Solid State Ionics 156 (2003) 59 – 69 www.elsevier.com/locate/ssi
Electrical properties of zirconia–alumina composites Jean-Claude M’Peko a,*, Deusdedit L. Spavieri Jr. a, Charles L. da Silva b, Carlos A. Fortulan b, Dulcina P.F. de Souza b, Milton F. de Souza a a
Department of Physics and Materials Science, IFSC, University of Sa˜o Paulo, C. Postal 369, CEP 13560-390, Sa˜o Carlos, SP, Brazil b Department of Materials Engineering, Federal University of Sa˜o Carlos, C. Postal 676, CEP 13565-905, Sa˜o Carlos, SP, Brazil Received 17 January 2001; received in revised form 18 December 2001; accepted 25 January 2002
Abstract Sintered zirconia – alumina composites, prepared in a wide range of compositions, are studied in terms of their electrical response. Both grain conductivity and dielectric constant show the typical characteristics expected from the percolation theory, with vc = 0.14 F 0.2 as the critical zirconia volume fraction for the onset of conduction. When the conducting zirconia phase is calcined prior to forming the composite, the whole system still shows a strongly reduced conduction response even for zirconia volume fractions (v) in the range of 0.4 – 0.5, after which it is considerably enhanced for v = 0.7. These results are discussed in terms of (i) the influence of the material’s microstructure and (ii) the effect of stress resulting from the alumina sintering on the calcined zirconia grains on the overall electrical response of the composite. D 2003 Elsevier Science B.V. All rights reserved. Keywords: ZrO2/Al2O3 composites; Electrical properties; Conductivity; Dielectric constant; Percolation
1. Introduction The study of composite materials, i.e., mixtures consisting of at least two phases of different chemical compositions, has been of great interest from both a fundamental and a practical standpoint. The macroscopic physical properties of such materials can be combined so as to produce materials with a desired average response. In the present work, we are particularly concerned with the effect of the state of the starting powders, particle size and sintering on the
*
Corresponding author. Tel.: +55-16-273-9814; fax: +55-16273-9811. E-mail address:
[email protected] (J.-C. M’Peko).
electrical properties of sintered alumina – zirconia (Al2O3 –ZrO2) mixtures. Owing to their immiscibility (the solubility of alumina in zirconia is below 1.0 wt.% [1]), mixtures of these two components constitute a good example of a diphasic composite. The mechanical and electrical characteristics of the individual phases and the diphasic system have been the subject of much research. It is known, for instance, that zirconia-doped alumina ceramics have a high toughness conferred by the martensitic tetragonal to monoclinic transformation of the zirconia grains inside the alumina phase [2,3]. Various studies have also dealt specifically with the peculiarities of the oxygen conduction mechanism in stabilized zirconiabased systems. The influence of dopants on the sinterability and electrical properties of such systems
0167-2738/03/$ - see front matter D 2003 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 2 7 3 8 ( 0 2 ) 0 0 6 11 - 2
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is a problem that has already been considered [1,4 – 6]. The particular effect of alumina doping on zirconia grain conductivity is found to be very low, while grain boundary conductivity decreases significantly [4]. In fact, it is well known that dopings of alumina in zirconia, the former exhibiting a conductivity several orders smaller than the latter, locate mainly at the grain boundary and triple points of the microstructure. In various studies of zirconia –alumina mixtures, the considered volume fractions of either zirconia or alumina do not always suffice to provide a complete picture of all the features of the composite material. From the electrical point of view, for instance, it is well known that diphasic-type systems in which one phase is much more conductive undergo a transition from insulator to conductor as the volume fraction of the conducting phase is increased, the total conductivity (r) following the percolation model [7,8]: r ¼ ro ðv vc Þt
ð1Þ
