Heat transfer through nanoscale multilayered thermal barrier coatings at elevated temperatures

Heat transfer through nanoscale multilayered thermal barrier coatings at elevated temperatures

Surface & Coatings Technology 275 (2015) 75–83 Contents lists available at ScienceDirect Surface & Coatings Technology journal homepage: www.elsevie...

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Surface & Coatings Technology 275 (2015) 75–83

Contents lists available at ScienceDirect

Surface & Coatings Technology journal homepage: www.elsevier.com/locate/surfcoat

Heat transfer through nanoscale multilayered thermal barrier coatings at elevated temperatures D. Josell a,⁎, J.E. Bonevich a, T.M. Nguyen a, R.N. Johnson b a b

Materials Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, United States Pacific Northwest National Laboratory, Richland, WA 99354, United States

a r t i c l e

i n f o

Article history: Received 11 December 2014 Revised 18 May 2015 Accepted in revised form 19 May 2015 Available online 23 May 2015 Keywords: Thermal barrier coating Heat transfer Interfacial thermal resistance Interfacial thermal conductance Multilayer Alumina Zirconia 7YSZ

a b s t r a c t Heat transfer through thermal barrier coatings (TBCs) composed of alternating nanometer thick layers of aluminum oxide and 7% yttria stabilized zirconia (7YSZ) was studied by pulsed heating at temperatures in the range 1275 K to 1375 K. The thermal diffusivity of the TBCs, deposited on thin metal foils by electron beam evaporation and coated with an opaque, submicrometer metal capping layer, was studied by applying a sub-μs duration heating pulse from a Q-switched laser to the substrate and then monitoring the temperature rise on the opposing, metal-capped surface of the TBC. The recorded temperature transients were modeled using properties of the constituent materials in order to obtain an upper bound of the thermal resistance associated with the interfaces between layers. The results thus provide insight into the feasibility of using interfacial thermal resistance in this material system to improve TBC performance by decreasing thermal conductivity. Published by Elsevier B.V.

1. Introduction 1.1. Background Thermodynamic considerations place well understood temperaturedependent limits on the possible efficiency of combustion engines. The desire for increased efficiency of airplanes and power plants thus pushes engine operation toward higher temperatures. Thermal barrier coatings (TBCs) are key to progress in this regard as they increase operating temperatures by reducing the temperatures experienced by key engine parts such as turbine blades and rotors consistent with material-related limitations. Absent voids, interface-related photon or phonon scattering and intermixing, the introduction of a higher thermal conductivity material into a lower thermal conductivity material will yield a composite of intermediate thermal conductivity. The question of relevance to thermal barrier applications is whether the introduction of sufficient interfaces can, specifically through their impact on phonon and/or photon mediated energy transport, more than compensate for the degraded bulk thermal conductivity, thereby producing a material for TBC applications with lower effective thermal conductivity than either constituent. There exists a substantial literature on a range of properties of multilayer TBCs ([1,2] and references therein). The broader search for ⁎ Corresponding author at: 100 Bureau Dr., NIST, Gaithersburg, MD 20899. E-mail address: [email protected] (D. Josell).

http://dx.doi.org/10.1016/j.surfcoat.2015.05.036 0257-8972/Published by Elsevier B.V.

advanced materials with lower thermal conductivity [3,4] includes study of thermal transport in TBCs composed of coated or layered nanoparticles [5,6] as well as homogeneous materials with controlled interface density [7,8] and multiphase [9] and multilayer TBCs [10]. In some cases, thermal conductivities are found to be below those anticipated using volume weighted properties. However, where interfaces are present, the overall transport properties of the composite material are typically provided without explicit evaluation of the impact of an interface. The elevated temperature, steady-state laser heatflux measurement approach used in some cases complicates such evaluation; these experiments can involve a temperature drop across the TBC of 200 K to 500 K [11] so that temperature dependent thermal conductivity (e.g., that of Al2O3 changes by 500% from 575 K to 1275 K) [12] likely overshadows interface properties. In other cases, uncontrolled internal geometry precludes such evaluation. At lower temperatures, an interfacial thermal resistance (ITR) ρ [cm2 K/W], also known as an interfacial thermal impedance, or its inverse, known as the Kapitza conductance, is usually used to relate heat flow across an interface by phonon conduction to the associated temperature discontinuity across the interface ([13–15] and references therein). In many cases the ITR is measured using multilayered materials specifically because such materials permit the interface density to be systematically varied. While, as with studies of TBCs, some studies focus on the overall transport properties, a large number of studies using a number of techniques have focused on evaluating ITR. Among these, room temperature thermoreflectance studies of a number of


