Atomic-scale insight and design principles for turbineengine thermal barrier coatings from theoryKristen A. Marino1, Berit Hinnemann2, and Emily A. Carter3

Department of Mechanical and Aerospace Engineering, Program in Applied and Computational Mathematics, and Andlinger Center for Energy and theEnvironment, Princeton University, Princeton, NJ 08544-5263

This contribution is part of the special series of Inaugural Articles by members of the National Academy of Sciences elected in 2008.

Contributed by Emily A. Carter, February 11, 2011 (sent for review December 21, 2010)

To maximize energy efficiency, gas turbine engines used in air-planes and for power generation operate at very high tempera-tures, even above the melting point of the metal alloys fromwhich they are comprised. This feat is accomplished in part viathe deposition of a multilayer, multicomponent thermal barriercoating (TBC), which lasts up to approximately 40,000 h beforefailing. Understanding failure mechanisms can aid in designing cir-cumvention strategies. We review results of quantum mechanicscalculations used to test hypotheses about impurities that harmTBCs and transition metal (TM) additives that render TBCs morerobust. In particular, we discovered a number of roles that Pt andearly TMs such as Hf and Y additives play in extending the life-time of TBCs. Fundamental insight into the nature of the bondingcreated by such additives and its effect on high-temperature evo-lution of the TBCs led to design principles that can be used to creatematerials for even more efficient engines.

Aircraft and power plants share a common source of usableenergy: Both employ turbine engines that combust fuel to

either propel airplanes or produce electricity. At a time in whichefficient use of energy is paramount, improving the efficiency ofturbine engines is one means to contribute to this global chal-lenge. Turbine engines operate via the Brayton cycle, which offerslower carbon dioxide emissions and lower cost for power genera-tion than other possible alternatives. Their efficiency can be in-creased by increasing the inlet temperature, which allows moreexpansion of gas that creates more pressure to drive the turbine.However, high-temperature operation, under oxidizing condi-tions, poses serious demands on the materials used to constructjet engine components. Materials must be found that are robustunder such harsh operating conditions. Engineers over the pastfew decades have improved greatly the thermomechanical prop-erties of the metal alloy comprising, e.g., the turbine blades, andhave created a multilayer coating for the blades that protectsagainst both heat and corrosion, referred to as a thermal barriercoating (TBC). These materials advances, along with internalcomponent cooling, have been astonishingly successful, allowingthe gas temperature to exceed the melting point of the metal alloyfrom which the engine components are constructed!

Despite these advances, more robust TBCs are desired, eitherto extend TBC service lifetime under present-day operatingconditions or to operate at even higher temperatures to achievemore efficient energy conversion. As a result, characterizationand optimization of TBC properties have continued to be activeareas of research. As is the case for most materials development,the usual path to improve TBCs relies on trial and error. Manymaterials compositions are fabricated, characterized, and tested.Unfortunately, characterization typically is performed postmor-tem, as virtually no instruments exist to characterize a TBC insitu during operation. The lack of in situ probes makes it difficultto establish structure-property relationships crucial for under-standing how TBCs evolve over time, how they fail, and ulti-mately how to delay failure. Moreover, characterization after

failure sees the sum of a multitude of effects that cannot be easilyseparated.

Given that these complexities cannot be disentangled bymeasurements, computer simulations offer an alternative routeto understanding, as long as the correct physics is contained inthe underlying model used for the material and phenomenonat hand. A distinct advantage of theoretical calculations is thatthe environmental conditions and material structure and compo-sition can be precisely controlled. This is in contrast to mostexperiments, in which materials often vary from laboratory tolaboratory due to manufacturing differences that produce differ-ent microstructures and impurity distributions. By contrast, com-puter simulations can separately investigate each process ofinterest in a well-characterized material, thereby allowing decon-volution of the plethora of atomic processes at work. Of course,the physical model used must be validated whenever possibleagainst available experimental data, in order to establish thecredibility of the simulations.

In this paper, we demonstrate how atomic-scale insight into thefunctionality of TBCs can be gleaned by employing quantum-mechanics-based computer simulations. This work has beencarried out in the Carter group over the past 15 y, with the initialaim of elucidating TBC failure mechanisms and how they relateto atomic-scale processes within different TBC layers. Once theorigins of failure were identified at the most fundamental level ofelectron distributions, basic concepts were extracted that wereused to propose and computationally test composition changesto coatings that would improve their high-temperature survivabil-ity. In what follows, we start by providing a brief summary ofcurrent knowledge about the composition of TBCs, their failuremechanisms, and the additives used to extend time to failure.We then formulate a list of questions, the answers to whichare essential to further understanding of TBCs and the factorsthat limit their lifetime. To varying degrees, answers to thesequestions are provided by insights gleaned from our computersimulations, which constitute the major focus of this review.

The Basics of Thermal Barrier CoatingsTurbine engine components are made of nickel (Ni)-based super-alloys, the microstructure and composition of which has beentailored to minimize deleterious changes at high temperature(e.g., creep). The idea of coating the metal parts with a materialwith low thermal conductivity has been around since the late1950s, and TBCs have been used since the 1980s, but it has been

Author contributions: K.A.M. and B.H. performed research; K.A.M., B.H., and E.A.C.analyzed data; K.A.M., B.H., and E.A.C. wrote the paper; E.A.C. designed research.

The authors declare no conflict of interest.1Present address: Department of Computational Chemistry and Physics, van’t HoffInstitute for Molecular Sciences, University of Amsterdam, Postbus 94157, 1090 GEAmsterdam, The Netherlands.