where v = vc is the onset conduction or percolation threshold, i.e., the critical volume fraction of the conducting phase after which the composite exhibits a strong increase of conductivity, while t is a constant determining the power law-conductivity behavior. The most frequent vc and t values for homogeneous powder mixtures are about 0.16 and 1.7, respectively [7– 10]. On the other hand, starting from the individual electrical properties of the phases integrating a composite medium, various models have been proposed to account for the overall composite electrical properties. Good reviews of these models and range of applicability presented by Landauer and McLachlan can be found in Refs. [9,10]. Let us refer here to Bruggeman’s symmetric Effective Medium Theory (EMT), which is the most commonly invoked approach for transport properties in inhomogeneous media. According to this model, the individual conductivities of the composite components and the total composite conductivity satisfy an equation of the type: v1 ½ðr1 rÞ=ðr1 þ 2rÞ þ v2 ½ðr2 rÞ=ðr2 þ 2rÞ ¼ 0
ð2Þ
where (r1, r2) and r are the conductivity of the individual phases and the conductivity of the mixture, respectively, while vi denotes the volume fraction of
the phases, so that Svi = 1. A similar equation can also be written in terms of the individual and total dielectric constants (e1, e2, e) of a two-phase mixture. Note that, as both Eqs. (1) and (2) clearly suggest, testing and proving the percolation or EMT (or in general any other two-phase mixture rules) behavior of composites, and obtaining for the case of Eq. (1) accurate estimations of the involved vc and t parameters, requires studies over a wide range of the diphasic compositions. In the study reported on herein, microstructural characteristics, bulk conductivity and the dielectric constant of zirconia – alumina composites were investigated over a wide range of zirconia concentrations in the system. Particular attention is paid on the influence of microstructure features, including state of the starting powders and internal stress effects, on the final electrical properties of the composite. The overall purpose of the present and future studies is basically to understand the development and manifestation of these effects on composite materials, and the alumina –zirconia system is first selected due to component immiscibility and system’s simplicity as well as for its very interesting practical applications.
2. Experimental procedure Two types of Al2O3 – ZrO2 composites were prepared from commercial alumina (AKP-50 Sumitomo, Japan) and stabilized zirconia (3YTZ, Tosoh, Japan). In the first type, the mixture of the as-received powders, in desired ratios varying from 15 to 100 vol.% of 3YTZ, was prepared in acetone with 1.0 wt.% polyvinylbutyral, PVB, as previously reported in Ref. [11]. The mixed powders were then dried and disk-shaped by uniaxial pressing, followed by isostatic pressing at 210 MPa. The sintering process of the molded samples was performed at 1500 and 1600 jC for 1 and 2 h. The final density of this set of samples, referred hereinafter to as ‘conventional’ AZ mixtures, ranged from 97% to 99% of the theoretical density, as measured by the Archimedes method. A second set of samples was prepared starting from a 3YTZ powder that was previously calcined at 1600 jC for 1 h, and then ball-milled for 3 h in acetone with zirconia balls, using high density polyethylene bottles. This calcined powder was mixed with alumina in acetone with 1.0 wt.%
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of PVB to form the composite material. Here, volume fractions of 40%, 50% and 70% of 3YTZ were considered for a comparative study with similar compositions in the first series of samples. These mixtures were also isostatically pressed into disk-shaped pellets at 210 MPa, and then sintered at 1500 and 1600 jC for 1 and 2 h. The final density of these samples, referred hereinafter to as ACZ mixtures, resulted in about 94% of the theoretical density. The sintered samples were then polished using a diamond paste of 1 Am and thermally etched at 1450 – 1500 jC for 6 min for microstructural observations by scanning electron microscopy (SEM). Platinum paste (DEMETRON 308 A Platinum paste) electrodes were applied to both sides of the sintered and polished samples for the impedance spectroscopy experiments, and the electrical data were taken with an impedance/gain-phase analyzer (Solartron SI 1260) at frequencies ranging from 1 Hz to 13 MHz. In this present report, we consider mainly the electrical data measured at 375 jC. The study also considers electrical results obtained from zirconia ceramic plates, made of the 3YTZ powder and sintered at 1600 jC for 2 h, before and during the application of external stress loadings.
