Thermal barrier coating materials

Thermal barrier coating materials

Thermal barrier coating materials by David R. Clarke† and Simon R. Phillpot‡ Improved thermal barrier coatings (TBCs) will enable future gas turbine...

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Thermal barrier coating materials

by David R. Clarke† and Simon R. Phillpot‡

Improved thermal barrier coatings (TBCs) will enable future gas turbines to operate at higher gas temperatures. Considerable effort is being invested, therefore, in identifying new materials with even better performance than the current industry standard, yttria-stabilized zirconia (YSZ). We review recent progress and suggest that an integrated strategy of experiment, intuitive arguments based on crystallography, and simulation may lead most rapidly to the development of new TBC materials.

Turbines should operate at as high temperature as possible to maximize their efficiency. Until about 15 years ago, relentless increases in operating temperatures were achieved through improved alloy design, the development of blades composed of textured microstructures and subsequently single crystals, and internal cooling by air flow through internal channels cast into the component. More recent increases in operating temperatures have been enabled by deposition of TBCs on high-temperature gas turbine components1,2. TBCs are complex, multifunctional thick films (typically 100 µm to 2 mm thick) of a refractory material that protect the metal part from the extreme temperatures in the gas (see Fig. 1). Indeed, in the hottest part of many gas turbine engines, the coatings enable metallic materials to be used at gas temperatures above their melting points. Under such heat flux conditions, it is the thermal conductivity of the coating that dictates the temperature drop across the TBC.

†Materials Department, University of California, Santa Barbara CA 93106, USA E-mail: [email protected] ‡Department of Materials Science and Engineering, University of Florida, Gainesville FL 32611, USA E-mail: [email protected]

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To illustrate the benefit of TBCs, it has been estimated3 that a 50% reduction in thermal conductivity will reduce the alloy temperature by about 55°C. This may not seem large, but it actually corresponds to the increase in hightemperature capability achieved over the last ~20 years by developments in single-crystal Ni-based superalloys. The current material of choice for TBCs is YSZ in its metastable tetragonal-prime structure. Since it has proven to be a highly durable TBC material, it is likely to remain the

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material of choice for turbines with current operating temperatures. However, in anticipation of still higher operating temperatures, for instance as embodied in the US Department of Energy’s Next Generation Turbine (NGT) program, the search is underway for TBCs that will be capable of operating at higher temperatures and for longer times than YSZ. While the primary function of TBCs is as a thermal barrier, the extremely aggressive thermomechanical environment in which they must function demands that they also meet other severe performance constraints. In particular, to withstand the thermal expansion stresses associated with heating and cooling, either as a result of normal operation or as a consequence of a ‘flame-out’, the coatings must be able to undergo large strains without failure. This ‘strain compliance’ is typically conferred through the incorporation of porosity in the microstructure by, for example, forming the coating by electron-beam evaporation or plasma spraying. Another less stringent but nevertheless rather practical requirement is that the material must not undergo phase transformations on cycling between room temperature and high temperatures. Such phase transformations are usually accompanied by volume changes, which detract from the strain compatibility and reversibility of the coating and, hence, its ability to withstand repeated thermal cycling. Practical TBC materials must also be able to resist erosion, which calls for high resistance to fracture and deformation. For air-breathing engines, which are by far the majority, the coatings must be able to withstand prolonged high temperatures in an oxidizing atmosphere. To satisfy this requirement, refractory oxides are the focus of the search for new and alternative TBC materials. Another perhaps less obvious requirement is that the coating material is thermodynamically compatible with the oxide formed by oxidation of the bond-coat. Indeed, the choice of Ni-based superalloys for turbine applications is based largely on their ability to form a slow-growing Al2O3, under oxidative conditions typical of operation (Al2O3 has the lowest oxygen diffusivity of the common oxides). This suggests that compatibility with Al2O3 is an additional constraint on the choice of new TBC materials, although it is possible to envisage a two-layer coating, an inner layer compatible with alumina, and an outer layer capable of prolonged higher temperature exposure that need only be compatible with the inner layer. TBCs are outstanding examples of multifunctional materials.

Fig. 1 Cross-sectional image of a YSZ thermal barrier coating deposited by electron-beam evaporation on a superalloy. During use at high temperatures, a thermally grown oxide (TGO) of Al2O3 forms on the metal beneath the TBC.

