Microstructure and electrical properties of porous PZT ceramics derived from different pore-forming agents

Acta Materialia 55 (2007) 171–181 www.actamat-journals.com

Microstructure and electrical properties of porous PZT ceramics derived from different pore-forming agents H.L. Zhang b

a,b

, Jing-Feng Li

b,*

, Bo-Ping Zhang

a

a School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China State Key Laboratory of New Ceramics and Fine Processing, Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, China

Received 15 April 2006; received in revised form 24 July 2006; accepted 25 July 2006 Available online 17 October 2006

Abstract Porous piezoceramics have promising applications in underwater sonar detectors or medical ultrasonic imaging. We report the electrical and acoustic properties based on different pore microstructures of porous lead zirconate titanate (PZT) ceramics, fabricated using stearic acid (SA) and polymethylmethacrylate (PMMA) as pore-forming agents. The corresponding ferroelectric and piezoelectric properties decreased with increasing porosity due to the decrease in volume fraction of PZT phase, and were in good agreement with a modified cubes model in the case of isolated porosity. The corresponding acoustic impedance decreased from 16 to 8 MRayls (106 kg/m2 s), with increasing porosity from 3% to 43%, due to low acoustic impedance of pore phase. The electrical properties of porous PZT ceramics were closely associated with porosity and the interconnection of pores, but only slightly associated with the shape of pores. However, the acoustic impedance was only connected to porosity, not to either shape or interconnection of pores.  2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Porous material; Electroceramics; Electrical properties; Acoustic properties; Pore-forming agent

1. Introduction The electrical properties of piezoelectric ceramics could be modified by the incorporation of various second phases, e.g. dielectric ceramics [1], metals [2], polymers [3] or introduced pores [4], to fabricate piezoelectric composites. Among those non-piezoelectric second phases are introduced pores, which have several special advantages. First, porous piezoelectric ceramics are composed of only the ceramics themselves, thus excluding any possible chemical reactions between the piezoelectric ceramic and the second phase during sintering. Second, the piezoelectric properties of porous piezoelectric ceramics are easy to tailor quantitatively, because the relationship between the electrical properties and porosity is roughly linear [5]. Third, porous piezoelectric ceramics are cheaper to produce than other piezoelectric composites using dielectric ceramics or metals *

Corresponding author. Tel.: +86 10 62784845; fax: +86 10 62771160. E-mail address: [email protected] (J.-F. Li).

as the second phase [1,2]. Finally, porous piezoelectric ceramics are very light and are thus more portable than other piezoelectric composites. Since porous piezoelectric ceramics have lower acoustic impedances than dense ceramics, they could be used to improve the mismatch of acoustic impedances at the interfaces of medical ultrasonic imaging devices [6] or underwater sonar detectors [7]. To this end, the electrical and acoustic properties of porous piezoelectric ceramics need thorough evaluations based on both porosity and pore morphology. Porous ceramics are fabricated by partial sintering [8] or by adding to the ceramic matrix a pore-forming agent (PFA), usually some pyrolyzable particulates [9]. In partial sintering, many experiments have to be conducted to seek for an appropriate sintering procedure to achieve the desirable porosity. In addition, a dense ceramic matrix is not obtained for the sake of partial sintering. By contrast, desirable porosity is obtained directly and easily by the PFA method, and the PFA-derived porous materials also possess built-in sites of pores for some selective

1359-6454/$30.00  2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2006.07.032

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applications. Earlier studies have reported the dielectric and piezoelectric properties of porous lead zirconate titanate (PZT) ceramics. Kumar et al. [10] and He et al. [11] found that the dielectric constant decreased and the dielectric loss increased with increasing porosity of porous PZT ceramics. Chen and Wu [12] and Piazza et al. [13] showed that the piezoelectric constant of porous PZT ceramics also decreased with increasing porosity. In addition to porosity, the properties of porous PZT ceramics are closely connected to their pore morphologies, i.e. the shape or connectivity of pores. In this study, porous PZT ceramics were fabricated using the PFA method. Because stearic acid (SA) is soft and deformable but polymethylmethacrylate (PMMA) is relatively hard, we used SA and PMMA, respectively, as the PFA to fabricate porous PZT ceramics so as to acquire different pore morphologies. The objective of the present study was to demonstrate the difference in both porosity and pore morphology between the SA- and PMMAderived porous PZT ceramics, and to evaluate the dependence of electrical properties on these pore microstructures. The electrical property evaluation is focused emphatically on dielectric constant, piezoelectric constant and acoustic impedance of the resultant porous PZT ceramics. 2. Experimental procedures 2.1. Sample preparation The starting materials were commercially available PZT, SA and PMMA powders, as shown in Table 1. The particle size of the SA powders was not measured due to their soft and highly deformable characteristics. The SA and PMMA powders as pore-forming agent were added to the PZT powders in the range of 0–50 vol.%. The powder mixtures with a small amount of polymeric binders were mixed in an agate mortar by an agate pestle. The milled powder mixtures were die-pressed at 100 MPa in B 10 mm and B 16 mm molds, respectively, and then cold-isostatically pressed (CIPed) at 200 MPa. The CIPed powder compacts were first heated at 200 C for 60 min to slowly remove organic SA or PMMA from the PZT ceramics. The powder compacts were then sintered at 1200 C for 1 h in a covered Al2O3 crucible containing PbZrO3 powders to protect against severe lead loss. The dilatometric tests were performed upon the CIPed powder

