A phenomenological model of fluctuation electron microscopy for a nanocrystal/amorphous composite

Fluctuation electron microscopy (FEM) is a quantitative electron microscopy technique in which we use the variance V of spatial fluctuations in nanodiffraction as a function of the diffraction vector magnitude k and real-space resolution R to detect medium-range order in amorphous materials. We have developed a model for V(k, R) from a nanocrystal/amorphous composite, which is an idealized form of the medium-range order in various amorphous materials found by previous FEM measurements. The resulting expression for V(k, R) as a function of the nanocrystal size, nanocrystal volume fraction, and the sample thickness connects the FEM signal to well-defined aspects of the material's structure, emphasizes the need for samples of controlled thickness, and explains in some cases the relative height of peaks in V(k). We give an example of interpreting FEM data in terms of this model using recent experiments on amorphous Al88Y7Fe5.