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Grain-boundary cation diffusion in ceria tetragonal zirconia determined by constant-strain-rate deformation tests
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Journal of the European Ceramic Society 34 (2014) 4469–4472
Short Communication
Grain-boundary cation diffusion in ceria tetragonal zirconia determined by constant-strain-rate deformation tests Santiago de Bernardi-Martín, Bibi Malmal Moshtaghioun, Diego Gómez García ∗ , Arturo Domínguez-Rodríguez Department of Condensed Matter Physics, University of Sevilla, P.O. Box 1065, 41080 Sevilla, Spain Received 17 April 2014; received in revised form 17 June 2014; accepted 24 June 2014 Available online 16 July 2014
Abstract Ceria tetragonal zirconia polycrystals with a content of 12 mol% ceria (CeTZP) have been tested in compression at constant strain rate between 1150 ◦ C and 1300 ◦ C. An accurate analysis of the stress–strain curves has permitted to determine the value of the grain boundary cation diffusion. The results are compared with those reported in literature for this alloy and yttria tetragonal zirconia polycrystals (YTZP). An isotopic effect is found to correlate both grain boundary diffusion coefficients. © 2014 Elsevier Ltd. All rights reserved. Keywords: Mechanical properties testing; Grain boundary diffusion; Grain growth; Ceria tetragonal zirconia
1. Introduction Zirconia (ZrO2 ) ceramics have received considerable attention in the literature of oxide ceramic materials along the past decades. This has been justified because of the promising mechanical properties, particularly the tetragonal phase, exhibiting a high toughness and strength as a consequence of the martensitic transformation to the monoclinic phase.1 Addition of yttria or ceria is known to increase the stability of the tetragonal ZrO2 phase. The first one gives rise to an alloy commonly called as ‘yttria tetragonal zirconia polycrystals’ or YTZP (Y concentration referred to Y2 O3 and not YO1.5 from now on), whereas the later one is identified as CeTZP. The knowledge of diffusitivies in yttria-zirconia fullstabilized ceramics was the subject of intense research, especially for the oxygen vacancies due to their remarkable ionic conductivity.2 In the case of CeTZP, the oxygen diffusion coefficient was determined by Ando et al.3 Regarding the cationic diffusion, its study became a hot topic after the discovery of the superplastic response at moderate temperatures in YTZP and
∗
Corresponding author. Tel.: +34 954559504; fax: +34 95 4612097. E-mail address: [email protected] (D. Gómez García).
http://dx.doi.org/10.1016/j.jeurceramsoc.2014.06.024 0955-2219/© 2014 Elsevier Ltd. All rights reserved.
the search of an explanation of this phenomenon became a landmark in the science of ceramics. A review of this can be found elsewhere.4 CeTZP has not concentrated so much attention until quite recently. The renewed interest in this system is based upon the following considerations: first, the CeTZP has a considerably wide range of tetragonal phase compared with that of YTZP, making it very attractive for diffusion studies. Second, the isovalency of Zr4+ and Ce4+ avoids the formation of electrical double layer at the grain boundaries, responsible for grain boundary matter transport controlled by extrinsic quantities, such as the number of cation dopants or the degree of segregation to the boundaries. The cation diffusion in CeTZP is thus free from local segregation effects: it solely depends on the properties of the chemical bonding and the crystallographic structure. The analysis of cation grain boundary diffusion in this system was reported by Sakka et al.5 through interdiffusion experiments. The present work was undertaken to determine this quantity by analysis of high-temperature mechanical tests in which grain growth occurs simultaneously together with grain boundary sliding. This approach has several advantages: the main so far is the easiness from a technical point of view and the possibility to be repeated in other ceramic alloys. Furthermore, comparison
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to other reported results achieved by static grain growth or sintering shrinkage are straightforward. 