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Acta Materialia 71 (2014) 1–10

Crystallization kinetics of amorphous lead zirconate titanate thinfilms in a microwave magnetic field

Y.N. Chen, Z.J. Wang ⇑, T. Yang, Z.D. Zhang

Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, 72 Wenhua Road, Shenyang 110016, China

Received 16 November 2013; received in revised form 25 February 2014; accepted 4 March 2014Available online 25 March 2014

Abstract

We investigated the crystallization process and kinetics of lead zirconate titanate (PZT) thin films fabricated in the magnetic field ofmicrowave irradiation. The PZT thin films were prepared by the sol–gel method and crystallized by microwave irradiation at 2.45 GHz.X-ray diffraction was used to identify the phases and to determine the volume fraction of the perovskite phase transformed during crys-tallization. Transmission electron microscopy gave information on nucleation, growth and grain structure. We also discussed how thecrystallization and phase transformations correlated to the ferroelectric properties of the resultant films. We found that an intermediatephase formed during initial crystallization; it had a perovskite-like crystal structure, but it had a smaller lattice constant than perovskitePZT and contained more Ti. This intermediate phase acted as a nucleation site for the perovskite PZT, which grew with a columnar grainstructure into the pyrochlore matrix throughout the film. Using Avrami’s model, we found the effective activation energy for crystalli-zation of the PZT films by microwave irradiation to be �214 kJ mol�1, lower than the activation energy for crystallization by conven-tional thermal processes. These results show that microwave irradiation indeed affected the crystallization of amorphous PZT thin filmsdifferently than conventional annealing.� 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: PZT thin film; Sol–gel; Microwave irradiation; Crystallization; Kinetics

1. Introduction

Lead zirconate titanate (Pb(ZrxTi1�x)O3; PZT) thinfilms have attracted interest for many applications in non-volatile ferroelectric random-access memory [1] and micro-electromechanical systems (MEMS) [2], such as atomicforce microscopy cantilevers [3] and MEMS shunt switches[4]. Many techniques for depositing ferroelectric PZT thinfilms have been studied, including physical methods, suchas magnetron sputtering [5] and pulsed laser deposition[6], as well as chemical methods, such as metalorganicchemical vapor deposition [7] and sol–gel methods [8,9].To fabricate well-crystallized PZT films with compositions

http://dx.doi.org/10.1016/j.actamat.2014.03.009

1359-6454/� 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights r

⇑ Corresponding author.E-mail address: wangzj@imr.ac.cn (Z.J. Wang).

close to the morphotropic phase boundary (Zr/Ti = 52/48),substrate temperatures or post-deposition annealing tem-peratures of 600–750 �C are often required. However,treatment at such high temperatures causes many adverseeffects, including interdiffusion between the films and sub-strate as well as evaporation of lead and lead oxide fromthe surface, changing the stoichiometry [10,11]. Thus, fab-ricating PZT films at lower treatment temperatures andtimes would be beneficial.

The sol–gel method is an effective chemical technique forfabricating PZT thin films and has been widely studied toachieve lower processing temperatures. This method typi-cally involves introducing a seed layer or template layerand modulating the Zr/Ti ratio and Pb excess in theprecursor solution. For example, by using a seed layer oflead titanate (PbTiO3), Kwok and Desu decreased the

eserved.

2 Y.N. Chen et al. / Acta Materialia 71 (2014) 1–10

crystallization temperature needed to produce perovskitePZT (Zr/Ti = 53/47) films to 550 �C for 15 min [12]. Huanget al. [13] reported crystallization of PZT (30/70) films at440 �C for 100 min, attributing the lower temperature tothe formation of a PtxPb interlayer. Suzuki et al. reportedcrystallization of pure perovskite PZT (53/47) films on Pt/Ti/SiO2/Si at 500 �C for 2 h by using a PbTiO3 seedinglayer with 50 mol.% excess PbO [14]. Then, by using seededdiphasic sol–gel precursors, Wu et al. reported crystalliza-tion of pure perovskite PZT (52/48) films at 410 �C for30 h and at 550 �C for 30 min [15]. More recently, by usinga low pyrolysis temperature (210 �C) to circumvent the for-mation of a pyrochlore phase, Li et al. reported crystalliza-tion of device-quality PZT (30/70) films at 450 �C for 1 h[16]. These reports clearly show that perovskite PZT filmscan be crystallized at low temperatures by introducing aseed layer and modulating the Zr/Ti ratio and Pb excessin the precursor solution; however, this process requires along annealing time. Another way to lower the processingtemperature is by annealing PZT films with special meth-ods, including laser irradiation or laser annealing [17–19]as well as microwave irradiation or microwave annealing[20–25].

