The Study Of Phase Problem In The Electron Crystallography And Fast Simulation Calculation

The image simulation is inevitable in analysis of high resolution electron microscopy. At present, this is performed with traditional multi-slice programs, which, if repeated thousands of times in the process of structure refinement, presents a real bottleneck for flexible application. In this dissertation, we developed a new numerical simulation method for dynamical electron diffraction in the crystals consisting of atomic columns, which reduces the numerical calculation from two dimension to one dimension and of course, is much faster than that of the conventional multi-slice method. The calculation formula is as following,where and U ( r|→) is the crystal potential. The above expression is described in the cylindrical coordinate.The properties of materials are uniquely determined by their structures, so the structure analysis is one of the most important problems in the science research. It is well known that the phase problem is the most difficult problem in the structure analysis. There is no general solution even in the X-ray structure analysis. There is a long way to go to solve phase problem in electron crystallography because of its short history compared to that of X-ray crystallography. Under this background, we developed an equation to solve the phase problem from the amplitude of exit wave function, which derived from Schr?dinger equation as follows. whereφis amplitude of the exit wave function, I is the intensity of exit wave function, which is measurable,αis the phase which is unknown. The above expression is a two dimension elliptic partial differential equation.The equation is universally applicative in electron microscopy because it is based on the Schr?dinger equation. The results calculated by equation (2) for crystals C₆N₄O₂H₄ and MgAl₂O₄ are in excellent agreement with that calculated by the conventional multi-slice method.