2. Experimental procedure High purity ceria-zirconia powders with 20 nm average grain size were cold-isostatically pressed under 300 MPa. Chemical analysis of the impurity content was carried out prior to any treatment. The analysis shows the presence of 0.002 wt% SiO2 , 0.005 wt% Fe2 O3 and 0.018% Na2 O as main impurities.6 A density of 50% the theoretical one was reached prior to sintering. The concentration of ceria was 12 mol%. The compacted pieces were heated at 1450 ◦ C for 30 min at 600 ◦ C/h in a conventional superkanthal furnace and cooled down to room temperature at about the same time rate. The recovered specimens were checked to be full-dense after density determination through the Archimedes method. The average grain size was obtained by means of scanning electron microscopy (SEM) observations prior to and after deformation and the ulterior analysis of the grain size distributions. Sintered samples were cut into parallelepipeds of dimensions 2.5 × 2.5 × 5.0 mm for uniaxial compression along the longer axis. Several samples were tested at constant strain-rate regime at fixed temperatures: 1150 ◦ C, 1200 ◦ C, 1250 ◦ C and 1300 ◦ C using a conventional Instron 1185 testing machine. Since the plasticity is ruled by diffusion-accommodated grain boundary sliding with the appearance of grain growth,7 data analysis can be performed by means of a classical power-law as shown: ε˙ = A
σn σn = A 2/m d2 d m + kt 0
= A
σn
σn = A 2/m 2/m d0m + kε/˙ε d02 1 + k(ε/˙εd0m )
(1)
where A is an empirical constant at constant temperature, σ the flow stress, ε the strain, ε˙ the strain rate, d0 the grain size at the onset of the compression test and k the kinetic constant of the conventional grain growth law: d m = d0m + kt, t being the time and d0 the grain size at initial time t = 0. The stress exponent n was calculated by means of strain rate jumps at constant temperature. A typical constant-strain-rate test at 1150 ◦ C is displayed in Fig. 1. The exponent “m” accounts for the grain growth law applicable to this case. Such exponent was determined by a non-linear fitting of the plastic region of the stress–strain curves to the following law (2a) derived from Eqs. (2b) and (1): log σ = a + b log(1 + cε)
2 kε log 1 + m nm ε˙ d0 2 kε =a+ log 1 + m ε˙ d0 nm
1 log σ = log n
ε˙ d02 A
(2a)
+
(2b)
where a, b, c are constants for a given stress–strain curve at constant strain rate and temperature. The accuracy and stability
Fig. 1. Stress–strain curve at 1150 ◦ C of CeTZP polycrystals. The strain rate was 10−5 s−1 and it was increased to 2 × 10−5 s−1 for stress exponent determination. The experimental data were fitted to Eq. (1) provided in the text.
of the fitting was assessed by the least-square method. As expected, the quantities b, c can be fitted with an error lower than 2%. On the contrary ‘a’ cannot be fitted unless errors of 10–13% are accepted. This is the consequence of the inaccuracy to choice the onset of the plastic regime, a common fact in all tests of plasticity. Fortunately, the quantity ‘a’ is not required at all for diffusion coefficient calculation. 3. Results and discussion The stress exponent was found to be n = 1.3 ± 0.2, in full agreement with the outputs reported by de Bernardi et al.7 after creep tests at the same temperature. The exponent m could be fitted to m = 2 or m = 3, both fittings being equally acceptable (r = 0.98 versus r = 0.96). The first one, a slightly better one, was chosen for calculations. A similar uncertainty was reported by Chaim in static grain growth experiments in YTZP8 and by Kumagai in electric current-activated assisted sintering tests.9 Both the as-received and post-mortem specimens were characterized through conventional scanning electron microscopy (SEM), in order to determine the grain size distribution prior to and after deformation. Grain boundaries were optically resolved by SEM after a rapid heat treatment of the previously polished surfaces. Fig. 2a and b shows the grain microstructure prior to and after constant strain-rate experiments at 1300 ◦ C, respectively. The microstructure in as-received samples was composed of equiaxial grains with an average grain size equal to 1.4 ± 0.6 m. After deformation the grains remained equiaxed; however there was a remarkable grain growth (Fig. 2b): the grain size, defined as the diameter of the equivalent circle of the same area in all cases was found to increase up to a factor 2 approximately: up to 2.6 ± 0.7 m when the test is performed at 1300 ◦ C at 10−5 s−1 and the final strain is 40%. The normalized grain distribution fits to a modified Gumbel function, in agreement with the theoretical steady-state grain size distribution of a collective of grain boundaries of equal mobilities under stress.10 The values of the stress exponent, together with the invariance of the normalized grain size distribution, are consistent with the
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Fig. 3. CeTZP diffusion coefficient versus 104 /T obtained from this study. The experimental data are fitted to an Arrhenius law, displayed as a dashed line. The results are plotted together with those reported in literature by Sakka et al. The plots labelled as HT and LT are grain boundary diffusion coefficients reported by Chaim in YTZP after static grain growth experiments. Table 1 Grain boundary diffusion coefficients (m2 s−1 ) versus the inverse of temperature. The activation energy is given in electron volts. Fig. 2. Scanning electron microscopy micrographs of the grain microstructure prior to (a) and after constant-strain-rate test (b).
