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Lu et al. Microstructures 2023;3:2023033 Microstructures
DOI: 10.20517/microstructures.2023.28

Research Article Open Access

Influence of kinks on the interaction energy between

ferroelastic domain walls in membranes and thin
films

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Guangming Lu , Kimura Hideo , Xiangdong Ding , Zhijun Xu , Ruiqing Chu , Guillaume F. Nataf , Ekhard K.
H. Salje 4
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School of Environmental and Materials Engineering, Yantai University, Yantai 264005, Shandong, China.
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State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, Shaanxi, China.
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GREMAN UMR7347, CNRS, University of Tours, INSA Centre Val de Loire, Tours 37000, France.
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Department of Earth Sciences, University of Cambridge, Cambridge CB2 3EQ, UK.
Correspondence to: Dr. Guangming Lu, School of Environmental and Materials Engineering, Yantai University, Yantai 264005,
Shandong, China. E-mail: luguangming1990@ytu.edu.cn; Prof. Ekhard K. H. Salje, Department of Earth Sciences, University of
Cambridge, Cambridge CB2 3EQ, UK. E-mail: ekhard@esc.cam.ac.uk
How to cite this article: Lu G, Hideo K, Ding X, Xu Z, Chu R, Nataf GF, Salje EKH. Influence of kinks on the interaction energy
between ferroelastic domain walls in membranes and thin films. Microstructures 2023;3:2023033.
https://dx.doi.org/10.20517/microstructures.2023.28
Received: 30 May 2023 First Decision: 17 Jul 2023 Revised: 28 Jul 2023 Accepted: 5 Aug 2023 Published: 11 Aug 2023
Academic Editors: Shujun Zhang, Alexei Gruverman Copy Editor: Fangling Lan Production Editor: Fangling Lan

Abstract
In thin samples, such as membranes, kinks inside ferroelastic domain walls interact through “dipolar” interactions
following a 1/d decay, where d is the distance between the walls. Simultaneously, the samples relax by bending.
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Bending is not possible in thick samples or can be suppressed in thin films deposited on a rigid substrate. In these
cases, wall-wall interactions decay as 1/d, as monopoles would do. In free-standing samples, we show a wide
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crossover regime between “dipolar” 1/d interactions and “monopolar” 1/d interactions. The surfaces of all samples
show characteristic relaxation patterns near the kink, which consists of ridges and valleys. We identify the sample
bending as the relevant image force that emanates from kinks inside walls in thin samples. When samples are
prevented from bending by being attached to a substrate, the dipolar force is replaced by “monopolar” forces, even
in thin samples. These results are important for transmission electron microscopy imaging, where the typical
sample size is in the dipolar range while it is in the monopolar range for the bulk.

Keywords: Kink interactions, Crossover regime for kink interactions, Ferroelectricity, Finite size dependent scaling

© The Author(s) 2023. Open Access This article is licensed under a Creative Commons Attribution 4.0
International License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, sharing,
adaptation, distribution and reproduction in any medium or format, for any purpose, even commercially, as
long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and
indicate if changes were made.

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