Recently, microwave heating techniques have attractedconsiderable attention as a new way to anneal sol–gel-derived PZT films because they offer many advantages suchas low energy cost, fine resultant microstructure, short pro-cessing time and low processing temperature. For example,Wang et al. crystallized perovskite PZT (52/48) films withgood electrical properties by using multimode microwaveirradiation with a frequency of 28 GHz at 480 �C for only5 min without needing to modify the precursors [20]. In sin-gle-mode microwave irradiation, the electric and magneticfields of the microwave can be spatially separated, exposingthe sample being treated to a reasonably pure electric ormagnetic field. Bhaskar et al. reported crystallizing perov-skite PZT films at 450 �C for 30 min in a microwave electricfield generated by a single-mode 2.45 GHz microwave heat-ing system with SiC rods acting as susceptors to absorb themicrowave energy and transfer the heat generated to thefilm [21,22]. By using the magnetic field of single-modemicrowave irradiation instead of the electric field, we crys-tallized PZT films similar to those of Bhaskar et al. at thesame temperature and time without needing to use SiCrods as susceptors [23–25]. In one of our previous studies,we also found that the pyrochlore phase transforms intothe perovskite phase via an intermediate pseudo-perovskitephase, which may be induced by microwave energy [25].These results suggest that the nucleation and growth ofperovskite grains in PZT films crystallized by microwaveirradiation may be different from those processes in PZTfilms crystallized by conventional thermal processing.However, the mechanism by which microwave irradiationinduces amorphous PZT to transform into perovskitePZT in thin films is not yet fully understood. Studyingthe kinetics of the formation of the perovskite phase,including its nucleation and growth, is fundamental to

optimizing the processing conditions of crystallizing PZT,specifically reducing its processing temperature and time.Additionally, understanding how microwave irradiationaffects the crystallization of amorphous PZT thin films inways different from conventional thermal annealing willimprove treatments of other functional thin films usingmicrowave irradiation.

In this study, we evaluated the transformation fromamorphous to perovskite in sol–gel-derived PZT filmsinduced by microwave irradiation. Using X-ray diffraction(XRD), we determined the volume fraction of the perov-skite phase transformed during this process. The nucle-ation site, crystal structure and grain growth wereidentified by transmission electron microscopy (TEM).We correlated the phase information to the ferroelectricproperties of the film, assessed the nucleation and growthkinetics and discussed the mechanism by which the micro-wave irradiation affected the phase transformation.

2. Experimental procedure

A B-doped Si wafer with an electrical resistivity of4–7 X cm was used as the substrate. To prepare thePt/Ti/SiO2/Si stack, the Si wafer was oxidized to produce500 nm of SiO2, and then Pt (200 nm)/Ti (50 nm)stacks were sputtered. The amorphous PZT films weredeposited on the Pt/Ti/SiO2/Si stacks using a sol–gelmethod. The precursor solution was prepared from leadacetate (Pb(CH3COO)2), zirconium-n-propoxide(Zr(OCH2CH2CH3)4) and titanium tetraisopropoxide(Ti((CH3)2CHO)4). 2-propanol [(CH3)2CHOH] was usedas the solvent. The final concentration of the solutionwas adjusted to 0.4 M with the atomic ratio ofPb:Zr:Ti = 1.1:0.52:0.48. We coated the substrate with pre-cursor using a spin coater, operated at 1500 rpm for 10 sand then at 4000 rpm for 40 s. The coated films were driedat 120 �C for 5 min and then pyrolyzed at 250 �C for 5 min.This coating, drying and pyrolizing process was repeatedonce more to obtain 300 nm thick amorphous PZT filmsfor microwave irradiation.