assumption of high-temperature plastic deformation mechanism controlled by diffusion-accommodated grain boundary sliding. De Bernardi et al.7 proved this statement after modelling hightemperature creep tests. This result validates the use of Eqs. (1), (2a) and (2b) for numerical fitting of the stress–strain curves. From this fitting, the kinetic constant for grain growth (k) can be determined and also the grain boundary diffusion coefficient, being proportional to such constant as described in literature11 : Dgb = kB T
kδgb mγgb d m−2 Ω
(3)
where δgb is the thickness of the grain boundary, taken as 10−9 m,7 Ω is the volume of cerium cations (9.1 × 10−31 m3 ),12 γ gb is the grain boundary energy, equal to 1 J m−2 in zirconia systems8 and kB is the Boltzmann’s constant. Finally, d is the final value of the grain size. As commented previously, m = 2 in our fitting. Fig. 3 displays the results achieved for grain boundary diffusion versus temperature together with the reported results for CeTZP5 and those measured by Chaim8 in YTZP (3 wt% yttria tetragonal zirconia) at temperatures lower than 1400 ◦ C (labelled as LT from now on) and higher than this value (labelled as HT). The numerical values for all reported results and the leastsquared fit to an Arrhenius law of our data are given in Table 1. The comparison of our results with those previously reported in literature allows concluding several remarks: first of all, the accuracy of this method is very reasonable: all data are within less than order of magnitude. Since mechanical tests are
12CeTZP (this work) CeTZP (Sakka et al. [5]) 3 wt%TZP (HT) (Chaim [8]) 3 wt%TZP (LT) (Chaim [8])
Dgb = 2.6 × 101 exp(−4.86/kB T) Dgb = 2.9 × 102 exp(−5.27/kB T) Dgb (YTZP-HT) = 1.2 × 102 exp(−5.00/kB T) Dgb (YTZP-LT) = 1.1 × 10−4 exp(−3.00/kB T)
considerably easier to be performed in conventional mechanical test laboratories, the method is powerful and fast to get insight into the grain-boundary diffusion properties of lowest species in ceramics. Secondly, the activation energy for cation diffusion is found to be 4.89 eV, which is within the experimental uncertainty, very similar to that obtained through interdiffusion measurements by Sakka et al.5 (5.27 eV), although our results shows the diffusion coefficient is within 2–3 times larger than their reported one (Fig. 3). Since the difference is much less than one order of magnitude, the agreement can be considered very reasonable. One very interesting point is the comparison between CeTZP and YTZP grain boundary diffusion coefficients. Chaim8 proved that there are two regimes in the high-temperature dependence of the grain boundary diffusion coefficient in YTZP: at temperatures lower than 1400 ◦ C the activation energy for cation diffusion is 3 eV whereas that quantity rises to 5 eV in the hightemperature regime (temperatures higher than 1400 ◦ C). Both diffusion coefficients have been extrapolated to the temperature range of our results, as displayed in Fig. 3. Chaim8 claims that the origin of these two regimes can be found in the effect of yttrium segregation in excess at the grain boundaries, inducing local phase transformation to the cubic phase at temperatures lower than 1400 ◦ C. This may be due to the fact that local concentration at the grain boundaries can excess the value for coexistence of cubic and tetragonal phase. In the high-temperature regime,
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the yttrium segregation weakens, the local concentration at the boundaries is lower, and it would explain the change in the activation energy and the absolute values of the diffusion coefficient. This explanation makes sense if the local concentration at the boundaries is over 8 mol% and the fact that the activation energy reaches low values can be justified as follows: the presence of yttrium segregation in excess at the grain boundaries is associated to an increase in the oxygen vacancies in the anion sublattice. Given the highly defective crystallographic structure at the grain boundaries it is reasonable to think that energy barrier for atomic migration should reduce. Such tendency has been reported in molecular dynamics simulations.13 However segregation to the grain boundaries is not reported in CeTZP. Even if there were cerium segregation to the boundaries, it would not induce a local increase of oxygen vacancies because zirconium and cerium cations are isovalent. Given that the crystallographic