Ferroelectric Ba0.27Sr0.75Nb2O5.78, with Tc = 348° ± 15°K, is a tungsten bronze-type structure crystallizing in the tetragonal system, with lattice constants a = 12.43024 ± 0.00002 and c = 3.91341 ± 0.00001 Å at 298°K, space group P4bm, and five formulas in the unit cell. The integrated intensities of 6781 structure factors were measured with PEXRAD, 875 symmetry-independent structure factors being significantly above background. The metal-atom positions were determined from the three-dimensional Patterson function and the oxygen atoms from subsequent Fourier series. The final agreement factor between measured and calculated structure factors is 0.0508. The structure consists of close-packed slightly puckered layers of oxygen atoms separated by nearly c / 2. The Nb atoms are slightly displaced from one layer, the Ba and Sr atoms from the other and in the same sense. The oxygen atoms in the Ba and Sr layer are disordered. Neither of the two independent sites occupied by the Ba and Sr atoms is fully filled. The 2a site is preferred by Sr, which is in distorted cubo-octahedral coordination; the Sr–O distances range from 2.547 ± 0.008 Å to 2.919 ± 0.008 Å. The 4c site, occupied by Ba and Sr, has distorted tricapped trigonal prismatic symmetry; the Ba/Sr–O distances range from 2.604 ± 0.009 Å to 3.035 ± 0.010 Å. The two independent Nb atoms fully occupy the 2b and 8d sites and are each in relatively regular octahedral coordination. The 2b site has Nb–O distances ranging from 1.92 ± 0.03 Å to 2.03 ± 0.03 Å; the 8d-site Nb–O distances range from 1.88 ± 0.03 Å to 2.11 ± 0.03 Å. A ferroelectric mechanism is proposed in which the metal atoms in the 2a, 2b, and 4c sites move, at the Curie temperature, into the oxygen layers. These metal atoms then acquire 4̄,222, or 2 point symmetry, respectively, as the space group transforms to P4̄b2. The remaining Nb atoms, in the 8d position, also rearrange so as to have half above and half below the oxygen layer. The absolute displacements of the metal atoms from their nearest mean planes of oxygen atoms, in space group P4̄bm, are directly related to the ferroelectric polarization sense.

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Ferroelectric Ba(4+x)Na(2 − 2x)Nb10O30, with a Curie temperature of 833°K, has a tungsten bronze-type structure and crystallizes in the orthorhombic system, with subcell lattice constants a = 17.59182 ± 0.00001, b = 17.62560 ± 0.00005, and c = 3.994915 ± 0.000004 Å at 298°K. The space group is Cmm2, and there are two formulas in the subcell. The c axis of the true cell is double that of the subcell. The integrated intensities of 6911 reflections within a reciprocal hemisphere of radius (sinθ)/λ = 1.02 Å−1 were measured with PEXRAD, 1873 symmetry-independent structure factors being significantly above background. The metal atom positions were determined from the three-dimensional Patterson function and the oxygen atoms from metal-phased Fourier series. The final agreement index between measured and calculated structure factors is 0.0579. The structure differs only in detail from previously determined tetragonal tungsten bronze structures. In the general formula (A1)2(A2)4C4(B1)2(B2)8O30, the B1 and B2 sites are fully occupied by Nb, the A2 sites by Ba and the A1 site by 87.0% Na and 6.5% Ba. Evidence from chemical analysis, x-ray density calculations and the present determination suggests that the best approximation to the formula of the crystal studied is Ba4.13Na1.74Nb10O30. The Ba and O atoms at z ≃ 12 are disordered in a manner similar to the O atoms in the Ba layer in barium strontium niobate. The four crystallographically independent Nb atoms, each in octahedral coordination, are linked to O atoms by distances ranging from 1.765 ± 0.021 to 2.270 ± 0.021 Å, with a mean value of 1.989 Å. Ba is 10 coordinated, with Ba–O distances ranging upward from 2.671 ± 0.013 Å. Na is 12 coordinated, with Na–O distances ranging from 2.660 ± 0.014 to 2.990 ± 0.015 Å, with a mean of 2.788 Å. The Nb-atom displacements from the mean oxygen planes lie in the range 0.171–0.205 Å; the parabolic relation with Curie temperature predicts a displacement of 0.204 Å. The measured value of Ps at room temperature is 40 μC cm−2: the linear relation between displacement and polarization predicts a saturation value of 44–53 μC cm−2. All metal atoms are displaced from the oxygen planes in the sense given by the macroscopic positive polarity.

Ferroelectric K(6−x−y)Li(4+x)Nb(10+y)O30, with x ≃ 0.07, y ≃ 0.23, and a Curie temperature of 613°K, crystallizes with a tungsten bronze-type structure in the tetragonal system. The lattice constants are a = 12.5764 ± 0.0002 and c = 4.0149 ± 0.0001 Å at 298°K. The space group is P4bm. There is one formula per unit cell. The integrated intensities of 6578 structure factors, inside a reciprocal hemisphere of radius (sinθ) / λ = 1.02 Å−1, were measured with PEXRAD. There are 998 symmetry-independent Fmeas significantly above background. Isomorphism with BaxSr(5−x)Nb10O30 allowed the metal atom positions to be deduced. Oxygen atom positions were obtained by Fourier series methods. Refinement of structural parameters by the method of least squares resulted in a final agreement factor R = 0.0401. The structure is generally like that of other tungsten bronzes of formula (A1)2(A2)4C4(B1)2(B2)8O30, with the A1 site occupied by 87% K and 13% Li, the A2 site by 99% K and 1% Li, and the C site by 94% Li and 6% Nb. The B sites are fully occupied by Nb. X-ray spectrochemical analysis and the present diffraction study suggest x ≃ 0.07 and y ≃ 0.23 for the nonstoichiometric formula above. Evidence for major positional disorder, excluding occupancy disorder, similar to that observed in BaxSr(5−x)Nb10O30 and in Ba(4+x)Na(2−2x)Nb10O30 is not present for K(6−x−y)Li(4+x)Nb(10+y)O30. The K/Li atom at the A1 site is 12 coordinated with average K/Li–O distance of 2.833 Å. The K/Li atom at the A2 site is nine coordinated with average K/Li–O distance of 3.024 Å. The Li/Nb atom at the C site has three nearest oxygen neighbors at an average distance of 2.153 Å and six additional next-nearest neighbors at an average distance of 2.542 Å. The two independent irregular NbO6 octahedra have an average Nb–O separation of 1.973 Å. The Nb atom displacements, of 0.167 and 0.160 Å from the nearest mean oxygen plane, may be compared with the value of 0.175 Å predicted from the parabolic relation with Curie temperature. All metal atoms are displaced from the mean planes of oxygen in the same sense, making the positive polarization direction parallel to the sense of this displacement.

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 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 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.