Dynamic effects in the scattering of electrons by small clusters of atoms

Abstract

Dynamic scattering corrections were calculated for 40 kV electrons diffracted by randomly oriented fcc clusters of argon and of gold atoms ranging in size from 13 to 135 atoms. Computations were carried out according to several variants of two limiting theoretical approaches, namely, the direct summing up of atomic contributions calculated through single–single and single–double scattered waves by modifications of Glauber theory, and the extrapolation to limitingly small crystallites of conventional dynamic theory in the Blackman and Fujimoto formulations. For the small clusters studied, integrated intensities of diffraction rings (through single–double scatterings) calculated for three dimensional crystallites differ insignificantly from Glauber theory intensities calculated by projecting atomic potential energies onto a plane perpendicular to the mean direction of the incident and scattered wave vectors. The fractional dynamic correction increases with cluster size very nearly as N2/3 in both the Glauber and Blackman–Fujimoto limiting treatments. For crystalline clusters 8–20 Å in diameter, the dynamic effect calculated by summing single–double scatterings is an order of magnitude larger than that according to Blackman–Fujimoto theory. For argon clusters the dynamic effect is not serious; but according to our direct sums, dynamic corrections for 16 Å spheres of gold are surprisingly large, exceeding 25% for 111 reflections. Since the direct sums have been verified experimentally for several vapor‐phase molecules, the present work indicates that, in the limit of very small scatterers, extrapolations from conventional two‐beam dynamic theory may seriously underestimate the magnitude of dynamic effects.