[J. Res. Natl. Inst. Stand. Technol. 105 Thermal-Conductivity ...microscope for temperature measure-ment, coatings as thin as 20 1m can, in principle, be measured using this tech-nique

Volume 105, Number 4, July–August 2000Journal of Research of the National Institute of Standards and Technology

[J. Res. Natl. Inst. Stand. Technol. 105, 591 (2000)]

Thermal-Conductivity Apparatus forSteady-State, Comparative Measurement

of Ceramic Coatings

Volume 105 Number 4 July–August 2000

A. J. Slifka

National Institute of Standards andTechnology,Boulder, CO 80303

[email protected]

An apparatus has been developed to mea-sure the thermal conductivity of ceramiccoatings. Since the method uses an infraredmicroscope for temperature measure-ment, coatings as thin as 20 �m can, inprinciple, be measured using this tech-nique. This steady-state, comparative mea-surement method uses the known thermalconductivity of the substrate material as thereference material for heat-flow measure-ment. The experimental method is validatedby measuring a plasma-sprayed coatingthat has been previously measured using anabsolute, steady-state measurementmethod. The new measurement method has

a relative standard uncertainty of about10 %. The measurement of the plasma-sprayed coating gives 0.58 W�m�1�K�l

which compares well with the 0.62W�m�1�K�l measured using the absolutemethod.

Key words: guarded hot plate; infraredmicroscope; thermal-barrier coating;thermal conductivity; yttria-stabilized-zirco-nia.

Accepted: April 17, 2000

Available online: http://www.nist.gov/jres

1. Introduction and Motivation

Ceramic coatings have applications primarily as wearcoatings and thermal barrier coatings. Thermal-barriercoatings (TBCs), which are ceramic coatings applied tometal substrates, have applications in aerospace, gasturbine engines, and diesel engines. Frequently a TBCprotects a metal substrate material from both high tem-perature and excessive wear or corrosion. One may askwhy a monolithic ceramic is not used in these applica-tions and in most wear applications. Monolithic ceram-ics have poor thermal shock resistance and low fracturetoughness. The metallic substrate that a coating is ap-plied to provides the necessary toughness to enablemany applications where coatings are used. Ceramicsare applied as graded, layered, or monolithic coatings.The thermal conductivities of these coatings must beknown for engineering design and for design of newcoating systems for future applications. As new coating

systems are developed with lower thermal conductivitiesand higher mechanical reliabilities, thinner coatings canbe used.

This work reports the development of a steady-statemeasurement method for determining the thermal con-ductivities of ceramic coatings. Thermal measurementson these coatings are almost always done with transientmethods. Due to the processing methods used to applyceramic coatings, primarily plasma-spray (PS) and elec-tron-beam physical-vapor-deposition (EB-PVD), thesecoatings develop unique microstructures [1]. The uniquemicrostructures and anisotropy of TBCs stretch the lim-its of the assumptions underlying the mathematics thatapply to transient measurement of thermal diffusivityand steady-state measurement of thermal conductivity.Even though the laser-flash technique has been appliedsuccessfully for measuring the thermal diffusivity of

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ceramic coatings, it is useful to have a steady-statemethod for comparison. At NIST, we have been measur-ing steady-state thermal conductivity of monolithic ce-ramics and ceramic coatings using a guarded-hot-plateapparatus [2, 3]. Many of the coatings sent to us formeasurement are 150 �m thick or less, and a coating of150 �m is as thin as can be reliably measured in ourguarded hot plate. Therefore, we need a steady-statemeasurement method for thinner coatings to comple-ment our guarded hot plate and to complement the laser-flash technique commonly used to measure thermalproperties of these coatings. The method developed hereuses an infrared microscope to measure temperaturedifferences on millimeter-sized specimens. Heat losscalculations in Sec. 3 show that the small size of thespecimens allows the measurements to be made in air,rather than vacuum, which simplifies the apparatusneeded. The noncontact nature of the infrared tempera-ture measurement is an advantage, because any contactbetween a sensor and a small specimen would affect thetemperature of the specimen.

TBCs are used to protect metals from oxidation andexcessive thermal environments. The thermal conduc-tivity of the metallic substrate is generally known, as itis usually an alloy that has been used for some time. Ametallic substrate coated with a TBC can be used in acomparative, steady-state measurement of thermal con-ductivity with the substrate as the known comparativespecimen. This scheme is similar to the ASTM E 1225-87 Standard Test Method for Thermal Conductivity ofSolids by Means of the Guarded-Comparative-Longitu-dinal Heat Flow Technique (cut-bar technique) [4].There are two significant differences between this stan-dard method and the method developed here. One is thatthe test method developed here operates on a muchsmaller size scale, allowing, in principle, measurementof features on the order of 10 �m. Additionally, thismethod needs no guarding for heat losses, because theheat losses are negligible compared to the standard ex-perimental uncertainty, despite the small size of thespecimen used. The short distance over which the tem-perature measurement is made is a major factor forensuring negligible heat losses.