2Present address: Haldor Topsøe A/S, Nymøllevej 55, DK-2800 Kgs. Lyngby, Denmark.3To whom correspondence should be addressed. E-mail: eac@princeton.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1102426108/-/DCSupplemental.

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an ever-present challenge to make these coatings durable andprevent them from spalling (chipping off) after some time inoperation (1).

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

The YSZ layer is not deposited directly onto the Ni-basedsuperalloy. One reason for this is that YSZ is transparent to oxy-gen diffusion, and under operation, oxygen would diffuse to theinterface 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 superalloybefore deposition of the YSZ. Two different classes of BC alloysexist: approximately 100-μm-thick MCrAlY (where M ¼ Co orNi) alloys in use since the 1960s and approximately 40- to 60-μm-thick PtNi aluminides developed more recently that are moreoxidation 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 ofBCs ensure good adhesion and corrosion protection (2). The lat-ter protective action is provided by the third component of theTBC, discussed next.

During YSZ deposition and engine operation, a thin thermallygrown oxide (TGO) layer forms between the YSZ and the BClayers. This oxide growth is driven by oxygen diffusion throughthe YSZ and cannot be avoided at typical operating tempera-tures. Use of the PtNi aluminide BC composition ensures thatthe TGO is alumina, Al2O3. During the initial stage of TGO for-mation, transient, metastable alumina phases can appear, buteventually the dense α-Al2O3 is the prevailing phase. The idealTGO, α-Al2O3, exhibits the lowest oxygen mobility of all ther-mally grown oxides (4, 5), inhibiting further corrosion of the Nialloy and leading to very slow growth, which we will see is crucialto long TBC lifetimes. Oxidation of the MCrAlY BCs produces a

mixture of alumina and chromia, which is usually a less idealTGO. Although a thin, dense TGO layer is protective againstoxidative corrosion by slowing further oxygen diffusion throughthe TGO to the superalloy, the TGO layer continues to grow dur-ing operation, albeit very slowly, and a thickness beyond 10 μmgenerally causes failure of the TBC (2, 3).

Some failure mechanisms have already been mentioned, but anonexhaustive list of proposed failure modes is as follows: forma-tion of less-adherent, Ni-rich oxides due to depletion of Al inthe BC and subsequent spallation; stress-induced delaminationof the thickened TGO layer upon thermal cycling due to thermalexpansion mismatches between the TGO and BC; and failure dueto external events such as foreign object damage, hot corrosion, orerosion. Even though there are many different failure events andmechanisms, one prevailing observation is that failure mostlyoccurs at the TGO/BC interface, due to either the increased thick-ness of the TGO or the presence of interfacial voids and/or dele-terious impurities, especially sulfur (3). As the TGO thickens andundergoes thermal cycling, thermal expansion mismatch strainbuilds up; once the strain energy exceeds the interface strength,spallation occurs.Numerous studies havenoted that sulfur-contain-ing BCs spallmuchmore rapidly than desulfurizedBCs (6, 7). Thus,two key strategies may be adopted to delay TBC failure: inhibitTGO growth to prevent strain buildup arising from increasedTGO thickness and increase adhesion of the TGO to the BC.

Both inhibition of TGO growth and prevention of coatingdelamination have been achieved by doping BCs with reactiveelements (REs), typically early transition metals such as Hf, Y,and Zr. Even though these elements have been used for over70 y, a clear picture of how they improve TBC stability remainselusive. Along the same lines, even though Pt-containing bondcoats have been in use for 30 y, the exact role of Pt is not fullyunderstood either. A wealth of experimental data is available, butas mentioned already, it originates mostly from postmortemmeasurements, making it difficult to extract details about atomic-scale processes. In the following, we give a summary of the mainexperimental observations regarding Pt and REs and how theyare thought to improve TBC lifetime.

(Pt,Ni)Al BCs contain typically only 5 at. % Pt, but this issufficient to render the BC more sulfur-tolerant over a rangeof sulfur concentrations (1–7 ppma) and to prevent delaminationat the TGO/BC interface. The origin of this sulfur tolerance andimproved adhesion is still under discussion; it has been suggestedthat Pt may hinder S segregation to the interfaces, thereby pre-venting void formation and delamination (6, 7). Electron micro-scopy reveals that S is found at voids (8), though it is not knownwhether interfacial S causes void formation (or growth) orwhether S just migrates to the voids once they have formed. Adifferent hypothesis is that Pt may enhance the selective forma-tion of alumina instead of spinels during BC oxidation by enhan-cing Al diffusion (9, 10). The latter suggestion has been supportedby a very interesting study of the oxidation of a Ni-rich NiAl alloy,where it was found that Pt prevents formation of Ni-rich spineloxides even at Al compositions as low as 35 at. %, compositions atwhich those spinels would form easily in the absence of Pt (11).Theory can make a valuable contribution toward explaining theeffect of Pt, simply because the effect of Pt on TGO/BC interfaceadhesion and on diffusion in NiAl can be evaluated separately.

REs are employed at very low concentrations near their solu-bility limit (a typical concentration for Hf is 0.05 at. %). Even inthese minute concentrations, REs are very effective in slowingdown TGO growth and preventing spallation. They also changethe morphology of the TGO layer so that a dense columnar struc-ture is obtained. By contrast, the previously discussed Pt additionsdo not have any effect on TGO growth rates or morphology (11).The only comprehensive theory explaining the RE effect is thedynamic segregation theory put forward by Pint in 1996, who pro-posed that the REs diffuse outward due to the oxygen potential

Fig. 1. A schematic of the three layers of a thermal barrier coating on top ofa Ni-based superalloy turbine blade. After application of the (Ni,Pt)Al bondcoat (approximately 50 μm thick), the YSZ ceramic topcoat of approximately100-μm thickness is deposited. A thin (<10 μm micron) layer of α-Al2O3 formsin between the YSZ and BC during deposition and operation and is known asthe TGO.

