Int J Thermophys (2011) 32:2092–2101DOI 10.1007/s10765-011-1067-y

Combined FPPE–PTR Calorimetry Involving TWRCTechnique II. Experimental: Application to ThermalEffusivity Measurements of Solids

Dorin Dadarlat · Mircea Nicolae Pop ·Mihaela Streza · Stephane Longuemart ·Michael Depriester · Abdelhak Hadj Sahraoui ·Viorica Simon

Received: 8 March 2011 / Accepted: 8 August 2011 / Published online: 9 September 2011© Springer Science+Business Media, LLC 2011

Abstract Photopyroelectric calorimetry in the front detection configuration (FPPE)and photothermal radiometry (PTR) were simultaneously used, together with thethermal-wave resonator cavity method (TWRC), in order to investigate the thermaleffusivity of solids inserted as backing layers in a detection cell. A new combinedFPPE–PTR–TWRC setup was designed. It was demonstrated experimentally that thePTR technique, combined with the TWRC method, is able to provide calorimetricinformation about the third layer of a detection cell. Applications on solids with dif-ferent values of the thermal effusivity (starting from metals, down to thermal isolators)are presented. The values of the thermal effusivity obtained with the PTR techniqueare similar to those obtained with the PPE technique, and in agreement with literaturevalues; the two methods reciprocally support each other. The accuracy of both methodsis higher when the values of the thermal effusivity of the backing layer and couplingfluid are close.

Keywords PPE calorimetry · PTR radiometry · Thermal parameters ·TWRC method

D. Dadarlat · M. N. Pop (B) · M. StrezaNational R&D Institute for Isotopic and Molecular Technologies,Donath Str. 65-103, 400293, Cluj-Napoca, Romaniae-mail: pop.mircea.n@gmail.com

S. Longuemart · M. Depriester · A. H. SahraouiUniversity of Lille—Nord de France, 59000, Lille, France

S. Longuemart · M. Depriester · A. H. SahraouiULCO, UDSMM, 59140, Dunkerque, France

V. SimonFaculty of Physics, Babes-Bolyai University, 400084, Cluj-Napoca, Romania

123

Int J Thermophys (2011) 32:2092–2101 2093

1 Introduction

In the front photopyroelectric (FPPE) configuration, the radiation impinges on thefront surface of the pyroelectric sensor, and the sample, in good thermal contact withits rear side, acts as a heat sink. In principle, a FPPE detection cell contains three layers:directly irradiated sensor, solid or liquid sample, and a semi-infinite backing material.The value of the dynamic thermal parameters of the layers of the detection cell can beobtained by performing frequency or thickness (in the case of liquid samples) scansof the amplitude or phase of the FPPE signal. The thickness scanning procedure isassociated with the so called thermal-wave resonator cavity (TWRC) method, intro-duced about 10 years ago by Mandelis and co-workers and developed later by othersgroups [1–8]. Recently, a combined FPPE–TWRC method was proposed, with thepurpose of measuring the thermal effusivity of a solid material (inserted as backing inthe detection cell) [9–12]. The main advantage of this configuration is connected withthe possibility of monitoring the properties (type and thickness) of the coupling fluid,in order to obtain the thermal effusivity of a solid.

Concerning the PTR technique, it was largely used in the past, together with thefrequency scan method, for calorimetric investigations of solid samples [13–18]. Insuch types of investigations, the investigated layer is the first, irradiated one, usuallya thermally thin and opaque solid, and the normalization of the PTR signal involvessome known thermally thick backings.

In a previous paper [19], we showed theoretically that the PTR technique canbe used together with the TWRC method for thermal inspection of a second and/orthird layer of a detection cell. In fact, for a three-layer detection cell (pyroelectricsensor/liquid layer/semi-infinite solid backing), the theory and mathematical simu-lations demonstrated that both FPPE and PTR calorimetry give similar information[19].