While failure to meet any of the above performance criteria can make any potential material unusable as a TBC, suitable thermal transport properties remain the first design criterion that must be met. In the remainder of this article, we focus purely on the thermal transport properties. For a review of TBCs as complete thermomechanical systems and for the materials research aspects, see4,5.

Thermal conductivity of high-temperature materials Somewhat surprisingly, the experimental investigation of thermal conductivity at very high temperatures has been a largely neglected field since the work of Kingery and colleagues in the 1950s6. They measured the thermal conductivity of many oxides as a function of temperature and studied the effects of porosity and of mixing two different oxides. They also demonstrated that, after correction for the temperature dependence of thermal expansion, the thermal conductivity of almost all oxides decreases as 1/T, in accord with thermal conductivity being controlled by the Umklapp inelastic phonon-phonon scattering process. The majority of their measurements (Fig, 2a) do not extend to the temperatures of interest for future TBCs, but they did find that three fluorite oxides, YSZ, UO2-x, and Th0.7U0.3O2+x, exhibit temperature-independent thermal conductivity at

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(a)

(b)

Fig. 2 (a) Thermal conductivity versus temperature for several refractory compounds (after9). The upturn A at the highest temperatures is a result of radiative transport through the material during measurement. (b) Materials usually exhibiting low thermal conductivity.

high temperatures, quite different from other crystalline oxides but very similar to that of fused silica. (Interestingly, monoclinic zirconia, which does not contain any stabilizers and hence no associated structural point defects, exhibits the classical 1/T dependence caused by Umklapp scattering.) The absence of the characteristic 1/T dependence was ascribed to the fact that both YSZ and UO2-x contain very high concentrations of point defects that scatter phonons. More recent measurements on materials are shown in Fig. 2b.

High-temperature thermal conductivity The thermal conductivity of a material is a measure of heat flow in a temperature gradient. In the first successful model for thermal conductivity, Debye used an analogy with the kinetic theory of gases to derive an expression of the thermal conductivity7: (1) κ = CVνmΛ/3 where CV is the specific heat, νm is the speed of sound, and Λ is the phonon mean free path. Both Kittel in 19498 and Kingery in 19559 suggested that the minimum value of the thermal conductivity at high temperatures was that given by eq 1 with the phonon mean free path equal to the interatomic spacing. This simple approach works quite well because, at temperatures in excess of the Debye temperature T > ΘD, the specific heat is close to its asymptotic, 24

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temperature-independent value of CV → 3kB per atom, as predicted by the Dulong-Petit equation7. Other, more sophisticated approaches also assume that the major contribution to thermal conductivity in the high-temperature regime is caused by phonons whose mean free path is the interatomic spacing. For instance, Cahill and Pohl10 have suggested that the value computed from their analysis for the minimum thermal conductivity differs by just ~20% from the limit of eq 1, where the phonon mean free path is equal to the lattice parameter. In a similar way, the low temperature-independent thermal conductivity of fused silica and other glasses has been attributed to their random structure precluding any long-wavelength phonon modes, with the dominant phonon contributions being limited by the size of the tetrahedral unit of the glass8,9. The minimum thermal conductivity for more complex, multicomponent materials also has a similar form11 and can be expressed12 as: (2) κmin = kBνmΛmin → 0.87kBΩa-2/3(E/ρ)1/2 where Λmin is the minimum phonon mean free path, Ωa = M/(mρNA) is the average volume per atom, E is the elastic modulus, and ρ is the density. (The different atoms in a molecule are replaced with an equivalent atom having a mean atomic mass given by M/m, where M is the molecular mass and m is the number of atoms per molecule.) The data for a variety of materials is plotted in Fig. 3, illustrating that

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Fig. 3 Minimum thermal conductivity of materials of interest as TBCs, together with other materials for comparison, calculated using eq 2. (Redrawn from12.)

materials with low thermal conductivity tend to have large volumes per atom and low specific elastic modulus E/ρ. A particularly important feature of the minimum thermal conductivity is that, in contrast to conductivity at lower temperatures, it is independent of the presence of defects such as dislocations, individual vacancies, and long-range strain fields associated with inclusions and dislocations. This is largely because these defects affect phonon transport over length scales much larger than the interatomic spacing. This also means that measurements at low and intermediate temperatures can be a poor guide to the thermal conductivity at high temperatures.