To produce the microwave irradiation, we used a single-mode microwave (frequency = 2.45 GHz) generator with awaveguide in TE103 mode; the wavelength (kg) of thestanding wave formed in this cavity was 12.24 cm. By mov-ing a plunger at the end of the waveguide, the electric andmagnetic fields could be maximized at a specific position.Each sample (10 � 10 mm2) was irradiated by placing itat the center of the highest magnetic field. The temperatureof the samples was measured during microwave irradiationby using an infrared thermometer (CTLaser2 M; Optris,Berlin, Germany). This sensor could not measure sampletemperatures below 300 �C. We measured the accuracy ofthe infrared pyrometer over the temperature range of400–700 �C by using Zn and Al films with known meltingpoint of 419.5 �C and 660.4 �C, respectively; all tempera-tures reported in this paper are accurate to within 5 �C.The amorphous PZT films coated on the substrates were

Fig. 1. XRD patterns of PZT films heated by microwave irradiation fordifferent times at (a) 525 �C, (b) 550 �C and (c) 575 �C. Pv: perovskitephase; Py: pyrochlore phase. The insets of (a), (b) and (d) show the (111)peak of the perovskite phase shifting toward lower 2h angles as theirradiation time increased.

Y.N. Chen et al. / Acta Materialia 71 (2014) 1–10 3

irradiated in the microwave magnetic field at 525, 550 and575 �C for 10–1200 s. For comparison, PZT films were alsoheated in a conventional electric furnace at 525, 550, 575and 600 �C for different times.

The PZT films were analyzed by XRD (Cu Ka radiation,D/max-2000; Rigaku, Tokyo, Japan). The microstructuresof the films were studied by TEM (Tecnai G2 F20; FEI,Eindhoven, The Netherlands) with an attached energy dis-persive X-ray spectroscopy detector and a high-angle annu-lar dark-field detector. The TEM specimens were groundand polished to a thickness of 20 lm and were then milledwith Ar ions until they were electron transparent by usinga Gatan precision ion-polishing system (PIPS 691; Gatan,Pleasanton, USA). Pt electrodes (diameter = 0.5 mm) weresputtered as top electrodes for electrical measurements. Thepolarization vs. electric field (P–E) hysteresis loop of eachfilm was measured at 1 kHz using a standard ferroelectrictesting system (TF2000E; Aixacct, Aachen, Germany).

3. Results and discussion

3.1. Crystallization of PZT films by microwave irradiation

Fig. 1 shows the XRD patterns of PZT films heated bymicrowave irradiation at various processing temperaturesand times. All the samples are amorphous before micro-wave irradiation. After irradiation at 525 �C for 30 s, at550 �C for 10 s, or at 575 �C for 1 s, a broad peak appearedthat we attribute to the (222) plane of the pyrochlorephase. At the same irradiation conditions, a small diffrac-tion peak appeared close to the Pt (111) peak, which seemsto correspond to the (111) plane of the perovskite phase.Increasing the irradiation time gradually increased theintensity of this peak, allowing us to confirm that it is the(111) perovskite peak. After irradiation at 525 �C for540 s, at 550 �C for 90 s or at 575 �C for 60 s, the (22 2)pyrochlore peak disappeared. All the films crystallized intothe perovskite phase and exhibited (11 1)-preferred orienta-tion, properties similar to those of the film crystallized byconventional annealing at 600 �C for 30 min, shown inthe first pattern at the top of Fig. 1c.

For comparison, Fig. 2 shows the XRD patterns of PZTfilms heated by conventional heating. The films heated at525 �C for 30 min and at 550 �C for 15 min showed onlya broad (22 2) pyrochlore peak. The film heated at575 �C for 2 min exhibited a small (111) peak for theperovskite phase. In contrast, when using microwave irra-diation, the small (111) perovskite peak appeared in filmsirradiated at 525 �C for only 30 s, at 550 �C for only 10 sand at 575 �C for only 1 s (Fig. 1a–c, respectively). Theseresults indicate that microwave irradiation induced the for-mation of the perovskite phase at low processing times. Byusing microwave irradiation, we obtained fully crystallizedperovskite PZT films at 525 �C for 20 min and at 575 �C foronly 60 s, much shorter times and lower temperatures thanthose required when using conventional heating, 600 �C for30 min.

