A revised version of the program VEC (visual computing in electron crystallography)

The program package VEC （Visual computing in Electron Crystallography） has been revised such that （i） a program converting one-line symbols to two-line symbols of （3＋1）-dimensional superspace groups has been incorporated into VEC so that the latter can interpret both kinds of symbols; （ii） a bug in calculating structure factors of onedimensionally incommensurate modulated crystals has been fixed. The correction has been verified by successfully matching the experimental electron microscopy image of an incommensurate crystal with a series of simulated images. The precompiled revised version of VEC and relevant materials are available on the Web at http：//cryst.iphy.ac.cn.

Comparison of Two Simulation Methods in Electron Crystallography： BW Method and a Modified Direct Product Method of Scattering Matrix

In this paper, a modified direct product method of scattering matrix （DPSM） was presented and the cal- culation formulawas derived as follows： φ（z）=∑n1/n!（Mz）nφ（O）and φ（z＋εj）=∑n1/n!（Mεj）nφ（z）,whereM is the scattering matrix of which the dimension can be reduced by ＇Bethe potential method＇ drastically and therefore the calculation speed can be increased tremendously without losing accuracy very much. The results calculated with the DPSM method are in almost exact agreement with those calculated with BW method. However, the calculation speed for the modified DPSM method is approximately three times faster than that for the BW method. Furthermore, the DPSM is suitable for computing all types of ma- trices without requiring symmetry or conjugate symmetry.

Modification of Analytical Expression of Electron Dynamical Diffraction

Assuming that the wave function φ>=eη, the Schrodinger equation can be written as. Neglecting the last two terms, an analytical expression of electron dynamical diffraction was derived by Qibin YANG et al. In this paper, the analytical expression is modified by further considering thesecond-order differential term When the accelerating voltage is not very high, or the sample is not very thin, the reciprocal vector g is large, the modification of the second-order differential is necessary; otherwise it can be neglected.

Quantitative Analysis of Zero and High Order Laue Zones Effects on the Exit Wave Function

The exit wave function including zero and high order Laue zones has been simulated by both multi-slice method and electron dynamic diffraction analytical expression. Coincidence of the simulations by these two methods was achieved. The calculated results showed that the exit wave function highly dominated by zero order Laue zone, while high order ones modify the exit wave function to some extent depending on the situation. High order Laue zone effects become important for the following cases: sample consists of light elements, the thickness is very thin, lattice planar spacing perpendicular to the direction of the incident beam is large, and the electron beam has long wavelength. In these cases the exit wave function should be corrected by adding high order Laue zone effects. The analytical expression is effective and convenient for dealing with high order Laue zone effects.