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metal/metal systems yielded values of 2.3 × 10−5 cm2 K/W and below [16]. Measurements on yttria-stabilized zirconia and amorphous silicon dioxide multilayers using the 3ω method found an upper limit of 1 × 10−6 cm2 K/W for YSZ/SiO2 interfaces [17]. Mirage technique measurements on Ti/Al multilayers found 2.1 × 10−6 cm2 K/W [18]. Larger values of ITR ranging from 10− 4 cm2 K/W to as high as 10−2 cm2 K/W have been found [13–15]. These are typically for the interfaces between highly dissimilar materials at and near room temperature. However, ITR measurements using contact probes and heatsinks [19,20] are incapable of separating the contribution of the internal interface of interest from that of the specimen/heatsink interface associated with the measurement approach. Values of ITR exceeding 10−2 cm2 K/W obtained using this technique are thus suspect. Indeed, even higher values have been found to be associated with the specimen/heatsink interface [21]. That said, an ITR as high as 10−2 cm2 K/W can substantially reduce thermal conductivity in micrometer-scale multilayer materials while even an ITR of order 10−4 cm2 K/W can do the same in nanometerscale multilayered materials. Such values suggest multilayer TBCs hold substantial promise for improving the performance of TBCs. However, at the elevated temperatures relevant to TBC operation, pulsed heating measurements of Cu/Fe multilayers at 1200 K determined the impact of interfaces on thermal transport could be captured using an ITR no higher than the mid 10−5 cm2 K/W [22]. Similar experiments on Mo/ alumina multilayers yielded an upper bound ITR of 6 × 10−5 cm2 K/W [23]. The authors are not aware of studies of ITR for oxide systems at temperatures relevant to the operation of thermal barrier coatings. This paper therefore details pulsed heating experiments conducted on alumina/7% yttria stabilized zirconia (7YSZ) multilayer thermal barrier coatings with modeling to quantify the impact of the internal interfaces on heat flow through these materials. 1.2. Interface resistance and thermal conductivity in multilayered materials If the basic bilayer repeat unit of a multilayer material is to be superior to an equivalent thickness of homogeneous material then the thermal resistance of the two layers (equal to the ratio of layer thickness d and thermal conductivity κ) plus the thermal resistance of the two interfaces between them (2ρ) must exceed the thermal resistance of a single layer of the lower conductivity material that is as thick as the two layers combined, i.e., d1 þ d2 d1 d2 b þ þ 2ρ: κ1 κ1 κ2


Here κ1 is the thermal conductivity of the lower conductivity material, κ2 that of the higher thermal conductivity material, while d1 and d2 are their respective thicknesses. The effective thermal resistivity of the composite material 1/κeff is given by   1 d2 −1 d1 ¼ ðd1 þ d2 Þ þ þ 2ρ : κeff κ1 κ2


For nonzero ITR ρ, this effective thermal resistivity can be made arbitrarily large by reducing the thicknesses d1 and d2 to zero. While arbitrarily small layers are not possible (or likely stable), the thermal resistivity should be maximized by making the layers, especially the higher conductivity constituent, as thin as possible. Just how thin the layers must be to obtain significant improvement depends on the value of the ITR and the difference between the thermal conductivities of the two constituents. 2. Experiment details The multilayer TBCs were deposited on metal foils from 1 cm to 2 cm across at Howmet Corporation and Pacific Northwest National

Laboratory.i Depositions were conducted using a 10 kW electron beam evaporator deposition system in a vacuum chamber with base vacuum of 10− 6 Torr (10−4 Pa) or better. Compositional modulation was accomplished using a rotating shutter that allowed only alternating exposure of the two sources. The controlled-power deposition rates were in the range 0.1 nm/s to 1 nm/s based on TBC thicknesses and deposition times. Depositions were conducted without additional oxygen, the stationary substrates maintained at temperatures between approximately 1275 K and 1350 K using quartz tube radiant heaters. A submicrometer metal capping layer was deposited on the surface of each TBC. The optically opaque top layer ensured that pyrometry measured the surface temperature alone in the event of significant radiative transport within the coating; it had negligible impact on thermal transport through the structure. Fig. 1 shows a cross-sectioned TBC imaged using a scanning electron microscope; the brighter layers are the 7YSZ. The thickness and average composition of each TBC were determined after the transport measurements were conducted. Using the number of layers in the TBC, the average thicknesses of the individual Al2O3 and 7YSZ layers were then determined. The deposits exhibit a columnar growth structure. Transmission electron microscopy (TEM) was conducted using a FEI Titan operating at a voltage of 300 kV. Fig. 2a shows a region of the same TBC imaged using scanning transmission electron microscope (STEM) mode. The line indicates the location where a scan of the elemental distribution within the layers was conducted. Integration of the energy dispersive X-ray (EDX) spectrum along the line, shown in Fig. 2b, indicates the elements present in the coating. The composition of select elements along the scan (from upper left to lower right in the image) is shown in Fig. 2c. Fig. 3 shows higher magnification TEM imaging of the same specimen; the relative contrast of the layers has switched from that obtained in STEM mode so that the Al2O3 layers are now brighter. There is some indication of porosity in Figs. 1 and 2, particularly between the columnar grains. TEM characterization of an Al2O3/7YSZ TBC with ≈ 5 nm layer thickness similar to that of specimens for which thermal transport was examined is shown in Fig. 4. The columnar structure and scalloping of the layers are similar to those seen with the TBC having thicker layer. The nonplanarity arises within the thickness of the deposit as well as from the underlying Nb substrate surface. Regions of decreased density are evident between the columnar grains. Fig. 4b shows no such porosity within a single grain. In metal/metal multilayers with similarly thin layers, epitaxy of the layers within a column grain is sometimes observed [24,25]. A diffraction pattern obtained from the multiple layers within the grain pictured in Fig. 4c is inset; the probe beam, with diameter slightly larger than the grain width, was centered in the middle of the image. The brightest spots, exhibiting 2-fold symmetry, indicate a single orientation for the contributing layers. The integrity of the layering is seen in the lower and higher magnification images. It is also evident in the overlaid compositional map of the Zr distribution in Fig. 4c obtained in STEM mode; fluorescence induced by the higher energy X-rays generated in the adjacent Zr prevented acquisition of a corresponding Al map at this length scale. Pulsed heating experiments at temperatures ranging from approximately 1250 K to 1375 K were used to measure thermal transport through the coatings. As these temperatures are similar to those associated with the TBC depositions, and test durations were shorter than the deposition times, the microstructures shown are representative of both as-deposited and post-study microstructures. The TBCs on the substrates upon which they were deposited were tested in a vacuum