YSZ – the current material of choice The initial choice of YSZ (4 mol% Y2O3) as a TBC material was largely based on the simple fact that zirconia was one of the few refractory oxides that could also be deposited as thick films using the then-known technology of plasmaspraying. The identification of yttria as the optimum stabilizer and composition then followed from a series of more exacting testing, especially under thermal cycling conditions13. Originally, the low and temperatureindependent thermal conductivity of YSZ was attributed to the presence of a high point defect concentration associated with the substitution of Zr4+ ions by Y3+ ions in the fluorite structure, producing a small spacing between point defects. As an oxygen vacancy is introduced into the zirconia structure for every two Y3+ ions that substitute for a Zr4+

ion, in 4 mol% YSZ, for instance, the average distance between oxygen vacancies is only ~1 nm and the average distance between Y3+ ions is ~0.5 nm. Recently, a detailed simulation analysis14 of how the nature of the vibrational modes changes with yttria concentration has revealed that the picture of the phonon scattering length being determined by the point defect spacing alone is too simple. In monoclinic ZrO2, all of the vibrational modes have well-defined wavevectors and polarizations, characteristic of normal phonons. However, as yttria is added to the zirconia, the nature of the vibrational excitations changes. In particular, most vibrational modes no longer have a well-defined wavevector or polarization. For example, there is a phonon-like transverse acoustic mode in monoclinic ZrO2 at about 3 THz, which shows complete polarization along the z-direction. In a plot of the normalized displacement in the x-y and x-z planes, this mode would be characterized by a single point at the origin in the former and spots at z = +1 and z = -1 in the latter. The corresponding mode in 4 mol% YSZ (Fig. 4) shows an almost completely uniform distribution in the x-y and y-z planes, indicating an isotropic distribution of vibrations. This demonstrates that the concepts of polarization and wavevector are no longer relevant for this vibrational mode, i.e. it is not a phonon-like mode but is actually better characterized as a diffusive vibrational wavepacket. Furthermore, analysis shows that the vast majority of vibrational modes are similar in that, though they are still relatively spatially extended modes, they move more slowly than the sound velocity of phonon-like modes. As a result, the thermal conductivity is greatly diminished. A further significant contribution to the thermal conductivity comes from the few remaining lowest-energy modes, which remain phonon-like. A few of the high-frequency modes become spatially localized; these do not contribute to the thermal conductivity at all. Together, these results are very similar to those of an earlier analysis of the vibrational modes in amorphous Si (α-Si)15, and confirm the close correspondence between the thermal transport mechanisms in the chemically disordered YSZ and the structurally disordered α-Si. The new insight that a large concentration of defects changes the vibrational modes from pure phonons in undoped, monoclinic zirconia to a variety of other modes in 4 mol% YSZ, even though the material remains crystalline, may well be important in identifying new candidate TBC materials.

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(a)

(b)

Fig. 4 Scatter plot showing the normalized magnitudes of vibration of each atom in the x-y plane (a) and the y-z plane (b) for the mode close to 3 THz in 4 mol% Y2O3. For a pure transverse acoustic (TA) phonon mode, all the atoms would vibrate in the z-direction only; this would be indicated by a single point at the origin in (a) and points at z=-1 and +1 in (b). The larger scatter for this mode indicates that the concepts of polarization and wavevector are no longer meaningful in this material. (Reprinted from14. © 2001 Blackwell Publishing.)

The search for alternative TBC materials In seeking potential new TBC materials, it makes sense to explore other refractory materials. However, since there are numerous crystal structures known to the mineralogical and crystal-chemistry communities, and each can be formed from several different elements, there are literally thousands of possible compounds to search. Faced with this complexity, initial attempts have focused on exploring oxides with structures related to zirconia. More recently, the search has been broadened by using insights from atomistic simulations and crystal chemistry. Fluorite oxides A natural place to look for other TBC materials is among fluorite-structured materials. The obvious candidates include HfO2, CeO2, and ThO2; UO2 and transuranic fluoritestructured oxides are precluded for obvious reasons. Also, although doped ceria exhibits comparable thermal conductivity, it is not a practical choice because of volatilization. Measurements on both HfO2 and ThO2 are similar to those on monoclinic ZrO2. However, recent research has shown that co-doping zirconia and hafnia can result in reductions in thermal conductivity. The most intriguing observations have been made on co-doping YSZ with a mixture of one trivalent ion larger than Y3+ and another trivalent ion smaller than Y3+,

