Stress-dependent scaling behavior of dynamic hysteresis in bulk soft ferroelectricceramicRattikorn Yimnirun, Supattra Wongsaenmai, Supon Ananta, and Yongyut Laosiritaworn Citation: Applied Physics Letters 89, 242901 (2006); doi: 10.1063/1.2403182 View online: http://dx.doi.org/10.1063/1.2403182 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/89/24?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Identical scaling behavior of saturated dynamic hysteresis in rhombohedral lead zirconate titanate bulk ceramics J. Appl. Phys. 114, 244101 (2013); 10.1063/1.4858355 Stress-dependent scaling behavior of subcoercive field dynamic ferroelectric hysteresis in Pb ( Zn 1 ∕ 3 Nb 2 ∕ 3 )O 3 -modified Pb ( Zr 1 ∕ 2 Ti 1 ∕ 2 ) O 3 ceramic J. Appl. Phys. 103, 086105 (2008); 10.1063/1.2907755 Dynamic hysteresis and scaling behavior of hard lead zirconate titanate bulk ceramics Appl. Phys. Lett. 90, 112908 (2007); 10.1063/1.2713769 Temperature scaling of dynamic hysteresis in soft lead zirconate titanate bulk ceramic Appl. Phys. Lett. 90, 112906 (2007); 10.1063/1.2713336 Scaling behavior of dynamic hysteresis in soft lead zirconate titanate bulk ceramics Appl. Phys. Lett. 89, 162901 (2006); 10.1063/1.2363143

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 169.233.6.10

On: Mon, 01 Dec 2014 23:53:14

Stress-dependent scaling behavior of dynamic hysteresis in bulk softferroelectric ceramic

Rattikorn Yimnirun,a� Supattra Wongsaenmai, Supon Ananta, and Yongyut LaosiritawornDepartment of Physics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

�Received 12 September 2006; accepted 20 October 2006; published online 11 December 2006�

The effects of frequency f , field amplitude E0, and mechanical stress � on the hysteresis area �A�and their scaling relations were investigated on soft PZT bulk ceramics. The hysteresis area wasfound to depend on the frequency and field amplitude with a same set of exponents to the power-lawscaling for both with and without stresses, indicating the universality. The inclusion of stresses intothe power law was also obtained in the form of �A−A�=0�� f−0.25E0�0.44, which indicates thedifference of the energy dissipation between the under stress and stress-free conditions and revealshow the hysteresis area decays with increasing stresses. © 2006 American Institute of Physics.�DOI: 10.1063/1.2403182�

The dynamic hysteresis characteristics have become animportant consideration since hysteresis area �A� as a func-tion of the field amplitude E0 and frequency f presents lots ofinformation critical for many ferroelectric applications.1,2

Theoretical studies have been carried out to understand thedynamic response of hysteresis curves in spin and polariza-tion systems.3–5 In particular, attention is focused on the scal-ing law �A�� fmE0

n �where m and n are exponents that dependon the dimensionality and symmetry of the system�. Basedon three-dimensional models, it has been suggested that m=1/3 and n=2/3 as f →0, whereas m=−1 and n=2 as f→�.3,5,6 Experimental investigations on a few thin-film sys-tems have also been reported with variation in the scalingrelations obtained.5–11 On the contrary, there is only a singlereport on the scaling behavior studies of ferroelectric hyster-esis loops of bulk ferroelectric ceramics.12 More importantly,in many applications the ceramic specimens are often sub-jected to mechanical loading, either from the design of thedevice itself or from operating conditions which inducestresses.1,13 Therefore, a prior knowledge of how the materialproperties change under different load conditions in materi-als is inevitably crucial for proper design of a device and forsuitable selection of materials for a specific application. Inmany previous investigations the electrical properties of ce-ramics were found to depend strongly on stresses ���.14–18

Since f , E0, and � have been reported to impose significantinfluence on the dynamic hysteresis responses of ferroelec-tric ceramics, it is therefore the aim of this study to establishthe scaling behavior of the dynamic hysteresis responses ofbulk ceramics under the influence of the external stress.

