Incommensurate modulation in the high-${\mathit{T}}_{\mathit{c}}$ superconductor ${\mathrm{Ba}}_{1\mathrm{-}\mathit{x}}$${\mathrm{K}}_{\mathit{x}}$${\mathrm{BiO}}_3$ and its relation to the conducting properties

The incommensurate modulation in ${\mathrm{Ba}}_{1\mathrm{-}\mathit{x}}$${\mathrm{K}}_{\mathit{x}}$${\mathrm{BiO}}_3$ is studied by means of electron diffraction. Attention is paid to the symmetry of the modulation and the effect of electron irradiation. Interpretation of the modulation symmetry in cubic samples (0.3<x<0.5) as well as in orthorhombic samples (0.1<x<0.3) in the framework of a four-dimensional description allows one to determine it as a periodic displacement of the bismuth atoms. Satellite reflections corresponding to the modulation are observed only after irradiation with electrons. However, since the critical voltage is below 40 kV, it is believed that the modulation is in fact a fundamental material property. The incommensurability of the modulation for x<0.4 results in a partial charge disproportionation on the bismuth sites, which can explain the lack of superconducting properties for ${\mathrm{Ba}}_{1\mathrm{-}\mathit{x}}$${\mathrm{K}}_{\mathit{x}}$${\mathrm{BiO}}_3$ with x<0.4. In the superconducting phase ${\mathrm{Ba}}_{0.6}$${\mathrm{K}}_{0.4}$${\mathrm{BiO}}_3$, the modulation is commensurate, and high-resolution observations provide evidence for a modulation model without charge disproportionation, yielding a metallic behavior at room temperature.