Anharmonic atomic vibrations in the relaxor ferroelectric Pb(Mg1/3Nb2/3)O

Abstract

Structural analyses of the relaxor ferroelectric material Pb(Mg 1/3 Nb 2/3 )O 3 (PMN) with single-crystal x-ray diffraction under pressure in a diamond anvil cell indicate static atomic displacement and chemical disorder. Difference Fourier analysis within the framework of a harmonic oscillator model for the atomic vibrations reveals residual electron density on both the Pb and Nb (Mg) sites. Pb atoms in the A site of the ABO 3 perovskite structure exhibit a greater displacement than the Nb(Mg) atoms in the B-site, despite the fact that Pb is a much heavier atom. The displacement is interpreted in terms of an anharmonic statistical atomic motion. At pressures above 2.5 GPa the displacement disappears, consistent with previous observations. The difference Fourier maps reveal no residual electron densities greater than 1 e/Å 3 at any atomic position, and these are appear to be induced by the violation of local electrical neutrality arising from both Mg 2+ and Nb 5+ ions located at the octahedral site. Similar electron densities are observed at all experimental pressures and in refinements based on both harmonic and anharmonic models. The anharmonic parameters taken into account are the higher-order tensors of atomic elastic motion. At high pressure, where the relaxor transforms to a paraelectric phase, the residual electron densities disappear. 2

Structural transitions in Pb(In1∕2Nb1∕2)O3 under pressure

“…It has been shown that the butterfly shaped diffuse X-ray scattering is originated from PNRs in relaxors and is gradually suppressed with increasing pressure. 21,22,24,37,49 The Raman spectra obtained at high pressure in Pb-based relaxors is inconsistent with paraelectric cubic symmetry, and it also differs from the Raman spectra observed at low temperatures and ambient pressures. Several high-pressure studies on Pb-based relaxors such as PSN, 20 PMN, 22 (5) suggested that the transition to the high-pressure phase involves octahedral tilting.…”

“…Recent theoretical calculations and experiments point out that the displacement of Pb cation in these materials have strong correlations along particular crystallographic directions, that gives diffuse scattering in relaxor materials. 37,49 A common feature of high-pressure phase of Pb-based relaxors is a new peak appearing around 380 cm À1 in Raman spectra for all these studied Pb-based relaxor samples including PbTiO 3 . A similar peak appeared in PIN above 1 GPa, and the frequency of this peak is located around the bending mode region in general.…”

Pressure evolution of PbMg1/3Nb2/3O3 relaxor ferroelectric

“…This is why no further structural analysis is done on the sole basis of Bragg reflections. Notably, an accurate study of strong Bragg reflections for an analysis of anharmonic thermal vibrations does not report any superstructure spots up to 73 kbar [15]. That could be due to a point detector technique and collection of the data only for Bragg nodes expected for Pm3m symmetry, which obviously makes the results over-interpreted.…”

Electron hybridization and anharmonic thermal vibration effect on structure transition of SrTiO3 at high-pressure and low-temperature

“…We adopted a multimodal distribution in the probability density function using cumulant expansion and Gram-Charlier series expansion [34] [35]. We take into account of fourth-rank in T ij (hkl) in eq.…”