Spinel model

In conclusion, the real structure of Y-AI2O3 has still not been completely solved. The spinel model with occupancy of nonspinel sites and significant disorder, including the possible presence of protons and formation of surface OH groups, is currently the best interpretation of available data. 

Hulbert [77] discusses the consequences of the relatively large concentrations of lattice imperfections, including, perhaps, metastable phases and structural deformations, which may be present at the commencement of reaction but later diminish in concentration and importance. If it is assumed [475] that the rate of defect removal is inversely proportional to time (the Tammann treatment) and this effect is incorporated in the Valensi [470]—Carter [474] approach it is found that eqn. (12) is modified by replacement of t by In t. This equation is obeyed [77] by many spinel formation reactions. Zuravlev et al. [476] introduced the postulate that the rate of interface advance under diffusion control was also proportional to the amount of unreacted substance present and, assuming a contracting sphere (radius r) model... 

Spinels. There are limited experimental data on uranium and thorium partitioning between magnetite and melt (Nielsen et al. 1994 Blundy and Brooker 2003). Both studies find U and Th to be moderately incompatible. Blundy and Brooker s results for a hydrous dacitic melt at 1 GPa and 1025°C give Du and D h. of approximately 0.004. The accuracy of these values is compromised by the very low concentrations in the crystals and the lack of suitable SIMS secondary standards for these elements in oxide minerals. Nonetheless, these values are within the range of Djh of magnetites at atmospheric pressure 0.003-0.025 (Nielsen et al. 1994). It is difficult to place these values within the context of the lattice strain model, firstly because there are so few systematic experimental studies of trace element partitioning into oxides and secondly because of the compositional diversity of the spinels and their complex intersite cation ordering. 

Although the band model explains well various electronic properties of metal oxides, there are also systems where it fails, presumably because of neglecting electronic correlations within the solid. Therefore, J. B. Good-enough presented alternative criteria derived from the crystal structure, symmetry of orbitals and type of chemical bonding between metal and oxygen. This semiempirical model elucidates and predicts electrical properties of simple oxides and also of more complicated oxidic materials, such as bronzes, spinels, perowskites, etc. 

The model of Knozinger and Ratnasamy [60] is widely accepted as the most comprehensive way to rationalize the reactivity of the Al-OH groups on the alumina surface. This empirical model proposes that y-Al203 has a defective spinel structure, whose (111), (110) and (100) faces are covered by hydroxyl groups. Five configurations for the hydroxyl groups can be present (Scheme 11.3). 

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). 

Fig. 4. Computer-generated crystal structure models nop row. left to right) Cuprite, zinc-blende, rutile, perovskite. iridymite (second row) Cristobalite. potassium dihydrogen phosphate, diamond, pyrites, arsenic (third rowt Cesium chloride, sodium chloride, wurtzite. copper, niccolite (fourth row) Spinel, graphite, beryllium, carbon dioxide, alpha i uanz. [AT T Bel Laboratories ...

Intercalation of cations into a framework of titanium dioxide is a process of wide interest. This is due to the electrochromic properties associated with the process (a clear blue coloration results from the intercalation) and to the system s charge storage capabilities (facilitated by the reversibility of the process) and thus the potential application in rocking-chair batteries. We have studied alkali-metal intercalation and ion diffusion in the Ti02 anatase and spinel crystals by theoretical methods ranging from condensed-phase ab initio to semiempirical computations [65, 66]. Structure relaxation, electron-density distribution, electron transfer, diffusion paths and activation energies of the ion intercalation process were modeled. 

The mineral spinel (MgAl204) is the structural model for hundreds of minerals and synthesized compounds known as spinels. They share the formula lV M Ch. In a normal spinel Mn occurs in T sites and Mm are in O sites. In an inverse spinel such as NiF Ch the Ni2+ ions are in O sites and 1/2 of the Fe3+ ions are in T sites and 1/2 are in O sites. 

Figure 7.26. A model of spinel, MgAl204, with layers labeled and a similar view of the model showing the stacking of polyhedra.

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