In situ characterization of the grain and grain-boundary electrical responses of zirconiaceramics under uniaxial compressive stressesJean-Claude M’Peko, Deusdedit L. Spavieri Jr., and Milton Ferreira de Souza Citation: Applied Physics Letters 81, 2827 (2002); doi: 10.1063/1.1512328 View online: http://dx.doi.org/10.1063/1.1512328 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/81/15?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Probing grain boundaries in ceramic scintillators using x-ray radioluminescence microscopy J. Appl. Phys. 111, 013520 (2012); 10.1063/1.3676222 Effects of grain, grain boundary, and dc electric field on giant dielectric response in high purity CuO ceramics J. Appl. Phys. 104, 036107 (2008); 10.1063/1.2957063 Grain boundary electric characterization of Zn 7 Sb 2 O 12 semiconducting ceramic: A negative temperaturecoefficient thermistor J. Appl. Phys. 93, 5576 (2003); 10.1063/1.1566092 Grain-boundary and crack effects on the dielectric response of high-permittivity films and ceramics Appl. Phys. Lett. 81, 4224 (2002); 10.1063/1.1525394 Simulation of the charge transport across grain boundaries in p -type SrTiO 3 ceramics under dc load: Debyerelaxation and dc bias dependence of long-term conductivity J. Appl. Phys. 91, 3037 (2002); 10.1063/1.1448404

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In situ characterization of the grain and grain-boundary electricalresponses of zirconia ceramics under uniaxial compressive stresses

Jean-Claude M’Peko,a) Deusdedit L. Spavieri, Jr., and Milton Ferreira de SouzaDepartment of Physics and Materials Science, Sao Carlos Institute of Physics (IFSC),University of Sa˜o Paulo, C. Postal 369, CEP 13560-970, Sa˜o Carlos—SP, Brazil

~Received 27 June 2002; accepted 13 August 2002!

The electrical properties of ion-conducting tetragonal zirconia ceramics subjected to mechanicalstresses were studied using impedance spectroscopy. The material’s overall resistance~grain andgrain boundary! was found to increase when stress was applied perpendicularly to the measuringelectric field (s'E), while only comparatively discreet variations, involving a decreasing trend ofresistance, occurred when the electric field and mechanical stress were parallel (siE). Theincrement in electrical resistance fors'E was found to be consistent with an increase of theconduction process energy barrier. The mechanical effect reported here is of elastic nature, coveringa wide range of applied stresses. The electrical characteristics from cracking and fracturing at higherstresses are also presented. ©2002 American Institute of Physics.@DOI: 10.1063/1.1512328#

Zirconia–alumina ceramic composites are widely stud-ied from both the fundamental and applications standpoints,and constitute a fair example of bodies that may involveresidual stress effects after high temperaturemanufacturing.1–3 An in-depth evaluation of the averagephysical/chemical properties of such composites requires agood understanding of how each substance behaves individu-ally under a mechanical stress. Nondestructive dc electricalmeasurements have, for instance, been applied to monitor,but at a macroscopic level, total mechanical effects incement-based materials.4,5 The mechanical behavior of poly-crystalline ceramics, however, is often as complex as theheterogeneous nature of the materials.6,7 Indirect macro-scopic observations through mechanical or other researchprocedures have so far been the only way to investigate howstress effects internally affect the average properties of ce-ramic materials.

In this letter we report anin situ investigation of how amechanical stress affects the intra- and intergranular electri-cal responses of zirconia specimens. The study involved theapplication of the ac impedance spectroscopy~IS! method,which presumably provides a unique opportunity to electri-cally separate the grain and grain-boundary contributions.8,9

Tetragonal-zirconia samples were prepared from a com-mercial powder~3YTZ, Tosoh, Japan! following the standardceramic method. The study was conducted on dense samplesof 97%–99% of theoretical density after sintering at 1600 °Cfor 2 h. Electrical measurements were taken at temperaturefrom 150 to 250 °C, using an impedance/gain-phase analyzer~Solartron SI 1260! in the frequency range of 1 Hz to 1 MHz.A mechanical setup was coupled to the measuring system,and uniaxial compressive stresses of up to about 880 MPawere applied during the ac measurements. The results wereprocessed in terms of complex impedance@Z* (v)5Z82 jZ9# planes, from which the electrical parameters of inter-est ~resistancesR and/or capacitancesC! may be extracted.8

Figure 1 shows theZ9 versus Z8 impedance responses ofa representative zirconia ceramic without and with an ap-plied stress of 270 MPa at a temperature of 170 °C. Eachimpedance curve consists of two well-separated arcs identi-fied, according to classic procedures,8 as corresponding tothe grains at high frequencies~with C;10211 F) and grainboundaries at low frequencies~with C;1029 F). Bearing inmind that the resistanceR of each microregion basically re-duces, to a first approximation, to the corresponding imped-ance arc diameter, Fig. 1 reveals that both grain and grain-boundary resistances increased when the 270 MPacompressive stress was applied perpendicularly to the elec-tric field (s'E). Conversely, within an experimental errorof up to ;6%, comparatively few variations were observedfor the stress applied in the same direction as the electricfield (siE), the apparent trend being a slight decrease ofresistances.

