Heat conductivity of oxide coatings by photothermalradiometry between 293 and 1173 K

H. P. R. Frederikse and X. T. Ying

Optical generation and optical detection of thermal waves are used to determine the thermal properties ofthree different oxide coatings on stainless steel substrates at temperatures up to 1173 K. The thermaldiffusivities a and thermal conductivities K strongly depend on the method of preparation as well as on theenvironmental conditions during deposition. Our experimental values for a and K are generally lower thanhandbook data for bulk specimens of the same materials.

1. Thermal Wave Method

During the last dozen years, thermal waves havebecome an important tool for probing the thermalproperties and defect structure of solids and films.Because thermal wave propagation depends on theheat conductivity of the medium one can derive thisquantity from the spatial and/or temporal behavior ofthe wave.1'2 At the same time, deviations from theuniform thermal condition of a solid resulting fromvariations in composition or density, or from defects,domains, voids, etc. will produce variations in the ther-mal wave pattern. By means of scanning, an image ofthe thermal inhomogeneity of the solid or coating maybe constructed.3 This technique has great potentialfor the nondestructive testing of materials and devicesin many technological applications: semiconductingchips, heat engines, corrosion resistant layers, tribo-logical coatings, etc.

In most cases the thermal wave is produced by a laserbeam aimed at the surface of a solid or a coating undertest. Modulation of this beam creates a periodicallyvarying temperature right at the surface when thematerial is opaque at the laser wavelength (absorptioncoefficient > 104 cm-1). In this particular investiga-tion the samples consist of stainless steel substratescovered with oxide coatings. The thermal wave willpropagate through the oxide coating and will be par-tially reflected at the coating-substrate interface.The resulting surface temperature can be measured inseveral ways. The photoacoustic technique"4 em-

The authors are with U.S. National Institute of Standards andTechnology, Ceramics Division, Gaithersburg, Maryland 20899.

Received 17 March 1988.

ploys a small gas cell equipped with a microphone thatrecords the thermal vibrations of the gas. Anothermethod uses the deflection of a laser beam that skimsthe surface of the sample to register the temperaturevariation.5 6 In our case we utilize an IR detector tomeasure the modulated thermal radiation emitted bythe surface. The signal and phase of the detectorsignal are recorded by a lock-in amplifier, where theoutput of the laser beam modulator is used as thereference signal. This technique is known as photo-thermal radiometry (PTR).4,7 ,8 It differs from theother techniques in that the temperature detectiondoes not depend on the transfer of heat to a gas abovethe surface of the sample.

The present investigation deals with the determina-tion of the thermal conductivity of oxide coatings attemperatures up to 1173 K. An earlier publicationdescribes the experimental arrangement and the re-sults of measurements at room temperature.9 Of thevarious temperature detection schemes only the PTRmethod lends itself to ready application at high tem-peratures.

II. Experimental Details

In this experiment a mechanically chopped C02 la-ser beam ( = 10.6 im) was used as the modulated heatsource. A chopper with a two-sector blade permittedus to cover a frequency range between -9 and 330 Hz.The power delivered to the sample was of the order of100 mW. The samples were plasma sprayed oxidecoatings, 50-100gm thick, on 1.58-mm stainless steelsubstrates. They were mounted inside a cylindricalfurnace which enabled us to make measurements be-tween 293 and 1173 K. The temperatures were regu-lated (30C) and recorded by means of a Pt - Pt (10%Rh) thermocouple.

Two IR detectors were used in this experiment. Be-tween 293 and 773 K the emitted radiation was regis-

4672 APPLIED OPTICS / Vol. 27, No. 22 / 15 November 1988

tered by a liquid nitrogen cooled InSb photovoltaicdetector. The blackbody radiation from a 293 K sur-face has its maximum spectral emission at X = 10 Amand drops to 1% of the maximum at 3 gm. The InSbcell response peaks at 5.5gAm and cuts off at 6 gm. Theamount of radiation received by the cell between thetwo limits (3 and 6 im) is sufficient to produce anample signal (Fig. 1). The ac signal varies with tem-perature as T3 T. where AT is the temperature modu-lation amplitude. However, the dc blackbody radia-tion rises as T4 and tends to saturate the cell.Consequently, at T = 773 K, a small aperture wasplaced in front of the detector to limit the amount ofradiation received, thus preventing saturation of thesignal. At higher temperatures the InSb detectorcould not be employed. At 773 K and above, the peakof the blackbody radiation curve moves to lower wave-lengths; in this range a Ge photodiode (cutoff wave-length, 1.6 gim) functions very satisfactorily. Onceagain dc saturation has to be considered requiringdecreasingly smaller apertures at 973, 1073, and 1173K.

