We found that the high-pressure-synthesized material LiOsO 3 (see Supplementary Information) shows a structural transition at a temperature T s = 140 K. The room-temperature crystal structure of LiOsO 3 was initially examined using powder X-ray diffraction (XRD). The Goldschmidt diagram predicts that LiOsO 3 crystallizes into a LiNbO 3 -type structure 3,10 , and a preliminary refinement of the structure was carried out in the R-3c space group with Os at the 6b site 0,0,0 and O at the 18e siteTo investigate the position of the Li ion we turned to neutron diffraction, which is much more sensitive to Li than XRD. The neutron diffraction patterns collected above T s could be successfully described in the R-3c space group, in agreement with the XRD refinement, with the Li ion at the 6a position 0,0,1/4. Atomic absorption spectrometry (see Supplementary Information) indicated that the average Li mass was 2.77%, which corresponds to the composition Li 0.98 OsO 3 . We have used the stoichiometric composition throughout the structural analysis. The refinement indicated highly anisotropic thermal displacements of the Li ions with considerable extension along the c-axis (Table 1 and Fig. 1), which might indicate that the Li ions are distributed equally among equivalent 12c sites 0,0,z and 0,0,1/2-z either side of the oxygen layer at z = 1/4, as reported for LiNbO 3 and LiTaO 3 (refs 3, 11).The thermal variation of the structure of LiOsO 3 was studied by neutron diffraction for temperatures between 10 and 300 K. Figure 1a-d shows structural data obtained from refinements in the R-3c space group. The lattice parameters ( Fig. 1a) decrease uniformly from 300 K until T s = 140 K, below which the parameter c increases and a decreases with only a small variation in the unit-cell volume. Just below T s , the non-symmetry-breaking strain components e xx + e yy and e zz vary almost linearly (Fig. 1b). These 4 results show that the phase transition is continuous and the strain components behave like a secondary order parameter coupled to a primary one via a linear-quadratic free energy invariant 12 . The primary order parameter must necessarily be symmetry-breaking according to Landau's theory of second-order phase transitions 12 . Furthermore, the anisotropic thermal parameter 33 , which describes Li displacements along the c-axis, increases markedly below T s (Fig. 1c). This indicates that the primary structural instability involves the position of the Li ions along the c-axis (Fig. 1d).Given that the phase transition involves a change in symmetry, we find from representation theory 13 that there are three isotropy subgroups, R-3, R32 and R3c, which maintain the translational invariance of the R-3c space group and allow the transition to be continuous. These space groups were tested by refinement against the neutron diffraction data at 10 K. Note that R-3 and R32 should generate additional reflections below T s which were not observed in the experiment. The refinement in the non-centrosymmetric R3c space group gave the best de...
Crystal structure of ferroelectric silver niobate AgNbO3 was determined (Pmc21) by convergent beam electron, electron, neutron, and synchrotron diffraction techniques and first-principles calculations. The atomic displacements along the c axis in Pmc21 AgNbO3 are responsible for the spontaneous polarization, ferroelectricity, and the paraelectric−ferroelectric phase transition.
A new method to refine crystal structural parameters using convergent-beam electron diffraction (CBED), which is applicable to nanometre-size crystal structure analysis, is proposed. This method is based on the fitting between theoretical calculations and experimental intensities of energy-filtered two-dimensional CBED patterns containing higher-order Laue-zone (HOLZ) reflections. The use of HOLZ reflections is essential for the method because small displacements of atoms can be sensitively detected using HOLZ reflections with large reciprocal vectors. For this purpose, a new Omega-filter transmission microscope (JEM-2010FEF), which can take energy-filtered CBED patterns up to a high angle with a small distortion, and a new analysis program to refine structural parameters, which is based on many-beam Bloch-wave calculations and nonlinear least-squares fitting, have been developed. As a test example, a positional parameter and isotropic and anisotropic Debye-Waller factors of CdS have been refined. Two-dimensional CBED patterns calculated with the refined parameters show very good agreement with the experimental ones, and the refined values of the parameters also agree well with the result of a single-crystal X-ray diffraction experiment. Important problems of the analysis procedure are discussed item by item.
The method to refine crystal structure parameters (atom positions and Debye-Waller factors) using convergentbeam electron diffraction (CBED), which is applicable to crystal structur~ analysis of a small specimen area down to a few nm in diameter, is studied. The line profiles of higher-order Laue-zone reflections are recorded using imaging plates. Theoretical intensities are calculated based on the dynamical theory of electron diffraction with the aid of the generalized Bethe approximation to shorten calculation time. The structural parameters are determined by fitting the experimental profiles with the theoretical ones using a nonlinear leastsquares method. The present method has been applied to the low-temperature phase of SrTiO3. The structural parameter or the rotation angle of the oxygen octahedron has been determined to be qo --1.12 (4) °, which shows good agreement with that obtained from electron spin resonance experiments.
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