These results indicate that stress orientation is an impor-tant factor to consider when trying understanding the electri-cal response of materials under mechanical loads. Accordingto basic elements of mechanical properties of materials,6 thedeformation~e! of a specimen under an uniaxial compressivestress is considerably greater along the stress direction~z

a!Author to whom correspondence should be addressed; electronic mail:peko@if.sc.usp.br; jcpeko@yahoo.com

FIG. 1. Complex impedance dispersions,Z9 vs Z8, of a tetragonal-zirconiaceramic measured at 170 °C without and with an applied stress of 270 MPa(s'E andsiE).

APPLIED PHYSICS LETTERS VOLUME 81, NUMBER 15 7 OCTOBER 2002

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axis, for instance! than along the lateral directions~thex andy axes! where deformation is, moreover, of opposite sign(ex5ey52nez , wheren is Poisson’s ratio;n'0.2– 0.3 forzirconia!. Consequently, as seen in Fig. 1, notice that fors'E the ionic conduction process will occur across thestress direction along which the interionic spaces are re-duced, thus limiting charge carrier mobility. ForsiE, inturn, the conduction occurs crossing the lateral directionswhere such interionic spaces are somewhat increased, andthe transport properties should result discreetly improved toapparently undisturbed~that is, when compared to the corre-sponding resistance variations fors'E) depending on ex-perimental margin of error and stress magnitude.

Figure 2 illustrates the time dependence of the relativegrain ~g! and grain-boundary~gb! resistancesR(s)/R(s50) for data collected at 170 °C withs ('E)5205 MPa.Upon application of stress, the resistances first increasesharply, and then gradually saturate. After the stress is re-moved, the resistances again decrease to recover their initialvalues. That is, the material’s mechanical response shouldnot in such a case involve any permanent effect. In fact, farfrom their compressive strengths~2500 MPa for ideal zirco-nia!, elastic effects generally dominate the largest portion oftotal strain in ceramic materials at relatively lowtemperatures.6 The presence of an apparently noninstanta-neous contribution to the final intra- and intergranular resis-tances in Fig. 2, which would theoretically imply the consid-eration of nonelastic effects, was proven to involve athermoelastic effect. This consisted of an instantaneous,slight increase of the material’s temperature upon applicationof the stress~Fig. 2, inset!, altering momentarily the truegrain and grain-boundary resistances to be considered. Thequantitative characteristics of this totally reversible effect~onremoving the load! have been thermodynamically treated inthe literature.10 Resistance values of interest in Fig. 2 aremeasured after restoring, with increasing time~either onloading or unloading!, the initial temperature determined bythe heating source.

Considering that impedance dispersions such as thosedepicted in Fig. 1 basically result from a series connection ofgrains and blocking grain boundaries, that is, brick layer

model,8,11 the measured resistances can be expressed as

Rg5rg~mic!

dg

A

H

~dg1dgb!, Rgb5rgb

~mic!dgb

A

H

~dg1dgb!, ~1!

wherer (mic) is the microscopic specific resistivity,dg is thegrain size,dgb the grain boundary thickness,A the samplearea, H the sample thickness, whilen[H/(dg1dgb)'H/dg represents the~stress-independent! number of grainsand grain boundaries in the direction of the electric field. Itcan be proved that the ratioR(s)/R(s50) satisfies

F R~s!

R~s50!Gi

5F r~mic!~s!

r~mic!~s50!G

i

1

12e, ~2!

wherei[g or gb. We note that this ratio basically reduces tothe ratio of microscopic resistivities for small strains (e!1) as generally expected. The changes in resistance uponapplication of stress thus presuppose thatr (mic) is really astrain-dependent quantity. Differences in relative resistancebetween grains and grain boundaries in Fig. 2, as well as atother moderate stresses~i.e., excluding the region of highstress-induced damage processes, discussed later herein!, layfar below our relatively small 6% experimental error, regard-less of the measuring temperature. This general trend couldbe indicating that, while grains and grain boundaries areknown to be electrically different~e.g., normallyrgb@rg

owing to impurity segregation and space charge effects atgrain-boundary interfaces!,8,11 both microregions appear, inturn, to be mechanically equal or, at least, similar in nature.This observation is based on the fact that equal mechanicalstresses or strains are not, in principle, expected to also affectthe electrical responses of different materials equally.

