T-atoms

Figure C2.12.3. Secondary building units in zeolites. Each comer represents a T-atom (Si, Al) while tire connecting lines represent oxygen bridges witli tire oxygen atom in tire middle.

An extended set of physicochemical descriptors was used in this study, including, for example, partial atomic charge and effective polari2 ability of the protons, average of electronegativities of atoms two bonds away, or maximum, T-atomic charge of atoms two bonds away. 

In th is eon text, K is the total classical energy including kinetic energy. You can then investigate the potential energy surface in a purely classical way using the positions (Rj) and velocities (V = dKi/dt) of the con stitiieri t atom s. 

The one-eenter exchange integrals that INDO adds to the CNDO schcmccan be related to th e-Slater-Condon param eters h", O. and F used to describe atomic spectra. In particular, for a set of s, p,. p,.. t, atom ie orbitals, all the on e-ecn ter in tegrals are given as ... 

T atoms is just 10 and 15 times smaller than that for H. The value Z), 2 x 10 cm /s corresponds to the rate constant of transfer between two adjacent sites, 10 s (k = 4DJd where d is the distance between equilibrium positions equal to 2.7 A). 

The assignment of (hr) - 5) vibrational modes for a linear molecule and (hr) - 6) vibrational modes for a nonlinear molecule comes from a consideration of the number of degrees of freedom in the molecule. It requires hr) coordinates to completely specify the position of all t) atoms in the molecule, and each coordinate results in a degree of freedom. Three coordinates (x, y, and z) specify the movement of the center of mass of the molecule in space. They set the translational degrees of freedom, since translational motion is associated with movement of the molecule as a whole. Two internal coordinates (angles) are required to specify the orientation of the axis of a linear molecule during rotation, while three angles are required for a nonlinear... 

To calculate the fraction of occupied space in a close-packed structure, we considei a ccp structure, e can use the radius of the atoms to find the volume of the cube and ow muc o t at volume is taken up by atoms. First, we look at how the cube is built rom t e atoms. In Fig. 5.29, we see that the corners of the cubes are at the centers of etg t atoms, n y 1/8 of each corner atom projects into the cube, so the corner atoms collectively contribute 8xi/S=1 atom to the cube. There is half an atom on each of t e six aces, so the atoms on each face contribute 6 X 1/2 = 3 atoms, giving four... 

The electronic, rotational and translational properties of the H, D and T atoms are identical. However, by virtue of the larger mass of T compared with D and H, the vibrational energy of C-H> C-D > C-T. In the transition state, one vibrational degree of freedom is lost, which leads to differences between isotopes in activation energy. This leads in turn to an isotope-dependent difference in rate - the lower the mass of the isotope, the lower the activation energy and thus the faster the rate. The kinetic isotope effects therefore have different values depending on the isotopes being compared - (rate of H-transfer) (rate of D-transfer) = 7 1 (rate of H-transfer) (rate of T-transfer) 15 1 at 25 °C. 

The natural way to seek improvement on the plain FeS2—m, hep X2 model would be to take into account the T atoms in the form of rigid spheres whose size exceeds those of the original octahedral cavities. (The clearly less realistic FeS2—m, hep X model need not be considered separatly in this connection, but it should be noted that all conclusions for this model would be virtually identical with those drawn for FeS2—m, hep X2.) However, if the only modifying influence of T was due to its attributed spherical shape, this would produce a uniform overall expansion of all cell dimensions without appreciable alterations in the axial ratios. The thus modified atomic arrangement would fit the experimental... 

Hence, in order to establish a connection between the FeS2—m, hep A2 model and the structural facts for class A, the T atoms would have to take an almost non-constrained shape. This takes us so far away from the plain hep A 2 model that it seems artificial to pursue the line any further attempts to modify this model with respect to the shape and size of A2 lead to a similar conclusion. 

In these phases, the unit cell (superstructure cell, super-cell) contains along the oaxis n pseudo-cells of T atoms and m interpenetrating pseudo-cells of X atoms. These phases (Nowotny phases) have been called chimney-ladder phases because they contain rows of atoms X (the ladder ), with variable interatomic spacing from one compound to another, which are inserted into channels ( chimneys ) in the T array. The T metals in all of the superstructures form a (3-Sn-like array (see Chapter 7) with the number of T metal atoms in the formula of the compound corresponding to the number of (3-Sn-like pseudo-cells stacked in the c direction of the super-cell. The arrangement of the atoms in these phases can be compared to that found in the structure of TiSi2. 

Two empirical rules, moreover, have been enunciated. The first rule concerns the number of valence electrons for the Nowotny, T Xm, phases formed by the late transition metals, it is that the total number of valence electrons per T atom is 14. With reference to previously cited phases we have, for instance ... 

The three-dimensional framework structure of a zeolite is formed by linking BBUs in an infinite repeating lattice. The framework structure for zeolite type A (framework code LTA) is shown in Figure 2.4. Figure 2.4a shows the T-atom connectivity. Figure 2.4b is the same view with all rings of size 6 and smaller filled in... 

Not all frameworks built from tetrahedra as described above are considered to be zeolites. Dense phases are not considered to be zeolites, only those phases with some porosity. Generally, materials with pores accessible by windows defined by six T-atoms or less (six-rings) are not considered to be zeolites. In fact, the boundary between zeolites and dense phases is somewhat nebulous. lUPAC defines [1] zeolites as a subset of microporous or mesoporous materials containing voids arranged in an ordered manner and with a free volume larger than a 0.25 nm diameter sphere. The Structure Commission of the International Zeolite Association uses the criterion of framework density (T-atoms per lOOOA ) with the maximum framework density for zeolites ranging from 19 to 21. 

Figure 2.6 Eight-ring pore in LTA framework types. O-atoms and T-atoms are represented are large (0.135nm radius) and small (0.026 nm radius) spheres respestively. The...

T-atoms in ring Maximum free aperture (nm) Typical free apertures (nm) ... 

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