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ISSN : 1225-0562(Print)
ISSN : 2287-7258(Online)
Korean Journal of Materials Research Vol.27 No.9 pp.484-488
DOI : https://doi.org/10.3740/MRSK.2017.27.9.484

# Domain Wall Motions in a Near-Morphotropic PZT during a Stepwise Poling Observed by Piezoresponse Force Microscopy

Kwanlae Kim1,2
1Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, United Kingdom
2Department of Materials Science and Engineering, Yonsei University, Seoul 03722, Republic of Korea
Corresponding author : kwnlae.kim@daum.net (K. Kim, Univ. Oxford, Yonsei Univ.)
August 8, 2017 August 19, 2017 August 21, 2017

## Abstract

In the present study, domain evolution processes of a near-morphotropic PZT ceramic during poling was studied using vertical piezoresponse force microscopy (PFM). To perform macroscopic poling in bulk polycrystalline PZT, poling was carried out in a stepwise fashion, and PFM scan was performed after unloading the electric field. To identify the crystallographic orientation and planes for the observed non-180o domain walls in the PFM images, compatibility theory and electron backscatter diffraction (EBSD) were used in conjunction with PFM. Accurate registration between PFM and the EBSD image quality map was carried out by mapping several grains on the sample surface. A herringbone-like domain pattern consisting of two sets of lamellae was observed; this structure evolved into a single set of lamellae during the stepwise poling process. The mechanism underlying the observed domain evolution process was interpreted as showing that the growth of lamellae is determined by the potential energy associated with polarization and an externally applied electric field.

## 초록

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

## 1.Introduction

The material properties of ferroelectric ceramics are heavily dependent on domain structures and domain wall motions by externally applied electric field or mechanical stress.1) To understand the microstructures in ferroelectrics, intensive research has been conducted through modelling2-4) and characterization techniques.5-7) In particular, development of characterization techniques including scanning probe microscopy has provided advanced methods for observing domain structures.

Piezoresponse force microscopy(PFM) is one of the most powerful tools to observe ferroelectric domain structures because complex domain patterns can be effectively exposed.8-11) PFM images domain patterns based on distinct polarization directions in individual domain, so both 180° and non-180° domain structure can be clearly observed. In addition, advanced PFM techniques have been developed providing more quantitative data12-14) and more effectively visualized images.15) Meanwhile, PFM can locally control domain wall as well as image domain structures.16) However, inducing domain wall motion using the scanning probe is not an appropriate method to understand domain evolution processes during macroscopic poling process.

In the present study, domain evolution processes during macroscopic poling were observed using vertical PFM by applying electric field in a stepwise fashion. Electron backscatter diffraction(EBSD) was used in conjunction with PFM to identify habit planes for non-180° domain walls observed in PFM images. Compatibility condition was used to assist interpretation of the domain structures in the PFM images. Finally, the evolution process of herringbone-like domain pattern was observed and the mechanism underlying this evolution process is discussed.

## 2.Experimental

A soft polycrystalline PZT near morphotropic phase boundary, designated PZT-855 and distributed by APC international, was used. In this composition, both tetragonal and rhombohedral phases can coexist, so polarization switching between <100> and <111> can take place, generating high overall polarization and strain. Prior to the stepwise poling experiment, electric displacement(D3) versus electric field(E3), and strain(ε33) versus E3 were measured using a block of unpoled PZT. The obtained hysteresis loop (D3 vs. E3) and butterfly loop (ε33 vs. E3) are shown in Fig. 1. Pr, Ec, and ε33 indicate the remnant polarization, the coercive electric field, and the remnant strain, respectively.

For the stepwise poling experiment, another cuboid with 0.5 × 3 × 5mm3 dimension of unpoled PZT was prepared, and silver electrodes were painted on the two 0.5 × 5 mm2 faces of the cuboid. One of the 3 × 5 mm2 faces was polished to a mirror finish using a suspension of colloidal silica. During poling process, the sample was held in transformer oil and the two electrodes were linked to a high voltage amplifier and an electrometer. A Sawyer-Tower circuit17) was used to measure charge on the electrodes. The stepwise poling was carried out by successively loading and unloading over five times as shown in Fig. 2. The electric field increased to 0.5, 0.75, 0.9, 1.4, and 1.9 MVm−1 in each loading step. After each unloading, vertical PFM scan was carried out.

PFM works by exciting the local converse piezoelectric effect in the ferroelectric sample surface via alternating voltage applied through the scanning probe. The resulting mechanical oscillation in the sample surface is detected by the contact scanning probe, and the vertical position of the scanning probe is detected through the reflected laser beam from the scanning probe onto the photodetector. The surface displacement induced by PFM normally has both vertical and later components, so vertical and lateral PFM can be selectively used to detect each component. In this study, vertical PFM was carried out using a Veeco Dimension 3100 nanoscope. In this instrument, PFM signal is in the form of (Acosϕ)/Vac, where A and ϕ are the amplitude and the phase of the piezoelectric response signal, respectively, and Vac is the alternating voltage applied to the scanning probe. Bruker SCM-PIC scanning probes were used, and the driving frequency was set near contact resonance frequency(160- 200 kHz).

EBSD was used to obtain three Euler angles for the grain of interest to identify the crystallographic planes for the non-180° domain walls observed in PFM images. In the present work, an Evo LS 15 Environmental Scanning Electron Microscopy(ESEM) was used, and operated at 10-15 kV and 10 Pa pressure.

