Spinel unit cell

Figure 10. Equivalent plot to Figure 9 except AE gives the energy difference between fully inverse spinel, i.e., antispinel (75-Mntet(Li5n/ )oct04 Sub = substitutional elements or Mn) and spinel (s-Litet(Mn5n/ )oct04). Also, the x axis is now the average spin on the tetrahedral Mn since there are two tetrahedral Mn per inverse spinel unit cell. All of the chemical substitutions replace 50% of the Mn ions. In the anti-spinel, all of the octahedral Mn are chemically substituted. In the spinel half of the octahedral Mn are chemically substituted.

Figure 6.63 A portion of the inverse spinel unit cell found in many ferrites. From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission John Wiley Sons, Inc.

The structure of /J-In2S3 is not yet known with certainty. To a first approximation its structure is identical with that of the spinels, but additional lines in the x-ray pattern imply the existence of a superlattice whose origin must be sought in the ordering of existing vacancies. This superlattice is tetragonal, and results from the stacking of three spinel unit cells (7). 

Figure 15.9 Spinel unit cell showing anti ferromagnetic coupling between A (T-sites) and B (O-sites) sublattices.

In these general forms, two types of cation distributions are present the normal and the inverse. The normal configuration has for the spinel unit cell (Mg + 8A1 -H 5D I6O33), the Mg cations in the 8 tetrahedral sites and the AP" cations in the 16 octahedral sites. The inverse configuration has for... 

Eig. 2. Spinel stmcture where Q is oxygen, Q > A-sites, O, B-sites. A unit cell consists of eight fee subceUs with different cation occupants. Adapted from... 

Electrodes that are prepared from acid-leached LT-LiCo, xNix02 compounds (0< x<0.2) show significantly enhanced electrochemical behavior over the parent LT-LiCo1 xNix02 structure. The improved performance has been attributed to the formation of compounds with a composition and cation arrangement close to the ideal Li[B2]04 spinel structure (B = Co, Ni) [62]. These spinel-type structures have cubic symmetry, which is maintained on lithiation the unit cells expand and contract by only 0.2 percent during lithium insertion and extraction. 

Figure 5. Schematic representation of the ft -alumina structure. The aluminum (green) and oxygen (red) ions form spinel blocks which are separated from each other by oxygen bridges. The mobile sodium ions (blue) are located in the layer. The unit cell is indicated.

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... 

In general, spinel and other chalcogen-based thiospinels with Z=8 leads to the total unit cell content of 8 and 16 (8 a and 16 d sites) cations and 32 anions in the 32 e site corresponding to the formula A8B15O32. In spinels, the AX4 tet-rahedra share comers with BXg octahedra and the octahedra are Hnked together by sharing edges (Fig. 15.1). 

The spinel structure (one unit cell). The Mg2+ ions are located in the centers of the tetrahedra (stereo image)... 

The unit cell of (3-alumina is hexagonal, with lattice parameters a = 0.595 nm, c = 2.249 nm. The dominant features of the idealized structure of (3-alumina, with composition NaAlnOi7, are layers called spinel blocks stacked perpendicular to the c axis (Fig. 6.10a). These blocks are composed of four oxygen layers in a... 

The spinel blocks in (3-alumina are related by mirror planes that mn through the conduction planes that is, the orientation of one block relative to another is derived by a rotation of 180°. A second form of this compound, called (3"-alumina, has similar spinel blocks. However, these are related to each other by a rotation of 120°, so that three spinel block layers are found in the unit cell, not two. The ideal composition of this phase is identical to that of (3-alumina, but the unit cell is now rhombohedral. Referred to a hexagonal unit cell, the lattice parameters are a = 0.614 nm, c = 3.385 nm. The thickness of the spinel blocks and the conduction planes is similar in both structures.3... 

Figure 7.56. Characteristic sections of the cubic unit cell of MgAl204 (spinel). Compare the metal positions with those depicted in Fig. 7.30 for the atoms in the Cu2Mg-type Laves phases.

Fig. 7.16 (a) Lattice parameters and (b) voltage vs x for two forms of Li TiSj. The c parameter for the layered (IT) form is the distance between the layers the a parameter in the cubic (spinel) form is the edge of the cubic unit cell. Data from Sinha and Murphy (1986), Dahn and McKinnon (1984), and Dahn and Haering (1981b). 

A related system is that of the titanomaghemites, Fe2Ti05, which are formed by oxidation of the titanomagnetites. These are spinels with vacancies in some of the cation positions. The detailed distribution of cations and vacancies is not fully understood a discussion of the different models and possibilities is given by Lindsley (1976). A non-linear relationship between the unit cell size of titanomaghemite (a = 0.8483 nm) and that of maghemite (a = 0.835 nm) was matched by a non-linear increase in the Curie temperature from 80 to 450 °C (Dunlop Ozdemir, 1997). 

---