Atomic-scale insight and design principles for turbine engine thermal barrier coatings from theory

Abstract

To maximize energy efficiency, gas turbine engines used in airplanes and for power generation operate at very high temperatures, even above the melting point of the metal alloys from which they are comprised. This feat is accomplished in part via the deposition of a multilayer, multicomponent thermal barrier coating (TBC), which lasts up to approximately 40,000 h before failing. Understanding failure mechanisms can aid in designing circumvention strategies. We review results of quantum mechanics calculations used to test hypotheses about impurities that harm TBCs and transition metal (TM) additives that render TBCs more robust. In particular, we discovered a number of roles that Pt and early TMs such as Hf and Y additives play in extending the lifetime of TBCs. Fundamental insight into the nature of the bonding created by such additives and its effect on high-temperature evolution of the TBCs led to design principles that can be used to create materials for even more efficient engines.

Aircraft and power plants share a common source of usable energy: Both employ turbine engines that combust fuel to either propel airplanes or produce electricity. At a time in which efficient use of energy is paramount, improving the efficiency of turbine engines is one means to contribute to this global challenge. Turbine engines operate via the Brayton cycle, which offers lower carbon dioxide emissions and lower cost for power generation than other possible alternatives. Their efficiency can be increased by increasing the inlet temperature, which allows more expansion of gas that creates more pressure to drive the turbine. However, high-temperature operation, under oxidizing conditions, poses serious demands on the materials used to construct jet engine components. Materials must be found that are robust under such harsh operating conditions. Engineers over the past few decades have improved greatly the thermomechanical properties of the metal alloy comprising, e.g., the turbine blades, and have created a multilayer coating for the blades that protects against both heat and corrosion, referred to as a thermal barrier coating (TBC). These materials advances, along with internal component cooling, have been astonishingly successful, allowing the gas temperature to exceed the melting point of the metal alloy from which the engine components are constructed!

Despite these advances, more robust TBCs are desired, either to extend TBC service lifetime under present-day operating conditions or to operate at even higher temperatures to achieve more efficient energy conversion. As a result, characterization and optimization of TBC properties have continued to be active areas of research. As is the case for most materials development, the usual path to improve TBCs relies on trial and error. Many materials compositions are fabricated, characterized, and tested. Unfortunately, characterization typically is performed postmortem, as virtually no instruments exist to characterize a TBC in situ during operation. The lack of in situ probes makes it difficult to establish structure-property relationships crucial for understanding how TBCs evolve over time, how they fail, and ultimately how to delay failure. Moreover, characterization after failure sees the sum of a multitude of effects that cannot be easily separated.

Given that these complexities cannot be disentangled by measurements, computer simulations offer an alternative route to understanding, as long as the correct physics is contained in the underlying model used for the material and phenomenon at hand. A distinct advantage of theoretical calculations is that the environmental conditions and material structure and composition can be precisely controlled. This is in contrast to most experiments, in which materials often vary from laboratory to laboratory due to manufacturing differences that produce different microstructures and impurity distributions. By contrast, computer simulations can separately investigate each process of interest in a well-characterized material, thereby allowing deconvolution of the plethora of atomic processes at work. Of course, the physical model used must be validated whenever possible against available experimental data, in order to establish the credibility of the simulations.

In this paper, we demonstrate how atomic-scale insight into the functionality of TBCs can be gleaned by employing quantum-mechanics-based computer simulations. This work has been carried out in the Carter group over the past 15 y, with the initial aim of elucidating TBC failure mechanisms and how they relate to atomic-scale processes within different TBC layers. Once the origins of failure were identified at the most fundamental level of electron distributions, basic concepts were extracted that were used to propose and computationally test composition changes to coatings that would improve their high-temperature survivability. In what follows, we start by providing a brief summary of current knowledge about the composition of TBCs, their failure mechanisms, and the additives used to extend time to failure. We then formulate a list of questions, the answers to which are essential to further understanding of TBCs and the factors that limit their lifetime. To varying degrees, answers to these questions are provided by insights gleaned from our computer simulations, which constitute the major focus of this review.

The Basics of Thermal Barrier Coatings

Turbine engine components are made of nickel (Ni)-based superalloys, the microstructure and composition of which has been tailored to minimize deleterious changes at high temperature (e.g., creep). The idea of coating the metal parts with a material with low thermal conductivity has been around since the late 1950s, and TBCs have been used since the 1980s, but it has been an ever-present challenge to make these coatings durable and prevent them from spalling (chipping off) after some time in operation (1).

The structure of a state-of-the-art TBC consists of three layers (Fig. 1). The topmost layer is a ceramic material that constitutes the actual heat shield. The material of choice is yttria-stabilized zirconia (YSZ), because it possesses a unique combination of properties. First, doping ZrO₂ with 6–8 wt % Y₂O₃ ensures that the resulting YSZ adopts the tetragonal phase at all temperatures of interest, so that thermal-cycling-induced phase transitions—which otherwise would occur in pure zirconia, causing stress buildup—are avoided. Second, YSZ has one of the lowest thermal conductivities of all ceramics, because it possesses an unusual defect structure that scatters phonons, thereby hindering heat transport. Third, despite being a ceramic, its coefficient of thermal expansion is well matched to that of the metal superalloy so that stress buildup due to thermal expansion mismatch is minimized. Finally, YSZ has a low density, which minimizes weight, and it is very hard and therefore quite resistant toward foreign-body physical damage (2, 3).

Fig. 1.

A schematic of the three layers of a thermal barrier coating on top of a Ni-based superalloy turbine blade. After application of the (Ni,Pt)Al bond coat (approximately 50 μm thick), the YSZ ceramic topcoat of approximately 100-μm thickness is deposited. A thin (< 10 μm micron) layer of α-Al₂O₃ forms in between the YSZ and BC during deposition and operation and is known as the TGO.