structures of CeTZP and YTZP without segregation (i.e. in the HT regime) are very similar, one simple relation should exist among the grain boundary diffusion coefficients of both species. In fact, a careful numerical analysis of our results and those reported by Chaim for HT grain boundary diffusion allows finding a proportionality among them; i.e. Dgb (CeTZP) ∼ = ␣Dgb (YTZP). The proportionality constant α is approximately 0.8. This quantity is equal to √ MY-Zr /MCe i.e. the square root of the ratio of atomic masses of yttrium-zirconium cations to cerium ones. This result point out that there is just an isotope effect14 in the grain boundary diffusion coefficients in the very high-temperature regime for these two zirconia alloys. According to Schoen,14 such isotope effect is expected if the diffusion takes place by a cation-vacancy exchange in the cation sublattice. Molecular dynamics simulation reported a cation-vacancy exchange as the main mechanism account for cation diffusion of yttrium in the zirconia cation sublattice,13 in full agreement with the result found in this work. Finally, it is important to emphasize that this relationship does not seem to depend on the bulk concentration of the oxides, because the concentration of cations at the boundaries is the saturation one, independent on the bulk concentrations. 4. Conclusions The grain boundary diffusion coefficient in ceria-zirconia tetragonal polycrystals was determined via analysis of hightemperature constant-strain-rate compression tests. The results show that it is numerical identical to the homologous one in yttria-zirconia ceramics except for the mass dependence of the cerium cations; i.e. an isotope effect is reported. This fact has
significant implications on the mechanism for cation diffusion in these ceramics: a cation vacancy exchange is probably the main mechanism for diffusion of these species. Acknowledgements The authors acknowledge the financial support awarded by the Spanish National Authority through the project MAT201238205-C02-01 and from the ‘Junta de Andalucía’ Regional Government through the Project of Excellence P12-FQM-1079. The authors acknowledge Prof. Odriozola Gordon, from University of Seville, for supplying generously the spark plasma sintered specimens used in this study. References 1. Garvie RC, Hannik RHJ, Pascoe RT. Ceramic steel? Nature 1975;258:703–4. 2. Gonzalez-Romero RL, Meléndez JJ, Gómez-García D, Cumbrera FL, Domínguez-Rodríguez A. A molecular dynamics study of grain boundaries in YSZ: structure, energetics and diffusion of oxygen. Solid State Ionics 2012;219:1–10. 3. Ando K, Morita S, Watanabe R. Effects of the grain boundary and its movements on the oxygen self-diffusion in CeO2 –ZrO2 solid solutions. Yogyo Kyokaishi 1986;94:732–6. 4. Domínguez-Rodríguez A, Gómez-García D, Wakai F. High-temperature plasticity in yttria stabilized tetragonal zirconia polycrystals. Int Mater Rev 2013;58:399–417. 5. Sakka Y, Oishi Y, Ando K, Morita S. Cation interdiffusion and phase stability in polycrystalline tetragonal ceria-zirconia-hafnia solid solution. J Am Ceram Soc 1991;74:2610–4. 6. Cruz S, Poyato R, Cumbrera FL, Odriozola JA. Nanostructured spark plasma sintered Ce-TZP ceramics. J Am Ceram Soc 2012;95:901–6. 7. de Bernardi-Martín S, Gómez-García D, Domínguez-Rodríguez A, de Portu G. A first-study of the high-temperature plasticity of ceria-doped zirconia polycrystals. J Eur Ceram Soc 2010;30:3357–62. 8. Chaim R. Activation energy and grain growth in nanocrystalline Y-TZP ceramics. Mater Sci Eng A 2008;486:439–46. 9. Kumagai T. Estimation of stress exponent and activation energy for rapid densification of 8 mol% yttria-stabilized zirconia powder. J Am Ceram Soc 2013;96:852–8. 10. Moshtaghioun BM, Gómez-García D, Cumbrera-Hernández FL, Domínguez-Rodríguez A. A phase-field model of 2D grain size distribution in ceramics. J Eur Ceram Soc 2014;34:2731–6. 11. Yan MF, Cannon RM, Bowen HK. In: Fulrath RM, Pask JA, editors. Ceramic microstructures, vol. 76. Boulder, CO: Westview Press; 1977. p. 276. 12. Thomas JB, Bodnar RJ, Shimizu N, Chesner CA. Melt inclusions in zircon. Rev Miner Geochem 2003;53:63–87. 13. González-Romero RL, Meléndez JJ, Gómez-García D, Cumbrera FL, Domínguez-Rodríguez A, Wakai F. Cation diffusion in yttria-zirconia by molecular dynamics. Solid State Ionics 2011;204:1–6. 14. Schoen AH. Correlation the isotope effect for diffusion in crystalline solids. Phys Rev Lett 1958;1:138–40.