3. Results and discussions 3.1. Microstructural characterizations Fig. 1 shows the typical SEM micrographs corresponding to the ‘conventional’ AZ composites. The average grain size of alumina (dark phase) decreased with increasing the volume fraction of zirconia (white phase) in the composite, from 3.2 Am in the pure alumina samples (Fig. 1a) until it reached a nearly constant value of 1.3 Am (Fig. 1b) from 30 vol.%. Meanwhile, the average zirconia grain size was kept nearly constant at about 0.7 Am throughout the composite’s composition range. Inhibition of grain growth in zirconia-doped alumina materials is widely accepted and discussed in the literature as arising from a grain boundary pinning by zirconia, which prevents alumina boundary mobility and thus grain growth. The typical microstructures found in those composites whose zirconia phase had undergone prior calcination, i.e., the ACZ mixtures, are illustrated in Fig. 2.
Fig. 1. Electron micrographs of (a) pure alumina and (b) a ‘conventional’ alumina – zirconia (AZ) composite with 40 vol.% of 3YZT, both after sintering at 1600 jC for 2 h.
They consisted of zirconia particles or aggregates fairly well dispersed in the alumina phase (Fig. 2a). The average size of the zirconia particles is about 28 Am. Fig. 2b shows a clear electron micrograph of the interface between these zirconia particles and the alumina phase. As in the previous set of samples, the zirconia particles consisted of 0.7 Am zirconia grains that were sintered together, i.e. densified, during the calcination of the starting zirconia powder prior to forming the phase mixture. These aggregates
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finally heat-treated, the zirconia phase, already shrunken during calcination, must actually be subjected to fairly strong stress forces from the shrinkage of the alumina phase. Such stresses are considered to originate between neighboring alumina and zirconia grains at the contact points, i.e., all around the aggregate surface. It is interesting to explore the possible consequences of such a mechanical effect on the final composites’ electrical properties. From this point of view, note that this situation applies well when considering the sintering of composite materials consisting of two or more phases with a marked difference in thermal rates of shrinkage. It is finally noted that the average alumina grain size in these ACZ composite samples, containing 40– 70 vol.% of zirconia (Fig. 2b), is estimated to be about 3.3 Am, which is close to the value of 3.2 Am observed in the undoped alumina samples (Fig. 1a). The reason for this result lies in the microstructural features of these composites, in which no effective conditions for zirconia-induced alumina grain boundary pinning, i.e., no constraints for grain growth, can be expected provided most of the alumina grains are not in contact with the zirconia phase. 3.2. Electrical characterizations
Fig. 2. Electron micrographs of (a) a ‘modified’ alumina – zirconia (ACZ) composite with 40 vol.% of 3YZT sintered at 1600 jC for 2 h, and (b) a local picture of an aggregate surface.
already tended to have a spherical shape after the milling process during which, moreover, these particles resulted just partially broken as can be seen in Fig. 2a. For the reason expressed right below, this is the other situation, along with that of the ‘normal’ AZ composites microstructurally characterized above, we chose to conduct our electrical study. It is reasonable to infer that when such an ACZ composite powder is
Fig. 3 shows the typical behaviors of complex impedance planes corresponding to the alternating current (ac) measurements carried out at 375 jC in the ‘conventional’ AZ samples sintered at 1600 jC for 2 h. These plots show impedance dispersions consisting of two semicircles, which are identified as corresponding to the grains (bulk) and grain boundaries at high (left side arc) and low frequencies (right side arc), respectively, while the impedance spike at the lowest frequencies in Fig. 3b corresponds to the electrode’s contribution. From these plots, individual capacitance and resistance (or conductance) associated to each micro-region may be extracted after conventionally fitting the data according to the simplified brick (series) layer model [12,13]. This procedure was applied to all the impedance data covering the entire range of studied composite compositions. Some of the experimental results have recently been presented in the literature [11] and concern the electrical behavior, along with its thermal variations, of both grain and grain boundary micro-regions. We will
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Fig. 3. Complex impedance plots of AZ composites with (a) 20 and (b) 50 vol.% of 3YZT sintered at 1600 jC for 2 h. The data correspond to measurements performed at 375 jC.