The YSZ layer is not deposited directly onto the Ni-based superalloy. One reason for this is that YSZ is transparent to oxygen diffusion, and under operation, oxygen would diffuse to the interface and oxidize the metal superalloy forming fast-growing, Ni-rich oxides that would cause early failure of the coating (3). Therefore, a bond coat (BC) alloy is deposited on the superalloy before deposition of the YSZ. Two different classes of BC alloys exist: approximately 100-μm-thick MCrAlY (where M = Co or Ni) alloys in use since the 1960s and approximately 40- to 60-μm-thick PtNi aluminides developed more recently that are more oxidation resistant but less ductile than MCrAlY. In this review, although some of our findings are relevant for the MCrAlY BCs, we focus our attention on the PtNi aluminide BCs. Both types of BCs ensure good adhesion and corrosion protection (2). The latter protective action is provided by the third component of the TBC, discussed next.

During YSZ deposition and engine operation, a thin thermally grown oxide (TGO) layer forms between the YSZ and the BC layers. This oxide growth is driven by oxygen diffusion through the YSZ and cannot be avoided at typical operating temperatures. Use of the PtNi aluminide BC composition ensures that the TGO is alumina, Al₂O₃. During the initial stage of TGO formation, transient, metastable alumina phases can appear, but eventually the dense α-Al₂O₃ is the prevailing phase. The ideal TGO, α-Al₂O₃, exhibits the lowest oxygen mobility of all thermally grown oxides (4, 5), inhibiting further corrosion of the Ni alloy and leading to very slow growth, which we will see is crucial to long TBC lifetimes. Oxidation of the MCrAlY BCs produces a mixture of alumina and chromia, which is usually a less ideal TGO. Although a thin, dense TGO layer is protective against oxidative corrosion by slowing further oxygen diffusion through the TGO to the superalloy, the TGO layer continues to grow during operation, albeit very slowly, and a thickness beyond 10 μm generally causes failure of the TBC (2, 3).

Some failure mechanisms have already been mentioned, but a nonexhaustive list of proposed failure modes is as follows: formation of less-adherent, Ni-rich oxides due to depletion of Al in the BC and subsequent spallation; stress-induced delamination of the thickened TGO layer upon thermal cycling due to thermal expansion mismatches between the TGO and BC; and failure due to external events such as foreign object damage, hot corrosion, or erosion. Even though there are many different failure events and mechanisms, one prevailing observation is that failure mostly occurs at the TGO/BC interface, due to either the increased thickness of the TGO or the presence of interfacial voids and/or deleterious impurities, especially sulfur (3). As the TGO thickens and undergoes thermal cycling, thermal expansion mismatch strain builds up; once the strain energy exceeds the interface strength, spallation occurs. Numerous studies have noted that sulfur-containing BCs spall much more rapidly than desulfurized BCs (6, 7). Thus, two key strategies may be adopted to delay TBC failure: inhibit TGO growth to prevent strain buildup arising from increased TGO thickness and increase adhesion of the TGO to the BC.

Both inhibition of TGO growth and prevention of coating delamination have been achieved by doping BCs with reactive elements (REs), typically early transition metals such as Hf, Y, and Zr. Even though these elements have been used for over 70 y, a clear picture of how they improve TBC stability remains elusive. Along the same lines, even though Pt-containing bond coats have been in use for 30 y, the exact role of Pt is not fully understood either. A wealth of experimental data is available, but as mentioned already, it originates mostly from postmortem measurements, making it difficult to extract details about atomic-scale processes. In the following, we give a summary of the main experimental observations regarding Pt and REs and how they are thought to improve TBC lifetime.

(Pt,Ni)Al BCs contain typically only 5 at. % Pt, but this is sufficient to render the BC more sulfur-tolerant over a range of sulfur concentrations (1–7 ppma) and to prevent delamination at the TGO/BC interface. The origin of this sulfur tolerance and improved adhesion is still under discussion; it has been suggested that Pt may hinder S segregation to the interfaces, thereby preventing void formation and delamination (6, 7). Electron microscopy reveals that S is found at voids (8), though it is not known whether interfacial S causes void formation (or growth) or whether S just migrates to the voids once they have formed. A different hypothesis is that Pt may enhance the selective formation of alumina instead of spinels during BC oxidation by enhancing Al diffusion (9, 10). The latter suggestion has been supported by a very interesting study of the oxidation of a Ni-rich NiAl alloy, where it was found that Pt prevents formation of Ni-rich spinel oxides even at Al compositions as low as 35 at. %, compositions at which those spinels would form easily in the absence of Pt (11). Theory can make a valuable contribution toward explaining the effect of Pt, simply because the effect of Pt on TGO/BC interface adhesion and on diffusion in NiAl can be evaluated separately.

REs are employed at very low concentrations near their solubility limit (a typical concentration for Hf is 0.05 at. %). Even in these minute concentrations, REs are very effective in slowing down TGO growth and preventing spallation. They also change the morphology of the TGO layer so that a dense columnar structure is obtained. By contrast, the previously discussed Pt additions do not have any effect on TGO growth rates or morphology (11). The only comprehensive theory explaining the RE effect is the dynamic segregation theory put forward by Pint in 1996, who proposed that the REs diffuse outward due to the oxygen potential gradient and segregate to the metal-oxide interface and alumina grain boundaries (GBs) in the TGO where they block movement of cations and thus inhibit the outward diffusion of Al³⁺ cations resulting in growth predominantly by the inward diffusion of O^2- anions (12). Even though this theory is consistent with experimental observations, it is at present unresolved how the RE blocking works on the atomic scale. It is also relevant to understand which property exactly characterizes a good RE addition, both to understand the selection of present REs and to obtain previously undescribed ideas for other possible additions.

