Lock-in thermography for characterization of nuclear materials

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A simpliﬁed procedure of lock-in thermography was developed and applied for characterization of nuclear materials. The possibility of thickness and thermal diffusivity measurements with the accuracy better than 90% was demonstrated with different metals and Zircaloy-4 claddings.

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EPJ Nuclear Sci. Technol. 2, 20 (2016) Nuclear Sciences © A. Semerok et al., published by EDP Sciences, 2016 & Technologies DOI: 10.1051/epjn/2016015 Available online at: http://www.epj-n.org REGULAR ARTICLE Lock-in thermography for characterization of nuclear materials Alexandre Semerok*, Sang Pham Tu Quoc, Guy Cheymol, Catherine Gallou, Hicham Maskrot, and Gilles Moutiers Den-Service d’Études Analytiques et de Réactivité des Surfaces (SEARS), CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette, France Received: 23 September 2015 / Received in ﬁnal form: 2 February 2016 / Accepted: 22 February 2016 Published online: 15 April 2016 Abstract. A simpliﬁed procedure of lock-in thermography was developed and applied for characterization of nuclear materials. The possibility of thickness and thermal diffusivity measurements with the accuracy better than 90% was demonstrated with different metals and Zircaloy-4 claddings. 1 Introduction ΔT Lock-in thermography is a non-destructive method which may be applied to test and to ensure remote control over materials in severe environment (e.g. nuclear installations) in a wide temperature range. The method is based on the laser heating of a sample with a modulated laser power at a given frequency f(Hz) followed by measurements of a thermal radiation emitted by the sample. The phase shifts D’ between the laser power and the thermal radiation measured at different modulated frequencies are then Fig. 1. Phase shift of heating temperature. compared with those obtained with an analytical (3D + t) model developed at the LISL (DEN/DANS/DPC/SEARS) In the heating models [1,2] for a surface with a deposited in case of the heating of a sample covered by a deposited layer, we supposed that the layer/surface thermal resis- layer [1,2]. Thus, it is possible to provide a tool to tance (> 1). By diffusivity, deposited layer/surface thermal contact resis- applying the Fourier series analysis to the intensity of the tance, characterization of under-surface defects and their laser beam and the temperature in the stationary regime of evolution with time). The phase shift of heating tempera- the laser heating [2,3], the complex temperature amplitude ture is presented in Figure 1. of the front face of a plate can be written as: þ∞ að1 RÞ~I QðjÞ aeCL a Cz DT ðz; rÞ ¼ ∫ 2 2pifC v þ e 2 Model for the heating of a plate k 0 j a 2 k CðeCL eCL Þ C aeCL þ eCz þ eCz eaz J 0 ðjrÞdj; In a thermal model for homogeneous and isotropic plate Cðe eCL Þ CL with inﬁnite dimensions, we supposed that: ð1Þ – variations of the optical and thermal properties for a 2 2 jr2 j r surface covered by a deposited layer during its heating are with QðjÞ ¼ 20 exp 4 0 for the Gaussian beam; negligible; pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ – the surface roughness effect and heat exchange due to the C ¼ j2 2pifC v =k; ~I ¼ i a2 þ b2 eiFLP ; 1 1 sample surface/air convection are also negligible. p 1∫ FLP ¼ atan a1 ; b1 J 0 ðjrÞ ¼ p 0 cosðjrsintÞdt; 1=f a1 ¼ 2f ∫ 0 IðtÞcosð2pftÞdt; 1=f * e-mail: alexandre.semerok@cea.fr b1 ¼ 2f ∫ 0 IðtÞsinð2pftÞdt; IðtÞ ¼ I 0 ð1 cosð2pftÞÞ, This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
