Inelastic structure factor

This new factor can be regarded as an inelastic structure factor for the... 

Fig. 2. Neutron inelastic structure factors for intennultiplet transitions in praseodymium. The lines represent the calculated intensities of the Tj, Tj and transitions. The...

Nevertheless, Leggett et al. [1987] have argued, with some provisos, that [with the initial condition (O) = 1] and C(t) may be practically taken the same. If C(t) then obeys the damped oscillator equation (2.41), then the inelastic part of the structure factor has the Lorentzian form with the peaks at [Pg.25]

In this section we will discuss perturbation methods suitable for high-energy electron diffraction. For simplicity, in this section we will be concerned with only periodic structures and a transmission diffraction geometry. In the context of electron diffraction theory, the perturbation method has been extensively used and developed. Applications have been made to take into account the effects of weak beams [44, 45] inelastic scattering [46] higher-order Laue zone diffraction [47] crystal structure determination [48] and crystal structure factors refinement [38, 49]. A formal mathematical expression for the first order partial derivatives of the scattering matrix has been derived by Speer et al. [50], and a formal second order perturbation theory has been developed by Peng [22,34],... 

The dynamic calculations include all beams with interplanar distances dhki larger than 0.75 A at 120 kV acceleration voltage and thickness between 100 A and 300 A for the different zones. The structure factors have been calculated on the basis of the relativistic Hartree - Fock electron scattering factors [14]. The thermal difiuse scattering is calculated with the Debye temperature of a-PbO 481 K [15] at 293 K with mean-square vibrational amplitude

= 0.0013 A following the techniques of Radi [16]. The inelastic scattering due to single-electron excitation (SEE) is introduced on the base of real space SEE atomic absorption potentials [17]. All calculations are carried out in zero order Laue zone approximation (ZOLZ). 

Recently, the PDF method was extended to describe the local dynamics of disordered materials (Dmowski W, Vakhrushev SB, Jeong I-K, Hehlen M, Trouw F, Egami T (2006) Abstracts American conference on neutron scattering, St. Charles, IL, 18-22 June 2006, unpublished). The total PDF is obtained by the powder diffraction method so that S(Q) includes both elastic and inelastic intensities. To determine the dynamics we have to use an inelastic neutron scattering spectrometer and measure the dynamic structure factor, S(Q,a>), over a large Q and co space, and Fourier-transform along Q to obtain the dynamic PDF (DPDF). While the interpretation of the DPDF is a little... 

Detailed high-frequency (terahertz) dynamical studies of glasses have been probed by inelastic X-ray scattering (IXS) [139], The advantage of this technique is that with reliable measurements it allows determination of the so-called nonergodicity parameter f(q, T) as a function of wavevector q this quantity is defined by the long time limit of the density-density correlation function F(q, t) divided by the static structure factor [15],... 

What is accessible in an IXS experiment is the Fourier transform of F(q, t), which is called the dynamical structure factor, S(q,(t>). Thus, the nonergodicty parameter is obtained from the dynamical structure factor by taking the ratio of the elastic to inelastic contribution [139]. In the harmonic approximation for... 

Another way of probing dynamic xc effects experimentally is by inelastic X-ray scattering from bulk metals [201-203]. In this way, the so-called dynamical structure factor S q, to) can be measured which is proportional to the imaginary part of the full response function in reciprocal space. With this information at hand and with a first-principles calculation of the non-interacting response function, the connection (159) between and the response functions can be used to deduce information about / [204]. 

The direct reconstruction of a disordered system by EELS is an important technique by virtue of its wide applicability. The theory for this problem requires only simple expressions that connect the inelastic cross section with the structural characteristics of the system. The second goal of this chapter will be to develop this theory. Note that the modern source of information about distribution functions is the Fourier transform of the static structure factors for a system. 

Following Parceval s theorem [13], Eqs. (2.25) and (2.26) may be written as a relation between the second-differential inelastic scattering cross section Ig e) and the structure factors of the medium S,. For example, using (2.25) and (2.26), we obtain... 

A. Pasquarello, J. Samthein R. Car (1998). Phys. Rev. B, 57, 14133-14140. Dynamic structure factor of vitreous silica from first principles Comparison to neutron-inelastic-scattering experiments. 



---