Journal of the European Ceramic Society 34 (2014) 4469–4472
Short Communication
Grain-boundary cation diffusion in ceria tetragonal zirconia determined by constant-strain-rate deformation tests Santiago de Bernardi-Martín, Bibi Malmal Moshtaghioun, Diego Gómez García ∗ , Arturo Domínguez-Rodríguez Department of Condensed Matter Physics, University of Sevilla, P.O. Box 1065, 41080 Sevilla, Spain Received 17 April 2014; received in revised form 17 June 2014; accepted 24 June 2014 Available online 16 July 2014
Abstract Ceria tetragonal zirconia polycrystals with a content of 12 mol% ceria (CeTZP) have been tested in compression at constant strain rate between 1150 ◦ C and 1300 ◦ C. An accurate analysis of the stress–strain curves has permitted to determine the value of the grain boundary cation diffusion. The results are compared with those reported in literature for this alloy and yttria tetragonal zirconia polycrystals (YTZP). An isotopic effect is found to correlate both grain boundary diffusion coefficients. © 2014 Elsevier Ltd. All rights reserved. Keywords: Mechanical properties testing; Grain boundary diffusion; Grain growth; Ceria tetragonal zirconia
1. Introduction Zirconia (ZrO2 ) ceramics have received considerable attention in the literature of oxide ceramic materials along the past decades. This has been justified because of the promising mechanical properties, particularly the tetragonal phase, exhibiting a high toughness and strength as a consequence of the martensitic transformation to the monoclinic phase.1 Addition of yttria or ceria is known to increase the stability of the tetragonal ZrO2 phase. The first one gives rise to an alloy commonly called as ‘yttria tetragonal zirconia polycrystals’ or YTZP (Y concentration referred to Y2 O3 and not YO1.5 from now on), whereas the later one is identified as CeTZP. The knowledge of diffusitivies in yttria-zirconia fullstabilized ceramics was the subject of intense research, especially for the oxygen vacancies due to their remarkable ionic conductivity.2 In the case of CeTZP, the oxygen diffusion coefficient was determined by Ando et al.3 Regarding the cationic diffusion, its study became a hot topic after the discovery of the superplastic response at moderate temperatures in YTZP and
∗
Corresponding author. Tel.: +34 954559504; fax: +34 95 4612097. E-mail address: [email protected] (D. Gómez García).
http://dx.doi.org/10.1016/j.jeurceramsoc.2014.06.024 0955-2219/© 2014 Elsevier Ltd. All rights reserved.
the search of an explanation of this phenomenon became a landmark in the science of ceramics. A review of this can be found elsewhere.4 CeTZP has not concentrated so much attention until quite recently. The renewed interest in this system is based upon the following considerations: first, the CeTZP has a considerably wide range of tetragonal phase compared with that of YTZP, making it very attractive for diffusion studies. Second, the isovalency of Zr4+ and Ce4+ avoids the formation of electrical double layer at the grain boundaries, responsible for grain boundary matter transport controlled by extrinsic quantities, such as the number of cation dopants or the degree of segregation to the boundaries. The cation diffusion in CeTZP is thus free from local segregation effects: it solely depends on the properties of the chemical bonding and the crystallographic structure. The analysis of cation grain boundary diffusion in this system was reported by Sakka et al.5 through interdiffusion experiments. The present work was undertaken to determine this quantity by analysis of high-temperature mechanical tests in which grain growth occurs simultaneously together with grain boundary sliding. This approach has several advantages: the main so far is the easiness from a technical point of view and the possibility to be repeated in other ceramic alloys. Furthermore, comparison
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to other reported results achieved by static grain growth or sintering shrinkage are straightforward. 2. Experimental procedure High purity ceria-zirconia powders with 20 nm average grain size were cold-isostatically pressed under 300 MPa. Chemical analysis of the impurity content was carried out prior to any treatment. The analysis shows the presence of 0.002 wt% SiO2 , 0.005 wt% Fe2 O3 and 0.018% Na2 O as main impurities.6 A density of 50% the theoretical one was reached prior to sintering. The concentration of ceria was 12 mol%. The compacted pieces were heated at 1450 ◦ C for 30 min at 600 ◦ C/h in a conventional superkanthal furnace and cooled down to room temperature at about the same time rate. The recovered specimens were checked to be full-dense after density determination through the Archimedes method. The average grain size was obtained by means of scanning electron microscopy (SEM) observations prior to and after deformation and the ulterior analysis of the grain size distributions. Sintered samples were cut into parallelepipeds of dimensions 2.5 × 2.5 × 5.0 mm for uniaxial compression along the longer axis. Several samples were tested at constant strain-rate regime at fixed temperatures: 1150 ◦ C, 1200 ◦ C, 1250 ◦ C and 1300 ◦ C using a conventional Instron 1185 testing machine. Since the plasticity is ruled by diffusion-accommodated grain boundary sliding with the appearance of grain growth,7 data analysis can be performed by means of a classical power-law as shown: ε˙ = A