i Certain commercial equipment, instruments, or materials are identified in this paper in order to specify the experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the materials or equipment identified are necessarily the best available for the purpose.

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Fig. 1. A 7YSZ/Al2O3 multilayer thermal barrier coating imaged in cross-section at three different magnifications using a scanning electron microscope. The multilayer structure is evident with the uniformly thick 7YSZ layers appearing brighter due to the higher electron density. Although there are no voids apparent between them, the columnar grain structure is evident in the cleaved surface geometry. The scale bar is 2 μm in all images.

furnace using the Q-switched laser pulsed heating system previously used to study Cu/Fe and Mo/alumina multilayers [22,23]. The measurement system, without the Q-switch, has been described in greater detail [26]. The temperature in the tungsten specimen holder within the furnace was assessed before each experiment using an optical pyrometer aimed at a small hole in the side of the specimen holder, providing a near-blackbody temperature reading. The pyrometer was itself calibrated using a NIST certified calibrated tungsten lamp.

The laser pulse was applied to the substrate side of the specimens over a circular area approximately 4.5 mm in diameter. The resulting temperature transient on the metal-capped, TBC side of the specimens was assessed from the voltage response of an InGaAs detector viewing a smaller, centered region through an optical fiber. The radiance of the metal-capped TBC surface was recorded digitally at a 1 Mhz frequency, the thin metal capping layer ensuring the signal corresponded to the temperature at the surface of the TBC. Data recording started a specified

Fig. 2. a) An intermediate magnification image of a 7YSZ/Al2O3 multilayer thermal barrier coating imaged in cross-section using STEM mode. A line marks the location of a scan of the elemental distribution within the layers. b) The X-ray photoemission spectrum integrated along the line scan exhibits peaks associated with the Zr, Al, Y and O within the TBC. c) The variation of different peak intensities along the line scan yields the distribution of select elements within the layers.


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Fig. 3. Higher magnification views of a 7YSZ/Al2O3 multilayer thermal barrier coating imaged in cross-section by TEM.

period of time before application of the heating pulse to provide a baseline signal. Multiple pulsed heating experiments were performed on each specimen. The specimens are sufficiently thin as compared to the diameter of the irradiated region and the temperatures are sufficiently low that neither lateral heat flow nor radiative losses would be significant during measurements of the rear-surface temperature transient on homogeneous specimens [27–29]. 3. Model details The recorded transients were analyzed using a temperature and heat flux transfer matrix approach [29] to quantify heat flow through the layers in the TBC and underlying substrate. In this analysis, a 2 × 2 matrix relates sinusoidally oscillating temperature and heat fluxes on both sides of a material layer or interface with ITR. The matrix elements are

functions of the frequency ω and the thermal conductivity κ, thermal diffusivity α, and thickness d of the layer or interface with ITR ρ. For temperature To and heat flux Qo (into the layer) on one side and temperature T1 and heat flux Q1 (out of the layer) on the other side, the matrix relating the coefficients is 

Q0 T0


coshðkdÞ sinhðkdÞ=kκ

sinhðkdÞkκ coshðkdÞ

 Q1 ; T1


where k = (iω/α)1/2 with i = (− 1)1/2. Across an interface with ITR ρ the matrix relationship is: 

Q0 T0


1 ρ

0 1

 Q1 : T1


Fig. 4. Multilayer TBCs with ≈5 nm thick layers imaged in cross-section. a) Lower magnification TEM image indicates decreased deposit density and/or porosity at the boundaries between the columnar grains. b) A more uniform appearance is seen in higher magnification imaging of a single grain. c) The Zr distribution is mapped (inset left) in STEM mode using the Zr K-edge. Selected area diffraction (inset at upper left) of a region centered in the columnar grain indicates uniform crystal orientation within each type of layer in the grain.

