Critical assessment of the speckle statistics in fluctuation electron microscopy and comparison to electron diffraction

Abstract

The technique of fluctuation electron microscopy (FEM) is applied to thin films of amorphous germanium and of polycrystalline gold in a transmission electron microscope. Even though the method was introduced as a tool for quantitative analysis of structural fluctuations in amorphous materials, the basic principles are applicable to any disordered specimen independent of the dimension of disorder. Hence, we extended the technique of FEM to a well-known specimen, gold, whereby it was possible to reinterpret the results of the measurements on amorphous germanium. The hollow-cone dark field images, the statistical analysis of which is the basis of FEM, are examined with respect to the effects of frequency filtering, and are compared to electron diffraction. We find that the angular dependence of the normalised variance, as measured by FEM, yields information similar to the average intensity of hollow-cone dark field image series. Both plots are basically identical to a scan through a selected-area diffraction pattern convoluted by the corresponding angular resolution function. Hence, it appears questionable whether standard FEM analysis provides more information than the classical pair distribution function, which is experimentally limited to short-range order. Frequency selective analysis of the normalised variance, however, gives supplementary information on preferred inter-atomic distances related to the medium-range order of the specimen.