Spinel, crystal symmetry

The group theory analysis of the vibrational spectrum of the spinel stmeture [32] reveals that the crystal symmetry is cubic, correspondent to the space group 0 Fd3m) with eight formulas per unit cell. The primitive cell is rhombo-hedral with two formula units per cell. The vibrational spectrum of the spinel is... 

Cells based on this process (Eq. (47)) show lower cycling performance with respect to those based on the 4 V process because charge-discharge reactions are accompanied by an asymmetric lattice contraction-expansion of the Lii+.vMn204 electrode. This lattice distortion mainly results from the Jahn-Teller effect of the Mn + ion which transforms the crystal symmetry of the spinel oxide [118],... 

Cubic ferrites have the inverse spinel crystal structure, which is cubic in symmetry and is similar to the spinel structure (Section 12.2). The inverse spinel crystal structure might be thought of as having been generated by the stacking of close-packed planes... 

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. 

Cubed compound, in PVC siding manufacture, 25 685 Cube lattice, 8 114t Cubic boron nitride, 1 8 4 654 grinding wheels, 1 21 hardness in various scales, l 3t physical properties of, 4 653t Cubic close-packed (CCP) structure, of spinel ferrites, 11 60 Cubic ferrites, 11 55-57 Cubic geometry, for metal coordination numbers, 7 574, 575t. See also Cubic structure Cubic symmetry Cubic silsesquioxanes (CSS), 13 539 Cubic structure, of ferroelectric crystals, 11 94-95, 96 Cubic symmetry, 8 114t Cubitron sol-gel abrasives, 1 7 Cucurbituril inclusion compounds,... 

If the diffusion medium is isotropic in terms of diffusion, meaning that diffusion coefficient does not depend on direction in the medium, it is called diffusion in an isotropic medium. Otherwise, it is referred to as diffusion in an anisotropic medium. Isotropic diffusion medium includes gas, liquid (such as aqueous solution and silicate melts), glass, and crystalline phases with isometric symmetry (such as spinel and garnet). Anisotropic diffusion medium includes crystalline phases with lower than isometric symmetry. That is, most minerals are diffu-sionally anisotropic. An isotropic medium in terms of diffusion may not be an isotropic medium in terms of other properties. For example, cubic crystals are not isotropic in terms of elastic properties. The diffusion equations that have been presented so far (Equations 3-7 to 3-10) are all for isotropic diffusion medium. 

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... 

Coordination symmetry of iron and cobalt in staurolite The crystal field spectra of Fe2+ ions surrounded by oxygen in regular octahedral sites normally contain absorption bands centred near 1,000 nm or 10,000 cm-1 (see fig. 3.2). By changing from octahedral to tetrahedral coordination, absorption bands for tetrahedral Fe2+ ions would, according to eq. (2.7), be predicted to occur at (% x 10,000) or 4,444 cm-1 (2,250 nm) if the iron-oxygen distances remain identical in the two coordinations. Tetrahedrally coordinated Fe2+ ions in spinel, MgAl204, for example, produce an absorption band near 4,830 cm"1 (2,070 nm) ( 5.3.3). 

Such ordering optimizes the Mudclung energy. The classic illustration of this effect is found in the spinel Fe3+[Fc2+Fc3+]04. Ordering of the B-site Fe2+ and Fe3+ ions into alternate (001) B-site layers below 119°K distorts the crystal to orthorhombic symmetry (248,637,639). 

Such inversion must occur to a considerable degree in the glass-ceramics Ac as evident from the appearance of additional lines due to E A2 emissions resulting from the modified Cr(III) energy levels in the low symmetry characterizing cases of inverted spinel sites. This behaviour in crystals was thoroughly studied by Mikenda et al. ° . ... 

Millard et al. 1992 Maekawa et al. 1997), because of the distinct chemical shift ranges for " Al and Al in oxides. In spinel, " Al gives a narrow peak near +70 ppm, whereas the Al gives a broader peak near +10 ppm (Fig. 27). The tetrahedral site in spinel has cubic point symmetry which requires Cq = 0, but crystal defects and the [Mg,Al] disorder results in a small distribution of EFG s at the Al site, so that the peak at 70 ppm contains only the central transition. The earlier studies suffered from low MAS rates, which yield spinning sidebands that overlap the centerbands, and unequal excitation of the two Al NMR signals. 

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