A G. Evans et al Joumal of the European Ceramic Sociery 28(2008)1405-1419 thickness that causes delamination(Fig. 5). In practice, this approach to predicting the critical thickness has not been real- ized, because the mode II toughness is a notoriously difficult property to measure. Instead, estimates based on the mode I and mixed-mode delamination toughness have been invoked However, these results demonstrate order of magnitude varia- ons that depend on th used to form the interface. Instead of placing reliance solely on measurements, a simulation scheme that distinguishes the factors dominating the adhesion(Fig. 13)is being pursued. It has two basic ingredients. (i) The traction/separation characte istics during bond rupture at the interface are ascertained using a first principles approach based on density functional theory Wuum(i) These results are input to an embedded process zone(EPz) simulation of interface crack extension that captures the mul- tiplicative influence on the toughness of the plastic dissipation occurring in the bond coat. In general, the traction/separation GB curves are found to depend on the termination plane(stoichiom- etry)of the a-Al2O3, as well as the presence of dopants and impurities. For y-Ni(Al) alloys, the termination has been ascer- tained to be a mix of stoichiometric and al-rich the former is the least adherent(Fig. 14). Moreover, when present, S seg regates to this interface and further decreases the adhesion(by up to 70%), because the interfacial covalent-ionic Ni-O bonds eplaced with weaker ior with Hf obviates the detriment, especially when it segregates on interstitial sites(Hfn)(Fig. 14), because Hf-Ni and Hf-o bonds effectively knit the surfaces together. When integrated(Fig. 13), hese results establish a rationale for designing tough interfaces. Recall that Hf has the additional benefit that it affects the creep strength of the TGO when it segregates to the grain boundaries. 5. The insulating oxide Beyond the basic requirement that the thermal conductiv ity be low and(preferably) temperature invariant, the following properties are critical to system performance. Toughness affects all of the extrinsic mechanisms. Remarkably, the range realiz GB able among all(non-fibrous) oxides is fully encompassed by YSZ across the composition range between cubic and tetrag Fig 8.()Fractured cross section of a TGo illustrating the inner, columnar onal(Fig. 15). The cubic materials(c-ZrO2-20-YSZ)are portion of the oxide formed by inward diffusion of o and the outer, equiaxed exceptionally brittle(toughness, Ia6J/m), while partially portion formed by outward diffusion of AL. (b)Schematic diagram showing the stabilized tetragonal materials( t-Zr02-3-YSZ), which expe- rience a martensitic transformation to the monoclinic phase (m-ZrO,), are among the to strate and bond coat, as well as its creep strength, the TGo is formation mechanism is inapplicable for two related reasons also important. From a TGO perspective, the growth stress and(a) It is thermodynamically forbidden at elevated temperatures, the thickening rate are most influential specifically those above To(t/m)(Fig. 16a), wherein there is no driving force for the partitionless t->m transformation.(b) 4.3. Interface adhesion Repeated cycling across the To(t/m) results in disruptive vol- ume changes every time the t-Zro2 transforms to m-zrO2 on When rumpling is suppressed, durability is limited by delam- cooling and regenerates upon heating, with concomitant micro- ination along the interface between the TGO and the bond coat. cracking Compositions within the non-transformable tetragonal The energy release rate enabling this mechanism(Fig. 5)is com- () phase field, bound by the compositions for which To(t/m)is municated to the interface as a mode Il(shear)delamination. below ambient and To(c/t)is below the maximum operating tem- In principle, equating the energy release rate to the mode ll perature, provide the best performance Because tetragonality toughness of the interface predicts a lower bound on the tGo typically decreases with increasing dopant content the pre1412 A.G. Evans et al. / Journal of the European Ceramic Society 28 (2008) 1405–1419 Fig. 8. (a) Fractured cross section of a TGO illustrating the inner, columnar portion of the oxide formed by inward diffusion of O and the outer, equiaxed portion formed by outward diffusion of Al. (b) Schematic diagram showing the flux paths. strate and bond coat, as well as its creep strength, the TGO is also important. From a TGO perspective, the growth stress and the thickening rate are most influential. 4.3. Interface adhesion When rumpling is suppressed, durability is limited by delam￾ination along the interface between the TGO and the bond coat. The energy release rate enabling this mechanism (Fig. 5) is com￾municated to the interface as a mode II (shear) delamination. In principle, equating the energy release rate to the mode II toughness of the interface predicts a lower bound on the TGO thickness that causes delamination (Fig. 5). In practice, this approach to predicting the critical thickness has not been real￾ized, because the mode II toughness is a notoriously difficult property to measure. Instead, estimates based on the mode I and mixed-mode delamination toughness have been invoked. However, these results demonstrate order of magnitude varia￾tions that depend on the presence of segregants and the method used to form the interface. Instead of placing reliance solely on measurements, a simulation scheme that distinguishes the factors dominating the adhesion (Fig. 13) is being pursued. It has two basic ingredients. (i) The traction/separation character￾istics during bond rupture at the interface are ascertained using a first principles approach based on density functional theory. (ii) These results are input to an embedded process zone (EPZ) simulation of interface crack extension that captures the mul￾tiplicative influence on the toughness of the plastic dissipation occurring in the bond coat. In general, the traction/separation curves are found to depend on the termination plane (stoichiom￾etry) of the -Al2O3, as well as the presence of dopants and impurities. For -Ni(Al) alloys, the termination has been ascer￾tained to be a mix of stoichiometric and Al-rich. The former is the least adherent (Fig. 14). Moreover, when present, S seg￾regates to this interface and further decreases the adhesion (by up to 70%), because the interfacial covalent-ionic Ni–O bonds are replaced with weaker ionic-covalent S–Al bonds. Doping with Hf obviates the detriment, especially when it segregates on interstitial sites (HfI) (Fig. 14), because Hf–Ni and Hf–O bonds effectively knit the surfaces together. When integrated (Fig. 13), these results establish a rationale for designing tough interfaces. Recall that Hf has the additional benefit that it affects the creep strength of the TGO when it segregates to the grain boundaries. 5. The insulating oxide Beyond the basic requirement that the thermal conductiv￾ity be low and (preferably) temperature invariant, the following properties are critical to system performance. Toughness affects all of the extrinsic mechanisms. Remarkably, the range realiz￾able among all (non-fibrous) oxides is fully encompassed by YSZ across the composition range between cubic and tetrag￾onal (Fig. 15).22 The cubic materials (c-ZrO2 →20-YSZ) are exceptionally brittle (toughness, Γ ≈ 6 J/m2), while partially stabilized tetragonal materials (t-ZrO2 →3-YSZ), which expe￾rience a martensitic transformation to the monoclinic phase (m-ZrO2), are among the toughest (Γ > 300 J/m2). The trans￾formation mechanism is inapplicable for two related reasons. (a) It is thermodynamically forbidden at elevated temperatures, specifically those above T0(t/m) (Fig. 16a), wherein there is no driving force for the partitionless t→m transformation. (b) Repeated cycling across the T0(t/m) results in disruptive vol￾ume changes every time the t-ZrO2 transforms to m-ZrO2 on cooling and regenerates upon heating, with concomitant micro￾cracking. Compositions within the non-transformable tetragonal (t ) phase field, bound by the compositions for which T0(t/m) is below ambient and T0(c/t) is below the maximum operating tem￾perature, provide the best performance. Because tetragonality typically decreases with increasing dopant content75 the pre-