Amorphous Nanomaterials. Lin Guo

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element. This long hexapole arrangement generates a combined aberration that compensates the positive spherical aberration of the objective lens through suitable hexapole excitation. Moreover, in the early 2000s, several indirect aberration compensation methods had been developed for experimental determination of the axial aberration coefficient, which mainly relied on measurements taken from image wave functions [10] and were applicable to crystalline specimens as well as thin amorphous materials. Initially, a phase correlation function (PCF) [11] was used to determine the defocus difference between neighboring images at high accuracy. The absolute focus and astigmatism are subsequently measured from the restored image wave function of a reference image using a phase contrast index (PCI) function. This provided estimates of the coefficients of the wave aberration function, which can then recover both phase and modulus of the specimen exit wave function under either linear or nonlinear imaging, also enhancing resolution to complement direct aberration correction. After that, indirect and direct approaches have been combined [12], for a focal series data set, and the elimination of tilt-induced axial coma relaxes the requirement of using parallel illumination and enables the illumination to be converged onto the specimen area of interest, which reduced delocalization of image components in the electron optically corrected image. Also, localized compensation of higher order aberrations up to the fifth order was possible. Notably, for modern electron microscope, the Cs-TEM is equipped with double correctors. Taking JEM-2200FS as an example, when only HRTEM data are required, the upper corrector is switched off and the condenser system of the microscope can be used as normal. A small voltage is applied to one of the hexapoles in the upper corrector to compensate for a residue threefold astigmatism arising from the gun lens or any residue field from the first hexapole. When switching to STEM imaging, a small adjustment to transfer lenses in the upper corrector is possible which allows broad parallel illumination to be achieved satisfactorily with both upper hexapoles strongly excited. The correction of both pre- and post-field allows the use of a large condenser and objective aperture sizes [13].

Schematic illustration of the transversal inversion polarization domain wall in ferroelectric PZT. Arrows 
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