compacts 10 mm in diameter and 3 mm in thickness by a thermal analyzer (SETARAM, 92-16.18, TMA 92, Germany) to investigate the shrinkage of the powder compacts during sintering. Disc-shaped porous PZT samples 13 mm in diameter and 1.5 mm in thickness were obtained. In order to fabricate porosity-graded porous PZT samples, four layers of monolithic PZT, 90%PZT–10%SA (PMMA), 70%PZT–30%SA (PMMA) and 50%PZT–50%SA (PMMA) were layer-by-layer stacked into the B 16 mm mold. Each layer was designed to be roughly 0.5 mm in thickness. The following experimental procedures were similar to those described above. 2.2. Microstructure characterization A mercury porosimeter (AutoPore II 9220 V3.04, Micromeritics Instrument Co., Atlanta, GA) was used to determine the bulk density (including open and closed porosity) and the apparent density (including only closed porosity) of the resultant porous PZT samples. Mercury does not wet most ceramic materials, including PZT, so pressure must be applied to force it into pores. The intruded diameter D for a cylindrical pore at any applied pressure DP is calculated from the Washburn equation: D ¼ 4c cos ðhÞ=DP

ð1Þ

where c is surface tension of liquid mercury (0.474 N/m) and h is contact angle between the liquid mercury and the pore surface, usually assumed to be 140. In this study, pressures from 3.4 · 103 to 4.1 · 108 Pa were used to measure a broad range of pore sizes. The pore size distributions were present in the form of cumulative mercury volume penetrating per mass of specimen as a function of pore diameter. The microstructures were observed using a scanning electron microscope (SEM) (JSM-6460LV, JEOL, Tokyo, Japan). 2.3. Electrical property evaluation To evaluate the electrical properties, both surfaces of the samples were coated with Ag pastes and baked at 650 C for 30 min to form the Ag electrodes. The Ag-pasted samples were poled at 120 C for 10 min under a dc electric field of 20 kV/cm in a bath of silicone oil. The relative dielectric constant er was measured and the impedance– frequency curves were plotted using an impedance analyzer

Table 1 The starting materials used in the experiments

Chemical composition Particle size (lm) Density (g/cm3) Melting point (C) Boiling point (C) Source

Lead zirconate titanate (PZT)

Stearic acid (SA)

Polymethylmethacrylate (PMMA)

Pb(Zr0.516Ti0.484)O3 0.97 8.0 – – PZT-LQ, Sakai Chemical Industry, Osaka, Japan

C18H36O2 – 0.94 67 360 Yili Chemicals, Beijing, China

(C5H8O2)n 34–76 1.22 160 – Wako Chemicals, Japan

H.L. Zhang et al. / Acta Materialia 55 (2007) 171–181

50

Bulk porosity (%)

(4294A, Hewlett–Packard, Palo Alto, CA). The piezoelectric constant d33 was measured using a quasi-static piezoelectric d33 meter (ZJ-3A, Institute of Acoustic, Beijing, China). The ferroelectric hysteresis loops were measured for the poled samples using a high-voltage test system (RT6000 HVS, Radiant Technologies, Inc., Albuquerque, NM).

173

SA addition PMMA addition

40 30

1:1 ratio

20 10 0

3. Results

0

3.1. Porous microstructures

18

Shrinkage (%)

15 12 90% PZT-10% SA 70% PZT-30% SA 50% PZT-50% SA

6 3 0

b

400

600 800 1000 1200 o Temperature ( C)

18

Shrinkage (%)

15 12 9

90% PZT-10% PMMA 70% PZT-30% PMMA 50% PZT-50% PMMA

6 3 0 200

400

40

50

600 800 1000 1200 o Temperature ( C)

Fig. 1. Shrinkage curves of PZT powder compacts dispersed with different amounts of PFA of (a) SA and (b) PMMA.

