Based on the electron dynamic diffraction, phase shift of the exit wave function vs misorientation of the incident electron beam from the exact zone axis has been calculated for the [001] oriented copper. The result s...Based on the electron dynamic diffraction, phase shift of the exit wave function vs misorientation of the incident electron beam from the exact zone axis has been calculated for the [001] oriented copper. The result shows that the peak of phase shift is the maximum at the atom position as the electron beam along the exact [001] zone axis, and the peak value of phase shift decreases as increases of the misorientation. At small misorientation, i.e. less than 5 degree, change of the phase shift is minimal. The peak value of phase shift decreases significantly when the incident beam deviates form the zone axis over 10 degree and the exit wave has a planar configuration as the misoriention angle arrives -17 degree. The effect of this phase shift characteristics on the information extracted from the hologram has also been considered.展开更多
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 thi...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.展开更多
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...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.展开更多
Multibeams dynamical theory of electron diffraction has been used to calculate the fast electron thickness-integrated probability density on Ti and Al sites in the γ-TiAl phase as a function of the incident electron ...Multibeams dynamical theory of electron diffraction has been used to calculate the fast electron thickness-integrated probability density on Ti and Al sites in the γ-TiAl phase as a function of the incident electron beam orientation along \[100\], \[110\] and \[011\] zone axes, with the effect of absorption considered. Both of the calculation and experiments show that there are big differences in electron channeling effect for different zone axes or the same axis but with different orientations, so we should choose proper zone axis and suitable incident beam tilting angles when using the axial electron channeling statistical method to determine the site occupancies of impurities. It is suggested to calculate the channeling effect map before the experiments.展开更多
基金financially supported tional Natural Science Foundation of China No. 60271028.
文摘Based on the electron dynamic diffraction, phase shift of the exit wave function vs misorientation of the incident electron beam from the exact zone axis has been calculated for the [001] oriented copper. The result shows that the peak of phase shift is the maximum at the atom position as the electron beam along the exact [001] zone axis, and the peak value of phase shift decreases as increases of the misorientation. At small misorientation, i.e. less than 5 degree, change of the phase shift is minimal. The peak value of phase shift decreases significantly when the incident beam deviates form the zone axis over 10 degree and the exit wave has a planar configuration as the misoriention angle arrives -17 degree. The effect of this phase shift characteristics on the information extracted from the hologram has also been considered.
基金supported by the National Natural Science Foundation of China under the grant No.10074052Key Foundation of Education Department of Hunan Province No.01A003
文摘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.
基金National Natural Science Foundation of China(No.10374077)the Key Foundation of Education Department of Hunan Province 01A003the Scientific Fund of Education Department of Hunan Province 03C187
文摘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.
基金This work was supported by the National Natural Science Foundation of China.
文摘Multibeams dynamical theory of electron diffraction has been used to calculate the fast electron thickness-integrated probability density on Ti and Al sites in the γ-TiAl phase as a function of the incident electron beam orientation along \[100\], \[110\] and \[011\] zone axes, with the effect of absorption considered. Both of the calculation and experiments show that there are big differences in electron channeling effect for different zone axes or the same axis but with different orientations, so we should choose proper zone axis and suitable incident beam tilting angles when using the axial electron channeling statistical method to determine the site occupancies of impurities. It is suggested to calculate the channeling effect map before the experiments.
