Preferred orientation axis

The needle-like crystallites, when packed into a flat sample, will also tend to align parallel to the surface. However, the preferred orientation axis, which in this case coincides with the elongated axes of the needles, will be parallel to the sample surface. In addition to the nearly unrestricted distribution of needles axes in the plane parallel to the sample surface (which becomes nearly ideally random when the sample spins around an axis perpendicular to its surface), each needle may be freely rotated around its longest direction. Hence, if the axis of the needle coincides, for example, with the vector d. then reflections from reciprocal lattice points with vectors parallel to will be suppressed to a greater extent and reflections from reciprocal lattice points with vectors perpendicular to d / will be strongly increased. This example describes the so-called in-plane preferred orientation. 

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). 

Similarly, the shortest unit cell dimension is usually parallel to the chainlike formations in the structure (if any) and, simultaneously, to the longest dimension of the needle-like crystallites. In NiMnOaCOH), the a-axis is much shorter than the two others the needle-like crystallites are elongated along the [100] direction, with the additional preferred orientation axis [010] perpendicular to the flat sides of the needles (see the inset in Figure 6.23). 

The selection of the preferred orientation axis direction was based on the lowest residuals after attempting to refine texture in the March-Dollase approximation along the three major crystallographic axes. 

Fig. 1. Orientational order of the molecules in a liquid crystal. 9 is the angle between the long axis of a molecule and the direction of preferred orientation...

A summary of physical and chemical constants for beryUium is compUed ia Table 1 (3—7). One of the more important characteristics of beryUium is its pronounced anisotropy resulting from the close-packed hexagonal crystal stmcture. This factor must be considered for any property that is known or suspected to be stmcture sensitive. As an example, the thermal expansion coefficient at 273 K of siagle-crystal beryUium was measured (8) as 10.6 x 10 paraUel to the i -axis and 7.7 x 10 paraUel to the i -axis. The actual expansion of polycrystalline metal then becomes a function of the degree of preferred orientation present and the direction of measurement ia wrought beryUium. 

For a removal attempt a molecule is selected irrespective of its orientation. To enhance the efficiency of addition attempts in cases where the system possesses a high degree of orientational order, the orientation of the molecule to be added is selected in a biased way from a distribution function. For a system of linear molecules this distribution, say, g u n ), depends on the unit vector u parallel to the molecule s symmetry axis (the so-called microscopic director [70,71]) and on the macroscopic director h which is a measure of the average orientation in the entire sample [72]. The distribution g can be chosen in various ways, depending on the physical nature of the fluid (see below). However, g u n ) must be normalized to one [73,74]. In other words, an addition is attempted with a preferred orientation of the molecule determined by the macroscopic director n of the entire simulation cell. The position of the center of mass of the molecule is again chosen randomly. According to the principle of detailed balance the probability for a realization of an addition attempt is given by [73]... 

PET fibers in final form are semi-crystalline polymeric objects of an axial orientation of structural elements, characterized by the rotational symmetry of their location in relation to the geometrical axis of the fiber. The semi-crystalline character manifests itself in the occurrence of three qualitatively different polymeric phases crystalline phase, intermediate phase (the so-called mes-ophase), and amorphous phase. When considering the fine structure, attention should be paid to its three fundamental aspects morphological structure, in other words, super- or suprastructure microstructure and preferred orientation. 

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>. 

The mathematical expression of N(6, q>, i//) is complex but, fortunately, it can be simplified for systems displaying some symmetry. Two levels of symmetry have to be considered. The first is relative to the statistical distribution of structural units orientation. For example, if the distribution is centrosymmetric, all the D(mn coefficients are equal to 0 for odd ( values. Since this is almost always the case, only u(mn coefficients with even t will be considered herein. In addition, if the (X, Y), (Y, Z), and (X, Z) planes are all statistical symmetry elements, m should also be even otherwise = 0 [1]. In this chapter, biaxial and uniaxial statistical symmetries are more specifically considered. The second type of symmetry is inherent to the structural unit itself. For example, the structural units may have an orthorhombic symmetry (point group symmetry D2) which requires that n is even otherwise <>tmn = 0 [1], In this theoretical section, we will detail the equations of orientation for structural units that exhibit a cylindrical symmetry (cigar-like or rod-like), i.e., with no preferred orientation around the Oz-axis. In this case, the ODF is independent of t/z, leading to n — 0. More complex cases have been treated elsewhere [1,4]... 

Thermoplastic polymer macromolecules usually tend to become oriented (molecular chain axis aligns along the extrusion direction) upon extrusion or injection moulding. This can have implications on the mechanical and physical properties of the polymer. By orienting the sample with respect to the coordinate system of the instrument and analysing the sample with polarised Raman (or infrared) light, we are able to get information on the preferred orientation of the polymer chains (see, for example, Chapter 8). Many polymers may also exist in either an amorphous or crystalline form (degree of crystallinity usually below 50%, which is a consequence of their thermal and stress history), see, for example, Chapter 7. 

Many conformations were sampled by the usual MC procedure. The result is of course that there is no preferred orientation of the molecule. Each conformation can, however, be characterised by an instantaneous main axis this is the average direction of the chain. Then this axis is defined as a director . This director is used to subsequently determine the orientational order parameter along the chain. The order is obviously low at the chain ends, and relatively high in the middle of the chain. It was found that the order profile going from the centre of the molecules towards the tails fell off very similarly to corresponding chains (with half the chain length) in the bilayer membrane. As an example, we reproduce here the results for saturated acyl chains, in Figure 10. The conclusion is that the order of the chains found for acyl tails in the bilayer is dominated by intramolecular interactions. The intermolecular interactions due to the presence of other chains that are densely packed around such a chain,... 

This means that it is necessary to have a high degree of preferred orientation of hexagonal planes along the fiber axis if a high modulus is desired. To improve the orientation of graphite crystals, various kinds of thermal and stretching treatments. 

Directions indicated are poles of crystallographic planes contours show the density with which these crystal directions are aligned parallel to the tensile axis in multiples of the density for a sample with no preferred orientation... 

IB with the (lOO)-axis, parallel to the wire direction. It is generally found that the tips obtained by etching are much smaller than the average grain size of the crystallites composing the original wire. Thus the tips are usually part of a single crystal, almost invariably of preferred orientation with respect to the wire axis. 

Figure 9.2—Effect of the magnetic field on a nucleus with spin number of 1/2for an atom of a molecule present in solution. In the upper part of the sample tube, not influenced by the magnetic field, p has no preferred orientation with time. However, in the portion of the tube exposed to the external field, p traces the surface of a cone of revolution whose axis is aligned with B. Both possibilities are represented the projection of p is opposite or in the same direction as B.

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