lower than the corresponding volume fractions of added PFA. The dashed line denotes that the sites of added PFA can be wholly inherited by the resultant pores with the same volume fraction. When the volume fraction was less than 30%, the SA-derived porosity was a little less than the PMMA-derived porosity; this situation reversed when the volume fraction was larger than 30%. Fig. 3 shows the size distribution of open pores in the resultant porous PZT ceramics, which was characterized by a mercury intrusion method. As shown in Fig. 3a, for the SA-derived porous PZT ceramics, the size of open pores was tens of microns at 40% or 50% SA addition, then decreased down to several microns at 30% SA addition, Cumulative penetration volume (mL/g)

ð2Þ

where P is the bulk porosity, qTh is the theoretical density of PZT, and qB is the measured bulk density of porous PZT ceramics. As shown in Fig. 2, the resultant porosities were

200

30

Fig. 2. Bulk porosity of porous PZT ceramics produced by different amounts of PFA addition.

Cumulative penetration volume (mL/g)

P ¼ ðqTh  qB Þ=qTh  100%

9

20

PFA addition (vol.%)

Fig. 1 shows the shrinkage curves of the powder compacts containing various volume fractions of SA or PMMA as a function of temperature. As shown in the figure, most of the sintering shrinkages for the SA- or PMMA-added samples occurred above 1000 C. The shrinkages of the powder compacts were very close regardless of the change in SA content, and a similar case was obtained for the PMMA addition. Fig. 2 shows the bulk porosity of porous PZT ceramics produced by adding SA and PMMA as PFA, respectively. The bulk porosity of porous PZT ceramics was calculated by the following equation:

a

10

a 0.09

0.06 90% PZT-10% SA 80% PZT-20% SA 70% PZT-30% SA 60% PZT-40% SA 50% PZT-50% SA

0.03

0.00 1000

100 10 1 Pore diameter D (μ m)

0.1

b 0.08 0.06 0.04

90% PZT-10% PMMA 80% PZT-20% PMMA 70% PZT-30% PMMA 60% PZT-40% PMMA 50% PZT-50% PMMA

0.02 0.00 1000

100 10 1 Pore diameter D (μ m)

0.1

Fig. 3. Pore size distribution of (a) SA-derived and (b) PMMA-derived porous PZT ceramics characterized by the mercury intrusion method.

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a

50

Open porosity (%)

and finally the pores were hardly observed at 10% or 20% SA addition by this method. As shown in Fig. 3b, the size of open pores was only several microns even at 40% or 50% PMMA addition, and then decreased down to less than one micron at 30% PMMA addition. In comparison, the open pores derived from PMMA were smaller than those derived from SA. Lange et al. [14] hypothesized that a second phase with a certain size would become interconnected when its volume fraction exceeded 22%. The observed pore interconnection at above 30% addition of SA or PMMA in Fig. 3 is consistent with the theoretical prediction if the actual size of pores is considered. Furthermore, at 40% or 50% of PFA addition, the cumulative mercury intrusion increased more steeply in Fig. 3b than in Fig. 3a. This suggests that the open pores derived from PMMA have a somewhat narrower pore size distribution than those derived from SA. The comparison between Fig. 3a and b also shows that, at a given PFA addition, the cumulative mercury intrusion into the SA-derived porous PZT ceramics was slightly larger than that into the PMMA-derived ones. This difference implies that the SA-derived porous PZT ceramics might have a larger open porosity, PO, than the PMMA-derived ones. Fig. 4 shows the open and closed porosity for the SAand PMMA-derived porous PZT ceramics, respectively. The open porosity PO was calculated by PO = (1  qB/ qA) · 100%, and the closed porosity PC by PC = P  PO, where qA is the apparent density of porous PZT ceramics. The qA value was measured by the Archimedes method

40 30

SA addition PMMA addition

20 10

b

50

Closed porosity (%)

0 0

40 30

10

20 30 40 Bulk porosity (%)

50

SA addition PMMA addition

20 10 0 0

10

20 30 40 Bulk porosity (%)

50

Fig. 4. Bulk porosity vs. (a) open porosity and (b) closed porosity for the SA- and PMMA-derived porous PZT ceramics, respectively.

