Time-Resolved Measurements of Lattice Strain in Ferroelectric Crystals Induced by Application of Electric Field: Single Crystal Diffraction Study Chikako Moriyoshi and Yoshihiro Kuroiwa Department of Physical Science, Graduate School of Science, Hiroshima University, Higashihiroshima, Hiroshima 739-8526, Japan

ABSTRACT Piezoelectric ferroelectric crystals macroscopically deforms by the application of an electric field due to the piezoelectricity. Inversely, the electric polarization is generated in the crystals when an external stress is applied. Piezoelectric ferroelectric materials vibrate macroscopically at each proper frequency under the applied electric field. Such characteristics are widely used in electromechanical devices. To understand the mechanism of piezoelectric deformation in ferroelectric materials, it is necessary to examine the microscopic origin; i.e., how much and how fast atoms are displaced in crystals upon the application of a voltage at the microscopic level. We succeeded in the in situ observation of a change in the crystal-lattice size of ferroelectric tetragonal BaTiO3 with length of 10-14 m order and time of 10-6 s order during the piezoelectric vibration. The time-resolved measurements were performed at SPring-8 BL02B1 by combining a single crystal diffraction technique using high-energy X-rays and a high-speed time-resolved measurement technique. This achievement opens up possibilities for research on the dynamics of atomic displacements in an electronic device during operation.

1.

INTRODUCTION

Dielectric crystals macroscopically expand, contract, and deform upon the application of an electric field. Inversely, the electric polarization is generated in the crystals when an external stress is applied. Strain which is proportional to the electric field is called piezoelectric strain. This phenomenon was predicted by G. Lippman theoretically and observed by J. Curie and P. Curie experimentally at the end of 19th century. Nowadays, the piezoelectric effect is applied to many electric devices such as the ejection controller of ink in ink-jet printers and the touch panels of cell phones. If a dielectric material possesses spontaneous polarization and the polarization is reversed by the external electric field, the dielectric material is ferroelectric and piezoelectric simultaneously. In the ferroelectric materials, the electric-field-induced deformation mechanism is categorized to two types. One is an extrinsic deformation which is caused by the polarization reversal or rotation. This can be observed by macroscopic measurements such as a piezometer. The other is an intrinsic deformation which emerges from the atomic displacement. To observe this type of

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deformation, diffraction measurements have been believed to be effective. However, because the electric field induced atomic displacement is extremely small to detect, only a few measurements were performed by a conventional X-ray diffraction setup [1]. Recently, high-brilliant sources of synchrotron radiation (SR) X-ray and neutron enable us to observe the orientation change and unit cell change induced by the external electric field in ferroelectric ceramics [2] and single crystals [3]. Several mechanisms to explain the macroscopic deformation of ferroelectrics have been discussed; however, it is necessary to examine how atoms are displaced in crystals upon the application of the electric field to understand the intrinsic mechanism. To achieve this purpose, the time-resolved measurements have been extensively performed in the world [4-6]. SPring-8 has also made much effort to develop the time-resolved crystal structure measurement technique. For example, the fast atomic rearrangement during recording of DVD [7] and the fast polarization switching mechanism in ferroelectric thin films [8,9] have been clarified. Besides, the materials science studies have been performed using the accurate crystal structure analysis at the electron charge density levels by high-energy single crystal diffraction at SPring-8 BL02B1 [10-12]. In this study, by combining two advanced measurement techniques, i.e., a high-speed time-resolved measurements technique and a single crystal diffraction technique, we succeeded in the in situ observation of a change in the crystal-lattice size of piezoelectric crystals with time of microsecond order during piezoelectric vibration. The achievements of this study are expected to lead to developments in research on the dynamics of atomic displacement of shorter time-scale and enable the observation of atoms in electronic devices during operation [13].