The thermal conductivity of a PS TBC was measuredusing a guarded-hot-plate (GHP) apparatus which usesdisk-shaped specimens of 69.85 mm diameter. TheGHP method is an absolute, steady-state method fordetermining thermal conductivity. Furthermore, theguarded-hot-plate technique requires that the samplehave a thermal barrier that is somewhat thick, 150 �mor more, because there is a finite and measurable ther-mal contact resistance between the specimen and sensorplates. As coatings become increasingly thin, resolvingthe difference between the thermal resistance due to the

coating and the thermal resistance of the interface be-tween the specimen and sensor plate becomes difficult.Therefore, a new technique applicable to a smaller sizescale is needed. The device developed here uses a ther-mal microscopy system based on an infrared scannerwhich accurately determines temperature for thermal-conductivity measurements.

2. Development and ExperimentalMethod

2.1 Development

As mentioned earlier, this method is a variation of theASTM E 1225-87 methodology commonly known asthe cut-bar technique. In the cut-bar technique, a speci-men of unknown thermal conductivity is sandwichedbetween two pieces of material with known thermalconductivity using a thermal grease and a pliable metalfoil to eliminate interfacial thermal contact resistancebetween the materials. Thermocouples placed along thelengths of the three material pieces yield information onthe rate of heat flow through the two reference-materialsections of known conductivity. The heat-flow rate canthen be used to determine thermal conductivity of theunknown specimen using the one-dimensional Fourierconduction equation:

Q = � � AdTdx

, (1)

where Q is the rate of heat flow, � is the thermal con-ductivity, A is the cross-sectional area through which theheat flows, and dT /dx is the temperature gradient. Ex-perimentally, dT is approximated by �T , the finite tem-perature difference, and dx is approximated by �x , thedistance over which the temperature difference is mea-sured.

In the new measurement method, only one section ofknown material is used, the substrate on which the coat-ing is applied. A second section of known material onthe other side of the coating is impractical. In addition,the technology of applying TBCs does not allow for theuse of an aid for reducing thermal contact resistancebetween the coating and substrate. Most coating pro-cesses use a thin bond coat, typically MCrA1Y or someother alumina-former between the substrate and coat-ing, to provide adhesion and to function as a diffusionbarrier. Here M corresponds to a polyvalent metal, but istypically nickel. Because there is no cross-check fordetermination of heat flow using this method due to thefact that the substrate material of known conductivity ison only one side of the coating, the validity of the testmethodology is demonstrated by measuring a coating

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that has been previously measured in a guarded hot plate[3].

For the measurement of the thermal conductivity ofceramic coatings, temperature must be determined ac-curately on a spatial scale of tens or hundreds ofmicrometers. Infrared microscopy is one way of deter-mining temperature on the necessary size scale. How-ever, it is not commonly used due to the high cost of ascanning system and the potential problem with emissiv-ity. An infrared microscope detects radiation over a cer-tain wavelength range, which is 8 �m to 12 �m in thiscase. In order to determine temperatures accurately, ei-ther the emissivity must be known or temperature mustbe calibrated for the sample of interest. Softwareschemes can be used to correct for emissivity, but theyare generally not very good, and greater accuracy can beachieved with temperature calibration, which is themethod used for this work. Infrared microscopy has thedistinct advantage of being a noncontact method of tem-perature measurement.

The microscope itself is first calibrated using a sap-phire blackbody provided by the manufacturer. Mea-surements are done over a range of temperatures and theresults are compiled by the manufacturers proprietarysoftware. The temperature of the blackbody is indepen-dently monitored with a calibrated thermocouple placedbetween the blackbody mount (brass) and a heatingstage. The manufacturer supplies a set of three constants

that yields a linear relation between temperature anddetector output over the calibrated temperature range.

To increase the emittance of both the coating andsubstrate surface, each specimen is cross-sectioned, pol-ished, then carbon-coated on the side which is to beviewed by the microscope. Polishing down to a grit sizeof 1 �m diamond results in a surface finish with rough-ness of at most 0.25 �m and only a 0.1 �m differencein height between the coating and substrate. Since thesubstrate is significantly softer than the coating, thesubstrate polishes faster than the coating. Figure 1shows a profilometry trace of a polished specimen. Sub-sequent carbon coating results in only a slightly roughersurface, as shown in Fig. 2.

Each carbon-coated specimen is then placed in alarge isothermal block of copper or aluminum and im-aged with the microscope. Small calibrated thermocou-ples are used to determine that the specimen is isother-mal. These thermocouples are small enough to measurethe temperatures of the coating and substrate, but toolarge to be placed with the precision needed for mea-surement of thermal conductivity. The emissivities ofthe substrate and coating phases can be determined byusing the known temperature of the specimen. Theseknown emissivities are then used to determine specimentemperatures accurately. Due to the high emissivity ofthe carbon coating, any differences in emissivity aresmall. The measurement of thermal conductivity uses

Fig. 1. Profilometric trace of the 0.87 mm thick plasma-spray coating, after polishing but beforecarbon coating.

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Fig. 2. Profilometric trace of the 0.87 mm thick plasma-spray coating, after polishing and carboncoating.

temperature-difference measurements of both the coat-ing and substrate. The temperature differences are rela-tively small and scale linearly with emissivity. The spec-imens tested generally have a measured coatingemissivity of 0.97 and the substrate has an emissivity ofat least 0.85 after thin carbon coating. Although athicker carbon coating takes longer to produce, it resultsin a uniform emissivity of 0.97 over the entire specimen,and is preferred because it simplifies the measurement.

