Verification of sub-Å information transfer and its influence on the precision of structure determination by quantitative HRTEM

Abstract

Using quantitative diffractometry from a micrograph of an amorphous germanium film, the total contribution to the chromatic damping envelope by focus spread could be determined for a high-voltage ultra-high-resolution microscope operating at 1250kV. The major difficulties of quantification beyond the usual analysis of the zero crossings of the diffractograms are the proper correction for scattering factor, modulation transfer function, background and noise. Nonlinear imaging, inelastic scattering and depth of focus of thick specimens are considered to be minor effects at high voltages. The Fourier transform of a hyperbolic astigmatic image can be converted into a Thon diagram (or contrast transfer nomogram) using a special (modified polar-to-cartesian) coordinate transformation The resulting Thon diagram of Fig. la shows the weak phase contrast transfer as a function of spatial frequency (horizontal axes) and defocus (vertical axes). Diffractogram maxima can be seen out to 0.97 Å. A focus spread of Δ = 10nm could be determined by fitting the experimental to calculated Thon diagrams (Fig. 1 b).