To understand the crystallites formed during initial crys-tallization of the PZT films heated by microwave irradia-tion, we scanned the 2h peaks at 36–42� in detail; theseresults are shown in insets of Fig. 1a–c. The (111)

Fig. 2. XRD patterns of PZT films crystallized by conventional annealingat (a) 525 �C for 30 min, (b) 550 �C for 15 min and (c) 575 �C for 2 min.Pv: perovskite phase; Py: pyrochlore phase.

4 Y.N. Chen et al. / Acta Materialia 71 (2014) 1–10

perovskite peaks shifted toward lower angles with irradia-tion time, suggesting that their d-spacing increased duringcrystallization. Fig. 3 also shows that the d-spacing of the(111) planes increased with irradiation time at various tem-peratures; note that the d-spacing of the initial crystallitesremained nearly the same across the three temperaturesshown in Fig. 3. The d-spacing of 0.2331 nm is �1% smal-ler than the standard d-spacing of the perovskite phase(d111 = 0.2351 nm for PZT(52/48)). These results implythat the initial crystallites may be an intermediate phase.Various reports have shown that, in conventional heating,transition intermetallic PtxPb phases form during earlycrystallization of PZT thin films deposited on Pt/Ti/SiO2/Si substrates and that these intermediates lower the forma-tion temperature of (111)-oriented perovskite [13,26,27].Because these intermediate phases have lattice parametersclose to those of perovskite PZT, they may act as

Fig. 3. Variation of d-spacing of the (111) plane for various microwave-irradiation times. The d-spacing deviates �1% from that of standardperovskite value during initial crystallization. The error bars of the d-spacing indicate the range of measured values over three measurements.

nucleation sites (d111Pt3Ti = 0.2244 nm, d111Ptx-

Ti = 0.2340 nm). To determine whether the initial crystal-lite we observed was an intermetallic PtxPb phase, weused TEM to study the nucleation and growth of theperovskite phase in PZT films heated by microwave irradi-ation at 525 �C for various times.

Fig. 4a shows a cross-sectional TEM image of the PZTfilm heated by microwave irradiation at 525 �C for 30 s.The XRD data for this film (Fig. 1a) show that the filmwas in an early stage of crystallization. In this TEMcross-section, the film appears to have begun crystallizing;we observed initial crystallites at the bottom of the PZTfilm near the PZT/Pt interface. Some of the initial crystal-lites exhibited ferroelectric stripe-like patterns (inset ofFig. 4a), which were also clearly present in the well-crystal-lized perovskite PZT grains (Fig. 4c and d). This similarityshows that the initial crystallite was ferroelectric. We alsoobserved fine grains in other parts of the film, identifiedas pyrochlore by using a selected-area electron diffractionpattern (inset of Fig. 4a). Fig. 4b shows a high-resolutionTEM image of the initial crystallite marked with A inFig. 4a. The fast Fourier transform pattern of this crystal-lite revealed it to be a perovskite phase. The (111) planeparallel to the PZT/Pt interface exhibited a d-spacing of0.2330 nm, consistent with the XRD result of 0.2331 nm.Furthermore, the d-spacing of this crystallite’s (11 0) planeis smaller than that of the perovskite PZT. We also ana-lyzed the lattice parameters of other initial crystallites;these results are summarized in Table 1. The d-spacingsof these crystallites were smaller than the standardd-spacing of perovskite PZT by �1%. From these results,we conclude that the initial crystallites were an intermedi-ate phase with a crystal structure similar to that of perov-skite PZT but with smaller lattice parameters. Fig. 4cshows a TEM cross-section of a PZT film during interme-diate crystallization, heated by microwave irradiation for240 s; this image corresponds to the XRD data inFig. 1a. In this film, the perovskite grains had grown to athird of the film thickness. Fig. 4d shows another cross-sec-tion of a film irradiated for 1200 s; in this film, the colum-nar grains, perfectly crystallized into the perovskite phase,reached the surface of the film.

