A size effect on crystal structure has been investigated for barium titanate (BaTiO3) nanoparticles of 40-, 140-, and 430-nm sizes, by means of neutron and high-resolution synchrotron x-ray powder-diffraction and Raman-scattering techniques. These samples were prepared by a modified two-step thermal decomposition method from barium titanyl oxalate, resulting in very few lattice impurities. Rietveld analysis of the neutron-diffraction data for the 430-nm- and 140-nm-sized BaTiO3 particles was performed assuming a single phase of tetragonal (P4mm) structure. The axial ratio c∕a of tetragonal BaTiO3 decreases with a decrease in particle size from 430 to 140 nm. Barium titanate particles with a size of 40 nm consist of (1) tetragonal crystals (83 wt %) with a large cell volume and an axial ratio of unity c∕a=1.000(5) and of (2) a hexagonal phase (P63mmc, 17 wt %) with a large unit-cell volume. Rietveld and maximum-entropy method analyses suggest that there exist atomic displacements from the ideal site of a cubic structure and a spontaneous polarization of the tetragonal phase even in the 40-nm-sized BaTiO3 particles. The nuclear-density distribution of the 140-nm-sized particles with a high dielectric constant does not exhibit a large positional disorder, while the Ba atom of tetragonal BaTiO3 in the 40-nm-sized particles has a smaller atomic displacement parameter.

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Accurate nuclear-density distribution of bismuth oxide solution Bi1.4Yb0.6O3 compound has been studied at 384 °C and at 738 °C by the maximum-entropy method (MEM) and MEM-based pattern fitting combined with the Rietveld method using neutron powder diffraction data. The results reveal that the oxide ions have a complicated disorder spreading over a wide area, shift to the ⟨111⟩ directions from the ideal fluorite position and diffuse along the ⟨100⟩ directions.

Temperature dependence of lattice parameters of bismuth sesquioxide (Bi2O3) has been obtained between 26° and 778°C by the Rietveld method using neutron powder diffraction data. Lattice parameters and unit‐cell volume of α and δ phases increased, while the β angle of α phase decreased with an increase of temperature. Here the denotes the lattice parameter a of the α phase on the basis of pseudo‐fluorite lattice. The thermal expansion coefficients of α phase were 26.7, 6.6, and 9.0 (× 10−6°C−1) for and axes, respectively, indicating a large anisotropy. The α‐ to ‐δ phase transition of Bi2O3 was confirmed between 721° and 760°C on heating. At the α–δ transition point, the lattice parameters and unit‐cell volume discontinuously changed, indicating that the transition is of the first order.