σn σn = A 2/m d2 d m + kt 0
= A
σn
σn = A 2/m 2/m d0m + kε/˙ε d02 1 + k(ε/˙εd0m )
(1)
where A is an empirical constant at constant temperature, σ the flow stress, ε the strain, ε˙ the strain rate, d0 the grain size at the onset of the compression test and k the kinetic constant of the conventional grain growth law: d m = d0m + kt, t being the time and d0 the grain size at initial time t = 0. The stress exponent n was calculated by means of strain rate jumps at constant temperature. A typical constant-strain-rate test at 1150 ◦ C is displayed in Fig. 1. The exponent “m” accounts for the grain growth law applicable to this case. Such exponent was determined by a non-linear fitting of the plastic region of the stress–strain curves to the following law (2a) derived from Eqs. (2b) and (1): log σ = a + b log(1 + cε)
2 kε log 1 + m nm ε˙ d0 2 kε =a+ log 1 + m ε˙ d0 nm
1 log σ = log n
ε˙ d02 A
(2a)
+
(2b)
where a, b, c are constants for a given stress–strain curve at constant strain rate and temperature. The accuracy and stability
Fig. 1. Stress–strain curve at 1150 ◦ C of CeTZP polycrystals. The strain rate was 10−5 s−1 and it was increased to 2 × 10−5 s−1 for stress exponent determination. The experimental data were fitted to Eq. (1) provided in the text.
of the fitting was assessed by the least-square method. As expected, the quantities b, c can be fitted with an error lower than 2%. On the contrary ‘a’ cannot be fitted unless errors of 10–13% are accepted. This is the consequence of the inaccuracy to choice the onset of the plastic regime, a common fact in all tests of plasticity. Fortunately, the quantity ‘a’ is not required at all for diffusion coefficient calculation. 3. Results and discussion The stress exponent was found to be n = 1.3 ± 0.2, in full agreement with the outputs reported by de Bernardi et al.7 after creep tests at the same temperature. The exponent m could be fitted to m = 2 or m = 3, both fittings being equally acceptable (r = 0.98 versus r = 0.96). The first one, a slightly better one, was chosen for calculations. A similar uncertainty was reported by Chaim in static grain growth experiments in YTZP8 and by Kumagai in electric current-activated assisted sintering tests.9 Both the as-received and post-mortem specimens were characterized through conventional scanning electron microscopy (SEM), in order to determine the grain size distribution prior to and after deformation. Grain boundaries were optically resolved by SEM after a rapid heat treatment of the previously polished surfaces. Fig. 2a and b shows the grain microstructure prior to and after constant strain-rate experiments at 1300 ◦ C, respectively. The microstructure in as-received samples was composed of equiaxial grains with an average grain size equal to 1.4 ± 0.6 m. After deformation the grains remained equiaxed; however there was a remarkable grain growth (Fig. 2b): the grain size, defined as the diameter of the equivalent circle of the same area in all cases was found to increase up to a factor 2 approximately: up to 2.6 ± 0.7 m when the test is performed at 1300 ◦ C at 10−5 s−1 and the final strain is 40%. The normalized grain distribution fits to a modified Gumbel function, in agreement with the theoretical steady-state grain size distribution of a collective of grain boundaries of equal mobilities under stress.10 The values of the stress exponent, together with the invariance of the normalized grain size distribution, are consistent with the
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Fig. 3. CeTZP diffusion coefficient versus 104 /T obtained from this study. The experimental data are fitted to an Arrhenius law, displayed as a dashed line. The results are plotted together with those reported in literature by Sakka et al. The plots labelled as HT and LT are grain boundary diffusion coefficients reported by Chaim in YTZP after static grain growth experiments. Table 1 Grain boundary diffusion coefficients (m2 s−1 ) versus the inverse of temperature. The activation energy is given in electron volts. Fig. 2. Scanning electron microscopy micrographs of the grain microstructure prior to (a) and after constant-strain-rate test (b).
