A.G. Evans et al. Journal of the European Ceramic Society 28(2008)1405-1419 1411 4 Cross sections through a burner rig test specimen comprising an MCrAlY bond coat after thermal cycling to full life. (a) A section remote from the spalled showing the intact interface. (b) A region adjacent to the spalled zone showing that the delamination follows the interface except where it extends across a thickness heterogeneity. metastable phase until the excess solute precipitates, since 4.2. The stresses in the TGo the local driving force is insufficient. Conversely, Cr and Fe (cations soluble in a)accelerate the growth rate: a feature If all of the new a-Al2O3 formed at the interface with the elucidated by polishing the surface of bond coat alloys with bond coat, the ensuing volume increase would be accommodated Cr and Fe oxides and noting preferential growth of alumina by upward(rigid body) motion of the prior TGo, obviating on heterogeneous nuclei created at the polishing features growth stress. Instead, the outward counter-fiux of Al causes (scratches, grit-blast grooves, etc. )(Fig. 10). Given these some new a-Al2O3 to form at dislocations/ledges along the counteracting influences of the dopants, a compromise in transverse grain boundaries, as well as that formed on the the relative dopant levels is required. However, because a face of the TGO(Fig 9). That formed at the boundaries must be quantitative model is lacking, reliance has been placed on accommodated by lateral deformation of the neighboring grains empiricism, with adverse consequences for progress toward causing a compressive growth stress(Fig. 11). Since a-Al2O3 optimal doping strategies is susceptible to plastic deformation at the growth tempera (i) The relative inward and outward diffusive fluxes along the ture, the stress attains a"steady-state, wherein the strain-rate grain boundaries in the ensuing a-Al2O3 influences both induced by the growth is balanced by the creep-rate. The mag- thickening and elongation. The grain boundaries governing nitude of this stress has been measured in situ for the TGo these effects are clean and devoid of amorphous interphases formed on several different bond coats. It is measured to be of (although sub-monolayers of Hf or Zr can be entrained). The order, a growth -300MPa4(Fig. 12). While this stress level conventional picture is that, once a-Al2O3 is formed, oxide appears reasonable based on deformation mechanism maps for hickening is dominated by inward diffusion of O. In prac- a-Al2O3 and stress relaxation rates in a typical TGO, it remains tice, there is a counter-flux of cations, 73, 74 demonstrated by to develop a quantitative model. Moreover, the influences of using the following protocol. The alloy is oxidized to form role of dopants on growth strains and relaxations are poorly a continuous TGO, which is then polished at an angle, and understood. Upon cooling, because of its relatively low thermal re-oxidized. Some of the new oxide forms as ridges along expansion coefficient(relative to the substrate)a large in-plane locations where the oxide grain boundaries intersect the sur- compression develops(Fig. 12). At ambient, whenever the TGO face(Fig 9). There are corresponding ridges where the grain remains planar(no rumpling), the compressive stress is in the boundaries intersect the interface. Measurement of the vol- range, -35<0tgo<-6GPa, depending on the thermal expan- ume of these ridges allows assessment of the relative anion sion coefficient for the substrate. 8 When rumpling occurs, the and cation fluxes (note that, in Fig. 9 the inward and outward stress diminishes because of bending and elongation of the fluxes must be of comparable magnitude). Such measure- TGO 37.57 ments reveal that the counter-fluxes depend sensitively Rumpling is highly non-linear phenomenon, involving inter dopants such as Hf and Y entrained in the grain boundaries ctions between the tgo. bond coat and substrate and reliant of the growing oxide. The unresolved question is how to on many thermo-mechanical properties of the layers. The inte think about the atomic mechanisms of counter-diffusion, actions have been unearthed through the development of a code and how this process determines elongation strain. These and its validation by incisive experiments. While the rumpling fundamentals have not been addressed in the literature rate is strongly influenced by the strain misfits between the sulA.G. Evans et al. / Journal