These observations lead to a number of open questions that lend themselves to examination by theory.

• Can quantum-mechanical simulations give an explanation as to why TBCs primarily fail at the TGO/BC interface? How does this failure relate to materials properties on the atomic scale?

• Concerning the deleterious effect of S impurities, can this be understood in terms of interface adhesion on the atomic scale? How does S modify the chemical interactions at the TGO/BC interface?

• Regarding the influence of the Pt additive in the bond coat alloy, what are the effects on the atomic scale in terms of adhesion of the TGO/BC interface and on diffusion processes in the NiAl BC alloy? Why does Pt not have any influence on the growth rate or morphology of the TGO?

• Can we understand how the REs inhibit Al diffusion along GBs in the α-Al₂O₃ (TGO) layer? Which properties of Hf, Y, and Zr cause this effect, and why do they not also prevent O diffusion?

• By distilling the key properties needed for the different TBC layers, can we suggest alternative materials or additives for any of the components, or at least some general search strategies?

In what follows, all the questions posed above are answered to varying extents via use of quantum-mechanics-based materials simulations. To address these questions, it is necessary to build sufficiently representative and at the same time computationally tractable models. Although this is a standard procedure for bulk crystal and surface models, more choices have to be made for interfaces and GBs, as discussed in SI Text.

Results and Discussion

To elucidate atomic-scale determinants of interface strength and TGO growth and creep mechanisms, work in the Carter group approached TBCs from different angles, by characterizing bonding and adhesion of TBC interfaces, segregation and diffusion at interfaces, and bulk diffusion in the BC.

Clean TBC Interfaces.

Early on we evaluated the work of separation (W_sep) for bulk zirconia phases (13) and α-Al₂O₃ (14), as well as for models of the relevant heterogeneous interfaces, YSZ/TGO (15) and TGO/BC (16, 17). This series of calculations quantified that the weak links are the interfaces, with the latter being weakest of all. Specifically, the overall stability of the multilayered TBC is controlled by the strength of the TGO/BC (α-Al₂O₃/NiAl) interface, consistent with postmortem electron microscopy studies that show voids and initial delamination preferentially occurring at this interface (3). In particular, the ZrO₂/α-Al₂O₃ interface was predicted to be roughly twice as strong as the α-Al₂O₃/Ni alloy interface (W_sep = 1.2 J/m² versus 0.5–0.7 J/m², respectively). Local density of states (LDOS) and electron density difference analyses revealed that these trends could be attributed to the highly ionic character of α-Al₂O₃ and the resulting closed-shell nature of the O anions. Electron pair repulsions between the nearly filled 2p shell of the O anions and the nearly filled 3d shell of the Ni atoms are responsible for the very weak adhesion at the TGO/BC interface. In fact, the only useful cross-interface bonding was found to involve metal–metal interactions between the Ni in the BC and the Al cations in the TGO (17). The oxygen anions only destabilized the interface. By contrast, the LDOS of ZrO₂ show significant 4d occupation, which suggests that the O anions in zirconia are more like O^- than O^2-, i.e., the oxygen atoms have a partially open 2p shell that permits covalent bonding at interfaces (15). YSZ/Ni superalloy interfaces were also modeled (18); the more covalent zirconia indeed formed stronger bonds to Ni (W_sep ∼ 1 J/m²) than the ionic alumina. However, repulsions between the nearly filled 3d shell of the Ni atoms and the ZrO₂ O anions reduced the zirconia/nickel adhesive strength relative to the zirconia/alumina interface.

Identifying the key reason for weak TGO/BC interface adhesion to be the nearly closed-shell natures of Ni atoms and O anions allowed us to propose a strategy for increasing interfacial adhesion and thereby TBC lifetime: either by increasing covalency of the TGO so as to reduce oxygen anion repulsions with Ni or by adding early transition metals with open d shells that can form strong bonds to the O anions (19) of alumina. These hypotheses are evaluated in what follows.

Improving Interface Adhesion: A Covalent Thermally Grown Oxide.

To test the first proposed strategy that a more covalent oxide might improve adhesion to the metal substrate, we considered replacing the alumina TGO with silica, because it is much less ionic and has a similar (though not as robust) propensity to limit bulk oxygen diffusion. The YSZ/TGO and TGO/BC interfaces were modeled by the ZrO₂(111)/α-SiO₂(0001) and α-SiO₂(001)/Ni(111) interfaces, respectively (20). The adhesion of the ZrO₂/α-SiO₂ interface was predicted to be about twice as strong (W_sep ∼ 2.5 J/m²) as the ZrO₂/α-Al₂O₃ interface (W_sep ∼ 1.2 J/m²), consistent with our hypothesis. The increased adhesion is due to polar-covalent cross-interface bonds that increase local coordination around the Si and Zr atoms at the interface. Likewise, much stronger adhesion was predicted for the silica/Ni interface compared to alumina/Ni. The polar-covalent O-Ni bonds formed at the interface led to three times stronger adhesion of silica to Ni (W_sep ∼ 1.4 J/m²) compared to alumina on Ni (W_sep ∼ 0.5 J/m²). These results led us to suggest that silica might be worth considering as an alternative, mechanically more robust, oxidation barrier layer to replace alumina in the TBC. Because the formation energy of alumina is lower than that of silica, it would not be possible to increase adhesion by forming a layer of silica underneath alumina. Formation of silica as the TGO could be achieved by adding Si to the bond coat alloy in line with previous work (21). However, at high temperatures and in the presence of impurities or water, silica can become volatile or fracture as well as become more penetrable to oxygen, which would limit its use unless the YSZ topcoat affords sufficient thermal and chemical protection.

With this many caveats, it behooves us to move on to the second suggested strategy, namely to use early transition metals to enhance the adhesion of alumina, because it survives until very high temperatures in its crystalline form without degradation of its oxidation barrier capability.