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gradient and segregate to the metal-oxide interface and aluminagrain boundaries (GBs) in the TGO where they block movementof cations and thus inhibit the outward diffusion of Al3þ cationsresulting in growth predominantly by the inward diffusion of O2−

anions (12). Even though this theory is consistent with experi-mental observations, it is at present unresolved how the REblocking works on the atomic scale. It is also relevant to under-stand which property exactly characterizes a good RE addition,both to understand the selection of present REs and to obtainpreviously undescribed ideas for other possible additions.

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

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

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

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

• Can we understand how the REs inhibit Al diffusion along GBsin the α-Al2O3 (TGO) layer?Which properties ofHf, Y, andZrcause this effect, and why do they not also prevent O diffusion?

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

In what follows, all the questions posed above are answeredto varying extents via use of quantum-mechanics-based materialssimulations. To address these questions, it is necessary to buildsufficiently representative and at the same time computationallytractable models. Although this is a standard procedure for bulkcrystal and surface models, more choices have to be made forinterfaces and GBs, as discussed in SI Text.

Results and DiscussionTo elucidate atomic-scale determinants of interface strength andTGO growth and creep mechanisms, work in the Carter groupapproached TBCs from different angles, by characterizing bond-ing and adhesion of TBC interfaces, segregation and diffusion atinterfaces, 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 asfor models of the relevant heterogeneous interfaces, YSZ/TGO(15) and TGO/BC (16, 17). This series of calculations quantifiedthat the weak links are the interfaces, with the latter being weak-est of all. Specifically, the overall stability of the multilayeredTBC is controlled by the strength of the TGO/BC (α-Al2O3∕NiAl) interface, consistent with postmortem electron microscopystudies that show voids and initial delamination preferentiallyoccurring at this interface (3). In particular, the ZrO2∕α-Al2O3

interface was predicted to be roughly twice as strong as theα-Al2O3∕Ni alloy interface (W sep ¼ 1.2 J∕m2 versus 0.5–0.7 J∕m2, respectively). Local density of states (LDOS) and electrondensity difference analyses revealed that these trends could beattributed to the highly ionic character of α-Al2O3 and the result-ing closed-shell nature of the O anions. Electron pair repulsionsbetween the nearly filled 2p shell of the O anions and the nearlyfilled 3d shell of the Ni atoms are responsible for the very weakadhesion at the TGO/BC interface. In fact, the only useful cross-interface bonding was found to involve metal–metal interactionsbetween the Ni in the BC and the Al cations in the TGO (17). Theoxygen anions only destabilized the interface. By contrast, the

LDOS of ZrO2 show significant 4d occupation, which suggeststhat the O anions in zirconia are more like O− than O2−, i.e., theoxygen atoms have a partially open 2p shell that permits covalentbonding at interfaces (15). YSZ/Ni superalloy interfaces werealso modeled (18); the more covalent zirconia indeed formedstronger bonds to Ni (W sep ∼ 1 J∕m2) than the ionic alumina.However, repulsions between the nearly filled 3d shell of the Niatoms and the ZrO2 O anions reduced the zirconia/nickel adhe-sive strength relative to the zirconia/alumina interface.

Identifying the key reason for weak TGO/BC interface adhe-sion to be the nearly closed-shell natures of Ni atoms and Oanions allowed us to propose a strategy for increasing interfacialadhesion and thereby TBC lifetime: either by increasing cova-lency of the TGO so as to reduce oxygen anion repulsions withNi or by adding early transition metals with open d shells thatcan form strong bonds to the O anions (19) of alumina. Thesehypotheses are evaluated in what follows.

Improving Interface Adhesion: A Covalent Thermally Grown Oxide. Totest the first proposed strategy that a more covalent oxide mightimprove adhesion to the metal substrate, we considered replacingthe alumina TGO with silica, because it is much less ionic and hasa similar (though not as robust) propensity to limit bulk oxygendiffusion. The YSZ/TGO and TGO/BC interfaces were modeledby the ZrO2ð111Þ∕α-SiO2ð0001Þ and α-SiO2ð001Þ∕Nið111Þ inter-faces, respectively (20). The adhesion of the ZrO2∕α-SiO2 inter-face 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), consistentwith our hypothesis. The increased adhesion is due to polar-cova-lent cross-interface bonds that increase local coordination aroundthe Si and Zr atoms at the interface. Likewise, much strongeradhesion was predicted for the silica∕Ni interface comparedto alumina∕Ni. The polar-covalent O-Ni bonds formed at theinterface 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 worthconsidering as an alternative, mechanically more robust, oxida-tion barrier layer to replace alumina in the TBC. Because theformation energy of alumina is lower than that of silica, it wouldnot be possible to increase adhesion by forming a layer of silicaunderneath alumina. Formation of silica as the TGO could beachieved by adding Si to the bond coat alloy in line with previouswork (21). However, at high temperatures and in the presenceof impurities or water, silica can become volatile or fracture aswell as become more penetrable to oxygen, which would limitits use unless the YSZ topcoat affords sufficient thermal and che-mical protection.

