A projected potential image of a defect in an ordered alloy?

Abstract

The high-resolution performance of 100-kV transmission electron microscopes has improved dramatically in the past few years. Use of an objective lens with a spherial aberration coefficient C_s of 0.7 mm and a low incident beam divergence (α = 0.2 mrad) allows point-to-point resolutions shown by Bursill and Wood¹ to be ∼1.6 Å. These authors, however, distinguish between this ‘instrumental’ resolution and the resolution which can in principle be used for direct structural resolution and interpretation—only slightly better than 3 Å in the above conditions. The function sin χ, the part of the lens transfer function most directly dependent on the phase changes χ of the electrons as a function of lens defocus and spherical aberration, shows rapid oscillations for spacings smaller than ∼2.8 Å even for the optimum defocus condition for which sin χ is apparently −1 over a maximum range of spacings¹. Thus even if point-to-point resolutions in the 2–3 Å range are obtained, by careful limitation of the beam divergence, the images can only be related to the structure by very careful comparison with computed images. It is this fact and the limited improvement to be expected on any further reduction of C_s, as well as the severe geometric limitations imposed on specimen manipulation in such lenses, which has lead to the approach of using increased accelerating voltages with a concomitant reduction in electron wavelength, λ: the above ‘structure resolution’ limit is approximately 0.7C_s^¼λ^¾. Most of the high-resolution work to date has concentrated on the examination of materials in which there are strong projected charge distribution periodicities at relatively coarse spacings. To obtain further information on the difficulties involved in the examination of defects in metals (with generally smaller spacings of the important charge projec tions) we have studied the degree to which images of the ordered alloy Ag₃Mg can be related to naive descriptions of the projected charge distribution.