To analyze the chemical compositions of the initial crys-tallites, we performed semi-quantitative STEM-EDS on theinitial crystallite marked by B in Fig. 4a; these results areshown in Fig. 5. Fig. 5a shows a high-angle annulardark-field image, with the initial crystallite in the centerof the image, surrounded by a box. Fig. 5b–f shows theEDS results from the initial crystallite, revealing the ele-mental distribution of Pt, Pb, Zr, Ti and O. The Pt, Pb,Zr and O in the initial crystallite were nearly equal to itssurroundings; in contrast, the initial crystallite containedmore Ti (Fig. 5f) than in its surroundings. Combiningour XRD and TEM results, we conclude that the initialcrystallite, an intermediate phase formed during initialcrystallization, had a perovskite structure with a smallerlattice constant and contained more Ti than perovskite

Fig. 4. TEM images of PZT films crystallized by microwave irradiation at 525 �C. (a) Cross-sectional TEM image of the film irradiated for 30 s; (b)HRTEM image of a crystallite from (a) at the Pt/film interface; (c) cross-sectional TEM image of the film irradiated for 360 s, showing that the columnarperovskite grains grew into the pyrochlore layer; (d) cross-sectional TEM image of the film irradiated for 1200 s, showing that the columnar perovskitegrains grew to the surface of film.

Table 1Lattice parameters of crystallite nuclei, calculated from XRD and TEMdata.

PDF card XRD TEM

(100) 4.0360 – 3.99(110) 2.8500 – 2.82(101) 2.8900 – 2.87(111) 2.3510 2.3305 2.33(201) 1.8100 – 1.80

Fig. 5. (a) Cross-sectional STEM image of the PZT film; the area in the centerthe nucleus shown in (a).

Y.N. Chen et al. / Acta Materialia 71 (2014) 1–10 5

PZT. We denote this intermediate phase as Pv’ to distin-guish it from the perovskite PZT (Pv).

The crystallization of amorphous PZT thin films on Ptbottom electrodes using conventional heating has beenwidely studied. Brooks et al. [28] suggested that thePt(111) electrode acts as a nucleation site for the perov-skite PZT, which grows into the pyrochlore matrix. Thenucleation mechanisms for perovskite PZT during conven-

marked with the box is a crystal nucleus. (b–f) EDS elemental maps from

Fig. 6. Schematic of the crystallization process in PZT films induced bymicrowave irradiation.

6 Y.N. Chen et al. / Acta Materialia 71 (2014) 1–10

tional heating have also been analyzed: researchers believethat the perovskite heterogeneously nucleates on a Pt3Pbintermetallic phase generated by interfacial reactionbetween the film and Pt electrode; this intermetallic isbelieved to induce the phase transformation from pyroch-lore to perovskite [13,26,27]. In contrast, in the presentstudy, we found that the Pv’ intermediate phase, formedduring initial crystallization, acted as a nucleation site forthe perovskite PZT. This intermediate phase has not beenfound in crystallization of PZT films with compositionsclose to the morphotropic phase boundary [29–31] or inTi-rich PZT films heated by conventional thermal process-ing [26,27,32,33]. Thus, we believe that the intermediatephase was generated by microwave irradiation.

