Inelastic physical principles

The ratio of elastically to inelastically scattered electrons and, thus, their importance for imaging or analytical work, can be calculated from basic physical principles consider the differential elastic scattering cross section... 

Infrared and Raman spectroscopy are related by the fact that both permit the detection of bond vibrations. Like IR spectroscopy, the spectral bands are reported in cnT1. An important difference is that the wavelength and intensity of inelastically scattered light is measured in the Raman spectroscopic method. The Raman effect causes the scattered radiation to shift according to the energies of molecular vibrations. Although Raman spectroscopy involves a physical principle different from that in IR spectroscopy, the two techniques are complementary. 

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. 

In addition to the classic waste separation methods, which are based on the difference of the corresponding physical or physicochemical property between the various constituents of the waste stream, there have been also tested methods in the past, which are based on a combination of physical properties such as density, elasticity, and friction. These methods separate organic from inorganic materials, as well as heavy and resilient from light and inelastic. Ballistic, oscillating, and bounce and slide separators are some of the devices based on these principles. Because the necessary equipment is relatively simple, under certain materials characteristics, these separators could be used in relatively easy and low-cost waste recovery. 

To illustrate how thermodynamic principles can be used to formulate physical laws, let us consider the particular case of the inelastic behaviour of solids. The classic partition ... 

Phonon dispersion curves w(q) can be measured by inelastic neutron scattering techniques this important method will be discussed in [1.35]. The curves determined by experiments are mainly of interest because they provide chance of testing various models of interatomic forces. The forces between the atoms are governed by the electronic structure of the atoms involved, and in simple cases it is possible to derive force constants from "first principles" which are based on the electronic wave functions [4.1-5]. With the exception of some qualitative remarks about metals, we shall not discuss these microscopic models here but consider only certain phenomenological models for the interatomic forces. A good model should contain only a few, but physically meaningful, parameters. 

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