be especially concerned, here, with the behavior of the composite bulk (grain) properties. Simulation of all the impedance data to extract the values of resistance and capacitance involved was done using different simulation programs (Equivalent Circuit by Boukamp and ZView by Solartron) producing quite similar results with relatively low fitting errors of up to 15%. The conductivity r u L/R, and dielectric constant e u CL/eo, where L is a sample geometrical factor and eo = 8.854 pF/m is the vacuum dielectric constant, were then calculated. Fig. 4 depicts the behavior of the bulk conductivity of the samples upon volume fraction of the conducting zirconia phase. The average curve obtained suggests an insulating-type behavior for all the compo-
sites with the lower zirconia contents, followed thereafter by a strong rise of conductivity as the zirconia volume fraction was steadily increased. Consideration of the percolation theory and application of the conductivity dependence predicted by Eq. (1) led to an estimated conduction threshold of vc = 0.14 F 0.2. Although this value was lower than the approximately 0.25 reported by Kleitz et al. [14] for samples in the same two-phase system, it remained relatively close to the theoretical value of 0.16 expected for a perfectly random 3D system [8 –10]. Experimental vc results reported in the literature vary significantly [10,15 – 17], typically between 0.01 and 0.6 [10], depending on structural features (non-homogeneity or other non-random structural correlations) of the
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Fig. 4. Conductivity dependence of the zirconia – alumina composites with varying zirconia volume fractions. Open symbols correspond to AZ composites, closed symbols to ACZ composites.
prepared composites. On the other hand, the value of the exponent t in Eq. (1) was found to be in the order of t f 1.4 F 0.2, which is somewhat below the values of 1.65 – 2.0 generally referred to as the universal range [7,8,10]. It should be noted that percolation parameters must be more accurately estimated when a greater number of experimental points are involved, i.e., with a far more complete composition range of the composite. However, experimental constraints affecting the correct estimation of these parameters may also arise from the fact that each datum used in drawing a percolation curve requires separate samples, which may give rise to the inconvenient introduction of slight or even strong (in some cases) microstructural uncorrelations. For the sake of a comparative reference, the solid line in Fig. 4 shows the results obtained from the application of the symmetric Effective Medium Theory (EMT). The curve was generated from Eq. (2) using the values of r1(3YTZ) = 7.3 10 5 (V cm) 1 and r2(Al2O3) = 1.0 10 14 (V cm) 1; v1 u v, v2 u 1 v and r u rg. As pointed out elsewhere, this model works well except near the critical region, where it fails to predict the real location of the onset of conduction (vc = 0.33 for EMT). To accurately describe experimental percolation curves near the onset conduction, an empirical General Effective Medium
(GEM) equation has been proposed and successfully applied by McLachlan [10,17]. Fig. 5 illustrates, again by means of open symbols, the dependence of the bulk dielectric constant of the ‘conventional’ AZ composites upon the volume fraction of the conducting zirconia phase. While tending to reach the value of eg = 60 at the highest zirconia content, the dielectric constant shows a clear divergence in the vicinity of the onset conduction or percolation threshold, as has been also reported in other percolating systems [15 – 18], with a dielectric peak located, in the present case, at a critical volume fraction of vce c 0.15. Towards the lowest contents of zirconia, this property is expected to decrease continuously so as to reach the value of eg = 10, which corresponds to the pure alumina phase. The curve corresponding to the EMT, also presented in this figure by a solid line and generated using eg(Al2O3) = 10 and eg(3YTZ) = 60, again successfully describes the experimental results outside the conduction onset region. It should be noted, however, that while predicting the existence of a threshold (Fig. 4) in the transport properties of inhomogeneous media (a peculiarity that makes this model a particularly important approach in comparison to previous effective media theories or simple mixture rules), this model does not predict the critical behavior of the dielectric constant showing a peak.
Fig. 5. Dielectric permittivity dependence of the zirconia – alumina composites with varying zirconia volume fractions. Open symbols correspond to AZ composites, closed symbols to ACZ composites.