Due to its commercial availability and many practicalapplications, a donor-doped or soft lead zirconate titanate�PZT� ceramic was used in this study. The disk-shapedsamples of a commercially available soft PZT ceramic �PKI-552, Piezo Kinetics Inc., USA� with a diameter of 10 mmand a thickness of 1 mm were used in this study. Its basicproperties are dielectric constant �1 kHz� �r=3400, Curietemperature TC=200 °C, piezoelectric strain constants d33=550 pm/V and d31=−270 pm/V, planar coupling factorkp=0.63, mechanical quality factor Qm=75, and coercive

field �50 Hz� Ec=7.5 kV/cm. The dynamic hysteresis �P-E� loops were characterized at room temperature �25 °C� byusing a modified Sawyer-Tower circuit with f covering from2 to 100 Hz and E0 from 0 to 18 kV/cm. The electric fieldwas applied to a sample by a high voltage ac amplifier �Trek610D� with the input sinusoidal signal from a function gen-erator �HP 3310A�. The P-E loops were recorded by a digitaloscilloscope �HP 54645A, 100 MHz�. The detailed descrip-tions of this system were explained elsewhere.17 Effects ofthe external stress on the dynamic hysteresis were investi-gated with the compressometer, which was developed forsimultaneous applications of the mechanical stress and theelectric field.18 The compressive stress, applying parallel tothe electric field direction, was supplied by the servohydrau-lic load frame and monitored with the pressure gauge. TheP-E loops were recorded as a function of mechanical stressapplied discretely between 0 and 24 MPa for each appliedfield and frequency. At each constant stress, the loop wasobtained after 20 sampling cycles to average out the noisedeformation.

The hysteresis profiles for various frequencies f , fieldamplitude E0, and stress � are obtained. For a particularapplied stress, as expected, the dependence of the loop pat-tern and area �A� on f and E is remarkable. At fixed E0, theloop area �A�, remnant polarization �Pr�, and coercive field�Ec� decrease with an increase of frequency. For the depen-dence of the hysteresis loop on E0, the loop does not saturateat small fields �6 and 8 kV/cm�. With further increase in E0,�A�, Pr, and Ec increase until a well saturated loop isachieved. Similar stress-free observations have been reportedin thin films and bulk ceramics.5,9,12

Figure 1 displays the hysteresis loops under differentcompressive stresses during loading at fixed f of 100 Hz andfixed E0 of 18 kV/cm. The P-E loop area �A� is found todecrease steadily with increasing the stress. To investigatethe scaling behavior under the effect of applied stresses, in-stead of including only the field amplitude E0 and the fre-quency term f , the scaling relation should also include thestress ��� term, i.e.,

�A� � fmE0n�p. �1�

However, due to increasing number of exponents, to simplifythe problem, the validity of the scaling law �A����

a�Author to whom correspondence should be addressed; electronic mail:rattikornyimnirun@yahoo.com

APPLIED PHYSICS LETTERS 89, 242901 �2006�

0003-6951/2006/89�24�/242901/3/$23.00 © 2006 American Institute of Physics89, 242901-1 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 169.233.6.10

On: Mon, 01 Dec 2014 23:53:14

� f−0.25E0 is assumed, inspired by a stress-free investigationon bulk PZT,12 for all applied stresses. Consequently, thearea �A� for each stress is plotted against f−0.25E0, as shownin Fig. 2, and it can be seen from the least-squares linear fitsthat reasonably good linear relations can be found. As a re-sult, the condition of universality having m=−0.25 and n=1 in soft PZT bulk ceramic systems is confirmed, whereasthe proportional constant in Eq. �1� may still be a function of�. Therefore, Eq. �1� is generalized by writing