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For a multilayer TBC, multiplication of the matrices for all the layers and interfaces yields a single matrix relating the temperatures and heat fluxes on the front and rear surfaces of the entire specimen, substrate, TBC and coating 

Q Front TFront


M11 M21

M12 M22

 Q Rear : TRear


For applied heat flux associated with a sub-microsecond heating pulse on one side and zero heat loss on both surfaces otherwise, QFront = 1 (the transform of an infinitesimally short heating pulse) and QRear = 0. Eq. (5) then yields QFront = M12TRear. The rear surface temperature is obtained as a function of time following the heating pulse using the inverse Fourier transform of 1/M12(ω). The temperature on the rear surface is determined without the computational mesh and convergence issues of the full time and space solution, a considerable benefit for multilayer structures with thousands of layers. Furthermore, the matrices representing the hundreds or thousands of bilayer repeat units (Al2O3/interface/7YSZ/interface) of a periodic multilayer material can be replaced by just three matrices using eigenvector and eigenvalue decomposition. The form of these three matrices, expressed in terms of κ, α, and d of the layers, ρ of the interfaces and the number of bilayers has been detailed previously [22]. The full solution, including terms for the substrate, multilayer TBC and metal capping layer, has been used to analyze the data from pulsed heating experiment with Cu/Fe [22] and alumina/Mo [23] multilayers. Use of published recommended property values for the constituent layers leaves only the ITR ρ as a fitting parameter. It is noteworthy that if the individual layers are thin compared to the entire thickness of the multilayer TBC (i.e., the multilayer is composed of many bilayers) then the matrix solution for the multilayer approaches that for a homogeneous film of thermal conductivity κeff as given in Eq. (2) and thermal diffusivity αeff given by [22] "


 −1 # d1 κ1 d2 κ2 κ ¼ ðd1 þ d2 Þ þ κEff ≡ Eff : α1 α2 CEff


The expression in square brackets is the inverse of the specific heat per unit volume of the multilayer, the specific heats per unit volume of each type of layer (C = κ/α) weighted by the thicknesses of the layers, hence the definition αeff = κeff/Ceff. Nonetheless, the full solution was used to model the experimental transients obtained with the TBCs, unless indicated otherwise. 4. Results and discussion 4.1. Homogeneous substrates The metal substrate materials without TBCs were studied in order to improve the accuracy of the modeling for the TBC/substrate specimens. Data obtained during a pulsed heating experiment on a bare stainless steel substrate, shown in Fig. 5, demonstrates the temporal resolution of the measurement system. Calibration using black body pyrometry does permit both absolute temperature and temperature increase. However, as is typical in such experiments, the data is normalized to the maximum response and the baseline signal is nulled. Scaled in this manner, the transients are independent of the overall temperature rise for the modest (several degrees Kelvin) overall temperature increase associated with the plateaus in these experiments. The response can be characterized in terms of the time required to reach half the maximum response, t1/2. For adiabatic heating (no heat loss) and homogeneous specimens of thickness d this value is related to the thermal diffusivity α of the material using the relationship [27–31] 2

t1=2 ¼ 1:37

d : π2 α


Fig. 5. Normalized pulsed heating transients from a bare 53 μm thick stainless steel substrate with overlaid fitted curves from the solution for homogeneous material. a) Test temperature is 1441 K, thermal diffusivity α = 0.0593 cm2/s. b) Test temperature is 1356 K, thermal diffusivity α = 0.0584 cm2/s, slightly expanded timescale.

obtained from the full transient solution for homogeneous specimens. For nonzero heat loss from the front and back surfaces, the most commonly cited solution is a modification of Eq. (7) using an erroneous expansion in the Biot number [30]; the correct equation has been published [31] (and acknowledged by the authors of the original work [32]). For the conditions used in these experiments, heat loss from these surfaces is not a significant factor. Fig. 6 shows temperature transients recorded during pulsed heating experiments on bare Nb substrates. Fitting of results including that shown in Fig. 6a using the homogeneous solution yields a thermal diffusivity of ≈ 0.24 cm2/s. This is consistent with the recommended value of 0.26 cm2/s, stated to be within ± 13% of the true value in this temperature range [33]. Experimental repeatability is demonstrated in Table 1, which lists the thermal diffusivity values obtained from four pulsed heating experiments at each of three test temperatures. The standard deviations are seen to be 1% or less of the average value at each temperature. Indeed, measurements for each specimen studied in this paper reflect the consensus results of multiple pulsed heating experiments. In this case the system resolution and repeatability make clear the impact of oxygen exposure that occurs during deposition of the TBCs; the ≈ 20% reduction of thermal diffusivity is captured by the slower transient shown in Fig. 6b. The reduced transport reflects both the formation of a surface oxide, the darkened surface also underlying higher radiance providing improved signal to noise, as well as 3% (atomic) solubility of oxygen in Nb at temperatures near 1300 K [34]. The decreased thermal diffusivity is presumed to be associated with decreased thermal conductivity rather than increased specific heat. Table 2 summarizes values for the thermal conductivities and thermal diffusivities for all the materials contained in the TBCs,