2. DOMAIN STRUCTURE AND ELECTRIC-FIELD-INDUCED STRAIN OF FERROELECTRIC TETRAGONAL BaTiO3 Ferroelectric BaTiO3 has a cubic perovskite-type structure (space group Pm3m ) in the high-temperature phase. With decreasing temperature, BaTiO3 undergoes a first-order ferroelectric phase transition to the tetragonal phase (space group P4mm) at TC = 400 K. BaTiO3 shows successive structural phase transitions to the orthorhombic phase (space group Amm2) and to the rhombohedral phase (space group R3m). In this study, we concentrate our attention on the tetragonal phase. The spontaneous polarization appears along the c-axis. Six kinds of polarization orientation (twin) are possible in the crystal in the tetragonal phase. The phase diagram and possible orientations are shown in Figure 1. Some (or all) of those exist and form a domain structure which is formed to minimize the electronic energy and strain energy at domain boundary in the crystal. If the orientation angles of two adjacent domains are 90o and 180o, the domain structure is called 90o domain and 180o domain, respectively.

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Figure 1.. Ferroelectricc cubic-to-tetraagonal structurral phase transsition in BaTiO3. Six kinds of domain aree possible in the ferroeelectric phase.

m m macroscopicc strain is When tthe externall electric ffield is appplied to ferrroelectric materials, observed. Three kiinds of micrroscopic meechanism of o the macrooscopic straain are posssible, as is ws an intrinssic piezoeleectric strainn which is shown iin Figure 2 schematicaally. Figuree 2(a) show proportiional to E aand an electtrostrictive sstrain whichh is proporttional to E2. Figure 2(bb) shows a strain innduced by oorientation cchange of thhe spontaneeous polarizzation. Undeer some conndition, an electric--field-induced phase trransition maay occur ass shown in Figure 2(cc). To underrstand the macrosccopic deform mation mecchanism of ferroelectricc materials, it is necessary to idenntify these microsccopic originss experimenntally.

Figure 2. Schematic view v of possibble electric-fieeld-induced sttrain in ferroeelectric materiials. (a) Piezooelectric and electrostrrictive strain. ((b) Strain by oorientation chaange of spontaaneous polarizzation. (c) Straain by electricc-field phase transitionn.

we estimate each strainn shown in Figure 2 w when the electric field is applied along the Here, w cuubic of tetraggonal BaTiO O3. The tettragonal latttice parameeters are a = 3.9920 Å and c = 4.0361 Å, and the tetragonaliity is c/a = 1.0110. Fiirst, we esttimate the iintrinsic pieezoelectric strain inn Figure 2(aa). When the electric field Ei is applied, strainn ej is descrribed by ej = dijEi (i = 1,2,3; j = 1,2,3,4,5,6), where dij is a piezoeelectric tenssor componeent [14]. In the case of tetragonal BaTiO3 (point grouup 4mm), thrree componnents d31 = d32, d33 and d15 are posssible. When E = (0, 0, E3) is appplied, d33 aand d31 can bbe discussedd. The piezooelectric connstants repoorted are d33 = 136 ± 92 pm/V V and d31 = −53 ± 330 pm/V [3]]. When E3 = 10 kV/ccm, the lattiice parametters would

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become a = 3.99188 Å, c = 4.00366 Å, andd c/a = 1.01112. In this case, c we havve to detectt the strain -4 of (c/aa) ~ 10 . Second, in thhe polarizattion rotationn case Figurre 2(b), the strain is raather large and (c – a)/a ~ 110-2. It has been reported that B BaTiO3 unddergoes an electric-fielld-induced paraelecctric-ferroelectric phasee transition just above TC in the cuubic phase like Figure 2(c). The lattice pparameter chhange is c//c ~ 10-2 [1]. E hysteresis loop of feerroelectric materials, Figure 3 shows a schematic view of a typical P-E where thhe crystal iss in a multi domain statte initially. When W the positive electtric field is applied to the crysstal, the poolarization switching s ooccurs and the intrinsic lattice strain appeaars in one domain.. When the opposite eelectric fieldd is appliedd, the polariization swittching and the lattice strain occcur in the ssame way. The T shape of o P-E loop depends onn the magnittude and sppeed of the applied electric fieeld. To undderstand succh a macroscopic electric responsse, it is imp mportant to clarify hhow much aand how fastt the crystall structure chhanges undeer various conditions.