A diagram of the experimental setup is shown in Fig.2. A 1-D analysis of the diffusion and reflection of thethermal wave yields two simple formulas for the mag-nitude SI and the phase angle AO of the detectedsignal. The latter, measured with respect to a ther-mally thick reference sample (L >> AT), is given by thefollowing expression 2 7 9 :

A = tan'11(2R sin2x)/[exp(2x) - R2 exp(-2x)]} + Apo, (1)

where the terms within (1) are defined by

X=LItT=Fff, (la)

F =L o(-r/a), (lb)

R (I (- b)l(l + b), (Ic)

b = es/ec, (id)

e = (p, (le)

AT= (a/), (if)

and where L = sample thickness, R = thermal wavereflectivity at the film/substrate interface, K = thermalconductivity, p = density, C = specific heat, guT =

thermal diffusion length, e = effusivity, a = thermaldiffusivity, f = modulation frequency, A00 = phaseoffset correction term, and the subscripts s and c referto the substrate and coating, respectively.

A look at Eqs. (1) and (la) shows that AOk is a func-tion of the square root of the modulation frequency.By carefully fitting the experimental data to Eq. (1),the parameters R, F, and Ako can be calculated. F willyield a value for the thermal diffusivity a; using theknown values of Ks, ps, and C, of the stainless steePsubstrate we can calculate the thermal conductivity K

of the coating.

Ill. Results

The phase of the photothermal signal as a functionof modulation frequency was measured on three thin-

= 108

:.

* 104a,

E 104

XF 102

C 102a

: 10-2

C) 10-40.U) 0.1 0.5 1.0 5 10

2 x 101110

6 x 10104 x 10102 x 1010

1010

N

E

.C

at

U}a)

50 100Wavelength A, Hm

Fig. 1. Wavelength dependence of blackbody radiation for tem-peratures between 200 and 6000 K [from Handbook of Optics, W. G.Driscoll and W. Vaughan, Eds. (McGraw-Hill, New York, 1978), pp.1-15]. Superimposed are the detectivities D* of a Ge and of a liquid

nitrogen-cooled InSb photodetector.

C2 -laser

chopper control

printer

-L -j pre-amplifier

lock-in amplifier

Fig. 2. Experimental arrangement for photothermal radiometry.

film specimens and three reference specimens at anumber of temperatures between 293 and 1173 K.The three thin film specimens consisted of stainlesssteel 304 substrates plasma sprayed with coatings ofchromia (CS2), zirconia (ZS3), and alumina (AS3);coating thicknesses are given in Table I. The refer-ence specimens contained the same coating materialsas the thin-film specimens. The coating thicknesses ofthe reference coatings, -1 mm, were much greater thanthe longest diffusion length expected; gAT is of the orderof 0.17 mm forf= 9.

For a given set of measurements, a thin-film speci-men and a reference specimen of the same coatingmaterial were placed adjacent to each other in thefurnace. For the thin-film specimen, the temperaturesequence was as follows: 293-773 K with the InSbdetector followed by 773-1173 K with the Ge detector;the laser beam remained focused on the same spot ofthe sample during the set of measurements. Subse-quently, the whole furnace was lifted to aim the laserbeam at the reference specimen. The temperaturesequence for this set of measurements was reversed,from 1173 K down to room temperature.

Figure 3 presents examples of phase angle data ob-tained from specimen CS2. To correct for frequencyvariations of phase in the electronic equipment, at

15 November 1988 / Vol. 27, No. 22 / APPLIED OPTICS 4673

each frequency, the phase measurement of the refer-ence specimen was subtracted from the phase mea-surement of the thin-film specimen. Next, a least-squares curve fitting program was used to determinethe parameters F, R, and Ad0 . The approach to theminimum point of the least-squares sum in a multipa-rameter space was guided by a combination of the gradi-ent technique (far away from the minimum point) andthe linearized method (near the minimum point).'No weight factors were used in this procedure. Substi-'tuting these parameters in Eq. (1) yielded the solidcurves shown in Fig. 3. Recording the phase angle as afunction of modulation frequency for specimens ZS3and AS3 produced similar data. From the fit parame-ters we were able to compute a and K. Results of thedata analysis for the three specimens are presented inTable I. The values for a and K are considerablysmaller than most of the Handbook values for the bulkoxides.12 It is to be expected that a and K will varyfrom sample to sample; no systematic study was madeof the dependence of these quantities on thickness,powder size, or substrate temperature.