D. Josell et al. / Surface & Coatings Technology 275 (2015) 75–83 Table 2 Thermal diffusivities and thermal conductivities of test materials at temperatures near 1300 K for use in heat flow modeling [12,33,35]. These published recommended values have uncertainties that are 10% or higher near 1300 K. The values for Nb are based on experimental measurements of oxygen-exposed Nb specimens (Fig. 6b). The values for the stainless steel substrate have been similarly scaled from experimental results (Fig. 5). The properties of zirconium dioxide are used for 7% yttria stabilized zirconia (7YSZ). Material

Thermal conductivity κ (W/cm K)

Thermal diffusivity (cm2/s)

Zr2O (for 7YSZ) Al2O3 Mo Nb Stainless steel

0.021 0.067 1.05 0.59 0.25

0.0051 0.014 0.339 0.21 0.050

only ± 1% to 2% every 100 K for temperatures near 1300 K, a modest change compared to the noted uncertainties, the stated values are used for all modeling herein. 4.2. Multilayer TBCs

Fig. 6. Normalized pulsed heating transients from a bare 280 μm thick Nb substrate with overlaid fitted curves from the solution for homogeneous material. a) Test temperature is 1248 K, thermal diffusivity α = 0.242 cm2/s, tested as-received. b) Test temperature is 1381 K, thermal diffusivity α = 0.200 cm2/s. Tested after being exposed to oxygen at 1338 K during deposition of a thermal barrier coating. Darker (higher emissivity) oxidized surface is responsible for higher signal to noise as compared to as-received Nb.

substrates and capping layers to be used in modeling the experimental transients. The thermal diffusivity of oxidized Nb is included rather than the recommended value based on the measured impact of the oxidizing environment during the TBC depositions. The recommended thermal conductivity is similarly scaled. The thermal diffusivity of the stainless steel substrates is scaled down from the experimentally obtained value (see Fig. 5), as is the recommended thermal conductivity, for the same reason. Because the recommended property values change by

With better understanding of the substrate properties in hand, Fig. 7 shows a temperature transient recording during a pulsed heating experiment with multilayer TBC1 on its Nb substrate. Table 3 details relevant specimen parameters and test conditions. Predicted transients are shown for bulk properties with and without interface thermal resistance. The transient predicted using as-received α (and correspondingly higher κ) for the Nb substrate, with properties for the other materials from Table 2, rises more rapidly than is observed experimentally. Use of the properties for oxygen-exposed Nb yields a good fit to the data. For comparison, least squares fitting of the solution for a homogenous specimen to the experimental data provides a comparatively poor fit; although the layers in the TBC are thin enough that it can be modeled as homogeneous, the specimen is effectively a two layer specimen because of the underlying Nb substrate. The transient predicted using an interface thermal resistance ρ = 1 × 10−5 cm2 K/W overestimates the transient rise time substantially. A temperature transient recorded with multilayer TBC2 on its Nb substrate is shown in Fig. 8. Relevant details are provided in Table 3. Predicted transients are shown for ρ = (0, 1 and 2) × 10−5 cm2 K/W. The behavior of this TBC/substrate specimen is consistent with an interface thermal resistance of approximately 1 × 10− 5 cm2 K/W.

Table 1 Test temperatures and measured thermal diffusivity values for a series of pulsed heating experiments on a bare 281 μm thick as-received Nb substrate at test temperatures of approximately 1250 K, 1375 K and 1500 K. Average values are indicated with standard deviations of the four measurements in the final column. Temperature (°C)

Thermal diffusivity (cm2/s)

Thermal diffusivity (cm2/s)

969 975 977 980 1095 1100 1102 1103 1231 1232 1232 1232

0.247 0.242 0.240 0.244 0.244 0.244 0.242 0.239 0.237 0.237 0.236 0.239

0.243 ± 0.003

0.242 ± 0.003

0.237 ± 0.002

Fig. 7. Normalized pulsed heating transient for TBC1. The overlaid curves are model predictions using materials properties from Table 2 with ρ = 0 cm2 K/W and ρ = 1 × 10−5 cm2 K/W, substitution of as-received properties for the Nb substrate with ρ = 0 cm2 K/W, and a best-fit solution for homogeneous material.

