crystal structure analysis

For crystal structure analysis, the electron microscope (TEM) image is not used, but the electron diffraction is used because the spatial resolution of the TEM is around 0.1 nm, but the electron diffraction pattern achieves a spatial resolution of 0.001 nm. In structure analysis, there are two methods; one is to use kinematical diffraction, the other is to use dynamical diffraction. The former is applied when a crystalline specimen is thin and consists of light elements and the dynamical diffraction effect can be neglected. Actually, this method is used for protein crystal analysis. The intensities of each reflection are measured from a diffraction pattern. The phases of the reflections are obtained from the real and imaginary parts of the scattering factors which are obtained by Fourier transform of the corresponding TEM image. Then, the structure is obtained by Fourier synthesis of the intensities and phases. The latter method, which uses convergent-beam electron diffraction (CBED), is applied to structure analysis of nano-scale crystals in the field of materials science. The CBED method has more advantage to study the secondary structure of solid materials, or local structures due to lattice defects and lattice strain than to study the primary structure of crystals. A disk diffraction pattern is acquired by illumination of an electron beam with an incidence angle of several 10 mrad on a small specimen area of a diameter of 10 nm or less. The acquired disk diffraction pattern (CBED pattern) exhibits a two-dimensional rocking curve (intensity distribution) corresponding to the spread of the incidence beam angle. (The CBED pattern appears to be complex due to the dynamical diffraction effect, thus the pattern is greatly different from the Laue function or the rocking curve which is expected from kinematical diffraction.) The crystal structure is solved by the fitting between the simulated CBED pattern obtained by the full dynamical calculation and the experimentally-acquired CBED pattern. Since the phases of the diffracted waves are reflected in the diffraction intensities due to multiple diffraction effects, separate determination of the phases of the diffracted waves is not necessary, which is needed in the case of kinematical diffraction. In addition, an energy filter is effectively used to remove inelastic scattering. The third method is the pre-session method. In this method, to avoid the strong dynamical diffraction effect using illumination of a cone-shaped incident beam on a crystalline specimen with a tilt angle of several degrees from a zone axis, the intensities produced by the cone illumination are added for each reflection. The crystal structure is solved by applying the kinematical theory using the obtained intensities, where the direct method for X-ray diffraction is used to estimate the phases of the diffracted waves.

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