Figure 3 depicts the stress dependence of grain andgrain-boundary resistances measured at 170 °C. An increaseof resistance with increasing stress was observed, but with atrend of significantly diminishing the resistance/stress ratio.As presented in the Fig. 3 inset, a final marked increase inresistance, particularlyRgb , characterized the limiting high-stress region. The continuous behavior of resistance beforeloading and after unloading is summarized in Fig. 4. Theseresults demonstrate that the elastic nature of the mechanicaleffect, yieldingRinitial5Rfinal , stretches over a wide range ofapplied stresses, including the region of strongly reducedresistance/stress ratio~Fig. 3!. In turn, the limiting high-stress region presented in the Fig. 3 inset is indeed associatedwith cracking and fracturing in the material, yieldingRinitial

FIG. 2. Time dependence of the relative grain~g! and grain-boundary~gb!resistancesR(s)/R(s50) measured at 170 °C in a tetragonal-zirconia ce-ramic under a step compressive stress of 205 MPa.~Differences in thesteady resistances basically fall within the impedance fitting error!. Inset:corresponding loading- and unloading-induced variations of the material’stemperature.

FIG. 3. Stress dependence of grain and grain-boundary resistances (Rg andRgb) measured in a tetragonal-zirconia sample at 170 °C.

2828 Appl. Phys. Lett., Vol. 81, No. 15, 7 October 2002 M’Peko, Spavieri, Jr., and de Souza

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ÞRfinal ~Fig. 4!. As currently proposed for brittle materials,6

both Figs. 3~inset! and 4 suggest that this deleterious crack-ing process originated at and propagated mainly along thegrain boundaries, critically affectingRgb .

Figure 5 shows the inverse-temperature dependence ofmacroscopic grain and grain-boundary resistivities for boththe unstressed and perpendicularly (s'E) stressed materi-als, s5270 MPa. The data fit well the familiar Arrheniusequation:

r5r` exp~Q/kT!, ~3!

whereQ is the activation energy,k the Boltzmann constant,and T the absolute temperature. Apparent values ofQ aregiven in the graph, with the particularity thatQgb.Qg , astypically found in ceramics.8,11 Considering an involved-

graphical estimating error of about 0.02 eV, no variations ofQ were identified between the unstressed and stressed mate-rials based on this estimation procedure. However, a strain-induced increase of this parameter appears to reasonably beinvolved in the real source of resistivity increase fors'E:

r~s!5r 8 exp@~Q1DQ!/kT#, ~4!

where DQ is the stress-dependent activation energy incre-ment. From Eqs.~4! and~3!, and assuming, to a first approxi-mation, thatr`5r 8 , a rough but direct estimation ofDQfor isothermal measurements may be expressed as

DQ5kT ln@r~s!/r~s50!#. ~5!

The results~all in the order of meV! obtained at 170 °C arepresented in the Fig. 5 inset, and show clear variations ofDQ with increasing stress magnitude, the total behavior be-ing similar to that ofR(s) ~Fig. 3!. Considering aDQ esti-mation error of about 15%–20%, no apparent differences ofDQ were found either~1! with varying temperatures or~2!between grains and grain boundaries. The reason for bothR(s) andDQ(s) to strongly reduce their rate per unit stressis not yet clear to us. We can only speculate that this mightperhaps result from~i! a generation of low energy conduc-tion paths or~ii ! nonlinear elastic/pseudoelastic effects due tosome crystals’ distortion or reorientation. Further combinedexperiments are required to correctly answer this open ques-tion.

In summary, the present results suggest that, in the pres-ence of partially isostatic stresses, the electrical conductionprocesses of these zirconia materials will presumably be an-isotropic, since these processes are stress dependent. Thus,care must be taken when rigorously optimizing the physicalproperties of materials in which residual effects derivingfrom the material’s preparation may be present.

The first author~M’Peko! gratefully acknowledges fi-nancial support from FAPESP, a Brazilian research-fundingagency, through Grant No. 2000/04460-6. Dr. W. L. E. Ma-galhaes is partly acknowledged for some helpful discussions.

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FIG. 4. Grain and grain-boundary resistance characteristics of a tetragonal-zirconia ceramic before loading~initial Rg and Rgb) and after unloading~final Rg andRgb).

FIG. 5. Arrhenius plots of the macroscopic grain~g! and grain-boundary~gb! resistivities (r5RA/H) in the tetragonal-zirconia ceramic without andwith an applied stress (s5270 MPa). The data, those of grains approachingthe microscopic values fordgb!dg @see Eq.~1!#, are comparable to thosereported elsewhere~e.g., Ref. 8!. Estimated values of energy barrier incre-ment (DQ) ~see text! at 170 °C for different applied stresses are given in thefigure inset.

2829Appl. Phys. Lett., Vol. 81, No. 15, 7 October 2002 M’Peko, Spavieri, Jr., and de Souza

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