

Recall that the unit cell in the spinels comprises AgBi6032. In the normal structure, there are 16 B ions in octahedral sites and 8 A ions in tetrahedral ones. That corresponds to 96 octahedral B-0 bonds and 32 tetrahedral A-0 bonds or 128 bonds in all. In the inverse structure, we have 8 B ions in tetrahedral sites, 8 B ions in octahedral ones, and 8 A ions in octahedral sites. This corresponds to 48 octahedral B-O bonds, 32 tetrahedral B-O bonds and 48 octahedral A-O bonds or once again, 128 bonds in all. So the total number of M-O bonds, different types to be sure, is the same in both normal and inverse spinel structures. We could spend quite some time estimating the different bond energies of A-0 and B-O or of octahedral versus tetrahedral, but that would undoubtedly involve a lot of guesswork. We can at least observe that the bond count factor difference between the spinel... 

Nearly no eddy current losses occur in electrically insulating magnetic materials. This is one of the reasons for the importance of oxidic materials, especially of spinels and garnets. Another reason is the large variability of the magnetic properties that can be achieved with spinels and garnets of different compositions. The tolerance of the spinel structure to substitution at the metal atom sites and the interplay between normal and inverse spinels allow the adaptation of the properties to given requirements. 

Spinels have a crystal structure in which there is a face-centered cubic arrangement of O2 ions. There are two types of structures in which cations have octahedral or tetrahedral arrangements of anions surrounding them. In the spinel structure, it is found that the +3 ions are located in octahedral holes and the tetrahedral holes are occupied by the +2 ions. A different structure is possible for these ions. That structure has half of the +3 metal ions located in the tetrahedral holes while the other half of these ions and the +2 ions are located in the octahedral holes. In order to indicate the population of the two types of lattice sites, the formula for the compound is grouped with the tetrahedral hole population indicated first (the position normally occupied by the +2 ion, A) followed by the groups populating the octahedral holes. Thus, the formula AB204 becomes B(AB)04 in order to correctly... 

The spectra of the doped materials (Cr, Ni, Zn +, Li+, Co +, AP+) are similar to those seen for the nominally stoichiometric materials, and sets of resonances between 500 and 700 ppm are seen on cation doping in addition to that of the normal spinel environment (at ca. 500 ppm). Again, these resonances are assigned to lithium ions near manganese-(IV) cations. The lower intensity of the additional resonances seen on Cr + substitution, in comparison to Zn + or Ni + substitution, is consistent with the oxidation of fewer manganese ions near the depart ions. For the Li- and Zn-doped spinels, resonances at ca. 2300 ppm were also observed, which are assigned to lithium ions in the octahedral sites of the spinel structure. In the case of Zn doping, it is clear that the preference of Zn + for the tetrahedral site of the spinel structure forces the lithium onto the octahedral site. 

In a normal spinel structure, the formula is XY2O4 with 8 ions occupying the tetrahedral sites and 16 ions occupying the octa-... 

The point symmetry of the octahedral sites in the spinel-structure is Dsd- While the octahedra are perfect for an oxygen parameter u of 3/8, they are compressed along a threefold axis for u < 3/8, and expanded for u > 3/8. In the case of MgCr204 ( a0,385) and MgAl204 (21 = 0,387) ( normal spinels with Mg + in tetrahedral and Cr +, Al + in octahedral sites), the expansion is of the magnitude of about 4 to 5%. The corresponding splitting effects of the second absorption band in the remission spectra of the mixed-crystal powders (Mg)( > (Cr jAL-x) O4 (13) are about... 

Other half plus the minority cations (Te) occupy the B sites of the normal spinel structure. The structure is shown in Fig. 32, which shows that the C 9-like network of comer-connected tetrahedra (of atoms on B sites) is now composed of strictly alternating Li and Te atoms. The truncated tetrahedral interstices thus formed are centred by the remaining Li atoms (on the A sites). 

The striking features of the structure (when compared with that of a normal spinel, Fig. 29) are (a) that the Li(2)04 tetrahedra are very tilted, so that the anion array is grossly distorted from the approximate cubic eutaxy observed in the normal spinel structure and (b) that, by contrast, the cation array is almost exactly that of the normal structure, and very regular indeed. [There is a small tetragonal distortion of the unit cell -symmetry P4i22-which has c/( /2 a) = 0.9697, compared with unity for the equivalent ratio of the cubic cell of the normal spinel structure.]... 

Further adding to the complexity of the spinel structure are three possible arrangements of the metal ions in the cubic close-packed anions. The ordering of divalent metal ions (such as Mg2+) on the proper tetrahedral sites and all the trivalent ions (as Ai3+) in the correct octahedral sites, will give rise to the normal spinel structure. If the divalent ions occupy some of the octahedral sites and half of the trivalent ions move to the tetrahedral sites, the structure is then referred to as the inverse spinel structure. The last case exists when the tetrahedral sites and the octahedral sites are occupied by a mixture of di- and tri-valent ions. This type is known to generate the random spinel structure, and the exact composition and populations in the... 

Figure 1.41) have the oxygen ions in a nearly close-packed cubic array. The unit cell contains 32 oxygen ions, with 32 octahedral and 64 tetrahedral sites, of which 16 of the octahedral and 8 of the tetrahedral sites are filled. It is the position of these 24 cations within the unit cell that determines magnetic behavior. The distribution of cations in the sites is specific to the type of cations, and it must be determined experimentally. There are two idealized spinel structures. In the normal spinel, all the divalent ions are on the tetrahedral sites, as in ZnFe204. In the inverse spinel, the 8 occupied tetrahedral sites are filled with trivalent ions and the 16 occupied octahedral sites are equally divided between di- and trivalent ions (see Figure 6.63). The prototypical inverse spinel ferrite is magnetite, whose structure consists of an FCC oxygen array with Fe + and Fe + ions in the interstices.

The inverse spinel structure differs in that one type of cation occupies the tetrahedral and half of the octahedral sites of the spinel lattice, and the other cations occupy the remaining octahedral sites. This is indicated by writing the formula of, for example, zinc titanium spinel as Zn(TiZn)04. Spinels containing di- and tetravalent cations are mostly of the inverse type. Normal and inverse spinels should be regarded as idealized limiting structures, intermediate forms are often observed in practice. A... 

Magnesium chromium(III) oxide crystals are deep-green octa-hedra possessing the normal, cubic, spinel structure, a0 = 8.335 A., and having a melting point of approximately 2390°C. 

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