Symmetry crystal structures

The theoretical studies " have been focused on TiSi2. Some attempts, with use of high-symmetry crystal structures, have been made to understand some of the other titanium silicides. This paper deals vith Ti,5Si.3. Because of the crucial interplay between structure and bonding we have studied the proposed stable low-symmetry crystal structure. This will give a better picture of the electronic structure and the bonding properties in this system. An investigation of seven members in the Ti-Si system will be presented in a future publication. ... 

Fig. 2. Structures for the solid (a) fee Cco, (b) fee MCco, (c) fee M2C60 (d) fee MsCeo, (e) hypothetical bee Ceo, (0 bet M4C60, and two structures for MeCeo (g) bee MeCeo for (M= K, Rb, Cs), and (h) fee MeCeo which is appropriate for M = Na, using the notation of Ref [42]. The notation fee, bee, and bet refer, respectively, to face centered cubic, body centered cubic, and body centered tetragonal structures. The large spheres denote Ceo molecules and the small spheres denote alkali metal ions. For fee M3C60, which has four Ceo molecules per cubic unit cell, the M atoms can either be on octahedral or tetrahedral symmetry sites. Undoped solid Ceo also exhibits the fee crystal structure, but in this case all tetrahedral and octahedral sites are unoccupied. For (g) bcc MeCeo all the M atoms are on distorted tetrahedral sites. For (f) bet M4Ceo, the dopant is also found on distorted tetrahedral sites. For (c) pertaining to small alkali metal ions such as Na, only the tetrahedral sites are occupied. For (h) we see that four Na ions can occupy an octahedral site of this fee lattice.

Fig. 10. Unpolarized Raman spectra (T = 300 K) for solid Ceo, KaCeo, RbsCeo, NaeCeo, KaCco, RbeCeo and CseCeo [92, 93], The tangential and radial modes of Ag symmetry are identified, as are the features associated with the Si substrates. From the insensitivity of these spectra to crystal structure and specific alkali metal dopant, it is concluded that the interactions between the Cao molecules are weak, as are also the interactions between the Cao anions and the alkali metal cations.

Another recent database, still in evolution, is the Linus Pauling File (covering both metals and other inorganics) and, like the Cambridge Crystallographic Database, it has a "smart software part which allows derivative information, such as the statistical distribution of structures between symmetry types, to be obtained. Such uses are described in an article about the file (Villars et al. 1998). The Linus Pauling File incorporates other data besides crystal structures, such as melting temperature, and this feature allows numerous correlations to be displayed. 

Figure 6.1 The icosahedron and some of its symmetry elements, (a) An icosahedron has 12 vertices and 20 triangular faces defined by 30 edges, (b) The preferred pentagonal pyramidal coordination polyhedron for 6-coordinate boron in icosahedral structures as it is not possible to generate an infinite three-dimensional lattice on the basis of fivefold symmetry, various distortions, translations and voids occur in the actual crystal structures, (c) The distortion angle 0, which varies from 0° to 25°, for various boron atoms in crystalline boron and metal borides.

We have performed full-potential calculations on TisSia in its proposed stable crystal structure. The enthalpy of formation obtained from these calculations agrees well with the value deduced from experiment. Due to the low crystal symmetry, the possibility of a more complex bonding character arises. The charge density in this phase differs considerably from that in the hypothetical unstable structure, so two-electron bonds can be excluded in this phase. We have also showed that the opening of a quasigap in the Si DOS has its origin in the Ti-Si interaction. 

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