when the mercury pressure of 4.1 · 108 Pa achieved a maximum mercury intrusion into the porous sample. As shown in Fig. 4a, the open porosity increased with increasing bulk porosity in the range of 3–43%. The maximum PO value was close to 40% for the porous PZT ceramics produced by 50 vol.% SA addition. In comparison, the open porosity derived from SA was higher than that derived from PMMA at a given bulk porosity. This result is consistent with the cumulative intrusion measurements in Fig. 3. As shown in Fig. 4b, for the PMMA-derived porous PZT ceramics, it is clear that the closed porosity, PC, first increased to a peak value of about 15% and then decreased monotonously to <5% when the bulk porosity reached 40%. Similar results have also been reported in graphitederived porous Y2O3-stabilized ZrO2 ceramics (YSZ) [9]. For SA-derived porous PZT ceramics, it is of interest that their closed porosities did not change so much at various bulk porosities and that the values were lower than 10%. Fig. 5 shows the SEM micrographs of the SA-derived porous PZT ceramics, which were sintered at 1200 C for 1 h. The resultant pores were of irregular shape, and many pore channels and tiny voids were observed in the twodimensional section of the samples. The observations are consistent with earlier research [4]. As shown in Fig. 5b, some pores began to be interconnected when the SA addition was 30%. With further increasing porosity, the pore size also increased, and many pores were highly interconnected, as shown in Fig. 5c. The interconnection of pores explains the decrease in closed porosity at high bulk porosity, as shown in Fig. 4b. Fig. 6 shows the SEM micrographs of the PMMA-derived porous PZT ceramics, which were sintered at 1200 C for 1 h. Compared with the SA-derived irregular pores, the PMMA-derived pores were approximately spherical. This observation is proved by earlier investigations [10,11], in which PMMA was also used as PFA to produce porous PZT ceramics. As shown in Fig. 6a, the isolated spherical pores were uniformly dispersed in the PZT matrix at low bulk porosity. The diameter of these closed pores ranged from 10 to 80 lm. The irregular shape of the SA-derived pores explains why they had a broader pore size distribution than the PMMAderived pores, as shown in Fig. 3a and b. Similar to the SA-derived pores, the pores began to be interconnected at 30% PMMA addition, and more pores were interconnected at higher porosity, as shown in Fig. 6b and c. A comparison between Figs. 5 and 6 shows that the SAderived porous PZT ceramics had a more remarkable pore interconnection than the PMMA-derived ones. This evidence also explains why the former had higher open porosity than the latter, as shown in Fig. 4a. It is thus acceptable that the SA-derived closed porosity was as low as <10% even at the immediate bulk porosities from 15% to 35%, as shown in Fig. 4b. In fact, the small size of open pores at 30% SA or PMMA addition detected by the mercury intrusion method in Fig. 3 should be the cross-sectional diameter of the tiny channels interconnecting larger pores. Similarly, the large size of open pores at above 40% SA or

H.L. Zhang et al. / Acta Materialia 55 (2007) 171–181

PMMA additions should be the cross-sectional diameter of the coarse channels interconnecting pores. 3.2. Ferroelectric and piezoelectric properties Fig. 7 shows the relative dielectric constant, er, of porous PZT ceramics measured at 1 kHz as a function of bulk porosity. The er value decreased with increasing porosity in the range of 3–43% due to the volume fraction effect, which is consistent with previously reported results [10,11]. However, in the whole range of porosities the PMMA-derived porous PZT ceramics exhibited higher dielectric constants than the SA-derived ones, especially

Fig. 6. SEM micrographs of the microstructures of porous PZT ceramics produced by different amounts of PMMA addition: (a) 10 vol.%, (b) 30 vol.%, and (c) 50 vol.%.

1800 Parallel model

1500

Dielectric constant εr

Fig. 5. SEM micrographs of the microstructures of porous PZT ceramics produced by different amounts of SA addition: (a) 10 vol.%, (b) 30 vol.%, and (c) 50 vol.%.

175

1200 900

SA addition PMMA addition

600

Modified cubes model Serial model

300 0 0

10

20 30 40 Bulk porosity (%)

50

Fig. 7. Dielectric constant er of porous PZT ceramics as a function of bulk porosity.

H.L. Zhang et al. / Acta Materialia 55 (2007) 171–181

for those with >35% porosity. In addition, it is noted that the dielectric constants of the PMMA-derived porous PZT ceramics decreased almost linearly; however, there was a sudden decrease for the SA-derived porous PZT ceramics when P > 35%. This may be due to the easy interconnection of the SA-derived pores, and will be discussed later. Fig. 8 shows the ferroelectric hysteresis loops of porous PZT ceramics produced by the additions of SA and PMMA, respectively. The resultant porous PZT ceramics with various porosities all exhibited typical hysteresis loops, whose remnant polarization, Pr, decreased gradually with increasing porosity. Fig. 9 illustrates the measured remnant polarization of porous PZT ceramics as a function of porosity. As shown in Fig. 9, the Pr value decreases with increasing porosity, and is in broad agreement with the simple averaging model. The Pr value decreases because the volume fraction of ferroelectric PZT phase is decreased with increasing porosity. It is easily understood that porous PZT ceramics have proportionally reduced ferroelectric domains compared with dense PZT ceramics. It is noted that the Pr value suddenly decreased from the 70%PZT– 30%SA to the 60%PZT–40%SA sample in the SA-derived porous PZT ceramics. This observation is consistent with the sudden decrease in the corresponding dielectric constant of the SA-derived porous PZT ceramics in Fig. 7. As shown in Fig. 8, with increasing porosity, the coercive field, Ec, decreased only a little for the SA-derived porous PZT ceramics, and remained almost unchanged for the PMMA-derived porous PZT ceramics. The insensitivity of coercive field to porosity could be interpreted by space

