E噩≈S Journal of the European Ceramic Society 22(2002)337-345 www.elsevier.com/locate/jeurceramsoc Measurement of the t->m and m -t transformations in ce-tZP by dilatometry and impedance spectroscopy Andy Tiefenbach. Susanne Wagner, * Rainer Oberackerb. Bernd Hoffmann Institut fuir Keramik im Maschinenbau (IKM), Universitat Karlsruhe(TH), Haid und Neu- Strape 7, 76131 Karlsruhe, Germany Received 23 November 2000: received in revised form 23 March 2001; accepted 28 April 2001 Abstract The thermally induced t-m and m-t phase transformation of 9 mol% CeO2-stabilized ZrO, with mean grain sizes varying from 1.2 to 2.7 um has been characterized by dilatometry, XRD and impedance spectroscopy. XRD analysis indicates an increase in the volume fraction of the monoclinic phase from 0.69 to 0. 89 with increasing grain size, which could be quantitatively correlated with the impedance spectra of the materials. Based on these findings, the m-t retransformation could be studied in situ by impe- dance spectroscopy in the temperature range from 20-350oC. Depending on the grain size, the changes in the capacitive and resistive parts of the electrical impedance correlate well with the retransformation ranges obtained by dilatometry. Therefore, impedance spectroscopy is a useful analytical tool to study the transformation behaviour of zirconia ceramics. C 2001 Elsevi Science ltd. All rights reserved Keywords: Grain growth; Impedance spectroscopy; Non-destructive evaluation; Phase transformation; TZP: ZrO 1. ntroduction Cracks in TZP are consequently surrounded by a more taining monoclinic Polycrystalline tetragonal zirconia ceramics (TZP) conia Crack detection by non destructive testing meth belong to the group of transformation toughened cera- ods, which is difficult in ceramics, could be facilitated if mics, which were developed during the last two decades. the cracks could be traced by the response of such process Meanwhile, they have found practical application in a zones by methods with a sensitivity for phase composi- variety of mechanical components, which are subjected tion. The present work is part of a more comprehensive to static or cyclic loads. Their increased toughness research project, which evaluates the potential of results mainly from a zone of inelastic deformation impedance spectroscopy(IS)for this purpose. There are around the tip of propagating cracks, the so called pro- some studies for the characterization of undamaged cess zone. ,2 Triggered by the crack tip stress field, the ceramics by impedance spectroscopy. For the char- metastable tetragonal(t) phase inside the process zone acterization of damaged material there is only limited partially transforms to the stable monoclinic(m) sym- information in literature. The effect of loaded cracks at metry. The Martensitic t->m transformation involves a high temperatures on the electrical properties has been dilatational strain of about 4% and a shear strain of studied on yttria stabilized zirconia about 16% and is usually accompanied by microcrack In particular, the present work deals with the detection ing. The consequence of this process is an increas in of monoclinic phase constituents in Ce stabilized TZP the work of fracture. The transformation toughening (Ce-TZP) bulk materials by impedance spectroscopy. contribution AK is proportional to the square root of Ce-TZP was chosen for its high transformability, which the height h of the process zone, which develops on both allows to initiate the t-m transformation not only by sides of a propagating crack external stresses, but also by cooling to moderate cryo- genic temperatures. The thermally induced phase trans formation behaviour of Ce-TZP is schematically shown in Fig. 1. 0 0955-2219/01/S. see front matter C 2001 Elsevier Science Ltd. All rights reserved. PII:S0955-2219(01)00286
Measurement of the t!m and m!t transformations in Ce–TZP by dilatometry and impedance spectroscopy Andy Tiefenbacha , Susanne Wagnerb,*, Rainer Oberackerb, Bernd Hoffmanna a Institut fu¨r Werkstoffe der Elektrotechnik (IWE), Universita¨t Karlsruhe (TH), Adenauerring 20, 76131 Karlsruhe, Germany bInstitut fu¨r Keramik im Maschinenbau (IKM), Universita¨t Karlsruhe (TH), Haid und Neu-Strae 7, 76131 Karlsruhe, Germany Received 23 November 2000; received in revised form 23 March 2001; accepted 28 April 2001 Abstract The thermally induced t!m and m!t phase transformation of 9 mol% CeO2-stabilized ZrO2 with mean grain sizes varying from 1.2 to 2.7 mm has been characterized by dilatometry, XRD and impedance spectroscopy. XRD analysis indicates an increase in the volume fraction of the monoclinic phase from 0.69 to 0.89 with increasing grain size, which could be quantitatively correlated with the impedance spectra of the materials. Based on these findings, the m!t retransformation could be studied in situ by impedance spectroscopy in the temperature range from 20–350 C. Depending on the grain size, the changes in the capacitive and resistive parts of the electrical impedance correlate well with the retransformation ranges obtained by dilatometry. Therefore, impedance spectroscopy is a useful analytical tool to study the transformation behaviour of zirconia ceramics. # 2001 Elsevier Science Ltd. All rights reserved. Keywords: Grain growth; Impedance spectroscopy; Non-destructive evaluation; Phase transformation; TZP; ZrO2 1. Introduction Polycrystalline tetragonal zirconia ceramics (TZP) belong to the group of transformation toughened ceramics, which were developed during the last two decades. Meanwhile, they have found practical application in a variety of mechanical components, which are subjected to static or cyclic loads. Their increased toughness results mainly from a zone of inelastic deformation around the tip of propagating cracks, the so called process zone.1,2 Triggered by the crack tip stress field, the metastable tetragonal (t) phase inside the process zone partially transforms to the stable monoclinic (m) symmetry. The Martensitic t!m transformation involves a dilatational strain of about 4% and a shear strain of about 16% and is usually accompanied by microcracking.3 The consequence of this process is an increase in the work of fracture. The transformation toughening contribution KT is proportional to the square root of the height h of the process zone, which develops on both sides of a propagating crack. Cracks in TZP are consequently surrounded by a more or less extended process zone containing monoclinic zirconia. Crack detection by non destructive testing methods, which is difficult in ceramics, could be facilitated if the cracks could be traced by the response of such process zones by methods with a sensitivity for phase composition. The present work is part of a more comprehensive research project,4 which evaluates the potential of impedance spectroscopy (IS) for this purpose. There are some studies for the characterization of undamaged ceramics by impedance spectroscopy.58 For the characterization of damaged material there is only limited information in literature. The effect of loaded cracks at high temperatures on the electrical properties has been studied on yttria stabilized zirconia.9 In particular, the present work deals with the detection of monoclinic phase constituents in Ce stabilized TZP (Ce–TZP) bulk materials by impedance spectroscopy. Ce–TZP was chosen for its high transformability, which allows to initiate the t!m transformation not only by external stresses, but also by cooling to moderate cryogenic temperatures. The thermally induced phase transformation behaviour of Ce–TZP is schematically shown in Fig. 1.10 0955-2219/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII: S0955-2219(01)00286-2 Journal of the European Ceramic Society 22 (2002) 337–345 www.elsevier.com/locate/jeurceramsoc * Corresponding author. E-mail address:susanne.wagner@ikm.uni-karlsruhe.de (S.Wagner).