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

Improving Interface Adhesion: Transition Metal Additives. Our ear-liest work looked at the effect of various early transition metaladditives on the adhesion of the α-Al2O3ð0001Þ∕Nið111Þ inter-face as a model of the TGO/BC interface (22–24). Again, ouridea was to promote open-shell/covalent interactions across inter-faces to enhance bonding and hence TBC adhesion. Our calcula-tions confirmed this hypothesis. Adhesion with 0.5 monolayer(ML) of Si, Sc, Y, Ti, or Zr dopants was compared to adhesionwith a 0.5ML of Ni or Al “dopant” at the α-Al2O3ð0001Þ∕Nið111Þinterface. Sc, Y, Ti, and Zr all caused a very large increase inadhesion of approximately 70–100% relative to Ni, whereas Siand Al decreased adhesion by approximately 20–30%. The opend-shell nature of the early transition metals allows donor–accep-tor bonding between oxide ions and the transition metal dopantatoms to flourish (19) along with O 2p-metal 3d covalent bonds.

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The strong donor–acceptor bonds coupled with the lack ofclosed-shell repulsions characteristic of the undoped interfaceproduces a much stronger interface. Ti and Zr are known to helpextend the lifetimes of TBCs (25, 26); the enhanced adhesion wefound in these studies likely contributes to delaying spallation.

Although unexamined in our early studies of theα-Al2O3ð0001Þ∕Nið111Þ interface (22–24), given that Hf lies be-neath Ti and Zr in the periodic table, it was clear to us then thatHf should exhibit similarly enhanced adhesion for precisely thesame reasons. Later on, we explicitly proved this to be so by ex-amining the influence of Hf at a more realistic TGO/BC interfacemodel in which the BC was modeled by β-NiAl rather than pureNi (Fig. 2). The effect of Hf on the α-Al2O3ð0001Þ∕β-NiAlð110Þinterface is astonishingly large: The adhesion energy increasesby more than a factor of three, from 0.66 J∕m2 for the cleaninterface to 2.06 J∕m2 for the doped interface, even with only0.1 ML Hf present (17). This enhanced adhesion due to Hfwas confirmed later by Jiang et al. for a model of the γ-NiðAlÞ∕α-Al2O3 interface (27), despite their model being more appropri-ate for a supported catalyst than a TBC (by adopting the latticevectors of an alumina substrate). Our electronic structure analysisof the α-Al2O3ð0001Þ∕β-NiAlð110Þ interface revealed that Hfforms four mixed polar-covalent/donor–acceptor bonds to oxygenions at the alumina surface, the origin of its tremendously strongadhesion. At the same time, Hf remains bound to the Ni atomsof the NiAl BC alloy and does not disrupt other cross-interfaceNi-Al bonds. Thus, one role for Hf in TBCs is indeed a directand dramatic increase in the intrinsic adhesive strength of theTGO-bond coat alloy interface. It also explains why Hf seemsto be a preferred additive over Ti or Zr, because the improvementin adhesion is most pronounced with Hf.

Because Pt additions to the BC improve TBC lifetime, we alsoexamined Pt atoms placed at the α-Al2O3ð0001Þ∕β-NiAlð110Þ in-terface as either a substitute for Ni in NiAl or as an interstitialdopant. At 0.1 ML Pt, the work of separation hardly changedcompared to the clean interface (W sep ¼ 0.53 J∕m2) upon addi-tion of Pt in either position. We therefore concluded that Pt doesnot directly increase interface adhesion. Its beneficial role mustinvolve affecting other processes, possibly modifying diffusionprocesses in the TBC or preventing S segregation to the interface(17). In retrospect, and based on our earlier insights about whythe alumina∕Ni interface is weak, it seems obvious that Pt shouldnot improve TBC adhesion directly: It has a nearly filled d shelllike Ni and therefore cannot form strong bonds to oxygen.

Decoupling the Effect of S, Hf, and Pt on Interface Adhesion. Sulfuris an unavoidable coating contaminant known to be detrimentalto TBC adhesion. With only 0.1 ML of S present at theα-Al2O3ð0001Þ∕β-NiAlð110Þ interface (Fig. 2), the adhesionenergy drops precipitously (W sep ∼ 0.18 J∕m2) (17), confirmingsimilar findings by Zhang et al. (28) for an Nið111Þ∕Al2O3

interface. This direct and dramatic decrease in adhesion is dueto electron-pair–electron-pair repulsions between S atoms andO2− ions in alumina, which prevent formation of covalent bondsacross the interface (17). The weakened adhesion and a spatial

gap that develops at the interface helps explain Auger electronspectroscopy and electron microscopy measurements on TBCsthat find S present near voids between the bond coat alloyand the oxide. The elongated, weakened bonds across the S-con-taining metal/oxide interface and apparent S-O repulsion inducethe oxide and metal to separate. These findings provide a detailedunderstanding of how S accelerates TBC spallation.

The ideal additive binds strongly to both the TGO and the BCand in this way increases the adhesion between them. Separatingthe 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 exactlywhy they improve (or reduce, in the case of S) adhesion: Is itbecause they increase binding to the BC, to the TGO, or to both?To answer this question, we compared the interface results aboveto our theoretical studies of adsorption of these atoms on theNiAl(110) surface (29) and on the α-Al2O3ð0001Þ surface (30).On the NiAl(110) surface, Hf, Pt, and S display quite similarbinding energies of 4.91 eV for S, 5.30 eV for Pt, and 5.00 eVfor Hf. On the α-Al2O3ð0001Þ surface, the adsorbate bindingenergies 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 elec-tropositive. The electronegativity of S and Pt is the origin behindtheir weak bonds to alumina; they both prefer to reside in themetal as a result. By contrast, Hf transfers electrons to aluminaand subsequently forms multiple strong polar-covalent/donor–acceptor metal–oxygen bonds. Thus, relative binding to the TGOis the deciding factor for interface adhesion; although all ele-ments bind strongly to the BC, only Hf has strong interactionswith the TGO.

