THE EFFECT OF 3-FOLD ASTIGMATISM ON MEASUREMENTS OF GRAIN-BOUNDARY VOLUME EXPANSION BY HIGH-RESOLUTION TRANSMISSION ELECTRON-MICROSCOPY

In the absence of high-order aberrations, the lattice fringe technique should allow measurement of grain boundary rigid-body displacements t o accuracies about an order of magnitude better than the point-to-poin t resolution of the transmission electron microscope. The three-fold a stigmatism, however, introduces shifts of the lattice fringe pattern t hat depend on the orientation of the lattice relative to the direction of the three-fold astigmatism and thus produces an apparent shift bet ween the two grains bordering the grain boundary. By image simulation of grain boundary model structures, the present paper explores the eff ect of these extraneous shifts on grain boundary volume expansion meas urements, It is found that the shifts depend, among others, on zone ax is direction and the magnitude of the lattice parameter. For many grai n boundaries of interest, three-fold astigmatism correction to better than 100 nm appears necessary to achieve the desired accuracies.