The incommensurate modulation in the Bi₂Sr_2-xCa_xCuO₆ superconductor, and its relation to the modulation in Bi₂Sr_2-xCa_xCu₂O₈

The modulation of the (221) superconducting Bi₂Sr_2-xCa_xCuO₆ phase has been analyzed by X-ray diffraction, using four-dimensional symmetry theory. The pseudo-orthorhombic diffraction pattern is a superposition of two twin related components, such that the main reflections with hkl and hklm superimpose, but the satellite hklm and hklm do not. The latter feature allows separation of the twin intensities. The modulation analysis in superspace group P:Aa:1 shows displacements similar to those observed in the 2212 compound [Y. Gao et al., Science 241 (1988) 954] but with generally larger displacements. In particular, the c-axis displacement amplitude of the Cu atoms is increased to almost 0.5 Å. This and the obliqueness of the q vector (q=0.214a^*+0.61c^*) indicate the absence of a restraining influence exerted by the CuO₂/Sr(Ca)/CuO₂ double layers in the multi-Cu layer phases.