Multislice formula for inclined illumination

Abstract

A multislice formula for many-beam calculation of dynamical electron diffraction amplitudes which may be applied for inclined illumination has been derived based on the Schr6dinger equation. This formula clearly shows the following points: a specimen should be considered as sliced parallel to the entrance surface; a spherical propagation function should be used, giving the exact excitation error measured along the surface normal; the interaction constant in the phase-grating function should be changed; the phase grating should be projected along the beam direction. A new parameter for the strength of the upper-layer interaction in the case of the inclined illumination is proposed in terms of the excitation error of the reciprocal-lattice points used to define the projected potential. It is pointed out that the potential projected along the beam direction may better represent the upper-layer interactions for the inclined illumination.

Multislice Method for Large Beam Tilt with Application to HOLZ Effects in Triclinic and Monoclinic Crystals

“…In this section, three existing MSBT formulations are introduced in a unified form so as to clearly determine the differences between these formulations• First, we will present two MSBT formulations by following our previous approaches (Van Dyck, 1980;Chen, Van Dyck, Op de Beeck, Broeckx & Van Landuyt, 1995), then in the unified form we rewrite the third formula, which is derived by Wang, who followed Ishizuka's (1982) method based on the so-called first-principles approach (Wang, 1995).…”

“…Cowley, 1981;Van Dyck, 1980;Ishizuka, 1982;Wang, 1995). These formulations are identical for normal illumination but different for inclined illuminations.…”

A HREM study of nonbasal twinning and superlattices in ilmenite

“…Fig. l(b) shows the simulated image calculated for a thickness of 80 A and defocus value of -700 A based upon the multislice program written by Ishizuka (1982). By comparison with the projected structure of ilmenite, it is shown that under the Scherzer condition pairs of Fe atoms will be imaged as bright dots in the highresolution image, and therefore a direct relation between the high-resolution image and the structure of ilmenite can be observed under suitable conditions.…”

Electron-microscope study of the structure of Ag8S formed in the initial stage of silver sulfidation

“…Since the waves which are scattered with equal angles to the optical axis have high coherency, their contribution to the image intensity becomes high. The degree of coherence between the diffracted waves was taken into account in the calculation as the transmission cross coefficients (TCC) of the two individual waves (Ishizuka, 1982). Thus, the FT patterns of both the recorded images and calculated images are not the same as the electron diffraction patterns, as shown in Fig.…”