D. Josell et al. / Surface & Coatings Technology 275 (2015) 75–83


Table 3 Multilayer thermal barrier coating specimen geometry and test temperature for the pulsed heating experiments shown and modeled in Figs. 7 to 10. TBC4 is imaged in Figs. 1– 3. Thermal barrier coating

7YSZ thickness (nm)

Al2O3 thickness (nm)

Number of bilayers

Substrate/cap material, thickness (μm)

Temperature (K)

1 2 3 4

4.5 16.0 5.9 370

3.5 1.76 5.9 190

2625 1998 3416 200

Nb, 255/Nb, 0.5 Nb, 71/Nb, 0.9 Nb, 0/Nb, 0.5 SS, 51/Ti, 0.2

1265 1276 1320 1376

Unlike Fig. 7, there is a modest signal droop at longer time rather than a steady plateau. Specimens that were significantly wider than the 4.5 mm diameter heated region manifested such behavior, particularly if they had thicker TBCs; multiplying the layer thicknesses by the number of bilayers in Table 3 gives a total thickness for TBC2 of over 35 μm while TBC1 is only 21 μm. Slow heat transfer across the low diffusivity TBC versus rapid lateral heat transfer along the plane of the high diffusivity metal substrate to the unheated periphery of the specimen underlies the observed cooling. The temperature transient from multilayer TBC3 shown in Fig. 9 was obtained with the TBC tested as a free-standing thin film after it delaminated from its substrate. Relevant details are again found in Table 3. Predicted transients are shown for ρ = (0 and 1) × 10 − 5 cm 2 K/W. Because, absent the substrate, transients predicted by the multilayer solution are indistinguishable from transients predicted by the solution for homogeneous specimens, a least squares fit solution for a homogeneous specimen is also shown and indicates ITR of approximately 1.2 × 10−5 cm2 K/W. Least square fitting of the homogeneous solution to three pulsed heating experiments (one of which is shown) yields αeff values of (3.8, 4.3 and 4.4) × 10−3 cm2/s. Multiplying by Ceff = 4.45 J/cm3 K (obtained using the layer thicknesses from Table 3 and thermophysical properties from Table 2 in Eq. (5) yields κeff values of (1.7, 1.9 and 2.0) × 10− 2 W/cm K, slightly lower than the 2.1 × 10− 2 W/cm K of zirconia. The relatively large variation of the best-fit thermal diffusivities αeff results from the oscillations on the rising transient. This ringing of the measured radiative light flux is associated with geometry change arising from drum-head oscillations of the thin, suspended circular specimen induced by the thermal pulse rather than temperature fluctuations.

Fig. 8. Normalized pulsed heating transient for TBC2. The overlaid curves are model predictions using materials properties from Table 2 and the indicated values of interface thermal resistance ρ.

Fig. 9. Normalized pulsed heating transient for TBC3. The overlaid curves are model predictions using materials properties from Table 2 with interface thermal resistance ρ = 0 cm2 K/W and ρ = 1 × 10−5 cm2 K/W as well as a fit to the solution for homogeneous material. Ringing of the radiance used to determine the temperature is associated with drum-head oscillations of the suspended circular specimen rather than temperature fluctuations.

Fig. 10 shows a temperature transient recorded with multilayer TBC4 on a stainless steel substrate, relevant details again being located in Table 3. More modest ringing than in Fig. 9 is observed because of the thin substrate. The TBC is modeled as a homogeneous material with αeff = (5.0, 5.5 and 6.0) × 10−3 cm2/s. The κeff obtained from αeff = 5.5 × 10−3 cm2/s of the best fit using αeff Ceff is 2.7 × 10−2 W/cm K.

Fig. 10. Normalized pulsed heating transient TBC4. The overlaid curves are model predictions obtained using properties from Table 2 for the substrate and for the specific heat of the TBC, with the TBC treated as uniform material having thermal diffusivity αeff = (5, 5.5 and 6) × 10−3 cm2/s. Ringing of the radiance used to determine the temperature is associated with drum-head oscillations of the suspended circular specimen rather than temperature fluctuation.


