Treatment of Thermal Gratings in the Time and Frequency Domain

Abstract

In this contribution we present the range of applicability on solids and surfaces of the photothermal displacement technique refined by using laser-induced thermal gratings. A suitable theoretical calculation has been performed showing the characteristic dependence of the absorption-induced surface deformation on optical and thermophysical parameters as well as on pulsed and amplitude-modulated laser excitation. The potential of the grating technique for thermal diffusivity measurements and for the study of heat diffusion in a preferential direction is clearly demonstrated. Moreover equivalence and convertibility of both dynamic approaches for thermal diffusivity measurements is found. However, in relation to other applications the selected operation form (pulsed or c.w.-modulated) presents specific advantages which justify its choice. The equivalent and complementary information obtained in the time and frequency domain is discussed using for this purpose experimentally limiting cases which are commonly applied. Useful analytical expressions have been derived interpreting both depth and laterally resolved photothermal measurements of homogeneous material parameters. Thus, the photothermal displacement grating technique is suggested as an alternative, contactless method, sensitive to surfaces, in the field of non-destructive evaluation.     

Simultaneous Measurement of Thermal Diffusivity and Optical Absorption Coefficient of Solids Using PTR and PPE: A Comparison

Modulated photothermal radiometry (PTR) and a modulated photopyroelectric (PPE) technique have been widely used to measure the thermal diffusivity of bulk materials. The method is based on illuminating the sample with a plane light beam and measuring the infrared emission with an infrared detector (PTR) or the electric voltage produced by a pyroelectric sensor in contact with the sample (PPE). The amplitude and phase of both photothermal signals are recorded as a function of the modulation frequency and then fitted to the theoretical model. In this work, we compare the ability of modulated PTR and PPE to retrieve simultaneously the thermal diffusivity and the optical absorption coefficient of homogeneous slabs. In order to eliminate the instrumental factor, self-normalization is used, i.e., the ratio of the photothermal signal recorded at the rear and front surfaces. The influence of the multiple reflections of the light beam and the transparency to infrared wavelengths are analyzed. Measurements performed on a wide variety of homogeneous materials, transparent and opaque, good and bad thermal conductors, confirm the validity of the method. The advantages and disadvantages of both techniques are discussed.     

Thermophysical Properties of Thermal Sprayed Coatings on Carbon Steel Substrates by Photothermal Radiometry

Laser infrared photothermal radiometry (PTR) was used to measure the thermophysical properties (thermal diffusivity and conductivity) of various thermal sprayed coatings on carbon steel. A one-dimensional photothermal model of a three-layered system in the backscattered mode was introduced and compared with experimental measurements. The uppermost layer was used to represent a roughness-equivalent layer, a second layer represented the thermal sprayed coating, and the third layer represented the substrate. The thermophysical parameters of thermal sprayed coatings examined in this work were obtained when a multiparameter-fit optimization algorithm was used with the backscattered PTR experimental results. The results also suggested a good method to determine the thickness of tungsten carbide and stainless-steel thermal spray coatings once the thermophysical properties are known. The ability of PTR to measure the thermophysical properties and the coating thickness has a strong potential as a method for in situ characterization of thermal spray coatings.     

Thermal Wave Resonator Cavity Applied to the Study of the Thermal Diffusivity of Coffee Infusions

Among the photothermal methods, the photopyroelectric technique, in its several experimental configurations, has been extensively used to measure the thermal properties of liquids, mainly the thermal effusivity and diffusivity. In this paper, the use of the so-called thermal wave resonator cavity method, in the cavity-length-scan mode, to measure the thermal diffusivity of commercial coffee infusions with samples at different concentrations and degrees of degradation induced by heating cycles is reported. A linear relationship between the logarithm of the pyroelectric signal amplitude and the sample thickness was observed, in agreement with the basic theory for the experimental configuration used here, from which the thermal diffusivity values of the samples were obtained. The thermal diffusivity was found to be almost independent of the coffee concentration in water but that this parameter is sensitive to sample modifications induced by degradation. This work represents another step to demonstrate the capability of the used method for characterization of the thermal properties of liquids.     

Optical and Thermal Analysis of the Time Evolution of Curing in Resins by Photothermal Techniques

Four shades of a commercial visible-light curing dental resin are analyzed using photothermal techniques. The thermal effusivities of the dental resin shades before curing are measured using a variant of the conventional photoacoustic technique. The thermal diffusivities before and after curing are measured using infrared photothermal radiometry in the forward emission configuration. The time evolution process of the photocuring resin is monitored by photothermal radiometry in the forward and backward emission configurations. Inversion of the time evolution signal of the different configurations used permits one to obtain the time evolution of the thermal and optical properties during the photocuring. The thermal effusivity and thermal diffusivity exhibit exponential growth, while the optical absorption decreases exponentially due to the curing process. The relationship of these phenomena with the decrease of monomer concentration induced by the curing is discussed.     

