Dynamical electron diffraction simulation for non-orthogonal crystal system by a revised real space method

In the transmission electron microscopy, a revised real space (RRS) method has been confirmed to be a more accurate dynamical electron diffraction simulation method for low-energy electron diffraction than the conventional multislice method (CMS). However, the RRS method can be only used to calculate the dynamical electron diffraction of orthogonal crystal system. In this work, the expression of the RRS method for non-orthogonal crystal system is derived. By taking Na2 Ti3 O7 and Si as examples, the correctness of the derived RRS formula for non-orthogonal crystal system is confirmed by testing the coincidence of numerical results of both sides of Schrödinger equation; moreover, the difference between the RRS method and the CMS for non-orthogonal crystal system is compared at the accelerating voltage range from 40 to 10 kV. Our results show that the CMS method is almost the same as the RRS method for the accelerating voltage above 40 kV. However, when the accelerating voltage is further lowered to 20 kV or below, the CMS method introduces significant errors, not only for the higher-order Laue zone diffractions, but also for zero-order Laue zone. These indicate that the RRS method for non-orthogonal crystal system is necessary to be used for more accurate dynamical simulation when the accelerating voltage is low. Furthermore, the reason for the increase of differences between those diffraction patterns calculated by the RRS method and the CMS method with the decrease of the accelerating voltage is discussed.