4. Tiefenbach et al. Journal of the European Ceramic Society 22(2002)337-345 stabilized ZrO,(9Ce-TZP) has been characterized using dilatometry and impedance spectroscopy. This trans 2△T △T formation behaviour has been investigated in depen dence of the mean grain size of the 9Ce-TZP material The grain size was varied by annealing the samples for different times. The results obtained by dilatometry, TEM. and Xrd measurements will be correlated to changes in the electrical properties Mb Ab To 2. Experimental procedure Fig. I. Transformation curves for thermally induce transformation in Ce-TZP (schematically [lo) 2.1. Sample preparation During cooling of the tetragonal phase, the t->m For the sample preparation 9 mol% CeO2 stabilized transformation starts spontaneously at the so-called ZrO2 powder(9Ce-TZP, Unitec, UK)has been used Martensite burst-temperature Mb. A significant volume Plates of 65x45x 12 mm' were produced by pressing, fraction of the material takes part in this autocatalytic cold isostatic repressing and sintering at 1400C for 2 h transformation. Further cooling below Mb may result inin air. In order to vary the grain size, subsequent a gradual increase in the transformed volume. Upon annealing at 1400C in air for 16 to 256 h was carried heating, the reverse m-t transformation begins at the out. The required specimen shapes were manufactured Austenite(t) start temperature As and is completed by a from the plates by diamond cutting and grinding. All burst like reaction at the Austenite burst temperature specimens were annealed at 1200C for 1 h to remove Ab. The transformation temperatures depend on the residual stresses and the grinding induced monoclinic the material. Several mechanisms have been proposed to denoted in the following as the"initial state explain the grain size dependence of Mb. They include the nucleation process, which is favoured by a larger 2. 2. Phase transformation grain size and local residual stresses, which promote the transformation 1-l The tetragonal phase shows a By cooling the specimens down in cryogenic silicon large anisotropy in cristallographic thermal expansion oil, transformation of the tetragonal to monoclinic coefficient. This thermal anisotropy leads to high resi-(m-t) phase was induced. The transformation strain dual stresses after cooling which can be described by the was traced during cooling by strain which were relation applied to the specimens. Cooling was carried out down to -85C, where all of the specimens had undergo aTEA=△ath△dk/ their Martensitic burst reaction. The condition after t->m transformation and subsequent removing of the where Aath is the difference in the thermal expansion, specimens out of the silicon oil back to ambient condi- AT the temperature difference, dx the grain size and r tions is denoted the "transformed state the distance from the triple point. According to this After the specimens had been characterized, they were relation, the residual stresses are proportional to the used to investigate the temperature induced m-t retrans grain size and so the transformation potential increases formation. Retransformation was studied in two ways with increasing the grain size. This effect has been mea- sured by different authors. 0, n For 12 mol% ceria sta- 1. Heating the specimens a dilatometry bilized zirconia(12Ce-TZP)an increase of Mb from 175 (Netzsch 402)at a heating to 250 K has been detected increasing the grain size of 400°C. the ceramic from I to 8 um. The authors determined the transformation temperatures from the thermal with an impedance spectroscope, up to 3508pled 2. Heating the specimens inside a furnace, col expansion hysteresis using a dilatometer with a cooling The corresponding condition will be denoted the chamber. The reverse transformation can be explained retransformed state by the thermoelastic stability of the plate shaped monoclinic regions in the tetragonal matrix which are 2.3. Characterization of microstructure gradually reduced in thickness at temperatures beyond As and which become completely instable at Ab 10 Scanning(SEM) and transmission(TEM) electron n the present study the t-m transformation as microscopy were utilized for investigating the micro- ell as the m-t retransformation of 9 mol% CeO2 structure. The mean grain size was determined by the
During cooling of the tetragonal phase, the t!m transformation starts spontaneously at the so-called Martensite burst-temperature Mb. A significant volume fraction of the material takes part in this autocatalytic transformation. Further cooling below Mb may result in a gradual increase in the transformed volume. Upon heating, the reverse m!t transformation begins at the Austenite (t) start temperature As and is completed by a burst like reaction at the Austenite burst temperature Ab. The transformation temperatures depend on the stabilizer content. They increase with the grain size of the material. Several mechanisms have been proposed to explain the grain size dependence of Mb. They include the nucleation process, which is favoured by a larger grain size10 and local residual stresses, which promote the transformation.1113 The tetragonal phase shows a large anisotropy in cristallographic thermal expansion coefficient. This thermal anisotropy leads to high residual stresses after cooling which can be described by the relation. TEA ¼ thTdk=r ð1Þ where th is the difference in the thermal expansion, T the temperature difference, dk the grain size and r the distance from the triple point. According to this relation, the residual stresses are proportional to the grain size and so the transformation potential increases with increasing the grain size. This effect has been measured by different authors.10,11 For 12 mol% ceria stabilized zirconia (12Ce–TZP) an increase of Mb from 175 to 250 K has been detected increasing the grain size of the ceramic from 1 to 8 mm.11 The authors determined the transformation temperatures from the thermal expansion hysteresis using a dilatometer with a cooling chamber. The reverse transformation can be explained by the thermoelastic stability of the plate shaped monoclinic regions in the tetragonal matrix which are gradually reduced in thickness at temperatures beyond As and which become completely instable at Ab. 10 In the present study the t!m transformation as well as the m!t retransformation of 9 mol% CeO2 stabilized ZrO2 (9Ce–TZP) has been characterized using dilatometry and impedance spectroscopy. This transformation behaviour has been investigated in dependence of the mean grain size of the 9Ce–TZP material. The grain size was varied by annealing the samples for different times. The results obtained by dilatometry, TEM, and XRD measurements will be correlated to changes in the electrical properties. 2. Experimental procedure 2.1. Sample preparation For the sample preparation 9 mol% CeO2 stabilized ZrO2 powder (9Ce–TZP, Unitec, UK) has been used. Plates of 654512 mm3 were produced by pressing, cold isostatic repressing and sintering at 1400 C for 2 h in air. In order to vary the grain size, subsequent annealing at 1400 C in air for 16 to 256 h was carried out. The required specimen shapes were manufactured from the plates by diamond cutting and grinding. All specimens were annealed at 1200 C for 1 h to remove residual stresses and the grinding induced monoclinic phase in the near surface region. This condition will be denoted in the following as the ‘‘initial state’’. 2.2. Phase transformation By cooling the specimens down in cryogenic silicon oil, transformation of the tetragonal to monoclinic (m!t) phase was induced. The transformation strain was traced during cooling by strain gauges which were applied to the specimens. Cooling was carried out down to 85 C, where all of the specimens had undergone their Martensitic burst reaction. The condition after t!m transformation and subsequent removing of the specimens out of the silicon oil back to ambient conditions is denoted the ‘‘transformed state’’. After the specimens had been characterized, they were used to investigate the temperature induced m!t retransformation. Retransformation was studied in two ways: 1. Heating the specimens inside a dilatometer (Netzsch 402) at a heating rate of 2 K/min up to 400 C. 2. Heating the specimens inside a furnace, coupled with an impedance spectroscope, up to 350 C. The corresponding condition will be denoted the ‘‘retransformed state’’. 2.3. Characterization of microstructure Scanning (SEM) and transmission (TEM) electron microscopy were utilized for investigating the microstructure. The mean grain size was determined by the Fig. 1. Transformation curves for thermally induced t!m and m!t transformation in Ce–TZP (schematically [10]). 338 A. Tiefenbach et al. / Journal of the European Ceramic Society 22 (2002) 337–345