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while still preserving the metastable zirconia structure16. Similarly, reductions in thermal conductivity have been reported17 for compositions in which some of the Zr4+ is replaced with Hf4+. While the measurements have been made on porous coatings rather than dense materials, hence the contribution to the low thermal conductivity from porosity is unknown, the results indicate that these materials warrant further investigation. Pyrochlore oxides Since the fluorites do not offer any other viable candidate materials, attention has turned to the pyrochlores, A23+B24+O7, because several zirconate pyrochlores have lower thermal conductivity than YSZ3. This class of materials is also of fundamental interest because of the close relationship between the fluorite and pyrochlore structures (Fig. 5). The pyrochlore unit cell may be viewed as eight fluorite unit cells, each of which contains, on average, a single oxygen vacancy. The close relationship between the fluorite and pyrochlore structures is well illustrated by the yttriazirconia system. The pyrochlore Y2Zr2O7 is actually unstable to the disordered fluorite material (ZrO2)2-Y2O3, i.e. heavily doped YSZ. However, replacing the Y3+ ion with larger ions, such as La3+ or Gd3+, results in a stable pyrochlore structure up to at least 1500°C. Likewise, replacement of the Zr4+ ion by a smaller ion, such as Ti4+ or Mo4+, also stabilizes the pyrochlore structure.

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(a)

(b)

Unoccupied 8a

Fig. 5 (a) The unit cell of the high-temperature cubic phase of zirconia has the fluorite structure, with O ions shown in red and the smaller Zr ions shown in yellow. (b) One-eighth of the unit cell of the pyrochlore, A2B2O7 structure, with the oxygen in red, the B4+ ions in yellow, and the A3+ ions in blue.

The pyrochlores are also attractive because many are refractory up to temperatures well in excess of 1500°C and thermally stable. Moreover, they can be formed from a wide range of cations18, since the A site can have a notional charge of 3+ or 2+ and the B site cation can have a valence of either 4+ or 5+. Consequentially, there can be extensive intermixing of different ions on the same crystallographic sites. Thermal conductivities ranging from ~1.1 W/mK to ~1.7 W/mK at temperatures between 700°C and 1200°C have been reported for zirconates of Gd, Eu, Sm, Nd, and La19-22. Although other pyrochlore compositions have yet to be measured, they have been explored extensively using atomistic simulations23. The predicted thermal conductivities are shown in Fig. 6. These studies suggest that the zirconates may indeed have the lowest thermal conductivities of the stable pyrochlores – the plumbate pyrochlores have lower

thermal conductivities, but they decompose easily and are unsuitable for environmental reasons. Co-doping of pyrochlores on both A and B sites has been proposed to further reduce their conductivity and also to modify their thermal expansion coefficients22,24. Some success has been achieved, at least up to ~800°C, as exemplified by studies in which La2Zr2O7 was doped with 30 at.% of Nd, Eu, or Gd and the thermal conductivity reduced from ~1.55 W/mK to ~0.9 W/mK for Gd doping. For comparison, the undoped, fully dense stoichiometric Nd, Sm, and Gd zirconates25, and 97% dense La2Zr2O720, were all found to have essentially the same conductivity (~1.5-1.6 W/mK) at 700°C. Whether this temperature is sufficient to evaluate if the minimum thermal conductivity has been attained was not reported, but any further decreases are unlikely to be significant. Interestingly, site disorder alone does not appear to have much effect, at least

Fig. 6 Contour map of thermal conductivity κ as a function of the ionic radii of the A and B ions for pyrochlores A2B2O7, determined at T=1200°C by simulation. (Reprinted with permission from23. © 2004 Taylor and Francis.)