of the European Ceramic Society 28 (2008) 1405–1419 1411 Fig. 7. Cross sections through a burner rig test specimen comprising an MCrAlY bond coat after thermal cycling to full life. (a) A section remote from the spalled region showing the intact interface. (b) A region adjacent to the spalled zone showing that the delamination follows the interface except where it extends across a thickness heterogeneity. metastable phase until the excess solute precipitates, since the local driving force is insufficient. Conversely, Cr and Fe (cations soluble in ) accelerate the growth rate: a feature elucidated by polishing the surface of bond coat alloys with Cr and Fe oxides and noting preferential growth of alumina on heterogeneous nuclei created at the polishing features (scratches, grit-blast grooves, etc.) (Fig. 10). Given these counteracting influences of the dopants, a compromise in the relative dopant levels is required. However, because a quantitative model is lacking, reliance has been placed on empiricism, with adverse consequences for progress toward optimal doping strategies. (ii) The relative inward and outward diffusive fluxes along the grain boundaries in the ensuing -Al2O3 influences both thickening and elongation. The grain boundaries governing these effects are clean and devoid of amorphous interphases (although sub-monolayers of Hf or Zr can be entrained). The conventional picture is that, once -Al2O3 is formed, oxide thickening is dominated by inward diffusion of O. In prac￾tice, there is a counter-flux of cations,73,74 demonstrated by using the following protocol. The alloy is oxidized to form a continuous TGO, which is then polished at an angle, and re-oxidized. Some of the new oxide forms as ridges along locations where the oxide grain boundaries intersect the sur￾face (Fig. 9). There are corresponding ridges where the grain boundaries intersect the interface. Measurement of the vol￾ume of these ridges allows assessment of the relative anion and cation fluxes (note that, in Fig. 9 the inward and outward fluxes must be of comparable magnitude). Such measure￾ments reveal that the counter-fluxes depend sensitively on dopants such as Hf and Y entrained in the grain boundaries of the growing oxide. The unresolved question is how to think about the atomic mechanisms of counter-diffusion, and how this process determines elongation strain. These fundamentals have not been addressed in the literature. 4.2. The stresses in the TGO If all of the new -Al2O3 formed at the interface with the bond coat, the ensuing volume increase would be accommodated by upward (rigid body) motion of the prior TGO, obviating a growth stress. Instead, the outward counter-flux of Al causes some new -Al2O3 to form at dislocations/ledges along the transverse grain boundaries, as well as that formed on the sur￾face of the TGO (Fig. 9). That formed at the boundaries must be accommodated by lateral deformation of the neighboring grains, causing a compressive growth stress (Fig. 11). Since -Al2O3 is susceptible to plastic deformation at the growth tempera￾ture, the stress attains a “steady-state”, wherein the strain-rate induced by the growth is balanced by the creep-rate. The mag￾nitude of this stress has been measured in situ for the TGO formed on several different bond coats. It is measured to be of order, σgrowth ≈ −300 MPa54 (Fig. 12). While this stress level appears reasonable based on deformation mechanism maps for -Al2O3 and stress relaxation rates in a typical TGO, it remains to develop a quantitative model. Moreover, the influences of role of dopants on growth strains and relaxations are poorly understood. Upon cooling, because of its relatively low thermal expansion coefficient (relative to the substrate) a large in-plane compression develops (Fig. 12). At ambient, whenever the TGO remains planar (no rumpling), the compressive stress is in the range, −3.5 < σtgo < −6 GPa, depending on the thermal expan￾sion coefficient for the substrate.58 When rumpling occurs, the stress diminishes, because of bending and elongation of the TGO.37,57 Rumpling is highly non-linear phenomenon, involving inter￾actions between the TGO, bond coat and substrate and reliant on many thermo-mechanical properties of the layers. The inter￾actions have been unearthed through the development of a code and its validation by incisive experiments.36 While the rumpling rate is strongly influenced by the strain misfits between the sub-