ach et al. / Journal of line intercept method from SEM micrograph from polished and thermally etched specimens for TEM investigations were prepared by dimpling and ion milling. A Zeiss EM912 microscope with an accelerating voltage of 120 kv was used for TEM investigations. The phase analysis was performed at an X-ray diffractometer(Siemens model D500) using Cu-K -radiation and a secondary graphite monocromator. The monoclinic fraction was derived from the intensities of the (-lll)m,(111)m and(111) peaks according to the method described by Toraya et 2.4. Electrical measurements 2 The electrical measurements were performed at si mens with a dimension of10×8×12mm3 using an impedance analyser(SI 1260, Solartron)in air. Electro- des required for the electrical measurements were pre- pared by vacuum deposition of platinum. At the so contacted specimens impedance spectra were recorded over a frequency range from 1 Hz to 1 MHz at tem- peratures up to 350C. Heating of the samples was 2 realized by high-intensity infrared line heaters At room temperature, the impedance spectra indicate exclusively capacitive behaviour in the investigated fre- quency range. In the temperature range between 200 to 300C, all spectra show essentially one capacitive range 050100150200250300 at high frequencies and one ohmic range at low fre- Annealing Time [h] quencies. Thus, the spectra could be simulated simply by an electrical circuit with one R-C element 5(this is Fig. 2.(a) Microstructure of 9Ce-TZP after annealing for 256 h at shown in the experimental results in Fig. 7). The values time at 1400 .c 1400C;(b) grain size in 9Ce-TZP in dependence of the annealing of the circuit parameters R and C were obtained by least uare fitting. From the capacitance C of this circuit, the capacitance c of the sample and the effective perme ability eefr of the material were derived by the width of their size distribution are not essentially C=C(L/A) (2) changed compared to the as sintered microstructure. The annealing treatment results, however, in sig fef=c/Eo (3) nificant grain coarsening, which can be characterized by the mean grain size d, represented as data points in Fig 2b. They can be fitted by a common grain growth L denotes the length(10 mm)and A the cross-section lawl6 in the form of Eq. (5) (8 12 mm)of the specimens. The electrical conductance o was calculated from the resistive part r of the impe- d-do =kIg dance by 0=1/R(L/A) (4 where tg is the annealing time, do is the initial grain size, (4) k is a scaling constant and n is the grain growth expo- nent. A least square fit yields an exponent of n=4 and a scaling constant of k=0. 19 um"/h 3. Results 6a grain growth exponent of n=4 indicates grain oundary controlled grain growth of impure systems 3. 1. Microstructure of the materials in the initial state with a coalescence of a second phase by grain bound- ary diffusion. It correlates well with findings of Theu- Fig. 2a shows a SEM micrograph of the sample nissen for a similar 9Ce-TZP I7 The presence of a annealed for 256 h at 1400C. No exaggerated grain second phase has been detected in TEM investigations growth could be observed. The shape of the grains and(Fig. 4a)
line intercept method from SEM micrographs taken from polished and thermally etched specimens. Samples for TEM investigations were prepared by grinding, dimpling and ion milling. A Zeiss EM912 Omega microscope with an accelerating voltage of 120 kV was used for TEM investigations. The phase analysis was performed at an X-ray diffractometer (Siemens model D500) using Cu-Ka-radiation and a secondary graphite monocromator. The monoclinic fraction was derived from the intensities of the (111)m, (111)m and (111)t peaks according to the method described by Toraya et al.14 2.4. Electrical measurements The electrical measurements were performed at specimens with a dimension of 10812 mm3 using an impedance analyser (SI 1260, Solartron) in air. Electrodes required for the electrical measurements were prepared by vacuum deposition of platinum. At the socontacted specimens impedance spectra were recorded over a frequency range from 1 Hz to 1 MHz at temperatures up to 350 C. Heating of the samples was realized by high-intensity infrared line heaters. At room temperature, the impedance spectra indicate exclusively capacitive behaviour in the investigated frequency range. In the temperature range between 200 to 300 C, all spectra show essentially one capacitive range at high frequencies and one ohmic range at low frequencies. Thus, the spectra could be simulated simply by an electrical circuit with one R–C element15 (this is shown in the experimental results in Fig. 7). The values of the circuit parameters R and C were obtained by least square fitting. From the capacitance C of this circuit, the capacitance c of the sample and the effective permeability eff of the material were derived by: c ¼ C LðÞ ð =A 2Þ "eff¼c="0 ð3Þ L denotes the length (10 mm) and A the cross-section (812 mm) of the specimens. The electrical conductance was calculated from the resistive part R of the impedance by: ¼ 1=R Lð Þ =A ð4Þ 3. Results 3.1. Microstructure of the materials in the initial state Fig. 2a shows a SEM micrograph of the sample annealed for 256 h at 1400 C. No exaggerated grain growth could be observed. The shape of the grains and the width of their size distribution are not essentially changed compared to the as sintered microstructure. The annealing treatment results, however, in significant grain coarsening, which can be characterized by the mean grain size d, represented as data points in Fig. 2b. They can be fitted by a common grain growth law16 in the form of Eq. (5): d n d0 n ¼ ktg ð5Þ where tg is the annealing time, do is the initial grain size, k is a scaling constant and n is the grain growth exponent. A least square fit yields an exponent of n=4 and a scaling constant of k=0.19 mmn/h. A grain growth exponent of n=4 indicates grain boundary controlled grain growth of impure systems with a coalescence of a second phase by grain boundary diffusion. It correlates well with findings of Theunissen for a similar 9Ce–TZP.17 The presence of a second phase has been detected in TEM investigations (Fig. 4a). Fig. 2. (a) Microstructure of 9Ce–TZP after annealing for 256 h at 1400 C; (b) grain size in 9Ce–TZP in dependence of the annealing time at 1400 C. A. Tiefenbach et al. / Journal of the European Ceramic Society 22 (2002) 337–345 339
ach et al. Journal of 3. 2. Thermally induced transformation behaviour of 9Ce-TZp XRD measurements indicate a single phase tetragonal microstructure for the variations annealed up to 64 h, ely with a grain size of up to 1.8 um. In material with the grain size of 2.7 um, a monoclinic phase content of 30% was detected induced during cooling of his material from the annealing temperature to room temperature (Table 1). Due to the large grain size, this material undergoes a partial t-m transformation in the 1214161.8202.22.4262.8 near surface region on cooling from the stress relaxation Mean grain size [um treatment Fig. 3. Temperatures of the t-m transformation and m-t retrans- formation depending on the mean grain size. 4. Temperature induced t-m transformation represented in Fig. 4. They are in a good qualitative agreement with the XRd results. In the initial state, the During cooling the specimens to temperatures below material exhibits a single phase tetragonal micro- room temperature, a spontaneous transformation of the structure with a grain boundary phase located in the tetragonal to the monoclinic phase at the Martensitic triple points. No microcracks were detected in this con burst temperature Mb was detected from the Measure- dition. After the t-m transition, monoclinic as well as ments of the transformation strain. Fig. 3 presents the tetragonal grains are observed. Furthermore, micro- measured transformation temperatures Mb as a func- cracks have developed at the grain boundaries due to tion of the grain size. The material with the smallest the volume increase during the t-m phase transition grain size(1. 