Crystals octahedral holes

A FIGURE 23.8 Octahedral Holes in Closest-Packed Crystals Octahedral holes are found in a closest-packed stmcture. The octahedral hole is surrounded by six of the atoms in the closest-packed structure. 

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). 

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. 

Figure 5.18.1 The NaCl crystal structure consisting of two interpenetrating face-centered cubic lattices. The face-centered cubic arrangement of sodium cations (the smaller spheres) is readily apparent with the larger spheres (representing chloride anions) filling what are known as the octahedral holes of the lattice. Calcium oxide also crystallizes in the sodium chloride structure.

KEY TERMS face-centered cubic crystal lattice octahedral hole... 

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. 

Spinels have a crystal structure in which there is a face-centered cubic arrangement of O2 ions. There are two types of structures in which cations have octahedral or tetrahedral arrangements of anions surrounding them. In the spinel structure, it is found that the +3 ions are located in octahedral holes and the tetrahedral holes are occupied by the +2 ions. A different structure is possible for these ions. That structure has half of the +3 metal ions located in the tetrahedral holes while the other half of these ions and the +2 ions are located in the octahedral holes. In order to indicate the population of the two types of lattice sites, the formula for the compound is grouped with the tetrahedral hole population indicated first (the position normally occupied by the +2 ion, A) followed by the groups populating the octahedral holes. Thus, the formula AB204 becomes B(AB)04 in order to correctly... 

I shall take the simple view that most metal oxide structures are derivatives of a closest packed 02 lattice with the metal ions occupying tetrahedral or octahedral holes in a manner which is principally determined by size, charge (and hence stoichiometry) and d configuration (Jj). The presence of d electrons can lead to pronounced crystal field effects or metal-metal bonding. The latter can lead to clustering of metal atoms within the lattice with large distortions from idealized (ionic) geometries. 

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). 

In the free ion, the five 3c/ orbitals all have the same energy. In a crystal, these levels are split for example, if the ion occupied an octahedral hole, the 3c/levels would be split into a lower, triply degenerate level and a higher, doubly degenerate (e level. This is depicted in Figure 8.2. 

Chapter 1 is an introduction to crystal stractures and the iorric model. It introduces many of the crystal structures that appear in later chapters and discusses the concepts of iorric radii and lattice energies. Ideas such as close-packed structures and tetrahedral and octahedral holes are covered here these are used later to explain a number of solid state properties. 

Figure 6. Architecture of the [Ni 12(00)21-H]3 trianion in Compound 4 with 20% isotropic ellipsoids of nuclear motion, as determined from the neutron diffraction refinements. The single hydrogen atom was found to be localized in one of the two octahedral interstices rather than crystal-lographically disordered in both octahedral holes.

Because coordination compounds are usually considered to be covalently bonded, io a first approximation (see Chapter 11). extended complex structures in the solid can readily be related io them. Consider, for example, rhodium penlafluonde Obviously, it could be considered as an ionic structure, Rh5+5F , and indeed the crystal structure7 consists, in part, of hep-arranged fhjonde ions with rhodium in octahedral holes. However, closer inspection of the structure reveals that it consists of tetrnmeric units, Rh4F2ll, that are distinct from one another (Fig. 7.7). The environment about each rhodium atom, an octahedron of six fluonne atoms, is what we... 

This brings us to a class of compounds too often overlooked in the discussion of simple ionic compounds the transition metal halides. In general, these compounds (except fluorides) crystallize in structures that are hard to reconcile with the structures of simple ionic compounds seen previously (Figs. 4.1-4.3). For example, consider the cadmium iodide structure (Fig. 7.8). It is true that the cadmium atoms occupy octahedral holes in a hexagonal closest packed structure of iodine atoms, but in a definite layered structure that can be described accurately only in terms of covalent bonding and infinite layer molecules. 

If209 is crystallized at 213 K from ethyl acetate saturated with argon, inclusion crystals are formed which contain Ar atoms in one of the two types of octahedral holes in the close-... 

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 distance between the hole and the nearest-neighbor atom is all. A similar proof can be made for an octahedral hole on the center of an edge of the unit cell in Fig. 10-1( ) if we note that the actual crystal lattice consists of a three-dimensional stack of unit cells, as in Fig. 10-3. Each such edge-center hole is shared by four unit cells and there are 12 edges in a cube, so that the number of octahedral holes per unit cell is... 

There are competing advantages of tetrahedral and octahedral holes for housing impurities or second components of an alloy. If the crystal forces, whatever their nature, depend mostly on interactions between nearest-neighbors, the octahedral hole has the advantage of having more nearest-neighbors with which it interacts (6 instead of 4). 

Fig. 5 Left panel. Structural model of the disordered Na(NH3)+ units which are randomly aligned along eight equivalent (111) orientations and reside in the octahedral holes of the fee structure of (NH3)xNaA2C60. The Na+ ions and the NH3 molecules are positioned at the corners of the outer and inner cube, respectively. Right panel Coordination environment of a Na(NH3)+ pair in the octahedral hole of the (NH3)xNaA2C60 crystal structure. Only one of the possible eight orientations is shown for clarity...

The hep structure consists of a stacking of atomic layers in the sequence ABABAB- . The octahedral holes are located between adjacent layers, as shown in Fig. 10.2.3(a). In the crystal structure of nickel asenide, the As atoms constitute a hep lattice, and the Ni atoms occupy all the octahedral holes. In contrast, cadmium iodide, Cdl2, may be described as a hep of 1 anions, in which only half the octahedral holes are occupied by Cd2+ ions. The manner of occupancy of the octahedral interstices is such that entire layers of octahedral interstices are filled, and these alternate with layers of empty... 

The unique properties of the stable d5 Mn2+ ion is reflected by the fact that MnS and MnSe crystallize in three modifications, in the rocksalt, the cubic sphalerite and the hexagonal wurtzite structure. While in the NiAs structure of MnTe the cations occupy the octahedral holes of a hexagonal close-packing of anions they occupy half of the tetrahedral holes of this packing in the ZnO type modification of MnS and MnSe. The non-metallic character is evident already from the fact that the structure is undistorted (c/a = 1.61 for MnS and 1.63 for MnSe) and that the cations really are at the centres of one set of tetrahedral holes and not at the centre of the bipyramidal holes composed of two tetrahedra of the two different sets. 

If these compounds crystallized in their antistructure, which is a 2H—MoSa structure with all octahedral holes filled, semiconductivity would be feasible by assuming the cation in trigonal-prismatic coordination to be divalent and the one in octahedral coordination to be tetra-valent. 

---