30

2

20 10 0 -10 90% PZT-10% SA 80% PZT-20% SA 70% PZT-30% SA 60% PZT-40% SA 50% PZT-50% SA

-20 -30 -30

30

30 20 10

0

SA addition PMMA addition 10 20 30 Bulk porosity (%)

40

Fig. 9. Remnant polarization Pr of porous PZT ceramics as a function of bulk porosity.

charge accumulation at the surface of pore. The internal electric field established by the space charge at the pore surface may have a shield effect on the external electrical field applied to the sample. Since the effect of the field shield is proportional to porosity, the external electrical field needed to finish polarization remained almost unchanged in this study. The slight decrease in Ec value of the SA-derived porous PZT ceramics could be owing to the irregular shape of the resultant pores. Fig. 10 shows the piezoelectric constant, d33, of porous PZT ceramics as a function of bulk porosity. As shown in Fig. 10, the d33 value of porous PZT ceramics decreased with increasing porosity. The d33 value for the PMMAderived porous PZT ceramics decreased almost linearly in the porosity range of 3–40%. This result also shows a typical volume fraction effect of the piezoelectric phase in porous PZT ceramics. Chen and Wu [12] observed a decrease in the d33 value in the porosity range of 4–45% for porous PZT ceramics that were fabricated by a modified powder sintering method. Piazza et al. [13] also observed a decrease in the d33 value in the porosity range of 2–38% for porous PZT ceramics produced using graphite as PFA. The decrease in the d33 value was nearly the same for both kinds of porous PZT ceramics when P < 20%. Similar to the change of er value in Fig. 7, for the SA-derived porous PZT ceramics, the d33 value also suddenly decreased when P > 35%.

500

30

2

Polarization (μ C/cm )

b

-20 -10 0 10 20 Electric field (kV/cm)

Simple averaging model

0

20 10 0 -10 -20

90% PZT-10% PMMA 80% PZT-20% PMMA 70% PZT-30% PMMA 60% PZT-40% PMMA 50% PZT-50% PMMA

-30 -30

-20 -10 0 10 20 Electric field (kV/cm)

30

Fig. 8. P–E hysteresis loops of (a) SA- and (b) PMMA-derived porous PZT ceramics.

Piezoelectric constant d33(pC/N)

Polarization (μ C/cm )

a

40

Remnant polarization 2 Pr (μ C/cm )

176

400 300 200 100 0

Modified cubes model

SA addition PMMA addition

10

20 30 40 Bulk porosity (%)

50

Fig. 10. Piezoelectric constant d33 of porous PZT ceramics as a function of bulk porosity.

3.3. Acoustic properties Fig. 11 shows the measured impedance–frequency curves of porous PZT ceramics produced by the additions of SA and PMMA, respectively, in which only the base resonant vibration was shown for each porous PZT ceramic. As shown in the figure, the dependence of electrical impedance on frequency was similar regardless of the difference in PFA used. This suggests that the electrical impedance of porous PZT ceramics is related only to porosity, not to the shape or connectivity of pores. With increasing porosity, the resonant vibration frequency (fr) and antiresonant vibration frequency (fa) both decreased gradually, while the resonant vibration impedance (Zr) increased but the anti-resonant vibration impedance (Za) decreased. These results indicate that the porosity has a significant influence on the mechanical vibration of porous PZT ceramics subjected to electrical applications. Fig. 12 shows the acoustic impedance of the SA- and PMMA-derived porous PZT ceramics as a function of bulk porosity. The acoustic impedance of porous PZT ceramics was calculated by: Acoustic impedance ¼ qme D0 fr

ð3Þ

where qme is the measured bulk density of porous PZT ceramics, D0 is the diameter of the disc-shaped samples and fr is the resonant vibration frequency that was extracted from the corresponding curves in Fig. 11. As shown in Fig. 12, the acoustic impedance decreased linearly from 16 to 8 MRayls (106 kg/m2 s) for the SA-derived porous

a 60%PZT-40%SA

Impedance (Ω )

4

10

50%PZT-50%SA

3

10

70%PZT-30%SA 2

80%PZT-20%SA

10

90%PZT-10%SA

100

125 150 175 Frequency (kHz)

200

Impedance (Ω )

b 10

4

10

3

60%PZT-40%PMMA 50%PZT-50%PMMA

70%PZT-30%PMMA

10

2

80%PZT-20%PMMA 90%PZT-10%PMMA

100

125 150 175 Frequency (kHz)

200

Fig. 11. Impedance–frequency relationship for (a) SA- and (b) PMMAderived porous PZT ceramics.

