Crystal structures garnets

In the ceramics field many of the new advanced ceramic oxides have a specially prepared mixture of cations which determines the crystal structure, through the relative sizes of the cations and oxygen ions, and the physical properties through the choice of cations and tlreh oxidation states. These include, for example, solid electrolytes and electrodes for sensors and fuel cells, fenites and garnets for magnetic systems, zirconates and titanates for piezoelectric materials, as well as ceramic superconductors and a number of other substances... 

A variety of minerals are prized for their exquisite beauty, rarity, and exceptional durability. These extraordinary materials are classified as gemstones. One such mineral, silica, with a chemical composition of SK>2 (silicon dioxide), exhibits several crystal structures. Several gemstones are crystalline forms of silica, including amethyst, aquamarine, emerald, garnet, peridot, topaz, tourmaline, and zircon J l... 

Large instrumental mass fractionations have been observed during measurements of oxygen isotope ratios on Fe-Mg-Ca garnets in SIMS.83 Part of this fractionation depends on crystal structure and mineral composition. 

Figure 5.5 The crystal structure of garnet (pyrope) projected into a dodecahedron. Note the configuration of the eight-fold coordinated Mg sites (distorted cube) which share edges with [A106] octahedra and [Si04] tetrahedra.

The garnets are a group of minerals having the same crystal structure, but different compositions. Only two of the garnets are commonly red, pyrope, and almandine. The other species in this group occur in all colors except blue. 

Most trace elements have values of D< C 1, simply because they differ substantially either in ionic radius or ionic charge, or both, from the atoms of the major elements they replace in the crystal lattice. Because of this, they are called incompatible. Exceptions are trace elements such as strontium in plagioclase, ytterbium, lutetium, and scandium in garnet, nickel in olivine, and scandium in clinopyroxene. These latter elements acmally fit into their host crystal structures slightly better than the major elements they replace, and they are therefore called compatible. Thus, most chemical elements of the periodic table are trace elements, and most of them are incompatible only a handful are compatible. 

Static simulations of perfect lattices give the lattice energy and crystal structure of the garnets at 0 K. In the static limit, the lattice stmcture is determined by the condition 9 //9A = 0, where U is the internal energy, and the variables A define the structure (i.e., the lattice vectors, the atomic positions in the garnet unit cell, and the oxygen shell displacements). 

For auother possible reactiou mechauism for the formatiou of mixed oxides, binary alkoxide (glycoxide) may be formed prior to the formation of the mixed oxide. In fact, various binary glycoxides have been prepared and their crystal structures have been elucidated. Formation of BaTiOj by the glycothermal reaction may be explained by this mechanism, because Ba-Ti binary alkoxide is well established. However, formation of garnet phases (Sections III.C.l through III.C.3) cannot be explained by this mechanism because addition of seed crystals, in some cases, gives a product with a chemical composition completely different from that of the product obtained without the addition of the seed crystals. 

There are a variety of important crystal structures in aluminate systems. Among the most important are the spinel [16] and garnet structures [17,18]. These various structures reflect differences in the coordination polyhedron of both AI(III) and added components such as Mg(II), Ca(II), and the rare earth ions. In addition, studies of glass structure suggest a wealth of different coordination environments for both Al(III) and added components and structures that are not simply disordered forms of crystalline phases. 

When the O/Si ratio is 4, the structural units are the isolated (Si04) tetra-hedra which cannot join to each other but are connected by the positive ions in the crystal structure. The resulting structure is termed an island silicate for which garnets (Mg, Fe , Mn,Ca)3(Cr,Al, Fe )2(Si04)3 and olivines... 

Garnets are semiprecious gems with the chemical composition Ca3Al2Si30i2. The crystal structure is cubic and is made up of three building blocks tetrahedra, octahedra, and dodecahedra (distorted cubes). 

Magnetic ceramics are further classified according to their crystal structures into spinels, garnets, and hexagonal ferrites. Typical compositions and some of their magnetic properties are listed in Table 15.4. 

The general formula of magnetic garnets,is P3Q2R3O12 or 3Mc203 5Fe203, where Me is typically yttrium but can also be other rare earth ions. The basic crystal structure is cubic with an octahedron, a tetrahedron. 

Magnetic ceramics are ferrimagnetic and are classified according to their crystal structure into spinels, hexagonal ferrites, and garnets. 

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 ... 

Geller, S. Gilleo, M. A. (1957). The crystal structure and ferrimagnetism of yttrium-iron garnet Y3Fe2(Fe04)3. Journal of Physics and Chemistry of Solids, 3, 30-6. 

FIGURE 7.7 The crystal structure of garnet. The general formula is AsBsC004)3 where C is Si for the silicates. The B cation sits in an octahedral site while the largest cation A is located in a dodecahedron. The bcc unit cell has a lattice parameter of -1.1 nm. With 20 atoms in the chemical formula there ate 160 atoms in the unit cell. 

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