Electron Backscatter Diffraction Patterns Simulated By Multi-slice Methods

After several decades of development, EBSD technology has become one of the important means to analyze the microstructure of crystal materials. However, the EBSD patterns are mainly simulated using the kinematic electron diffraction theory in the commercial EBSD software. The simulated patterns by the kinematic electron diffraction theory consist with the experiment patterns geometrically, but these patterns cannot give reasonable explanation on the diffraction intensity information. The reason is that the interaction between the electrons and the samples is very complex, containing multiple elastic scattering and inelastic scattering processes in the EBSD. The dynamic electron diffraction theory needs to be employed in order to gain the fine EBSD patterns. The dynamic electron diffraction theory mainly contains Bloch wave(BW) method and multi-slice(MS) methods. Multi-slice methods contain the conventional multi-slice(CMS) method,(real space) RS method and(revised real space) RRS method. Recently, the EBSD patterns are successfully simulated by the BW method, which is suitable for dynamical transmission electron diffraction calculation. The algorithms of the BW method and the two multi-slice methods(CMS and RS methods) are different from one another, but a high-energy approximation is all taken in three methods to solve Schr?dinger equation. No any approximation to the forward scattering electrons is taken in the RRS method. In this paper, we mainly use the RS and RRS methods to simulate the EBSD patterns and further analyze the effect of various factors on the EBSD patterns by RRS method. The contents and results are as follows.Firstly, two kinds of multi-slice methods, including real space(RS) method and revised real space(RRS) method, are introduced based on Schr?dinger equation. The relationship between two kinds of dynamical electron diffraction methods is analyzed. Then, a computational model is established to deal with the EBSD scattering: the first part is the incident process; the second part is the coming out process. The first process needs not to be considered since we only care how the electron beams carry the sample information and come out from the samples. The second process can be simulated by the dynamical theory for transmission electron diffraction based on the reciprocity principle.Secondly, the EBSD patterns obtained by the RS and RRS methods are compared in detail with the different calculation parameters(the accelerating voltages, the Debye-Waller factors and the aperture radius). The view field of the EBSD patterns simulated by the RRS method is larger than that by the RS method under the same calculation conditions. The Kikuchi bands not crossing the center poles are bent for the EBSD patterns simulated by the RRS method, which is more consistent with the real situation. The lattice parameters based on the radii of HOLZ rings by the RRS method are more accurate than those by the RS method. The reason for the differences between the two methods is analyzed and discussed. The calculation time of the second RRS method and the third RRS method is also compared. These results reveal that the second RRS method is most suitable for accurately simulating the EBSD patterns by balancing accuracy and calculation time.Thirdly, the accurate simulation of EBSD patterns is performed by the RRS method. The simulated EBSD patterns by the RRS method are compared with the experimental EBSD pattern. There are some differences between their diffraction contrast and resolution owing to the inelastic scattering. Then the effects of the electron energy spread and tilted incident beams on the EBSD pattern characteristics are simulated by the RRS method. The former affects the contrast and resolution of EBSD patterns, while the latter affects the specific details of the EBSD patterns.Fourthly, the effect of depth of the incident electron beams on the EBSD patterns are simulated by the RRS method. Within a certain depth range, the characteristics of the diffraction patterns at different depth are not the same. This effect has nothing to do with the symmetry of the crystal structure. These diffraction characteristics cannot be obtained from the experimental patterns. However, the detail information can be obtained by the dynamical electron diffraction calculation. It is very helpful to deeply understand the relationship between the EBSD pattern and the incident depth. It is very beneficial to understand the relationship between the EBSD pattern and incident depth. On the other hand, more information related the incident depth can also be obtained from the experimental patterns.