Lattices isomorphism

When a tetravalent ion, such as Ti4+, replaces, the Si4+ in a silicate lattice isomorphously, the generation of Brpnsted acidity is not anticipated. In fact, no experimental evidence exists for a purely Brpnsted acid-catalyzed reaction in a well-synthesized and pure sample of TS-1 and in the absence of H202. Lewis acid-catalyzed reactions can, of course, occur because of the coordinatively unsaturated Ti ions, as mentioned above (Section II.B). 

Detection of the solvent present in solvates and its interaction with the lattice (isomorphic desolvates). 

Our discussion of solids and alloys is mainly confined to the Ising model and to systems that are isomorphic to it. This model considers a periodic lattice of N sites of any given symmetry in which a spin variable. S j = 1 is associated with each site and interactions between sites are confined only to those between nearest neighbours. The total potential energy of interaction... 

The Ising model is isomorphic with the lattice gas and with the nearest-neighbour model for a binary alloy, enabling the solution for one to be transcribed into solutions for the others. The tlnee problems are thus essentially one and the same problem, which emphasizes the importance of the Ising model in developing our understanding not only of ferromagnets but other systems as well. 

Onsager s solution to the 2D Ising model in zero field (H= 0) is one of the most celebrated results in theoretical chemistry [105] it is the first example of critical exponents. Also, the solution for the Ising model can be mapped onto the lattice gas, binary alloy and a host of other systems that have Hamiltonians that are isomorphic to the Ising model Hamiltonian. 

One of the most important parameters that defines the structure and stability of inorganic crystals is their stoichiometry - the quantitative relationship between the anions and the cations [134]. Oxygen and fluorine ions, O2 and F, have very similar ionic radii of 1.36 and 1.33 A, respectively. The steric similarity enables isomorphic substitution of oxygen and fluorine ions in the anionic sub-lattice as well as the combination of complex fluoride, oxyfluoride and some oxide compounds in the same system. On the other hand, tantalum or niobium, which are the central atoms in the fluoride and oxyfluoride complexes, have identical ionic radii equal to 0.66 A. Several other cations of transition metals are also sterically similar or even identical to tantalum and niobium, which allows for certain isomorphic substitutions in the cation sublattice. 

The Laue data (Table I) contain first-order reflections only from planes with all indices odd. This fact, together with the absence of reflections with mixed indices on oscillation photographs, shows the lattice to be face-centered. Of the two face-centered space groups isomorphous with point group Td, Td and Td, the latter requires that no odd-order reflections occur from planes (khl) with h — lc. The numerous observed... 

Isomorphism. TiC is isomorphous with TiN and TiO. Thus oxygen and nitrogen as impurities, or as deliberate addition, can substitute for carbon to form binary and ternary solid solutions over a wide range of homogeneity. These solutions may be considered as Ti(C,N,0) mixed crystals. TiC forms solid solutions with the other monocarbides of Group IV and V. It is the host lattice for WC.li" ... 

Additional observations reflect on the high stability of the DTU host lattice and illustrate its versatile capability to form clathrates with different guests. The crystalline 1 1 complexes of DTU with diethylether (Fig. 29) and diethylamine are isomorphous with the structure of the propanamide adduct (Fig. 24). However, in these structures the hydrogen bonds do not form a continuous pattern but are, rather, confined to... 

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