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 A at 298°K. The complete x‐ray scattering pattern within a reciprocal lattice hemisphere of radius (sinθ)/λ = 1.02 A−1 was determined with PEXRAD. A total of 4812 reflections were measured, resulting in 631 independent and significantly nonzero Fmeas. 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 A. 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 A. 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 A 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.