Some general conclusions about oxide-metal adhesion canbe reached from these interface studies. Prior to our work, oneconventional model of metal-oxide adhesion was a purely classi-cal electrostatic one (31), in which the ionic oxide polarized themetallic conductor, with the consequence that more ionic oxidesand/or thicker films should improve adhesion. However, ourcalculations showed that the opposite is also possible: Morecovalent oxides can form stronger bonds to metals and thickerfilms can actually weaken adhesion. What determines the adhe-sion strength are the local interactions at the interface, eitherclosed-shell repulsions that weaken interfacial bonding or localpolar-covalent/donor–acceptor interactions that strengtheninterfacial adhesion.

Adsorption and Diffusion on the α-Al2O3ð0001Þ Surface.Having inves-tigated the interface adhesion of all relevant interfaces in theTBC, we move to consider the transport of Al, O, and dopantspecies in the TGO. To fully elucidate the effect of REs on diffu-sion of Al and O along the alumina GBs in the TGO, calculationof diffusion pathways of these elements at a number of differentGBs sufficiently representative for the real TGO would have tobe carried out. This is not possible with present-day computa-tional methods and resources, but here we demonstrate theinsights one can glean from simpler models.

As a baseline point of comparison for future GB diffusion stu-dies, we chose the basal plane of alumina, i.e., the α-Al2O3ð0001Þsurface, on which to examine adsorption (30) and diffusion (32)of Al, O, Hf, Y, Pt, and S. The electropositive metals Al, Y, andHf all adsorb on the same threefold hollow site, namely the sitewhere the next Al ion would be if the bulk crystal continued. Thisis also the place one would intuitively place an adsorbate thatdonates electrons. Upon adsorption, the neutral metal adatomstransfer electrons to neighboring Al ions on the surface and be-come ions themselves Al → Alþ, Hf → Hf3þ, and Y → Y2þ to 3þ.The extent of charge transfer correlates with bond strengths(Hfð4.27 eVÞ > Yð3.90 eVÞ > Alð2.31 eVÞ), suggesting that thepartially ionized metal adatoms then experience back donationfrom nearest-neighbor O anion lone pairs, with the strength of

Fig. 2. Structure of the (A) clean, (B) S-doped, and (C) Hf-dopedα-Al2O3ð0001Þ∕NiAlð110Þ interfaces (17). The atoms shown are Ni (blue), Al(gray), O (red), S (yellow), and Hf (cyan).

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those interactions directly proportional to the extent of ioniza-tion. Because Hf and Y bind more strongly than Al, from athermodynamic standpoint Hf and Y can displace Al from itsadsorption site and thereby act as site blockers. We also find thatAl, Hf, and Y diffuse via almost the same pathway across thesurface; all metal cations may prefer this pathway that allows theirpositive charge to be screened as much as possible by the close-packed layer of oxygen underneath them. As with charge transferand binding energy trends, Hf (2.29 eV) and Y (1.03 eV) havehigher diffusion barriers than Al (0.71 eV). Since the preexpo-nential factors for all three are similar, the calculated diffusivitiesfor Hf and Y are several orders of magnitude lower than for Al.The increase in diffusion barrier from Al to Y to Hf originates inthe required breaking and forming of increasingly strong bonds asthe atom diffuses. Thus, this work provides insight on the me-chanism by which Hf and Y slow TGO growth; namely to inhibitAl diffusion by moving more slowly and blocking sites throughwhich Al would be expected to diffuse. Again, it is their open-shell d electrons that render Hf and Yefficient site and diffusionblockers for Al transport because they form strong bonds to thealumina surface. This suggests that, apart from those metalcations (e.g., Ti and Sc), which are small and therefore mobilein alumina (33), many early transition metals will be effectiveat slowing alumina growth by inhibiting aluminum ion diffusion.

By contrast with the metal cations, oxygen adsorbs on top of asurface oxygen ion with a binding energy of 2.18 eV, forming aperoxide ion (O2

−) via a covalent bond. Oxygen diffusion involvesa barrier of 1.69 eV, more than twice as high as for Al diffusion,because the peroxide bond must nearly break completely in orderfor O to diffuse. Therefore, O diffusion on the alumina surface ismuch slower than Al diffusion. Additionally, the diffusion path-ways of Al and O are quite different, thereby allowing both Aland O to diffuse simultaneously. This also explains why Hf andY are neither site nor path blockers for O diffusion, as O bothadsorbs on a different site and diffuses along a different pathwaythan 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 butdiffuses with a very low overall barrier (0.66 eV). Thus Pt cannotact as a site or diffusion path blocker for Al because it does notadsorb or diffuse on the same path. Even though the diffusionpathways for O and Pt coincide, Pt diffuses much faster thanO and therefore will not inhibit its diffusion. Furthermore, Ptbinds much more strongly to NiAl than to alumina, indicatingthat Pt would prefer to remain in NiAl and not diffuse into alu-mina (30). Our findings that Pt diffuses easily on alumina andprefers to stay in NiAl are consistent with observations that Ptdoes 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 transferoccurring. The fact that Pt binds on the same site as S, but morestrongly, suggests that one role for Pt may be to displace and/orblock S from segregating to the interface, thereby mitigating thelatter’s harmful effects.

