A Morales-Rodriguez et al /Journal of the European Ceramic Sociery 29(2009)1625-1630 Q is probably due to the highly extrinsic character of this oxide; In this study, the laminates were deformed in isostrain co even a very few at ppm of impurities/dopants change drastically ditions. French et al. 32have developed a creep model for duplex the mechanical behavior. 22-25 The creep of large-grained alu- microstructures by assuming an isostress(alternate plates of mina has been usually associated with a Coble diffusion creep each phase aligned perpendicular to the applied stress)or isos- mechanism,20-22,26 where the transport of matter along grain train(plates are parallel to the applied stress)model; the latter boundaries is both the deformation and rate-controlling mech- one coincides with the configuration of the present laminates. In anism. The steady-state strain rate in the Coble model is given this case, the overall(applied) composite stress oc is given by by the following equation he relation- 150σg2 (2) Oc=fAIOAl+ fzTAOZTA where o al and azTA are the stresses supported by the Al2O3 where 52 is the atomic volume, k is the Boltzmanns constant, and ZTA layers, respectively, and fAl and fzta the correspond 8 is the grain boundary width and Dgd is the grain boundary ing volume fractions. This model has been successfully used to diffusion coefficient, determined by the slower ionic specie explain the high-temperature mechanical behavior of laminated he diffusion behavior in alumina is a far from simple matter metal33 and ceramic,34 composites. Owing to the higher creep today(see, for example, the recent reviews by Heuerz7and Hard- strength of the alumina phase in comparison with ZTA, Eq (3) ing et al. ).Reported aluminum and oxygen diffusivities exhibit can be simplified to a considerable scatter, both in activation energy and in absolute magnitude of the coefficient, due probably to small variations ac= fAIOAl in impurity content which significantly influence the diffusion kinetics. It must be noted, however, that oxygen diffuses slower That is, the strain rate of the laminate will be controlled by the than aluminum both in the bulk and along(sub)grain boundaries alumina phase. This is consistent with the value n=1 found in when measured on the same suite of crystals.29,30 The creep rate the laminates, also reported in monolithic alumina. 20-22In the of monolithic alumina(Eq (2) should be thus associated with isostress configuration, where the softer(ZTA) phase would be oxygen diffusion along grain boundaries. Fig. displays the oxy- the rate-controlling phase, a stress exponent n=2 was found. 10 gen diffusivities in bulk(D')and along grain boundaries(Deb) Regarding the creep activation energy, both alumina and ZTA measured by Prot et al. 2in undoped and yttria-doped alumina monoliths have Q values in the same range, which precludes a (although contaminated with >1000 at ppm Si), along with the quantitative comparison corresponding activation energies. Recent data by Nakagawa et Assuming that the alumina phase controls the overall al. on high-purity and yttria-doped alumina bi-crystals are also mechanical behavior of the laminates, the diffusion coefficient plotted in Fig. 6. Despite the scatter, the experimental data sug- Dgb in Eq(2)can be deduced from the laminate creep data gests that the activation energy for grain boundary diffusion is with o =OAI=0c/0.40=2.500c(Eq(4);8 is assumed to be larger than for bulk diffusion I nm, as usual, and S2=2.20 x 10-m. These apparent dif fusion coefficients are reported in Fig. 6. The good agreement between both sets of data(diffusion and creep) confirms the T(C) 17001600 1500 1400 validity of the previous hypothesis, i. e, the composite creep rate is primarily controlled by the Al2O3 layers 921 kJ/mol [29 Despite the apparent good agreement with pristine alumina (Fig. 6), several features suggest that the deformation of the 627 kJ/mol 31 laminates may be related to grain boundary diffusion in doped alumina rather than in pure-alumina 1016E800029 729 KJ/mol [313 (i) EDX(energy dispersive X-ray )/SEM linescans performed layers(Fig. 7) show the presence of yttrium and zirconium in these layers in an approximate 590 kJ/mol [291 ratio(alumina layer ZTA layer)1: 4 and 1: 9, respectively; he aluminum ratio is 2: 1, in agreement with the amount 636kmol[29 62 kJ/mol [31 of alumina in the two types of layers. Such a cation diffu sion from ZTA layers towards Al2O3 layers is due to the 505.2545.6586.0 no data on zirconium diffusion in alumina, but lesage et 104T(K) alhave reported that yttrium diffuses rapidly in poly crystalline alumina, reaching depths larger than 100 um(the undoped(solid lines)and, s in bulk (D')and along grain boundaries(Ds)in same order as the layer thickness in the laminates)after dif- Fig. 6. Oxygen difft yttrium-doped(dashed lines)alumina deduced fror fusion experiments, along with the corresponding activation energies.29,31 fusion of 17 h at 1408C. This unintentional doping of the Apparent diffusion coefficients deduced from creep data(Eq (2)are also plotted alumina layers explains the damage mode exhibited by the na layers(Figs. 5 and 7). In high-purity alumina,1628 A. Morales-Rodríguez et