For a typical detection cell configuration as presented in Fig. 1, in the approx-imation of one-directional heat propagation and thermally thin limit for the sensor(exp(±σpLp) = 1 ± σpLp), the normalized complex FPPE signal is given by [13–17,19]

Fig. 1 Layout of the detection configuration

123

2094 Int J Thermophys (2011) 32:2092–2101

V PPEn = σpLp + blp

(σpLp

) + blp

[1−Rblexp(−2σl L l)

1+Rblexp(−2σl L l)

] (1)

where

σ j = (1 + i) a j , μ = (2α/ω)1/2, bi j = ei/e j , Ri j = (1 − bi j )/(bi j + 1) (2)

In Eqs. 1 and 2, ω is the angular chopping frequency of radiation, and σ and a arethe complex thermal diffusion coefficient and the reciprocal of the thermal diffusionlength (a = 1/μ), respectively. Symbols “p”, “l,” and “b” refer to the pyroelectricsensor, liquid layer (acting as a coupling fluid in the PPE configuration), and back-ing material, respectively. The normalization of Eq. 1 was performed with the signalobtained with a very thick liquid layer (exp(−σl L l) = 0).

In the same approximation, the PTR signal is given by [19,20]

V PTRn = A− B+

A+B−(3)

where

A± = 1 + blp ± (1 − blp)exp(−2σpLp)

B± = {1 + blp + Rbl(1 − blp)exp(−2σl L l)

± [1 − blp + Rbl(1 + blp)exp(−2σl L l)

]exp(−2σpLp)

}(4)

The conclusion of the previous theoretical paper [19] was that both normalized FPPEand PTR signals (Eqs. 1, 3, 4) depend on the thermal effusivity of the backing material.The theory indicates that, in all cases, for both PPE and PTR signals, the informationcan be extracted only from the thermally thin regime for the sensor and liquid layer.The very similar behaviors of the PPE and PTR signals give the opportunity to obtaininformation in the same thickness range; in conclusion, in one experimental run (onethickness scan), we can extract both PPE and PTR information. The thermally thickregime for the coupling fluid, combined with the thermally thin regime for the sen-sor, is used for normalization purposes. On the other hand, the two methods preserveall the advantages of the TWRC technique. The most important (if compared withfrequency scanning procedures) is the possibility of keeping a thermally thin regimefor the sensor and changing the thermal regime of the liquid from thermally thin tothermally thick.

This paper presents experimental results obtained with the combined PPE–PTR–TWRC method.

2 Experimental Setup

The design of the experimental setup is presented in Fig. 2. The pyroelectric sensor,a 100 µm thick LiTaO3 single crystal (ep = 3.66 × 103 W · s1/2 · m−2 · K−1;αp =1.36 × 10−6 m2 · s−1), provided with Cr–Au electrodes on both faces, is glued on a

123

Int J Thermophys (2011) 32:2092–2101 2095

Fig. 2 PPE–PTR–TWRC experimental setup

rotating stage. The backing material is situated on a micrometric stage. The modulatedradiation (30 mW YAG laser) is partially absorbed by the front electrode of the sensor.The space between the sensor and the backing material accommodates the liquid layer.The liquid’s thickness variation is performed with a step of 0.03 µm (9062M-XYZ-PPP Gothic-Arch-Bearing Picomotor) and the data acquisition was taken each 30thstep. The “rough” control of the liquid’s thickness and the parallelism between thebacking and sensor are assured by three- and six-axis micrometric stages. During thescanning procedure, the sample’s thickness variation is very rigorously controlled, butthe absolute sample’s thickness is not precisely known. Its correct value is obtained asa result of a fitting procedure [19]. The IR radiation emitted by the pyroelectric sensorwas collected with parabolic mirrors and sent to the surface of a cooled HgCdTe IRdetector.

All the measurements were performed at room temperature. The PPE and PTRsignals were processed with SR 830 lock-in amplifiers. The internal oscillator of thelock-in used in PPE measurements gave the reference signal for the second lock-in andassured, at the same time, modulation of the incident radiation. The data acquisition,processing, and analysis were performed with adequate software.

In all measurements, the liquid layer (coupling fluid between the sensor and thebacking) was ethylene glycol (es = 8.14 × 102 W · s1/2 · m−2 · K−1;αs = 9.36 ×10−8 m2 · s−1). Several backing solids with different values of thermal effusivity(polypropylene, teflon, textolite, bakelite, dental polymer, glass, steel, and brass) wereselected for investigations, thus covering a large range for the typical effusivity spec-trum of solids.