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4.3. Discussion Pulsed heating transient experiments are a straightforward, highly accurate approach for measuring thermal diffusivity of homogeneous materials such as substrates or free-standing films. However, evaluation of results from pulsed heating experiments on layered structures, or to translate experimental results into thermal conductivity, requires independent knowledge of volumetric specific heat(s). In this work, independent measurements of average composition and/or layer thickness were used with published recommended property values for the majority oxide constituents. Inaccuracy in the determination of volume fraction and/or deviation of specific heat from a volumetric dependence will result in inaccurate determination of the thermal conductivity of the multilayer that is of principle interest. Significantly, specimens with relatively thick Nb, thinner stainless steel, and no substrate at all yielded similarly small values of interfacial thermal resistance ρ in the range (0 to 1) × 10−5 cm2 K/W, the lower value from the results for TBC1 and the higher value from the results for TBC2 and TBC3. Table 4 summarizes the multilayer TBCs examined in this study. The thermal resistance associated with a single bilayer obtained by adding the ratios of the layer thicknesses and thermal conductivities (values from Table 3) of the two layers is compared to the value of ITR obtained by analysis of the data from the particular specimen. For the TBC with 370 nm thick 7YSZ layers the bulk contribution is so large that the predicted transient is insensitive to interface contributions of this magnitude and measurement variation precludes a meaningful estimate; this also likely underlies the slightly negative and zero values of ITR obtained for the TBCs with 57 nm thick 7YSZ layers. For the TBCs with 7YSZ layer thickness of 16 nm and ≈ 6 nm, the average ITR value is 1.3 × 10−5 cm2 K/W; the 95% confidence interval obtained from two standard deviations of the data from the average value is (1.3 ± 0.8) × 10−5 cm2 K/W. With a length scale significantly coarser than, and independent of the layer thickness, the intergranular regions of lower porosity observed by the electron microscopy should not yield a dependence of thermal transport on layer thickness. Nonetheless, the possibility of reduced thermal transport due to these regions suggests that values of ITR obtained in this study are to be viewed as upper bounds on the actual value. For the TBCs with layers of nanometer thickness, predicted transport properties are strongly influenced by the value of ITR (see Eq. (2)). Thus, while measurement insensitivity to ITR of 10−5 cm2 K/W explains the seemingly anomalous results for the TBCs with 57 nm and thicker layers, this is not the case for the TBCs with 1 nm and 2 nm thick layers. The absence of impact from the interfaces, and associated ITR, is unambiguous; the transport properties are consistent with ITR of

“zero” (or well below 10−5 cm2 K/W). The conductivity of these materials is thus higher than that of the more coarsely layered structures, behavior analogous to that reported for multilayered Au/Si versus homogeneous annealed material [15]. It is possible that interface roughness and/or diffuseness indicated by microscopy (Figs. 3 and 4) degrades layer integrity in the very finest layers and underlies this behavior. Such interdiffusion is observed in annealing studies of alumina/zirconia multilayers with nanoscale layers, albeit they contain nonequilibrium structures due to room temperature fabrication and zirconia rather than 7YSZ [36]. In any case, the consistency of the predictions, which are based on bulk properties, with the experimental results for TBCs having these thinnest and thickest of layers supports the reasonableness of assumptions made in the modeling including neglect of explicit radiative transfer within multilayer TBCs such as has been modeled in other analyses [37,38]. Using Eq. (2), a 1 × 10−5 cm2 K/W value of ITR, thermal conductivities from Table 2 and layer thicknesses for the four specimens examined in Table 3, values obtained for κeff are 0.0171 W/cm K (TBC1), 0.0180 W/cm K (TBC2), 0.0207 W/cm K (TBC3) and 0.0272 W/cm K (TBC4). The thermal conductivities of two of the TBCs are thus expected to be significantly lowered from the 0.021 W/cm K value of ZrO2 by the interface thermal resistance: TBC1 due to its especially thin layers and TBC2 due to its very small volume fraction of Al2O3. TBC3 is expected to exhibit conductivity essentially unchanged from that of ZrO2, its high fraction of Al2O3 balancing out the interface effects. TBC4 is expected to exhibit conductivity that is higher than that of ZrO2, its behavior being dominated by the Al2O3 substitution rather than interface effects due to its especially thick layers. The summary in Table 4 indicates that a number of the TBCs exhibit ITR that is a substantial fraction of the thermal resistance associated with the material in the layers. For the TBCs with 7YSZ approximately 6 nm thick (which includes TBC3) the two interfaces in each bilayer increase the thermal resistance by approximately 50%; this reduces the thermal conductivity by approximately one-third (Eq. (2)). Based on the summary in Table 4, it is unclear if the absence of ITR with TBC1 reflects the decrease of ITR clearly evident with the thinner layers or just measurement scatter. The experimental and predicted thermal conductivities for TBC4 are consistent, both ≈ 0.027 W/cm K, albeit because the interfaces having a negligible impact due to the thick layers. As the very thinnest layers offer no further advantage, an approach for improved performance of thermal barrier coatings might instead involve looking for pairs of materials whose thermal conductivities are not only low but also closer together than those of Al2O3 and 7YSZ so that interfacial thermal resistance can add to the performance of the superior material rather than making up for the deficit introduced by incorporation of the inferior.