2 A. Semerok et al.: EPJ Nuclear Sci. Technol. 2, 20 (2016) where: z and r, respectively, are the propagation direction of 1 10 100 1000 10000 the laser beam and the radial distance from the center of the -30 heated zone at the sample surface; Cv, k and L: the fmin volumetric speciﬁc heat, the thermal conductivity and the -45 Phase shift (°) thickness of the sample; a and R: the laser absorption coefﬁcient and the reﬂectivity of the sample surface; r0: the laser beam radius at 1/e intensity, I(t) and I0: the intensity of -60 the laser beam and its amplitude; f, t and i: the repetitive rate ϕmin frequency of the laser, the time and the complex unity; j and -75 t: the variables of the integration; FLP: the phase of the laser power. The phase shift between the laser and the thermal power -90 Laser frequency (Hz) can be found by the expression: Fig. 2. Phase shift for SS 304L plate of 400 mm thickness. D’ ¼ atanðReðDT Þ=ImðDT ÞÞ: ð2Þ The phase shift can be written as: D’ ¼ atanðReðDT n Þ=ImðDT n ÞÞ: ð6Þ 2.1 Environmental effect It depends on the parameters k, rc, a, L, r0, h. For thin The heat exchange with the environment by convection metal plates, the environmental effect on the phase shift mechanism can be introduced by the conditions of limits at may be considered as negligible. For example, for SS 304L of z = 0 and z = L [4]: 400 mm thickness, the phase shifts are not affected by the environment even for a material with h = 100 W/m2 K ∂DT ∂DT (water) [4]. ¼ mðT z¼0 T a Þ; ¼ mðT z¼L T a Þ; ð3Þ ∂z z¼0 ∂z z¼L where: m ¼ h=k, h(Wm–2 K–1) is a coefﬁcient of thermal 2.2 Simple analytical expressions exchange with environment by convection. The environ- ment temperature Ta is supposed to be equal to the initial The numerical simulation of laser heating is used to ﬁt the temperature of the plate, thus: T z¼0 T a ¼ DT ðt; z ¼ 0; rÞ; calculated phase shifts with the experimental ones by T z¼L T a ¼ DT ðt; z ¼ L; rÞ. The losses by thermal emis- adjusting the material properties. A typical dependence of sion are supposed to be negligible. a phase shift on a laser modulation frequency is presented The solution of the heat equation: in Figure 2. For the laser beam with a diameter satisfying 2 r0/100 L r0/2, one may observe a minimum on the ∂DT ∂ DT ∂2 DT 1 ∂DT phase shift curve with the corresponding values ’min rc ¼k þ þ and fmin. ∂t ∂z2 ∂r2 r ∂r ð4Þ az Multiparameter simulation of laser heating enables one þ að1 Rc ÞIðt; rÞe ; to determine the effect of the interaction parameters and the material properties on the phase shifts [3–7]. Two on 0 z L with the initial condition DT ðt ¼ 0; z; rÞ ¼ 0 analytical expressions were derived to relate laser param- was obtained for the nth harmonic of the laser repetition eters, sample properties, ’min and fmin. This inter-relation- frequency: ship may provide rapid measurements of thickness L and ∞ diffusivity D of a sample with 99% accuracy: að1 RÞ~I n QðjÞ DT n ðz ¼ 0; rÞ ¼ ∫ 2 rc J 0 ðjrÞ 2 k 0 j a 2p i n f CL k L½mm ¼ r0 ½mm=z’ lnð90 =’min Þ; ð7Þ e eaL m þ a m þ a mþa CL CL þ 1 dj; e e mC mþC mþC ð5Þ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ D mm2 =s ¼ 1=zf r0 ½mm L½mm f min ½Hz; ð8Þ where: C ¼8 j2 2p i n f rc=k; m ¼ h=k; < jr20 j2 r20 with z’ and zf calculated values (Fig. 3). QðjÞ ¼ expð Þ the Gaussian beam; : 2 4 r0 J 1 ðjr0 Þ top-hat beam; qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ p 3 Experimental J n ðjrÞ ¼ p1 ∫ 0 cosðnt jrsintÞdt; ~ I n ¼ i a2n þ b2n ei’L ; n 1=f ’nL ¼ a tanðbn =an Þ; an ¼ 2f ∫ 0 IðtÞsinð2pnftÞdt; The experimental setup with a compact ﬁber laser (low 1=f divergent near the Gaussian beam with M2 = 1.1, beam bn ¼ 2f ∫ 0 IðtÞcosð2pnftÞdt: radius r0 ≅ 1 mm, 1060 nm wavelength) is simple in its