2.2 Experimental Method

Figure 3 shows a schematic drawing of the primaryfeatures of the measurement system. The infrared mi-croscope has a single detector that is cooled by liquidnitrogen and is sensitive to a range of wavelength from8 �m to 12 �m. An internal rotating mirror scans thethermal image across the detector. The substrate side ofthe specimen is glued to a copper block through whichwater is pumped at constant temperature for cooling.Cyanoacrylate adhesive gives a repeatable joint betweenthe specimen and copper cooling block and also allowsspecimens to be easily removed with a moderate me-chanical shock. This preserves the carbon coating andallows subsequent retesting without any changes to thespecimen.

The infrared microscope has a fixed field-of-view of1.6 mm by 1.6 mm, so the specimen can be as small as1.6 mm by 1.6 mm by the specimen thickness. The

specimen could be larger and the microscope could viewjust the part of interest of the viewed side. In fact, sincethe heat that is conducted through a specimen of squarecross-section and a given thickness is proportional to thelength of a side squared and the heat lost to convection

Fig. 3. Schematic drawing of the primary features of the measure-ment method.

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is proportional to the length of a side, a larger squarespecimen will have a higher conduction-to-convective-loss ratio. However, calculations show that heat lossesare negligible for the small specimens used here, typi-cally 3 mm by 3 mm by 5 mm. One of the reasons fora small specimen is that it is difficult to obtain large,uniform, state-of-the-art specimens from industrial andacademic sources. In addition, there is a practical reasonfor a small specimen. The infrared microscope has afixed operating distance of 4 mm, limiting the availablespace near the instrument for the sample. The position-ing stage will handle a reasonable mass, but the mass ofa cooling stage that can remove the necessary amount ofheat from a large specimen becomes unmanageable.

The most practical method for heating the specimenis by means of a laser which provides an efficient non-contact source of heat. The desired heating power isabout 0.5 W to 1 W flowing through the specimen. A 10W, continuous-beam infrared laser is used to heat theceramic coating. The laser beam is defocussed, or ex-panded, and then limited by an aperture to produce aspot that covers the entire end of the specimen. Theaperture cuts out the central portion of the beam,providing uniform heating. Since an aperture is used,only about 20 % of the laser power goes into heating thespecimen. The laser is computer controlled to providerepeatability between successive runs. The Invar1-stabi-lized laser provides power at less than 2 % variation overthe 30 min duration of a test, which provides the stabil-ity necessary for the heat-flow to achieve steady-state.Heat flowing through the coating to the substrate isconducted away from the copper block by the coolingwater.

The infrared microscope has a very short depth offield, about 10 �m. Experiments show that the mea-sured temperatures are sensitive to focus. Measuredtemperature differences change by 25 % when the im-age is moved 30 �m out of focus. Fortunately, the spec-imen stage is very stiff and the focussing is fine enoughto easily be within 10 �m of apparent correct focus asdefined by the observer. Experiments show that changesof 10 �m from the apparent correct focus do not changethe recorded temperature significantly. The infrared mi-croscope, laser, and beamline optics are set up on anoptical table to reduce vibration that would cause addi-tional apparent thermal noise. Since water is pumpedthrough the cooling block, vibrations cannot be com-pletely eliminated, but the lines connecting the coolingwater bath to the cooling block are long and flexible.

1 Certain commercial equipment, instruments, or materials are identi-fied in this paper to foster understanding. Such identification does notimply recommendation or endorsement by the National Institute ofStandards and Technology, nor does it imply that the materials orequipment identified are necessarily the best available for the purpose.

The infrared scanning system allows temperature sen-sors to be placed, via software, on the field of view inincrements of 11 �m. These temperature spots are notphysical sensors, but rather a software device that mea-sures the temperature of a single pixel in the scannedfield-of-view. The temperature spots can be placed atprecise x -y coordinates. The software temperature sen-sors can be repeatably placed at fixed distances, two ormore on the coating and two or more on the substrate.The consistency of the data can be checked by placingmore than two temperature spots on the coating andsubstrate. The greater the spot spacing, the greater thetemperature difference between temperature spots and,hence, the greater the precision of the measurement. Thetemperatures of the four spots are measured at a rate of6 to 25 times per second for 30 min. This stream oftemperature data is used to verify steady-state tempera-ture during the test; the data are averaged to determineprecise temperatures. There is significant random ther-mal noise internal to the infrared scanner that can beminimized by this averaging. The temperature differ-ence �T , across a fixed, known distance �x , of thesubstrate is used in conjunction with the known thermalconductivity � of the substrate material to calculate theheat flow rate Q through the specimen with Eq. (1). Thetemperature difference �T , across a fixed, known dis-tance of the coating �x is then used along with thecalculated heat flow rate Q and the measured cross-sec-tional area A in Eq. (1) to determine the thermal conduc-tivity of the coating � .

