Phase tetrahedric

Haber (59, 113) has reported data supporting the concept that the low-valence cation is responsible for propylene activation. He studied the kinetics of catalyst reduction for a-, /)-, and y-bismuth molybdates using both hydrogen and propylene as reductants. Because the coordination of molybdenum varies among the three phases (tetrahedral in a phase, tetrahedral and octahedral in /3 phase, and octahedral in y phase), the... 

Gil-Av, E., Feibush, B., and Charles-Sigler, R. (1966) Separation of enantiomers by gas liquid chromatography with an optically active stationary phase. Tetrahedr. Lett. 1009-1015. 

Fig. 55. Four-phase tetrahedral envelopes adjacent to the M-saturated YBajjCui. M jjOf, solid solutions for M = Fe, Co and Mg/Ni/Zn, in subsolidus (pseudoquaternary) tetrahedral phase diagrams, as seen by room-temperature PXD after firing at 900°C in oxygen.

There are two classes of solids that are not crystalline, that is, p(r) is not periodic. The more familiar one is a glass, for which there are again two models, which may be called the random network and tlie random packing of hard spheres. An example of the first is silica glass or fiised quartz. It consists of tetrahedral SiO groups that are linked at their vertices by Si-O-Si bonds, but, unlike the various crystalline phases of Si02, there is no systematic relation between... 

Mujica A and R J Needs 1993. First-principles Calculations of the Structural Properties, Stability, aind Band Structure of Complex Tetrahedral Phases of Germanium ST12 and BC8. Physical Review B48 17010-17017. 

Ab initio, gas phase calculations found two minima and one maximum for the reaction coordinate, leading to an exothermic formation of the tetrahedral complex. Oneminimum is an ion-dipole... 

The pentahalides of phosphorus, PX, in the gas phase exhibit varying tendencies to dissociate into trihaUde and halogen. InstabiUty increases with increasing ionic radius of the halogen. The pentafluoride appears to be thermally stable. Dissociation of the pentachloride, a few percent at 100°C and 101.3 kPa (1 atm), is essentially completed at 300°C (36). The pentabromide is partially dissociated in the Hquid state and totally dissociated above ca 35°C (39). Pentaiodide does not exist. The molecules of PF and PCl in the vapor phase are trigonal bipyramids. In the crystalline state, both pentachloride and pentabromide have ionic stmctures, ie, [PClJ IPClg] and [PBr4]" PBrJ , respectively. The PX" 4 cations are tetrahedral and the PX anion is octahedral (36,37). 

Properties. Physical properties of titanium tetrachloride are given ia Table 17. la the vapor phase, the titanium tetrachloride molecule is tetrahedral and has a Ti—Cl bond length of 218 pm. The regular tetrahedral coordination is retained ia the soHd, although each of the chlorines is crystaHographicaHy differeat ia the monoclinic lattice (131). 

Zirconium tetrachloride is a tetrahedral monomer in the gas phase, but the soHd is a polymer of ZrCl octahedra arranged in zigzag chains in such a way that each zirconium has two pairs of bridging chlorine anions and two terminal or t-chlorine anions. The octahedra are distorted with unequal Zr—Cl bridge bonds of 0.2498 and 0.2655 nm. The physical properties of zirconium tetrachloride are given in Table 7. 

The extent of substitution of magnesium and siUcon by other cations in the chrysotile stmcture is limited by the stmctural strain that would result from replacement with ions having inappropriate radii. In the octahedral layer (bmcite), magnesium can be substituted by several divalent ions, Fe ", Mn, or Ni ". In the tetrahedral layer, siUcon may be replaced by Fe " or Al ", leaving an anionic vacancy. Most of the other elements which are found in vein fiber samples, or in industrial asbestos fibers, are associated with interstitial mineral phases. Typical compositions of bulk chrysotile fibers from different locations are given in Table 3. 

Figure 1.11 The formation of metal clusters during the nucleation of a new phase. The co-ordination is first tetrahedral, leading to 5-fold symmetry, until the 13-atom icosahedron is formed which transforms into the cubic icosahedron of the stable phase...

The higher solubility of carbon in y-iron than in a-iroii is because the face-ceiiued lattice can accommodate carbon atoms in slightly expanded octahedral holes, but the body-centred lattice can only accommodate a much smaller carbon concentration in specially located, distorted tetrahedral holes. It follows that the formation of fenite together with cementite by eutectoid composition of austenite, leads to an increase in volume of the metal with accompanying compressive stresses at die interface between these two phases. 

The most stable conformation of cyclohexane is the chair. Electron diffraction studies in the gas phase reveal a slight flattening of the chair compared with the geometry obtained when tetrahedral molecular models are used. The torsion angles are 55.9°, compared with 60° for the ideal chair conformation, and the axial C—H bonds are not perfectly parallel but are oriented outward by about 7°. The length of the C—C bonds is 1.528 A, the length of the C—H bonds is 1.119 A, and the C—C—C angles are 111.05°. ... 

Aldehydes and ketones undergo reversible addition reactions with alcohols. The product of addition of one mole of alcohol to an aldehyde or ketone is referred to as a hemiacetal or hemiketal, respectively. Dehydration followed by addition of a second molecule of alcohol gives an acetal or ketal. This second phase of the process can be catalyzed only by acids, since a necessary step is elimination of hydroxide (as water) from the tetrahedral intermediate. There is no low-energy mechanism for base assistance of this... 

Phosphorus (like C and S) exists in many allotropic modifications which reflect the variety of ways of achieving catenation. At least five crystalline polymorphs are known and there are also several amorphous or vitreous forms (see Fig. 12.3). All forms, however, melt to give the same liquid which consists of symmetrical P4 tetrahedral molecules, P-P 225 pm. The same molecular form exists in the gas phase (P-P 221pm), but at high temperatures (above 800°C) and low pressures P4 is in equilibrium with the diatomic form P=P (189.5 pm). At atmospheric pressure, dissociation of P4 into 2P2 reaches 50% at 1800°C and dissociation of P2 into 2P reaches 50% at 2800°. 

In the vapour phase As is known to exist as tetrahedral Asa molecules with (As-As 243.5 pm) and when the element is sublimed, a yellow, cubic modification is obtained which probably also contains Asa units though the structure has not yet been determined because the crystals decompose in the X-ray beam. The mineral arsenolamprite is another polymorph, e-As it is possibly isostructural with metallic orthorhombic P. 

Water is a volatile, mobile liquid with many curious properties, most of which can be ascribed to extensive H bonding (p. 52). In the gas phase the H2O molecule has a bond angle of 104.5° (close to tetrahedral) and an interatomic distance of 95.7 pm. The dipole moment is 1.84 D. Some properties of liquid water are summarized in Table 14.8 together with those of heavy water... 

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