Close packing octahedral hole

Sodium Chloride (NaCI) (Cubic Close Packed, Octahedral Holes Fully Occupied)... 

An unusual crystal arrangement is exhibited by the isomorphous compounds CrCl and Crl. The close-packed cubic array of Cl or I atoms has two-thirds of the octahedral holes between every other pair of chlorine or iodine planes filled with chromium atoms. Alternate layers of the halogen compounds are held together by van der Waals forces (39,40). 

Compounds that have the empirical formulas MCr02 and DCr204 where M is a monovalent and D a divalent cation, are known as chromites. These are actually mixed oxides and probably are better written as M20-Cr203 and D0-Cr203, respectively. The oxides of D are largely spinels, ie, the oxygen atoms define a close-packed cubic array having the octahedral holes occupied by the Cr(III) cation and the tetrahedral holes occupied by D (54). Chromite ore is an important member of this class of oxides. 

Fig. 16.2. Both the f.c.c. and the c.p.h. structures are close-packed. Both contain one octahedral hole per atom, and two tetrahedral holes per atom. The holes in the f.c.c. structures ore shown here.

The holes in the close-packed structure of a metal can be filled with smaller atoms to form alloys (alloys are described in more detail in Section 5.15). If a dip between three atoms is directly covered by another atom, we obtain a tetrahedral hole, because it is formed by four atoms at the corners of a regular tetrahedron (Fig. 5.30a). There are two tetrahedral holes per atom in a close-packed lattice. When a dip in a layer coincides with a dip in the next layer, we obtain an octahedral hole, because it is formed by six atoms at the corners of a regular octahedron (Fig. 5.30b). There is one octahedral hole for each atom in the lattice. Note that, because holes are formed by two adjacent layers and because neighboring close-packed layers have identical arrangements in hep and ccp, the numbers of holes are the same for both close-packed structures. 

FIGURE 5.30 The lot ations of (a) tetrahedral and (b) octahedral holes Note that both types of holes are defined by two neighboring close-packed layers, so they are present with equal abundance in both hep and ccp structures. 

Many metals have close-packed structures, with the atoms stacked in either a hexagonal or a cubic arrangement close-packed atoms have a coordination number of 12. Close-packed structures have one octahedral and tivo tetrahedral holes per atom. 

The rock-salt structure is a common ionic structure that takes its name from the mineral form of sodium chloride. In it, the Cl- ions lie at the corners and in the centers of the faces of a cube, forming a face-centered cube (Fig. 5.39). This arrangement is like an expanded ccp arrangement the expansion keeps the anions out of contact with one another, thereby reducing their repulsion, and opens up holes that are big enough to accommodate the Na+ ions. These ions fit into the octahedral holes between the Cl ions. There is one octahedral hole for each anion in the close-packed array, and so all the octahedral holes are occupied. If we look carefully at the structure, we can see that each cation is surrounded by six anions and each anion is surrounded by six cations. The pattern repeats over and over, with each ion surrounded by six other ions of the opposite charge (Fig. 5.40). A crystal of sodium chloride is a three-dimensional array of a vast number of these little cubes. 

Buckminsterfullerene is an allotrope of carbon in which the carbon atoms form spheres of 60 atoms each (see Section 14.16). In the pure compound the spheres pack in a cubic close-packed array, (a) The length of a side of the face-centered cubic cell formed by buckminsterfullerene is 142 pm. Use this information to calculate the radius of the buckminsterfullerene molecule treated as a hard sphere, (b) The compound K3C60 is a superconductor at low temperatures. In this compound the K+ ions lie in holes in the C60 face-centered cubic lattice. Considering the radius of the K+ ion and assuming that the radius of Q,0 is the same as for the Cft0 molecule, predict in what type of holes the K ions lie (tetrahedral, octahedral, or both) and indicate what percentage of those holes are filled. 