3. Heat Loss Calculations

A useful measurement of thermal conductivity shouldbe as simple as possible, so the conductivity is measuredin air. The specimen could be enclosed in a vacuumchamber, but the complexity of adding a vacuum systemis undesirable at this point. Since the measurement isdone in air and the operating equation is one-dimen-sional, heat-loss calculations must be performed to de-termine whether convection and radiation strongly af-fect the heat flow. For radiative heat losses, heat-flowrates are calculated based on a typical conductive heat-flow rate. Since convective heat transfer is complex, atwo-dimensional analysis that gives the temperature pro-files of the specimen is used. The calculations show thatthe heat-flow through the specimen is dominated byunidirectional solid conduction.

3.1 Radiative Heat Losses

The heat loss by radiation can be calculated by start-ing with Planck’s blackbody radiation law and deter-mining the heat flow rate as:

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Q = S�� (T 4 � T 4amb), (2)

where S is the applicable surface area of the specimenradiating heat, � is the emissivity of the specimen sur-face, � is the Stefan-Boltzmann constant, T is the ther-modynamic temperature of the object radiating energy,and Tamb is the thermodynamic temperature of themedium into which radiation is received. For typicaloperating conditions of 50 �C above room temperature,with 1 W flowing through the specimen by solid con-duction, the total radiative heat loss is on the order ofone milliwatt. A major factor keeping this heat lossdown is the small surface area and thinness of the coat-ing.

3.2 Convective Heat Losses

The specimen geometry used in these measurementshas the appearance of a fin of uniform cross-section.One might think that the traditional heat-transfer analy-sis of a one-dimensional fin of uniform cross-sectioncan be used in this case to determine the convective heatloss for this measurement method. It cannot, because theexperimental condition used here includes a heat-gener-ation term that does not occur in the treatment for theone-dimensional fin equation. The addition of the heat-generation term, from the heating laser, makes the heatbalance different for this experimental case from that ofthe one-dimensional fin analysis. Therefore, a represen-tative two-dimensional analysis is used to examine themagnitude of convective heat losses from the specimenand the resulting temperature profile.

Since the specimens used for this experimentalmethod are square in cross-section, a two-dimensionalanalytical approach can be used to investigate the tem-perature profile in the specimen and the resulting con-vective heat losses. Symmetry allows us to use only aquadrant of the specimen sectioned lengthwise as shownin Fig. 4. The analysis is valid for any of the four equiv-alent sections shown in Fig. 4. The problem is to solvethe two-dimensional Laplace equation since the experi-ment is performed at steady-state:

2T (x , y )x 2 +

2T (x , y ) y 2 = 0 (3)

subject to the boundary conditions

T (x , y ) = Thot at x = 0, (4)

T (x , y ) = Tcold at x = a , (5)

T (x , y ) y

= 0 at y = 0, (6)

Fig. 4. Schematic drawing of how the three-dimensional specimen isseparated into representative, equivalent two-dimensional sections.

and �T (x , y )

y+ h T (x , y ) = h Tamb at y = b . (7)

Thot and Tcold are the hot and cold thermodynamic tem-peratures of the body in question and h is a heat-transfercoefficient. The constants a and b are position coordi-nates defining the length and width of the body. TheLaplace equation has many solutions. One convergentsolution is

T (x , y ) = �n�Bn sin�nx

a �cosh�nya ��

+ Thot + (Tcold � Thot)xa

, (8)

which satisfies the boundary conditions shown in Eqs.(4-7). The boundary condition shown in Eq. (7) is usedto determine the constant terms Bn . For the remainder ofthe derivation, T will be used in place of T (x , y ) forsimplicity. The first and second derivatives of the solu-tion, Eq. (8), are

Tx

=�n�Bn

na

cos�nxa �cosh�ny

a ��+(Tcold � Thot)

a,

(9)

2Tx 2 = �

n

Bn��na �2�sin�nx

a �cosh�nya �, (10)

Ty

= �n

Bn�na �sin�nx

a �sinh�nya �, (11)

and2Ty 2 = �

n

Bn�na �2 sin�nx

a �cosh�nya �. (12)

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Equations (10) and (12) show that the solution satisfiesthe Laplace equation, Eq. (3). Substitution of Eqs. (8)and (11) into Eq. (7) yields

� �n�Bn�n

a �sin�nxa �sinh�nb

a ��+ h��

n�Bn sin�nx

a �cosh�nba �� + Thot

+ (Tcold � Thot)xa� = h Tamb, (13)

which can be put into the form of a Fourier sine series:

�n

Bn sin�nxa �� n

asinh�nb

a � + h cosh�nba ��

= h�Tamb � Thot � (Tcold � Thot)xa�. (14)

The term in brackets on the left side of Eq. (14) is aconstant. Using the definition of the Fourier sine series[6] yields the coefficients Bn :

Bn [constant ] =2a �

a

0

h�Tamb � Thot � (Tcold � Thot)xa�

sin�nxa �d x . (15)

The integration yields

Bn =

2a

[h (Tamb � Thot) �a

n(1 � cos(n)) + h (Tcold � Thot)

an

cos(n)]

� n

asinh�n b

a � + h cosh�n ba � .

