Inelastic incoherent scattering

In the previous section the elastic scattering by a spherical particle was treated classically. Of course, ultimately the photons incident on the particle are scattered by the molecules that comprise the particle. The scattered photons remain linked in phase and interfere coherently with the incident radiation and that scattered by the other molecules. The standard classical theory of elastic light scattering described in Sect.4.2 treats the process as a boundary value problem. 

In the inelastic scattering considered here the scattered radiation arises from molecular transitions and has a frequency (and wavelength) that is different from the incident radiation. It is assumed in what follows that the inelastically scattered radiation can be measured independently of the incident and elastically scattered components at the exciting frequency by means of filters or a monochromator. 

The inelastically scattered photons may or may not be scattered in phase. If they retain a phase relationship with one another the scattered radiation is coherent. If the inelastically scattered photons are emitted with random phases, as in spontaneous Raman and fluorescence, the radiation is said to be incoherently scattered. Because incoherent scattering seems to have the most immediate potential for applications in aerosol studies it will be emphasized in what follows. However, the case of coherent scattering by molecules embedded in particles is also of potential significance and will also be considered briefly in the next section. 

Before considering the effects of the particle on the inelastic scattering by a molecule, let us consider the radiation pattern to be assumed for the active molecule. In order to emphasize, in this section, the effects of the optical and geometrical properties of the particle, a simple model is assumed in which the active molecule emits the photons through electric-dipole transitions and the molecule is assumed to be isotropically polarizable, i.e., its dipole moment p is given by 

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It is important to note that expression (23) can be applied to the crystalline phase intensities only if we include, in the first integral, its own smooth diffuse background and not just the intensity belonging to the crystalline peaks. In fact, a pure crystalline sample also has a smooth background due to the incoherent inelastic scattering (i.e. Compton scattering), the TDS, disorder scattering and, very often, unresolved tails of overlapped peaks. 

D.H. Johnson, C.V. Bemey, S. Yip S.-H. Chen (1979). J. Chem. Phys., 71, 292-297. Analysis of neutron incoherent inelastic scattering of normal and deuterated formic acid. 1. Planar chain model. 

P.S. Goyal, B.C. Boland, J. Penfold, A.D. Taylor J. Tomkinson (1987). In Dynamics of Molecular Crystals, (Ed.) J. Lascombe, Elsevier, Amsterdam, 429-434. Higher librational modes of the NH ion in ammonium halides high resolution incoherent inelastic scattering spectra. 

Incoherent inelastic scattering from a proton in a harmonic potential well the Einstein oscillator model... 

Q> X F (Q, t). When we take the Fourier transforms, we have the convolution of the incoherent inelastic scattering functions for the three types of motion ... 

The terms elastic and inelastic scattering of electrons describe that which results in no loss of energy and some measureable loss of energy respectively. If the incident electron beam is coherent (i.e. the electrons are in phase) and of a fixed wavelength, then elastically scattered electrons remain coherent and inelastic electrons are usually incoherent. 

Ruffle, S. V. Michalarias, I. Ei, ].-C. Ford, R. C. Inelastic Incoherent Neutron Scattering Studies of Water Interacting with Biological Macromolecules. /. Am. Chem. Soc. 2002, 124, 565-569. 

Clarke, N.S. Hall, P.G. (1992) Adsorption of water vapour by iron oxides. 3. Inelastic incoherent neutron scattering from water adsorbed on magnetite Evidence for an icelike structure. Langmuir 8 645-649... 

Figure 2.4 Different types of interactions of electrons with a solid 1, X-ray or optical photons 2, back-scattered electrons 3, secondary electrons 4, coherent elastic scattering 5, inelastic scattering 6, incoherent elastic scattering.

Incoherent inelastic neutron scattering is efficient in detecting M—H vibrations because the intensity of scattering is proportional to the square of the atomic vibrational amplitude (oc 1/atomic mass) and the scattering cross section (moderately high for H). HCo(CO)4 and H3M3(CO)12 (M = Mn and Re) have been studied, for example.93... 

The above molecular dynamics results have been confirmed by incoherent inelastic neutron scattering (IINS) measurements on xenon hydrate (Tse et al., 2001 Gutt et al., 2002). In earlier measurements on methane hydrate, the dominant... 

S 1(q) characterizes the so-called incoherent scattering, while L 1(q) is related to the total cross section of all the inelastic scattering processes. With q —> 0, becomes the sum of squares of dipole matrix elements ... 

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