TO4 tetrahedra

Figure 5.44 shows the conformation of the hexagonal rings on the tetrahedral sheet for limiting values of the rotational angle = 0° and 12°, respectively). Due to structural constraints, the value of depends directly on the mean cation-to-oxygen distances in [TO4] tetrahedra (4) and in octahedra (4,), according to... 

Zeolites can be briefly defined as crystallised solids made up of a sequence of TO4 tetrahedra linked together by their comer oxygens two tetrahedra share only one oxygen. The clement T can vary considerably Si, AL P, Ga, B, Ge,... The specific sequence of these tetrahedra in the structure creates a mono-, two- or three-dimensional microporous network made up of pores and/or cavities. 

In a zeolite, where the framework comprises TO4 tetrahedra (T silicon or aluminium), the chemical shift of the silicon, compared to tetramethylsilane adopted as reference, varies with the number of aluminium atoms located in the second co-ordination sphere (cf. Fig. 13.6). From the NMR spectrum, it is possible to obtain the concentration of each of these configurations and, by applying Lowenstein s rule (no Al-O-AI links), calculate the atomic Si/Al ratio of the framework using the formula ... 

Parameters of GVFF for silicates and aluminosilicates obtained from first-principles calculations were reported by Ermoshin et al. ° ° Having assumed that the dynamics of zeolite lattices can be described in terms of vibrations of the TO4 tetrahedra (T = Si, Al) and shared 03T-0(H)-T03 tetrahedra, the authors calculated the matrix of second derivatives of the total energy in Cartesian coordinates, the Hessian matrix H, for molecular models of such units. The matrix H was then transformed into a matrix of force constants in internal coordinates F... 

Structural units with corner-sharing between uranyl polyhedra and TO4 tetrahedra (T = S, Cr, Se, Mo)... 

OD stmctural units observed in uranyl oxysalts with TO4 tetrahedra and their black-and-white graphs are given in Fig. 32, and the compounds are listed in Table 6. At present, we are aware of three types of finite clusters with comer sharing between AnOn and TO4 polyhedra. Note that the unit [(U02)2(T04)4(H20)4]" shown in Fig. 32f contains two uranyl pentagonal bipyramids with uranyl cations coordinated by two H2O molecules in a cis-configuration. 

The cl/2a graph (Fig. 33) corresponds to two chemically different chains shown in Fig. 36. One chain (Fig. 36a) consists of An0e(Fl20) pentagonal bipyramids and TO4 tetrahedra, whereas another one (Fig. 36b) is built by comer sharing between AnOe square bipyramids and TO4 tetrahedra. 

The remarkable class of ID stmctural units with comer-sharing actinyl polyhedra and TO4 tetrahedra are uranyl selenate nanotubules that have recently been described by Krivovichev et al. [173, 174]. They will be considered in detail in Chapter 11. 

Table 10. Crystallographic data for actinyl compounds based on structural units with edge sharing between actinyl coordination polyhedra and TO4 tetrahedra...

Garnet-structure ferrites. Garnet, ideally A3 B2[T04]3, is isometrie (Ia3d) with a straeture built of TO4 tetrahedra and BOe oetahedra linked by shared vertiees that form AOg dodeeahedra. The A-sites aeeommodate divalent (Ca, Mn, Fe) and trivalent (Y, REE) elements. The B-site may contain various di-, tri- (Fe, Al, Ga, Cr, Mn, In, Sc, Co), tetra- (Zr, Ti, Sn, Ru) and even pentavalent elements (Nb, Ta, Sb). The T-sites are filled with tetravalent (Si, Ge, Sn) but may be also occupied by trivalent (Al, Ga, Fe) and pentavalent (P, V, As) elements. Synthetic garnets form multicomponent solid solutions that provide opportunities for incorporating of HEW elements into the structure [149]. 

Crystalline aluminosilicates (zeolites) have pores with diameters of the order of 1 nm. The smallness and regularity of these pores account for shape-selectivity and many of the important applications of zeolites in acid catalysis. Zeolite frameworks consist of linked TO4 tetrahedra (T = Si, Al). The zeolites that have been most often investigated as supports for metal clusters are faujasites (zeolites X and Y), which have three-dimensional pore structures incorporating nearly spherical cages with diameters of about 1.2 nm connected by apertures that are 12-membered oxygen rings, with diameters of about 0.75 nm. Zeolite LTL, which is used as the support for industrial aromatization catalysts, has a two-dimensional pore structure consisting... 

The frameworks of molecular sieves are constructed from 4-connected TO4 tetrahedra. Deem and Newsam developed an approach to optimize an initially arbitrary T-atom configuration with respect to a cost function based on the T—T distances, T—T—T angles, and number of first-neighbor T-atoms, by simulated annealing using the Monte Carlo method.147,211 This method could be used to solve 4-connected crystal structures, as well as to predict unknown hypothetical structures. 

Zeolites molecular sieves are porous inorganic crystals built from TO4 tetrahedra. In zeolites, T represents silicon or aluminium atom. Ibe overall composition of zeolites is given by the formula as follows ... 

Translational proton motion through the zeolite lattice appears to be much less likely because the proton has to leave the AlH-O-Si site and move to Si-O-Si sites that have a lower proton affinity. Hence, it is expected that the barriers for intersite jumps that occur between neighboring TO4 tetrahedra with T = Ah, Si are... 

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