2 um) transforms at -60C, whereas the transformation temperature of the material with 2.7 um 4.1. Electrical properties grain size is -15C. The experiments show more or less a linear grain size dependence of the transformation At room temperature only the capacitive part of the temperature Mb on the grain size. impedance can be measured, from which the effective Quantitative XRD analysis indicate a fraction of the permittivity Eeff of the different materials was derived monoclinic phase of 70-90%, corresponding to a tetra- Eeff Of the tetragonal phase ranges from 38 to 39 and is gonal fraction of 30-10%, after the cooling treatment essentially independent from the grain size, as can be (Table 1). The volume fraction of the monoclinic phase seen from the materials annealed up to 64 h in Table 1 in the transformed materials increases monotonously The permittivity of the material annealed for 256 h is at with the grain size from 69% at 1. 2 um to 89%at 2.7 the same level, in spite of its high near surface mono- um grain size. Transformation takes place almost com- clinic phase content. This indicates a very thin tetra- pletely at Mb. No significant increase in the monoclinic gonal/ monoclinic surface layer of this material in the was observed between samples cooled only to initial state, induced by cooling from the annealing Mb and samples, which were further cooled down to temperature of 1400C to room temperature 85°C. There is a reproducible, drastic decrease in the per TEM micrographs of the microstructure in the initial mittivity of all materials after the cooling induced t-m state and after the t->m transformation treatment are transformation as shown in table 1 differences of 30% for specimens with a grain size of 1. 2 um and of 36% for th ial with the largest grain size of 2 Microstructure and electrical properties of 9Ce-TZP before and after um have been measured. This shows that the cooling ling induced t-m transformation induced phase transformation occurs in the bulk of the Annealing time(h) materials and is not limited to near surface regions The effective permittivity after transformation decrea Mean grain size (um) es monotonously with increasing grain size. This is nitial state obviously caused by the higher monoclinic volume frac- XRD vol fraction m (% tion in the coarser grained materials. In Fig. 5, the effec- 38.4 tive permittivity is plotted versus the tetragonal phase After t→ m trans content measured by XRD. When the data are fitted by XRD vol fraction m (% Eff. permittivity 26.7 26.0 25.5 24.4 a linear regression, the extrapolation to 0% tetragonal phase yields an effective permittivity of the pure mono- a Near surface region clinic material of Em=22.5. Under physical aspects, a
3.2. Thermally induced transformation behaviour of 9Ce–TZP XRD measurements indicate a single phase tetragonal microstructure for the variations annealed up to 64 h, respectively with a grain size of up to 1.8 mm. In the material with the grain size of 2.7 mm, a monoclinic phase content of 30% was detected, induced during cooling of this material from the annealing temperature to room temperature (Table 1). Due to the large grain size, this material undergoes a partial t!m transformation in the near surface region on cooling from the stress relaxation treatment. 4. Temperature induced t!m transformation During cooling the specimens to temperatures below room temperature, a spontaneous transformation of the tetragonal to the monoclinic phase at the Martensitic burst temperature Mb was detected from the Measurements of the transformation strain. Fig. 3 presents the measured transformation temperatures Mb as a function of the grain size. The material with the smallest grain size (1.2 mm) transforms at 60 C, whereas the transformation temperature of the material with 2.7 mm grain size is 15 C. The experiments show more or less a linear grain size dependence of the transformation temperature Mb on the grain size. Quantitative XRD analysis indicate a fraction of the monoclinic phase of 70–90%, corresponding to a tetragonal fraction of 30–10%, after the cooling treatment (Table 1). The volume fraction of the monoclinic phase in the transformed materials increases monotonously with the grain size from 69% at 1.2 mm to 89% at 2.7 mm grain size. Transformation takes place almost completely at Mb. No significant increase in the monoclinic fraction was observed between samples cooled only to Mb and samples, which were further cooled down to 85 C. TEM micrographs of the microstructure in the initial state and after the t!m transformation treatment are represented in Fig. 4. They are in a good qualitative agreement with the XRD results. In the initial state, the material exhibits a single phase tetragonal microstructure with a grain boundary phase located in the triple points. No microcracks were detected in this condition. After the t!m transition, monoclinic as well as tetragonal grains are observed. Furthermore, microcracks have developed at the grain boundaries due to the volume increase during the t!m phase transition. 4.1. Electrical properties At room temperature only the capacitive part of the impedance can be measured, from which the effective permittivity "eff of the different materials was derived. "eff Of the tetragonal phase ranges from 38 to 39 and is essentially independent from the grain size, as can be seen from the materials annealed up to 64 h in Table 1. The permittivity of the material annealed for 256 h is at the same level, in spite of its high near surface monoclinic phase content. This indicates a very thin tetragonal/monoclinic surface layer of this material in the initial state, induced by cooling from the annealing temperature of 1400 C to room temperature. There is a reproducible, drastic decrease in the permittivity of all materials after the cooling induced t!m transformation as shown in Table 1. Differences of 30% for specimens with a grain size of 1.2 mm and of 36% for the material with the largest grain size of 2.7 mm have been measured. This shows that the cooling induced phase transformation occurs in the bulk of the materials and is not limited to near surface regions. The effective permittivity after transformation decreases monotonously with increasing grain size. This is obviously caused by the higher monoclinic volume fraction in the coarser grained materials. In Fig. 5, the effective permittivity is plotted versus the tetragonal phase content measured by XRD. When the data are fitted by a linear regression, the extrapolation to 0% tetragonal phase yields an effective permittivity of the pure monoclinic material of "m ¼ 22:5. Under physical aspects, a Table 1 Microstructure and electrical properties of 9Ce–TZP before and after cooling induced t!m transformation Annealing time (h) 0 16 64 256 Mean grain size (mm) 1.2 1.6 1.8 2.7 Initial state XRD vol. fraction m (%) 0 0 0 0/30a Eff. permittivity 38.1 38.9 38.6 38.4 After t!m transition XRD vol. fraction m (%) 69 78 83 89 Eff. permittivity 26.7 26.0 25.5 24.4 a Near surface region. Fig. 3. Temperatures of the t!m transformation and m!t retransformation depending on the mean grain size. 340 A. Tiefenbach et al. / Journal of the European Ceramic Society 22 (2002) 337–345
