Scattering vector dependence

Here G(a) is the intensity scattered by the particles with diameters between a and art-da, kfi is Boltzmann s constant, T the temperature, k the scattering vector (dependent on scattering angle and wavelength), t the correlation time and n the viscosity. To find the mass fraction distribution, F(a), we use... 

The Bragg equation shows that diffraction occurs when the scattering vector equals a reciprocal lattice vector. The scattering vector depends on the geometry of the experiment whereas the reciprocal lattice is determined by the orientation and the lattice parameters of the crystalline sample. Ewald s construction combines these two concepts in an intuitive way. A sphere of radius 1//1 is constructed and positioned in such a way that the Bragg equation is satisfied, and diffraction occurs, whenever a reciprocal lattice point coincides with the surface of the sphere (Figure 1.8). 

Fig. 2 Scattering vector dependence of scattering intensity of gelatin gel [251.

Fig. 5 Scattering vector dependence of the scattering intensity of polylacryl amide) gel prepared in the presence of polylethylene glycol) (4wt%) [28].

Fig. 6 Scattering vector dependence of the scattering intensity during the late stage spinodal decomposition of poly(y-benzyl-L-glutamate) liquid crystal gel when quench gelled from 333 K to 283 K [30].

Even though lasers are still commonly used as the source of incident radiation, static scattering does not require coherence. Therefore, other forms of radiation such as X-ray and neutrons, even when pulsed, are suitable sources. The scattering vector dependence of the intensity, /(Q), of the radiation scattered by particles has the form... 

A.G. Pelmenshchikov, E.A. Paukshtis, V.G. Stepanov, V.I. Pavlov, E.N. Yurchenko, K.G. lone, S. Beran et al.. Scattering vector dependence of mutual diffusion coefficients for rodUke micelles in aqueous sodium halide solutions. J. Phys. Chem. 93, 6720-6725 (1989)... 

FIGURE 4.4 Scattering vector dependence of static strnctnre factor. Black circles measured S(q) for the system at ( ) = 0.027. Black line calculated S q) for dispersion of monodisperse repulsive spheres. Dark gray line calculated S(q) for a repulsive system with size polydispersity only. Gray line calculated S q) for repulsive system with size and charge polydispersity. 

See Table 8.1 for the dependence of derived properties on the power of the magnitude of scattering vector H. 

S is the scattering vector, Mj is the atomic displacement parameter in this simplified notation assumed to be isotropic, 6 is the scattering angle, and 1 the wavelength of the incident radiation. The atomic displacement depends on the temperature, and hence so does the Debye-Waller factor. If an atom is modeled by a classical oscillator, then the atomic displacement would change linearly with temperature ... 

In the diffraction pattern from a crystalline solid, the positions of the diffraction maxima depend on the periodicity of the stmcmre (i.e. the dimensions of the unit cell), whereas the relative intensities of the diffraction maxima depend on the distribution of scattering matter (i.e. the atoms or molecules) within the unit cell. In the case of XRD, the scattering matter is the electron density within the unit cell. Each diffraction maximum is characterized by a unique set of integers h, k and I (Miller indices) and is defined by a scattering vector H in three-dimensional... 

Fig. 14. Temperature dependence of the scattered intensity, I, and the relaxation rate, T, for 2.5% polyacrylamide gel in water. Here T is divided by the square of the scattering vector, q2...

Here I0 is the intensity of the x-ray beam, r0 = e2/mc2 is the classical electron radius (2.82 x 10 15 m)., P(9,) is the polarization of the x-rays it depends on the angle between the polarization and the scattering vector. For horizontally polarized x-rays, it takes the form P(0, < >) = 1 - sin220 sin2t)>, where 20 is the scattering angle and < > the azimuthal angle with respect to the vertical direction. The formfactor ) is the Fourier transform of the atomic electron density ... 

Fig. 5.1. Time dependence of a typical classical trajectory in the photodissociation of C1CN — Cl 4- CN(j). (a) R(t) (solid line) is the Cl-CN separation and 7(t) (dashed line) is the orientation angle of CN with respect to the scattering vector R (for the definition of coordinates see Figure 3.1). (b) The angular momentum j(t) of CN (solid line) and the torque F1 = -dV/dj (dashed line).

Fig. 23 Angular dependence of Rayleigh ratio (Rw(q)) of segmented PNIPAM-seg-St copolymer chains in water measured from static LLS, where K is a constant, q is the scattering vector and polymer concentration (C) was 7.2 x 10-7 g/mL. The inset shows the temperature dependence of the hydrodynamic radius distribution /(Rh) determined from dynamic LLS [94]...

Fig. 38 Scattering vector (q) dependence of scattered light intensity (I) of resultant P(DEA-co-DMA) mesoglobules formed under different heating rates [139]...

Bley, F., Amilius, Z., and Lefebvre, S. (1988) Wave vector dependent kinetics of short-range ordering in 62Ni0.765Feo.235, studied by neutron diffuse scattering. Acta metall. 36, 1643-1652. 

In order to introduce some notation and definitions, we consider a polymer block with n monomers of segment length b. Defining Ti as the interdistance between two monomers i and j in that block, and Q as the scattering wave-number (often called scattering vector ), various types of correlations can be considered depending on the number of summations involved ... 

Xab appears here as a universal parameter. However, it was found experimentally to depend on a number of factors [30-33] such as temperature, molecular weight, composition, inter-monomer distance (and therefore on the scattering vector Q), isotopic constitution, tacticity, microstructure, etc. These dependencies are shortcomings of the crude RPA description. The scattered intensity (macroscopic cross section d (Q)/d 2) is given by ... 

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