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in dense Gd2Zr2O7; suitably heat-treated, this compound can be produced as either the pyrochlore or its fluorite allotrope, and yet the thermal conductivity was the same within experimental accuracy25. Moreover, thermal conductivity was found to vary only slightly over a wide range of (ZrO2)2-Gd2O3 compositions away from the pyrochlore stoichiometry, especially at high temperature25. Together, these observations raise the intriguing question as to what factors determine whether co-doping can lead to significant reductions in high-temperature thermal conductivity. Other oxides Apart from the fluorites and pyrochlores, many other oxide compounds have been proposed as candidate lowconductivity materials. These include the garnets (Y3AlxFe5-xO12)26, monazite (LaPO4)27, and the magnetoplumbite lanthanum hexaaluminate (LaMgAl11O19)28. While they all have rather low thermal conductivity (<~3 W/mK), none offer the prospect of compositions with lower conductivity than the pyrochlore zirconates. In contrast to these other classes of oxide, the perovskites, ABO3, comprise a class of crystal structures that can accommodate a wide variety of different ions in solid solution, including ions with large atomic mass. Many compositions are stable to very high temperatures. Although some members exhibit rather low thermal conductivity at high temperatures, none has yet been found to have conductivity as low as the zirconate pyrochlores. One explanation is that the perovskite structure is more rigid, as the octahedra are corner sharing. Several that appear promising on the basis of their mean molecular weight unfortunately undergo phase transitions at intermediate temperatures. For instance, SrZrO3 transforms from orthorhombic to pseudo-tetragonal at about 730°C, accompanied by a change in volume20. However, one hopeful development in the area of perovskites is a recent report of very low thermal conductivity in a coating made of a layered perovskite with Ruddlesden-Popper structure29. While fully dense materials have not been studied, the very wide range of potential compositions in this class of crystal structure and the possibility of forming a variety of other layered structures, there is plenty of scope for further work on perovskites. Glasses and nanocrystalline materials For many years, it was considered that the high-temperature conductivity of silica glass represented the lower limit – the so-called amorphous limit – to the thermal conductivity of

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materials at high temperatures. Although amorphous materials can have significantly lower thermal conductivity at room temperatures than their crystalline counterparts, the data suggest that the difference is not significant at temperatures well in excess of the Debye temperature. Nevertheless, some have advocated using nanocrystalline materials, as they offer the potential of limiting thermal conductivity by incorporating grain boundary scattering as an extrinsic phonon-scattering phenomenon. This may prove to be an effective strategy for many materials, but there is not yet any definitive evidence at elevated temperatures. A first study of nanocrystalline-stabilized zirconia ceramics has indicated that there is no grain size effect30, while a later study on films has shown a significant effect for grains below ~25 nm31. Even so, the benefit conferred by being nanocrystalline was less than that associated with the disorder of Y ions and O vacancies in YSZ. A major concern with amorphous and nanocrystalline materials is their long-term stability at elevated temperature: glassy materials tend to crystallize and nanocrystalline materials tend to rapidly coarsen and lose any initial advantages of being nanocrystalline. Nanocomposites may be more resistant to coarsening, but early investigations of zirconia/alumina laminates indicated that they became spheroid and then coarsened. Nevertheless, the potential of nanocomposites for thermal barrier applications has not been explored systematically. Of particular interest would be nanoporous materials that resist coarsening of the porosity while retaining their fracture toughness.

Future directions The search for low thermal conductivity materials for thermal barriers is only just beginning. The vast range of chemical compositions of all refractory oxides and minerals precludes a purely Edisonian approach to identifying promising compositions; it is simply too time consuming and costly. The most rapid progress will probably only be made by using a combination of intuition about crystal structures and complementary atomic-level simulations to guide experiment. Two recent examples serve to illustrate this. The first is the systematic investigation of pyrochlore compositions using simulations, resulting in the predicted thermal conductivities mapped in Fig. 6. The capabilities of such simulations are illustrated in Fig. 7, which compares the calculated and experimental values of the thermal

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Fig. 7 There is a strong linear correlation between experimental and calculated values of the thermal conductivity, with the calculated values being typically ~10% larger. The data are for the five experimentally investigated pyrochlores (circles) and for YSZ (square).

conductivity for YSZ and pyrochlore materials. Although the simulated values of the thermal conductivity are uniformly somewhat higher than the experimental values, they are highly correlated. While the higher values could be the result of limitations in the simulation approach, they are most likely to be the result of the absence of chemical disorder, impurities, and, in particular, porosity in the simulations.