Improving Interface Adhesion: Transition Metal Additives.

Our earliest work looked at the effect of various early transition metal additives on the adhesion of the α-Al₂O₃(0001)/Ni(111) interface as a model of the TGO/BC interface (22–24). Again, our idea was to promote open-shell/covalent interactions across interfaces to enhance bonding and hence TBC adhesion. Our calculations confirmed this hypothesis. Adhesion with 0.5 monolayer (ML) of Si, Sc, Y, Ti, or Zr dopants was compared to adhesion with a 0.5 ML of Ni or Al “dopant” at the α-Al₂O₃(0001)/Ni(111) interface. Sc, Y, Ti, and Zr all caused a very large increase in adhesion of approximately 70–100% relative to Ni, whereas Si and Al decreased adhesion by approximately 20–30%. The open d-shell nature of the early transition metals allows donor–acceptor bonding between oxide ions and the transition metal dopant atoms to flourish (19) along with O 2p-metal 3d covalent bonds. The strong donor–acceptor bonds coupled with the lack of closed-shell repulsions characteristic of the undoped interface produces a much stronger interface. Ti and Zr are known to help extend the lifetimes of TBCs (25, 26); the enhanced adhesion we found in these studies likely contributes to delaying spallation.

Although unexamined in our early studies of the α-Al₂O₃(0001)/Ni(111) interface (22–24), given that Hf lies beneath Ti and Zr in the periodic table, it was clear to us then that Hf should exhibit similarly enhanced adhesion for precisely the same reasons. Later on, we explicitly proved this to be so by examining the influence of Hf at a more realistic TGO/BC interface model in which the BC was modeled by β-NiAl rather than pure Ni (Fig. 2). The effect of Hf on the α-Al₂O₃(0001)/β-NiAl(110) interface is astonishingly large: The adhesion energy increases by more than a factor of three, from 0.66 J/m² for the clean interface to 2.06 J/m² for the doped interface, even with only 0.1 ML Hf present (17). This enhanced adhesion due to Hf was confirmed later by Jiang et al. for a model of the γ-Ni(Al)/α-Al₂O₃ interface (27), despite their model being more appropriate for a supported catalyst than a TBC (by adopting the lattice vectors of an alumina substrate). Our electronic structure analysis of the α-Al₂O₃(0001)/β-NiAl(110) interface revealed that Hf forms four mixed polar-covalent/donor–acceptor bonds to oxygen ions at the alumina surface, the origin of its tremendously strong adhesion. At the same time, Hf remains bound to the Ni atoms of the NiAl BC alloy and does not disrupt other cross-interface Ni-Al bonds. Thus, one role for Hf in TBCs is indeed a direct and dramatic increase in the intrinsic adhesive strength of the TGO-bond coat alloy interface. It also explains why Hf seems to be a preferred additive over Ti or Zr, because the improvement in adhesion is most pronounced with Hf.

Fig. 2.

Structure of the (A) clean, (B) S-doped, and (C) Hf-doped α-Al₂O₃(0001)/NiAl(110) interfaces (17). The atoms shown are Ni (blue), Al (gray), O (red), S (yellow), and Hf (cyan).

Because Pt additions to the BC improve TBC lifetime, we also examined Pt atoms placed at the α-Al₂O₃(0001)/β-NiAl(110) interface as either a substitute for Ni in NiAl or as an interstitial dopant. At 0.1 ML Pt, the work of separation hardly changed compared to the clean interface (W_sep = 0.53 J/m²) upon addition of Pt in either position. We therefore concluded that Pt does not directly increase interface adhesion. Its beneficial role must involve affecting other processes, possibly modifying diffusion processes in the TBC or preventing S segregation to the interface (17). In retrospect, and based on our earlier insights about why the alumina/Ni interface is weak, it seems obvious that Pt should not improve TBC adhesion directly: It has a nearly filled d shell like Ni and therefore cannot form strong bonds to oxygen.

Decoupling the Effect of S, Hf, and Pt on Interface Adhesion.

Sulfur is an unavoidable coating contaminant known to be detrimental to TBC adhesion. With only 0.1 ML of S present at the α-Al₂O₃(0001)/β-NiAl(110) interface (Fig. 2), the adhesion energy drops precipitously (W_sep ∼ 0.18 J/m²) (17), confirming similar findings by Zhang et al. (28) for an Ni(111)/Al₂O₃ interface. This direct and dramatic decrease in adhesion is due to electron-pair–electron-pair repulsions between S atoms and O^2- ions in alumina, which prevent formation of covalent bonds across the interface (17). The weakened adhesion and a spatial gap that develops at the interface helps explain Auger electron spectroscopy and electron microscopy measurements on TBCs that find S present near voids between the bond coat alloy and the oxide. The elongated, weakened bonds across the S-containing metal/oxide interface and apparent S-O repulsion induce the oxide and metal to separate. These findings provide a detailed understanding of how S accelerates TBC spallation.

The ideal additive binds strongly to both the TGO and the BC and in this way increases the adhesion between them. Separating the binding of the representative elements of interest (e.g., Hf, Pt, and S) to the BC from their bonds to the TGO can tell us exactly why they improve (or reduce, in the case of S) adhesion: Is it because they increase binding to the BC, to the TGO, or to both? To answer this question, we compared the interface results above to our theoretical studies of adsorption of these atoms on the NiAl(110) surface (29) and on the α-Al₂O₃(0001) surface (30). On the NiAl(110) surface, Hf, Pt, and S display quite similar binding energies of 4.91 eV for S, 5.30 eV for Pt, and 5.00 eV for Hf. On the α-Al₂O₃(0001) surface, the adsorbate binding energies differed more strongly: 1.78 eV for S, 2.02 eV for Pt, and 3.52 eV for Hf. S and Pt are relatively electronegative, but not nearly as electronegative as O, whereas Hf is quite electropositive. The electronegativity of S and Pt is the origin behind their weak bonds to alumina; they both prefer to reside in the metal as a result. By contrast, Hf transfers electrons to alumina and subsequently forms multiple strong polar-covalent/donor–acceptor metal–oxygen bonds. Thus, relative binding to the TGO is the deciding factor for interface adhesion; although all elements bind strongly to the BC, only Hf has strong interactions with the TGO.