�A� = G���f−0.25E0 + F��� , �2�

where both G��� and F��� are assumed to be a function of �representing slope function and y-intercept function for a“linear relation” in Eq. �2�, and their values are presented vialinear-fit functions in Fig. 2. Next, to obtain the scaling formas indicated in Eq. �1�, the slope function G��� is assumed totake a form of power-law function, i.e., G���=a+b�c, and anonlinear fit for G��� gives a=0.136±0.021, b=−0.019±0.015, and c=0.439±0.173 with R2�0.994. How-ever, for the y-intercept function F���, the scattering data inF��� do not follow a trivial power-law scaling form. Instead,the reasonably well-fitted function that suits F��� in the cur-

rent study is found to take a quadratic function. So F���=a0+a1�+a2�2 is written and a least-squares fit is per-formed to give a0=−0.019±0.006, a1=0.002±0.001, anda2=−1.149�10−4±4.850�10−4 with R2�0.878. As a re-sult, from Eq. �2�, it is therefore possible to write the scalingarea

�A� − F���G���

= f−0.25E0, �3�

and by plotting this scaling area ��A�−F���� /G��� againstf−0.25E0 all the data should collapse onto a single linear linehaving a y intercept at zero. The data collapsing of the scal-ing area from all f , E0, and � was found to confirm Eq. �3� asevident in Fig. 3.

On the other hand, it is of interest if the scaling of �A� ina form given by Eq. �1� is allowed. Therefore, by discardingminor loops which usually occur at very low E0, F�����A��E0→0� will be small in comparing to �A� and can bediscarded in Eq. �3� at some intermediately high fields.12

Consequently, �A�� �a+b�c�f−0.25E0 may be written and bysubstituting the fitted parameters, it is found that

FIG. 1. �Color online� Hysteresis loops for soft PZTceramic at various � �f =100 Hz and E0=18 kV/cm�.

FIG. 2. �Color online� Scaling of hysteresis area �A�against f−0.25E0 for soft PZT ceramic at various �.

242901-2 Yimnirun et al. Appl. Phys. Lett. 89, 242901 �2006�

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 169.233.6.10

On: Mon, 01 Dec 2014 23:53:14

�A� − �A�=0� = �A − A�=0� � f−0.25E0�0.44, �4�

where �A�=0� refers to the stress-free hysteresis area whichwill be a dominant term for zero stress. Note that from theappearance of stress �, �A−A�=0�, referring to the differencein energy dissipation between under stress and stress-freeconditions, increases with increasing stress suggesting a de-cay of �A� with � at a rate of �0.44 as observed in experi-ments. As a result, it can be concluded that the difference ofthe hysteresis area between under stress and stress-free con-ditions scales with frequency, field amplitude, and stress viaexponents m=−0.25, n=1, and p=0.44. However, at a par-ticular fixed stress, Eq. �4� gives f−0.25E0 which is the origi-nal form for how the area scales with the frequency and thefield amplitude.12

To understand the scaling relation obtained, at leastqualitatively, one needs to consider the following statements.Since the P-E loop area indicates the polarization dissipationenergy subjected to one full cycle of electric field applica-tion, the loop area is therefore directly related to volumeinvolved in the switching process during the application ofelectric field.17–19 Hence, when the mechanical stress is ap-plied, more and more ferroelectric domains are constrainedby the applied stress and cannot be reoriented by the electricfield so as to participate in the polarization reversal. Conse-quently, both the saturation and remnant polarizations be-come lower with increasing the compressive stress. The po-larization dissipation energy is consequently found todecrease with increasing the applied stress, indicating thatthe sample volume contributing to polarization reversal de-creases with the increasing stress. Similar observations havealso been reported in other investigations.14–18,20–22

In summary, the scaling behavior of the dynamic hyster-esis of the soft PZT bulk ceramics under the effect of me-chanical stress has been investigated. With the presence ofthe external stress, the scaling law for the loop area yields thesame set of exponents to frequency and field amplitude instress-free condition which confirms the condition of univer-sality in bulk system. Furthermore, the difference of the en-ergy dissipation between the under stress and stress-free con-

ditions is found to scale with f−0.25E0�0.44. As a result, thestudy provides a detailed understanding of how the energydissipation of the hysteresis properties behaves in responseto various conditions especially the mechanical stress.

