X-ray diffuse scattering in SrTiO₃and model of atomic displacements

Abstract

The scattering intensity of synchrotron radiation in a compact three‐dimensional volume of the reciprocal space (sinθmax/λ = 0.6283 Å−1) of an SrTiO3 single crystal has been measured at temperatures of 115, 130 and 293 K. The curvilinear features of the diffuse pattern were modelled according to the displacements of both cations correlated along the axis [001]cub (where the subscript cub denotes the cubic structure). The results show that Sr2+ is displaced from the ideal positions along the crystallographic axis [001]cub, forming a short chain composed of about three Sr2+ ions along [001]cub, while the Ti4+ ions are moved in the directions [111]cub, or alternatively [101]cub or [011]cub. The Ti4+ displacements are also correlated along [001]cub, forming a similarly short chain.

Atomistic modeling of diffuse scattering in cubic PbZrO3

“…[22] Similar DS lines related to octahedral disorder have been reported for NaNbO 3 [35] and SrTiO 3 . [7] Highly structured, sharp DS for oxygen atoms indicates that the anti-ferrodistortive tilting mode is rather strong and indeed may play an important rather than a secondary role in stabilizing the low-temperature AFE phase. From separate contributions to total DS, it can be deduced that the bending of diffuse lines is coming from PbÀO interaction (no bending for a calculation with O alone) and thus contains information on the coupling of the tilting and Pb-based modes.…”

“…in cubic SrTiO 3 related to octahedral tilting. [7] Recent works reported DS around selected Bragg reflections in patterns of cubic PZO. The strongly anisotropic shape of these diffuse features, reminiscent of those in FE relaxors, has been attributed to a specific correlation pattern related to the flexoelectric coupling of optic and acoustic modes.…”

Lattice dynamics and Raman spectrum of BaZrO3 single crystals

“…In contrast, in SrTiO 3 or CaTiO 3 , both contribution are or equal strength. Those compounds also share common experimental signatures related to local disorder of the Ti 4+ ion in the octahedral cage, with the presence of intense diffuse scattering [50], and distinctive features in XANES [51]. We therefore expect that studies of the local structure in BaZrO 3 will be insightful to reveal the details and dynamics and disorder, and we note that a previous study has already proposed anomalous Ba displace-ments, revealed by anomalously large DebyeâĂŞWaller (DW) factor in BaZrO 3 structural refinements [11].…”

Lattice instabilities in bulk EuTiO3

“…In addition, the atomic displacement parameters, ADP, of Eu, Ti and O at 180 K extracted in the harmonic approximation are 21.0(8), 7.3(5) and 7.5(5) (x10 −3 Å 2 ) respectively and do not show any substantial irregularity vs temperature. Note that in isostructural SrTiO 3 the atomic displacements of Sr and Ti in the antiferrodistortive phase are comparable [29] to that of Eu in EuTiO 3 .…”