Diffraction cylinder

Several levels of interpretation have been proposed in the literature [9,16-19]. The 00./ reflexions are attributed to diffraction by the sets of parallel c-planes tangent to the cylinders in the walls as seen edge on along the beam direction their positions are independent of the direction of incidence of the electron beam. 

Figure 7-44 shows the sequence of events involved in diffraction of a blast vave about a circular cylinder (Bishop and Rowe 1967). In these figures the shock fronts are sho m as thick lines and their direction of movement by arrows normal to the shock front. In Figure 1.13a, the incident shock 1 and reflected shock are joined to the cylinder surface by a Mach stem M. R is now much weaker and is omitted in succeeding figures. 

Some virus particles have their protein subunits symmetrically packed in a helical array, forming hollow cylinders. The tobacco mosaic virus (TMV) is the classic example. X-ray diffraction data and electron micrographs have revealed that 16 subunits per turn of the helix project from a central axial hole that runs the length of the particle. The nucleic acid does not lie in this hole, but is embedded into ridges on the inside of each subunit and describes its own helix from one end of the particle to the other. 

Fig. 5. Image and optical diffraction pattern of praseodymium-induced crystals, (A). Crystallization was induced with 8 PrCU. Doublet tracks so prominent in vanadate-induced crystals are not evident in crystals induced with lanthanides. This results in an approximate halving of the A-axis of the unit cell. Magnification x 222000. (B) The image of the superimposed top and bottom lattices of the flattened cylinder give rise to two separate diffraction patterns. (C) Projection map of praseodymium-induced crystals. Map scale 0.55 mm per A. From Dux et al. [119].

Recently, a low-resolution model of the chromatin core particle has been derived from a combination of single-crystal X-ray diffraction and electron microscopic data (Finch et al., 1977). The particle is described as a flat cylinder 110 A in diameter and 57 A in height. A similar shape and similar dimensions were found to be consistent with the low-angle neutron scattering from core particles in solution (Pardon et al., 1977 Suau et al., 1977). Some conclusions may be drawn concerning the conformation of the DNA. Presumably, the strong 28 A periodicity apparent in the crystal data (Finch et al., 1977) corresponds to the pitch of the DNA superhelix wound about the histone core. X-Ray and spectroscopic data suggest that the DNA super-... 

In Chapter 8 we shall derive the field scattered by an infinite cylinder of arbitrary radius and refractive index we shall also consider scattering by a finite cylinder in the diffraction theory approximation. Although the finite cylinder scattering problem is not exactly soluble, we can obtain analytical expressions for the amplitude scattering matrix elements in the Rayleigh-Gan s approximation. 

Although we have repeatedly referred to an infinite cylinder, it is clear that no such cylinder exists except as an idealization. So what we really have in mind is a cylinder long compared with its diameter. Later in this section we shall try to acquire some insight into how long a cylinder must be before it is effectively infinite by considering scattering in the diffraction theory approximation. 

Equation (8.43) provides us with an approximate criterion, subject to the limitations of diffraction theory, for when a finite cylinder may be regarded as effectively infinite if R > 10, say, there will be comparatively little light scattered in directions other than those in a plane perpendicular to the cylinder axis. The greater is R, the more the scattered light is concentrated in this plane in the limit of indefinitely large R, no light is scattered in directions other than in this plane. We may show this as follows. The phase function may be written in the form p(0, ) = G(0, )F(0, ), where... 

We need consider only scattering directions in the plane = tt/2 (or < > = 377/2) because p vanishes outside this plane we also have 0 = 0 when = 77/2 and 0 = - 6 when = 377/2, where 0 = 0 is the forward direction. Thus, we may take the phase function for scattering by an infinite cylinder in the diffraction theory approximation to be... 

The phase function (8.44) vanishes in the backward direction (0 = 77) and at those angles for which sin0 = mr/x, where n is an integer. This gives us a means for estimating the diameter of cylinders sufficiently large that diffraction theory is a good approximation because sin 01 < 1, the diameter d is... 

Figure 8.10 Phase function for scattering of unpolarized light by an infinite cylinder. The arrows indicate minima according to diffraction theory.

Due to the polish of the walls of the cylinders used, a distinct diffraction pattern can be observed in the ocular 201). A photograph of this pattern is shown in Fig. 6.2 a. A more detailed discussion of this pattern will be given below. For the moment it suffices to state that the central (zero order) maximum can completely be extinguished by crossing the... 

The structure of PBT fibres, has not been completely resolved although efforts are continuing using diffraction analysis, For example Adams et al. 95) have interpreted the x-ray diffraction patterns of oriented PBT fibres in terms of a nematic arrangement of molecules which are treated as periodic cylinders packed in an hexagonal array. The cylinders are oriented parallel to each other but are arbitrarily displaced axially. Unfortunately although the model explains many features of the diffraction pattern it predicts a fibre density which is well below the observed experimental value. 

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