Anisotropy factor

In crystals with the LI2 structure (the fcc-based ordered structure), there exist three independent elastic constants-in the contracted notation, Cn, C12 and 044. A set of three independent ab initio total-energy calculations (i.e. total energy as a function of strain) is required to determine these elastic constants. We have determined the bulk modulus, Cii, and C44 from distortion energies associated with uniform hydrostatic pressure, uniaxial strain and pure shear strain, respectively. The shear moduli for the 001 plane along the [100] direction and for the 110 plane along the [110] direction, are G ooi = G44 and G no = (Cu — G12), respectively. The shear anisotropy factor, A = provides a measure of the degree of anisotropy of the electronic charge... 

Table I. Experimental and calculated lattice constants a (in A), elastic constants, bulk and shear moduli (in units of 10 ) for the M3X (X = Mn, Al, Ga, Ge, Si) intermetallic series. Also listed are values of the anisotropy factor A and Poisson s ratio V. The experimental data for a are from Ref. . The experimental data for B, the elastic constants, A and v are taken from Ref. . The theoretical values for NiaSi are from Ref.. Also listed in the table are values of the polycrystalline elastic quantities-shear moduli G, Yoimg moduli (in units of and the ratio The experimental data for these quantities are from Ref. ...

The Au SG clusters were optically active in the visible and UV spectral range, with the anisotropy factors in the order of several tens to hundred parts per million. The origin of the observed optical activity in core-based electronic transitions has been previously discussed [24]. The key question is whether the gold cluster is intrinsically chiral or whether the optical activity is induced by the chiral ligation environment. The first possibility has been supported by theoretical studies performed by Garzon and... 

Figure. 1 Structural parameters variations of the evaporated and sol-gel samples for the main crystalline phases average grain dimension (a), unit cell mass modifications Am (b), lattice microstrain factor (c), lattice profile anisotropy factor AO (d).

The degree of CP absorption is usually expressed by the difference in absorption of left-and right-handed CP light (circular dichroism, A A) or by the so-called anisotropy factor g ... 

Figure 6. Form anisotropy factor vs. the degree of cross-linking...

Eqs. (3), (5) and (6) depend on the particular form of eq.( 1). If the main step interaction term in eq.(l) is proportional to rather than p, the expressions for E( /) would be different, particularly for the Mf = izH case. Whereas the variation of B(ji/2) with miscut a isstrong(atan a/cos a) for p dependence, it is weak a 1 /cos a) for p dependence. Thus a measurement of B(n/2) for several miscut surfaces, although tedious, would be a means to distinguish between those dependences. The anisotropy factor, eq.(6), would also exhibit a weaker variation with miscut for p dependence. 

The factor R may be called a diffusion anisotropy factor for the surface. For diffusion of a W on the W (110), Tsong Casanova find a diffusion anisotropy factor of 1.88 from a set of data taken at 299 K, and of 2.14 from a set of data taken at 309 K. The average is 2.01, which agrees with the theoretical value, 2, to within 0.5%. A more detailed general analysis has since then been reported,137 and diffusion anisotropy on the W (110) surface has also been observed in field emission experiments.138 It should be noted, however, that the same ratio can be expected if an adatom jumps instead in the [001] and [110] directions with an equal frequency. Thus a measurement of surface diffusion anisotropy factor alone does not establish uniquely the atomic jump directions. The atomic jump directions can, of course, be established from a measurement of the displacement distribution function in two directions as discussed in the last section. Such measurements can only be done with atomic resolution field ion microscopy. 

Fig. 11.4. Velocities of bulk and surface waves in an (001) plane the angle of propagation in the plane is relative to a [100] direction, (a) Zirconia, anisotropy factor Aan = 0.36 (b) gallium arsenide, anisotropy factor Aan = 1.83 material constants taken from Table 11.3. Bulk polarizations L, longitudinal SV, shear vertical, polarized normal to the (001) plane SH, shear horizontal, polarized in the (001) plane. Surface modes R, Rayleigh, slower than any bulk wave in that propagation direction PS, pseudo-surface wave, faster than one polarization of bulk shear wave propagating in...

This is identical in form to the equation for V (z) in an isotropic material. But of course R hkl (8) is quite different from any isotropic reflectance function. For a cubic material an anisotropy factor can be defined as... 

Self-diffusion along the boundary in Exercise 9.6 is highly anisotropic because diffusion along the tilt axis (parallel to the dislocations) is much greater than diffusion transverse to it (i.e., perpendicular to the dislocations but still in the boundary plane). Find an expression for the anisotropy factor,... 

The polarization measurements showed that the Cl atoms and SnCl fragments had the same anisotropy factor 3 = 0.21 0.01, which, if the dissociation is fast compared with molecular rotation, suggests that there is a angle of 46.5 0.4° between the transition dipole moment and the dissociation direction. 

Chromophores which are asymmetric by nature are characterized by the absence of a center and plane of symmetry in the group of atoms participating in the optical transition. The rotational strength of these are usually larger when compared with chromophores that become optically active due to substitution. This is demonstrated in Mason and Schnepp s8 study of trans-cyclooctene, a-pinene and /1-pi none. They pointed out that the g (anisotropy factor, g = Ae/e) value of the major bands in trans -cyclooctene is relatively high as expected for an intrinsically asymmetric chromophore when compared with the other two olefins. 

Tab. 1 Anisotropy factors of different types of inherently dissymmetric alkenes.

These compounds exhibit axial chirality, and irradiation induces isomerization of the styrene moiety, which results in simultaneous racemization of the molecule. Irradiation of methyl ester 10 (R = OMe) at 251 nm indeed gave rise to a fast and selective racemization process. However, a very low anisotropy factor (g254 = 7.5 x 10 5) was found for methyl ester 10 (R = OMe). The magnitude of g was increased... 

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