123

2096 Int J Thermophys (2011) 32:2092–2101

3 Results and Discussion

As mentioned in the Sect. 1, the information is contained both in the amplitude andphase of the two PPE and PTR signals. In the following, we will consider only thephase of the two signals, for the reasons well known and largely discussed in thepast [11,12]. Concerning the liquid’s thickness range, the thermally thin region is ofinterest [19]. The experimental setup allows a double thickness and frequency scan.This is why the first experimental step is to perform a thickness scan of the liquidlayer at several frequencies (at each thickness step, we perform a frequency scan over3–4 frequencies). Figure 3 presents typical thickness scans for a detection cell hav-ing ethylene glycol as the coupling fluid and steel as the backing, at three differentfrequencies.

It is well known that the chopping frequency is directly connected with the thermaldiffusion length (see Eq. 2); the purpose of such a procedure is to select the optimumthickness scanning region. The presence in the graph of the point “A” is very important:it indicates that the sensor and the backing are in contact. Analyzing Fig. 3, it seemsthat all three frequencies are suitable; we selected 1 Hz, because, at this frequency,the thermally thin regime for the sensor is better fulfilled.

Typical thickness scans of the phase of the PPE and PTR signals are displayed inFigs. 4 and 5.

The values of the thermal effusivity, in both PPE and PTR cases, were calculatedusing a fitting procedure with the absolute thickness value and thermal effusivity as

0 100 200 300 400 500 6005

10

15

20

25

30

35

40

45

50

55

60

65

PP

E p

hase

, deg

Relative thickness, μm

PPE

1 Hz

3 Hz

5 Hz

A

Fig. 3 Typical thickness scans for the phase of the PPE signal for a detection cell with steel as backinglayer, at three different modulation frequencies

123

Int J Thermophys (2011) 32:2092–2101 2097

-100 0 100 200 300 400 500 600-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Nor

mal

ized

pha

se, r

ad

Relative thickness, μm

PPEf=1 Hz

full dots-experimentalempty dots-best fit

steel

dentalpolymer

glass

bakelite

Fig. 4 Typical thickness scans for the normalized phase of the PPE signal for different backing materi-als, together with the best fit obtained with Eq. 1. The fit parameters were: absolute thickness value andbacking’s thermal effusivity

-100 0 100 200 300 400 500 600 700-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Relative thickness, μm

Nor

mal

ized

pha

se, r

ad

steel

glass

dentalpolymer

bakelite

full dots-experimentalempty dots-best fit

PTRf=1 Hz

Fig. 5 Typical thickness scans for the normalized phase of the PTR signal for different backing materials,together with the best fit obtained with Eqs. 3 and 4. The fit parameters were: absolute thickness value andbacking’s thermal effusivity

fitting parameters. The results of the fitting procedure are also displayed in Figs. 4 and 5,and the results, obtained for the values of the thermal effusivity, for the investigatedsolids are presented in Table 1.

123

2098 Int J Thermophys (2011) 32:2092–2101

Table 1 Room-temperaturevalues of thermal effusivity forthe investigated solids, asobtained from PPE and PTRmeasurements, togetherliterature data

Material Thermal effusivity (W · s1/2 · m−2 · K−1)

PPE PTR Literature

Steel 6400 4900 6090–7187 [21,22]

Glass 1360 1280 1275–1600 [21–23]

Textolite 1040 1020 1000–1810 [21]

Dental polymer 980 980 870–1110 [10]

Bakelite 760 680 681 [21]

Teflon 690 690 600–700 [21]

Propylene 520 490 –

0 20 40 60 80 100 120 140 160 180

400

600

800

1000

1200

1400

1600

1800

2000

ΔL, μm

The

rmal

effu

sivi

ty, W

⋅ s1/

2 ⋅m-2

⋅K-1

PTRf=1 Hz

ΔL=16.2 μme

bak=680 W ⋅s1/2⋅m-2⋅K-1

Fig. 6 Contour map of the precision of the fit performed with Eq. 3 on the experimental data obtained onbakelite backing. X-axis represents the correction term in the measurement of the absolute liquid’s thick-ness. The shape of the contour curves indicates a bad localization of the position of the backing, but goodprecision in the value of the thermal effusivity

Table 1 indicates that the results obtained for the thermal effusivity of the investi-gated solids, with the two techniques, PPE and PTR (a contact and a noncontact one),are similar, and they also agree with literature data.