Acoustic impedance (MRayls)

H.L. Zhang et al. / Acta Materialia 55 (2007) 171–181

177

18 SA addition PMMA addition

15 12 9 6 0

10

20 30 40 Bulk porosity (%)

50

Fig. 12. Acoustic impedance of porous PZT ceramics as a function of bulk porosity.

PZT ceramics with increasing porosity from 3% to 43%, and from 16 to 7.5 MRayls for the PMMA-derived porous PZT ceramics with increasing porosity from 3% to 40%. The decrease of acoustic impedance with increasing porosity is consistent with earlier research [15]. There was no apparent discrepancy in the dependence of acoustic impedance on porosity between the SA- and PMMA-derived porous PZT ceramics. It thus suggests that the acoustic impedance of porous PZT ceramics is sensitive just to porosity, not to the shape or connectivity of pores. 4. Discussion 4.1. Effect of PFA on porous microstructures As shown in Fig. 2, the resultant porosity was less than the corresponding volume fraction of PFA added. This result could be explained by the following model. Fig. 13 shows schematic illustration of sintering of a PFA-dispersed powder compact. Fig. 13a shows the dispersion of added PFA particulates having various sizes and shapes. When the powder compact was heated at 200 C in air, the added SA or PMMA pyrolyzed, leaving the pores with the same volume fraction, as shown in Fig. 13b. In the following sintering stage, the pores (see A site in Fig. 13b) and the surrounding ceramic matrix shrank at the same ratio, as shown in Fig. 13c. However, some small pores (see B site) and the tiny channels (see C site) connecting large pores disappeared due to the sintering. As a result, the volume fraction of the pores contributing to bulk porosity was less than the volume fraction of SA or PMMA added. Nevertheless, Barea et al. [16] reported that the resultant porosity in porous mullite was higher than the volume fraction of added starch for the sake of starch swelling at high temperature. These results show the difference in pore-forming ability of the PFAs used. The present study showed that the different PFAs added affected both the pore morphology and porosity of the resultant porous PZT ceramics. As shown in Figs. 5 and 6, the SA-derived pore was of irregular shape but the PMMA-derived pore was approximately spherical, and

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Fig. 13. Schematic illustration of sintering of a PFA-dispersed powder compact: (a) a ceramic–PFA composite compact CIPed at room temperature; (b) pyrolysis of organic PFAs at 200 C; and (c) final densification of the powder compact at 1200 C.

the former became interconnected more easily than the latter. The difference in pore morphology arises mainly from the different characteristics of SA and PMMA as the PFA, which in turn influences the porosity obtained. As shown in Fig. 2, the porous PZT ceramics derived from PMMA had higher bulk porosity than those derived from SA when the PFA addition was less than 30%, but the situation was reversed when the PFA addition was more than 40%. This porosity discrepancy could be related to the difference in pore morphologies between the SA- and PMMA-derived pores, as shown in Figs. 5 and 6. It can be deduced that the volume shrinkage for a spherical void is the least among all the void geometries when subjected to the same linear shrinkage argument, as shown in Fig. 13c. Because of the difference in pore shape, a PMMA-derived spherical pore has less volume shrinkage than a SA-derived irregular pore during sintering of porous PZT ceramics. Accordingly, a larger pore volume is retained in the PMMA-

derived porous PZT ceramics than in the SA-derived ones. Generally, the power compacts would reach the same volume shrinkage during sintering, no matter what PFA is added. With this in mind, a higher porosity could thus be expected for the addition of PMMA than SA. However, as shown in Fig. 2, the PMMA-derived bulk porosity became lower than the SA-derived one when the PFA addition was more than 30%; the reason for this anomaly is not very clear at present. The different PFAs used would also have influence on the proportion of open to closed porosity for porous PZT ceramics. As shown in Fig. 4a, both SA- and PMMA-derived porosities were mainly closed at P < 10%, since the pore spacing is too far then. When 10% < P < 35%, the SA-derived open porosity was much higher than the PMMA-derived one due to the easy interconnection among the SA-derived pores. Because the PMMA-derived pore is spherical but the SA-derived pore is irregular and has a much smaller aspect ratio than the spherical pore, the SA-derived pores become interconnected more easily. That is to say, the percolation transition limit for pore interconnection is closely related to the shape of pore. Accordingly, the SA-derived irregular pores would have a percolation transition limit less than that of the PMMA-derived spherical pores. When P > 35%, the discrepancy of open porosity diminished gradually between the SA- and PMMA-derived porous PZT ceramics, because the pores contact each other at such a high volume fraction that the PMMA-derived pores have also achieved easy interconnection. As stated above, the SA and PMMA used as PFAs have resulted in different pore morphologies and porosities, and the difference in the porous microstructures could in turn lead to different electrical properties for porous PZT ceramics. 4.2. Effect of porous microstructure on properties The electrical and acoustic properties of porous PZT ceramics are related to both pore morphology and porosity. First, we discuss the dependence of dielectric properties on pore morphology and porosity. Porous ceramics can be regarded as a pore-solid composite whose dielectric property could be predicted by some theoretical models. In this study, the following well-known general empirical equation [17] was used to predict the dielectric constants of the resultant porous PZT ceramics: X ear ¼ V i eari ð4Þ i