(16)

The resulting temperature profile can be used to deter-mine the convective heat loss by integrating the temper-ature profile over the specimen surface, thereby obtain-ing

Q = �a

0

�b

0

h [T (x , y ) � Tamb]dy d x , (17)

and multiplying the result by 8 since the two-dimen-sional approximation of the three-dimensional probleminvolves half the height of one of the four surfaces of thespecimen exposed to convection. The results show thatthe convective heat losses for the ceramic and metal are0.028 W and 0.017 W, respectively, for a typical 1 W

conductive heat flow. This yields a total convective heatloss of 4.5 %. This value is based on heat losses over theentire length of the specimen. The pertinent heat lossshould be calculated only over the distance over whichthe temperature measurement is made, which is a frac-tion of the total specimen length. The heat loss over thedistance in which the measurements are made is at most10 % of this calculated value of 4.5 %. This short lengthover which measurements are typically made is anothersignificant advantage of this measurement method.

4. Specimen Preparation

Due to the necessarily small size of the specimens,care must be taken in specimen preparation. All of thespecimens received are in the form of disks, rangingfrom 3 cm to 7 cm in diameter, coated on one side. Across-section specimen of 3.5 mm to 4 mm square wasinitially cut from the original disk with a low-speeddiamond saw, in order to minimize damage to the coat-ing microstructure. The cut surfaces of the specimenwere then dry polished with SiC papers of decreasingparticle size to remove the damaged surface materialfrom the saw cuts. As the abrasive particle size de-creases, the depth of damage decreases. Bonded-dia-mond platens were used for the final polishing step onthe side of the specimen to be viewed by the microscopewhich ensured that the surface remained flat, as well assmooth. The specimen was held in a polishing rig de-signed to prepare specimens for viewing by transmis-sion electron microscopy (TEM). Diamond-slurry lap-ping is the best form of final polish [7], but the slurrycan fill pores with oils that are hard to remove. Thus thefinal step was to polish with bonded-diamond platenslubricating only with water. Following polishing, speci-mens were ultrasonically cleaned in high-purity ethanol,then air-dried to remove artificial impurities due to pol-ishing from the existing pores of the coatings. Since theinfrared microscope detector operates at wavelengthsfrom 8 �m to 12 �m, a final polish to an averageroughness of 6 �m would be theoretically sufficient toprovide a surface smooth enough for diffraction-limitedspatial resolution, but polishing was continued down to0.5 �m. The final polish resulted in a scratch-free sur-face that was flat enough so that most of the field-of-view was in focus for a particular measurement. Onlyone of the four sides of the specimen needed to bepolished this finely because only one side was viewedfor measurement. The other three cut sides, as well asthe bottom of the substrate, were polished with SiCpapers down to an average roughness of 14 �m.

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5. Results

A nominally 1 mm thick plasma-spray (PS) coatingof 8 % mass fraction yttria-stabilized-zirconia was mea-sured by both a guarded hot plate (GHP) technique andwith the infrared microscopy system described here.The measurement of this coating in the GHP providesthe validation of this test method. The GHP technique isan absolute, steady-state method for measurement ofthermal conductivity. Numerous materials have beenpreviously measured by this high-temperature GHP [3,8, 9]. Thermal conductivity of PS yttria-stabilized-zir-conia can be found in the literature ranging from 0.4 to1.6 W�m�1�K�1 depending upon porosity and yttria con-tent [1, 10, 11, 12]. A set of plasma-sprayed coatingsnominally 1 mm, 2 mm, and 3 mm thick were measuredin the GHP [3]. The coatings were air-plasma-sprayed atthe Thermal Spray Laboratory of the State University ofNew York (SUNY) at Stony Brook. Each specimen hada 0.1 mm NiCrAlY bond coat between the substrate of

410 stainless steel and a coating of yttria-stabilized zir-conia of mass fraction 8 % yttria.

Figure 5 is an optical micrograph of the 0.87 mm(nominally 1 mm) coating measured by both the GHPtechnique and with the infrared microscopy system. Topromote adhesion, the stainless steel substrate was sand-blasted before the bond coat was applied. The applica-tion of the thin bond coat results in a very rough surfacefor application of the ceramic coating. The coating hasa porosity of 16.5 %, measured by size and mass usingweighted x-ray density values of 6.072 g�cm�3 for te-tragonal, 6.175 g�cm�3 for cubic, and 5.796 g�cm�3 forthe monoclinic phase of 8 % mass fraction yttria-stabi-lized zirconia. PS coatings of this composition are con-sidered to contain only the tetragonal phase [10]. How-ever, plasma-sprayed yttria-stabilized zirconia coatingscontaining all three phases of zirconia, monoclinic, te-tragonal, and cubic, have been reported [13, 14]. Speci-mens prepared at the same laboratory using the samespray parameters and with an equivalent starting powder

Fig. 5. Optical micrograph of the 0.87 mm thick plasma-spray coating on a 0.1 mm thick NiCrAlY bond coat on a stainless steelsubstrate.

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were analyzed using neutron diffraction [15]. By usinga full Rietveld refinement analysis, the as-sprayed coat-ing had all three phases of zirconia present, with tetrag-onal being the dominant phase.