Financial supports from the Thailand Research Fund�TRF�, Commission on Higher Education �CHE�, and Fac-ulty of Science and Graduate School of Chiang Mai Univer-sity are gratefully acknowledged.

1K. Uchino, Ferroelectric Devices �Dekker, New York, 2000�, p. 145.2O. Auciello, J. F. Scott, and R. Ramesh, Phys. Today 51�7�, 22 �1998�.3M. Rao, H. R. Krishnamurthy, and R. Pandit, Phys. Rev. B 42, 856�1990�.

4M. Acharyya and B. K. Chakrabarti, Phys. Rev. B 52, 6560 �1995�.5J.-M. Liu, H. L. W. Chan, C. L. Choy, Y. Y. Zhu, S. N. Zhu, Z. G. Liu, andN. B. Ming, Appl. Phys. Lett. 79, 236 �2001�.

6M. Rao and R. Pandit, Phys. Rev. B 43, 3373 �1991�.7J.-M. Liu, H. L. W. Chan, C. L. Choy, and C. K. Ong, Phys. Rev. B 65,014416 �2001�.

8Q. Jiang, H. N. Yang, and G. C. Wang, Phys. Rev. B 52, 14911 �1995�.9B. Pan, H. Yu, D. Wu, X. H. Zhou, and J.-M. Liu, Appl. Phys. Lett. 83,1406 �2003�.

10Y.-H. Kim and J.-J. Kim, Phys. Rev. B 55, R11933 �1997�.11J.-H. Park, C.-S. Kim, B.-C. Choi, B. K. Moon, J. H. Jeong, and I. W.

Kim, Appl. Phys. Lett. 83, 536 �2003�.12R. Yimnirun, Y. Laosiritaworn, S. Wongsaenmai, and S. Ananta, Appl.

Phys. Lett. 89, 162901 �2006�.13K. Uchino, Piezoelectric Actuators and Ultrasonic Motors �Kluwer Aca-

demic, Boston, 1997�, p. 129.14J. Zhao, A. E. Glazounov, and Q. M. Zhang, Appl. Phys. Lett. 74, 436

�1999�.15D. Viehland and J. Powers, J. Appl. Phys. 89, 1820 �2001�.16D. Zhou, M. Kamlah, and D. Munz, J. Eur. Ceram. Soc. 25, 425 �2005�.17R. Yimnirun, Y. Laosiritaworn, and S. Wongsaenmai, J. Phys. D 39, 759

�2006�.18R. Yimnirun, S. Ananta, A. Ngamjarurojana, and S. Wongsaenmai, Appl.

Phys. A: Mater. Sci. Process. 81, 1227 �2005�.19M. E. Lines and A. M. Glass, Principles and Applications of Ferroelec-

trics and Related Materials �Clarendon, Oxford, 1977�, p. 102.20J. F. Shepard, Jr., F. Chu, B. Xu, and S. Trolier-McKinstry, Mater. Res.

Soc. Symp. Proc. 493, 81 �1997�.21T. Kumazawa, Y. Kumagai, H. Miura, M. Kitano, and K. Kushida, Appl.

Phys. Lett. 72, 608 �1998�.22X. Lu, J. Zhu, X. Li, Z. Zhang, X. Zhu, D. Wu, F. Yan, Y. Ding, and Y.

Wang, Appl. Phys. Lett. 76, 3103 �2000�.

FIG. 3. �Color online� The collapse of the scaling area��A�−F���� / ��� against f−0.25E0 on a same linear line�with small fluctuation� for soft PZT ceramic.

242901-3 Yimnirun et al. Appl. Phys. Lett. 89, 242901 �2006�

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 169.233.6.10

On: Mon, 01 Dec 2014 23:53:14