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The modulations and Pairing of Atoms in Bi_2Sr_2CaCu_2O_8+x High Temperature Superconductor as Revealed by the Fast Fourier Transform and Filtering

The modulations of the structure, which seems to be crucial for excellent superconducting properties of Bi_2Sr_2CaCu_2O_8.33 HTSC, along its short tetragonal b axis, and the accompanying pairing of Bi atoms along another short tetargonal a axis, was simultaneously revealed by the appropriate tilting of the specimen according to the electron beam in the microscope during HREM analysis (D. Kunstelj, D. Babic, D. Bagovic, B. Leontic, Z. Vucic, J. Gladic: Long-Range Pairing of Bismuth Atoms and the Modulations in Bi_2Sr_2CaCu_2O_8+x High-Temperature Superconductor, Phys. Stat. Sol. (a) 165 (1998) 467-482). HREM figures were processed (Adobe Acrobat) and analyzed by the computer programms including the Fourier transforms and filtering (ProFFT and Origin 4.0). It is shown that the apparent periodicity of the modulations, as appear in the electron micrographs, depend on the active reflections forming the EM picture in the kinematical or the dynamical case. The pairing of Bi atoms introduce, otherwise forbidden, (101) reflection, which, along with the modulations, is sign of lowering the symmetry of the tetragonal structure, the situation proper for good superconducting properties. It is shown that the subatomic shifts within pairs, which cannot be satisfactory measured from the HREM micrographs, can be calculated down to the one tenth of the resolution of the microscope by measurement of the ratios of intensities of (101) and (202) maxima in the FFT of the HREM picture of pairs.

electron microscopy; superconductivity; FFT filtering

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