assumption of high-temperature plastic deformation mechanism controlled by diffusion-accommodated grain boundary sliding. De Bernardi et al.7 proved this statement after modelling hightemperature creep tests. This result validates the use of Eqs. (1), (2a) and (2b) for numerical fitting of the stress–strain curves. From this fitting, the kinetic constant for grain growth (k) can be determined and also the grain boundary diffusion coefficient, being proportional to such constant as described in literature11 : Dgb = kB T
kδgb mγgb d m−2 Ω
(3)
where δgb is the thickness of the grain boundary, taken as 10−9 m,7 Ω is the volume of cerium cations (9.1 × 10−31 m3 ),12 γ gb is the grain boundary energy, equal to 1 J m−2 in zirconia systems8 and kB is the Boltzmann’s constant. Finally, d is the final value of the grain size. As commented previously, m = 2 in our fitting. Fig. 3 displays the results achieved for grain boundary diffusion versus temperature together with the reported results for CeTZP5 and those measured by Chaim8 in YTZP (3 wt% yttria tetragonal zirconia) at temperatures lower than 1400 ◦ C (labelled as LT from now on) and higher than this value (labelled as HT). The numerical values for all reported results and the leastsquared fit to an Arrhenius law of our data are given in Table 1. The comparison of our results with those previously reported in literature allows concluding several remarks: first of all, the accuracy of this method is very reasonable: all data are within less than order of magnitude. Since mechanical tests are
12CeTZP (this work) CeTZP (Sakka et al. [5]) 3 wt%TZP (HT) (Chaim [8]) 3 wt%TZP (LT) (Chaim [8])
Dgb = 2.6 × 101 exp(−4.86/kB T) Dgb = 2.9 × 102 exp(−5.27/kB T) Dgb (YTZP-HT) = 1.2 × 102 exp(−5.00/kB T) Dgb (YTZP-LT) = 1.1 × 10−4 exp(−3.00/kB T)
considerably easier to be performed in conventional mechanical test laboratories, the method is powerful and fast to get insight into the grain-boundary diffusion properties of lowest species in ceramics. Secondly, the activation energy for cation diffusion is found to be 4.89 eV, which is within the experimental uncertainty, very similar to that obtained through interdiffusion measurements by Sakka et al.5 (5.27 eV), although our results shows the diffusion coefficient is within 2–3 times larger than their reported one (Fig. 3). Since the difference is much less than one order of magnitude, the agreement can be considered very reasonable. One very interesting point is the comparison between CeTZP and YTZP grain boundary diffusion coefficients. Chaim8 proved that there are two regimes in the high-temperature dependence of the grain boundary diffusion coefficient in YTZP: at temperatures lower than 1400 ◦ C the activation energy for cation diffusion is 3 eV whereas that quantity rises to 5 eV in the hightemperature regime (temperatures higher than 1400 ◦ C). Both diffusion coefficients have been extrapolated to the temperature range of our results, as displayed in Fig. 3. Chaim8 claims that the origin of these two regimes can be found in the effect of yttrium segregation in excess at the grain boundaries, inducing local phase transformation to the cubic phase at temperatures lower than 1400 ◦ C. This may be due to the fact that local concentration at the grain boundaries can excess the value for coexistence of cubic and tetragonal phase. In the high-temperature regime,
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the yttrium segregation weakens, the local concentration at the boundaries is lower, and it would explain the change in the activation energy and the absolute values of the diffusion coefficient. This explanation makes sense if the local concentration at the boundaries is over 8 mol% and the fact that the activation energy reaches low values can be justified as follows: the presence of yttrium segregation in excess at the grain boundaries is associated to an increase in the oxygen vacancies in the anion sublattice. Given the highly defective crystallographic structure at the grain boundaries it is reasonable to think that energy barrier for atomic migration should reduce. Such tendency has been reported in molecular dynamics simulations.13 However segregation to the grain boundaries is not reported in CeTZP. Even if there were cerium segregation to the boundaries, it would not induce a local increase of oxygen vacancies because zirconium and cerium cations are isovalent. Given that the crystallographic