Figure 3.. Schematic vview of P-E hyysteresis loop of BaTiO3-tyype ferroelectrric materials w with domain sttructure and crystal sttructure. Totall polarization contains conntributions of both the dom main orientatioon (extrinsic) and crystal structure (intrinsic).

NGLE CRY YSTAL SR DIFFRAC CTION OF TETRAGO ONAL BaT TiO3 UNDER 3. SIN STATIC C ELECTR RIC FIELD D A BaTiiO3 single ccrystal cut into the sizze of 5 × 2.5 2 mm2 was w polishedd to a platee with the thicknesss d = 0.1 mm. The thhickness dirrection wass cubicc. The as-poolished sam mple had a 2 small reemanent pollarization off Pr ~ 15 C C/cm . This was because of the resiidual stress caused by polishinng and dom main clampping whichh was induuced by oxxygen vacaancies [15,116]. After annealinng the sampple at 1200oC for 24 h in air, Pr inncreased up to ~35 C//cm2, whichh indicated that dom main switchhing smoothhly occurredd in the samp mple. Gold ellectrodes w were sputtereed on both sides off the sample. w want to t observe only latticce parameteers precisely, observiing the higgh-angular When we

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diffractiion profile m may be moost effectivee [17]. Furthhermore, ussing a lowerr-energy SR R X-ray is also goood to detectt small channge in latticce parameteers [18]. In this study, however, w we tried to use a hiigh-energy SR. S The higgh-energy S SR seems too be unsuitaable to analyyze the preccise lattice parametter because it reduces the angulaar resolutionn. Howeverr, if many diffraction spots are observed, it can reeduce the sttandard devviation of thhe observedd lattice parrameters staatistically. mine the latttice param meters of buulk crystal, it is necesssary to obbserve the Besides, to determ diffractiion intensitiies from thee inner area of the sampple. Since thhe transmission power of X-rays dependss on the eneergy and typpe of samplee material, a suitable energy for thhis purpose should be selectedd. The energgy dependennce of the trransmission ratio of X-rays for BaTiO3 of thicckness 0.1 mm is shown s in Figure F 4. Thhe conventional CuK  radiation, whose enerrgy is 8 keV, has an -6 extremeely small trransmission ratio, I/I0 ~ 10 , andd cannot peenetrate deeeply into thhe BaTiO3 sample. CuK radiiation has diisadvantagee because the diffractionn from the ssurface elecctrode area is mainlly observed. The higher the energyy of the X-rrays we use,, the larger tthe transmisssion ratio we can obtain. Usinng the 35 keV k X-ray, w we can obseerve the difffraction from a sufficieently deep t sample aas the transm mission ratiio is as highh as 0.8. Forr this reasonn, we used thhe SR that area of the can provvide high ennergy and brrilliant X-raay beam.

Figure 4.. Transmissionn ratio of X-raays I/I0 for BaT TiO3 (thicknesss of 0.1 mm) as a function of energy of X-rays. X

d m measuremen nts with trannsmission geeometry weere performeed using a SR singgle crystal diffraction large cyylindrical tw wo dimensioonal imagingg plate (IP) camera withh a 1/4 three-axis gonniometer at BL02B11 in the SP Pring-8 synnchrotron raadiation facility [10]. T The energyy of SR waas 35 keV (waveleength: 0.35442(1) Å). The beam m collimatioon size waas 150 m m. The meaasurement temperaature was 3000 K in the tetragonal pphase of BaaTiO3. A typpical diffracction patternn recorded on IP is shown in Figure F 5. The diffractionn spots in thhe range of d > 0.25 Å w were clearlyy observed. Althouggh the SR-irradiated aarea inevitaably involved both BaaTiO3 and electrodes, no clear diffractiion pattern ooriginating ffrom the goold electrodees was obserrved.

