Multiple structural components and their competition in the intermediate state of antiferroelectric $\mathrm{Pb}(\mathrm{Zr},\mathrm{Ti}){\mathrm{O}}_{3}$

Multiple structural components and their competition in the intermediate state of antiferroelectric $Pb (Zr, Ti) O_{3}$

Zheyi An, Hiroko Yokota, Nan Zhang, Marek Paściak, Jan Fábry, Miloš Kopecký, Jiří Kub, Guanjie Zhang, A. M. Glazer, T. R. Welberry, Wei Ren, and Zuo-Guang Ye

Phys. Rev. B 103, 054113 – Published 23 February 2021

Abstract

Antiferroelectric perovskites form an important family of functional electric materials, which have high potential in energy storage and conversion applications. However, a full understanding of their crystal structural formation is still lacking. ${PbZrO}_{3}$ -based materials can serve as a model system for investigation, not only because ${PbZrO}_{3}$ was the first discovered antiferroelectric, but also because it undergoes a typical phase transition sequence from a high-temperature paraelectric to the low-temperature antiferroelectric phase, passing through a possible intermediate phase that is poorly understood. Here we employ a combination of optical and scattering experiments and theoretical calculations to reveal the nature of the intermediate state. Evidence is found that this peculiar state consists of multiple short-range and long-range structural components, and their competition is crucial in stabilizing the antiferroelectric phase. External stimuli such as temperature change or chemical substitution can easily alter each component's energy landscape and thereby change the materials' electrical properties. These findings provide insights into understanding antiferroelectric-ferroelectric competition and can be useful in designing alternative antiferroelectric materials.

Received 29 October 2020
Revised 17 January 2021
Accepted 3 February 2021

DOI:https://doi.org/10.1103/PhysRevB.103.054113

Physics Subject Headings (PhySH)

Antiferroelectricity Crystal structure Ferroelectricity Phase diagrams Phase transitions by order

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Zheyi An ^1,*, Hiroko Yokota ^2,*, Nan Zhang ^1,†, Marek Paściak ^3,‡, Jan Fábry³, Miloš Kopecký³, Jiří Kub³, Guanjie Zhang¹, A. M. Glazer^4,§, T. R. Welberry⁵, Wei Ren¹, and Zuo-Guang Ye ⁶

¹Electronic Materials Research Laboratory, Key Laboratory of the Ministry of Education & International Center for Dielectric Research, School of Electronic Science and Engineering, Xi'an Jiaotong University, Xi'an 710049, China
²Department of Physics, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba City 263-8522, Japan and JST PRESTO, 7 Goban-cho, Chiyoda-Ku, Tokyo 102-0076, Japan
³Institute of Physics of the Czech Academy of Sciences, Na Slovance 2, 182 21 Prague 8, Czech Republic
⁴Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom and Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
⁵Research School of Chemistry, Australian National University, Canberra ACT 2601, Australia
⁶Department of Chemistry and 4D LABS, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia, Canada V5A 1S6

^*These authors contribute equally to this work.
^†nzhang1@xjtu.edu.cn
^‡pasciak@fzu.cz
^§mike.glazer@physics.ox.ac.uk

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Vol. 103, Iss. 5 — 1 February 2021