Some general conclusions about oxide-metal adhesion can be reached from these interface studies. Prior to our work, one conventional model of metal-oxide adhesion was a purely classical electrostatic one (31), in which the ionic oxide polarized the metallic conductor, with the consequence that more ionic oxides and/or thicker films should improve adhesion. However, our calculations showed that the opposite is also possible: More covalent oxides can form stronger bonds to metals and thicker films can actually weaken adhesion. What determines the adhesion strength are the local interactions at the interface, either closed-shell repulsions that weaken interfacial bonding or local polar-covalent/donor–acceptor interactions that strengthen interfacial adhesion.

Adsorption and Diffusion on the α-Al₂O₃(0001) Surface.

Having investigated the interface adhesion of all relevant interfaces in the TBC, we move to consider the transport of Al, O, and dopant species in the TGO. To fully elucidate the effect of REs on diffusion of Al and O along the alumina GBs in the TGO, calculation of diffusion pathways of these elements at a number of different GBs sufficiently representative for the real TGO would have to be carried out. This is not possible with present-day computational methods and resources, but here we demonstrate the insights one can glean from simpler models.

As a baseline point of comparison for future GB diffusion studies, we chose the basal plane of alumina, i.e., the α-Al₂O₃(0001) surface, on which to examine adsorption (30) and diffusion (32) of Al, O, Hf, Y, Pt, and S. The electropositive metals Al, Y, and Hf all adsorb on the same threefold hollow site, namely the site where the next Al ion would be if the bulk crystal continued. This is also the place one would intuitively place an adsorbate that donates electrons. Upon adsorption, the neutral metal adatoms transfer electrons to neighboring Al ions on the surface and become ions themselves Al → Al⁺, Hf → Hf³⁺, and Y → Y^2+ to 3+. The extent of charge transfer correlates with bond strengths (Hf(4.27 eV) > Y(3.90 eV) > Al(2.31 eV)), suggesting that the partially ionized metal adatoms then experience back donation from nearest-neighbor O anion lone pairs, with the strength of those interactions directly proportional to the extent of ionization. Because Hf and Y bind more strongly than Al, from a thermodynamic standpoint Hf and Y can displace Al from its adsorption site and thereby act as site blockers. We also find that Al, Hf, and Y diffuse via almost the same pathway across the surface; all metal cations may prefer this pathway that allows their positive charge to be screened as much as possible by the close-packed layer of oxygen underneath them. As with charge transfer and binding energy trends, Hf (2.29 eV) and Y (1.03 eV) have higher diffusion barriers than Al (0.71 eV). Since the preexponential factors for all three are similar, the calculated diffusivities for Hf and Y are several orders of magnitude lower than for Al. The increase in diffusion barrier from Al to Y to Hf originates in the required breaking and forming of increasingly strong bonds as the atom diffuses. Thus, this work provides insight on the mechanism by which Hf and Y slow TGO growth; namely to inhibit Al diffusion by moving more slowly and blocking sites through which Al would be expected to diffuse. Again, it is their open-shell d electrons that render Hf and Y efficient site and diffusion blockers for Al transport because they form strong bonds to the alumina surface. This suggests that, apart from those metal cations (e.g., Ti and Sc), which are small and therefore mobile in alumina (33), many early transition metals will be effective at slowing alumina growth by inhibiting aluminum ion diffusion.

By contrast with the metal cations, oxygen adsorbs on top of a surface oxygen ion with a binding energy of 2.18 eV, forming a peroxide ion () via a covalent bond. Oxygen diffusion involves a barrier of 1.69 eV, more than twice as high as for Al diffusion, because the peroxide bond must nearly break completely in order for O to diffuse. Therefore, O diffusion on the alumina surface is much slower than Al diffusion. Additionally, the diffusion pathways of Al and O are quite different, thereby allowing both Al and O to diffuse simultaneously. This also explains why Hf and Y are neither site nor path blockers for O diffusion, as O both adsorbs on a different site and diffuses along a different pathway than the metal cations.

Pt adsorbs on the same site as O with about the same strength (2.02 eV) and follows the same diffusion pathway as O but diffuses with a very low overall barrier (0.66 eV). Thus Pt cannot act as a site or diffusion path blocker for Al because it does not adsorb or diffuse on the same path. Even though the diffusion pathways for O and Pt coincide, Pt diffuses much faster than O and therefore will not inhibit its diffusion. Furthermore, Pt binds much more strongly to NiAl than to alumina, indicating that Pt would prefer to remain in NiAl and not diffuse into alumina (30). Our findings that Pt diffuses easily on alumina and prefers to stay in NiAl are consistent with observations that Pt does not affect alumina growth kinetics or morphology (11) and that Pt is not found at alumina GBs (34).

Sulfur interacts most weakly with the basal plane of alumina, preferring the same site as Pt and O, with little charge transfer occurring. The fact that Pt binds on the same site as S, but more strongly, suggests that one role for Pt may be to displace and/or block S from segregating to the interface, thereby mitigating the latter’s harmful effects.

Structure, Ion Segregation, and Creep of the Σ11 Tilt Alumina GB.

