Long-period modulated structures of Bi₂Sr₂(Ca_1−xPr_x)Cu₂O_8+δ ceramics studied by electron diffraction and high-resolution electron microscopy

Seven specimens of Bi₂Sr₂(Ca_{1− x}Pr_x)Cu₂O_{8 + δ} ceramics in the concentration range 0 < x < 0.64 have been prepared by solid-state reaction. The sample with x = 0.16 was examined in detail by means of electron diffraction and an intensity distribution of lattice reflections in reciprocal space was constructed on the basis of the experimental results. The intensity distribution is consistent with a calculation using a long-period modulated-structure (LPMS) model. This model with b = 37b₀ takes the (3,1)₅ mode of lattice modulation having the modulation period 2.31b₀ (1.25 nm). The period is defined as the reciprocal of the wave number of a satellite reflection. The specimens with other concentrations also showed an intensity distribution of lattice reflections similar to that of x = 0.16. On the basis of the above results, lattice modulation periods have been examined for all the prepared specimens. The period decreases roughly from ~ 1.2₈ to ~ 1.1₅ nm with increasing concentration x. Seven modulation modes of the lattice have been determined by high-resolution observation; the modulation period of the LPMS model with each modulation mode is also nearly equal to the measured period.