The mode of the incommensurate modulation in the b direction of the ${\mathrm{Bi}}_{1.8}$${\mathrm{Sr}}_2$(${\mathrm{Ca}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Y}}_{\mathit{x}}$)${\mathrm{Cu}}_{2.2}$${\mathrm{O}}_{\mathit{z}}$ (0.05<x<0.75) system is investigated by means of electron diffraction and high-resolution lattice imaging. The change of period of the long-period structure with x is found to be basically due to the mixing ratio of domains of two modulation periods with b=4.5${\mathit{b}}_0$ and 5${\mathit{b}}_0$ or 4.5${\mathit{b}}_0$ and 4${\mathit{b}}_0$, thus creating periods of b=4.75${\mathit{b}}_{0–}$4.0${\mathit{b}}_0$. The fundamental orthorhombic lattice has dimensions of a≃b≃${\mathit{b}}_0$ (0.54 nm) and c≃${\mathit{c}}_0$ (3.1 nm). The change of the mixing mode from one to the other mentioned above occurs just in the yttrium concentration range, 0.45<x<0.65, which also corresponds to the superconductor (metallic)-to-semiconductor transition boundary. The mixing modes of the domains are directly recorded as a contrast modulation with half periods, 4.5${\mathit{b}}_0$/2 and 5${\mathit{b}}_0$/2 or 4.5${\mathit{b}}_0$/2 and 4${\mathit{b}}_0$/2 in high-resolution lattice images. These images are reproduced well by a multislice computer-simulation technique.

• Received 5 November 1990

DOI:https://doi.org/10.1103/PhysRevB.43.13066