Although the α-Al₂O₃(0001) surface model delivered useful insights, an actual GB model would be more representative of the alumina polycrystal that grows during operation. Of the many GBs formed in α-Al₂O₃, we chose the Σ11 tilt GB—the subject of previous experimental (35) and theoretical (36–38) work—to test our findings. A detailed scan of possible translations parallel to the GB interface revealed a previously undescribed structure (39) for the clean GB that is lower in energy than previously proposed structures based on transmission electron microscope (TEM) data and classical potential simulations (36).

TEM and energy-dispersive X-ray (EDX) maps have shown that REs segregate to α-Al₂O₃ GBs (12, 40–42). To study ion segregation, we identified the most stable adsorption sites for Al, O, Y, and Hf atoms (Fig. 3) at our model GB, again by screening many adsorption sites at the global minimum GB structure, followed by structural relaxation of the lowest energy candidates (39). O adsorption sites were spread evenly across the unit cell but varied significantly in energy, suggesting that some high-energy (4–5 eV) structures might need to be accessed during O diffusion. Likewise, Al adsorption sites were spread fairly uniformly but with an energy range 1–2 eV smaller, perhaps indicative of smaller diffusion barriers. We found it is thermodynamically favorable for both Y and Hf to segregate to the GB interface rather than substitute for Al cations in bulk alumina, consistent with TEM and EDX measurements. However, fewer Hf than Y atoms are accommodated at the GB interface, thereby validating previously proposed (43) relationships between covalent radius and tendency to segregate. As expected from their similar cationic character, Y and Hf adsorption sites overlap strongly with those of Al. The relative energies of these sites ranged up to approximately 7 eV, much higher than for Al, suggesting that barriers for Hf and Y diffusion along the GB probably also are much higher than for Al (39).

Fig. 3.

Comparison of adsorption sites of Al (blue), O (red), Y (pink), and Hf (green) on the interface plane of a Σ11 alumina grain boundary (39) with aluminum (small gray spheres) and oxygen (large grayish-white spheres). (Left) Side view and (Right) top view. For easier viewing, the top part of the grain boundary has been removed in the top view (Right).

Our detailed predictions (39) are consistent with the outlines given in the dynamic segregation theory of Pint et al. (12) The adsorption sites for Hf and Y are very similar to those for Al, thereby explaining the inhibition of Al diffusion. Although only minute concentrations are added to the bond coat alloy, when Y and Hf segregate to GBs they are present in locally high concentrations that very effectively block Al diffusion along GBs. And as O adsorption sites do not all overlap with the ones for the REs, their diffusion pathways could be different, which explains the limited effect that some REs have on O diffusion rates. In contrast to the 2–3× reduction in oxide growth due to Y doping, experiments have shown that Hf decreases oxide growth by a factor of ten, suggesting that Hf also has some effect on O transport (44). Interestingly, large metal cation dopants such as Zr, Sr, and Lu were also observed to inhibit high-temperature creep deformation of polycrystalline alumina (42); as one mechanism of creep (Coble creep) involves atom/ion diffusion, this finding is consistent with our predictions that such large metal cations inhibit Al diffusion.

We also investigated the influence of a variety of metal additives on alumina GB sliding (45), which is another mode of high-temperature creep that can destabilize the TGO/BC interface by increasing tensile stress. It is known from experiment that early transition metal dopants increase creep activation energies (40, 42, 46). We identified minimum and maximum energy structures along the preferred sliding pathway for the pristine GB and for GBs doped with a series of early transition metals, as well as with barium (Ba), gadolinium, and neodymium. The presence of these dopants greatly increases the GB sliding barrier, again because of the strong, multiple bonds formed between them and the oxide ions in alumina. GB sliding occurs by a series of bond breaking and forming events across the GB. The presence of large cations inhibits the regeneration of metal–oxygen bonds during sliding, thereby raising the barrier to sliding. Trends in predicted GB sliding energies are in good agreement with recently measured creep activation energies in polycrystalline alumina (40, 47, 48), lending further credence to the notion that GB sliding plays a dominant role in alumina creep. Moreover, we found that Ba—an element not found in current bond coat alloys (33)—provided the best alumina creep inhibition of all (39).

Ni and Al Defect Formation and Diffusion in the NiAl Bond Coat Alloy.

As discussed earlier, Pt has been added to the BC for decades, because it lengthens TBC lifetime. However, the mechanism by which this benefit is achieved remains unclear despite a multitude of measurements trying to discern it (7). Because Pt does not affect the oxidation kinetics of the TGO, the mechanism by which Pt benefits TBC lifetime has been suggested to be different than that of REs (11). Above we discussed that Pt at the α-Al₂O₃/NiAl(110) interface does not directly strengthen adhesion of the oxide to the metal, that Pt prefers to stay in NiAl because it only weakly interacts with alumina, and that its fast diffusion on alumina renders it incapable of inhibiting Al or O ion diffusion needed to slow TGO growth. As such, we began to examine whether the main role of Pt (in addition to inhibiting S segregation discussed above) is to affect the high-temperature evolution of the NiAl BC alloy, such as the diffusion kinetics of Al and Ni in NiAl.

The idea that Pt enhances Al diffusion in NiCrAl alloys was suggested in 1976 by Felten (49) and more recently in NiAl alloys by Gleeson et al. (10). Svensson et al. (9) inferred that Al diffusion in NiAl accelerated upon Pt additions from the observation of reduced void formation at the α-Al₂O₃/NiAl interface. This concept would be consistent with experimental evidence showing that Pt prevents the formation of Ni-rich oxides on NiAl alloys with Al levels low enough that they form on the pure alloy (11). Alumina preferentially forms on NiAl as long as the level of Al in the alloy is high enough, but once the level of Al is too low, brittle, fast-growing Ni-rich oxides begin to form, hastening failure of the coatings. If Pt were to enhance Al diffusion to the interface, it would ensure a high enough local Al concentration to keep forming alumina.