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Figure 5. Diffraction iimage of BaT TiO3 single cryystal recordedd on two-dimeensional detecctor Imaging Plate P (IP) at SPring-8 BL02B1 using high-energyy SR X-ray of 35 keV ( = 00.35 Å). The ddiffraction spots in the rangee of d > 0.25 Å are cleaarly observed..

First, ass a preliminnary measurrement, the diffraction spots undeer the static electric field E were observed. Figure 6 shows the ddiffraction sspots recordded on the IP P with varyiing E. At E = 0, there o T (440)c spot from tthe c-domaiin and the was a 990 domain structure inn the samplee initially. The (044)a sspot from tthe a-domaiin were sim multaneously observedd from the iirradiated aarea. With increasing E, the inntensity of (044)a decrreased, and the sample became moono domainn at E > 4 t tetragonnal lattice paarameters a and c weree also observved in this kV/cm. The E-depeendence of the measureement. The lattice elonngated alongg the c-axis, while it shhrunk alongg the a-axis under the electric field along the c-axis, as a has been reported [3,19].

Figure 6.. Diffraction spots of BaTiO O3 recorded onn IP under stattic external eleectric field. Att E = 0, the peeak of (440)c from the c-domain andd the peak off (044)a from the a-domainn are observeed in this areaa. With increaasing E, the intensity of (044)a decrreases. The sam mple is monoddomain at E > 4 kV/cm.

4.

ME-RESOL LVED SINGLE CRYSTAL SR D DIFFRACT TION OF B BaTiO3 TIM

Next, w we investigaated the tim me dependennce of the inntrinsic lattiice strain reesponse of tetragonal BaTiO3 during andd after the polarizatioon reversal when the electric fielld antiparalllel to the main tetragoonal BaTiO O3 was appllied. The exxperimentall setup of polarizaation in thee mono dom

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time-ressolved singlle crystal difffraction meeasurement installed inn SPring-8 BL02B1 B is ddepicted in Figure 77. The 16677 s X-ray ppulse was generated g byy an X-ray chopper. Thhe X-ray puulse width was 4 s,  which deefined the tiime resolution of this eexperiment. A cyclic drriving (pumpp) electric voltage Vext(t) appllied to the ssample was a bipolar ssquare wavee of 600 Hzz frequencyy (1667 s period). The amplittude of Vext((t) was 125 V (electric field E = 122.5 kV/cm), which was sufficient mple mono domain, as shown in F Figure 6. Thhe time t when an X-ray pulse for makking the sam irradiateed the sampple was coontrolled byy a delay ggenerator. T This setup enabled e us to obtain informaation on the crystal struucture at the arbitrary  t of s ordeer by collectting the inteensity data at t over o many cycles and summing them. Threee SR oscilllation phottographs obbtained at differennt angles bettween the nnormal of the sample pllate and the incident beeam were reecorded on the IP aat each t. T The oscillatiion angle annd the expossure time were w 10o andd 10 min resspectively, in one photographh. The tetraagonal lattiice parametters a and c of BaTiiO3 at eachh t were determinned by leasst-squares ccalculation using posittions of aboout 600 difffraction spots in the range off sin / < 1.25 Å-1 (d > 0.4 Å).

Figure 7.. Experimentaal setup for tim me-resolved sinngle crystal diiffraction measurement instaalled in SPingg-8 BL02B1. The SR X X-ray is monoochromatized to be 35 keV, and the 1667 s X-ray puulse is generatted by an X-rray chopper. The exterrnal electric ppotential Vext(tt) is a bipolar square wave whose periodd is 1667 s (600 ( Hz). Thee diffraction spots from m the BaTiO3 single crystal plate at each  t are detectedd by a large cyylindrical IP ccamera.