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The divergence of the dielectric constant of composite materials when approaching vc from below has actually become an experimental fact, which is classically attributed in the literature to large capacitance effects from the contribution of the percolative clusters blocked by thin insulating barriers [18]. With increasing zirconia content in the composite, this contribution, which does remain associated to the formation of space charge in the system, should begin to disappear above the onset conduction after the first ‘infinite’ percolative cluster becomes formed, i.e., after the conducting component begins to form continuous paths across which the space charge is free to move until it finally reaches the electrodes. Fig. 5 shows that, thereafter, the composite’s dielectric constant correctly follows the behavior predicted by the two-phase EMT. In fact, we note that, although the dielectric constant near vc has been less exhaustively studied than conductivity, an analysis of its behavior should provide additional information on the total percolating response of composite materials. The good agreement obtained between the experimental AZ composite data presented here and the percolation theory indicates that, after sintering, the conducting zirconia does not suffer cross effects, such as internal stresses for instance, which could clearly affect the materials’ average electrical response. Fig. 6 now shows the impedance dispersion behavior observed at 375 jC in the ACZ sample containing 50 vol.% of zirconia calcined prior to forming the composite material. This figure is representative of the general features of impedance obtained in the ACZ samples with 40 and 50 vol.% of zirconia. Excluding the spike from the electrode contribution at the lowest frequencies, a careful analysis of these impedance data, combined with an electric modulus identification procedure [12,19], allowed us to conclude that four overlapping arcs occurred. Within a reasonable margin of error of about 20%, resulting from the strong arcs overlapping, the frequencies of the different arc maxima (relaxation frequencies) in Fig. 6 are, for instance, from the left to the right side, f1 c 2 106 Hz, f2 c 8 105 Hz, f3 c 5 103 Hz and f4 c 4 102 Hz. Under equal measuring conditions, in Fig. 3b, the relaxation frequencies for the same composite composition but in the AZ set of samples are f c 3 106 Hz for the grains and f c 5 103 Hz for the grain boundaries. To a first approximation, as
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Fig. 6. Complex impedance plots of a zirconia – alumina (ACZ) composite with 50 vol.% of 3YZT sintered at 1600 jC for 2 h. The data correspond to measurements performed at 375 jC.
is well known from the series layer model theory [12,13], each relaxation frequency in the ZWvs. ZV-type plots obeys the relation 2pfiRiCi = 1. From this relation, it follows that fi~ri/ei, i.e., the relaxation frequency basically represents an intrinsic property of the corresponding micro-region of the ceramic material. On comparing the order of magnitude of the above four fi values from the ACZ sample data with the two values from the corresponding AZ sample data, in Fig. 6, both semicircles 1 and 2 are thus identified as belonging to the grains, while semicircles 3 and 4 are both associated to the grain boundaries. It is reasonable to expect that stress effects from the alumina shrinkage on the calcined zirconia particles should affect the electrical response of the ACZ samples. The actual question to explore is how do these effects manifest in terms of impedance dispersion and magnitude. Appropriate experiments and studies are currently being conducted to analyze this problem in depth. For instance, preliminary evidence supporting the statement that stresses clearly affect the electrical response of materials is given in Fig. 7a and b. The experiment consisted in recording the electrical response of zirconia ceramic plates, prepared from the as-received 3YTZ powder, during uniaxial compressive loads. The figures particularly correspond to impedance measurements taken at 175 jC from one of these ceramic plates, for a 265-MPa of external stress applied in the perpendicular direc-
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Fig. 7. (a) Complex impedance plots and (b) frequency dependence of the imaginary part of impedance measured at 175 jC on a zirconia ceramic plate, illustrating the variation in the initial impedance magnitude (open symbols) when the material was subjected to an external stress of 265 MPa (closed symbols).