Because Ni and Al diffusion in NiAl must occur via lattice vacancies due to the large size of both elements, we first explored Pt’s effect on forming key defects central to a number of postulated mechanisms for Ni and Al diffusion through NiAl (50). NiAl has a CsCl structure, which consists of two interpenetrating simple cubic lattices of Ni and Al. Four types of point defects can form in NiAl to accommodate deviations from stoichiometry: Ni and Al vacancies (V_Ni, V_Al), Ni antisites (Ni on the Al sublattice, Ni_Aland Al antisites (Al on the Ni sublattice, Al_Ni) (51). Our predicted formation energies for these defects (V_Ni: 0.41 eV, V_Al: 1.87 eV, Ni_Al: 1.02 eV, and Al_Ni: 1.61 eV) are consistent with experimental evidence that Ni antisite atoms form in Ni-rich NiAl rather than Al vacancies, and Ni vacancies form in the Al-rich alloy instead of Al antisites. The predicted defect formation energy for a Pt atom residing on either the Ni or Al sublattices shows that Pt strongly prefers the Ni sublattice, consistent with it being isovalent with Ni. The effect of Pt on the stability of each point defect was determined by placing a Pt atom in the closest Ni site to the defect, to quantify its maximal influence. In all cases, Pt promotes formation of these defects, as evidenced by significant decreases in their formation energies (V_Ni:  - 0.23 eV, V_Al: 1.09 eV, Ni_Al: 0.50 eV, and Al_Ni: 1.06 eV), suggesting repulsive interactions between Pt and Ni or Al (50). Indeed, density difference plots (Fig. 4) reveal an increase in electron density around the Pt atom such that a s²d⁹-like Pt anion is formed, due to its higher electronegativity (52). In turn, the more diffuse Pt anion destabilizes nearby Ni and Al atoms, favoring Ni vacancy formation in particular.

Fig. 4.

Contour plots of density differences between undoped and 1.9 at. % Pt-doped bulk NiAl showing (001) and (101) planes (52). The (001) plane (A) contains only Ni atoms and the Pt atom, whereas the (101) plane in B contains Ni atoms, Al atoms, and the Pt atom. The atomic positions are indicated on the plane. The legend limits represent ± 5% change from a uniform electron density containing the same number of electrons in the same volume. The plots were created using VESTA (68).

Although radioactive tracer experiments have determined the diffusivity of Ni in NiAl (53), none have been performed for Al diffusion due to the lack of a suitable radioactive isotope. Numerous computational (e.g., 53) studies have been unable to concretely determine the dominant mechanism of Ni diffusion in stoichiometric NiAl. Although the ultimate goal was to model a BC alloy, which is typically Ni-rich, we began by examining five proposed mechanisms in pure stoichiometric NiAl: next-nearest-neighbor (NNN) jumps, the triple defect mechanism, and three variants of the six-jump cycle (54). By comparing our calculated preexponential factors and activation energies with experimental data (D₀ ∼ 3 × 10^-5 m²/s; Q ∼ 3 eV) (53), we concluded that the triple defect mechanism and the six-jump cycle in the [110] direction were viable pathways for Ni diffusion in pure NiAl. The two variants of the six-jump cycle in the [100] direction had activation energies above 4 eV, leading us to conclude they do not contribute to Ni diffusion. Although the calculated activation energy of a NNN Ni jump was approximately 3.0 eV (54), this jump was excluded based on experimental results (53).

Although the triple defect mechanism leads to long-range propagation of Ni and Al atoms (in opposite directions), NNN Ni jumps and the six-jump cycle do not lead to long-range Al diffusion. Because NiAl is symmetric, we proposed analogous mechanisms to the Ni diffusion mechanisms that could lead to propagation of Al atoms (55). Because both mechanisms start with a Ni vacancy defect, we examined the NNN Al jumps and the six-jump cycle starting with an Al vacancy. Although the activation energy of the NNN Al jump was calculated to be 3.1 eV, the lack of Al vacancies in the alloy suggests that NNN Al jumps will not contribute to Al diffusion. The calculated activation energies for the three six-jump cycles starting with an Al vacancy ranged from 3.3 to 4 eV. Because the activation energy of the triple defect mechanism was only 3 eV (55), we concluded that both Ni and Al diffuse via the triple defect mechanism in stoichiometric NiAl.

Isotope experiments show that Ni diffusion is enhanced in Ni-rich NiAl (53) and the antistructure bridge (ASB) mechanism (56) has been proposed to account for it. Here Ni atoms are suggested to diffuse via bridges formed by Ni antisite atoms, which as noted earlier are the constitutional defects in Ni-rich NiAl. For Ni concentrations slightly above 50%, the ASB mechanism will lead only to a local enhancement, but for alloys with a high enough concentration of Ni, a percolation threshold of Ni antisite atoms is reached, and the ASB mechanism could contribute to long-range Ni diffusion (53). We predicted that the ASB mechanism is indeed viable for Ni diffusion in Ni-rich NiAl, with a smaller activation energy (approximately 2.2–2.3 eV compared to 3 eV in stoichiometric NiAl), depending on the direction of overall atomic motion (57). Although our model alloy was only 53 at. % Ni, the calculated barriers were in excellent agreement with the observed activation energy of approximately 2.4 eV in a 56.6 at. % Ni alloy (53). (A percolation threshold of approximately 55 at. % Ni (53) must be reached for the ASB mechanism to contribute to long-range Ni diffusion and hence be quantifiable experimentally.)

