Competition between composite and modulated configurations in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ and its relation to oxygen stoichiometry

The possible interpretation of the compound ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ as a composite or a single modulated incommensurate structure is deeply interconnected with the existence of discontinuous atomic domains in the superspace description of the structure. Single-crystal neutron diffraction data have been used to obtain Fourier maps within the superspace description, which show that some atomic domains are indeed either discontinuous, like that of the atoms in the BiO layers, or strongly anharmonic. This contrasts with the structural models of this material, which usually consider a single modulated incommensurate structure with continuous modulations containing a few harmonics. The results demonstrate that these models are bound to yield unrealistic configurations for the so-called bridging zones in the BiO layers. The intrinsic discontinuous features of the atomic modulations, especially the longitudinal sawtooth modulations of the oxygens in the ${\mathrm{Bi}}_2{\mathrm{O}}_2$ slabs, are shown to be the signature of two competing length scales corresponding to the ${\mathrm{Bi}}_2{\mathrm{O}}_2$ slabs and the perovskite blocks ${\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_6.$ In principle, this feature can be naturally included in a modulated composite description with occupational steplike modulations. An ideal composite configuration can be also proposed as a reference structure for describing the effects of the strong coupling between the ${\mathrm{Bi}}_2{\mathrm{O}}_2$ slabs and the perovskite blocks ${\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_6,$ including its effect on the compound stoichiometry, in particular its oxygen content.