A. Semerok et al.: EPJ Nuclear Sci. Technol. 2, 20 (2016) 3 Iron 1,56 0,58 1 Molybdenum 1,54 0,56 1,52 0,54 Nickel 1,5 0,52 ζφ 1,48 0,5 Titanium ζf 1,46 0,48 Tungsten 1,44 0,46 1,42 Zinc 0,44 Thermal diffusivity (cm2/s) 1,4 0,42 304L Stainless 1,38 0,4 Steel -90 -75 -60 -45 -90 -75 -60 -45 Iron φmin φmin Iron Fig. 3. Calculated values of z’ and zf parameters. 0,1 Molybdenum Molybdenum Nickel Electric generator Nickel Laser Titanium Sample Titanium Tungsten Reference ZnSe lens Tungsten Entrance IR detector t Zinc 0,01 Zinc Phase shift Lock-in amplifier Temperature amplitude ΔT 300 500 700 304L Stainless Steel Fig. 4. Scheme of the experimental setup. Temperature (K) 304L Stainless Steel arrangement (Fig. 4) and enables one to make remote Fig. 5. Comparison of the measured thermal diffusivities along measurements with a millimeter lateral resolution in a wide with the referenced values from literature (presented as solid lines) distance range (from some centimeters up to several [8]. The square points – Dm2 and the circle points – Dm1 (see Tab. 1 meters). for Dm deﬁnition). 3.2 Zircaloy-4 cladding characterization 3.1 Metal plates characterization After the characterization of the metal plates by the above The lock-in thermography for a plate characterization was procedure, the method was used for studying Zircaloy-4 validated with a set of etalon samples. The obtained results claddings (Fig. 6). The schematic comparison of the on plate thickness and diffusivity measurements are cladding diameter and the one of the heated zone (with presented in reference [3]. These results have demonstrated the tested zone on it) is presented in Figure 6. As the heated ≈90% accuracy of thickness and thermal diffusivity zone diameter is smaller than the one of Zy4 cladding, the measurements. The measured thermal diffusivities along heated zone may be considered as a plane surface, and thus, with the referenced values from literature are summarized the same procedure as the one for metal plates may be in Figure 5. followed. Table 1. Thickness and thermal diffusivity measurements for Zy4 claddings with oxide layers. Zircaloy-4 claddings with oxide layers Oxide thickness mm 5 10 15 Laser mean power W 2.7 2.7 2.7 Temperature °C 100 ± 5 100 ± 5 100 ± 5 Dref reference cm2/s 0.073 ± 0.003 0.073 ± 0.003 0.073 ± 0.003 Lref reference mm 570 ± 2.5 570 ± 2.5 570 ± 2.5 r0 measured mm 1740 ± 30 1740 ± 30 1740 ± 30 ’min measured ° 53.3 ± 0.5 53.1 ± 0.5 54.7 ± 0.5 fmin measured Hz 3.1 ± 0.3 3.1 ± 0.3 3.4 ± 0.3 Lm measured mm 594 ± 15 598 ± 15 564 ± 15 Dm1 measured with Lm cm2/s 0.068 ± 0.006 0.069 ± 0.006 0.071 ± 0.006 Dm2 measured with Lref cm2/s 0.066 ± 0.006 0.066 ± 0.006 0.071 ± 0.006
4 A. Semerok et al.: EPJ Nuclear Sci. Technol. 2, 20 (2016) ø9.5mm Zircaloy-4 claddings -40 Phase shift (°) -50 -60 Virgin at 70°C heated zone Virgin at 330°C -70 with 5μm oxide layer at 100°C (ø 3.5mm) with 10μm oxide layer at 100°C with 15μm oxide layer at 100°C -80 1 10 100 1000 10000 Frequency (Hz) Fig. 7. Phase shifts for Zy4 claddings as a function of modulated tested zone frequency. (ø 1.6mm) Reference 0,1 Zy4 virgin at 70°C Zircaloy-4 Thermal diffusivity Zy4 virgin at 330°C Fig. 6. On the left: schematic comparison of the Zy4 cladding 0,09 Zy4 with oxide layer at 100°C diameter and those of the heated zone (in red) and of the tested 0,08 (cm2/s) zone on it (in blue). On the right: the picture of Zy4 claddings. 0,07 Some Zy4 claddings were artiﬁcially oxidized (on the right in the picture). 