Table 4 Multilayer thermal barrier coating specimens examined in this study, ordered by 7YSZ layer thickness. The thermal resistance associated with the two layers in each bilayer is compared to the best fit ITR value. The four specimens TBC1–TBC4 for which analysis of experimental results is presented in greater detail are indicated. Thermal barrier coating

7YSZ thickness (nm)

Al2O3 thickness (nm)

Number of bilayers

Thermal resistance of bilayer without interfaces (10−5 cm2 K/W)

Interfacial thermal resistance of one interface (10−5 cm2 K/W)


370 57 57 16 6.3 6.2 6.0 5.9 4.5 3.0 1.8 2.6 1.0 0.9

190 6.6 6.6 1.8 6.5 7.2 8.5 5.9 3.5 2.1 2.1 2.4 1.3 1.2

200 800 800 1998 5130 1534 670 3416 2625 670 1534 900 16,320 16,320

200 28 28 7.9 4.0 4.0 4.1 3.7 2.7 1.7 1.2 1.6 0.67 0.61

–a –b 0 1.5 1.4 2 0.9 1.2 0 1.5 0.1 0.2 0 0



a b

Fit is insensitive to the value of interfacial thermal resistance due to layer thickness. Transient rises more rapidly than bulk prediction so fit yields an unphysical, negative interfacial thermal resistance.

D. Josell et al. / Surface & Coatings Technology 275 (2015) 75–83

5. Conclusions Pulsed heating experiments using a system capable of measuring specimen surface temperature with microsecond resolution were used to measure the thermal transport properties of multilayer thermal barrier coatings. The multilayer 7YSZ and aluminum oxide coatings were studied both on and off metal substrates. An analysis utilizing temperature and heat flux matrices for the layers and interfaces was used to model the results, the analysis taking advantage of the multilayer periodicity to substantially simplify calculations. The experimental temperature transients are found to be well predicted using reference properties of the constituent layers and an interfacial thermal resistance of approximately 1 × 10−5 cm2 K/W or less. The interfaces thus have only a modest impact on thermal transport in multilayer materials with layers more than a few tens of nanometers thick in the ≈1250 K to 1375 K temperature range of this study. Acknowledgments The authors thank Albert Feuerstein (formerly Howmet) for providing some of the multilayer thermal barrier coatings examined in this study. References [1] R. Braun, U. Schulz, C. Leyens, P.E. Hovsepian, A.P. Ehiasarian, Oxidation and fatigue behaviour of gamma-TiAl coated with HIPIMS CrAlYN/CrN nanoscale multilayer coatings and EB-PVD thermal barrier coatings, Int. J. Mater. Res. 101 (2010) 648–656. [2] D.E. Wolfe, J. Singh, K. Narasimhan, Synthesis and characterization of multilayered TiC/TiB2 coatings deposited by ion beam assisted, electron beam-physical vapor deposition (EB-PVD), Surf. Coat. Technol. 165 (2003) 8–25. [3] A.M. Limarga, S. Shian, R.M. Leckie, C.G. Levi, D.R. Clarke, Thermal conductivity of single- and multi-phase compositions in the ZrO2–Y2O3–Ta2O5 system, J. Eur. Ceram. Soc. 34 (2014) 3085–3094. [4] D.R. Clarke, S.R. Phillpot, Thermal barrier coating materials, Mater. Today 8 (2005) 22–29. [5] A. Karthik, P. Manivasakan, S. Arunmetha, R. Yuvakkumar, V. Rajendran, Production of Al2O3-stabilized tetragonal ZrO2 nanoparticles for thermal barrier coating, Int. J. Appl. Ceram. Technol. 10 (2013) 887–899. [6] L. Wang, Y. Wang, X.G. Sun, J.Q. He, Z.Y. Pan, C.H. Wang, A novel structure design towards extremely low thermal conductivity for thermal barrier coatings — experimental and mathematical study, Mater. Design 35 (2012) 505–517. [7] D.E. Wolfe, J. Singh, R.A. Miller, J.I. Eldridge, D.M. Zhu, Tailored microstructure of EBPVD 8YSZ thermal barrier coatings with low thermal conductivity and high thermal reflectivity for turbine applications, Surf. Coat. Technol. 190 (2005) 132–149. [8] J. Singh, D.E. Wolfe, R.A. Miller, J.I. Eldridge, D.M. Zhu, Tailored microstructure of zirconia and hafnia-based thermal barrier coatings with low thermal conductivity and high hemispherical reflectance by EB-PVD, J. Mater. Sci. 39 (2004) 1975–1985. [9] R. Vassen, M.O. Jarligo, T. Steinke, D.E. Mack, D. St ver, Overview on advanced thermal barrier coatings, Surf. Coat. Technol. 205 (2010) 938–942. [10] M.P. Schmitt, A.K. Rai, R. Bhattacharya, D. Zhu, D.E. Wolfe, Multilayer thermal barrier coatings (TBC) architectures utilizing rare earth doped YSZ and rare earth pyrochlores, Surf. Coat. Technol. 251 (2014) 56–63. [11] D. Zhu, R.A. Miller, B.A. Nagaraj, R.W. Bruce, Thermal conductivity of EB-PVD thermal barrier coatings evaluated by a steady-state laser heat flux technique, Surf. Coat. Technol. 138 (2001) 1–8.


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