tion with respect to the external electric field. As can be seen in Fig. 7a, the uniaxial stresses clearly gave rise to an increase of both the grain and grain boundary arc diameters and, thus, resistances. The variations registered in the present case reach values of about 18% for the grains and 22% for the grain boundaries, giving a total effect of about 20%. These results are in fact a promising indication that, well below their maximum mechanical resistance, internal stress effects in such materials can eventually be
detected and closely analyzed by impedance spectroscopy. As an apparent trend, Fig. 7b particularly reveals that both the initial relaxation frequencies (indicated by arrows) slightly decreased when stress was applied on the material: from 1.9 to 1.2 kHz in the case of the grains, and from 7.2 to 5.0 Hz in that of the grain boundaries. Returning to the results presented in Fig. 6, since one out of every two relaxation frequencies of the grains and of the grain boundaries closely resembled each micro-region relaxation frequency found for the same composite composition in the AZ set of samples (Fig. 3b), then the electrical response of the ACZ samples most probably consists of one intrinsically unperturbed and one perturbed contributions. In conformity with the results presented in Fig. 7b, the relaxation frequency of each perturbed contribution is shifted towards a lower value, but remains sufficiently close to that of the corresponding unperturbed component so as causing a strong impedance arc overlapping. It is important here to point out that samples belonging to the ACZ set with 70 vol.% of zirconia (thus less alumina than the two previous ACZ samples) showed an impedance dispersion approaching that of Fig. 3b, i.e., with basically one semicircle for the grains, while the grain boundaries still displayed two arcs, the second one (arc 4 in Fig. 6) being, however, much more smaller especially at the higher temperatures. In general, the results for this composite composition were reasonably expected if one considers a strong reduction of the residual internal stress field caused by the reduction of the alumina volume fraction shrinking on the zirconia particles during composite sintering. Because totally isostatic stress forces are not expected to produce two different electrical responses for each micro-region, the reason for the appearance of two semicircles for the grains and for the grain boundaries (Fig. 6) may be attributed to some differences in the distribution of stress throughout the ceramic body, although the sum of stresses over the whole material must, of course, be zero. According to this work, the consequence of an unequal spatial stress distribution throughout the material (as clearly expected for example between grains or particles located at the material’s external surface and those located in its bulk) should be such that, for some grains and grain boundaries, the final magnitude and direction of the resulting stress in relation to that of the
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applied electric field do not (practically) affect the corresponding electrical response. Based on the series layer model, the total lowfrequency resistance and capacitance of the grains, which is within the frequency window wherein the grains (unperturbed and perturbed contributions) dominate the material’s overall electrical response, must be estimated, respectively, as [13]: Rg ¼ R1 þ R2 ;
Cg ¼ ðC1 R21 þ C2 R22 Þ=ðR1 þ R2 Þ2 ð3Þ
The closed symbols in both Figs. 4 and 5 precisely illustrate, respectively, the total grain conductivity and dielectric constant data calculated for the ACZ set of samples. Due to the considerable arc overlapping, estimation of the individual Ri and Ci values involved relatively high but still acceptable (in terms of impedance spectroscopy) fitting errors, up to about 29%. It should be noted that, even with conducting zirconia phase contents as high as 40 – 50 vol.%, the entire system’s grain conductivity still remained quite small. The dielectric constant in these two cases showed higher values, in the order of 152 F 46 for the ACZ composite with 40 vol.% of zirconia, and 164 F 49 for the ACZ composite with 50 vol.% of zirconia. In the ACZ composite with 70 vol.% of zirconia, the grain conductivity increased considerably compared to the cases with 40 and 50 vol.% of zirconia content, while the corresponding dielectric constant decreased, closely approaching the previous values indicated by open symbols. As we pointed out earlier herein, typical vc values usually vary over a wide range of about 0.01 to 0.6 [10], owing to the strong influence of microstructural features on the quantitative characteristics of the percolation phenomenon in real composite materials. In fact, it was shown in Section 3.1 that a strong variation of the microstructural features of the alumina – zirconia samples occurred when the zirconia was heat-treated prior to forming the composite (Figs. 1 and 2). Here, it is appropriate to consider Kusy’s model, according to which the percolation threshold parameter is strongly dependent upon the ratio between the radius of the insulating (ri) and conducting (rc) particles in the composite system: vc~(ri/ rc) 1 [10,20]. Although the grain size of zirconia was found to be basically the same in all the composite
