Electron crystallographic image-processing investigation and superstructure determination for (Pb_0.5Sr_0.3Cu_0.2)Sr₂(Ca_0.6Sr_0.4)Cu₂O_y

An electron crystallographic image-processing technique based on the combination of high-resolution electron microscopy and electron diffraction has been developed to investigate the commensurate structural modulation in the high-T_c superconductor (Pb_0.5Sr_0.3Cu_0.2)Sr₂(Ca_0.6Sr_0.4)Cu₂O_y. After symmetry averaging, a structure image was obtained by image deconvolution at the resolution limited by that of the electron microscope. Then phase extension was employed to enhance the image resolution up to about 1.25 Å by means of the electron diffraction data corrected with an empirical method. In the final projected potential map, the occupational and/or positional modulation is clearly observed for all atoms, including oxygen. The key points of determining superstructures by the technique are studied and discussed.