Hole, octahedral

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. 

In many of the transition metals, such as titanium, vanadium and molybdenum, carbon, nitrogen and oxygen atoms can fit into octahedral holes, and hydrogen into the teualredral holes. The fit here is estimated by assuming the atoms all have incompressible radii, and die contact must be such tlrat tire interstitial atoms do not rattle around in the holes. 

In the face-centred cubic structure tirere are four atoms per unit cell, 8x1/8 cube corners and 6x1/2 face centres. There are also four octahedral holes, one body centre and 12 x 1 /4 on each cube edge. When all of the holes are filled the overall composition is thus 1 1, metal to interstitial. In the same metal structure there are eight cube corners where tetrahedral sites occur at the 1/4, 1/4, 1/4 positions. When these are all filled there is a 1 2 metal to interstititial ratio. The transition metals can therefore form monocarbides, niU ides and oxides with the octahedrally coordinated interstitial atoms, and dihydrides with the tetrahedral coordination of the hydrogen atoms. 

The higher solubility of carbon in y-iron than in a-iroii is because the face-ceiiued lattice can accommodate carbon atoms in slightly expanded octahedral holes, but the body-centred lattice can only accommodate a much smaller carbon concentration in specially located, distorted tetrahedral holes. It follows that the formation of fenite together with cementite by eutectoid composition of austenite, leads to an increase in volume of the metal with accompanying compressive stresses at die interface between these two phases. 

Fig. 16.1. Ionic ceramics, (a) The rocksalt, or NoCl, structure, (b) Magnesia, MgO, has the rocksalt structure. It can be thought of as an f.c.c. packing with Mg ions in the octahedral holes. ( ) Cubic zirconia ZrOj an f.c.c. packing of Zr with O in the tetrahedral holes, (d) Alumina, AljOj a c.p.h. packing of oxygen with Al in two-thirds of the octahedral holes.

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.

Therefore the relationship between these interconvertible structures originates from a cubic anion lattice of 32 0 ions in the cell. With 32 Fe ions in the octahedral holes stoichiometric FeO is formed. Replacement of a number of Fe ions with two-thirds of their number of Fe ions maintains electrical neutrality but provides non-stoichiometric Fei 0. Continual replacement in this way to leave 24 Fe atoms in the cubic cell produces Fej04, and... 

It has the VF3 structure (Rh-F 1.961 A) having a hep array of fluorines with rhodium occupying 1/3 of the octahedral holes. Various hydrates have been reported... 

Less important oxides are Ag203, obtained impure by extended anodic oxidation of silver, and Ag30, obtained hydrothermally from Ag/AgO at 80°C, 4000 bar, which is a metallic conductor with the anti-BiI3 structure containing an hep array of silvers with oxide ions occupying 2/3 of the octahedral holes [32]. 

Such simple considerations led Scholten and Konvalinka to confirm the form of the dependence of the reaction velocity on the pressure, as had been observed in their experiments. Taking into account a more realistic situation, on the polycrystalline hydride surface with which a hydrogen molecule is dealing when colliding and subsequently being dissociatively adsorbed, we should assume rather a different probability of an encounter with a hydride center of a /3-phase lattice, an empty octahedral hole, or a free palladium atom—for every kind of crystallite orientation on the surface, even when it is represented, for the sake of simplicity, by only the three low index planes. 

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. 

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. 

In an ionic solid, the coordination number means the number of ions of opposite charge immediately surrounding a specific ion. In the rock-salt structure, the coordination numbers of the cations and the anions are both 6, and the structure overall is described as having (6,6)-coordination. In this notation, the first number is the cation coordination number and the second is that of the anion. The rock-salt structure is found for a number of other minerals having ions of the same charge number, including KBr, Rbl, MgO, CaO, and AgCl. It is common whenever the cations and anions have very different radii, in which case the smaller cations can fit into the octahedral holes in a face-centered cubic array of anions. The radius ratio, p (rho), which is defined as... 

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 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. 

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. 

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. 

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. 

YjAlsOn)—YAG Most garnets are silicates, whereas yttrium aluminum garnet (YAG) is an aluminate. In YAG, both the tetrahedral and the octahedral holes of the garnet structure are occupied by Al-ions and the quasi-cubic holes are occupied by Y-ions. 

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...

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... 

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