Structure, Ion Segregation, and Creep of the Σ11 Tilt Alumina GB.Although the α-Al2O3ð0001Þ surface model delivered useful in-sights, an actual GB model would be more representative of thealumina polycrystal that grows during operation. Of the manyGBs formed in α-Al2O3, we chose the Σ11 tilt GB—the subjectof previous experimental (35) and theoretical (36–38) work—totest our findings. A detailed scan of possible translations parallelto the GB interface revealed a previously undescribed structure(39) for the clean GB that is lower in energy than previously pro-posed structures based on transmission electron microscope(TEM) data and classical potential simulations (36).

TEM and energy-dispersive X-ray (EDX) maps have shownthat REs segregate to α-Al2O3 GBs (12, 40–42). To study ionsegregation, we identified the most stable adsorption sites forAl, O, Y, and Hf atoms (Fig. 3) at our model GB, again by screen-ing 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 cellbut varied significantly in energy, suggesting that some high-energy (4–5 eV) structures might need to be accessed duringO diffusion. Likewise, Al adsorption sites were spread fairlyuniformly but with an energy range 1–2 eV smaller, perhaps in-dicative of smaller diffusion barriers. We found it is thermodyna-mically favorable for both Y and Hf to segregate to the GBinterface rather than substitute for Al cations in bulk alumina,consistent with TEM and EDX measurements. However, fewerHf than Yatoms are accommodated at the GB interface, therebyvalidating previously proposed (43) relationships between cova-lent radius and tendency to segregate. As expected from theirsimilar cationic character, Y and Hf adsorption sites overlapstrongly with those of Al. The relative energies of these sites ran-ged up to approximately 7 eV, much higher than for Al, suggestingthat barriers for Hf and Y diffusion along the GB probably alsoare much higher than for Al (39).

Our detailed predictions (39) are consistent with the outlinesgiven in the dynamic segregation theory of Pint et al. (12) Theadsorption sites for Hf and Y are very similar to those for Al,thereby explaining the inhibition of Al diffusion. Although onlyminute concentrations are added to the bond coat alloy, when Yand Hf segregate to GBs they are present in locally high concen-trations that very effectively block Al diffusion along GBs. Andas O adsorption sites do not all overlap with the ones for the REs,their diffusion pathways could be different, which explains thelimited effect that some REs have on O diffusion rates. In con-trast to the 2–3× reduction in oxide growth due to Y doping, ex-periments have shown that Hf decreases oxide growth by a factorof 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 creepdeformation of polycrystalline alumina (42); as one mechanismof creep (Coble creep) involves atom/ion diffusion, this findingis consistent with our predictions that such large metal cationsinhibit Al diffusion.

We also investigated the influence of a variety of metal addi-tives on alumina GB sliding (45), which is another mode of high-temperature creep that can destabilize the TGO/BC interface byincreasing tensile stress. It is known from experiment that early

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) withaluminum (small gray spheres) and oxygen (large grayish-white spheres).(Left) Side view and (Right) top view. For easier viewing, the top part ofthe grain boundary has been removed in the top view (Right).

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transition metal dopants increase creep activation energies (40,42, 46). We identified minimum and maximum energy structuresalong the preferred sliding pathway for the pristine GB and forGBs doped with a series of early transition metals, as well as withbarium (Ba), gadolinium, and neodymium. The presence of thesedopants greatly increases the GB sliding barrier, again because ofthe strong, multiple bonds formed between them and the oxideions in alumina. GB sliding occurs by a series of bond breakingand forming events across the GB. The presence of large cationsinhibits the regeneration of metal–oxygen bonds during sliding,thereby raising the barrier to sliding. Trends in predicted GB slid-ing energies are in good agreement with recently measured creepactivation energies in polycrystalline alumina (40, 47, 48), lendingfurther credence to the notion that GB sliding plays a dominantrole in alumina creep. Moreover, we found that Ba—an elementnot found in current bond coat alloys (33)—provided the bestalumina 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 bywhich this benefit is achieved remains unclear despite a multitudeof measurements trying to discern it (7). Because Pt does notaffect the oxidation kinetics of the TGO, the mechanism bywhich Pt benefits TBC lifetime has been suggested to be differentthan that of REs (11). Above we discussed that Pt at theα-Al2O3∕NiAlð110Þ interface does not directly strengthen adhe-sion of the oxide to the metal, that Pt prefers to stay in NiAlbecause it only weakly interacts with alumina, and that its fastdiffusion on alumina renders it incapable of inhibiting Al or Oion diffusion needed to slow TGO growth. As such, we beganto examine whether the main role of Pt (in addition to inhibitingS segregation discussed above) is to affect the high-temperatureevolution of the NiAl BC alloy, such as the diffusion kinetics of Aland Ni in NiAl.

The idea that Pt enhances Al diffusion in NiCrAl alloyswas suggested in 1976 by Felten (49) and more recently in NiAlalloys by Gleeson et al. (10). Svensson et al. (9) inferred that Aldiffusion in NiAl accelerated upon Pt additions from the obser-vation of reduced void formation at the α-Al2O3∕NiAl interface.This concept would be consistent with experimental evidenceshowing that Pt prevents the formation of Ni-rich oxides on NiAlalloys with Al levels low enough that they form on the pure alloy(11). Alumina preferentially forms on NiAl as long as the levelof Al in the alloy is high enough, but once the level of Al istoo low, brittle, fast-growing Ni-rich oxides begin to form, hasten-ing failure of the coatings. If Pt were to enhance Al diffusion tothe interface, it would ensure a high enough local Al concentra-tion to keep forming alumina.

