Tetrahedrally close-packed structures type

Structure types have been established. Similar to Al, the M2X3 crystals (M = Ga, In, Tl X = S, Se, Te) are mostly based on M-defect tetrahedral structures, namely W (Ga2S3, In2Se3) and ZB (Ga2Se3, Ga2Te3, In2Te3). At atmospheric pressure, 283 can be present in three modifications. The low-temperature a-form is a cubic close-packed structure of S atoms, where 70% of the In atoms are randomly distributed on octahedral sites and the rest remain on tetrahedral sites. The P-form is related to the spinel structure, and the y-modification is hexagonal. 

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. 

An important contribution to the structure analysis of intermetallic phases in terms of the coordination polyhedra has been carried out by Frank and Kasper (1958). They described several structure types (Frank-Kasper structures) as the result of the interpenetration of a group of polyhedra, which give rise to a distorted tetrahedral close-packing of the atoms. Samson (1967, 1969) developed the analysis of the structural principles of intermetallic phases having giant unit cells (Samson phases). These structures have been described as arrangements of fused polyhedra rather than the full interpenetrating polyhedra. 

Sphalerite and wurtzite structures general remarks. Compounds isostructural with the cubic cF8-ZnS sphalerite include AgSe, A1P, AlAs, AlSb, BAs, GaAs, InAs, BeS, BeSe, BeTe, BePo, CdS, CdSe, CdTe, CdPo, HgS, HgSe, HgTe, etc. The sphalerite structure can be described as a derivative structure of the diamond-type structure. Alternatively, we may describe the same structure as a derivative of the cubic close-packed structure (cF4-Cu type) in which a set of tetrahedral holes has been filled-in. This alternative description would be especially convenient when the atomic diameter ratio of the two species is close to 0.225 see the comments reported in 3.7.3.1. In a similar way the closely related hP4-ZnO... 

As pointed out in the description of the cubic close-packed structure (cF4-Cu type), this structure may be described (especially for certain values of the atomic diameter ratio) as a derivative of the Cu-type structure in which two sets of tetrahedral holes have been filled-in. 

Zr fAl3, hP7, structural type (a tetrahedrally close-packed phase) Hexagonal, space group P6, N. 174. 

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. 

Both Y-AI2O3 and TI-AI2O3 are members of a class of binary oxides in which the oxygen packing is of the cubic close packing type, with the cations situated partly in tetrahedral and partly in octahedral positions. These compounds are called spinels after the mineral spinel which has the composition MgAhC. In spinel Mg2+ occupies tetrahedral and Al3+ occupies octahedral positions. The unit cell of a cubic close packed structure is shown in Fig. 8.5. 

There are two types of interstitial sites in the close-packed structure of early transition metals, i.e., the tetrahedral sites and the octahedral sites. The nitrogen atoms occupy only the octahedral sites since the tetrahedral sites are too small to accommodate them. There is one octahedral site per atom of the host metal (see Ch. 3, Sec. 5.0 and Figs. 3.14, 3.15, and 3.16). 

The structures of many binary and ternary scandium borides and carbides may be deducted from other structure types by a multiple substitution of larger atoms by B-B or C-C pairs or by the inclusion of B or C atoms into the cavities of the parent structure types. The same is valid for the structures of scandium intermetallics with the 6B elements. The Ti7Si2, NiAs, ErAgSc2 and Al2Mg04 structure types can be obtained by an inclusion of cations of metals into the octahedral and tetrahedral cavities of different packings (usually close ones) of 6B anions. Frequently the inclusion of atoms causes a distortion of the parent close-packed structure. 

Ceo is ti = 1.034 nm = 10.34 A). The lattice constant of the FCC crystal composed ofCeo units is 14.16 A,just3% smaller than the value 14.62A, which is what we would expect for incompressible spheres in contact with their nearest neighbors. The free space between such spheres is enough to accommodate other atoms. In fact, structures in which this space is occupied by alkali atoms (Li, Na, K, Rb and Cs) have proven quite remarkable they exhibit superconductivity at relatively high transition temperatures (see Table 13.1). The positions occupied by the alkali atoms are the eight tetrahedral and four octahedral sites of the cubic cell, shown in Fig. 13.7. When all these sites are occupied by alkali atoms the structure has the composition M3C60. Solids with one, two, four and six alkali atoms per Ceo have also been observed but they correspond to structures with lower symmetry or to close-packed structures of a different type (like the BCC crystal). All these crystals are collectively referred to as doped fullerides . 

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. 

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