where er is the relative dielectric constant of porous materials, eri and Vi are the dielectric constant and volume fraction of the ith material, and a is a constant. The value of a is determined to be a = 1 and a = 1 for serial and parallel mixing models, respectively. Nevertheless, these models have not considered the shape of pores in porous materials. Assuming that the relative dielectric constant

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of pore is unity, a modified cubes model incorporating a parameter Ks indicative of pore shape had been proposed to predict the relative dielectric constant of porous dielectric ceramics [18,19]: (  2=3  2=3 ) 1 P P 0  er ¼ er 1 þ 1=3  0  Ks er  1 K s2=3 þ 1 K s P ð5Þ where er and e0r are the relative dielectric constant of porous materials and the solid matrix, respectively, P is porosity and Ks is the shape factor of pore. The value of Ks is denoted as, for example, Ks = 1.0 for a spherical pore. The empirical equation and the modified cubes model were, respectively, used to correlate the measured dielectric constant data in this study. As shown in Fig. 7, the measured dielectric constant data points for porous PZT ceramics fall between the predictions of the serial and parallel models. The serial and parallel models have predicted two extreme cases of the mixing of two components. Because most pores in porous PZT ceramics are closed at low porosity, the dielectric constants measured at low porosity are closer to the prediction of the parallel model. While more and more pores are interconnected at higher porosity, the measured dielectric constant data are found to change toward the prediction of the serial model. The case is true for the two data points of the SA-derived porous PZT ceramics at >35% porosity, as well as the data point of the PMMA-derived porous PZT ceramics at about 40% porosity. The observation is consistent with the SEM micrographs in Figs. 5 and 6 that show the interconnection of pores at high porosity. Recently, Li and Dunn [20] presented a method to successfully determine the upper and lower bounds for dielectric constant of a porous PZT– PNN piezoelectric ceramic using the Hashin–Shtrikman variational principle. This method is valid for statistically homogeneous multiphase composites with arbitrary microgeometry and anisotropy, and could thus acquire a narrower prediction than the parallel and serial models, but it requires some numerical calculations. The Hashin– Shtrikman-type bounds for dielectric constant of porous PZT ceramics deserve further study. When the shape of pores is considered, the dielectric constant of the PMMA-derived porous PZT ceramics agrees well with the prediction by the modified cubes model with Ks = 1.0, which is consistent with the SEM observation of the PMMA-derived spherical pores in Fig. 6. The dielectric constant of the SA-derived porous PZT ceramics also agrees with the prediction at low porosity of <20%, although the SA-derived pores are not spherical, as shown in Fig. 5. However, as shown in Fig. 7, the SA-derived dielectric constant decreased suddenly at high porosity but the PMMA-derived dielectric constant decreased only a little. This discrepancy is due mainly to the fact the SAderived pores have easier interconnection than the PMMA-derived ones. The above results indicate that the dielectric constant of porous PZT ceramics is not sensitive

