Diffuse scattering from the lead-based relaxor ferroelectric PbMg_1/3Ta_2/3O₃

Abstract

The relaxor ferroelectric PbMg1/3Ta2/3O3 was studied by single‐crystal neutron and synchrotron X‐ray diffraction, and its detailed atomic structure modelled in terms of static Pb displacements that lead to the formation of polar nanoregions. Similar to the other members of the Pb‐based relaxor family like PbMg1/3Nb2/3O3 or PbZn1/3Nb2/3O3 the diffuse scattering in the [H00]/[0K0] scattering plane has a butterfly shape around the h00 Bragg reflections and is orthogonal to the scattering vector for hh0 peaks. In the [HH0]/[00L] plane the diffuse scattering is elongated along the 〈112〉 directions and is orthogonal to the scattering vector for hhh reflections. It is found that a model consisting of correlated Pb displacements along the 〈111〉 directions reproduces adequately the main features of the diffuse scattering in PbMg1/3Ta2/3O3 when the correlation lengths between the Pb‐ion displacement vectors are longest along the 〈111〉 and shortest along the 〈11〉 and 〈10〉 directions.

Role of random electric fields in relaxors

“…The origin of this diffuse scattering is extremely controversial. Numerous models of the underlying shortrange structural order have been proposed to explain the experimental data (25,(28)(29)(30)(31)(32). Neutron backscattering measurements (33,34), which provide very sharp energy resolution ðΔE ∼ 1 μeVÞ, show that truly elastic (i.e., static) diffuse scattering in PMN first appears at a temperature T d = 420 ± 20 K that coincides with that at which the lowest-frequency transverse optic (TO) phonon is softest and overdamped; it also grows monotonically on cooling (35).…”

Crystal symmetry breaking and vacancies in colloidal lead chalcogenide quantum dots

“…26), well below the DSE-based results. We attribute such overestimation to the well-known anisotropic and anharmonic distribution of Pb atom displacements 8,33 , accounted for neither in powder diffraction analyses nor in our model. Nevertheless, the χ 2 values for the vacancy level indicated by DFT remains markedly lower than for a stoichiometric PbS core (see Supplementary Fig.…”

Lead-free and lead-basedABO3perovskite relaxors with mixed-valenceA-site andGe1, Devreugd2, Phelan3 et al. 2013Phys. Rev. B624490View full textAdd to dashboardCite

“…These are consistent with the results of previous x-ray and neutron scattering studies. 17,26,69 As is the case with other lead-based, B-site disordered relaxors such as PZN, 21 PMT, 29 PST, 70 and PSN, 34 these contours can all be approximated by a superposition of one or more ellipsoidal distributions of diffuse scattering that are centered on each Bragg peak and oriented with the long axis aligned along 110 . 21 Following the usage established by Xu et al in Ref.…”

“…[25][26][27][28] The diffuse scattering in these compounds has been extensively studied and many different models have been proposed to explain the experimental data. Among these models, some assume (a) the presence of thin, pancake-shaped PNR, 21,[29][30][31] (b) three-dimensional PNR for which the domain walls are parallel to {110} crystallographic planes, 32 (c) correlated Pb displacements oriented along 110 , 29,30,33 or (d) correlations between PNR embedded in an atomically disordered matrix (ADM). 34 But to date there is little consensus on its origin.…”

“…34 But to date there is little consensus on its origin. 21,29,30,[32][33][34][35] In 2006, Matsuura et al made the interesting observation that the compositional dependence of the diffuse scattering in PMN-xPT correlates with that of the longitudinal piezoelectric coefficient d 33 . 36 More specifically, the peak diffuse scattering intensity at the Brillouin-zone center (q = 0), the q-integrated diffuse scattering intensity, and the associated correlation length measured along [11 0] all increase rapidly as the system is doped towards the MPB, 36 which is where the piezoelectric coefficient d 33 is largest.…”