Preferred orientation magnitude

The population parameter of hydrogen has been refined to a value of 62(5) % and, therefore, the chemical composition of the material is NiMnOsHs, or NiMn03.5(0H)5, where 5 = 0.62(5). Hence, a fraction of the Mn atoms should be in the 4+ oxidation states. The latter was confirmed by the magnetic susceptibility measurements. The preferred orientation parameters, refined for both preferred orientation axes, i.e. [010] and [100], are 0.74 and 1.40, respectively, resulting in the texture factors ranging between 0.52 and 2.10, which corresponds to the preferred orientation magnitude of about 4. 

The preferred orientation correction was accounted for in two ways during the refinement. First, the March-Dollase approach with one texture axis [001] resulted in x = 1.247(2) and correction coefficients ranging from 0.52 to 1.39, which gives the preferred orientation magnitude of 2.70. Second, the 8 -order spherical harmonics expansion, which corresponds in this crystal system to six adjustable parameters (200, 400, 600, 606, 800, and 806) was attempted with the March-Dollase preferred orientation correction (i) left as is but fixed (i.e. the spherical harmonics were in addition to the March-Dollase model), or (ii) eliminated. Both ways result in practically an identical result except for the magnitudes of the coefficients. In the second case, the correction coefficients ranged from 0.61 to 1.54, which corresponds to the preferred orientation magnitude of 2.52. 

For an oriented polymer, the magnitude of the observed second moment static magnetic field H0, which can be conveniently defined by the polar and azimuthal angles A, transverse isotropy, to which the following discussion is limited, the observed second moment will depend only on the angle A, there being no preferred orientation in the plane normal to the 3 direction. The treatment follows that originally presented by McBrierty and Ward 9>. 

For a nematic LC, the preferred orientation is one in which the director is parallel everywhere. Other orientations have a free-energy distribution that depends on the elastic constants, K /. The orientational elastic constants K, K22 and K33 determine respectively splay, twist and bend deformations. Values of elastic constants in LCs are around 10 N so that free-energy difference between different orientations is of the order of 5 x 10 J m the same order of magnitude as surface energy. A thin layer of LC sandwiched between two aligned surfaces therefore adopts an orientation determined by the surfaces. This fact forms the basis of most electrooptical effects in LCs. Display devices based on LCs are discussed in Chapter 7. 

It shall be assumed in this chapter that molecular arrangement in the bulk of solid explosives, and all amorphous and liquid explosives, has no preferred orientation direction. The diffraction patterns in this case are isotropic around the primary X-ray beam, and the vector quantity, x, can be replaced by its scalar magnitude. It is customary to speak of diffraction profiles, rather than patterns, when isotropy obtains and the diffraction profiles are derived by integration of the (circularly-symmetric) diffraction pattern over the azimuthal component of the scattering angle. 

The relative magnitudes of the Tg values in the two-phase region should be related to the development of microstructure in mesophase pitch, as discussed earlier. Tg will also be a useful parameter in defining the maximum temperature at which fibres can be oxidized without molecular motion causing some decrease in extent of preferred orientation. 

For steric reasons, the preferred orientation of the addition to a monosubstituted alkene is to the unsubstituted end of the C = C bond however, the polarity of the C = C bond can influence the magnitude of the regiosectivity and this effect is dependent on the electronegativity of the substituents on the alkene. Polarity can also have a major effect on the rate of the condensation polyhaloalkyl radicals behave generally as electrophiles whose addition is retarded by electron-withdrawing and assisted by electron-donating substituents. 

If the coefficients are calculated for 1-methoxy-1,3-butadiene the termini are -1-0.3 and —0.58 (or —0.3 and -1-0.58). For acrylonitrile the coefficients are -1-0.2 and —0.66 (or —0.2 and -1-0.66). The cycloaddition reaction proceeds so that the coefficients match, in terms of both phase (essential) and coefficient magnitude -1-0.3 with -1-0.2 and —0.58 with —0.66. Thus, the preferred orientation of reactants (diene and dienophile) for the initial bonding interaction is displayed and this orientation agrees with the regioselectivity reported in Fig. 8.33. 