0,06 0,05 To study the effect of the oxide layer on the measured 0 200 400 600 thermal diffusivity, some Zy4 claddings were artiﬁcially Temperature (°C) oxidized in a furnace at different regimes (temperature, environment, time) to obtain oxide layers of different Fig. 8. Measured and reference values of thermal diffusivity as a thickness (5–15 mm). For 5 mm, 10 mm, and 15 mm oxide function of temperature (°C) for Zy4 claddings. layer thickness, the regimes, respectively, were as follows: (500 °C, in air, for 37 hours), (550 °C, in air, for 23 hours), diffusivity D were derived. These expressions and the lock- and (550 °C, in water vapor, for 51 hours). The surface of in thermography measurements (the minimal phase shift Zy4 with the oxide layer of 10 mm thickness has suffered ’min and the corresponding minimal modulated frequency nitriding effect, while the samples with 5 mm and 15 mm fmin [6,7]) are used to measure the thickness and the thermal oxides were of a good quality. diffusivity of the samples. The obtained results are in The results on Zy4 claddings characterization are agreement with experimental data within an accuracy of presented in Figures 7 and 8 and in Table 1. At low 90%. The developed method may be applied for any modulation frequency (f < 20 Hz), the phase shift is poorly material with a high absorption coefﬁcient a, that is, for any affected by the presence of the oxide layer (Fig. 7). Thus, for plate with aL >> 1. Based on the results obtained, we may Zircaloy-4 claddings, ’min and fmin method may be used to conclude that a rapid remote in situ control over determine thickness and thermal diffusivity (see Tab. 1). components in nuclear installations may be ensured with The measurement relative deviations were less than 10%. a good spatial resolution (of the order of a laser beam At higher modulation frequency (f > 20 Hz), a clear diameter 2r0). effect of the oxide layer on the phase shifts is observed (Fig. 7). Due to the fact that ZrO2 layers are semitranspar- Authors acknowledge DEN/DANS/DMN/SRMA/LC2M team ent, the theoretical models for phase shift calculation [1,2] for Zircaloy-4 claddings supply. are not applicable in this case. However, there are all the reasons to suppose that further development of the thermal model of heating a semi-transparent layer on a metal plate References will provide an adequate on-line in situ characterization of oxide formation. 1. A. Semerok, F. Jaubert, S.V. Fomichev et al., Laser lock-in thermography for thermal contact characterisation of surface layer, Nucl. Instrum. Methods Phys. Res. A 693, 98 (2012) 2. A. Semerok, S.V. Fomichev, F. Jaubert et al., Active laser 4 Conclusions pyrometry and lock-in thermography for characterisation of deposited layer on TEXTOR graphite tile, Nucl. Instrum. The homemade thermal model of the local heating of a Methods Phys. Res. A 738, 25 (2014) homogeneous and isotropic plate with inﬁnite dimensions 3. S. Pham Tu Quoc, G. Cheymol, A. Semerok, New contactless was developed and veriﬁed by characterizing different method for thermal diffusivity measurements using modulated metal plates and Zircaloy-4 claddings. Two analytical photothermal radiometry, Rev. Sci. Instrum. 85, 054903 expressions (7) and (8) for sample thickness L and thermal (2014)
A. Semerok et al.: EPJ Nuclear Sci. Technol. 2, 20 (2016) 5 4. S. Pham Tu Quoc, Caractérisation des propriétés d’un 6. D. Melyukov, P.-Y. Thro, Patent CEA FR2980846-A1, Procédé matériau par radiométrie photothermique modulée, CEA de détermination sans contact de l’épaisseur d’un échantillon, 2013 PhD Thesis, France, 2014 7. S. Pham Tu Quoc, G. Cheymol, A. Semerok, Patent CEA 5. D. Melyukov, Étude et développement d’une méthode de FR1355905, Procédé de détermination de la diffusivité caractérisation in-situ et à distance de dépôts en couches thermique et système pour la mise en œuvre, 2013 minces par pyrométrie active laser, CEA PhD Thesis, France, 8. Y.S. Touloukian, R.W. Powell, C.Y. Ho, M.C. Nicolaou, 2011 Thermal diffusivity (IFI/Plenum, New York, 1973) Cite this article as: Alexandre Semerok, Sang Pham Tu Quoc, Guy Cheymol, Catherine Gallou, Hicham Maskrot, Gilles Moutiers, Lock-in thermography for characterization of nuclear materials, EPJ Nuclear Sci. Technol. 2, 20 (2016)