Body-centered cubic structure octahedral

Figure 5.8 Interstitial diffusion (a) interstitial diffusion involving the direct migration of an interstitial atom to an adjacent site in the crystal (b, c) some of the octahedral and tetrahedral interstitial sites in the body-centered cubic structure of metals such as iron and tungsten and (d) the total number of octahedral and tetrahedral sites in a unit cell of the body-centered cubic structure. Diffusion paths parallel to the unit cell edges can occur by a series of alternating octahedral and tetrahedral site jumps, dashed line.

Many of these compounds (MHn) show large deviations from ideal stoichiometry (n = 1,2, 3) and can exist as multiphase systems. The lattice structure is that of a typical metal with atoms of hydrogen on the interstitial sites for this reason they are also called interstitial hydrides. This type of structure has the limiting compositiOTis MH, MH2, and MH3 the hydrogen atoms fit into octahedral or tetrahedral holes in the metal lattice, or a combination of the two types. In fee and hep structures, we find 1 octahedral site (r = 0.414) and 2 tetrahedral sites (r = 0.255), and in bcc (body-centered-cubic) structures we find 3 octahedral site (r = 0.155) and 6 tetrahedral sites (r = 0.291). 

Fig. 2. Structures for the solid (a) fee Cco, (b) fee MCco, (c) fee M2C60 (d) fee MsCeo, (e) hypothetical bee Ceo, (0 bet M4C60, and two structures for MeCeo (g) bee MeCeo for (M= K, Rb, Cs), and (h) fee MeCeo which is appropriate for M = Na, using the notation of Ref [42]. The notation fee, bee, and bet refer, respectively, to face centered cubic, body centered cubic, and body centered tetragonal structures. The large spheres denote Ceo molecules and the small spheres denote alkali metal ions. For fee M3C60, which has four Ceo molecules per cubic unit cell, the M atoms can either be on octahedral or tetrahedral symmetry sites. Undoped solid Ceo also exhibits the fee crystal structure, but in this case all tetrahedral and octahedral sites are unoccupied. For (g) bcc MeCeo all the M atoms are on distorted tetrahedral sites. For (f) bet M4Ceo, the dopant is also found on distorted tetrahedral sites. For (c) pertaining to small alkali metal ions such as Na, only the tetrahedral sites are occupied. For (h) we see that four Na ions can occupy an octahedral site of this fee lattice.

Fluorite oxides are the most common and classical oxygen ionconducting materials. The crystal structure consists of a cubic oxygen lattice with alternate body centers occupied by 8-coordinated cations. The cations are arranged into a face-centered cubic structure with the anions occupying the tetrahedral sites. This leaves a rather open architecture, with large octahedral interstitial voids, as shown in Figure 1-6. 

The crystal structures and coordination polyhedra in LFMoC2-type and Ho2Cr2C3 type compounds are comparable. The metal positions in both structures constitute a distorted body-centered cubic arrangement with a similar order of the two kinds of metal atoms. Nevertheless, in the UMoC2-type structure one third of the (distorted) octahedral voids formed by the metal atoms are filled by carbon atoms, in the Ho2Cr2C3 structure only one quarter of the voids are filled. 

The transition metal carbides and nitrides have often been called interstitial compounds [70] however, this is somewhat misleading. The small boron, carbon, or nitrogen atoms certainly occupy octahedral or trigonal prismatic voids of the metal sublattice, but the arrangement of the metal atoms themselves is different from that of the element. In the monocarbides the transition metal atoms show cubic close packing. However, titanium, zirconium, and hafnium are packed hexagonally and vanadium, niobium, and tantalum are body centered cubic [1]. Thus, these monocarbides are inorganic compounds with their individual crystal structures and they should not be considered as an interstitial compound of a transition metal host lattice. 

La Nd) which crystallize in a filled C0AS3 structure. The polyanions form discrete X.i units which are squares in skutterudite but rectangles in the filled type (in LaFePi2 the P-P distances are 2.288 and 2.356 A, the P-P-P angle is 90.0°). The transition-element cations are in distorted octahedral coordination (LaFe4P,2 P-Fe-P = 97.9° and 82.1° instead of 90°) while the rare earth ions occupy the two nearly icosahedral voids at (0,0,0) and (5,5,5) of the body-centered cubic cell. 

Figure 5 shows the different kinds of bulk interstitial sites in perfect face-centered cubic (fee), hexagonal close-packed (hep), and body-centered cubic (bcc) lattice structures. The sites populated by H atoms in ihe concentration range of solid solution are known to be the octahedral sites for the fee metals, whereas they are most probably the tetrahedral sites for the bcc and hep metals [66] In fee and hep metals, there are one octahedral site and two tetrahedral sites per metal atom, whereas in bcc metals there ate three octahedral and six tetrahedral sites per metal atom. 

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 sodium chloride (NaCl also called the rock salt structure) and zinc blende (ZnS) structures are based on a face-centered cubic lattice. In both structures the anions sit on the lattice points that lie on the corners and faces of the unit cell, but the two-atom motif is slightly different for the two structures. In NaCl the Na ions are displaced from the CF ions along the edge of the unit cell, whereas in ZnS the Zn ions are displaced from the ions along the body diagonal of the unit cell. This difference leads to different coordination numbers. In sodium chloride, each cation and each anion are surrounded by six ions of the opposite type, leading to an octahedral coordination environment. In zinc blende, each cation and... 

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