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Figure 1
Reciprocal space maps and domain configurations of a PZT single crystal (crystal 1) in AFE, IM, and cubic phases. (a)–(c) X-ray scattering data on the (h k 1) plane at 150 °C (AFE phase), 215 °C (IM state), and 240 °C (cubic phase), respectively. The square and circle indicate a typical quarter and M-point reflection, respectively. The arrow points to the incommensurate spot. Insets of (d)–(f) show mappings of |sinδ| values from the same area of the crystal at 140 °C (AFE phase), 232 °C (IM state), and 240 °C (cubic phase), respectively. Black lines are projections of the principal optic axes on the ${001}_{p c}$ plane, indicating ferroelastic domain orientations. Histograms of the orientations are shown in (d)–(f).
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Figure 2
Diffraction patterns and DS intensities during phase-change process of two crystals. (a)–(d) Data containing $M$ point (–2.5 2.5 0), quarter reflection (–2.25 2.75 0), and IC spot (–2.16 2.84 0) collected from crystal 1 at 150 °C, 180 °C, 210 °C, and 230 °C, respectively. (g)–(j) Data containing $M$ point (–1.5 0.5 0), quarter reflection (–1.25 0.75 0), and IC spot (–1.16 0.84 0) collected from crystal 2 at 136 °C, 198 °C, 207 °C, and 224 °C, respectively. The arrows point to the IC points. It should be noted that due to the structure factor being additive for $h + k + l = even$ , diffuse scattering around (–1 1 0) is stronger than that around (–2 3 0). Three-dimensional (3D) intensity was integrated over a range in $l$ corresponding to around ± 0.1 reciprocal lattice unit (r.l.u.) to produce two-dimensional (2D) patterns. (e), (f) Intensity developments along $[110]_{p c}$ at more temperatures. One-dimensonal (1D) diffraction pattern was obtained by integrating 2D images over a range along [–1 1 $0]_{p c}$ with ± 0.1 r.l.u. width.
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Figure 3
Integrated DS intensities of superstructure reflections evolving with temperature. 1D intensities of reflections in the same area on the main planes, as in Figs. 2 and 2, and on half plane (h k 0.5), were integrated along $[110]_{p c}$ . (a) $M$ point (−2.5 2.5 0), quarter reflection (averaged over −2.25 2.75 0 and −1.75 3.25 0), IC point (averaged over −2.16 2.84 0 and −1.84 3.16 0), and $R$ point (−1.5 2.5 0.5) on crystal 1. (b) $M$ point (−1.5 0.5 0), quarter reflection (−1.25 0.75 0), and $R$ point (−1.5 −1.5 0.5) on crystal 2. The intensity of the weak IC point (−1.16 0.84 0) in (b) was multiplied by 50 to make it visible. The dashed lines are a guide for the eyes.
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Figure 4
The diffuse scattering intensity with crystal 2 of a selected region on the (h k 0.5) plane evolving with temperature. 3D intensity was integrated over a range in $l$ corresponding to ± 0.1 r.l.u. to produce 2D patterns.
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Figure 5
Powder diffraction and modeled local structure in the IM state. (a) X-ray total scattering intensity ( $λ = 0.161 669 Å$ ) in the 2θ range between ${222}_{p c}$ and ${321}_{p c}$ with ${PbZr}_{0.95} {Ti}_{0.05} O_{3}$ ceramic powder at 210 °C−250 °C. Inset of (a) zoomed-in plot of an M-point reflection, the position of which corresponds to ${7 / 2 1 / 2 0}_{p c}, {5 / 2 5 / 2 0}_{p c}$ , and ${3 / 2 5 / 2 2}_{p c}$ . (b) Experimental PDF pattern generated from total scattering data at 210 °C and the best-fit PDF. Dashed lines indicate the fitted PDF components of Phase 1 and Phase 2. (c) Experimental (red) and refined (black) HRPD data with ${PbZr}_{0.94} {Ti}_{0.06} O_{3}$ ceramic powder at 200 °C with arrows indicating M-point positions. Blue and orange lines indicate the calculated patterns from Rietveld-refined Phase 1 (Pc) and Phase 2 (Cm) structures, respectively. Logarithmic values of intensities are used to demonstrate the low-intensity $M$ points. Full-range data are shown in Fig. S4 of the Supplemental Material [34]. (d), (e) Schematic drawings of modeled Phase 1 and 2 structures, respectively. The arrows represent displacement vectors of Pb cations. The orange arrows (Pb1 and Pb4) and planes belong to chain I while the blue ones (Pb2 and Pb3) belong to chain II.
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Figure 6
Competition among local-structural components. Schematic diagram showing the proportions of local-structural components as a function of temperature in a typical AFE PZT crystal. Proportions of components at a certain temperature equal to the intersection of this diagram and a vertical line at this temperature. The dashed lines correspond to the cases discussed in Figs. 2–2, respectively.
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Physical Review B

covering condensed matter and materials physics

Multiple structural components and their competition in the intermediate state of antiferroelectric $Pb (Zr, Ti) O_{3}$

Zheyi An, Hiroko Yokota, Nan Zhang, Marek Paściak, Jan Fábry, Miloš Kopecký, Jiří Kub, Guanjie Zhang, A. M. Glazer, T. R. Welberry, Wei Ren, and Zuo-Guang Ye

Phys. Rev. B 103, 054113 – Published 23 February 2021

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Physical Review B

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Multiple structural components and their competition in the intermediate state of antiferroelectric Pb(Zr,Ti)O3

Zheyi An, Hiroko Yokota, Nan Zhang, Marek Paściak, Jan Fábry, Miloš Kopecký, Jiří Kub, Guanjie Zhang, A. M. Glazer, T. R. Welberry, Wei Ren, and Zuo-Guang Ye

Phys. Rev. B 103, 054113 – Published 23 February 2021

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Multiple structural components and their competition in the intermediate state of antiferroelectric $Pb (Zr, Ti) O_{3}$