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C/a ratio

The detailed first principles study of the three stable polymorphs has been performed recently using the LCAO technique The main drawback of that work is that no cell optimization was performed for anatase or brookite. The energy-volume curves that were used to calculate the bulk modulus, B, and its pressure derivative, B, have been produced by varying the volume with the c/a ratio and fractional atomic coor nates being fixed at experimental values which makes results unreliable. [Pg.20]

Fig. 3 Total energy of CuZn for different c/a ratios and constant volume (a). Binding energy versus volume curves (b) for fct (circle) and B2 (square) unit cell. Fig. 3 Total energy of CuZn for different c/a ratios and constant volume (a). Binding energy versus volume curves (b) for fct (circle) and B2 (square) unit cell.
Table 3 Elastic constants and bulk moduli for hexagonal close-packed elements. Comparison is made between the results of our tight-binding parametrization (TB) and experiment (Exp). The tight-binding results include internal relaxation. Calculations were performed at the experimental volume, but at the c/a ratio which minimized the energy for that volume. Note that in a hexagonal crystal, Cee = (Ch - Ci2)/2. Table 3 Elastic constants and bulk moduli for hexagonal close-packed elements. Comparison is made between the results of our tight-binding parametrization (TB) and experiment (Exp). The tight-binding results include internal relaxation. Calculations were performed at the experimental volume, but at the c/a ratio which minimized the energy for that volume. Note that in a hexagonal crystal, Cee = (Ch - Ci2)/2.
In the case of Ni-Al the martensitic transformation occurs in a composition range between 62 and 67 at.% Ni where the excess Ni is accommodated randomly on the A1 sublattice. The resulting c/a ratio of the LIq structure is around 0.85, depending on composition. Below 63 at.% Ni the martensite structure has a (52) sequence of close packed planes (Zhdanov notation) which is currently denoted as 14M (formerly as 7R). At higher Ni contents this typical sequence is lost and the martensite plates are simply internally twinned without a specific periodicity. [Pg.323]

To a good approximation this structure can be regarded as f.c.c. based with (002) planes composed alternatively of Tl and Al the cubic crystallographic notation Is. therefore, commonly used. If we denote as c and a the lattice parameters In the [001) and 11001/1010) directions, respectively, the c/a ratio is 1.02 at the stoichiometric composition and Increases to 1.03 at Al-rich compositions (Duwez and Taylor 1952 Huang, et al. 1987). [Pg.355]

While the c/a ratio deviates only by about 2% from one, it is not ideal and this has significant consequences for the pseudotwin and 120° rotational fault. It results in a misfit at these interface which is compensated by a network of misfit dislocations (Kad and H2izzledine 1992). In contrast, the non-ideal c/a ratio does not invoke any misfit at ordered twins. However, the misfit dislocations present at interfaces are about fifty lattice spacings apart and thus there are large areas between them where the matching of the lamellae is coherent. The structures and... [Pg.363]

Methylmagnesium chloride has been added to various d-(4-substituted-phenyl) <5-oxo esters 15 (X = H, Cl 13, F, Cl, Br, OC11,) which provides the diastereomeric -lactones 1642. The electronic properties of the phenyl 4-substituent have no significant influence on the diastereoselectivity. Except for the 4-methoxyphenyl compound, which is unreactive even at 60 °C, a ratio of ca. 40 60 in favor of the anti-Cram product is observed at 60 "C in tetrahydrofuran as reaction solvent. Lowering the reaction temperature to 0 °C slightly increases the anti-Cram selectivity in the case of the 4-fluoro-, 4-chloro-, and 4-bromo-substituted compounds. On the other hand, a complete loss of reactivity is observed with the <5-phenyl- and <5-(4-methylphenyl)-substituted h-oxo esters. [Pg.44]

Even smaller c/a ratios are observed for the more electron-rich arsenides and antimonides (e.g. 1.39 for NiAs). Since the ideal c/a ratio of hexagonal closest-packing is 1.633, there is a considerable compression in the c direction, i.e. in the direction of the closest contacts among the metal atoms. [Pg.196]

A face-centred cubic cell (having a unit edge a0), compressed along an axis, when the reduction corresponds to a face-centred tetragonal cell with a c a ratio... [Pg.109]

Figure 7.49. A comparison between tetragonal structures (see the values of the c/a ratios). Figure 7.49. A comparison between tetragonal structures (see the values of the c/a ratios).
Ti by V up to 10% makes the system metallic, the c/a ratio of the solid solution corresponding to that of the high-temperature metallic phase of Ti203-... [Pg.343]

A transition of this kind from metal to insulator will occur when some parameter, for instance the specific volume, the c/a ratio or the composition in an alloy, changes in such a way that two bands cease to overlap, producing a full valence band and an empty conduction band with an energy gap between them (see Fig. 4.1). A simple case is that due to the change in volume of a divalent metal. In any divalent metal, if the volume increases sufficiently, an s-like valence band will separate off from a p-like conduction band, the density of states going from the form of Fig. 1.13(b) to that of Fig. 1.13(c). The most favourable case is mercury,... [Pg.20]

The c/a ratio is greater than for V02, which implies that the n band (i.e. that with d-orbital lobes in the basal plane) is more occupied than in V02 (Goodenough 1971, p. 352). But we think that if it were not ferromagnetic, the n band, in contradistinction to V02, would be wholly above the Fermi energy. The Hubbard correlation term U, however, produces localized moments for the 3d2 states, as explained in Chapter 3, and these, if oriented ferromagnetically, would just fill the tjj band. The filled band (for spin-up electrons) will now overlap the n band, allowing ferromagnetic interaction of Zener or RKK Y type between the d2 moments, as described in Chapter 3. The T2 term in the resistivity could be explained as in Chapter 2, Section 6. [Pg.193]

Fig. 7. Anisotropic thermal expansion of GdNij measured by x-ray powder diffraction (this work). The lines indicate the corresponding values of the isostructural YNij (nonmagnetic reference), scaled to coincide with GdNij at ISO K for allowing a direct comparison (the c/a ratio has not been scaled). Fig. 7. Anisotropic thermal expansion of GdNij measured by x-ray powder diffraction (this work). The lines indicate the corresponding values of the isostructural YNij (nonmagnetic reference), scaled to coincide with GdNij at ISO K for allowing a direct comparison (the c/a ratio has not been scaled).

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See also in sourсe #XX -- [ Pg.20 ]

See also in sourсe #XX -- [ Pg.210 , Pg.211 ]

See also in sourсe #XX -- [ Pg.3 , Pg.4 ]




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