Perfect parallel

The ir spectra acquired in this way are extremely sensitive to the orientation of the surface molecules. Molecules must have a significant component of a molecular vibration perpendicular to the surface to be sensed by coupling with the highly directional electric field. Molecules whose dipole moments are perfectly parallel to the surface caimot couple to the existing electric fields, and therefore, are ir transparent by this method. This selectivity of the approach for molecule dipole moments perpendicular as opposed to parallel to the surface is known as the surface selection rule of irras. 

If all the molecules are perfectly parallel, S would equal 1. In an isotropic Hquid, f 6) is constant so that < cos 0 > equals 1/3 and S is therefore 2ero. The order parameter for Hquid crystals falls somewhere between these limits and decreases somewhat with increasing temperature. 

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°. ... 

Consider the same pair of spin-i particles as above. We can choose to measure say the a component of the spin of particle 1 and the component of the spin of particle 2. If d and /3 are not perfectly parallel, then there are four possible results of two measurements tl4-2, 4-it2, 4-i4-2. Quantum mechanics predicts the probability for each of these results P)t where the probabilities... 

Fig. 17 The ultimate strength of a fibre with perfectly parallel oriented chains of finite length is determined by the strength of the secondary bonding...

This equation describes the orientation around a common axis called the director of the domain. For perfectly parallel orientation (P2) equals 1. The orientation of the directors in the solution is described by the order parameter PD. The overall orientational order of the anisotropic solution is given by... 

Table 7 Estimates of the ultimate tensile strength for perfectly parallel orientation of the chains in the polymer fibre calculated with the equation aL=2.3 f5 V(gec) and / =0.1...

Diffraction is a scattering phenomenon. When x-rays are incident on crystalline solids, they are scattered in all directions. In some of these directions, the scattered beams are completely in phase and reinforce one another to form the diffracted beams [1,2]. Bragg s law describes the conditions under which this would occur. It is assumed that a perfectly parallel and monochromatic x-ray beam, of wavelength A, is incident on a crystalline sample at an angle 0. Diffraction will occur if... 

In agreement with the small correlation coefficient, the eigenvectors are nearly perfectly parallel to the coordinate axis. Using tables, we find... 

Consider a single-crystal its crystal structure belongs to one of the 32 point groups and prepare a thin foil for electron microscopy with the shape of a perfect parallel slab. Depending on the way this slab is cut from the single-crystal, 31 different types of specimen can be obtained if symmetry elements are taken into account. These 31 types of specimen will give 31 different types of diffraction pattern named diffraction groups. 

Equations (2.75) and (2.76) represent two extremes. The former applies to a perfectly monochromatic beam incident on a perfectly parallel, smooth slab (although perfection in this sense is not absolute but lies within certain tolerance limits). On the other hand, the latter equation is appropriate to what might be called the perfectly imperfect case a slab-beam combination that has been carefully prepared to eliminate all interference effects. Theory has little to say about cases intermediate between these two extremes. Thus, if quantitative data are to be extracted from transmission measurements, some care must be... 

BARYTOCALCITE. This mineral is a carbonate of barium and calcium il crystallizes in the monoclinic system but occurs massive as well. Il lias a perfect cleavage parallel to the prism and one, less perfect, parallel to the base fracture, sub-conchoidal brittle hardness, 4 specific gravity, 3.66-3.71 luster, vitreous color, white or gray or may be greenish or yellowish transparent to translucent. Barytocalcite is found in Cumberland. England, associated with barite and fluorite. 

Fig. 5. A simple semiconductor laser. It is a p-n junction in a semiconductor crystal the end laces of which are flat and perfectly parallel, thus, the faces form a pair of sendreflecliag mirrors tliat bounce plioious back anJ forth llirough tlie active layer of thecrystal. Current injection causes photons to arise by spontaneous emission. Those photons traversing the semiconductor cause an avalanche of stimulated emission. Refleclious at the mirrors are self-rednforcing provided that the wavelength of the photon fits evenly into the length of the laser. See also Fig. 6...

Oriented, polycrystalline specimens. If, for example, all Az = A = 0 the array would be a three-dimensionally ordered domain i.e. a "single crystal". The most highly organized fibers are ones in which many such domains are oriented with only the helix axes parallel. As I indicated above, such fibers provide X-ray diffraction patterns like those from a rotated single crystal. The not-quite-perfect parallelism of the domains causes the intensity to be distributed along arcs instead of concentrated in spots (see Fig. 2). 

Crystallinity refers to a regular, ordered, three-dimensional crystal lattice portion of a polymer (Kroschwitz, 1990) where the polymer chains align themselves in perfect parallel array. There are no purely crystalline polymers, as all polymers, even so-called crystalline polymers, have some portion of amorphous content. Nonetheless, crystalline regions of polymers can form up to 98% of the polymer structure (Rosen, 1993) and have consequent large impacts on mechanical behavior. 

Figure 1 shows an experimental image of a T-0 layer silicate (lizardite). The 0.7-nm periodicity is clearly apparent, and no subperiodicities (<0.7 nm) or superperiodicities (>0.7 nm) can be detected. This image was obtained at or near Scherzer focus, and the crystal was oriented such that the basal planes were perfectly parallel to the electron beam, as determined by electron diffraction patterns of the areas from which the images were obtained. Thus, this image was taken under nearly ideal conditions in that both the focus conditions and orientation were carefully controlled. 

Coupling is largest at 180° the Karplus relationship J vs. dihedral angle when the orbitals of the two C-H bonds are perfectly parallel... 

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