Inelasticity measures

Whilst photons have wavelengths similar to interatomic distances for crystallographic work, or energies similar to molecular vibrational energies for spectroscopic work, a neutron has both, i.e. neutrons are suitable for simultaneous elastic and inelastic measurements. 

Fig. 4. 13 Variation of inelasticity measures (a) and ( ), and the first cycle energy input E ( ), with degree of phase separation as expressed by the integrated SAXS peak intensity. Results shown are for PU2 and PUS (a), and PUS and PUIO (b). Also shown is the Mullins factor in each case (o). The lines have no significance except to guide the eye [175].

Fig. 2. Time (x) and scattering vector (Q) raqge for various scattering experiments on dynamics SANS ILL spectrometers Dll and DI7 relaxation after stepstrain, cyclic experiments, steady couette shear. Elastic neutron scattering ILL spectrometer D20, also real time experiment. Neutron Spin Echo (NSE) ILL spectrometer, inelastic measurement and classical quasielastic light scattering (QELS) (from Ref. )...

There are two broad classes of neutron scattering measurement. In diffraction measurements, the energy of the scattered radiation is not analyzed, so only the intensity versus Q is determined. Such measurements determine the structure of the sample. In a second class, the scattered energy is analyzed, so the intensity versus Q and h(0 is determined. This type of measurement is able to give structural and dynamic information about the sample, and is often called an inelastic measurement. In the special case where there are diffusive motions in the sample, which broaden the sharp incident spectrum, the term quasi-elastic is used. Neutron scattering instruments are optimized for one or the other of these types of measurement. 

Reservoirs . Figure 5.18 shows an example the left track gives the total carbon TC (black curve), derived from the inelastic measurement, but also the total inorganic carbon TIC (shaded blue) computed from carbonate minerals using capture spectroscopy elements. The green shaded difference is the total organic content TOC. The right trace shows this TOC from neutron spectroscopy compared with the red core data. 

Figure Al.7.12. Secondary electron kinetic energy distribution, obtained by measuring the scadered electrons produced by bombardment of Al(lOO) with a 170 eV electron beam. The spectrum shows the elastic peak, loss features due to the excitation of plasmons, a signal due to the emission of Al LMM Auger electrons and the inelastic tail. The exact position of the cutoff at 0 eV depends on die surface work fimction.

Radiation probes such as neutrons, x-rays and visible light are used to see the structure of physical systems tlirough elastic scattering experunents. Inelastic scattering experiments measure both the structural and dynamical correlations that exist in a physical system. For a system which is in thennodynamic equilibrium, the molecular dynamics create spatio-temporal correlations which are the manifestation of themial fluctuations around the equilibrium state. For a condensed phase system, dynamical correlations are intimately linked to its structure. For systems in equilibrium, linear response tiieory is an appropriate framework to use to inquire on the spatio-temporal correlations resulting from thennodynamic fluctuations. Appropriate response and correlation functions emerge naturally in this framework, and the role of theory is to understand these correlation fiinctions from first principles. This is the subject of section A3.3.2. 

Another specialized application of EM image contrast is mass measurement. Using the elastic dark-field image in the STEM or the inelastic image in the EETEM, a direct measurement of the scattering mass can be performed. Eor reviews on this teclmique see [60.61]. 

Egerton R F 1976 Measurement of inelastic/elastic scattering ratio for fast electrons and its use in the study of radiation damage Phys. Status Solid a 37 663-8... 

It is important to differentiate between brittie and plastic deformations within materials. With brittie materials, the behavior is predominantiy elastic until the yield point is reached, at which breakage occurs. When fracture occurs as a result of a time-dependent strain, the material behaves in an inelastic manner. Most materials tend to be inelastic. Figure 1 shows a typical stress—strain diagram. The section A—B is the elastic region where the material obeys Hooke s law, and the slope of the line is Young s modulus. C is the yield point, where plastic deformation begins. The difference in strain between the yield point C and the ultimate yield point D gives a measure of the brittieness of the material, ie, the less difference in strain, the more brittie the material. 

Energy Spectrometry (EDS) uses the photoelectric absorption of the X ray in a semiconductor crystal (silicon or germanium), with proportional conversion of the X-ray energy into charge through inelastic scattering of the photoelectron. The quantity of charge is measured by a sophisticated electronic circuit linked with a computer-based multichannel analyzer to collect the data. The EDS instrument is... 

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