In Eq. 2.78 the multiplier 7 is calculated as a sum over all N symmetrically equivalent reciprocal lattice points and t is the preferred orientation parameter refined against experimental data. The magnitude of the preferred orientation parameter is defined as t = TJT, where Tx is the factor for Bragg peaks with reciprocal lattice vectors perpendicular, and T is the same for those which are parallel to the preferred orientation axis, respectively. In the case of the ellipsoidal preferred orientation function this parameter is equal to z for the needles (in-plane preferred orientation) and 1/t for platelets (axial preferred orientation). 

Here the preferred orientation parameter, represents needles and its inverse represents plates. An example of the March-Dollase preferred orientation function for needles with magnitude = 2.5 is shown in... 

The magnitude of the preferred orientation can be evaluated using the following function ... 

The magnitude of the preferred orientation is the ratio between the maximum and the minimum correction factors, which in this case, is the ratio between the correction factors for reflections whose reciprocal lattice vectors are parallel to d oro and those, which are perpendicular to d ojo, i-e. T /Tx. 

The final Rietveld refinement yields a reasonable structural model Figure 7.28), which fits nicely as a new member in the series of VaOy-based structures with vanadium oxide layers differing only by the orientations of the square pyramids and tetrahedra. A specific feature of this refinement is a strong preferred orientation along two axes, [100] and [010], with parameters Tioo = 0.76 and toio = 1.38 in a 2 to 1 ratio. The preferred orientation multipliers range from 0.58 to 2.08, which results in a total magnitude of about 4, similar to the case described in the previous section. 

Anisotropy in the upper mantle is primarily attributed to the preferred alignment of olivine and, to a lesser extent, the alignment of other upper-mantle minerals. Evidence comes from measurements on mantle xenoliths (Mainprice Silver 1993 Ben Ismail Mainprice 1998) and ophiolites (Nicolas Christensen 1987) and laboratory deformation studies (Zhang Karato 1995). These measurements help guide the interpretation of seismic observations. It is conventionally assumed that the anisotropy is c.4-5% in magnitude and has hexagonal symmetry with a horizontal synunetry axis (azimuthal anisotropy) (Mainprice Silver 1993). Numerical simulations of the lattice preferred orientation... 

Obtained on a polycrystalline sample with a considerable amount of preferred orientation. f Spontaneous moment per U atom (ref. [16]). e / . increases rapidly and non-linearly with increasing pressure, reaching 5.9 K at 11.3 kbar. h The value could be of the order of magnitude of 100. 

Magnetic resonance (ESR and NMR) studies have provided additional details about the orientational motion of the water molecules adsorbed by vermiculites. ESR spectra of Cu-vermiculite and NMR spectra of Mg- and Na-vermiculite indicate clearly that the primary solvation shells of the cations on the two-layer hydrate are octahedral complexes with a preferred orientation relative to the siloxane surface. For Cu-vermiculite, the symmetry axis through the solvation complex, Cu(H20)6 , makes an angle of about 45 with the siloxane surface on Na-vermiculite the axis through Na(H20)6 makes an angle of 65°. The value of Tc, the correlation time for the rotation of Na(H20)6 around its symmetry axis, is about 10 s at 298 K. This value is four orders of magnitude larger than Tc for a solvation complex around a monovalent cation in aqueous solution. Not quite as disparate are T2 for Na(H20)6, equal to 100 ps at 298 K, and t2 for a monovalent solvation complex in dilute aqueous solution, equal to about 5 ps at the same temperature. These data show that the siloxane surface retards the orientational motion of the water molecules. 

Basically, birefringence is the contribution to the total birefringence of two-phase materials, due to deformation of the electric field associated with a propagating ray of light at anisotropically shaped phase boundaries. The effect may also occur with isotropic particles in an isotropic medium if they dispersed with a preferred orientation. The magnitude of the effect depends on the refractive index difference between the two phases and the shape of the dispersed particles. In thermoplastic systems the two phases may be crystalline and amorphous regions, plastic matrix and microvoids, or plastic and filler. See amorphous plastic coefficient of optical stress compact disc crystalline plastic directional property, anisotropic ... 

---