The PS coating was measured using x-ray diffractionand the phase composition determined using the Ri-etveld-refinement method [16]. Because of a heavy dif-fraction-peak overlap, it is difficult to accurately deter-mine volume fractions and even prove the existence ofall three phases of yttria-stabilized zirconia. This espe-cially applies to the cubic and tetragonal phases, inparticular when present in small quantities. To minimizethis problem, the x-ray diffraction pattern was collectedusing CuK� radiation, thus eliminating uncertainty andadditional peak overlap introduced by the CuK�1,2 dou-blet. Figure 6 shows the diffraction pattern. An enlargedview centered around 27 � is shown in Fig. 7. The linethrough the data is from a Rietveld refinement usingonly the tetragonal phase. The line below the data showsthe difference between the data and the refinement re-sult. When the monoclinic phase is included in the re-finement, shown in Fig. 8, the fit to the data is verygood. A small addition of cubic phase in the Rietveld

refinement results in only a 0.1 % better fit. We there-fore cannot state conclusively that the cubic phase existsin this specimen. The refined lattice parameters andmass fractions for all three phases that result from thebest-fit refinement are given in Table 1. Mass fractionsgiven assume no texture in all three phases. An attemptto introduce different preferred orientations failed,which indicates that the coating is texture free.

Figure 9 shows the results of GHP measurements ofthe thermal conductivity � of the PS coating. Eventhough the specimen includes a bond coat and a metallicsubstrate, the GHP measurements give the thermal con-ductivity of just the coating. Near room temperature,where the infrared microscope measurements are made,the thermal conductivity � is 0.62 W�m�1�K�1. Thethermal conductivities of these types of coatings areexpected to be almost independent of temperature be-cause of the strong phonon and geometric scatteringmechanisms at work. The disordered lattice of stabilizedzirconia, with numerous oxygen vacancies, scattersphonons [17]. Since the microstructure is composed ofsplats, there are thermally resistive interfaces betweenthe splats. The grain structure within the splats is very

Fig. 6. X-ray diffraction result for the 0.87 mm thick plasma-spray coating.

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Table 1. Phase composition mass fractions w and lattice parameters a , b , and c , and the angle � of the three crystallographic phases inyttria-staliilized zirconia coating of mass fraction 8 % yttria, obtained by x-ray diffraction

Phase w a b c �% nm nm nm �

Tetragonal 87.0(1) 0.36157(1) 0.51551(1)Monoclinic 11.6(1) 0.51660(8) 0.52022(8) 0.53221(7) 99.156(8)Cubic 1.4(2) 0.5099(1)

Fig. 7. Enlarged view of part of the x-ray spectrum of the plasma-spray coating showing a calculated fit using only the tetragonal phase.

fine. Figure 10 shows a transmission electron mi-crograph of a PS coating. The grains within the splatsare on the order of 100 nm in diameter. The inset in Fig.10 shows an electron diffraction pattern from the indi-cated grain. The diffraction pattern shows that the grainis either cubic or tetragonal.

Figure 11 is an infrared micrograph showing a repre-sentative measurement of thermal conductivity of thecoating [18]. The designations 0 through 3 index thespots for temperature measurement. The spots areplaced via software at specific locations at precise 5 �mintervals. The line shown in the figure going through thetemperature spots determines the location of measure-ment of the temperature profile along the line. The

white temperature profile is shown in the window at thelower left corner of the image, with temperatures givenin degrees Celsius. Notice in the temperature-profilewindow that along the coating the temperature profilehas a smooth slope corresponding to the thermalresistance of the coating. The sharp temperature dropcorresponds to the interfacial thermal resistance at thecoating/bond coat interface. The flattening slope corre-sponds to the thermal resistance of the NiCrAlY bondcoat. The bump in the thermal profile is due to ceramicparticle contamination in the bond coat. The horizontalslope is due to the substrate, which has a thermal con-ductivity almost 40 times higher than that of the coating.Measurements were made at 6 different specimen

600


Fig. 8. Enlarged view of part of the x-ray spectrum of the plasma-spray coating showing a calculated fit using both tetragonal and monoclinicphases

Fig. 9. Results of thermal conductivity measurement of three thick-nesses of 8 % mass fraction yttria-stabilized-zirconia coatings de-posited by air-plasma spray.

locations, with repeated tests at each location. The aver-age thermal conductivity � of the coating for the 12measurements is 0.58 W�m�1�K�1 12 %, which com-pares well with the GHP result of 0.62 W�m�1�K�1. Theagreement of these data with the GHP measurementdemonstrates the validity of the experimental method. Avalue of 0.65 W�m�1�K�1 has been reported for a low-density yttria-stabilized-zirconia specimen of 8 % massfraction of yttria that was air-plasma-sprayed and mea-sured with the laser-flash technique [11, 19].

6. Uncertainty

This measurement method is comparative, so uncer-tainties from systematic effects propagate when measur-ing the heat flow of the known substrate material andsimilarly when using this measurement to determinethermal conductivity of the coating. Equation (1) is thebasis for calculating both the heat-flow rate Q from theknown thermal conductivity of the substrate material,and the subsequent thermal conductivity � of the coat-ing. Since all of the factors are in the form of products

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Fig. 10. Transmission electron micrograph of the 8 % mass fraction yttria-stabilized-zirconia coating showing the small crystallite sizewithin the splats.

or quotients, if the uncertainties are expressed in relativeterms, a summation in quadrature of the individual rela-tive uncertainties gives the combined relative standarduncertainty [20]. Table 2 shows the relative standarduncertainties for the measurement of both heat flow Qobtained from a measurement of the substrate, and ther-mal conductivity � from a measurement of the coating.The substrate and coating components have been sepa-rated for clarity.

