Uncompensated Polarization in Incommensurate Modulations of Perovskite Antiferroelectrics

Tao Ma, Zhongming Fan, Bin Xu, Tae-Hoon Kim, Ping Lu, Laurent Bellaiche, Matthew J. Kramer, Xiaoli Tan, and Lin Zhou

Phys. Rev. Lett. 123, 217602 – Published 19 November 2019

Abstract

Complex polar structures of incommensurate modulations (ICMs) are revealed in chemically modified ${PbZrO}_{3}$ perovskite antiferroelectrics using advanced transmission electron microscopy techniques. The Pb-cation displacements, previously assumed to arrange in a fully compensated antiparallel fashion, are found to be either antiparallel, but with different magnitudes, or in a nearly orthogonal arrangement in adjacent stripes in the ICMs. Ab initio calculations corroborate the low-energy state of these arrangements. Our discovery corrects the atomic understanding of ICMs in ${PbZrO}_{3}$ -based perovskite antiferroelectrics.

Received 24 May 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.217602

Physics Subject Headings (PhySH)

Antiferroelectrics Electronically polarized systems Ferroelectrics

Density functional calculations Transmission electron microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Tao Ma ^1,‡, Zhongming Fan^2,‡, Bin Xu^3,4, Tae-Hoon Kim¹, Ping Lu⁵, Laurent Bellaiche³, Matthew J. Kramer^1,2, Xiaoli Tan^2,*, and Lin Zhou ^1,2,†

¹Ames Laboratory, U.S. Department of Energy, Ames, Iowa 50011, USA
²Department of Materials Science and Engineering, Iowa State University, Ames, Iowa 50011, USA
³Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, Arkansas 72701, USA
⁴School of Physical Science and Technology, Soochow University, Suzhou, Jiangsu 215006, China
⁵Sandia National Laboratories, P.O. Box 5800, MS 1411, Albuquerque, New Mexico 87185, USA

^*Corresponding author. xtan@iastate.edu
^†Corresponding author. linzhou@ameslab.gov
^‡T. M. and Z. F. contributed equally to this work.

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Vol. 123, Iss. 21 — 22 November 2019

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Images

Figure 1
(a) Typical HAADF-STEM image of CMs in ${PbZrO}_{3}$ , with the SAED pattern shown in the inset. A Pb-displacement vector map is overlaid on the image, showing the antiparallel displacements of Pb cations in adjacent stripes. (b) Schematic model of the CMs for ${PbZrO}_{3}$ proposed by Sawaguchi et al. [7]. $A$ site (Pb), gray; $B$ site (Zr), blue. (c) Typical bright-field TEM image of ICMs in a Sn, Ti, Nb comodified ${PbZrO}_{3}$ ceramic, with the SAED pattern shown in the inset. The ICMs are rendered as fine fringes with a periodicity of $\sim 2 nm$ . (d) Schematic model of the ICMs as a mixture of stripes with a stochastic thickness of two to four layers of the ${110}_{c}$ plane, proposed by He and Tan [11]. $A$ site (Pb), gray; $B$ site (Zr, Sn, Ti, Nb), pink.
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Figure 2
The top row is the typical bright-field TEM images of 90° domains in (a) PZ-3, (d) PZ-5, and (g) PZ-6. (Insets) SAED patterns taken from the domain boundary region showing two sets of satellite spots, from which the periodicity of the ICMs ( $n$ value) was calculated. The middle row shows the Pb-displacement vector maps overlaid on the HAADF-STEM images taken from the upper domains in (b) PZ-3, (e) PZ-5, and (h) PZ-6. The Pb displacements in this row are in an antiparallel arrangement, but those in the wider stripes (blue) have a larger magnitude than the ones in the narrower stripes (yellow). The bottom row presents the Pb-displacement vector maps taken from the lower domains in (c) PZ-3, (f) PZ-5, and (i) PZ-6, where the Pb displacements tend to form in a nearly orthogonal arrangement in adjacent stripes.
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Figure 3
(a)–(c) Pb-displacement magnitudes, extracted from the Pb-displacement vector maps, and the corresponding polarizations in (a) PZ-3, (b) PZ-5, and (c) PZ-6. The upper plots in each panel (blue) are from the antiparallel side showing the components along the two antiparallel $⟨ 110 ⟩_{c}$ directions, whereas the lower plots in each panel (pink) are from the orthogonal sides showing the components along the two orthogonal $⟨ 100 ⟩_{c}$ directions. The displacements were averaged from ten layers of Pb cations along the length direction of the ICM stripes. (d) Overall polarizations in the antiparallel and orthogonal sides of the three specimens calculated from the corresponding vector maps.
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Figure 4
(a) DFT calculated energies of the antiparallel and orthogonal domain structures relative to the AFE phase ( $P b a m$ -like) for ${PbZrO}_{3}$ and $Pb ({Zr}_{0.5} {Sn}_{0.5}) O_{3}$ . (b),(c) DFT optimized antiparallel and orthogonal domain structures of ${PbZrO}_{3}$ . (d),(e) DFT optimized antiparallel and orthogonal domain structures of $Pb ({Zr}_{0.5} {Sn}_{0.5}) O_{3}$ . Pb, gray; Zr, blue; Sn, green; O, red. Pb displacements are denoted in blue and yellow in different stripes. The atom position and displacement data used to create (b)–(e) are listed in Tables S4, S5, S6, and S7, respectively, in the Supplemental Material [20].
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