Determination of phases of complex scattering amplitudes and two-particle structure factors by investigating diffractograms of thin amorphous foils

Abstract

In this study we analyse diffractograms of elastically filtered images of thin amorphous foils of carbon, silicon and germanium using the weak object approximation. The use of this approximation leads to a contrast transfer function containing a phase η(u) depending on the spatial frequency u. Furthermore, the derivative of this phase is included in the envelope function of the contrast transfer function. The phase can be attributed to the breakdown of the first-order Born approximation leading to complex scattering amplitudes characterized by this phase η(u). We analyse contrast transfer characteristics to determine the phase of complex scattering amplitudes of carbon, silicon and germanium as a function of spatial frequency and to measure the two-particle structure factor of the corresponding amorphous specimens. The contrast transfer characteristics were calculated from diffractograms of focal series of elastically filtered images. The phases measured show a decay with increasing spatial frequency and additional oscillations. The results for the two-particle structure factor also decay with increasing spatial frequency and contain low local maxima. Both can be attributed to voids or inhomogeneities within the amorphous structure.