t time deppendence off the electricc voltage V(t) V between the electroddes on the Figure 88(a) shows the BaTiO3 sample when the driving (pump) electric e fieldd of the bipoolar square wave type Vext(t) was t polarityy change of o Vext(t), thhough the applied.. The polarrity of V(t)) changed following the oscillatiion of V(t) w was observed, especiallly right aftter the polarrity change of Vext(t). V(t) had a periodiccity of t0 = 1667 s,, which waas the sam me as the pperiod of Vext(t); therefore, the polarizaation reversaal cycle in the sample was induceed by cycliic Vext(t). Thhe expressioon of V(t) could bee reduced too V(t) = V V(t + nt0), w which expreessed V(t) inn one periodd. The shape of V(t) did not change untiil the samplle broke owing to fatiguue after n ~ 107 polarizzation reverssal cycles. Thus thhe pump-proobe methodd could be aapplied witthin this polarization reversal cyccles. Since V(t) heeld the relattion V(t + t0/2)  -V( t), we investigated thhe time depeendence of the lattice

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strain ass a function of t from t = 0 to t0//2 in the nexxt stage.

Figure 8. (a) Time dependence of electric e voltagge V(t) betweeen electrodes of BaTiO3 sinngle crystal pplate when a cyclic driiving electric voltage of bipolar square wave type iss applied. Whhen the directtion of Vext chhanges, V(t) changes ggradually in thhat direction annd shows the behavior of a damped oscillation. The shhape of V has a periodicity of 1667  s, which is thhe same as thaat of Vext. t is defined as thhe time in eacch period. (b) Enlarged V(t)) within half period. There are charaacteristic timee regions nameed I to VI. (c)) Tetragonalityy c/a versus  t plot. (c/a)0 = 1.0110 in the steadyy state.

t plot obtainned by the Figure 88(b) shows V(t) withinn the half peeriod. A tetrragonality cc/a versus  time-ressolved singlle crystal SR S diffractioon system is i shown inn Figure 8(cc). The chaaracteristic time reggions namedd I to VI in Figure 8(b)) were observed. Regioon I was a steady state under Vext with a nnegative pollarity. The sample was in the monoo domain staate. The c/aa in region I was c/a = 1.0110. When the polarity of o Vext becoomes positivve, polarizaation reverssal from –P Ps to +Ps graduallly occurred in the sam mple and com mpleted at  t ~ 50 s (region II).. The BaTiO O3 sample should bbe in a multti domain sttate in this ppolarization reversal tim me region. E Each spot did not split in this rregion. Thiss indicates tthat the dom main switchhing process in this meeasurement was 180o switchinng, and 90o switching did not occcur or occurrred negligiibly. In regiion II, c/a ddecreased. This is because the electric ffield opposite to the sppontaneous polarizationn was applied to the

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sample. After an increase in V(t) at t ~ 60 s (region III), where c/a also increased to c/a = 1.0114, both V(t) and c/a(t) behaved similarly to a damped oscillation (regions IV and V). The frequency of the oscillation was about 20 kHz for a large amplitude component, though V(t) contains also higher frequency components, as the square wave possesses many frequencies as Fourier components. c/a oscillated around c/a = 1.0110 in regions IV and V. Finally, the oscillation of V(t) and c/a(t) diminished at t ~ 800 s (region VI). This oscillation behavior observed in Figures 8(b) and 8(c) from region III to region VI is attributed to the piezoelectric vibration. Thus, this time-resolved experiment can demonstrate that the intrinsic lattice strain is indeed vibrating during the vibration of piezoelectric materials in phase.