Concerning the accuracy of the PTR results, as in the case of previously reportedPPE experiments [9,24], it is higher when the value of the thermal effusivity of thebacking material is close to that of the coupling fluid (see Figs. 6, 7).

In the case of good thermal conductors, the sensitivity of the method is better (seeFigs. 4, 5), but the accuracy is low. Figure 8 presents the case of brass as a backinglayer. The value obtained for the thermal effusivity is 15 500 W · s1/2 · m−2 · K−1, butthe shape of the sensitivity map indicates that the error can be huge.

123

Int J Thermophys (2011) 32:2092–2101 2099

0 20 40 60 80 100 120 140 160

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

ΔL, μm

The

rmal

effu

sivi

ty, W

⋅s1/

2 ⋅m-2

⋅K-1)

PTR f=1 HzΔL=34.2 μme

steel=4900 W⋅s1/2⋅m-2⋅K-1

Fig. 7 Contour map of the precision of the fit performed with Eq. 3 on the experimental data obtained onsteel backing. X-axis represents the correction term in the measurement of the absolute liquid’s thickness.The shape of the contour curves indicates a good localization of the position of the backing, but lowerprecision in the value of the thermal effusivity

0 20 40 60 80 100 120 140 160 180

5000

10000

15000

20000

25000

30000

35000

40000

ΔL, μm

The

rmal

effu

sivi

ty, W

⋅s1/

2⋅ m

-2⋅K

-1

PTRf=1 Hz

ΔL=54.9 μme

brass=15550 W ⋅s1/2⋅m-2⋅K-1

Fig. 8 Contour map of the precision of the fit performed with Eq. 3 on the experimental data obtained onbrass backing. X-axis represents the correction term in the measurement of the absolute liquid’s thickness.The shape of the contour curves indicates a very good localization of the position of the backing, but hugeerror in the value of the thermal effusivity

123

2100 Int J Thermophys (2011) 32:2092–2101

4 Conclusions

As a general conclusion, the experimental investigations, performed with the combinedFPPE–PTR–TWRC technique, support the theoretical predictions developed previ-ously [19]. In our opinion, the main result of the paper is the use (for the first time, toour knowledge) of the PTR technique together with the TWRC technique. We provedthat the PTR is able to offer information not only on the first, irradiated layer, butalso on a third layer of a sandwiched cell. Information on the second layer (couplingfluid) is also possible. The results obtained with the PTR technique are in good agree-ment with those obtained with PPE calorimetry and with literature data. As a generaltrend, the discrepancy between the results obtained with PTR and PPE increases withincreasing value of the thermal effusivity of the backing, the relative value (definedas: erel = (ePPE − ePTR)/ePPE) ranging from 0 to 23 %. Additionally, it was demon-strated experimentally that the accuracy of both methods is higher when the valuesof the thermal effusivity of the backing layer and coupling fluid are close. The mainadvantages of the combined PPE–PTR–TWRC technique were pointed out at the endof the Sect. 1. We want to mention here only the fact that, in the paper, the two tech-niques were used in such a way to support each other. This means that, for both type ofmeasurements, the fitting procedure was used to calculate the thermal effusivity of thebacking material. The next step is to take more advantages from the two methods. Forexample, they can be used to obtain simultaneously two thermal parameters of one ofthe first two layers (sensor or coupling fluid). For this purpose, we have to develop aprocedure that allows the calculation of the absolute thickness of the liquid layer in adifferent way (not through the same fitting used to obtained the thermal effusivity), orits absolute measurement. One can also add frequency scans at different thicknessesof the coupling fluid and obtain, from these scans, the thermal effusivity of the sen-sor and coupling fluid, and/or the thermal diffusivity of the sensor, as suggested in[5,6,25]. In any case, the two methods, as presented in the paper, will always supporteach other, but they are not able to give complementary information, because Eqs. 1,3, and 4 contain the same thermal parameters.

