A quantitative measure of medium-range order in amorphous materials from transmission electron micrographs

We propose an extension to the technique of fluctuation electron microscopy that quantitatively measures a medium-range order correlation length in amorphous materials. In both simulated images from computer-generated paracrystalline amorphous silicon models and experimental images of amorphous silicon, we find that the spatial autocorrelation function of dark-field transmission electron micrographs of amorphous materials exhibits a simple exponential decay. The decay length measures a nanometre-scale structural correlation length in the sample, although it also depends on the microscope resolution. We also propose a new interpretation of the fluctuation microscopy image variance in terms of fluctuations in local atomic pair distribution functions.