Equation (1), applied to the substrate material, is usedto measure heat flow Q through the specimen. From asignal-to-noise viewpoint, the temperature-differencemeasurement of the substrate is less certain than that forthe coating due to the relatively high thermal conductiv-ity of the substrate, and therefore low measured temper-ature difference. The level of uncertainty in the thermalconductivity � of the metallic substrates is 5 %. Thecross-sectional area A through which heat flows has alevel of uncertainty of 0.5 %. The measurement of tem-perature difference �T is affected by thermal noise be-cause the measurement is done in air. In addition, the

scanner itself has significant internal thermal noise. Ac-cording to the manufacturer, 85 % of the radiation thatis measured by the detector comes from the microscopelens and other internal sources, rather than from thespecimen. As mentioned earlier, a stream of temperaturedata for each temperature spot is averaged to minimizethis effect of thermal noise. Based on repeated experi-ments, when the heat flow is low enough that the mea-sured temperature difference T between the two temper-ature spots on the substrate is less than 0.3 K themeasurement repeatability is greater than 25 %, andtherefore unreliable. However, most measurements havea substrate temperature difference of about 1.0 K. Therelative standard deviation of the substrate temperaturedifference data is slightly over 4 %, so the relative stan-dard uncertainty of the temperature measurement isabout 5 %. For measurements with a substrate tempera-ture difference of less than 0.3 K, the standard deviationdoes not change significantly, but the thermal conduc-tivity results show an uncertainty in reproducibilitygreater than 25 %, which is considered unacceptable.

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Fig. 11. Infrared image of the 8 % mass fraction yttria-stabilized-zirconia plasma-spray coating showing the linealong which the temperature profile is measured and the temperature spots are placed for thermal conductivitydata acquisition [13].

Table 2. Relative standard uncertainties for the measurement of thermal conductivity

Q �Heat flow rate, Thermal conductivity,

substrate coating% %

Substrate thermal 5 Heat flow rate Q 7.4conductivity �

Cross-sectional area A 0.5 Cross-sectional area A 0.5

Temperature 5 Temperature 5difference �T difference �T

Measurement length 2 Measurement length 2�x �x

Total 7.4 Total 9.2

Temperature spots are placed on the field-of-view viasoftware at precise coordinates. The 1.6 mm square fieldis divided into a 140 � 140 grid available for spot place-ment. This divides the field up into 11.4 �m regions.The manufacturer gives no claim on the precision of thetemperature spot placement, so linear distance testingwas done in-house. Measurement of length �x by the

infrared microscope was verified by measuring a 125�m copper grid used to support specimens for transmis-sion electron microscopy. Based on these measure-ments, the relative standard uncertainty in measurementof linear distance is 2 %. Since the field-of-view of themicroscope is fixed and the temperature spots are placedon a grid via software, the repeatability is excellent.

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As mentioned earlier, the individual relative standarduncertainties can be summed in quadrature to yield thecombined relative standard uncertainty since Eq. (1)shows all factors as products or quotients [20]. Sum-ming the relative standard uncertainties in quadrature forthe measurement of heat flow yields a resulting relativecombined standard uncertainty for the heat flow rate Qof 7.4 %. Using this result and taking into account thestandard uncertainties once again for temperature differ-ence �T , distance between temperature spots �x , andcross-sectional area A the combined relative standarduncertainty for measurement of thermal conductivity �is 9.2 %. A relative expanded uncertainty of the mea-surement of � is about 18 %, by using a coverage factork of 2 [20].

7. Conclusions

A steady-state, comparative method for determiningthe thermal conductivity of thermal-barrier coatings hasbeen developed. This method has been validated bymeasuring a PS coating that was previously measuredby an accepted steady-state technique. The measure-ment of the PS coating using the infrared microscopeyields a value for thermal conductivity of 0.58W�m�1�K�1 12 %. This compares well with the mea-sured value of 0.62 W�m�1�K�1 from the GHP. Thecombined relative expanded uncertainty of the infraredmicroscope measurements is 18 % at a 95 % confidenceinterval. The GHP has a lower limit on coating thicknessfor reliable measurement of about 150 �m, whereas thethermal microscopy system can measure coatings asthin as 20 �m, in principle, which allows steady-statemeasurement of thermal conductivity at a size scale anorder of magnitude smaller than other methods.

The use of an infrared microscope enables tempera-ture profile measurement across a specimen. This abil-ity will be exploited in the future in an attempt to quan-tify the interfacial thermal resistance between differentmaterials.

Acknowledgments

The author wishes to acknowledge the contributionsof John M. Phelps and B. James Filla of the MaterialsReliability Division of NIST for their help with micro-graphs and analysis of guarded-hot-plate results. Theauthor also wishes to acknowledge diffraction workdone by D. Balzar of the Materials Reliability Divisionof NIST and J. K. Stalick of the Reactor Division ofNIST. This work was completed as part of the author’sPh.D. dissertation at the Colorado School of Mines.

