Real space modulation in Bi2Sr2CanCun + 1O6+2n and Tl2Ba2CuO6 superconductors derived from electron diffraction...

We will try to illustrate here that, simply from the geometry of the electron diffraction pattern of an incommensurably modulated structure, conclusive information can be obtained on the real space shape of this modulation. The method applied here is based on the 3 + 1 dimensional description of symmetry operations and can be summarized as follows: 1) reconstruct the three-dimensional reciprocal space geometry of the modulated structure from electron diffraction information along different zone axes; 2) deduce the complete Bravais type symbol of the four-dimensional structure from the general reflection conditions; and 3) derive the modulation function for each atom type from the superspace symmetry elements which result from the information of both modulation and basic structure. This method will be applied here in short on the Bi2Sr2CanCun + 1O6+2n strucutre, for which system the results are in agreement with the ones recently obtained from neutron diffraction. For Tl2Ba2CuO6 where no data from other diffraction techniques are available, a more complete calculation will be performed, in order to determine the shape of the displacement function for the different atom types; the results are in agreement with the observed High Resolution Electron Microscopy (HREM) images.