Scattering wave vector

Fig. 3.19 Single chain dynamic structure factor Schain(Q>0/5(Q)chain from a M =80 kg/mol PEP melt at T=492 K for the following scattering wave vectors Q=0.03 A Q=0.05 A Q=0.068 A" 0=0.077 A (from above), Q=0.09 A Q=0.115 A"LThe solid lines represents a fit with Eq. 3.39. (Reprinted with permission from [43]. Copyright 2003 The American Physical Society)...

Fig. 9 Schematic diagram of the scattering geometry. The incident, reflected and scattered wave vectors are indicated by kinc, kref and kscat, respectively while PM is the photomultiplier tube and 9 and correspond to the incident and scattering angles...

Ewald s42 sphere of reflections in reciprocal space explains when and in which direction diffraction will occur. A vector k is drawn from the "origin of the reciprocal lattice" O (e.g., the center of the crystal) parallel to the incident X-ray beam, to "hit" a reciprocal lattice point A. If the vector G (or k) represents the distance between two reciprocal lattice points A and B, then in the direction O to B a scattered wave (vector k or S) will appear. Ewald drew a circle (in 2D) or a sphere (in 3D), called the sphere of reflection of radius 2%/X, around the point O diffraction occurs when this sphere intersects a reciprocal lattice point (Figs. 8.5 and 8.6). As the crystal and/ or the detector are moved, the reciprocal lattice points which cross the Ewald sphere satisfy Eq. (8.3.2) or (8.3.3), and a diffracted beam is formed in direction k. ... 

In quasi-one-dimensional conductors, the one-dimensional electron gas instability is responsible for the formation of a charge density wave (CDW) with wave vector 2kF and/or 4kF via electron-phonon coupling. Thus the measurement, in reciprocal wave vector units, of the corresponding 4 and 2kF scattering wave vectors gives the value and twice the value of the charge transfer p, respectively (e.g., see Ref. 114). 

Figure 1. USANS scattering intensity of Disp and NonDisp coatings as function of scattering wave vector q in a log-log plot. The error bars are smaller than...

The largest magnitude of scattering wave vector q occurs in the backscattering geometry ... 

The standing-wave vibrational oscillations are most easily detected by coherent scattering of a variably delayed probe pulse phase matched for diffraction with scattering wave vector qo. The oscillations give rise to spatial modulation of the dielectric tensor ... 

Fig. 1. Powder x-ray profiles of solid Ceo at atmospheric pressure (top) and 1.2-GPa hydrostatic pressure (bottom). Dots are experimental points (approximately 70 per point), and the solid curves are least-squares fits to an fee structurewith adjustable lattice constant a. The fitted relative intensities have no physical significance in this simple model. The scattered wave vector Q = 4TTsin6/X, where 0 is the Bragg angle for these profiles wavelength = 0.71 A. Indexing of the strongest peaks is indicated. The high-Q shoulder on the (311) is the weak (222) reflection the low-Q shoulder on the (111), observed to some extent in all our nominally pure Cfio samples, is presently unidentified. The variable intensity of this shoulder has litde eflfect on the lattice constant of a particular sample, so we can safely conclude that it has no effect on the compressibility derived from the present data.

For S V S2, the variationsof I and D with the scattering wave-vectors are in good agreement with the predictions of the theories of critical phenomena. These theories lead to three independent determinations of the correlation length of the critical concentration fluctuations (H). 

For S v Si, we observed variations of I with the scattering wave-vector but this was not the case for the diffusion coefficient. Furthermore, the autocorrelation function of the scattered intensity showed significant deviations from an exponential form. This indicates an increasing polydispersity of the droplets when S increases. 

Draw a sphere centered on the tail of this vector with radius 1/2. The incident wave vector Sq defines the radius of the sphere. The scattered wave vector s, also of length 1/2, points in a direction from the sample to the detector. This vector is drawn also starting from the center of the sphere and also terminates at a point on the surface. The scattering vector h = s - So completes the triangle from the tip of s to the tip of Sq, both lying on the surface of the sphere. 

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