Because Ni and Al diffusion in NiAl must occur via lattice va-cancies due to the large size of both elements, we first exploredPt’s effect on forming key defects central to a number of postu-lated mechanisms for Ni and Al diffusion through NiAl (50).NiAl has a CsCl structure, which consists of two interpenetratingsimple cubic lattices of Ni and Al. Four types of point defects canform in NiAl to accommodate deviations from stoichiometry: Niand Al vacancies (VNi, VAl), Ni antisites (Ni on the Al sublattice,NiAland Al antisites (Al on the Ni sublattice, AlNi) (51). Ourpredicted formation energies for these defects (VNi: 0.41 eV,VAl: 1.87 eV, NiAl: 1.02 eV, and AlNi: 1.61 eV) are consistentwith experimental evidence that Ni antisite atoms form in Ni-richNiAl rather than Al vacancies, and Ni vacancies form in the Al-rich alloy instead of Al antisites. The predicted defect formationenergy for a Pt atom residing on either the Ni or Al sublatticesshows that Pt strongly prefers the Ni sublattice, consistent withit being isovalent with Ni. The effect of Pt on the stability of eachpoint defect was determined by placing a Pt atom in the closest Nisite to the defect, to quantify its maximal influence. In all cases,

Pt promotes formation of these defects, as evidenced by signi-ficant decreases in their formation energies (VNi: − 0.23 eV,VAl: 1.09 eV, NiAl: 0.50 eV, and AlNi: 1.06 eV), suggesting re-pulsive interactions between Pt and Ni or Al (50). Indeed, densitydifference plots (Fig. 4) reveal an increase in electron densityaround the Pt atom such that a s2d9-like Pt anion is formed,due to its higher electronegativity (52). In turn, the more diffusePt anion destabilizes nearby Ni and Al atoms, favoring Ni vacancyformation in particular.

Although radioactive tracer experiments have determinedthe diffusivity of Ni in NiAl (53), none have been performedfor Al diffusion due to the lack of a suitable radioactive isotope.Numerous computational (e.g., 53) studies have been unable toconcretely determine the dominant mechanism of Ni diffusion instoichiometric NiAl. Although the ultimate goal was to model aBC alloy, which is typically Ni-rich, we began by examining fiveproposed mechanisms in pure stoichiometric NiAl: next-nearest-neighbor (NNN) jumps, the triple defect mechanism, and threevariants of the six-jump cycle (54). By comparing our calculatedpreexponential factors and activation energies with experimentaldata (D0 ∼ 3 × 10−5 m2∕s; Q ∼ 3 eV) (53), we concluded that thetriple defect mechanism and the six-jump cycle in the [110] direc-tion were viable pathways for Ni diffusion in pure NiAl. The twovariants of the six-jump cycle in the [100] direction had activationenergies above 4 eV, leading us to conclude they do not contri-bute to Ni diffusion. Although the calculated activation energy ofa NNN Ni jump was approximately 3.0 eV (54), this jump wasexcluded based on experimental results (53).

Although the triple defect mechanism leads to long-rangepropagation of Ni and Al atoms (in opposite directions), NNNNi jumps and the six-jump cycle do not lead to long-range Aldiffusion. Because NiAl is symmetric, we proposed analogousmechanisms to the Ni diffusion mechanisms that could lead topropagation of Al atoms (55). Because both mechanisms startwith a Ni vacancy defect, we examined the NNN Al jumps andthe six-jump cycle starting with an Al vacancy. Although the ac-tivation 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 jumpswill not contribute to Al diffusion. The calculated activation en-ergies for the three six-jump cycles starting with an Al vacancyranged from 3.3 to 4 eV. Because the activation energy of thetriple defect mechanism was only 3 eV (55), we concluded thatboth Ni and Al diffuse via the triple defect mechanism in stoichio-metric NiAl.

Isotope experiments show that Ni diffusion is enhanced inNi-rich NiAl (53) and the antistructure bridge (ASB) mechanism(56) has been proposed to account for it. Here Ni atoms are sug-gested to diffuse via bridges formed by Ni antisite atoms, which asnoted earlier are the constitutional defects in Ni-rich NiAl. For Niconcentrations slightly above 50%, the ASB mechanism will lead

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 Bcontains Ni atoms, Al atoms, and the Pt atom. The atomic positions areindicated on the plane. The legend limits represent �5% change from a uni-form electron density containing the same number of electrons in the samevolume. The plots were created using VESTA (68).

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only to a local enhancement, but for alloys with a high enoughconcentration of Ni, a percolation threshold of Ni antisite atomsis reached, and the ASB mechanism could contribute to long-range Ni diffusion (53). We predicted that the ASB mechanismis indeed viable for Ni diffusion in Ni-rich NiAl, with a smalleractivation energy (approximately 2.2–2.3 eV compared to 3 eV instoichiometric NiAl), depending on the direction of overall atom-ic motion (57). Although our model alloy was only 53 at. % Ni,the calculated barriers were in excellent agreement with the ob-served activation energy of approximately 2.4 eV in a 56.6 at.% Ni alloy (53). (A percolation threshold of approximately55 at. % Ni (53) must be reached for the ASB mechanism tocontribute to long-range Ni diffusion and hence be quantifiableexperimentally.)

