The garnet structure

The garnet ferrites are the basis of materials for many high-technology devices for magnetooptical, microwave and memory applications. These ferrites have thus been extensively studied as ceramics, single crystals, thin and epitaxial films, etc. The prototype, yttrium iron garnet or YIG has also been used for many fundamental studies. 

The crystal structure is that of the garnet mineral, MnjAljSijOij. Si and Mn can be substituted by Y and A1 by a double substitution mechanism  

The O polyhedra define three kinds of cation site dodecahedral (eight-fold), octahedral (six-fold) and tetrahedral (four-fold). Rare earths, R, occupy the largest, dodecahedral sites, while Fe cations enter the octahedral and tetrahedral sites. The notation for the site occupancy is as follows  

All the polyhedra in garnets are distorted and twisted (Geschwind, 1961). Octahedral cations form a body centred cubic sublattice the octahedra are distorted along one of the three-fold axes this trigonal axis coincides with the [111] direction of the unit cell. Fig. 2.17. The octahedra 

Each octahedron shares six edges with dodecahedra and only corners with tetrahedra. Each tetrahedron shares two edges with dodecahedra octahedra and dodecahedra share only corners. Each dodecahedron 

The ordered arrangement of two kinds of ion in the octahedral sites is also found in the tetragonal (pseudocubic) high-pressure forms of CaGe03 and CdGe03. The structures of the polymorphs of CaGe03 provide an excellent illustration of the 

The structure of Zn2Mo3 Og presents several points of interest. There is ABCB. .. type of c.p. oxygen atoms. The Mo atoms occupy octahedral holes in groups of three, as shown in Fig. 5.22(d), p. 177. Owing to the metal-metal interactions (Mo-Mo, 2-52 A) the compound is diamagnetic. One-half of the Zn atoms occupy tetrahedral and the remainder octahedral holes, the mean bond lengths being Zn-4 0,1-98 A, Zn-6 0,2-10 A. 

Complex oxides tend to be isostructural with complex fluorides rather than with complex chlorides, but note the isostructural oxides and chlorides with c.p. A B X3 structures. Other exceptions include BaaVOs, isostructural with CS3C0CIS (and the Mn and Fe salts), and Sr4MOg (M = Pt, Ir, Rh), isostructural with K4CdCl6. 

In Ca2Fe20s layers are formed from FeOs octahedra sharing 4 equatorial vertices, and these layers are joined through vertex-sharing tetrahedra Fe04 to form 3D framework of composition Fe20s. This framework consists of equal numbers of tetrahedra and octahedra which share vertices  

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The garnet structure has high overall symmetry (cubic) but a complex structure (Bragg and et al., 1965). The prototype is the mineral Grossularite... 

YjAlsOn)—YAG Most garnets are silicates, whereas yttrium aluminum garnet (YAG) is an aluminate. In YAG, both the tetrahedral and the octahedral holes of the garnet structure are occupied by Al-ions and the quasi-cubic holes are occupied by Y-ions. 

Finally, the particular relationship between the Cr3Si-type structure and the garnet structure (see 7.6.8) may be pointed out. The position of the cations, indeed, in the garnet structure correspond to the Cr3Si arrangement. 

The variety of symmetries in the garnet structure (coordinations 4, 6, and 8) allows considerable compositional range. Table 5.16 lists the elements commonly present in positions X, X and Z. The diadochy of Al, Ti" ", and Fe in the tetrahedral site has been confirmed by Mossbauer spectroscopy on natural Fe-Ti-bearing garnets (Schwartz and Burns, 1978), and the presence of phosphorus in these sites, observed in upper mantle garnet, is attributable, according to Bishop et al. (1976), to coupled substitutions of the type... 

Hawthorne F. C. (1981b). Some systematics of the garnet structure. J. Solid State Chem., 37 157-164. 

The octahedral sites in the garnet structure are of the point symmetry... 

This structure is very common, and its structural parameters have been the subject of considerable discussion We shall see later (Sect. 3.3) that (very much as in the example of the spinel structure, Sect. 3.2) the parameters of the garnet structure can be simply understood as a result of the oxygen atoms finding the appropriate positions within the cation array to produce the correct bond lengths. 

Fig. 33. The (A,nCi/2)3B array of cations in the garnet structure, A3B2C3Xi2, projected on 100. Compare Fig. 34...

From the beginning it was noted that the structure was dominated by large columnar elements of the garnet structure type The doubt has been about the remaining parts (between the garnet columns). The garnet structure itself is rather complicated it has only recently been given a satisfactory description in terms of articulated, cation-centred polyhedra The vesuvianite structure is even more complex. 

CT-VPP-REDOR) or the pulse duration fp (CT-VPD-REDOR) then produces CT-REDOR curves, from which the second moment may be evaluated with distinctively superior accuracy as compared to the values obtained from a parabolic fit to the conventional REDOR data. When restricting the experiment to short dipolar evolution times, the two-spin approximation may be applied for the data analysis, which proves to be especially attractive for amorphous solids, for which the exact spin geometry is unknovm. The data presented on the model compoimds illustrate the various facets of CT-REDOR NMR spectroscopy. First application examples, namely, the evaluation of the heteronuclear Li-Ti dipolar couplings within the garnet structure of Li5La3Nb20i2, the determi-nation of the intemuclear B- P distance in frustrated Lewis pairs, the analysis of Na- F dipolar interaction in fluormica or Na- P... 

Yudintsev, S. V. 2001. Incorporation of U, Th, Zr, and Gd into the garnet-structured host. In Proceedings of the 8th International Conference on Radioactive Waste Management and Environmental Remediation. The American Society of Mechanical Engineers, New York, CD-ROM. 

Yudintsev, S. V., Lapina, M. I., Ptashkin, A. G., Iou-DINTSEVA, T. S., Utsonomiya, S., Wang, L. M. Ewing, R. C. 2002. Accommodation of uranium into the garnet structure. Materials Research Society Symposium Proceedings, 713, 477-480. 

Carnets. Both YAG, yttrium aluminum garnet. YjAIsOi3, and GGG, gadolinium gallium garnet. GdiGa 0,2. have the garnet structure and were used al one time as diamond imitations. These have been supplanted by cubic zirconia. 

The crystal field spectra and derived A0 and CFSE parameters for several garnets containing octahedrally coordinated trivalent transition metal ions are summarized in table 5.3. The values of A0 and CFSE reflect the variations of metal-oxygen distances in the garnet structures. 

Although most materials grown by LPE have the garnet structure, spinel ferrites can be grown similarly, and films of hexagonal ferrites are also prepared ". Only small quantities are required, and the crystallographic quality of the film can be high, but a suitable substrate is required and the measurement or device must be made on a thin layer rather than a bulk crystal. 

II. In some complex oxide structures the environments of the different kinds of metal ion are so different that the structure is not possible for a binary oxide. The size difference between the ions necessary for the stability of the structure may be too large (as in the perovskite and related structures) or the two (or more) oxidation states required for charge balance in the structure may not be possible for one metal. (The scheelite structure, for example, calls for equal numbers of 8- and 4-coordinated atoms in oxidation states totalling 8.) It should be noted that positions of different coordination number in complex oxide structures are not necessarily occupied by atoms of different metals. Just as one kind of ion occupies coordination groups of two kinds in certain exceptional binary oxides, as noted above, so we find the same phenomenon in some complex oxides. In the garnet structure (p. 500) there are positions of 4-, 6-, and 8-coordination for metal ions. In... 

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