Several factors may have contributed to the formationof the Pv’ intermediate phase. The first mechanism ischarge transfer induced by the microwave irradiation atthe PZT/Pt interface, which consists of materials with dif-ferent dielectric constants and conductivities. The transfor-mation from amorphous or pyrochlore to perovskiterequires the ordering of the lead, titanium and zirconiumcations, a process likely to be sluggish. Microwave irradia-tion may have induced interfacial space charges anddipoles at the PZT/Pt interface, causing a new orderingof ions and atoms on the PZT side [34]. The second mech-anism may have to do with differences in thermal expan-sion. In one of our previous studies, we investigated theheating behaviors of PZT/Pt/Ti/SiO2/Si, PZT/SiO2/Si,Pt/Ti/SiO2/Si and SiO2/Si multilayered structures, heatedby single-mode 2.45 GHz microwave irradiation in themagnetic field; we found that the heating of the Pt/Ti/SiO2/Si samples mainly originated from contributions ofthe Pt/Ti layers and the Si substrate and that the Pt/Ti lay-ers were more effectively heated than the Si substrate [35].Heating during microwave irradiation can be consideredsimilar to ohmic heating induced by an alternating mag-netic field [36]; the higher electric conductivity of the Pt/Ti layers led to a higher eddy current, explaining why thePt/Ti layer was more effectively heated than the Si sub-strate. During microwave irradiation, the heat originatedfrom the Pt/Ti/SiO2/Si substrate and the heating rate wasvery fast (�10 �C s�1) [37]. Differences in the thermalexpansion coefficients between the PZT film and substratemay have led to great stress at the PZT/Pt interface, a pos-sible driving force for ionic motion. The intermediate phasePv’ and Pt have a smaller lattice mismatch (1.7%) than dothe perovskite Pv and Pt (2.8%), which induces the forma-tion of the intermediate phase. The third mechanism maybe related to the intermediate phase being rich in Ti: whilePbTiO3, PbZrO3 and PZT have the same perovskite struc-ture, their crystallization temperatures increase as follows:PbTiO3 < PbZrO3 < PZT [38]. Furthermore, reports haveshown that Ti-rich amorphous PZT thin films can be crys-tallized into the perovskite phase at low temperatures[32,33]. Although we have discussed the formation of theintermediate phase and some possible mechanisms, furtherresearch is needed. The presence of the Pv’ intermediate

phase may have changed the path of phase transitions,reducing the activation energy of nucleating the perovskitephase. We will discuss more on this issue in detail later inthe next section.

Based on our experimental results and analysis, we pro-pose a tentative mechanism for the crystallization of PZTfilms during microwave irradiation; a schematic of this pro-cess is shown in Fig. 6. First, the Pv’ crystallites induced bymicrowave irradiation homogenously form at the bottomof the film near the PZT/Pt interface (Fig. 6a). Then, theyact as nuclei for the formation of the perovskite phase (Pv).As the irradiation time increases, the columnar perovskitegrains grow vertically in vertical lamellae, and the interfacebetween the pyrochlore (Py) and the perovskite remainsalmost flat (Fig. 6b). The lamellar growth occurs becausethe nuclei of the perovskite grains on the intermediatephase (Pv’) are homogenously spaced and because thegrowth rates of the perovskite grains with (111)-preferredorientation are nearly the same, which occurs because thetemperature gradient remains the same across the grainsas they linearly diverge from the electrode/substrate andbecause the microwave irradiation directly affects the Py/Pv interface. Finally, the columnar perovskite grains reachthe surface of the film, perfectly crystallizing the film intothe perovskite phase (Fig. 6c).

We investigated how the crystallization process influ-enced the ferroelectric properties of the PZT films by mea-suring polarization vs. electric field (P–E) hysteresis loopsat 1 kHz. Fig. 7 shows the P–E hysteresis loops of PZTfilms heated by microwave irradiation at 525, 550 and575 �C for various times. During initial crystallization, allthe films exhibited quasi-linear P–E and remanent polar-

Fig. 7. P–E hysteresis loops of the PZT films, heated by microwave irradiation at (a) 525 �C, (b) 550 �C and (c) 575 �C for different irradiation times; (d)remanent polarization as a function of irradiation time. The error bars denote the range of measurements after five measurements, using different topelectrodes; no error bar means that the range was smaller than the height of the symbol used for the data point.