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to the shape of pores, but is closely related to the interconnection of pores. The modified cubes model had also been used to predict the piezoelectric constant d31of porous piezoelectric ceramics [18,19]. Considering the relationship of d33  2–2.5d31, the theoretical model is rewritten as follows: 8  1=3   1=3 9 > > P > > 1  KPs = < Ks P 1=3 0 ð6Þ d 33 ¼ d 33 1  1=3 þ > > 1  P 1=3 K 1=3 Ks > > s ; : where d33 is the piezoelectric constant of porous ceramics, d 033 is the piezoelectric constant of ceramic bulk materials, and P and Ks are defined above. As shown in Fig. 10, the variations of piezoelectric constant d33 agree well with the theoretical prediction using Ks = 1.0, for both the PMMAderived porous PZT ceramics in the whole porosity range of 3–40% and the SA-derived porous PZT ceramics in the partial porosity range of 3–20%. However, the value of d33 decreases dramatically for the SA-derived porous PZT ceramics at P > 35%, which is similar to the change of dielectric constant er in Fig. 7 and to the sudden decrease of remnant polarization Pr for the 60%PZT– 40%SA sample in Fig. 8a. The reason should also be connected to the easy interconnection of the SA-derived pores at high porosity. Since mechanical loadings are involved in the piezoelectric response of porous PZT ceramics, the irregular shape or the interconnection of pores could affect the mechanical loading and further degrade the corresponding piezoelectric constant. By contrast, stress concentration on the surface of the PMMA-derived spherical pores may not be severe. Therefore, the d33 value of the PMMA-derived porous PZT ceramics decreased smoothly with increasing porosity, as shown in Fig. 10. The graded variations of piezoelectric constant with porosity for porous PZT ceramics were utilized by Li et al. [4] to develop a porosity-graded piezoelectric actuator, which can effectively remove the interface debonding observed frequently in conventional bimorph-type piezoelectric actuators. It is of interest that, unlike the dielectric and piezoelectric constants, the acoustic impedance of porous PZT ceramics is related only to porosity. As shown in Fig. 12, the acoustic impedance decreased with a similar law for both the SA- and PMMA-derived porous PZT ceramics when the porosity was increased, irrespective of the difference in pore morphology of these two porous ceramics. 4.3. Applications of porous PZT ceramics The fact that the acoustic impedance of porous PZT ceramics decreased with increasing porosity allows us to use this material. In such practical applications as ultrasonic imaging [6] or underwater sonar [7], there is usually a huge difference in acoustic impedance between PZT ceramics (>10 MRayls) and human tissue (from 1 to 2 MRayls) or water (1.5 MRayls). If a porosity-graded

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layer is inserted between dense PZT ceramics and human tissue or water, the acoustic impedances on the opposite sides of the interface could be well matched. For this purpose, we fabricated the porosity-graded porous PZT ceramics in this study. Fig. 14 shows SEM micrographs of the porosity-graded porous PZT ceramics derived from SA and PMMA, respectively. The porosity-graded material consisted of the four layers of monolithic PZT, 90%PZT–10%SA, 70%PZT–30%SA and 50%PZT–50%SA (from left to right) for the SA addition (Fig. 14a), or of monolithic PZT, 90%PZT–10%PMMA, 70%PZT–30%PMMA and 50%PZT–50%PMMA (from left to right) for the PMMA addition (Fig. 14b). The thickness of each layer was designed to be 0.5 mm and the total thickness of the porosity-graded structure was about 2.0 mm. Of course,

one can fabricate the structure with a different thickness to meet the actual requirements. The microstructures of each compositional layer have been shown in Figs. 5 and 6, and the corresponding porosity is shown in Figs. 2 and 4. In comparison, the SA-derived pores were thin and oval in shape but the PMMA-derived pores were more spherical. As shown in Fig. 14, the SA-derived porosity-graded porous PZT ceramics showed more remarkable interconnections between pores than the PMMA-derived ones. According to the results shown in Fig. 12, the acoustic impedance will decrease gradually along the direction from the monolithic PZT side to the 50%PZT–50%SA (or PMMA) side. This kind of porosity-graded structure could be incorporated into relevant devices to achieve a good match of acoustic impedances at their interface. This work has been left for future study. 5. Conclusion Porous PZT ceramics of 3–43% porosity were produced at 1200 C using SA as a pore-forming agent (3–40% for the case of PMMA). The SA-derived pores were irregularly oval-like but the PMMA-derived pores were nearly spherical. At a given bulk porosity, the SA-derived porous PZT ceramics had higher open porosity resulting from pore interconnection than the PMMA-derived ones. The dielectric constant er, remnant polarization Pr and piezoelectric constant d33 all decreased linearly with increasing porosity in the range of 3–20% for the SA-derived porous PZT ceramics, and in the range of 3–40% for the PMMAderived porous PZT ceramics, regardless of the shape of pores. The variation of dielectric constant or piezoelectric constant with increasing porosity was well predicted by a modified cubes model. The electrical properties for the SA-derived porous PZT ceramics decreased sharply when the porosity was more than 35%, which is attributed to the easy interconnection of the SA-derived pores. The acoustic impedance of the SA- or PMMA-derived porous PZT ceramics decreased linearly with a similar law with increasing porosity, irrespective of pore morphology. The graded varied acoustic impedance of the porosity-graded porous PZT ceramics (from 16 to 8 MRayls) could make them promising candidates for application to underwater sonar detectors or medical ultrasonic imaging. Acknowledgements The project was supported by the National Natural Science Foundation of China (Grant Nos. 50325207, 50402002) and the Ministry of Sciences and Technology of China through 973-Project (Grant No. 2002CB613306). References

Fig. 14. SEM micrographs showing the porosity-graded microstructures of (a) SA- and (b) PMMA-derived porous PZT ceramics.

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