The other example is the recent identification of a previously unconsidered composition, based on the following heuristic argument. The search for prospective, low thermal conductivity materials mirrors, in some regards, the search for materials with high thermal conductivity. Based on the observations that diamond, beryllium oxide, and aluminum nitride all exhibit high thermal conductivities at and around room temperature, it has been concluded that highconductivity materials will have low atomic weight, highly directional, covalent bonding, isotopic purity, and high specific elastic modulus. So, conversely, materials with low thermal conductivity at high temperatures can be expected to have the opposite characteristics: high average atomic weight, loose bonding, and highly disordered and distorted structures. YSZ and glasses have many of these attributes. It also suggests crystal structures containing elements of high atomic weight that, although crystalline, would exhibit considerable vibrational freedom of some of their structural subunits. One such material, W3Nb14O44, which has the tungsten bronze structure, has recently been identified on this basis32. It consists of blocks of corner-shared octahedra with Nb and W distributed among the octahedral sites and W atoms in the channels between blocks. As shown in Fig. 2b, its thermal conductivity is intermediate between zirconia and the pyrochlore zirconates. This suggests that this heuristic argument can be used for the initial identification of candidate materials for simulation and testing. MT

REFERENCES 1. National Research Council, Coatings for High Temperature Structural Materials; Trends and Opportunities, National Academy of Sciences, Washington, DC, (1996)

15. Allen, P. B., et al., Philos. Mag. B (1999) 79 (11-12), 1715 16. Zhu, D., and Miller, R. A., Ceram. Eng. Sci Proc. (2002) 23 (4), 457

2. Jones, R. L., In Metallurgical and Ceramic Protective Coatings, Chapman and Hall, London, (1996)

17. Murphy, K. S., US patent 0 118 873 (2003) A1

3. Maloney, M. J., Thermal Barrier Coatings Systems and Materials, US Patent 6 117 560, (2000)

19. Maloney, M., US Patents 6 177 200 and 6 231 991 (2001)

4. Clarke, D. R., and Levi, C. G., Annu. Rev. Mater. Res. (2003) 33, 383 5. Evans, A. G., et al., Prog. Mater. Sci. (2001) 46 (5), 505 6. Many of these results are summarized in Kingery, W. D., et al., Introduction to Ceramics, 2nd edn, Wiley Interscience, New York, (1976) 7. See, for example, Kittel C., Introduction to Solid State Physics, Wiley Interscience, New York, (1995) 8. Kittel, C., Phys. Rev. (1949) 75, 972

18. Hyde, B. G., et al., Mater. Sci. Technol. (1994) 11, 339 20. Vassen, R., et al., J. Am. Ceram. Soc. (2000) 83 (8), 2023 21. Suresh, G., et al., J. Alloy Compounds (1998) 269 (1-2), L9 22. Lehmann, H., et al., J. Am. Ceram. Soc. (2003) 86 (8), 1338 23. Schelling, P. K., et al., Philos. Mag. Lett. (2004) 84 (2), 127 24. Vassen, R., et al., International Patent Application, WO 02081768 (2002) A2 25. Wu, J., et al., J. Am. Ceram. Soc. (2002) 85 (12), 3031 26. Padture, N., et al., J. Am. Ceram. Soc. (1997) 80 (4), 1018

9. Kingery, W. D., J. Am. Ceram. Soc. (1955) 38 (7), 251

27. Sudre, O., et al., Ceram. Eng. Sci. Proc. (2001) 22 (3), 367

10. Cahill, D., and Pohl, R., Solid State Commun. (1989) 70 (10), 927

28. Friedrich, C. J., et al., J. Therm Spray Tech. (2001) 10 (4), 592

11. Clarke, D. R., Surf. Coat. Technol. (2003) 163-164, 67

29. See http://atfinet.com

12. Levi, C. G., Curr. Opin. Solid State Mater. Sci. (2004) 8 (1), 77

30. Raghavan, S., et al., Scripta Mater. (1998) 39 (8), 1119

13. Stecura, S., NASA Report TM-86905, NASA, Cleveland, (1985)

31. Yang, H.-S., et al., Acta Mater. (2002) 50 (9), 2309

14. Schelling, P. K., and Phillpot, S. R., J. Amer. Ceram. Soc. (2001) 84 (12), 2997

32. Winter, M., PhD Thesis, University of California, Santa Barbara, in preparation

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