Y.N. Chen et al. / Acta Materialia 71 (2014) 1–10 7

izations of <1 lC cm�2. These results occurred because,during this crystallization step, the ferroelectric perovskitephase was very thin and only lay at the bottom of the filmnear the PZT/Pt interface; the paraelectric pyrochlorephase was the predominant phase, as indicated by XRDand TEM results. As the irradiation time increased, thehysteresis loops became tilted as the perovskite phase grew,and the remanent polarization (Pr) increased abruptly.Fig. 7d shows how the remanent polarization and coercivefield (Ec) varied with microwave irradiation time, demon-strating that the development of ferroelectricity in thePZT films correlated to the phase transition from amor-phous to perovskite.

3.2. Activation energy of crystallization in PZT films heated

by microwave irradiation

The crystallization kinetics in PZT films heated bymicrowave irradiation can be analyzed by following thegeneral approach described by the Avrami transformationkinetics equation [39,40]:

fðtÞ ¼ 1� expð�ktnÞ ð1Þ

where f(t) is the volume fraction of the transformed perov-skite phase, t is the irradiation time, k is a temperature-dependent crystallization-rate constant and n is the Avramicoefficient, which is temperature independent but sensitiveto reaction conditions, including the nucleation and growthrate.

Fig. 8a shows the relative intensity as a function of irra-diation time, fit to the Avrami model. These data were nor-malized against the intensity of the XRD (111) peak of theperovskite phase from films conventionally annealed at600 �C for 30 min. Note that the transformed fraction inthe films crystallized by microwave irradiation at 575 �Cfor 60 s is more than 100%; this behavior occurred becausethe crystallization of the microwave-irradiated film wasmuch more complete. Taking logarithms and rearrangingEq. (1), we plotted ln{ln [1/(1 � f(t))]} vs. ln t, yielding alinear series of points with slope n and intercept lnk; Fig. 8b shows representative fits of the data at the threetemperatures. The extracted Avrami coefficient is �0.8,which agrees well with values predicted for one-dimensional linear growth and thickening of very largeplates [40], suggesting that the transformation frompyrochlore to perovskite occurred via diffusion-limited

Fig. 8. (a) Fraction of transformed perovskite as a function of time atvarious temperatures; (b) Avrami plot of volume fraction ln{ln[1/(1 � f)]}as a function of the natural logarithm of time at various temperatures. Theerror bars in (a) and (b) denote the range of the fraction of transformedperovskite after three measurements. (c) Arrhenius plot of the reactionconstant as a function of the reciprocal temperature, used to determine theactivation energy. The error bars indicate one standard deviation of ln k

calculated by linear fitting.

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growth and that the structural transformation occurred atthe phase interface. Our TEM results showed that thecolumnar perovskite grains grew uniformly and verticallyfrom the PZT/Pt interface and that the perovskite/pyroch-

lore interface was flat, like the interface of a thickeningplate (Fig. 4a, c and d). Thus, our theoretical and experi-mental results are very consistent.

The temperature dependence of the reaction rate con-stant k can be described by the Arrhenius equation [41]:

k ¼ A exp � Ea

RT

� �ð2Þ

where A is the pre-exponential factor, Ea is the apparentactivation energy of crystallization and R is the molargas constant. Fig. 8c shows the plot of ln k vs. 1/T; fromthe slope of this line, we obtained an activation energy of214 kJ mol�1 for the PZT films crystallized by microwaveirradiation. The crystallization kinetics during conven-tional annealing of sol–gel-derived PZT thin films has beenwidely studied, allowing us to compare the value obtainedin the present report [42–46] The present activation energyis lower than the values obtained by Griswold et al. [43]and Babushkin et al. [44] – 275 and 310 kJ mol�1, respec-tively – for similar sol–gel-derived PZT(53/47) films crys-tallized by conventional thermal processes. This decreasemay have been caused by the presence of the intermediatephase, a direct effect of microwave irradiation. As discussedbefore, the intermediate phase was likely induced by micro-wave irradiation during initial crystallization. The latticemismatch between the intermediate phase and Pt was smallcompared with that between the perovskite and Pt, reduc-ing the activation energy of nucleation. Huang et al. re-ported that the formation of an intermetallic PtxPb phaseduring initial crystallization of a PZT thin film depositedon Pt/Ti/SiO2/Si substrate reduced the nucleation activa-tion energy for forming the perovskite phase; they reportedan activation energy of 179 kJ mol�1 for forming theperovskite phase in the Ti-rich PZT (30/70) films [26].The direct effect of microwaves on the growth of the perov-skite grains can be considered within the framework of theponderomotive driving force model and may have implica-tions for reduced energy use in solid-state processing [47].Models of the enhanced ion transport and related effectshave suggested that these behaviors occur because of gradi-ents in the mobility of mobile-charged species near grainboundaries or other physical interfaces. Whittaker re-searched diffusion in microwave-heated ceramics (YbBa2-

