Wavevector scattered

Small-angle neutron scattering data lit to the Debye function multiplied by a zero wavevector scattering. Data are for 0.31% (circles), 0.63% (squares), 0.93% (triangles), and 1.19% (upside down triangles) PMMA with... 

Unlike the typical laser source, the zero-point blackbody field is spectrally white , providing all colours, CO2, that seek out all co - CO2 = coj resonances available in a given sample. Thus all possible Raman lines can be seen with a single incident source at tOp Such multiplex capability is now found in the Class II spectroscopies where broadband excitation is obtained either by using modeless lasers, or a femtosecond pulse, which on first principles must be spectrally broad [32]. Another distinction between a coherent laser source and the blackbody radiation is that the zero-point field is spatially isotropic. By perfonuing the simple wavevector algebra for SR, we find that the scattered radiation is isotropic as well. This concept of spatial incoherence will be used to explain a certain stimulated Raman scattering event in a subsequent section. 

The Maxwell theory of X-ray scattering by stable systems, both solids and liquids, is described in many textbooks. A simple and compact presentation is given in Chapter 15 of Electrodynamics of Continuous Media [20]. The incident electric and magnetic X-ray helds are plane waves Ex(r, f) = Exo exp[i(q r — fixO] H(r, t) = H o exp[/(q r — fixO] with a spatially and temporally constant amplitude. The electric field Ex(r, t) induces a forced oscillation of the electrons in the body. They then act as elementary antennas emitting the scattered X-ray radiation. For many purposes, the electrons may be considered to be free. One then finds that the intensity /x(q) of the X-ray radiation scattered along the wavevector q is... 

For times less than the Rouse time of an entanglement segment, Tg and short distances, the chain behaves as if it were free since no section has moved far enough to be strongly affected by the tube constraint. The characteristic decay-rate of the scattering function at wavevector k is dominated by the Rouse-time of chain segments whose size is the order of k % k. A detailed calculation gives for t % [2]... 

The zone axis coordinate system can be used for specifying the diffraction geometry the incident beam direction and crystal orientation. In this coordinate, an incident beam of wavevector K is specified by its tangential component on x-y plan = k x + k y, and its diffracted beam at Kt+gt, for small angle scatterings. For each point inside the CBED disk of g, the intensity is given by... 

Figure 1.3 The addition of waves scattered by an angle 2 from an atom at the origin and one at a vector r from the origin. The wavevectors k q and k jj are in the directions of the incident and diffracted beams, respectively, and k o = k h =l/...

Scattered waves from different atoms are nearly parallel. We label these with the single wavevector k jj. 

The Fermi surface plays an important role in the theory of metals. It is defined by the reciprocal-space wavevectors of the electrons with largest kinetic energy, and is the highest occupied molecular orbital (HOMO) in molecular orbital theory. For a free electron gas, the Fermi surface is spherical, that is, the kinetic energy of the electrons is only dependent on the magnitude, not on the direction of the wavevector. In a free electron gas the electrons are completely delocalized and will not contribute to the intensity of the Bragg reflections. As a result, an accurate scale factor may not be obtainable from a least-squares refinement with neutral atom scattering factors. 

Figure 1.5. (a) Wavevector dependence of scattering intensity [10] at different times (b) time dependence of integrated intensity [10] (c) wavevector... 

As discussed in Section II, measured excess scattering intensity, after a melt is cooled below its melting point, increases exponentially with time at all scattering wavevectors and the inverse of niax (at which intensity is a maximum) diverges as These observations are similar to those... 

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