4. Tiefenbach et al. Journal of the European Ceramic Society 22(2002)337-345 B Fig. 5. Effective permittivity in dependence of the tetragonal phase 200nm (a) expected. The re-transformation m-t is known to take place over an extended temperature interval and causes raction of about 1%. ho part of the transformation reaction should occur close The volume decrease during transformation can be easily measured using dilatometry. Fig. 6 shows the dilat- ometer curves of the m-t retransformation for the materials with the different grain sizes. At 250C the retransformation process starts, first for the material with the smallest grains. The onset temperature As shifts to higher temperatures when the grain size increases. The Austenite temperature Ab increases from 29 to 342 oC increasing the grain size from 1.2 to 2.7 um(Fig 3). At B was confirmed by XRD measurements carried out after 200nm the dilatometer experiments The dilatometer curves show some differences in the relative length change during retransformation. For the 9Ce-TZP materials with a grain size <1. 8 um, the Fg.4.(a) rograph of tetragonal zirconia(A) tetragonal relative length change at the retransformation tempera grain, (B) dary. (C) grain boundary phase in a triple point; ture increases with the grain size. This can be explained b)TEM of transformed zirconia with, (A)monoclinic by the increasing volume fraction of monoclinic phase grain.(B) grain,(C)microcracks at the grain boundary prior to the retransformation treatment. The measured nduced by transformation contraction for the material with a grain size of 2.7 um however is much smaller than the contraction of the linear relation represents a parallel connection of a tet- other annealed samples, despite of its higher monoclinic ragonal and a monoclinic layer, that means a parallel phase fraction. The reason for this smaller contraction connection of two capacitors. The dashed and dotted are probably crack face displacements, which hinder a urve in Fig. 5 were obtained using the Maxwell-Wagner complete crack closure during the m-t transformation relation as well as the series layer model, a serial connec- tion of the two layers. The applicability of these models 5. Electrical properties will be discussed in Section 6 Besides dilatometry, impedance spectroscopy was applied to study the retransformation process. The 5. The m-t retransformation electrical measurements were performed at temperatures up to 350oC. In a first step, the materials with the dif- Heating the transformed specimens beyond the Aus- ferent grain sizes were investigated in their initial (tet- enite temperature Ab, a m-t retransformation is ragonal) state. In the second step, the specimens after
linear relation represents a parallel connection of a tetragonal and a monoclinic layer, that means a parallel connection of two capacitors. The dashed and dotted curve in Fig. 5 were obtained using the Maxwell–Wagner relation as well as the series layer model, a serial connection of the two layers. The applicability of these models will be discussed in Section 6. 5. The m!t retransformation Heating the transformed specimens beyond the Austenite temperature Ab,am!t retransformation is expected. The re-transformation m!t is known to take place over an extended temperature interval and causes a linear contraction of about 1%. However, the main part of the transformation reaction should occur close to Ab. The volume decrease during transformation can be easily measured using dilatometry. Fig. 6 shows the dilatometer curves of the m!t retransformation for the materials with the different grain sizes. At 250 C the retransformation process starts, first for the material with the smallest grains. The onset temperature As shifts to higher temperatures when the grain size increases. The Austenite temperature Ab increases from 296 to 342 C increasing the grain size from 1.2 to 2.7 mm (Fig. 3). At a temperature of 350 C, the retransformation process is completed for all investigated zirconia materials. This was confirmed by XRD measurements carried out after the dilatometer experiments. The dilatometer curves show some differences in the relative length change during retransformation. For the 9Ce–TZP materials with a grain size 41.8 mm, the relative length change at the retransformation temperature increases with the grain size. This can be explained by the increasing volume fraction of monoclinic phase prior to the retransformation treatment. The measured contraction for the material with a grain size of 2.7 mm however is much smaller than the contraction of the other annealed samples, despite of its higher monoclinic phase fraction. The reason for this smaller contraction are probably crack face displacements, which hinder a complete crack closure during the m!t transformation. 5.1. Electrical properties Besides dilatometry, impedance spectroscopy was applied to study the retransformation process. The electrical measurements were performed at temperatures up to 350 C. In a first step, the materials with the different grain sizes were investigated in their initial (tetragonal) state. In the second step, the specimens after Fig. 5. Effective permittivity in dependence of the tetragonal phase content. Fig. 4. (a) TEM micrograph of tetragonal zirconia (A) tetragonal grain, (B) grain boundary, (C) grain boundary phase in a triple point; (b) TEM micrograph of transformed zirconia with, (A) monoclinic grain, (B) tetragonal grain, (C) microcracks at the grain boundary induced by transformation. A. Tiefenbach et al. / Journal of the European Ceramic Society 22 (2002) 337–345 341
4. Tiefenbach et al. Journal of the European Ceramic Society 22(2002)337-345 10.5 0.000 → Initial Tetragona -0.004 口-1.2pm 1.8pm V-27μm 7 250 85,23 log(f /Hz) Fig. 7. Bode characteristics of 9Ce-TZP before and after Fig. 6. Relative length change AlLo during heating of t-m trans- formation at 200 and 250C for a grain size of 1. 2 um. formed 9Ce-TZP 3.4 the cooling induced t->m transformation have been 3.2 initial state 3.0 Fig. 7 compares the impedance spectra of specimens reverse in the initial state and after t-m transformation at 200 transformation and 250oC in form of Bode plots. For the variations 26 annealed up to 256 h, one obtains qualitatively similar t->m- converted In the initial state one recognizes a capacitive transi- ion region at low frequencies and an ohmic region over 2.0 the mid-frequency range as well as a high-frequency 200225250275300325350 capacitive field. As a consequence of the t-m transfor- mation, the electrical properties change clearly. At high Fig. 8. Normalized capacitances of the materials in their initial(tet frequencies, there is still a purely capacitive behaviour ragonal) state and during the m-t retransformation after cooling Compared to the initial state, the magnitude of the induced t→ m transition impedance is by far higher. Therefore, a reduced capacity determines the electrical behaviour. At lower fre- beyond 225C. This leads to an increase of the capaci quencies, a superposition of ohmic and capacitive fields tance. The largest capacitance gradients, which indicate can be observed. The characteristics have higher magni- the onset temperature of the reverse m-t transforma- tudes compared to the initial state. At low frequencies, tion, shift to higher temperatures with increasing grain one finds a dominating capacitive transition region. size. With continuing temperature increase, the normal Furthermore, at 250C and frequencies between 10 and ized capacitance approaches asymptotically the corre- 1000 Hz, a field with a predominantly ohmic character sponding value of the pure tetragonal materials. This is observed. Decreasing the temperature, this field shifts indicates the completion of the retransformation pro to lower frequencies. From these impedance spectra the cess at temperatures, which are in good agreement with normalized capacitance c and the normalized con- the dilatometer experiments. ductance o were derived by a single R-C element simu The normalized conductance derived from the r-c lation according to Section 2. simulation element is plotted in Fig. 9 versus the reci In Fig. 8 the normalized capacitance is plotted in procal temperature. The electrical conductance of the lependence of the measurement temperature. Below monoclinic and tetragonal phase differs significantly. In 225C, the values of c for t-m transformed materials the Arrhenius plot the curves are characterized by three are clearly lower than in the corresponding, purely tet- different intercepts. A first linear section at low tem ragonal initial states. Here, the lower permittivity of the peratures, where the material is still predominantly predominantly monoclinic 9Ce-TZP materials takes monoclinic, is followed by a transition region where the effect. The value c decreases with increasing the volume m-t phase transformation takes place. With increasing fraction of the monoclinic phase or grain size, respec- grain size of the specimens, this transition region shifts tively. This correlates well with the results from the to higher temperatures. Beyond 300C, all character permittivity measurements at room temperature (see istics end in a second linear dependence, where finally Table 1). With increasing temperature, the values of c all grains are tetragonal again. The grain size hardly then slowly increase for all materials. Depending on the affects conductivity outside of the transition regions. If grain size, the reverse m-t transformation start one extrapolates the conductance of the tetragonal