Cu3O7�d embedded in YBa2Cu3O7�d) and provided directevidence that the microwaves directly influenced ion trans-port during high-temperature sintering [48]. Because themicrowaves concentrated lattice defects and enhanced ionmobility at the interface, they also increased the masstransport. In the present study, the columnar perovskitegrains grew vertically and uniformly from the PZT/Ptinterface through the pyrochlore matrix throughout thecrystallization process. The microwaves may have directlyinfluenced ion transport at the Pv/Py interface, reducingthe activation energy of growing the perovskite phase.

Fig. 9 shows a schematic of the phase transition path,demonstrating how the Gibbs energy varies during PZTcrystallization induced by microwave irradiation and con-

Fig. 9. Schematic of crystallization associated with the Gibbs energy ofactivation in the PZT film as well as the microwave-energy transfer path.

Y.N. Chen et al. / Acta Materialia 71 (2014) 1–10 9

ventional annealing. During conventional annealing, theamorphous phase transforms to the perovskite phasethrough the pyrochlore phase (the solid dark line). Duringmicrowave irradiation, the phase transition from amor-phous to pyrochlore still occurs, meaning the activationenergy (Ea0) is the same as that in conventional annealing.However, the phase transition path for pyrochlore toperovskite differs between microwave irradiation and con-ventional annealing. During initial crystallization, the tran-sient phase (Pv’) forms before the perovskite phase (Pv),which then grows on Pv’, reducing the Gibbs energy ofactivation (Ea) to Ea1 and Ea2 (the dashed red line). There-fore, the emergence of Pv’ changes the phase transitionpath, reducing the activation energy of nucleating theperovskite phase. During grain growth of the perovskitephase, ion transport at the Pv/Py interface is also enhancedby the microwave irradiation. This also reduces the Gibbsenergy of activation to Ea3 (the dashed blue line). Thus,crystallization from amorphous to perovskite in PZT filmsrequires a lower activation energy when a film is heated bymicrowave irradiation.

4. Conclusions

We prepared PZT thin films using a sol–gel method andthen crystallized them by using microwave irradiation at2.45 GHz in the magnetic field of the microwave. To studythe crystallization and kinetics of the transformation fromamorphous to perovskite PZT in the thin films, we usedXRD to identify the phases grown and the volume fractionof the transformed perovskite phase, and we used TEM toinvestigate the grain structure, nucleation and growth. Ourresults show that an intermediate phase (Pv’) formed dur-ing initial crystallization; this phase had a perovskite crys-tal structure with a smaller lattice constant and higher Ticontent than perovskite PZT. The intermediate phase actedas a nucleation site for the perovskite, which grew with a

columnar grain structure into the pyrochlore matrixthroughout the whole film. We confirmed this crystalliza-tion process by assessing how the ferroelectric propertiesof the films varied. The effective activation energy for theformation of the perovskite phase using microwave irradi-ation was �214 kJ mol�1, lower than that for perovskitecrystallized by conventional thermal processes. Theseresults demonstrate that, in crystallization of PZT filmsheated by microwave irradiation, the microwave radiationinduced an intermediate phase, which lowered the crystal-lization temperature and enhanced the growth rate of theperovskite phase.

Acknowledgements

We gratefully acknowledge the partial support of thiswork by the Hundred Talents Program of the ChineseAcademy of Sciences, the National Natural ScienceFoundation of China (Nos. 51072202 and 51172238), theNational Basic Research Program (No. 2010CB934603)of China and the Ministry of Science and Technology ofChina.

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