Amorphous scattering vector

In the two-phase model [6], the material is assumed to consist of randomly distributed micropores surrounded by a matrix, mainly consisting of amorphous carbon. From the scattered intensity, the scattering cross section r/ir/dn as a function of the scattering vector q can be obtained, if correlation effects between the scattering entities are neglected. Thus, for randomly distributed pores with uniform sizes the scattering cross section is related to the number Ap of micropores and the contrast between the pore phase and the carbon matrix [7] ... 

The observed diffraction pattern for PHT as obtained in a lateral scan of the detector is shown in Figure 2.21. It is essential to notice that the scattering vector in this geometry is parallel to the substrate (or the layer). It is seen that the hOO reflections, well known from bulk samples, not unexpectedly also appear for the thin layer, and also the amorphous broad peak around Q=. 4 A is present, but the 010- reflection at g= 1.67 A is totally absent. The same absence of 010 reflections was found for POT and for POPT. This result is quite significant, because it shows that in the thin layers there are no 010 planes oriented normal to the layer surface, thus the crystallographic ft-axis must... 

Figure 16. Radial distribution functions G(r) of the diamondlike amorphous carbon samples generated by tight-binding molecular dynamics (solid curve) compared with the neutron scattering data of Ref. 65 (dotted curve). The theoretical results have been convoluted with the experimental resolution corresponding to the termination of the Fourier transform at the experimental maximum scattering vector = 16 A. (From Ref. 62.)...

Random crystalline-amorphous copolymers have the tendency to aggregate in rod-like structures exhibiting a density modulation along the rod (see Sect. 5.1). The form factor appropriate for an ensemble of isotropically oriented cylinders is given by the orientational average of A(Q,R,L,a), the Fourier transform of a cylinder with a as the angle between its axis of symmetry and the scattering vector Q [55] ... 

It shall be assumed in this chapter that molecular arrangement in the bulk of solid explosives, and all amorphous and liquid explosives, has no preferred orientation direction. The diffraction patterns in this case are isotropic around the primary X-ray beam, and the vector quantity, x, can be replaced by its scalar magnitude. It is customary to speak of diffraction profiles, rather than patterns, when isotropy obtains and the diffraction profiles are derived by integration of the (circularly-symmetric) diffraction pattern over the azimuthal component of the scattering angle. 

The development of the physical chemistry of rubber was greatly aided by the clear definition of an "ideal" state for this material. An ideal rubber is an amorphous, isotropic solid. The liquidlike structure of rubber was discovered very soon after the technique of X-ray scattering was developed. An isotropic material is characterized by physical properties that do not depend on the orientation of the sample. The deformation of an isotropic solid can be characterized by only two unique moduli the modulus of compression, K, and the shear modulus, G. A solid is characterized by equilibrium dimensions that are functions of temperature, pressure, and the externally imposed constraints. It is convenient to define a shape vector, L, whose components are the length, width, and height of a rectangular parallelepiped. For a system with no external constraints, the shape vector can be expressed as ... 

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