the cooling induced t!m transformation have been tested. Fig. 7 compares the impedance spectra of specimens in the initial state and after t!m transformation at 200 and 250 C in form of Bode plots. For the variations annealed up to 256 h, one obtains qualitatively similar spectra. In the initial state one recognizes a capacitive transition region at low frequencies and an ohmic region over the mid-frequency range as well as a high-frequency capacitive field. As a consequence of the t!m transformation, the electrical properties change clearly. At high frequencies, there is still a purely capacitive behaviour. Compared to the initial state, the magnitude of the impedance is by far higher. Therefore, a reduced capacity determines the electrical behaviour. At lower frequencies, a superposition of ohmic and capacitive fields can be observed. The characteristics have higher magnitudes compared to the initial state. At low frequencies, one finds a dominating capacitive transition region. Furthermore, at 250 C and frequencies between 10 and 1000 Hz, a field with a predominantly ohmic character is observed. Decreasing the temperature, this field shifts to lower frequencies. From these impedance spectra the normalized capacitance c and the normalized conductance were derived by a single R–C element simulation according to Section 2. In Fig. 8 the normalized capacitance is plotted in dependence of the measurement temperature. Below 225 C, the values of c for t!m transformed materials are clearly lower than in the corresponding, purely tetragonal initial states. Here, the lower permittivity of the predominantly monoclinic 9Ce–TZP materials takes effect. The value c decreases with increasing the volume fraction of the monoclinic phase or grain size, respectively. This correlates well with the results from the permittivity measurements at room temperature (see Table 1). With increasing temperature, the values of c then slowly increase for all materials. Depending on the grain size, the reverse m!t transformation starts beyond 225 C. This leads to an increase of the capacitance. The largest capacitance gradients, which indicate the onset temperature of the reverse m!t transformation, shift to higher temperatures with increasing grain size. With continuing temperature increase, the normalized capacitance approaches asymptotically the corresponding value of the pure tetragonal materials. This indicates the completion of the retransformation process at temperatures, which are in good agreement with the dilatometer experiments. The normalized conductance derived from the R–C simulation element is plotted in Fig. 9 versus the reciprocal temperature. The electrical conductance of the monoclinic and tetragonal phase differs significantly. In the Arrhenius plot the curves are characterized by three different intercepts. A first linear section at low temperatures, where the material is still predominantly monoclinic, is followed by a transition region where the m!t phase transformation takes place. With increasing grain size of the specimens, this transition region shifts to higher temperatures. Beyond 300 C, all characteristics end in a second linear dependence, where finally all grains are tetragonal again. The grain size hardly affects conductivity outside of the transition regions. If one extrapolates the conductance of the tetragonal Fig. 8. Normalized capacitances of the materials in their initial (tetragonal) state and during the m!t retransformation after cooling induced t!m transition. Fig. 6. Relative length change L/L0 during heating of t!m transformed 9Ce–TZP. Fig. 7. Bode characteristics of 9Ce–TZP before and after t!m transformation at 200 and 250 C for a grain size of 1.2 mm. 342 A. Tiefenbach et al. / Journal of the European Ceramic Society 22 (2002) 337–345
T/°C This effect could be used as a very simple non destruc 250 tive method to detect phase transformations in TZP tetragonal materials, which seems not to be recognized at present /4H=1.06e6 Due to its significance, even quantitative phase analysis seems to be possible, as can be seen from Fig. 5. A linear △Hmn=064eV relationship between Eeff and the volume content of tet- ragonal phase is given by the parallel layer model[Eq (6)where both, the monoclinic and the tetragonal layer, t->m converted connect the two electrodes -6 fer =Em+x(E-Em) Fig 9. Arrhenius plots of the normalized conductances of tetragonal This linear relation is, however, not exactly justified grains and during the reverse m-t transformation of the t-m trans. but an approximation of a linear relationship to 0% formed materials depending on the reverse temperature for different tetragonal phase should be adequate for the estimatio of E phase to lower temperatures, it is about 1.8 times higher A physically better justified correlation between Eeff than the measured conductance of the monoclinic and the volume content of tetragonal phase x t can be grains. Also, the activation energy with 1.06 eV is sig- derived from the Maxwell-Wagner model. Assuming a nificantly higher than that of the monoclinic phase with dispersion of spheres of tetragonal grains in a con 0.64eV tinuous medium of the monoclinic phase the following expression can be given a 6. Discussion Sef -m Et+2Em -2x,(Em -E1) With respect to the grain size dependence of the transformation temperatures Mb and Ab, the results are The third model. which can be used for the estimatio in qualitative agreement with literature. The transfor- of the tetragonal volume content, is the series layer mation temperatures of the investigated 9 mol% Ce- model, based on the relation: 2I TZP are, however, much more sensitive to the grain size as it is the case for the 12 mol% TZP measured by Becher Eefr=Em Et-xEt-Em) (8) et al. For the former Mb increases from -60 to -15oC for grain sizes of 1.2 and 2.7 um, respectively. For the latter, the interval of grain size ranges from about 2 to On the basis of a permittivity of &t-38 for the pure 8 um for a corresponding temperature interval. This has tetragonal and a permittivity of Em=22.5 for the pure to be expected as a consequence of the different trans- monoclinic material, the curves in Fig. 5 have been formation entropy changes in the differently stabilized derived. It can be mentioned that the Maxwell-Wagner materials. The increasing Mb temperatures indicate an model and the parallel layer model correspond better to increasing transformation tendency, which also explains the measured values than the series layer model the higher monoclinic content with increasing grain size At enhanced temperatures, impedance spectroscopy Impedance spectroscopy at room temperature indi- provides two characteristic properties of the material cates a drastic decrease of permittivity during the trans- the normalized capacitance c and the normalized con- formation of the tetragonal to the monoclinic phase in 9 ductance o. Both characteristics change significantly mol% Ce-TZP from about 38 to 22.5. This is mainly with the phase composition. The dilatometer experi caused by the change of crystal structure. Since all oxide ments and impedance spectroscopy agree well with ceramics are ionic crystals, 8 the differences in the lattice respect to the transformation behaviour, characterized parameters and the different relocatability of the ions by the Austenite temperature Ab. From the value of take effect to the ionic polarization. capacity determined experimentally from the impedance This is the essential contribution to the total polariza measurements, even quantitative relationships could be tion and finally it determines the effective permittivity derived for the volume fractions of the monoclinic and of the material. The magnitude of this contribution is tetragonal phase during the entire transformation pro- predominantly determined by the oscillator thickness of cess, e.g. by application of Eqs. (6)8). The con- the ionic bonds. 20 A smaller influence on the permittiv- ductance characteristics show different activation ity decrease might also result from textures as well as energies for the monoclinic and the tetragonal phase from the air volume of opened cracks induced by n the temperature range 200-300C only volume volume extension after t-m transformation ffects are detectable That means the permittivity and
