Tetrahedral hole, description

The importance of the geometrical factor in determining the stability of these phases has been pointed out (Pearson 1972). In a simplified description, Laves phases AM2 of the MgCu2 type may be presented as cubic face-centred packing of large spheres A which form tetrahedral holes that are occupied by tetrahedra of smaller spheres M. The ideal value of the radius ratio rA/rM is 1.225. The values experimentally observed for the various Laves types range from 1.05 to 1.7. 

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. 

The fluorite structure is named after the mineral form of calcium fluoride, CaF2, which is found in the U.K. in the famous Derbyshire Blue John mines. The structure is illustrated in Figure 1.39. It can be described as related to a ccp array of calcium ions with fluorides occupying all of the tetrahedral holes. There is a problem with this as a description because calcium ions are rather smaller than fluoride ions, and so, physically, fluoride ions would not be able to fit into the tetrahedral holes of a calcium ion array. Nevertheless, it gives an exact description of the relative positions of the ions. The diagram in Figure 1.39(a) depicts the fourfold tetrahedral coordination... 

The fluorite structure. Figure 7-9, can be described as having the calcium ions in a cubic close-packed lattice, with eight fluoride ions surrounding each one and occupying all of the tetrahedral holes. An alternative description of the same structure, shown in... 

Figure 2-1. A-L112O3 structure. It consists of a hep Ln3+sublattice with one half of both octahedral and tetrahedral holes occupied by CF (a). The (Ln202)n layers have C3 symmetry. An alternative description consists of linked sevenfold LnOy polyhedra (y.

Fluorite, CaF2, shows a radius ratio of 0.96, which predicts that the calcium ions will occupy cubic holes formed by the fiuoride anions. Note in Figure 7.22a that the calcium ions do indeed occupy such sites. However, as required by stoichiometry (see Problem 7.39), half of the cubic holes must be unoccupied. (Note that the center of the unit cell is an unoccupied cubic hole formed by the fluoride ions.) The unit cell of the lattice therefore cannot be the simple cubic of fluorides with one calcium in the body. Rather, a larger unit cell of fee calcium ions with fluorides filling the tetrahedral holes is the more appropriate description. Note that the coordination number of the fluorides is 4, which is consistent with Equation (7.6). Table 7.11 indicates that there is a 90% correlation between the known crystal structure and the calculated radius ratio for compounds that assume the fluorite structure. 

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. 

A More Detailed Description of the Two Classes of Oxyanion Holes in Enzymes enzyme substrate complex tetrahedral intermediate 1... 

As for the corresponding iono-covalent ternary oxides, the structure of the quaternary R-M-O-N and higher oxynitrides will be advantageously described fi"om the coordination polyhedra of M atoms, the tetrahedra for example in silicates, the larger R atoms being located within the holes formed by the different arrangements of these structural units. Such a description is particularly well adapted to the case of tetrahedra and octahedra. Three types of environment for M atoms can be pointed out in the rare-earth-containing oxynitrides, namely tetrahedral, octahedral and cubic . 

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