To study the maximum effect of Pt on the five diffusion mechanisms for Ni diffusion in stoichiometric NiAl and the ASB mechanism for Ni diffusion in the Ni-rich alloy, a Pt atom was placed in the Ni site in closest proximity to the defect clusters involved in the mechanisms. As in the case of the point defects discussed above, Pt greatly stabilized all defect cluster intermediates. By contrast, in all cases Pt had little effect on the calculated preexponential factors and migration energies (within 0.1 eV of those in pure NiAl). However, the substantial decreases in the defect formation energies produce large increases in the diffusion rate because these energies appear in the exponential of the diffusion coefficient. Therefore, Pt enhances Ni and Al diffusion by stabilizing the point defects and defect clusters that are intermediate minima along the diffusion pathways (52, 55, 57).

As Pt increases the rate of Al and Ni diffusion in NiAl, it likely increases the rate of Al diffusion to the interface. Experiments have shown when NiAl is oxidized, Al diffuses toward the surface and Ni diffuses away from the surface (58). From our results, we can conclude that one mechanism by which Pt promotes TBC lifetime is by keeping the concentration of Al at the interface high enough to prevent the formation of brittle, Ni-rich oxides, which are more prone to spallation than alumina.

Conclusions

First principles quantum mechanics simulations of atomic-scale mechanisms by which turbine engine TBCs fail has led to fundamental discoveries as to how and why certain additives (Hf, Y, Pt, etc.) in the coatings improve stability, and ultimately to suggestions for how to improve these high-temperature coatings that protect turbine engine components vital for electricity production and transportation. The key findings follow:

• The weakest link in the TBC is the interface between the TGO comprised of α-Al₂O₃ and the underlying NiAl-based BC alloy due to poor cross-interfacial bonding.

• Sulfur impurities directly and seriously weaken that same interface due to strong repulsions between S and O electron pairs.

• Adding hafnium to the BC dramatically increases adhesion of the TGO to the BC alloy, by forming very strong Hf-O bonds. These strong bonds are formed because of Hf’s open d shell, which allows for both polar-covalent and donor-acceptor bonding to flourish. The improved adhesion is one mechanism by which Hf improves the TBC lifetime. Similar, though less dramatic, increases in TBC adhesion were found for other early transition metal additives such as Sc, Y, Ti, and Zr.

• Hf and Y readily segregate to oxide GBs and block sites along the Al diffusion pathway at oxide GBs, thereby slowing oxide growth. Oxide growth continues slowly because of oxygen anion diffusion that can proceed via a different pathway. By delaying oxide growth, the strain energy of the growing oxide is minimized, extending TBC lifetime.

• Hf and Y (or any early transition metal, rare earth, and even some alkaline earth) additives increase barriers to alumina GB sliding because of their strong cross-boundary bonds to oxygen. These predictions were validated by comparison with high-temperature creep measurements in polycrystalline alumina (GB sliding is a key mechanism in creep). By inhibiting GB sliding, these additives act to limit the tensile stress perpendicular to the TGO/BC interface, delaying spallation of the coating.

• Platinum additives do not directly increase TGO/BC adhesion nor does Pt inhibit diffusion in the oxide; Pt would rather stay in the NiAl BC than be found in the alumina (the TGO). This latter finding is consistent with observed growth kinetics and morphology of the TGO, both of which are unaffected by the presence of Pt. Some evidence is provided that Pt may prevent S from getting to the TGO/BC interface by blocking the sites S prefers.

• Pt’s main role is to promote point defect (vacancies and antisite atoms) and defect cluster formation in NiAl. By so doing, Pt greatly accelerates Ni and Al diffusion in NiAl, primarily by means of the triple defect mechanism, and in Ni-rich BCs, also by the antistructure bridge mechanism. The predicted diffusivities are much larger in the presence of just a few percent Pt. By accelerating Ni and Al diffusion, Al atoms are kept in high concentration at the interface between the NiAl BC alloy and the TGO, even in Ni-rich NiAl alloys. By keeping the local Al concentration high, the TGO is comprised only of alumina, rather than Ni aluminate spinel. The latter is fast growing and less adherent; inhibition of its formation prevents rapid failure of the coating.

The precise roles of Hf and other reactive elements, as well as that of Pt, were not known prior to this work. Although other roles for these elements may be discovered in ensuing studies, the key roles that these additives play have finally been elucidated. Moreover, analysis of electron distributions in these materials led to basic insights into why Hf, for example, is so effective, and led to the exploration of a variety of elements not all of which are present in current bond coat alloy formulations. As a result, it was discovered that Ba is extraordinarily effective at inhibiting GB sliding, due to its ability to form many bonds to oxygen anions at alumina GBs. We anticipate that Ba could be a useful additive to consider in future BC formulations.

Finally, by delving into the nature of the chemical bonds in this complex multicomponent coating, we leave the reader with two general principles that may prove useful for materials design beyond the present subject of TBCs:

• To improve adhesion, reduce creep, slow diffusion and hence growth, add elements that strengthen chemical bonds at interfaces. For oxides, these will be early transition metals, rare earths, or alkaline earths that form strong bonds to oxygen.

• To accelerate vacancy-mediated diffusion, add isoelectronic but more electronegative elements that withdraw electrons; the resultant anion repels neighbors that will enhance vacancy formation and hence transport.

Computational Methods

Many simulation methods based on quantum mechanics exist (59); here we primarily used Kohn–Sham density functional theory (DFT) (60, 61) as implemented in the CASTEP (62) and VASP (63, 64) codes. DFT is advantageous because it permits use of periodic boundary conditions to simulate large crystals while usually providing a good balance between accuracy and computational expense (59). Because its exact expression is unknown except in certain simple limits, the DFT electron exchange–correlation functional must be approximated. For most of the results discussed here, the Perdew–Wang (65) and closely related Perdew–Burke–Ernzerhof (66, 67) exchange–correlation functionals within the generalized gradient approximation (GGA) were used, because DFT-GGA generally provides accurate structures and energetics for the materials classes considered here. Apart from these general issues, choices for a number of parameters have to be made, and these are documented in more detail in the original references. Further methodological details are given in SI Text.