The structures of five phases in the ${\mathrm{Ba}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{K}}_{\mathit{x}}$${\mathrm{BiO}}_{3}$ system for 0\ensuremath{\le}x\ensuremath{\le}0.5 and temperatures below 473 K have been determined by neutron powder diffraction. Bulk superconductivity occurs only in a cubic perovskite phase which exists for x\ensuremath{\ge}0.37 (at 10 K). At room temperature, as the potassium concentration is decreased, the cubic structure distorts first by ${\mathrm{BiO}}_{6}$ octahedral tilting and then by symmetric oxygen breathing-mode distortions. Semiconducting behavior for the monoclinic phase at 0\ensuremath{\le}x\ensuremath{\le}0.1 can readily be explained on the basis of a commensurate charge-density wave. The semiconducting orthorhombic phase, which extends from the monoclinic phase to the cubic superconducting phase, contains only octahedral tilting distortions that would not be expected to destroy metallic behavior. Thus, this commensurate structure provides no explanation for the metal-insulator transition. An incommensurate modulation extending across the semiconducting region of the phase diagram has been observed by electron diffraction, but is not observed by neutron diffraction. It is not clear whether this incommensurate modulation is responsible for the nonmetallic behavior.

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Structural phase diagram of theBa1−xK<mml:mrow...