Amorphous atomic scattering amplitude

Interference between X-rays scattered at different atomic centres occurs in exactly the same way as for an atom. The scattered amplitude becomes a function of an atomic distribution function. In an amorphous fluid, a gas or non-crystalline solid the function is spherically symmetrical and the scattering independent of sample orientation. It only depends on the radial distribution of scattering centres (atoms). 

Much more in ormation can be gained in this respect by recording diffraction patterns of the same amorphous material by using two different radiations, e.g. X-rays and neutrons (see e.g. Henninger and Buschert, 1967). As shown in Section 2.3.2 the effective number of electrons Kf for X-rays varies monotonously with Z, while the scattering amplitudes bf for neutrons vary irregularly with the nuclear species. If only two types of atoms are present and experimental conditions are selected in such a manner that, for instance, > Kj, but bj > fiy, then the peaks in which i-i pairs are predominant will be greatly enhanced in the X-ray RDF relative to the neutron RDF. 

The above treatment assumes a single atomic component system whereas the rare earth transition metal amorphous materials (R-T) are two component and thus three pair correlation functions, G(r), exist, one each for the possible R-R, R-T, and T-T combinations. These are lumped together to produce the observed scattered intensity function, but may be separated by experiments on isotopically substituted alloys which have different neutron scattering amplitudes, or as in the case of Co-P by separating the magnetic components using polarized neutrons (Bletry and Sadoc, 1975). 

The distribution of electrons in matter in the crystalline, amorphous, gaseous or liquid states is described by the electron density function p(r) whose value is given in units of electrons per unit volume [eA ] or [enm ]. The number of electrons contained in a volume element d is p(r)d T. This function has pronounced maxima at the centers of atoms and broad minima between them. The function also represents the X-ray scattering power per unit volume, the amplitude of the radiation scattered by the volume dh being proportional to the number of classical electrons that it contains. 

How could the amorphous structure be characterized in a way that would allow comparison to experimentally measurable quantities In the case of crystals and quasicrystals we considered scattering experiments in order to determine the signature of the structure. We will do the same here. Suppose that radiation is incident on the amorphous solid in plane wave form with a wave-vector q. Since there is no periodic or regular structure of any form in the solid, we now have to treat each atom as a point from which the incident radiation is scattered. We consider that the detector is situated at a position R well outside the solid, and that the scattered radiation arrives at the detector with a wave-vector q in this case the directions of R and q must be the same. Due to the lack of order, we have to assume that the incident wave, which has an amplitude exp(iq r ) at the position r of an atom, is scattered into a spherical wave exp(i q R — r )/ R — r . We then have to sum the contributions of all these waves at the detector to find the total amplitude A(q, q R). This procedure gives... 

Different types of interactions with the sample define different contrast images, which can be controlled via the lens system. Basically, two types of contrast are of most interest in TEM amplitude contrast (or diffraction contrast) and phase contrast. In the first case, electrons are elastically scattered by the atoms of an amorphous or crystalline or diffracted material as the Bragg condition. In this type of contrast include the thickness contrast/mass Z and the diffraction. In phase contrast, occurs the elastic scattering of electrons atoms of a crystal [12, 21]. In contrast range, bright-field or dark-field images are the most common types in TEM analysis, especially bright field. 

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