phase to lower temperatures, it is about 1.8 times higher than the measured conductance of the monoclinic grains. Also, the activation energy with 1.06 eV is significantly higher than that of the monoclinic phase with 0.64 eV. 6. Discussion With respect to the grain size dependence of the transformation temperatures Mb and Ab, the results are in qualitative agreement with literature. The transformation temperatures of the investigated 9 mol% Ce– TZP are, however, much more sensitive to the grain size as it is the case for the 12 mol% TZP measured by Becher et al.11 For the former, Mb increases from 60 to 15 C for grain sizes of 1.2 and 2.7 mm, respectively. For the latter, the interval of grain size ranges from about 2 to 8 mm for a corresponding temperature interval. This has to be expected as a consequence of the different transformation entropy changes in the differently stabilized materials. The increasing Mb temperatures indicate an increasing transformation tendency, which also explains the higher monoclinic content with increasing grain size. Impedance spectroscopy at room temperature indicates a drastic decrease of permittivity during the transformation of the tetragonal to the monoclinic phase in 9 mol% Ce–TZP from about 38 to 22.5. This is mainly caused by the change of crystal structure. Since all oxide ceramics are ionic crystals,18 the differences in the lattice parameters and the different relocatability of the ions against each other take effect to the ionic polarization. This is the essential contribution to the total polarization19 and finally it determines the effective permittivity of the material. The magnitude of this contribution is predominantly determined by the oscillator thickness of the ionic bonds.20 A smaller influence on the permittivity decrease might also result from textures as well as from the air volume of opened cracks induced by volume extension after t!m transformation. This effect could be used as a very simple non destructive method to detect phase transformations in TZP materials, which seems not to be recognized at present. Due to its significance, even quantitative phase analysis seems to be possible, as can be seen from Fig. 5. A linear relationship between "eff and the volume content of tetragonal phase is given by the parallel layer model21 [Eq. (6)] where both, the monoclinic and the tetragonal layer, connect the two electrodes. "eff ¼ "m þ xtðÞ ð "t "m 6Þ This linear relation is, however, not exactly justified, but an approximation of a linear relationship to 0% tetragonal phase should be adequate for the estimation of "m. A physically better justified correlation between "eff and the volume content of tetragonal phase xt can be derived from the Maxwell–Wagner model. Assuming a dispersion of spheres of tetragonal grains in a continuous medium of the monoclinic phase the following expression can be given as:22,23 "eff ¼ "m "t þ 2"m 2xtð Þ "m "t "t þ 2"m þ xtð Þ "m "t ð7Þ The third model, which can be used for the estimation of the tetragonal volume content, is the series layer model, based on the relation:21 "eff ¼ "m "m "t "t xtð Þ "t "m ð8Þ On the basis of a permittivity of "t=38 for the pure tetragonal and a permittivity of "m=22.5 for the pure monoclinic material, the curves in Fig. 5 have been derived. It can be mentioned that the Maxwell–Wagner model and the parallel layer model correspond better to the measured values than the series layer model. At enhanced temperatures, impedance spectroscopy provides two characteristic properties of the material: the normalized capacitance c and the normalized conductance . Both characteristics change significantly with the phase composition. The dilatometer experiments and impedance spectroscopy agree well with respect to the transformation behaviour, characterized by the Austenite temperature Ab. From the value of capacity determined experimentally from the impedance measurements, even quantitative relationships could be derived for the volume fractions of the monoclinic and tetragonal phase during the entire transformation process, e.g. by application of Eqs. (6)–(8). The conductance characteristics show different activation energies for the monoclinic and the tetragonal phase. In the temperature range 200–300 C only volume effects are detectable. That means the permittivity and Fig. 9. Arrhenius plots of the normalized conductances of tetragonal grains and during the reverse m!t transformation of the t!m transformed materials depending on the reverse temperature for different grain sizes. A. Tiefenbach et al. / Journal of the European Ceramic Society 22 (2002) 337–345 343
ach et al. Journal of ionic conductivity of the grains predominantly influence 2. Hannik, R, Kelly, P. and Muddle C. Transformation the impedance spectra. 24 Cracks as well as grain bound- toughening in zirconia-containing ceramics. J. Am. Cera. Soc. aries are not detectable up to 300C. However, above 2000,83(3),461-487 00 oC two ohmic and two capacitive ranges are 3. Chen, I. W, Model of transformation toughening in brittle observed in the impedance spectra. For a microstructural materials. J. A. Ceram. Soc., 1991. 74(10). 2564-2572. 4. Tiefenbach. A. Elektrische Charakterisierung mechanischer interpretation of this behaviour the brick layer model, a Schadigungen in ZrO -Keramik. VDI-Fortschrittsberichte, VDI- network with 2 R-C elements. can be used. 15,25 In the Verlag. Dusseldorf. 1999. model the first ohmic range at low frequencies and the 5. Bauerle, J.B., Study of solid electrolyte polarization by a com- followed capacitive transition region can be assigned to the behaviour of the grain boundaries, whereas the high 6. Kleitz, M, Bernard, H, Fernandez, E and Schouler, E, Impe- frequency range can be associated to the grains. In fur dance spectroscopy and electrical resistance measurements on ther work it has been demonstrated that cracks influ stabilized zirconia In adv in Ceramics 3. Science and Technolog ence the low frequency range of these high temperature of Zirconia. Am. Cera. Soc., 1981, pp. 310-336 spectra. 26 7. Muccillo, E. N and Kleitz, M, Impedance spectroscopy of Mg artially-stabilized zirconia and cubic phase decomposition. J. Er. Ceran.Soc,1996,16.453-465 8. Magistris, A. and Chiodelli, G, The dielectric responce of zirco- 7. Conclusions la-based materials. Adv. in Ceramics 24B. In science and Tech- ology of Zirconia ll1. Am. Ceram Soc., 1988, pp. 895-900 Comparing the electrical results with dilatometer and 9. Dessmond, L and Kleitz, M. Effects of mechanical damage on e electrical properties of zirconia ceramics. J. Eur. Ceram. Soc. XRD measurements, the following statements can be derived 10. Reyes-Morel, P. E, Cherng. J - S and Chen, L -W, Transforma- tion plasticity of CeOxstabilized tetragonal zirconia polycrystals 1. The temperature ranges of the m-t retransfor mation of 9Ce-TZP materials measured by dilato- Il, pseudoelasticity and shape memory effect. J. Am. Ceram c.,1988,71(8),648 metry correlate well with results of impedance Il. Becher, P. F. and Swain, M.V. Grain-size-dependent transfor spectroscopy. Both test methods show the same mation behavior in polycrystalline tetragonal zirconia. J.AIm. increase of the transformation temperature Ab Ceran.Soc.,1992,753),495502 with increasing grain size of the 9 mol% Ce-TZP K. B. Bleier Warwick, W.H., Influence of ZrO2 grain size and content on the 2. The evaluation of the impedance spectra shows, System. J. Am. Ceram Soc., 1993, 76(3), 657-663 that the permittivity and the electric conductivity of 13. Schmauder, S. and Schubert H, Significance of internal stresses the monoclinic phase is significantly lower com- pared to the tetragonal phase. From permittivity polycrystals during degradation. J. Am. Ceram. Soc., 1986, 69(7 measurements of t-m transformed material, the 14. Toraya, H, Yoshimura, M. and Somiya, S, Calibration curve tetragonal as well as the corresponding monoclinic for quantitative analysis of the monoclinic-tetragonal ZrO2 sys- phase content can be estimated. If the grain size tem by X-ray diffraction. J. Am. Ceram. Soc., 1984, 67, 183- ncreases, the monoclinic phase fraction after the 15. Beekmans, N. M. and Heyne, L, Correlation between impe. cooling induced t-m transition increases. These results agree quantitatively well with XRD mea Electrochim. Acta. 1976. 