al. / Journal of the European Ceramic Society 29 (2009) 1625–1630 Q is probably due to the highly extrinsic character of this oxide; even a very few at.ppm of impurities/dopants change drastically the mechanical behavior.22–25 The creep of large-grained alu￾mina has been usually associated with a Coble diffusion creep mechanism,20–22,26 where the transport of matter along grain boundaries is both the deformation and rate-controlling mech￾anism. The steady-state strain rate in the Coble model is given by the following equation: ε˙ = 150 π σΩ kTd3 δDgb (2) where Ω is the atomic volume, k is the Boltzmann’s constant, δ is the grain boundary width and Dgb is the grain boundary diffusion coefficient, determined by the slower ionic specie. The diffusion behavior in alumina is a far from simple matter today (see, for example, the recent reviews by Heuer27 and Hard￾ing et al.28). Reported aluminum and oxygen diffusivities exhibit a considerable scatter, both in activation energy and in absolute magnitude of the coefficient, due probably to small variations in impurity content which significantly influence the diffusion kinetics. It must be noted, however, that oxygen diffuses slower than aluminum both in the bulk and along (sub)grain boundaries when measured on the same suite of crystals.29,30 The creep rate of monolithic alumina (Eq. (2)) should be thus associated with oxygen diffusion along grain boundaries. Fig. 6 displays the oxy￾gen diffusivities in bulk (Dl ) and along grain boundaries (Dgb) measured by Prot et al.29 in undoped and yttria-doped alumina (although contaminated with >1000 at.ppm Si), along with the corresponding activation energies. Recent data by Nakagawa et al.31 on high-purity and yttria-doped alumina bi-crystals are also plotted in Fig. 6. Despite the scatter, the experimental data sug￾gests that the activation energy for grain boundary diffusion is larger than for bulk diffusion. Fig. 6. Oxygen diffusivities in bulk (Dl ) and along grain boundaries (Dgb) in undoped (solid lines) and yttrium-doped (dashed lines) alumina deduced from diffusion experiments, along with the corresponding activation energies.29,31 Apparent diffusion coefficients deduced from creep data (Eq.(2)) are also plotted (squares). In this study, the laminates were deformed in isostrain con￾ditions. French et al.32 have developed a creep model for duplex microstructures by assuming an isostress (alternate plates of each phase aligned perpendicular to the applied stress) or isos￾train (plates are parallel to the applied stress) model; the latter one coincides with the configuration of the present laminates. In this case, the overall (applied) composite stress σc is given by the relation32: σc = fAlσAl + fZTAσZTA (3) where σAl and σZTA are the stresses supported by the Al2O3 and ZTA layers, respectively, and fAl and fZTA the correspond￾ing volume fractions. This model has been successfully used to explain the high-temperature mechanical behavior of laminated metal33 and ceramic9,34 composites. Owing to the higher creep strength of the alumina phase in comparison with ZTA, Eq. (3) can be simplified to: σc = fAlσAl (4) That is, the strain rate of the laminate will be controlled by the alumina phase. This is consistent with the value n = 1 found in the laminates, also reported in monolithic alumina.20–22 In the isostress configuration, where the softer (ZTA) phase would be the rate-controlling phase, a stress exponent n = 2 was found.10 Regarding the creep activation energy, both alumina and ZTA monoliths have Q values in the same range, which precludes a quantitative comparison. Assuming that the alumina phase controls the overall mechanical behavior of the laminates, the diffusion coefficient Dgb in Eq. (2) can be deduced from the laminate creep data with σ ≡ σAl = σc/0.40 = 2.50σc (Eq. (4)); δ is assumed to be 1 nm, as usual, and Ω = 2.20 × 10−29 m3. These apparent dif￾fusion coefficients are reported in Fig. 6. The good agreement between both sets of data (diffusion and creep) confirms the validity of the previous hypothesis, i.e., the composite creep rate is primarily controlled by the Al2O3 layers. Despite the apparent good agreement with pristine alumina (Fig. 6), several features suggest that the deformation of the laminates may be related to grain boundary diffusion in doped￾alumina rather than in pure-alumina: (i) EDX (energy dispersive X-ray)/SEM linescans performed across the alumina layers (Fig. 7) show the presence of yttrium and zirconium in these layers in an approximate ratio (alumina layer:ZTA layer) 1:4 and 1:9, respectively; the aluminum ratio is 2:1, in agreement with the amount of alumina in the two types of layers. Such a cation diffu￾sion from ZTA layers towards Al2O3 layers is due to the elevated temperatures during sintering (1550 ◦C). There is no data on zirconium diffusion in alumina, but Lesage et al.35 have reported that yttrium diffuses rapidly in poly￾crystalline alumina, reaching depths larger than 100 m (the same order as the layer thickness in the laminates) after dif￾fusion of 17 h at 1408 ◦C. This unintentional doping of the alumina layers explains the damage mode exhibited by the alumina layers (Figs. 5 and 7). In high-purity alumina, two