Dark field microscopy for diffraction analysis of amorphous carbon solids

Diffraction methods for determining structure in non-crystalline materials often rely solely on the determination of pair correlation functions, extracted from measurements of the diffracted intensity. A dark field image of a non-crystalline solid taken with a conventional transmission electron microscope contains phase information lost in the measurement of the diffracted intensity which can be accessed by evaluating a variance function. This variance function is defined in terms of spherical averages of the diffracted intensity and the mean square of the diffracted intensity. The latter contains higher order correlation information derived from correlations between two pairs of atoms. We examine the sensitivity of the variance function, to subtle atomic structural differences between carbon network structures. The structures have similar pair correlations, but different levels of diamond like bonding. The variance function is shown to give improved discrimination between the networks.