21.303-310 surements 16. Brook, R. J, Controlled grain growth. In Treatise on Materials Science and Technology. Vol. 9. ed. F. F.Y. Wang. Academic Thus, it can be stated, that impedance spectroscopy is Press, New York, 1976, pp. 331-364 a useful tool for the investigation of the transformation 17. Theunis process in TZP ceramics ultra)fine-grained tetragonal zirconia ceramics. PhD thesis, Ur ersity Twente, Netherlands. Acknowledgements miken. In Werkstoffe und Bauelemente der elektrotechnik, band Keramik. Teubner- Verlag, Stuttgart, 1994. This work was funded by the Deutsche For- 19. Salmang. H. and Scholze, H, Keramik. Teil 1, 6. Auflage Springer-Verlag, Berlin. 1982. schungsgemeinschaft (DFG) under contract Nos. Ho 20. Wersing, W, High frequency ceramic dielectrics and their appli- 693/1 I and ob104/4 Elsevier Applied Science, 1991. 67-119. 21. MacDonald, J.R., Impedance Spectroscopy. J. Wiley Sons References 22. Maxwell, J. C, Electricity and Magnetism, voL. 1. Clarendon 1. Sun, Q, Zhao, Z, Chen, X, Xu. X. and Dai, F. Press. London. 1892. d localised transformation 23. Wagner, K. W, Explanation of the dielectric fatigue phenom- plastic zones in tetragonal polycrystalline ceramics. J. enon on the basis of Maxwells concept. Archiv fuir Elek Am. Ceran.Soc.,1994,77(5).1352-1356 trotechnik, Springer-Verlag, Berlin, 1914
ionic conductivity of the grains predominantly influence the impedance spectra.24 Cracks as well as grain boundaries are not detectable up to 300 C. However, above 300 C two ohmic and two capacitive ranges are observed in the impedance spectra. For a microstructural interpretation of this behaviour the brick layer model, a network with 2 R–C elements, can be used.15,25 In the model the first ohmic range at low frequencies and the followed capacitive transition region can be assigned to the behaviour of the grain boundaries, whereas the high frequency range can be associated to the grains. In further work it has been demonstrated that cracks influence the low frequency range of these high temperature spectra.26 7. Conclusions Comparing the electrical results with dilatometer and XRD measurements, the following statements can be derived: 1. The temperature ranges of the m!t retransformation of 9Ce–TZP materials measured by dilatometry correlate well with results of impedance spectroscopy. Both test methods show the same increase of the transformation temperature Ab with increasing grain size of the 9 mol% Ce–TZP samples. 2. The evaluation of the impedance spectra shows, that the permittivity and the electric conductivity of the monoclinic phase is significantly lower compared to the tetragonal phase. From permittivity measurements of t!m transformed material, the tetragonal as well as the corresponding monoclinic phase content can be estimated. If the grain size increases, the monoclinic phase fraction after the cooling induced t!m transition increases. These results agree quantitatively well with XRD measurements. Thus, it can be stated, that impedance spectroscopy is a useful tool for the investigation of the transformation process in TZP ceramics. Acknowledgements This work was funded by the Deutsche Forschungsgemeinschaft (DFG) under contract Nos. Ho 693/11 and Ob 104/4. References 1. Sun, Q., Zhao, Z., Chen, W., Qing, X., Xu, X. and Dai, F., Experimental study of stress-induced localised transformation plastic zones in tetragonal zirconia polycrystalline ceramics. J. Am. Ceram. Soc., 1994, 77(5), 1352–1356 . 2. Hannik, R., Kelly, P. and Muddle, B. C., Transformation toughening in zirconia-containing ceramics. J. Am. Ceram. Soc., 2000, 83(3), 461–487. 3. Chen, I. W., Model of transformation toughening in brittle materials. J. Am. Ceram. Soc., 1991, 74(10), 2564–2572. 4. Tiefenbach, A., Elektrische Charakterisierung mechanischer Scha¨digungen in ZrO2-Keramik. VDI-Fortschrittsberichte, VDIVerlag, Du¨sseldorf, 1999. 5. Bauerle, J. B., Study of solid electrolyte polarization by a complex admittance method. J. Phys. Chem. Solid, 1969, 2657– 2670. 6. Kleitz, M., Bernard, H., Fernandez, E. and Schouler, E., Impedance spectroscopy and electrical resistance measurements on stabilized zirconia. In Adv. in Ceramics 3. Science and Technology of Zirconia. Am. Ceram. Soc., 1981, pp. 310–336. 7. Muccillo, E. N. and Kleitz, M., Impedance spectroscopy of Mgpartially-stabilized zirconia and cubic phase decomposition. J. Eur. Ceram. Soc., 1996, 16, 453–465. 8. Magistris, A. and Chiodelli, G., The dielectric responce of zirconia-based materials. Adv. in Ceramics 24B. In Science and Technology of Zirconia III. Am. Ceram. Soc., 1988, pp. 895–900. 9. Dessmond, L. and Kleitz, M., Effects of mechanical damage on the electrical properties of zirconia ceramics. J. Eur. Ceram. Soc., 1992, 9, 35–39. 10. Reyes-Morel, P. E., Cherng, J.-S. and Chen, I.-W., Transformation plasticity of CeO2-stabilized tetragonal zirconia polycrystals: II, plseudoelasticity and shape memory effect. J. Am. Ceram. Soc., 1988, 71(8), 648–657. 11. Becher, P. F. and Swain, M. V., Grain-size-dependent transformation behavior in polycrystalline tetragonal zirconia. J. Am. Ceram. Soc., 1992, 75(3), 495–502. 12. Becher, P. F., Alexander, K. B., Bleier, A., Waters, S. B. and Warwick, W. H., Influence of ZrO2 grain size and content on the transformation response in the Al2O3–ZrO2 (12 mol% CeO2) System. J. Am. Ceram. Soc., 1993, 76(3), 657–663. 13. Schmauder, S. and Schubert, H., Significance of internal stresses for the martensitic transformation in yttria-stabilized zirconia polycrystals during degradation. J. Am. Ceram. Soc., 1986, 69(7), 534–540. 14. Toraya, H., Yoshimura, M. and Somiya, S., Calibration curve for quantitative analysis of the monoclinic-tetragonal ZrO2 system by X-ray diffraction. J. Am. Ceram. Soc., 1984, 67, 183– 184. 15. Beekmans, N. M. and Heyne, L., Correlation between impedance, microstructure and composition of calcia-stabilized zirconia. Electrochim. Acta, 1976, 21, 303–310. 16. Brook, R. J., Controlled grain growth. In Treatise on Materials Science and Technology. Vol. 9, ed. F. F. Y. Wang. Academic Press, New York, 1976, pp. 331–364. 17. Theunissen, G., Microstructure, fracture toughness and strength of (ultra)fine-grained tetragonal zirconia ceramics. PhD thesis, University Twente, Netherlands. 18. Waser, R., Hennings, D. and Baiatu, T., Die elektrischen Keramiken. In Werkstoffe und Bauelemente der Elektrotechnik, Band 5: Keramik. Teubner-Verlag, Stuttgart, 1994. 19. Salmang, H. and Scholze, H., Keramik. Teil 1, 6. Auflage, Springer-Verlag, Berlin, 1982. 20. Wersing, W., High frequency ceramic dielectrics and their application for microwave components. In Electronic Ceramics. Elsevier Applied Science, 1991, 67–119. 21. MacDonald, J. R., Impedance Spectroscopy. J. Wiley & Sons, New York, 1987. 22. Maxwell, J. C., Electricity and Magnetism, vol. 1. Clarendon Press, London, 1892. 23. Wagner, K. W., Explanation of the dielectric fatigue phenomenon on the basis of Maxwell’s concept. Archiv fu¨r Elektrotechnik, Springer-Verlag, Berlin, 1914. 344 A. Tiefenbach et al. / Journal of the European Ceramic Society 22 (2002) 337–345
4. Tiefenbach et al. Journal of the European Ceramic Society 22(2002)337-345 345 4. Barhmi. A, Schouler. E. Hammou, A. and Kleitz, M. Elec- ionic conductivity in ceramic Gd, Zr1-Oz-x/2) solid solutions. trical properties of tetragonal partially stabilized zirconia. In hys.Sat.Sol.(a),1981,63.229-24 Advances in Ceramics, Vol. 24B. Am. Ceram. Soc.. 1988. pp 26. Tiefenbach. A. and Hoffmann. B. Influence of a crack on the 885-894 electrical impedance of polycrystalline ceramics. J. Eur. Ceram 5. van Dijk, T. and Burggraaf, A. J, Grain boundary effects on Soc.2000,20,2079-2094
24. Barhmi, A., Schouler, E., Hammou, A. and Kleitz, M., Electrical properties of tetragonal partially stabilized zirconia. In Advances in Ceramics, Vol. 24B. Am. Ceram. Soc., 1988, pp. 885–894. 25. van Dijk, T. and Burggraaf, A. J., Grain boundary effects on ionic conductivity in ceramic GdxZr1xO2(x/2) solid solutions. Phys. Stat. Sol. (a), 1981, 63, 229–240. 26. Tiefenbach, A. and Hoffmann, B., Influence of a crack on the electrical impedance of polycrystalline ceramics. J. Eur. Ceram. Soc., 2000, 20, 2079–2094. A. Tiefenbach et al. / Journal of the European Ceramic Society 22 (2002) 337–345 345