IV. Discussion

Probably the major uncertainty stems from the un-even thickness of the coatings. A measurement of theprofile of some of the coatings indicated a variation ofup to 15% in the thickness over a distance of severalmillimeters. Because the laser beam was not wellfocused, having a width of -0.6 mm, the thickness ofthe coating at the point of measurement could wellvary by the amount mentioned above. Consideringthat the thermal diffusivity a is proportional to L2 [seeEqs. (la) and (d)] the error in a may be as much as30%. On the other hand, the actual curve fitting yieldsvalues of F with a precision of 1-2%. Therefore, theprecision of a, and hence its temperature dependence,is considerably better than 30%.

The high accuracy of F (and a) derives from the factthat the expression for A [Eq. (1)] has two specialfeatures in the range of higher x values, which areindependent of R: the crossover point, AO = 0 at x =

25.00

O 20.00a)

ro 15.00

LO 10.00

n 5.00-5i> 0.00

LUJ -5.00

-10.00 0.00 5.00 0.00 0. 25100

SQUARE ROOT OF FREQUENCY (Hz

Fig. 3. Relative phase vs square root of the modulation frequencyforsampleCS2atthreetemperatures: 0,295K, 0,961K; ,1173

K.

1.57, and the minimum at x = 1.96. Because therelative positions of these two points along the fre-quency axis are fixed, the fit to the experimental datais greatly improved. This results in a precise value forF. On the other hand, the values for R depend on themagnitude of AOk between x = 0.2 and 0.4, especiallywhere Atk has a maximum. In several cases the lowerlimit of the frequency range (f = 9) did not permitinclusion of the maximum value of Atk. As a result thevalues of R, and consequently of K, were significantlyless precise than the values for F and a.

Another fact, which fortunately did not affect theresults of the experiments, should be mentioned. Innearly all cases the thick oxide coatings of the refer-ence specimens separated from their substrates duringthe temperature cycle. However, this delamination isnot important because the thermal wave does notreach the interface, and thus the reference specimenscan be considered infinitely thick.

V. Conclusions

The temperature dependence of the thermal diffu-sivity a and the heat conductivity K is shown in Figs. 4(a)and (b), respectively. The solid curves in the figure

Table I. Thermal Diffusivity a and Thermal Conductivity X of Three Different Oxide Coatings Between 295 and 1173 KO

Chromia on steel CS3 Zirconia on steel ZS3 Alumina on steel AS3L 55 m L = 92,um L = 73.5 Am

T a K T at K T a KK cm2/s W/cm- K K cm2/s W/cm- K K cm 2/s W/cm- K

295 0.0059 0.0163 295 0.0051 0.0103 295 0.0085 0.0068525 0.0050 0.0138 524 0.0042 0.0060 553 0.0055 0.0054773 0.0051 0.0141 817 0.0034 0.0070 773 0.0060 0.0054867 0.0055 0.0175 878 0.0036 0.0054 868 0.0059 0.0053961 0.0059 0.0186 969 0.0040 0.0033 972 0.0056 0.0066

1066 0.0066 0.0205 1073 0.0045 0.0036 1072 0.0055 0.00871173 0.0072 0.0200 1171 0.0044 0.0026 1172 0.0042 0.0100

- - - 293 0.0031b 0.0069 1173 0.012c 0.0055c

a Samples obtained from Accumetrix Corp., Arlington, VA.b Ref. 12, p. 351.c H. L. Anderson, Ed., Physics VadeMecum (American Institute of Physics, New York, 1981), p. 43.