5. PIEZOELECTRICITY OF TETRAGONAL BaTiO3 Intrinsic piezoelectricity of tetragonal BaTiO3 can be discussed using the observed c/a(t). In this experiment d33 and d31 are estimated because only E3 was applied to the BaTiO3 sample. Figure 9 shows a c/a versus E = E3 plot obtained from c/a(t) and V(t) in Figure 8. Open rectangles indicate the data obtained at t < 50 s, when the polarization reversal occurred in the BaTiO3 sample and there existed a transient 180o domain structure. Solid circles indicate the data obtained at t > 50 s, when the sample was in the mono domain state after the polarization reversal. Both sets of data are fitted by a linear relation. The tetragonality c/a is related to E by the equation c/a = (c/a)0(1 + E), where (c/a)0 is c/a at E = 0 and  = d33 – d31 under this experimental condition within the linear response theory [14]. In Figure 9, (c/a)0 was the same in both time regions within the error, (c/a)0 = 1.01092 ± 0.00001 at t < 50 s and (c/a)0 = 1.01093 ± 0.00003 at t > 50 s. On the other hand, the parameter  = 210 ± 30 pm/V at t > 50 s was about two times as large as  = 100 ± 10 pm/V at t < 50 s. This result suggests that the lattice strain is affected by the existence of the 180o domain structure in the sample. The extrinsic lattice strain induced by domain walls minimizes the response of the lattice strain averaged in the sample against the electric field. Actually the reported piezoelectric constants d33 and d31 were scattered in the d33 = 68.5 ~ 316.6 pm/V and −d31 = 33.4 ~ 103.3 pm/V ranges [20-24], i.e.,  = 102 ~ 420 pm/V. Such a large discrepancy of dij among the literature values is explained by the domain structures. Our result, i.e.,  = 210 ± 30 pm/V at t > 50 s, in the mono domain state agrees with the d33 = 149 ± 54 pm/V and d31 = −82 ± 61 pm/V of BaTiO3 derived by SR single crystal diffraction under the static electric field [3]. This indicates that diffraction measurements can determine the intrinsic lattice strain reproducibly.

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Figure 9.. Relationshipp between c/a and E of BaT TiO3 in time-reesolved measuurement. The tendency is w well fitted by c/a = (c/aa)0(1 + E), w where (c/a)0 = 1.01092 ± 0.00001 and  = 100 ± 30 pm/V p for t = 0 ~ 49 s, aat which the sample iss in the transieent multi domaain state, and (c/a)0 = 1.010093 ± 0.000033 and  = 210 ± 30 pm/V foor t = 58 ~ 830 s, att which the saample is in thee mono domainn state. Here,  is the differrence betweenn piezoelectric coefficients, d33 – d13.

6.

ONCLUDIN NG REMAR RKS CO

The tim me-resolvedd X-ray difffraction syystem compposed of high-energy h y and high--brilliance synchrootron radiattion X-ray source, sinngle crystaal diffractioometer, andd an X-rayy chopper synchroonized with a cyclic ellectric fieldd enables uss to investiggate the dyynamic respponse of a lattice sstrain in bullk tetragonaal BaTiO3 too an electriic field. Thiis system prrovides the structural informaation of botth extrinsic and intrinssic responsees of piezooelectric maaterials to an a applied electric field. Recently the SPrring-8 BL022B1 beamliine has beenn well-deveeloping for tthe people want to knoow the acccurate timee-averaged structure information i n of singlee crystals. who w Furtherm more, our sstudy has shhown that B BL02B1 alsso has muchh potential for the timee-resolved measureements, eveen though SR S from a bbending maggnet is usedd at BL02B B1. We wouuld like to developp a more useer-friendly tiime-resolveed single cryystal diffracttion system in the near future.

OWLEDGE EMENTS ACKNO It is im mpossible to thank all tthe people who have hhelped our experimentts. The timee-resolved single crystal c diffrraction meaasurements were suppoorted by Drr. Hitoshi O Osawa, Dr. Kunihisa Sugimoto, and Prof. Shigerru Kimuraa (Japan S Synchrotronn Radiationn Researchh Institute EN/SPring-88), and otheer many peeople who (JASRI))/SPring-8),, and Prof. Masaki Taakata (RIKE manage SPring-8. G Good singlee crystal sam mples were provided byy Dr. Yuukii Kitanaka, Prof. Yuji Miyayama (The Univeersity of Tookyo). We also thank them for Noguchhi, and Proff. Masaru M fruitful discussion about electtric response of ferroellectrics. Wee should thaank our stuudents Mr. Shozo Hiramoto H a and Mr. Hiisanori Ohkkubo who did all-nighht experimeents and annalyses at

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SPring-8. The SR experiments were carried out with the approval of JASRI (Proposal Nos. 2010A1306, 2010A0083, 2010B0083, and 2011A0083). This study was partially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan.

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