Octahedral interstices

In three-dimensional closest packing, the spherical atoms are located in position 4(a). There are two types of interstices octahedral and tetrahedral holes which occupy positions 4(b) and 8(c), respectively. The number of tetrahedral holes is twice that of the spheres, while the number of octahedral holes is equal to that of the spheres. The positions of the holes are shown in Fig. 10.1.1. 

In close-packed arrays of anions X, both kinds of interstices, octahedral and tetrahedral ones, may simultaneously be occupied by cations M. In order to obtain a layer structure occupation of the tetrahedra and octahedra has to be such that periodically an empty layer alternates with a three-dimensional block. An example with only one kind of mixed layer is shown in Figure 25. 

Titanium Dichloride. Titanium dichloride [10049-06-6] is a black crystalline soHd (mp > 1035 at 10°C, bp > 1500 at 40°C, density 31(40) kg/m ). Initial reports that the titanium atoms occupy alternate layers of octahedral interstices between hexagonaHy close-packed chlorines (analogous to titanium disulfide) have been disputed (120). TiCl2 reacts vigorously with water to form a solution of titanium trichloride andUberate hydrogen. The dichloride is difficult to obtain pure because it slowly disproportionates. 

Titanium Trichloride. Titanium trichloride [7705-07-9] exists in four different soHd polymorphs that have been much studied because of the importance of TiCl as a catalyst for the stereospecific polymerization of olefins (120,124). The a-, y-, and 5-forms are all violet and have close-packed layers of chlorines. The titaniums occupy the octahedral interstices between the layers. The three forms differ in the arrangement of the titaniums among the available octahedral sites. In a-TiCl, the chlorine sheets are hexagonaHy close-packed in y-TiCl, they are cubic close-packed. The brown P-form does not have a layer stmcture but, instead, consists of linear strands of titaniums, where each titanium is coordinated by three chlorines that act as a bridge to the next Ti The stmctural parameters are as follows ... 

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... 

When is approximately the same size as Ti (i.e. M = Mg, Mn, Fe, Co, Ni) the stmcture is that of ilmenite, FeTi03, which consists of hep oxygens with one-third of the octahedral interstices occupied by and another third by Ti This is essentially the same structure as corundum (AI2O3, p. 243) except that in that case there is only one type of cation which occupies two-thirds of the octahedral sites. 

Phase equilibria in Ti-H alloys are sensitive to pressure. A new phase appears in near-eutectoid alloys at P > 20 kbar with a tetragonal structure and hydrogen re-distributed from tetra- to octahedral interstices. 

This compound has the cubic fluorite structure with one octahedral interstice per Ce atom. Therefore, a =1, and S = 2 for CeH2. We can therefore write ... 

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. 

KT1 does not have the NaTl structure because the K+ ions are too large to fit into the interstices of the diamond-like Tl- framework. It is a cluster compound K6T16 with distorted octahedral Tig- ions. A Tig- ion could be formulated as an electron precise octahedral cluster, with 24 skeleton electrons and four 2c2e bonds per octahedron vertex. The thallium atoms then would have no lone electron pairs, the outside of the octahedron would have nearly no valence electron density, and there would be no reason for the distortion of the octahedron. Taken as a closo cluster with one lone electron pair per T1 atom, it should have two more electrons. If we assume bonding as in the B6Hg- ion (Fig. 13.11), but occupy the t2g orbitals with only four instead of six electrons, we can understand the observed compression of the octahedra as a Jahn-Teller distortion. Clusters of this kind, that have less electrons than expected according to the Wade rules, are known with gallium, indium and thallium. They are called hypoelectronic clusters their skeleton electron numbers often are 2n or 2n — 4. 

The number of octahedral holes in the unit cell can be deduced from Fig. 17.1(c) two differently oriented octahedra alternate in direction c, i.e. it takes two octahedra until the pattern is repeated. Flence there are two octahedral interstices per unit cell. Fig. 17.1(b) shows the presence of two spheres in the unit cell, one each in the layers A and B. The number of spheres and of octahedral interstices are thus the same, i.e. there is exactly one octahedral interstice per sphere. 

The size of the octahedral interstices follows from the construction of Fig. 7.2 (p. 53). There, it is assumed that the spheres are in contact with one another just as in a packing of spheres. A sphere with radius 0.414 can be accommodated in the hole between six octahedrally arranged spheres with radius 1. 

From Fig. 17.1 we realize another fact. The octahedron centers are arranged in planes parallel to the a-b plane, half-way between the layers of spheres. The position of the octahedron centers corresponds to the position C which does not occur in the stacking sequence ABAB... of the spheres. We designate octahedral interstices in this position in the following sections by y. By analogy, we will designate octahedral interstices in the positions A and B by a and j3, respectively. 

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

In cubic closest-packing, consideration of the face-centered unit cell is a convenient way to get an impression of the arrangement of the interstices. The octahedral interstices are situated in the center of the unit cell and in the middle of each of its edges [Fig. 17.3(a)], The octahedra share vertices in the three directions parallel to the unit cell edges. They share edges in the directions diagonal to the unit cell faces. There are no face-sharing octahedra. 

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). 

Structure Types with Occupied Octahedral Interstices in Closest-packings of Spheres... 

For the structures of M2C and M2N the question arises is there an ordered distribution of occupied and unoccupied octahedral holes There are several possibilities for an ordered distribution, some of which actually occur. For example, in W2C occupied and unoccupied octahedral holes alternate in layers this is the Cdl2 type. In /3-V2N there are alternating layers in which the octahedral holes are one-third and two-thirds occupied. The question of ordered distributions of occupied interstices is the subject of the following sections. 

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