Tetrahedral and octahedral interstitial holes are formed by the vacancies left when anions pack in a ccp array, (a) Which hole can accommodate the larger ions (b) What is the size ratio of the largest metal cation that can occupy an octahedral hole to the largest that can occupy a tetrahedral hole while maintaining the close-packed nature of the anion lattice (c) If half the tetrahedral holes are occupied, what will be the empirical formula of the compound MVAV, where M represents the cations and A the anions ... 

The prototype hard metals are the compounds of six of the transition metals Ti, Zr, and Hf, as well as V, Nb, and Ta. Their carbides all have the NaCl crystal structure, as do their nitrides except for Ta. The NaCi structure consists of close-packed planes of metal atoms stacked in the fee pattern with the metalloids (C, N) located in the octahedral holes. The borides have the A1B2 structure in which close-packed planes of metal atoms are stacked in the simple hexagonal pattern with all of the trigonal prismatic holes occupied by boron atoms. Thus the structures are based on the highest possible atomic packing densities consistent with the atomic sizes. 

Fig. 1 Atomic arrangement of X (open circles) and T (filled circles) in projection for (a) hexagonal close-packing of X with T occupying half the octahedral holes (positions of the other half being indicated by crosses), and (b) the FeS2—m type structure, where the X—X pairs are emphasized by connecting bars...

The alkalides. The first crystalline alkalide to be prepared in this manner was [Na+(2.2.2)].Na. This salt is obtained as shiny, gold-coloured crystals (Dye etal., 1974). The 23Na nmr spectrum yields a narrow upfield signal for the Na- ion (Dye, Andrews Ceraso, 1975) the X-ray structure indicates close-packed sodium cryptate cations with Na" anions occupying octahedral holes between the cryptate layers (Tehan, Barnett Dye, 1974). 

Another point which should be underlined is that the same structure can be differently viewed and described (Parthe and Gelato 1984, Franzen 1986). The simple rock-salt structure, for instance, can be viewed as a cubic close-packed set of anions with cations in octahedral holes, as XY6 octahedra sharing edges, as a stacking sequence of superimposed alternate triangular nets, respectively, of X and Y atoms... 

Several cubic structures, therefore, in which (besides 0, 0, 0 0, K, M M, 0, M M, M, 0) one or more of the reported coordinate groups are occupied could be considered as filled-up derivatives of the cubic close-packed structures. The NaCl, CaF2, ZnS (sphalerite), AgMgAs and Li3Bi-type structures could, therefore, be included in this family of derivative structures. For this purpose, however, it may be useful to note that the radii of small spheres which fit exactly into tetrahedral and octahedral holes are, respectively, 0.225. and 0.414... if the radius of the close-packed spheres is 1.0. For a given phase pertaining to one of the aforementioned types (NaCl, ZnS, etc.) if the stated dimensional conditions are not fulfilled, alternative descriptions of the structure may be more convenient than the reported derivation schemes. 

Similar considerations may be made with reference to the other simple close-packed structure, that is to the hexagonal Mg-type structure. In this case two basic derived structures can be considered the NiAs type with occupied octahedral holes and the wurtzite (ZnS) type with one set of occupied tetrahedral holes (compare with the data given with an origin shift in 7.4.2.3.2). For a few more comments about interstices and interstitial structures see 3.8.4. See Fig. 3.35. 

This structure could also be described as derived from a cubic close-packed array of atoms (Bi atoms) by filling all the tetrahedral and octahedral holes with Li atoms. 

This shape of the powder pattern is that predicted (5) for an 7 = nucleus in axial symmetry. This situation occurs for the Al nuclei in a-AljOs which is a hexagonal close-packed array of oxygen atoms with the aluminum atoms ordered in of the holes octahedrally coordinated with oxygen atoms. 

Nitrogen Compounds.—The formation of ZrNj 9 by a new method of evaporation synthesis has been described. The compound LiZrN2 has been prepared from LijN and ZrNi 22 and X-ray crystallographic studies have shown that the crystals contain hexagonally close-packed nitride ions, with Zr" and Li ions in octahedral and tetrahedral holes, respectively. ... 

---