To study the maximum effect of Pt on the five diffusionmechanisms for Ni diffusion in stoichiometric NiAl and the ASBmechanism for Ni diffusion in the Ni-rich alloy, a Pt atom wasplaced in the Ni site in closest proximity to the defect clustersinvolved in the mechanisms. As in the case of the point defectsdiscussed above, Pt greatly stabilized all defect cluster intermedi-ates. By contrast, in all cases Pt had little effect on the calculatedpreexponential factors and migration energies (within 0.1 eVof those in pure NiAl). However, the substantial decreases inthe defect formation energies produce large increases in the dif-fusion rate because these energies appear in the exponential ofthe diffusion coefficient. Therefore, Pt enhances Ni and Al diffu-sion by stabilizing the point defects and defect clusters that areintermediate minima along the diffusion pathways (52, 55, 57).

As Pt increases the rate of Al and Ni diffusion in NiAl, it likelyincreases the rate of Al diffusion to the interface. Experimentshave shown when NiAl is oxidized, Al diffuses toward the surfaceand Ni diffuses away from the surface (58). From our results, wecan conclude that one mechanism by which Pt promotes TBC life-time is by keeping the concentration of Al at the interface highenough to prevent the formation of brittle, Ni-rich oxides, whichare more prone to spallation than alumina.

ConclusionsFirst principles quantum mechanics simulations of atomic-scalemechanisms by which turbine engine TBCs fail has led to funda-mental discoveries as to how and why certain additives (Hf, Y, Pt,etc.) in the coatings improve stability, and ultimately to sugges-tions for how to improve these high-temperature coatings thatprotect turbine engine components vital for electricity productionand transportation. The key findings follow:

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

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

• Adding hafnium to the BC dramatically increases adhesion ofthe 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-acceptorbonding to flourish. The improved adhesion is one mechanismby which Hf improves the TBC lifetime. Similar, though lessdramatic, increases in TBC adhesion were found for otherearly transition metal additives such as Sc, Y, Ti, and Zr.

• Hf and Y readily segregate to oxide GBs and block sites alongthe Al diffusion pathway at oxide GBs, thereby slowing oxidegrowth. Oxide growth continues slowly because of oxygenanion diffusion that can proceed via a different pathway. Bydelaying oxide growth, the strain energy of the growing oxideis minimized, extending TBC lifetime.

• Hf and Y (or any early transition metal, rare earth, and evensome alkaline earth) additives increase barriers to alumina GBsliding 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 slid-ing, these additives act to limit the tensile stress perpendicularto the TGO/BC interface, delaying spallation of the coating.

• Platinum additives do not directly increase TGO/BC adhesionnor does Pt inhibit diffusion in the oxide; Pt would rather stayin the NiAl BC than be found in the alumina (the TGO). Thislatter finding is consistent with observed growth kinetics andmorphology of the TGO, both of which are unaffected bythe presence of Pt. Some evidence is provided that Pt mayprevent S from getting to the TGO/BC interface by blockingthe sites S prefers.

• Pt’s main role is to promote point defect (vacancies and anti-site atoms) and defect cluster formation in NiAl. By so doing,Pt greatly accelerates Ni and Al diffusion in NiAl, primarily bymeans of the triple defect mechanism, and in Ni-rich BCs, alsoby the antistructure bridge mechanism. The predicted diffusiv-ities are much larger in the presence of just a few percent Pt.By accelerating Ni and Al diffusion, Al atoms are kept in highconcentration at the interface between the NiAl BC alloy andthe TGO, even in Ni-rich NiAl alloys. By keeping the local Alconcentration high, the TGO is comprised only of alumina,rather than Ni aluminate spinel. The latter is fast growingand less adherent; inhibition of its formation prevents rapidfailure of the coating.

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

Finally, by delving into the nature of the chemical bonds inthis complex multicomponent coating, we leave the reader withtwo general principles that may prove useful for materials designbeyond the present subject of TBCs:

• To improve adhesion, reduce creep, slow diffusion and hencegrowth, add elements that strengthen chemical bonds at inter-faces. For oxides, these will be early transition metals, rareearths, or alkaline earths that form strong bonds to oxygen.

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

Computational MethodsMany simulation methods based on quantum mechanics exist(59); here we primarily used Kohn–Sham density functional the-ory (DFT) (60, 61) as implemented in the CASTEP (62) andVASP (63, 64) codes. DFT is advantageous because it permits useof periodic boundary conditions to simulate large crystals whileusually providing a good balance between accuracy and compu-tational expense (59). Because its exact expression is unknownexcept in certain simple limits, the DFT electron exchange–cor-relation functional must be approximated. For most of the resultsdiscussed here, the Perdew–Wang (65) and closely related Per-dew–Burke–Ernzerhof (66, 67) exchange–correlation functionalswithin the generalized gradient approximation (GGA) were used,because DFT-GGA generally provides accurate structures andenergetics for the materials classes considered here. Apart fromthese general issues, choices for a number of parameters have to

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be made, and these are documented in more detail in the originalreferences. Further methodological details are given in SI Text.

ACKNOWLEDGMENTS. Financial support for all of this work has been continu-ously provided by the Air Force Office of Scientific Research; the work began

because of a simple suggestion from an amazingly astute program manager(Dr. Michael R. Berman) that one of us look into what a theorist might beable to contribute to the understanding of thermal barrier coatings so crucialto the efficient operation of aircraft. Thus began more than a decade ofresearch, that which is summarized here.

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