Determination of space group of incommensurate modulation structure phases in Bi high temperature superconductors

The investigation of microstructures of the Bi-2212 and Bi-2223 phases in Bi high temperature superconductors is very significant for improving technology of production and researching superconducting properties and mechanisms. The determination of space groups for the Bi-2212 and Bi-2223 phases is a key problem, which is very complicated because of their incommensurate modulation structures. The supercell structures of the Bi-2212 and Bi-2223 phases with incommensurate modulation structures were determined by convergent beam electron diffraction (CBED). The point group of the supercell of the Bi-2212 phase with type A modulation structure is 2 mm, its space group is I2mm. The point group of the supercell of the Bi-2223 phase with type B modulation structure is mmm, its space group is Ibmm. The effects of the rocking curve for the symmetries of CBED patterns were discussed according to experimental results. The simulation results of CBED patterns for the Bi-2212 phase confirmed the symmetries of CBED patterns to be the symmetries of the supercell with modulation structure, but not to be the symmetries of the subcell structure.