Relativistic calculations of intensity distributions in elemental maps using contrast transfer functions

Abstract

The interpretation of highly resolved elemental maps is not straightforward: one has to consider the quantum mechanical nature of the scattering process as well as the influence of the microscope. Existing calculations of the contrast in elemental maps are based on a non-relativistic approach, while in most of the currently installed electron microscopes, the electrons penetrate the specimen with relativistic energies >/= 200 keV. Therefore, we have recalculated the intensity distribution in elemental maps based on a fully relativistic theory. Using the concept of contrast transfer functions, the simulations account for lens aberrations as well as the defocus. Surprisingly, the results exhibit considerable deviations between the relativistic and non-relativistic calculations even in the region of low acceleration voltages such as 100 kV. These differences increase with increasing acceleration voltage and are strongly dependent on aperture and energy loss. Quantitative simulations and evaluations of highly resolved elemental maps should therefore make use of a fully relativistic theory.

Calculation of inelastic scattering processes of relativistic electrons in oriented crystals

“…The calculations show marked differences between relativistic and nonrelativistic results. Similar effects have been demonstrated by Knippelmeyer [10] and Dwyer [11] in simulations of images, where the relativistic calculation exhibits strong deviations from nonrelativistic results even at voltages of 80 or 100 kV.…”

Design of oxy-fluoride glass-ceramics containing NaLaF4 nano-crystals

“…8). As the measured signal in a transmission electron microscope is not only influenced by the specimen, but also by the instrumental parameters, the corresponding transfer functions have been included in the calculation [40]. The main instrumental effects are the aberration of the lens system and the modulation transfer of the CCD camera.…”

Energy-filtered transmission electron microscopy based on inner-shell ionization

“…We note in passing that Knippelmeyer and Kohl [27] have shown that relativistic corrections can make a significant difference to the form of calculated elemental maps. For the current parameters -low energy loss and moderate (effective) aperture size -we can tolerably neglect these corrections, and the calculations presented here assume the non-relativistic model for the inelastic transition.…”

“…Nevertheless, it has been established that direct interpretation of EFTEM images is not always possible, making simulation a necessary adjunct to experiment [26][27][28][29]. Previous simulation work has focused on making the complex calculations as timeefficient as possible.…”