structures of CeTZP and YTZP without segregation (i.e. in the HT regime) are very similar, one simple relation should exist among the grain boundary diffusion coefficients of both species. In fact, a careful numerical analysis of our results and those reported by Chaim for HT grain boundary diffusion allows finding a proportionality among them; i.e. Dgb (CeTZP) ∼ = ␣Dgb (YTZP). The proportionality constant α is approximately 0.8. This quantity is equal to √ MY-Zr /MCe i.e. the square root of the ratio of atomic masses of yttrium-zirconium cations to cerium ones. This result point out that there is just an isotope effect14 in the grain boundary diffusion coefficients in the very high-temperature regime for these two zirconia alloys. According to Schoen,14 such isotope effect is expected if the diffusion takes place by a cation-vacancy exchange in the cation sublattice. Molecular dynamics simulation reported a cation-vacancy exchange as the main mechanism account for cation diffusion of yttrium in the zirconia cation sublattice,13 in full agreement with the result found in this work. Finally, it is important to emphasize that this relationship does not seem to depend on the bulk concentration of the oxides, because the concentration of cations at the boundaries is the saturation one, independent on the bulk concentrations. 4. Conclusions The grain boundary diffusion coefficient in ceria-zirconia tetragonal polycrystals was determined via analysis of hightemperature constant-strain-rate compression tests. The results show that it is numerical identical to the homologous one in yttria-zirconia ceramics except for the mass dependence of the cerium cations; i.e. an isotope effect is reported. This fact has
significant implications on the mechanism for cation diffusion in these ceramics: a cation vacancy exchange is probably the main mechanism for diffusion of these species. Acknowledgements The authors acknowledge the financial support awarded by the Spanish National Authority through the project MAT201238205-C02-01 and from the ‘Junta de Andalucía’ Regional Government through the Project of Excellence P12-FQM-1079. The authors acknowledge Prof. Odriozola Gordon, from University of Seville, for supplying generously the spark plasma sintered specimens used in this study. References 1. Garvie RC, Hannik RHJ, Pascoe RT. Ceramic steel? Nature 1975;258:703–4. 2. Gonzalez-Romero RL, Meléndez JJ, Gómez-García D, Cumbrera FL, Domínguez-Rodríguez A. A molecular dynamics study of grain boundaries in YSZ: structure, energetics and diffusion of oxygen. Solid State Ionics 2012;219:1–10. 3. Ando K, Morita S, Watanabe R. Effects of the grain boundary and its movements on the oxygen self-diffusion in CeO2 –ZrO2 solid solutions. Yogyo Kyokaishi 1986;94:732–6. 4. Domínguez-Rodríguez A, Gómez-García D, Wakai F. High-temperature plasticity in yttria stabilized tetragonal zirconia polycrystals. Int Mater Rev 2013;58:399–417. 5. Sakka Y, Oishi Y, Ando K, Morita S. Cation interdiffusion and phase stability in polycrystalline tetragonal ceria-zirconia-hafnia solid solution. J Am Ceram Soc 1991;74:2610–4. 6. Cruz S, Poyato R, Cumbrera FL, Odriozola JA. Nanostructured spark plasma sintered Ce-TZP ceramics. J Am Ceram Soc 2012;95:901–6. 7. de Bernardi-Martín S, Gómez-García D, Domínguez-Rodríguez A, de Portu G. A first-study of the high-temperature plasticity of ceria-doped zirconia polycrystals. J Eur Ceram Soc 2010;30:3357–62. 8. Chaim R. Activation energy and grain growth in nanocrystalline Y-TZP ceramics. Mater Sci Eng A 2008;486:439–46. 9. Kumagai T. Estimation of stress exponent and activation energy for rapid densification of 8 mol% yttria-stabilized zirconia powder. J Am Ceram Soc 2013;96:852–8. 10. Moshtaghioun BM, Gómez-García D, Cumbrera-Hernández FL, Domínguez-Rodríguez A. A phase-field model of 2D grain size distribution in ceramics. J Eur Ceram Soc 2014;34:2731–6. 11. Yan MF, Cannon RM, Bowen HK. In: Fulrath RM, Pask JA, editors. Ceramic microstructures, vol. 76. Boulder, CO: Westview Press; 1977. p. 276. 12. Thomas JB, Bodnar RJ, Shimizu N, Chesner CA. Melt inclusions in zircon. Rev Miner Geochem 2003;53:63–87. 13. González-Romero RL, Meléndez JJ, Gómez-García D, Cumbrera FL, Domínguez-Rodríguez A, Wakai F. Cation diffusion in yttria-zirconia by molecular dynamics. Solid State Ionics 2011;204:1–6. 14. Schoen AH. Correlation the isotope effect for diffusion in crystalline solids. Phys Rev Lett 1958;1:138–40.