Ferroelectric Tungsten Bronze-Type Crystal Structures. II. Barium Sodium Niobate Ba(4 + x)Na(2 − 2x)Nb10O30

Abstract

Ferroelectric ${\mathrm{Ba}}_{\text{(4+x)}}{\mathrm{Na}}_{\text{(2\hspace{0.17em}−\hspace{0.17em}2x)}}{\mathrm{Nb}}_{10}{O}_{30}$ , with a Curie temperature of 833°K, has a tungsten bronze‐type structure and crystallizes in the orthorhombic system, with subcell lattice constants $\text{a\hspace{0.17em}=\hspace{0.17em}17.59182\hspace{0.17em}±\hspace{0.17em}0.00001, b\hspace{0.17em}=\hspace{0.17em}17.62560\hspace{0.17em}±\hspace{0.17em}0.00005}$ , and $\text{c\hspace{0.17em}=\hspace{0.17em}3.994915\hspace{0.17em}±\hspace{0.17em}0.000004 Å}$ 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 $\mathrm{(sin}{\text{θ)/λ\hspace{0.17em}=\hspace{0.17em}1.02 Å}}^{\text{−1}}$ 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 ${\text{(A1)}}_2{\text{(A2)}}_4{C}_4{\text{(B1)}}_2{\text{(B2)}}_8{O}_{30}$ , the $\text{B1}$ and $\text{B2}$ sites are fully occupied by Nb, the $\text{A2}$ sites by Ba and the $\text{A1}$ 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 Ba_4.13Na_1.74Nb₁₀O₃₀. The Ba and O atoms at $\mathrm{z\hspace{0.17em}\simeq \hspace{0.17em}}\frac{1}{2}$ 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 $P_s$ 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.