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samples studied (about 0.7 Am), the particles to be considered in this ACZ set of samples are actually the zirconia aggregates and the individual alumina grains. Their radii are far from comparable, rci28 Am and rii3.3 Am, giving rise to a strong shift of the onset conduction towards higher zirconia contents. According to this model, a threshold value of vc c 0.6 can be predicted for the ratio ri/rc c 0.1 [20]. This agrees well, as a tendency, with the new percolative curve drawn in Fig. 4 to connect the closed points. Because the conduction threshold in the case of this ACZ composites shifted to higher contents of zirconia, it is reasonable to expect (in Fig. 5) a shift of the dielectric constant peak towards this new conduction onset, a fact which basically explains the high dielectric constant values observed for the ACZ samples with 40 and 50 vol.% of zirconia compared to equal compositions in the AZ set of samples. Independently of this fact and the relatively high margin of error involved during estimation of the electrical parameters of the above two ACZ samples, these tended in addition to show dielectric constant values relatively higher than the highest values obtained at the dielectric peak for the AZ samples. On the basis of the series layer theory, this result can be accounted for by considering the development of a moderate internal grain process of interfacial polarization associated with the occurrence of an additional impedance arc for the grains (that from the perturbed contribution, Fig. 6) in these two ACZ composites as compared to the AZ composites (Fig. 3). This is a well-known polarization mechanism that has been largely treated in the literature [13,21]. Fig. 8 particularly shows the bulk dielectric constant –conductivity dependence for all the composite samples studied. Note that the data corresponding to the ACZ system (closed symbols) with 40 and 50 vol.% of zirconia basically fall into the critical region of the percolation threshold effect, following well the data correlation according to which low conductivities are correctly matched to high dielectric permittivities from the critical divergence behavior. Such a critical percolating behavior may be particularly important for practical applications that require high dielectric constants coupled with low conductivities. In the present study, accomplishment of a percolative-type behavior for the ACZ samples suggests that this phenomenon predominates over the strain effects
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4. Conclusions
Fig. 8. Dielectric permittivity – conductivity correlation in the zirconia – alumina composites with varying zirconia volume fractions. Open symbols correspond to AZ composites, closed symbols to ACZ composites.
derived from the internal stresses generated by the shrinkage of alumina on the calcined zirconia. However, our impedance results clearly suggest that the latter acted largely throughout the ceramic body. For instance, the two resistances associated to the grains in Fig. 6 are R1 c 1.2 103 V for the unperturbed grain contribution and R2 c 1.0 105 V for the perturbed grain contribution. In such a case, the unperturbed grain contribution electrically represents only about 1 – 2% of the total grain response. This result suggests that most of the ACZ bulk material is subjected to the internal stresses, contributing to an additional decrease of the material’s total (grain and grain boundary) conductivity, in addition to the Kusy effect. Although they are also particle size-dependent [22,23], possible residual stress effects generated by the difference between the thermal expansion coefficients of both the alumina and zirconia components forming the composite materials have not been considered here as a probable driving force of this additional decrease in conductivity. This is because the split of each grain and grain boundary impedance arc into two arcs (Fig. 6) was not observed in the AZ composites (Fig. 3), and was also considerably reduced in the ACZ composites with lower alumina content, as mentioned earlier.
The microstructural and electrical characteristics of zirconia –alumina composites were studied in this work. In the ‘conventionally’ formed AZ mixtures, zirconia was found to inhibit alumina grain growth, with the grain size varying from 3.2 to 1.3 Am as zirconia was increased from 0 to 30 vol.%. The alumina grain size remained constant as zirconia was further increased. Meanwhile, a zirconia grain size of about 0.7 Am was found to be basically constant in all the studied compositions. A different situation arose when the zirconia was calcined prior to forming the composite materials. The final microstructures in this ACZ system consisted of zirconia aggregates of about 28 Am dispersed in the alumina phase, which preserved a grain size of about 3.3 Am as in the prepared pure alumina samples (3.2 Am). These microstructural features were found to exert a strong influence on the final electrical response of the materials. While the conventionally formed AZ mixtures showed a percolation threshold of about 0.14 of zirconia content, this value shifted to about 0.6 for the ACZ mixtures. The latter result agrees well with the Kusy model, which prevents strong variations in quantitative percolation parameters, depending on the microstructural correlation features (differences in particle size of the mixed components) in the composite materials. Although minor compared to the Kusy effect, the influence on the electrical conductivity due to internal strains deriving from the shrinkage of alumina on the calcined zirconia was demonstrated. Depending on the material’s applications being projected, such effects involving mechanical interactions between mixed particles may constitute a practical problem and should therefore be carefully taken into account in the material’s preparation and sintering, particularly in the case of conducting composite and graded materials.
Acknowledgements The first author (M’Peko) acknowledges the support from the Brazilian research funding FAPESP through grant no. 2000/04460-6.
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