We present a fully atomistic model of polar nanoregions (PNRs) in the relaxor ferroelectric PbMg 1/3 Nb 2/3 O 3. Our molecular dynamics calculations reproduce both the characteristic form of the neutron diffuse scattering distribution and its temperature dependence. A shell model was used with a modified version of a published interatomic potential that was based on ab initio calculations. The parameters of this potential were optimized for the present work to provide a better description of the O atom interactions, as these are particularly important for neutron scattering. At high temperatures the Pb ions are displaced from their mean site positions in a direction that has an isotropic distribution, but at low temperatures the distribution condenses into eight localized sites displaced from the average position along each of the eight possible 1 1 1 directions. At intermediate temperatures (300 K) the distribution is cuboidal with some preference for 1 1 1 displacements but with all possible displacement directions present. Longitudinal correlations between the displacements of Pb-Mg/Nb and Pb-O increase monotonically in magnitude as the temperature changes from 700 K to 10 K with the sign of the Pb-O correlation being negative. At low temperatures this increase in correlation results in polar nanoregions that are clearly visible in plots of the local structure, although the exact form of these domains is more difficult to visualize. We show that the form of these PNRs can be revealed by an examination of conditional displacement distributions at low temperatures. Therein a strongly anisotropic cooperative displacement behavior is found. Remnants of this correlation pattern persist at much higher temperatures, but progressively a relatively smaller proportion of the Pb ions appears to be taking part and there is a substantially larger random component. It seems likely that the onset of the characteristic structured diffuse scattering at around 400 K coincides with the appearance of this cooperative displacement behavior.
Pair distribution function analysis of neutron-scattering data and of ab initio molecular dynamics results have been employed to study short-range structural correlations and their temperature dependence in a heavily disordered dielectric material Sr x Ba 1−x Nb 2 O 6 (x = 0.35, 0.5, and 0.61). Intrinsic disorder caused by a partial occupation of the cationic sites by differently sized Sr and Ba atoms and their vacancies introduces important local strains to the structure and directly influences the Nb-O 6 octahedra tilting. The resulting complex system of tilts is found to be both temperature and Sr-doping sensitive with the biggest tilt magnitudes reached at low temperatures and high strontium contents, where ferroelectric relaxor behavior appears. We find evidence for two Nb-O 6 subsystems with different variations of niobium-oxygen bond lengths, distinct dynamics, and disparate levels of deviation from macroscopic polarization direction. These findings establish a detailed picture of the local structure of Sr x Ba 1−x Nb 2 O 6 and provide a deeper insight into the origins of the materials dielectric properties.
Incommensurate satellite reflections modulating along the 〈110〉* directions have been observed in the electron diffraction patterns of single crystals of the relaxor ferroelectric Pb2ScTaO6 (PST) recorded via transmission electron microscopy. The satellites occur characteristically within a specific temperature range and display differing or variable modulation vectors relative to their primary reflections. The satellites represent a weak frustrated antiferroelectric state in PST, termed the incommensurate antiferroelectric (IAFE) state. The observed IAFE state coexists with the ferroelectric and paraelectric states within a specific temperature regime and is dynamic in nature, meaning that the dispositions of the satellites can be altered by varying the temperature applied to the crystal, in‐situ in the transmission electron microscope. The observed satellites are associated with thin, needle‐shaped, closely packed striated domains of about 5–15 nm in width. The satellites appear exclusively in crystals of PST with an advanced degree of 1:1 chemical long‐range order, exceeding 90%. The satellites and their domains are interpreted as originating from a displacive, antiferroelectric coupling of the ions, driven in particular by the Pb ions. The Monte Carlo (MC) method was used exhaustively to evaluate the structural regimes that lead to the occurrence of the IAFE state. In the MC simulations, the displacements were correlated with the ferroelectric and antiferroelectric couplings, resulting in the IAFE domains and their associated satellites of differing dispositions or modulation vectors. The results of the MC simulations agree well with the electron diffraction observations, supporting the model of an antiferroelectric displacement with an incommensurate modulation of the Pb ions in the 〈110〉* directions.
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