Tetrahedral cavity

One example is the tertiary bond found in the wurtzite structure of ZnO (67454). All members of the Zn chalcogenide series crystallize with structures based on the close packing of the chalcogenide ions, with Zn occupying half the tetrahedral cavities. The higher members, ZnSe and ZnTe (31840), crystallize with the cubic sphalerite structure while ZnO crystallizes with the hexagonal wurtzite structure. ZnS (60378, 67453) is known in both forms. 

In the sphalerite structure the anions form a cubic close packed array. The structure has a single adjustable parameter, the cubic cell edge. The 0 ions are too small for them to be in contact in this structure (see Fig. 6.4) so ZnO adopts the lower symmetry hexagonal wurtzite structure which has three adjustable parameters, the a and c unit cell lengths and the z coordinate of the 0 ion, allowing the environment around the Zn " ion to deviate from perfect tetrahedral symmetry. In the sphalerite structure the ZnX4 tetrahedron shares each of its faces with a vacant octahedral cavity (one is shown in Fig. 2.6(a)), while in the wurtzite structure one of these faces is shared with an empty tetrahedral cavity which places an anion directly over the shared face as seen in Fig. 2.6(b). The primary coordination number of Zn " in sphalerite is 4 and there are no tertiary bonds, but in wurtzite, which has the same primary coordination number, there is an additional tertiary bond with a flux of 0.02 vu through the face shared with the vacant tetrahedron. 

When a sphere lies on top of three other spheres in a close-packed structure, there is a cavity between those spheres, the so-called tetrahedral cavity (figure 4.2). Those same close-packed structures also contain octahedral cavities formed by six spheres, as shown in figure 4.4. 

Many crystal lattices can be described by filling the tetrahedral and /or octahedral cavities in close-packed structures with other particles. In many cases the particle will be too big to fill a certain cavity. In those cases the particles of the close-packed structure will shift a little and in this way the perfect close-packed structure is lost. Small particles sooner fit in a tetrahedral cavity and larger ones in an octahedral one. Thus we speak of a tetrahedral and an octahedral coordination of a particle in the cavity and the number of nearest neighbours is called the coordination number. 

In order to be able to describe the ideal crystal structure , it is important to bear in mind that there are two tetrahedral cavities and one octahedral one present for every sphere in a close-packed structure. With the help of Table 4.1 and the rules for octahedral and tetrahedral coordination the description of the following crystal structures are now easily understood when we bear in mind that in an ionic crystal lattice the larger negative ions form the close-packed structure and that the octahedral and tetrahedral cavities are filled with positive ions. 

This structure can be described as a cubic close-packed structure of sulphide ions. For every sulphide ion there are two tetrahedral cavities, one of which is occupied by a zinc ion. Other compounds with this structure are for example CuCl, BeS and CdS. 

This form of magnetism can be demonstrated by means of lodestone or magnetite (Fe304) which freely occurs in nature. A unit of this contains one Fe2+ ion, two Fe3+ions and four O2 ions. Its crystal structure is a cubic close packing of oxygen ions with an Fe 3+ ion in 1/8 of the tetrahedral cavities, an Fe 3+ ion in 1/4 of the octahedral cavities and an Fe2+ions in 1/4 of the octahedral cavities. Magnetic dipoles at tetrahedral sites line up antiparallel to the external field and dipoles in the octahedral cavities line up parallel to the field. 

The position of the intercalated DMSO molecule in the interlayer space of kaolinite is such that the first S-C group is almost parallel with the surface of kaolinite and the second S-C group is directed into the tetrahedral cavity of kaolinite [130, 131]. The S=0 group has 40.3° inclination to the basal surface of kaolinite. The methyl group of DMSO is influenced by both the opposing mineral surfaces. In addition, the intercalation of DMSO molecule results in the expansion of kaolinite from 7.2 to 11.19 A phase [132]. The formation of H-bonds between DMSO and surface OH groups of the octahedral side and weak H-bonds with the tetrahedral side of kaolinite was suggested [133-139]. 

The different orientation of the intercalated and adsorbed DMSO molecule with respect to the surface of kaolinite was found [148]. In the adsorbed system, the molecular C-O-C plane of DMSO is almost parallel with the basal surface of dickite. In the intercalated system, one of the methyl groups directs towards the center of the tetrahedral cavity and the second S-C bond is almost parallel with the plane of basal oxygen atoms (see Fig. 5). These positions and orientations are in agreement with the NMR experiments [130, 131, 137] where the existence of two non-equivalent methyl groups of the interlayer DMSO molecules in kaolinite was confirmed. 

Since the dominant feature of packings of spheroidal particles is the constrictions between the tetrahedral cavities formed by the Alumina microspheres, a more realistic model is required, based on the random sphere packing models. Such models are obviously more complex. Conversely, they permit a more realistic representation of the pore space among the spheroidal particles. A preliminary model has been reported for sorption [20] and relative permeability Pr [21]. 

Ellipsoidal cryptands of type (12) generally complex alkylammonium cations relatively weakly. However the spherical cryptand (13) contains four nitrogen atoms which define a tetrahedral cavity large enough to complex the tetrahedral cation. The crystal structure... 

A difference Fourier map, calculated at this point, reveals an additional small electron density maximum in the tetrahedral cavity next to the partially occupied V2. Thus, it is reasonable to assume that the V2 site splits into two independent partially occupied positions with the coordinates, which distribute V atoms in a random fashion in two adjacent tetrahedral positions rather than being simply vanadium-deficient. We label these two sites as V2a (corresponding to the former V2) and V2b (corresponding to the Fourier peak). Refinement of this model slightly improves the fit. Subsequently, additional profile parameters (F, F , and sample displacement) were included in the refinement, followed by a typical procedure of refining the porosity in the Suortti approximation with fixed atomic coordinates and Ui o, and then fixing the porosity parameters for the remainder of the refinement. 

H20( ) and is illustrated in Fig. 11.7(a), The central tetrahedral cavity and the centres of the twelve octahedra are all occupied by A1 atoms. (For another view of this group of twelve octahedra see MSIC Fig. 107(b).) Figure 11.7(b) shows the FW12O40 ion built from groups of three octahedra sharing additional vertices instead of edges, as in Fig. 11.7(a). 

There are two basic structural motifs in which a tetranuclear cluster could accommodate an interstitial atom - fully encapsulated within a tetrahedral cavity or partially encapsulated between the wings of a butterfly framework. 

As far as we are aware there are no examples of the location of an H atom, by neutron diffraction, within a tetrahedral cavity, and so the debate continues. 

Anslyn and co-workers have developed a series of tripodal Cu(II) complexes 108 and 109 in which the metal ion and three cationic organic groups form a tetrahedral cavity designed to host phosphate [71]. Receptor 108 is built from the tris(2-ethylamino)amine skeleton with appended benzylamine... 

Kitazawa, T. Nishikiori, S. Yamagishi, A. Kuroda, R. Iwamoto. T. Tetrahedral guest in a tetrahedral cavity A neopentane molecule encaged in a three-dimensional cadmium cyanide framework. J. Chem. Soc.. Chem. Coimnun. 1992. 413-415. 

Figure 3.50 The formation of a tetrahedral capsule based around four gallium ions and four deprotonated ligands. The tetrahedral cavity is shown and one of the ligands is emphasised to show that linearity and rigidity are not essential (for clarity, counter-cations are not shown).

A variety of cationic species such as tetraalkylammonium cations are encapsulated within the tetrahedral cavity in water. 

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. 

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