## 3.Results and Discussion

The theory of compatible domains is briefly introduced here to distinguish between 180° and non-180° domain walls. Ferroelectric domain patterns minimize the total energy by forming electrically and mechanically compatible domain configuration. To achieve energy minim- ization, domain wall must satisfy electrical and mechanical compatibility conditions.18) For a pair of domains i and j with the spontaneous strain states εi, εj, and spontaneous polarization vectors pi, pj, the interface normal vector, n, must satisfy18)

$ε i − ε j = 1 2 ( a ⊗ n + n ⊗ a ) ,$
(1)

$( p i − p j , ) ⋅ n=0,$
(2)

in which a can be any vector satisfying Eq. (1). A unique domain wall orientation, n, can be identified from Eqs. (1) and (2), and domain walls are formed at certain crystallographic planes. However, there is one exceptional case when εi = εj. In this case, Eq. (1) can be solved by setting a = 0, and a continuous set of solutions for n is generated by Eq. (2). This special case corresponds to 180° domain structure in which strain states are identical across a domain wall. Consequently, a 180° domain wall has no habit plane, and are normally observed as curvy lines.

Fig. 3(a) shows the AFM topography image with 19 × 19 μm2 size, and PFM scan was performed for the grain marked “G”. This AFM image was used to retrace the grain “G” through scanning electron microscope. Fig. 3(b) shows EBSD image quality map, and the grain “G” can be identified by comparing the positions, shapes, and sizes of the other grains marked “1”-“12”. In this image quality map, grain boundaries(dark contrast) are observed due to the inability of the EBSD to identify a unique crystallographic orientation at these points. Fig. 3(c) shows the PFM image observed from the grain “G”. Using the EBSD data, crystallographic orientation for the grain “G” was obtained. To identify the crystallographic planes for the non-180° domain walls(straight lines) observed in Fig. 3(c), all the orientations that can be generated by {110} and {100} planes were compared with the observed domain wall orientations. Note that, as mentioned earlier, spontaneous polarization directions are <100> in tetragonal and <111> in rhombohedral phase, so non-180° domain walls can be formed at {110} planes in tetragonal and at {110} and {100} planes in rhombohedral phase. Therefore, in this case, the phase of the grain “G” cannot be identified because (101) and (110) planes can be formed in both tetragonal and rhombohedral.

Figs. 4(a)-(f) show six PFM images acquired from the grain “G” before poling, after Step 1, 2, 3, 4, and 5, respectively. Note that each PFM scan was taken after completely unloading electric field. Back-switching in ferroelectric domains during electrical unloading process has been observed using transmission electron microscopy by Qi et al.19) Therefore, similar back-switching may have taken place prior to each PFM observation in the present study. In Fig. 4(a), the herringbone-like domain structure marked “H1” and “H2” can be seen. To study the gradual domain evolution process of this herringbone structure, six lamellae were marked “A” to “F”, and their evolution process is schematically shown in Figs. 4(g)-(j). One set of lamellae “A” and “B” are oriented along (101) and another set of lamellae “C”-“F” are oriented along (110) planes. In this evolution process, two sets of lamellae are competing to grow under externally applied electric field. As can be seen from the PFM images and the schematics, the lamellation “B” grew and “D” retreated after poling step 2 and 3. When the electric field increased to 1.4 MVm−1, the lamellation “C”, “D”, and “F” disappeared while “A” and “B” grew and were broadened. In general, the potential energy due to polarization in an externally applied electric field is represented as3)(3)

$f E = − α ( P i ⋅ E i )$
(3)

where α is a scaling factor, Pi is the polarization vector at lattice site i, and Ei is applied electric field vector. When Pi is closely oriented with Ei, the domain is likely to grow pushing the domain wall toward the neighboring domain. When two sets of lamellae are competing to grow, the lamellae set with a smaller net value of fE is likely to grow and overwrite the other set of lamellae. As can be seen from the series of PFM images, polarization switching during poling was carried out via pattern evolution rather individual polarization switching.

## 4.Conclusion

The evolution process of ferroelectric domain pattern in a near-morphotropic PZT during a stepwise poling was studied using PFM. Using EBSD and PFM data, and compatibility theory, crystallographic orientation and crystallographic planes for the observed non-180° domain walls were identified. The herringbone-like domain pattern consisting of two sets of lamellae was observed from the certain grain. A series of PFM images taken after each poling step show that one set of lamellae grew and overwrote the other set of lamellae. As a result, the herringbone- like domain pattern was evolved into a single lamellar pattern. The mechanism underlying the observed evolution process was interpreted using the minimization of the potential energy due to polarization in an externally applied electric field.

## Figure

(a) Measured electric displacement(D3) versus electric field (E3) and (b) measured strain(ε33) versus electric field(E3) of PZT- 855, with no mechanical loading.

Electric displacement as a function of electric field during five poling steps.

The grain of interest marked “G” in (a) AFM topography image was retraced by (b) EBSD image quality map. (c) Crystallographic orientation and planes for the observed non-180° domain walls in the PFM image.

(a)-(f) A herringbone-like domain pattern evolves into a single lamellation during a stepwise poling. (g)-(j) Schematics depict the evolution process of the herringbone-like domain pattern.

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