Defocussed TEM contrast from small helium bubbles in copper

Abstract

The theoretical defocussed contrast of the TEM images of bubbles is computed using simulations based on the two-beam dynamical theory of electron diffraction. The bubble parameters used are chosen to be typical of the small (∼ 2 nm in diameter) bubbles found in gas-bubble superlattices. Simulated images are calculated for single equilibrium bubbles, for isolated columns of equilibrium bubbles and for single overpressured bubbles in copper. The calculated images are found to depend strongly on many parameters: the depth, pressure and radius of bubbles; foil thickness; diffracting vector; excitation error; defocus level, small deviations from the Bragg angle and number of bubbles included in the column. Representative examples are presented and comparisons made with experiment. It is concluded that simulations provide a very useful framework for guiding the broad choice of imaging parameters and provide a basis for the interpretation of the complicated imaging behavior often encountered in practice. Various methods for measuring bubble radii from TEM micrographs are assessed.