The importance of averaging to interpret electron correlographs of disordered materials

The development of effective new tools for structural characterization of disordered materials and systems is becoming increasingly important as such tools provide the key to understanding, and ultimately controlling, their properties. The relatively novel technique of correlograph analysis (i.e., the approach of calculating angular autocorrelations within diffraction patterns) promises unique advantages for probing the local symmetries of disordered structures. Because correlograph analysis examines a component of the high-order four-body correlation function, it is more sensitive to medium-range ordering than conventional diffraction methods. As a follow-up of our previous publication, where we studied thin samples of sputtered amorphous silicon, we describe here the practical experimental method and common systematic errors of electron correlograph analysis. Using both experimental data and numerical simulations, we demonstrate that reliable structural information about the sample can only be extracted from the mean correlograph averaged over a sufficient number of individual results.