Plane of scattering

Figure Bl.23.4. Schematic diagram of TOE scattermg and recoiling spectrometry (TOF-SARS) illustrating the plane of scattering fonned by the ion beam, sample and detector. TOE spectra (a) are collected with fixed...

If the Raman radiation is observed through a polarizer with its electric vector perpendicular to the plane of scattering ( c in Fig. 2.4-6) then the equation 2.4-13 changes ... 

Fig. 12. The angles involved in a polarization experiment for the case where both planes of scatterings are in the plane of the paper.

Place the particle to the origin of the coordinate system xyz. We will observe scattered light in the plane yOx (plane of scattering). The angle between the incident wave direction and the scattered wave direction will be referred to as a scattering angle d (Figures 2.1 2.5). 

Let the particle be illuminated by linearly polarized light from negative x values with its plane of polarization matching the plane of scattering (horizontally polarized light) with the electric field strength vector... 

In the case of vertically polarized incident light with its plane of polarization perpendicular to the plane of scattering (Figure 2.4), Equation 5 takes the form... 

The external reflection of infrared radiation can be used to characterize the thickness and orientation of adsorbates on metal surfaces. Buontempo and Rice [153-155] have recently extended this technique to molecules at dielectric surfaces, including Langmuir monolayers at the air-water interface. Analysis of the dichroic ratio, the ratio of reflectivity parallel to the plane of incidence (p-polarization) to that perpendicular to it (.r-polarization) allows evaluation of the molecular orientation in terms of a tilt angle and rotation around the backbone [153]. An example of the p-polarized reflection spectrum for stearyl alcohol is shown in Fig. IV-13. Unfortunately, quantitative analysis of the experimental measurements of the antisymmetric CH2 stretch for heneicosanol [153,155] stearly alcohol [154] and tetracosanoic [156] monolayers is made difflcult by the scatter in the IR peak heights. 

W L Bragg [7] observed that if a crystal was composed of copies of identical unit cells, it could then be divided in many ways into slabs with parallel, plane faces whose distributions of scattering matter were identical and that if the pathlengths travelled by waves reflected from successive, parallel planes differed by integral multiples of the... 

After propagation into the back focal plane of tire objective lens, the scattered electron wave can be expressed in tenns of the spatial frequency coordinates k as... 

Figure B2.3.5. Typical time-of-flight spectra of DF products from the F + D2 reaction [28]- The collision energies and in-plane and out-of-plane laboratory scattered angles are given in each panel. The DF product vibrational quantum number associated with each peak is indicated. Reprinted with pennission from Faiibel etal [28]. Copyright 1997 American Chemical Society.

Figure B2.3.7. Schematic apparatus of crossed molecular beam apparatus with synclirotron photoionization mass spectrometric detection of the products [12], To vary the scattering angle, the beam source assembly is rotated in the plane of the detector. (By pemrission from AIP.)...

The intensity of the vertically polarized scattered light is proportional to sin 0 which, in polar coordinates, is described by a figure 8-shaped curve centered at the origin and having maximum values of 1 at 0 = 90°, Because 0 is symmetrical with respect to the z axis, this component of scattered light is described in three dimensions by a doughnut-shaped surface in which the hole has shrunk to a point - centered symmetrically in the xy plane. 

Although the usual absorption and scattering spectroscopies caimot distinguish enantiomers, certain techniques are sensitive to optical activity in chiral molecules. These include optical rotatory dispersion (ORD), the rotation by the sample of the plane of linearly polari2ed light, used in simple polarimeters and circular dichroism (CD), the differential absorption of circularly polari2ed light. 

Figure 10 Elastic incoherent structure factors for lipid H atoms obtained from an MD simulation of a fully hydrated DPPC bilayer, and quasielastic neutron scattering experiments on DPPC bilayers at two hydration levels for (a) motion in the plane of the bilayer and (b) motion m the direction of the bilayer normal.

We finish this section by comparing our results with NMR and incoherent neutron scattering experiments on water dynamics. Self-diffusion constants on the millisecond time scale have been measured by NMR with the pulsed field gradient spin echo (PFGSE) method. Applying this technique to oriented egg phosphatidylcholine bilayers, Wassail [68] demonstrated that the water motion was highly anisotropic, with diffusion in the plane of the bilayers hundreds of times greater than out of the plane. The anisotropy of... 

Figure 18.6 Diffraction of x-rays by a crystal, (a) When a beam of x-rays (red) shines on a crystal all atoms (green) in the crystal scatter x-rays in all directions. Most of these scattered x-rays cancel out, but in certain directions (blue arrow) they reinforce each other and add up to a diffracted beam, (b) Different sets of parallel planes can be arranged through the crystal so that each corner of all unit cells is on one of the planes of the set. The diagram shows in two dimensions three simple sets of parallel lines red, blue, and green. A similar effect is seen when driving past a plantation of regularly spaced trees. One sees the trees arranged in different sets of parallel rows.

In image mode, the post-specimen lenses are set to examine the information in the transmitted signal at the image plane of the objective lens. Here, the scattered electron waves finally recombine, forming an image with recognizable details related to the sample microstructure (or atomic structure). 

Figure 1 Plane wave scattering from two consecutive iines of a one-dimensionai diffraction grating. The wave scatters in-phase when the path difference (the difference in iength of the two dotted sections) equais an integrai number of waveiengths.

The dimensionality of the diffraction problem will have a strong effect on how the diffraction pattern appears. For example in a ID problem, e.g., diffraction from a single Une of atoms spaced apart, only the component ofS in the direction along the line is constrained. For a 2D problem, e.g., the one encountered in RHEED, two components of S in the plane of the surface are constrained. For a 3D problem, e.g., X-ray scattering from a bulk crystal, three components of S are constrained. 

For a given structure, the values of S at which in-phase scattering occurs can be plotted these values make up the reciprocal lattice. The separation of the diffraction maxima is inversely proportional to the separation of the scatterers. In one dimension, the reciprocal lattice is a series of planes, perpendicular to the line of scatterers, spaced 2Jl/ apart. In two dimensions, the lattice is a 2D array of infinite rods perpendicular to the 2D plane. The rod spacings are equal to 2Jl/(atomic row spacings). In three dimensions, the lattice is a 3D lattice of points whose separation is inversely related to the separation of crystal planes. 

---