Evolution of ferroelastic domain walls during phase transitions in barium titanate nanoparticles

Jiecheng Diao, Xiaowen Shi, Tadesse A. Assefa, Longlong Wu, Ana F. Suzana, Daniel S. Nunes, Darren Batey, Silvia Cipiccia, Christoph Rau, Ross J. Harder, Wonsuk Cha, and Ian K. Robinson

Phys. Rev. Materials 4, 106001 – Published 27 October 2020

Abstract

In this work, ferroelastic domain walls inside ${BaTiO}_{3}$ (BTO) tetragonal nanocrystals are distinguished by Bragg peak position and studied with Bragg coherent x-ray diffraction imaging (BCDI). Convergence-related features of the BCDI method for strongly phased objects are reported. A ferroelastic domain wall inside a BTO crystal has been tracked and imaged across the tetragonal-cubic phase transition and proves to be reversible. The linear relationship of relative displacement between two twin domains with temperature is measured and shows a different slope for heating and cooling, while the tetragonality reproduces well over temperature changes in both directions. An edge dislocation is also observed and found to annihilate when heating the crystal close to the phase transition temperature.

Received 6 June 2020
Revised 4 September 2020
Accepted 11 September 2020

DOI:https://doi.org/10.1103/PhysRevMaterials.4.106001

Physics Subject Headings (PhySH)

Ferroelectric domains

X-ray imaging

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jiecheng Diao ^1,*, Xiaowen Shi^3,†, Tadesse A. Assefa ², Longlong Wu ², Ana F. Suzana ², Daniel S. Nunes¹, Darren Batey³, Silvia Cipiccia³, Christoph Rau³, Ross J. Harder ⁴, Wonsuk Cha ⁴, and Ian K. Robinson ^1,2,‡

¹London Centre for Nanotechnology, University College London, London WC1E 6BT, United Kingdom
²Condensed Matter Physics and Materials Science Department, Brookhaven National Lab, Upton, New York 11793, USA
³Diamond Light Source, Oxfordshire, OX11 0QX, United Kingdom
⁴Advanced Photon Source, Argonne National Lab, Lemont, Illinois 60439, USA

^*Corresponding author: jiecheng.diao.18@ucl.ac.uk
^†Present address: Department of Physics, New Mexico State University, Las Cruces, New Mexico 88003, USA and Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY, 12180, USA.
^‡Corresponding author: i.robinson@ucl.ac.uk

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Issue

Vol. 4, Iss. 10 — October 2020

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Images

Figure 1
Ferroelastic domain walls in ${BaTiO}_{3}$ nanocrystal at room temperature. (a)–(c) Diffraction patterns of a ${BaTiO}_{3}$ nanocrystal at the angles indicated. The location of the 101 and 110 powder rings on the area detector is plotted with yellow dashed lines as guides to the eye. Omega is the self-rotation angle of the sample stage. (d) and (f) Reconstructed images of 101 and 110 diffraction patterns in (a) and (c), respectively, shown as isosurfaces of amplitude to give the shape of crystal. The color on the shape of nanocrystal represents the complex phase, which can be reverted to displacement of crystal unit-cell origins. (e) A joint view of (d) and (f), which gives a good match in shape. (g) A sketch of the two parallel ferroelastic domain walls inferred from these data at the position indicated by a black box in (e), which shows changes in the polarization direction upon crossing domain wall. The Q direction is denoted, which is determined by the difference of the incident and diffracted x-ray beam wave vectors. It denotes the Bragg reflection that was measured. The isosurface plots here and in the other figures were generated using the 3D visualization software paraview [33].
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Figure 2
Simulation of split peak diffraction pattern reconstructions. A nanoparticle with three domains was used to generate a 3D diffraction pattern of which the central slice is shown in a 512 × 512 pixel array. The two peaks corresponding to the hemispherical sides and cylindrical center were given an extra gap offsetting the two diffraction patterns by 0, 5, 15, 40 pixels from (a) to (d). Their reconstructed images are shown as isosurfaces colored by the image phase in (e) to (h), respectively.
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Figure 3
BCDI isosurface image of a ${BaTiO}_{3}$ nanoparticle containing two domains separated by a ferroelastic domain wall at 387.2 K. Five orthogonal views and a cross section are shown, as labeled, along with the Q vector for the section view.
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Figure 4
Images of a ${BaTiO}_{3}$ nanoparticle upon crossing through its tetragonal-cubic phase transition. The top row is a series of contour views of the isosurface. The second row shows phase (displacement) cross-section maps taken in the middle of the nanocrystal, while the bottom row shows strain (a derivative of displacement) maps as a function of temperature.
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Figure 5
(a) Average displacement difference between the two domains upon heating and cooling are shown by a solid line. Tetragonality of this crystal over heating and cooling are shown by a dashed line. (b) Line plot of displacement over distance across the twin boundary.
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Figure 6
Dislocation annihilation upon heating. (a) Reconstructed crystal image at 387.2 K. (Left) A dislocation line through crystal is colored. (Right) A slice view across the dislocation line. (b) Same as (a), but temperature is 389.9 K. (c) Displacement field plotted vs rotation angle around the low-density core. Both experimental results and simulated curve from linear elastic theory are presented.
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