8. References

[1] R. B. Dinwiddie, S. C. Beecher, W. D. Porter, and B. A.Nagaraj, The effect of thermal aging on the thermal conductivityof plasma sprayed and EB-PVD thermal barrier coatings, paper96-GT-282 in Proceedings of the International Gas Turbine andAeroengine Congress, Birmingham, U.K., ASME (1996).

[2] B. J. Filla, A steady-state high-temperature apparatus for mea-suring thermal conductivity of ceramics, Rev. Sci. Instrum. 68(7), 2822-2829 (1997).

[3] A. J. Slifka, B. J. Filla, J. M. Phelps, G. Bancke, and C. C.Berndt, Thermal conductivity of a zirconia thermal barrier coat-ing, J. Therm. Spray Technol. 7 (1), 43-46 (1998).

[4] Standard Test Method for Thermal Conductivity of Solids byMeans of the Guarded-Comparative-Longitudinal Heat FlowTechnique, E 1225-87, Annual Book of ASTM Standards,14.02, ASTM (1994).

[5] K. E. Goodson and M. I. Flik, Solid layer thermal-conductivitymeasurement techniques, Appl. Mech. Rev. 47(3), 101-112(1994).

[6] C. R. Wylie and L. C. Barrett, Advanced Engineering Mathe-matics, McGraw-Hill, New York (1982) p. 348.

[7] M. F. Smith, D. T. McGuffin, J. A. Henfling, and W. B. Lenling,A comparison of techniques for the metallographic preparationof thermal sprayed samples, in Thermal Spray Coatings: Proper-ties, Processes and Applications, T. F. Bernecki, ed., ASM Inter-national, Materials Park, Ohio (1992) pp. 97-104.

[8] A. J. Slifka, B. J. Filla, and J. M. Phelps, Thermal conductivityof magnesium oxide from absolute, steady-state measurements,J. Res. Natl. Inst. Stand. Technol. 103 (4), 357-363 (1998).

[9] B. J. Filla and A. J. Slifka, Thermal conductivity measurementsof Pyroceram 9606 using a high-temperature guarded-hot-plate,in Thermal Conductivity 24, P. S. Gaal and D. E. Apostolescu,eds., Technomic, Lancaster, Pennsylvania (1998) pp. 85-96.

[10] R. Taylor, J. R. Brandon, and P. Morrell, Microstucture, compo-sition and property relationships of plasma-sprayed thermal bar-rier coatings, Surf. Coat. Technol. 50, 141-149 (1992).

[11] L. Pawlowski and P. Fauchais, Thermal transport properties ofthermally sprayed coatings, Int. Mat. Rev. 37 (6), 271-289(1992).

[12] R. Brandt, L. Pawlowski, G. Neuer, and P. Fauchais, Specificheat and thermal conductivity of plasma sprayed yttria-stabi-lized zirconia and NiAl, NiCr, NiCrAl, NiCrAlY, NiCoCrAlYcoatings, High Temp. High Pres. 18, 65-77 (1986).

[13] Z. Yin, X. Xiang, J. Zhu, and Z. Lai, Microstructure characteris-tic of plasma sprayed ZrO2/NiCoCrAlY graded coating, in Func-tionally Graded Materials 1996, Elsevier Science, Amsterdam,The Netherlands (1997) pp. 269-274.

[14] T. Troczynski, S. Cockcroft, and H. Wong, Thermal barriercoatings for heat engines, Key Eng. Mat. 122-124, 451-462(1996).

[15] J. Ilavsky and J. K. Stalick, Phase composition of plasma-sprayed yttria stabilized zirconia, in Thermal Spray: A UnitedForum for Scientific and Technological Advances, C. C. Berndt,ed., ASM International, Materials Park, Ohio (1997) p. 692.

[16] H. M. Rietveld, A profile refinement method for nuclear andmagnetic structures, J. Appl. Crystallogr. 2, 65-71 (1969).

[17] D. P. H. Hasselmann, L. F. Johnson, L. D. Bentsen, R. Syed, H.L. Lee, and M. V. Swain, Thermal diffusivity and conductivityof dense polycrystalline ZrO2 ceramics: A survey, Am. Ceram.Soc. Bull. 65(5), 799-806 (1987).

[18] A false-color image which shows the heat distribution in greaterdetail is available from the author.

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[19] L. Pawlowski, D. Lombard, and P. Fauchais, Structure-thermalproperties-relationship in plasma sprayed zirconia coatings, J.Vac. Sci. Technol. A 3(6), 2494-2500 (1985).

[20] B. N. Taylor, and C. E. Kuyatt, Guidelines for evaluating andexpressing the uncertainty of NIST measurement results, NISTTechnical Note 1297 (1994).

About the author: Andrew J. Slifka is a materials re-search engineer in the Materials Reliability Division ofthe NIST Materials Science and Engineering Labora-tory. The National Institute of Standards and Technologyis an agency of the Technology Administration, U.S.Department of Commerce.

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[J. Res. Natl. Inst. Stand. Technol. 105 Thermal-Conductivity ...microscope for temperature measure-ment, coatings as thin as 20 1m can, in principle, be measured using this tech-nique