Crystal Structure of Piezoelectric Bismuth Germanium Oxide Bi₁₂GeO₂₀

Piezoelectric Bi₁₂GeO₂₀ crystallizes in the cubic system with space group I23 and lattice constant a = 10.1455±0.0008 Å at 298°K. The complete x‐ray scattering pattern within a reciprocal lattice hemisphere of radius (sinθ)/λ = 1.02 Å⁻¹ was determined with PEXRAD. A total of 4812 reflections were measured, resulting in 631 independent and significantly nonzero F_meas. The crystal structure was solved using three‐dimensional Patterson and Fourier series, and refined by the method of least squares. The final agreement factor R is 0.062. The germanium atoms occupy geometrically regular tetrahedra, with Ge–O=1.717±0.028 Å. The bismuth atoms are heptacoordinated: five oxygen atoms form an incomplete octahedral arrangement, with Bi–O distances ranging from 2.076±0.027 to 2.640±0.028 Å. The remaining two oxygen atoms are electrostatically coordinated, on either side of the 6s² inert electron pair in Bi³⁺, at distances of 3.082 and 3.170 Å from bismuth. The Bi atom vibrates anisotropically. The absolute configuration of the atomic arrangement has been determined. The positive piezoelectric polarization induced by compressive stress applied along 〈111〉 is given by the normal to a triangular GeO₄ tetrahedral face in the direction from the Ge atom to the face.