Acknowledgments This work was supported in part by the Romanian Ministry of Education and Researchthrough the National Research Program PN09 44 02 03 and by Bilateral (NIRDIMT Cluj Napoca-Univ.Littoral Dunkerque) Brancusi Project. One of the authors (MNP) wishes to thank for the financial supportprovided from programs co-financed by The Sectoral Operational Programme Human Resources Develop-ment, Contract POSDRU 88/1.5/S/60185—“DOCTORAL STUDIES: THROUGH SCIENCE TOWARDSSOCIETY.”

References

1. A. Mandelis, A. Matvienko, in Pyroelectric Materials and Sensors, ed. by D. Remiens (ResearchSignpost, Trivandrum, Kerala, 2007), pp. 61–81

2. S. Delenclos, M. Chirtoc, A. Hadj Sahraoui, C. Kolinsky, J.M. Buisine, Rev. Sci. Instrum. 73, 2773(2002)

3. J. Shen, A. Mandelis, Rev. Sci. Instrum. 66, 4999 (1995)4. J. Shen, A. Mandelis, H. Tsai, Rev. Sci. Instrum. 69, 197 (1998)5. S. Pittois, M. Chirtoc, C. Glorieux, W. van den Bril, J. Thoen, Anal. Sci. (Japan) 17, S110 (2001)6. P.C. Menon, R.N. Rajesh, C. Glorieux, Rev. Sci. Instrum. 80, 054904 (2009)

123

Int J Thermophys (2011) 32:2092–2101 2101

7. L.A. Balderas-Lopez, A. Mandelis, J.A. Garcia, Rev. Sci. Instrum. 71, 2933 (2000)8. L.A. Balderas-Lopez, A. Mandelis, Rev. Sci. Instrum. 74, 700 (2003)9. M. Streza, M.N. Pop, K. Kovacs, V. Simon, S. Longuemart, D. Dadarlat, Laser Phys. 19, 1340 (2009)

10. D. Dadarlat, M. Streza, M.N. Pop, V. Tosa, S. Delenclos, S. Longuemart, A. Hadj Sahraoui, J. Therm.Anal. Calorim. 101, 397 (2010)

11. D. Dadarlat, Laser Phys. 19, 1330 (2009)12. D. Dadarlat, C. Neamtu, Acta. Chim. Slovenica 56, 225 (2009)13. M. Depriester, P. Hus, S. Delenclos, A.H. Sahraoui, Rev. Sci. Instrum. 76, 074902 (2005)14. M. Depriester, A.H. Sahraoui, P. Hus, F. Roussel, Appl. Phys. Lett. 94, 231910 (2009)15. F. Cernuski, A. Figari, J. Mater. Sci. 35, 5891 (2000)16. E. MacCormack, A. Mandelis, M. Munidasa, B. Farahbakhsh, H. Sang, Int. J. Thermophys. 18, 221

(1997)17. A. Gijsbertsen, D. Bicanic, J.L. Gielen, M. Chirtoc, Infrared Phys. Technol. 45, 93 (2004)18. U. Bernini, P. Maddalena, E. Massera, A. Ramaglia, Opt. Commun. 168, 305 (1999)19. D. Dadarlat, M.N. Pop, M. Streza, S. Longuemart, M. Depriester, A. Hadj Sahraoui, V. Simon, Int.

J. Thermophys. 31, 2275 (2010)20. A. Mandelis, Diffusion-Wave Fields: Mathematical Methods and Green Functions (Springer,

New York, 2006), pp. 148–15121. A. Mandelis, Principles and Perspectives of Photothermal and Photoacoustic Phenomena

(Elsevier, New York, Amsterdam, London, Tokyo, 1992)22. Y.S. Touloukian, Thermophysical Properties of High Temperatures Solid Materials (MacMillan,

New York, 1967)23. J.H. Perry, Chemical Engineering Handbook (McGraw-Hill, New York, 1963)24. D. Dadarlat, M. Streza, N.M. Pop, V. Tosa, J. Phys. Conf. Ser. 182, 012023 (2009)25. A.H. Sahraoui, S. Longuemart, D. Dadarlat, S. Delenclos, C. Kolinsky, J.M. Buisine, Rev. Sci. Instrum.

74, 618 (2003)

123