Octahedral holes in close-packed

Ionic crystals can also be described in terms of the interstices, or holes, in the structures. Figure 7-5 shows the location of tetrahedral and octahedral holes in close-packed structures. Whenever an atom is placed in a new layer over a close-packed layer, it creates a tetrahedral hole surrounded by three atoms in the first layer and one in the second (CN = 4). When additional atoms are added to the second layer, they create tetrahedral holes surrounded by one atom in the one layer and three in the other. In addition, there are octahedral holes (CN = 6) surrounded by three atoms in each layer. Overall, close-packed structures have two tetrahedral holes and one octahedral hole per atom. These holes can be filled by smaller ions, the tetrahedral holes by ions with radius 0.225r, where r is the radius of the larger ions, and the octahedral holes by ions with radius 0.414r. In more complex crystals, even if the ions are not in contact with each other, the geometry is described in the same terminology. For example, NaCl has chloride ions in a cubic close-packed array, with sodium ions (also in a ccp array) in the... 

FIGURE 7-5 Tetrahedral and Octahedral Holes in Close-packed Layers, (a) Tetrahedral holes are under each x and at each point where an atom of the first layer appears in the triangle between three atoms in the second layer, (b) An octahedral hole is outlined, surrounded by three atoms in each layer. 

In contrast to 31283, the corresponding selenide and telluride have structures in which Bi occupies octahedral holes in close-packed assemblies of Se or Te atoms. Interesting examples of some of the more complex types of close packing are found in 313863, Bi2Te28, Bi2Te3 (the last two being the minerals tetradymite and tellurobismuthite respectively), and in 313864. 

FIGURE 6.11 Occupation pattern of octahedral holes between close-packed layers of sulfur atoms in LiTiS2. 

Figure 1-5. Octahedral and tetrahedral hole in close-packed layers ofspeheres. From Shriver and Atkins Inorganic Chemistry.

The octahedral holes in a close-packed structure are much bigger than the tetrahedral holes—they are surrounded by six atoms instead of four. It is a matter of simple geometry to calculate that the radius of a sphere that will just fit in an... 

The rhombohedral unit cells for rhodium and iridium trifluorides (44) contain two formula units. The structure can be related to the first structure type by considering anion positions, which here correspond to a hexagonal, close-packed array. There are no vacant anion sites and the cations occupy one-third of the octahedral holes. This leads to M—F—M angles of 132°, characteristic for filling adjacent, octahedral holes in a hexagonal close-packed lattice. Alternatively, the structure can be described as a linking of octahedra through all corners, but the octahedra are now tilted with respect to each other. 

There are commonly void spaces (holes) in a crystal that can sometimes admit foreign particles of a smaller size than the hole. An understanding of the geometry of these holes becomes an important consideration as characteristics of the crystal will be affected when a foreign substance is introduced. In the cubic close-packed structure, the two major types of holes are the tetrahedral and the octahedral holes. In Fig. 10-1(h), tetrahedral holes are in the centers of the indicated minicubes of side a/2. Each tetrahedral hole has four nearest-neighbor occupied sites. The octahedral holes are in the body center and on the centers of the edges of the indicated unit cell. Each octahedral hole has six nearest-neighbor occupied sites. 

The most stable form of the oxide A1203 is a-alumina with the comndum stmcture where Al3+ ions occupy two-thirds of the octahedral holes in a hexagonal close-packed oxide lattice. Another form g-A1203 has a defect spinel structure. So-called b-alumina is... 

Some ternary and mixed-valency oxides have the spinel structure where metal ions occupy a proportion of tetrahedral and octahedral holes in a cubic close-packed lattice. Examples include M304 with M=Mn,... 

If the fluorine atoms are assumed to occupy iipproximately the same volume in all three unit cells and the platinum, osmium, and antimony atoms occupy little more than octahedral holes in the close-packed fluorine-atom arrangement, then the O2 and NO must occupy approximately the same volume as a potassium ion. If, as recommended by Zachariasen, the effective volume of a fluorine atom is taken as 18 A , then O2 and NO would each occupy 20 A . This small volume implies that they are cations, Oj and NO+ (Zachariasen s value for the volume of the K+ is 21 A ). 

When the radius ratio is less than 0.59 the alloy is normal and the mclal—interstitial atom arrangement is face-centred cubic, close-packed hexagonal or body-centred cubic. The complex interstitial alloys have a radius ratio greater than 0.59 and are less stable. Carbon and nitrogen always occupy octahedral holes in interstitial alloys hydrogen always occupies the smaller tetrahedral interstices. In face-centred cubic and close-packed hexagonal lattices there are as many octahedral holes as metal atoms and twice as many tetrahedral holes. 

As already noted only the sharing of a pair of opposite faces has to be considered an infinite chain of composition AX3 is then formed. A number of crystalline trihalides consist of infinite molecules of this type, and chain ions of the same kind exist in BaNi03 and CsNiCl3. In the Zrl3 structure the metal atoms occupy one-third of the octahedral holes in a close-packed assembly of halogen atoms to form infinite chains perpendicular to the planes of c.p. halogen atoms ... 

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