Measurement of the Thermal Diffusivity of Solids with an Improved Accuracy

A photothermal radiometry technique is being developed at the NPL with the goal of improving the accuracy of thermal diffusivity measurements. The principle is to perform a laser-induced thermal experiment while simultaneously making accurate measurements of the experimental boundary conditions. A numerical three-dimensional heat diffusion model based on thermal transfer functions has been developed to account for the measured boundary conditions. The thermal diffusivity is determined from the experimental data by a nonlinear, least-squares fit to the model. Experiments carried out on pure metals at 900 K demonstrate good agreement between the theoretical predictions and experimental data, and uncertainties of about 1.5% for the thermal diffusivities of platinum, titanium, and germanium were obtained.     

A Novel Comparative Photothermal Method for Measuring Thermal Diffusivity

A novel comparative method has been developed at the National Physical Laboratory (NPL) to measure the thermal diffusivity of semi-infinite samples without a priori knowledge of the boundary conditions. It is based on photothermal radiometry, and involves the detection of modulated thermal radiance from a target irradiated by a modulated, focused diode laser beam with a power of 1W. The technique exploits the fact that the frequency response of the surface temperature modulation scales with thermal diffusivity for a given target geometry (this is a fundamental property of the heat diffusion equation). In the process two samples are measured, one of which is known, and the diffusivity of the second material is derived from scaling the results over frequency. Measurements on samples of platinum and Inconel have shown the validity of the methodology but also raised issues concerning the difficulty of accurate measurements due to surface coatings or roughness.Paper presented at the Fifteenth Symposium on Thermophysical Properties, June 22--27, 2003, Boulder, Colorado, U.S.A.     

Thermal Diffusivity Measurements of Candidate Reference Materials by the Laser Flash Method

The National Metrology Institute of Japan (NMIJ) in AIST has investigated the laser flash method in order to establish a thermal diffusivity standard for solid materials above room temperature. A uniform pulse-heating technique, fast infrared thermometry, and a new data analysis method were developed in order to reduce the uncertainty in thermal diffusivity measurements. The homogeneity and stability of candidate reference materials such as isotropic graphite were tested to confirm their qualification as thermal diffusivity reference materials. Since graphite is not transparent to both the heating laser beam and infrared light for thermometry, the laser flash method can be applied to graphite without black coatings. Thermal diffusivity values of these specimens with different thicknesses, were measured with changing heating laser pulse energies. A unique thermal diffusivity value can be determined for homogeneous materials independent of the specimen thickness, by extrapolating to zero heating laser pulse energy on the plot of apparent thermal diffusivity values measured with the laser flash method as a function of heating laser pulse energy.Paper presented at the Fifteenth Symposium on Thermophysical Properties, June 22--27, 2003, Boulder, Colorado, U.S.A.     

Suggestions regarding thermal diffusivity measurements on pyrolytic graphite and pyrolytic boron nitride by the laser pulse method

The laser pulse method can be successfully applied to the measurement of thermal diffusivity of isotropic materials subject to some assumptions. For anisotropic materials, this method is applicable to the measurement of principal thermal diffusivity only on the condition that there is no difference in direction between the principal axis and that of the temperature gradient. After analyzing the heat conduction process in an anisotropic solid, it has been shown that large errors in the measurement of thermal diffusivity would exist if the direction of the principal axis deviates inconspicuously from that of the temperature gradient. The experimental results of thermal diffusivity of highly oriented pyrolytic graphite (HOPG) samples with various deviation angles have been compared with the analytical results. The laser pulse method is not applicable to measurements on semitransparent pyrolytic boron nitride (PBN). We adopted a two-layer composite sample to measure the thermal diffusivity of PBN in the c direction and a particular graphite-PBN composite sample has been prepared which has a very low thermal resistance at the interface. The thermal diffusivity and thermal conductivity of PG (below 2300°C) and PBN (below 1000°C) are given.Invited paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Mirage effect from thermally modulated transparent carbon nanotube sheets

The single-beam mirage effect, also known as photothermal deflection, is studied using a free-standing, highly aligned carbon nanotube aerogel sheet as the heat source. The extremely low thermal capacitance and high heat transfer ability of these transparent forest-drawn carbon nanotube sheets enables high frequency modulation of sheet temperature over an enormous temperature range, thereby providing a sharp, rapidly changing gradient of refractive index in the surrounding liquid or gas. The advantages of temperature modulation using carbon nanotube sheets are multiple: in inert gases the temperature can reach > 2500 K; the obtained frequency range for photothermal modulation is ~100 kHz in gases and over 100 Hz in high refractive index liquids; and the heat source is transparent for optical and acoustical waves. Unlike for conventional heat sources for photothermal deflection, the intensity and phase of the thermally modulated beam component linearly depends upon the beam-to-sheet separation over a wide range of distances. This aspect enables convenient measurements of accurate values for thermal diffusivity and the temperature dependence of refractive index for both liquids and gases. The remarkable performance of nanotube sheets suggests possible applications as photo-deflectors and for switchable invisibility cloaks, and provides useful insights into their use as thermoacoustic projectors and sonar. Visibility cloaking is demonstrated in a liquid.     