4674 APPLIED OPTICS / Vol. 27, No. 22 / 15 November 1988

0.0 120

U)-4

E'-0.0080

>U)

0 0.0040

I

0.0000

-0.0250

E90 .0200

50.0150

0C-)

Z0 0 1 000

tX 0.0050

I0.0000

* *

200..... 400..... 600....... 00.. I..1000 ......0 ... 266 400 600 860 ... '00b

TEMPERATURE ( K)

(a)

1'00 14o

+,,+

*x~~~~

0 0. .4 .66 800 1 000TEMPERATURE ( K)

(b)

Fig. 4. (a) Thermal diffusivity a and (b) thermal conductivity K forthree oxide coatings as a function of temperature. The experimen-tal data points for both a and K have been fit by an empirical

expression of the form AlT + BT + C; +, CS3; X, ZS3; *, AS3.

are fits of a and K to an expression of the form A/T +BT + C, where T is the temperature in kelvins. Theo-retical treatments of the high temperature thermalconductivity K of pure monocrystalline insulators pre-dict that K is inversely proportional with tempera-ture.1 3 This is confirmed by experiments on MgO,A12 03 , and several other oxides; however, for polycrys-talline solids with large grains as well as for porousmaterials and glasses K appears to be nearly constantwith temperature above 300-500 K.1 4 The same tem-perature behavior should apply to the thermal diffu-sivity a because a = K/pC, and the specific heat C isnearly independent of temperature when T approach-es or exceeds the Debye temperature.

All our oxide coatings show a small decrease in K just

above 300 K followed by very little change with tem-perature up to 1173 K. This behavior, as well as thelow values of a and K,

12 seems to indicate that multi-phonon scattering is not the main mechanism whichcontrols the flow of heat. Rather the high contactresistance between grains as well as the large porositycould well be the main reasons for the strong imped-ance experienced by the thermal waves.

The authors want to thank A. Feldman for manyhelpful discussions. They are grateful to P. Desai atCINDAS, who provided them with recent stainlesssteel data.

This work was supported by the Office of Nonde-structive Evaluation at NBS.

X. T. Ying is a Guest Scientist from Fudan Universi-ty, China.

References

1. A. Rosencwaig, Photoacoustics and Photoacoustic Spectrosco-py (Wiley, New York, 1980).

2. A. Rosencwaig and A. Gersho, "Theory of the PhotoacousticEffect with Solids," J. Appl. Phys. 47, 64 (1976).

3. A. Rosencwaig, "Thermal-Wave Imaging in a Scanning ElectronMicroscope," in International Advances in NondestructiveTesting, Vol. 11 (Gordon & Breach, London, 1985), pp. 105-174.

4. S. 0. Kanstad and P. E. Nordal, "Photoacoustic and Photother-mal Techniques for Powder and Surface Spectroscopy," Appl.Surf. Sci. 6, 372 (1980).

5. A. C. Boccara, D. Fournier, and J. Badoz, "Thermo-OpticalSpectroscopy: Detection by the Mirage Effect," Appl. Phys.Lett. 36, 130 (1980).

6. K. R. Grice, L. J. Inglehart, L. D. Favro, P. K. Kuo, and R. L.Thomas, "Thermal Wave Imaging of Closed Cracks in OpaqueSolids," J. Appl. Phys. 54, 6245 (1983).

7. R. T. Swimm, "Photoacoustic Determination of Thin-FilmThermal Properties," Appl. Phys. Lett. 42, 955 (1983).

8. A. Lachaine, "Thermal Analysis by Photoacoustic Phase Mea-surements: Effect of Sample Thickness," J. Appl. Phys. 57,5075 (1985).

9. H. P. R. Frederikse and A. Feldman, "Thermal Wave Inspectionof Heat Resistant Ceramic Coatings," Nondestructive Testingof High-Performance Ceramics, A. Vary and J. Snyder, Eds.(The American Ceramics Society, Westville, OH, 1987), pp. 177-182.

10. Data Center, CINDAS, Purdue U., West Lafayette, IN; privatecommunication (1988).

11. W. J. Kennedy, Jr., and J. E. Gentle, Statistical Computing(Marcel Dekker, New York, 1980), Chap. 10.3.

12. Ceramic Source '86 (The American Ceramic Society, Westville,OH, 1986), pp. 350-351.

13. J. E. Parrott and A. D. Stuckes, Thermal Conductivity of Solids(Pion, London, 1975), p. 114.

14. Ref. 13, Figs. 6.1 and 6.2.

0

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