Random spinel

Both ordered and normal spinels should disorder at high temperature, since the entropy of the random spinel is larger. The disordering reaction for a normal spinel can be described by a quasi-chemical reaction... 

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... 

The nature of a spinel is described by a parameter X, the fraction of B atoms in tetrahedral holes some authors refer to the degree of inversion y (= 2X). For a normal spinel X = 0, and for an inverse spinel X =. Intermediate values are found (e.g. in a random spinel), and X is not necessarily constant for a given spinel but can in some cases be altered by appropriate heat treatment. For NiMn204 X varies from 0 37 (quenched) to 0-47 (slow-cooled). Values of X have been determined by X-ray and neutron diffraction, by measurements of saturation magnetization, and also by i.r. measurements. In favourable cases l.r. bands due to tetrahedral AO4 groups can be identified showing, for example, that in Li(CrGe)04 Li occupies tetrahedral positions. ... 

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. ... 

Structure types have been established. Similar to Al, the M2X3 crystals (M = Ga, In, Tl X = S, Se, Te) are mostly based on M-defect tetrahedral structures, namely W (Ga2S3, In2Se3) and ZB (Ga2Se3, Ga2Te3, In2Te3). At atmospheric pressure, 283 can be present in three modifications. The low-temperature a-form is a cubic close-packed structure of S atoms, where 70% of the In atoms are randomly distributed on octahedral sites and the rest remain on tetrahedral sites. The P-form is related to the spinel structure, and the y-modification is hexagonal. 

Still more surprising are certain crystals in which a set of equivalent positions is only partially occupied, some sites here and there at random being empty. The spinel group also provides examples of this type of structure. The cubic (y) form of Fe2Oa, for instance, gives an X-ray... 

Figure 7(A) shows the superlattice assembly from the cube-like particles, while Fig. 7(B) is the assembly from the polyhedron-shaped particles. The fast Fourier transformation (FFT) of these two images reveals that both assemblies have a cubic packing. But the different shapes possessed by each group of particles affect the crystal orientation of individual particles within the superlattices. XRD of the self-assembled cubelike particles on Si (100) substrate shows the intensified (400) peak, Fig. 7(C), and that of polyhedron-shaped particles reveals the strong reflections of (220), Fig. 7(D). These are markedly different from that of a 3D randomly oriented spinel structured MnFe204 nanoparticle assembly, which shows a strong (311) peak. These indicate that each of the cube-like particles in the cubic assembly has preferred crystal orientation with 100 planes parallel to the Si substrate while for the polyhedron-shaped particle assembly, the 110 planes are parallel to the substrate.

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