Interstice tetrahedral

When discussing metal alloys (Section 4.3), we saw that atoms of non-metallic elements such as H, B, C, and N can be inserted into the interstices (tetrahedral and octahedral holes) of a lattice of metal atoms to form metal-like compounds that are usually nonstoichiometric and have considerable technological importance. These interstitial compounds are commonly referred to as metal hydrides, borides, carbides, or nitrides, but the implication that they contain the anions H, B3, C4, or N3- is misleading. To clarify this point, we consider first the properties of truly ionic hydrides, carbides, and nitrides. 

When spheres of a given size are close-packed, the spaces between the layers of spheres (the voids or interstices) can be filled with smaller spheres. If the spheres represent cations and anions, the structures of ionic solids can be visualized. There are two types of interstices between layers of close-packed atoms - tetrahedral holes or interstices and octahedral holes or interstices. Tetrahedral holes are formed when one sphere in a layer fits over or under three spheres in a second layer. Octahedral holes are formed when three spheres in one layer fit over or under three spheres in a second layer. The two types of holes have different numbers per close-packed sphere, different sizes, and different coordination numbers and coordination geometries. The coordination number of the anion would be the number of cations in contact with the anion. The coordination geometry of the anion would be the geometrical arrangement of the cations which surround the anion. Related statements can be made regarding the coordination number and coordination geometry of the cation. 

In FCC structure, there are two kinds of interstices, tetrahedral and octahedral. 

For the alkali metal doped Cgo compounds, charge transfer of one electron per M atom to the Cgo molecule occurs, resulting in M+ ions at the tetrahedral and/or octahedral symmetry interstices of the cubic Cgo host structure. For the composition MaCgg, the resulting metallic crystal has basically the fee structure (see Fig. 2). Within this structure the alkali metal ions can sit on either tetragonal symmetry (1/4,1/4,1/4) sites, which are twice as numerous as the octahedral (l/2,0,0) sites (referenced to a simple cubic coordinate system). The electron-poor alkali metal ions tend to lie adjacent to a C=C double... 

Figure 5.2 Unit cell of CaF2 showing eightfold (cubic) coordination of Ca by 8F and fourfold (tetrahedral) coordination of F by 4Ca. The structure can be thought of as an fee array of Ca in which all the tetrahedral interstices are occupied by F.

Table 3 suggests that Al cation in y-Al203 structure can be replaced by Mg both in tetrahedral and octahedral interstices, but Li can only enter into an octahedral interstices of the lattice. Diffusion for Ca cation into the y-Al203 bulk is rather difficult, since f t = 0 72 is at the upper limit of the allowed range. For K cation such a diffusion is impossible because f,ci = 0.99 is out of the allowed range. 

As can be seen from Fig. 17.2(b), there is one tetrahedral interstice above and one below every sphere, i.e. there are two tetrahedral interstices per sphere. 

Octahedral and Tetrahedral Interstices in the Cubic Closest-packing... 

If we consider the unit cell to be subdivided into eight octants, we can perceive one tetrahedral interstice in the center of every octant [Fig. 17.3(b)], Two tetrahedra share an edge when their octants have a common face. They share a vertex if their octants only have a common edge or a common vertex. There are no face-sharing tetrahedra. 

There are four spheres, four octahedral interstices and eight tetrahedral interstices per unit cell. Therefore, their numerical relations are the same as for hexagonal closest-packing, as well as for any other stacking variant of closest-packings one octahedral and two tetrahedral interstices per sphere. Moreover, the sizes of these interstices are the same in all closest-packings of spheres. 

The typical structure for the composition MH2 is a cubic closest-packing of metal atoms in which all tetrahedral interstices are occupied by H atoms this is the CaF2 type. The surplus hydrogen in the lanthanoid hydrides MH2 to MH3 is placed in the octahedral interstices (Li3Bi type for LaH3 to NdH3, cf. Fig. 15.3, p. 161). 

Occupation of Tetrahedral Interstices in Closest-packings of Spheres... 

SiS2 offers another variant of the occupation of one-quarter of the tetrahedral interstices in a cubic closest-packing of S atoms. It contains strands of edge-sharing tetrahedra (Fig. 

The structure of wurtzite corresponds to a hexagonal closest-packing of S atoms in which half of the tetrahedral interstices are occupied by Zn atoms. In addition, any other stacking variant of closest-packings can have occupied tetrahedral interstices. Polytypes of this kind are known, for example, for SiC. 

Packings of spheres having occupied tetrahedral and octahedral interstices usually occur if atoms of two different elements are present, one of which prefers tetrahedral coordination, and the other octahedral coordination. This is a common feature among silicates (cf. Section 16.7). Another important structure type of this kind is the spinel type. Spinel is the mineral MgAl204, and generally spinels have the composition AM2X4. Most of them are oxides in addition, there exist sulfides, selenides, halides and pseudohalides. 

In the following, we start by assuming purely ionic structures. In spinel the oxide ions form a cubic closest-packing. Two-thirds of the metal ions occupy octahedral interstices, the rest tetrahedral ones. In a normal spinel the A ions are found in the tetrahedral interstices and the M ions in the octahedral interstices we express this by the subscripts T and O, for example Mgr[Al2](904. Since tetrahedral holes are smaller than octahedral holes, the A ions should be smaller than the M ions. Remarkably, this condition is not fulfilled in many spinels, and just as remarkable is the occurrence of inverse spinels which have half of the M ions occupying tetrahedral sites and the other half occupying octahedral sites while the A ions occupy the remaining octahedral sites. Table 17.3 summarizes these facts and also includes a classification according to the oxidation states of the metal ions. 

The required local charge balance between cations and anions which is expressed in Pauling s rule causes the distribution of cations and anions among the octahedral and tetrahedral interstices of the sphere packing. Other distributions of the cations are not compatible with Pauling s rule. 

What fraction of the tetrahedral interstices are occupied in solid C1207 ... 

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