Optical measurements of thermal diffusivity of a material

The measurement of thermal diffusivity of a material (in particular, a thin film) is important for various reasons, e.g., to predict the heat transfer in the solid subjected to a thermal process, to monitor surface composition or morphology, or to detect invisible subsurface defects like delaminations. This measurement can be done in a noncontact manner using various photothermal methods. Such methods typically involve pulsed heating of the surface by small amounts using a laser source; the decay of the surface temperature after this pulsed photothermal heating is then probed to provide the thermal diffusivity. Various probing methods have been developed in the literature, including the probing of reflection, refraction, and diffraction from the pulsed heated area, infrared thermal radiometry, and surface deformation. This paper provides an overview of such techniques and some examples of their applications.     

Thermal wave interferometry for measuring the thermal diffusivity of thin slabs

Thermal wave interferometry applied to the evaluation of thermal diffusivity of freestanding coatings and single layers is herewith presented. Measurements on a set of eight different materials (oxides free copper, an aluminium alloy, Armco iron, AISI 316 stainless steel, Nimonic90 and IN738 nickel based alloys and Yttria partially stabilised Zirconia coatings) have been carried out. The corresponding thermal diffusivity values cover a very large range (about three order of magnitude). A comparison of 1D and 3D models has been done in order to optimise the main measurement parameters. Sample thickness, heating beam size and modulation frequency range have been selected in order to maximise the photothermal signal and its phase variation as a function of the frequency. Experimental results give evidence of a very good agreement between literature and experimental values for all samples confirming the capability of this technique for measuring the thermal diffusivity of thin slabs.     

Measurements of Thermal Diffusivity for Thin Slabs by a Converging Thermal Wave Technique

The measurement of thermal diffusivity for thin slabs by a converging thermal wave technique has been studied. Temperature variation at the center of the heat source ring that is produced by a pulsed high-power laser is detected by an infrared detector. A computer program based on the finite difference method is developed to analyze the thermal diffusivity of the slabs. Materials of both high thermal diffusivity (CVD diamond wafer) and low thermal diffusivity (stainless-steel foil) have been used for the measurements. The measurements have been performed by varying the size and the thickness of specimen. The converging thermal wave technique has proved to be a good method to measure the thermal diffusivity of a CVD diamond without breaking the wafer into small specimens. The technique can be applied for a small slab if the diameter of the slab is two times larger than that of the heat source ring. The sensitivity of thickness in measuring the thermal diffusivity is low for ordinary CVD diamond. The use of the converging thermal wave technique for nonhomogeneous, nonuniform, and anisotropic materials has been accomplished by applying the finite difference method.     

Thermal Conductivity Measurement of Submicron-Thick Films Deposited on Substrates by Modified ac Calorimetry (Laser-Heating Ångstrom Method)

Technological development, especially in microelectronics, necessitates the development of new and improved methods for measuring the thermal properties of materials, especially in the form of ultrathin films. Previously, modified ac calorimetry (laser-heating Ångstrom method) using a scanning laser as the energy source was developed and shown to provide accurate values of thermal diffusivity and derived thermal conductivity for a broad range of materials in the form of free-standing thin sheets or films, wires including fiber bundles, and some films on substrates. This paper describes further applications of the modified ac-calorimetry technique for measurements of the thermal conductivity of thin films deposited on substrates. It was used to measure successfully the thermal conductivities of 1000- to 3000-Å-thick aluminum nitride films, aluminum oxide films, etc., which were deposited on a glass substrate. It was also shown to be suitable for developmental measurements on submicron-thick chromatic films deposited on a PET substrate, which are photothermal recording layers, used in the media of CD-R drives of computer systems.     

Thermal diffusivity of diamond/Si composite films measured by an ac calorimetric method

In measurements of thermal diffusivity, by an ac calorimetry method, on films of materials of high thermal diffusivity, attention should be paid to the effects of the sample length, i.e., the reflection of ac temperature waves at the sample edge. For such a case, the apparent thermal diffusivity of the sample having a finite length is given analytically as a function of frequency. Measurements were performed on diamond/Si composite films. The overall behavior of the frequency dependence of the apparent thermal diffusivity obtained is satisfactorily explained by the analytical expression. The true thermal diffusivity is obtained by fitting a theoretical curve to the experimental results. Especially when the apparent thermal diffusivity saturates in a high-frequency region, the saturated value gives the true thermal diffusivity.     

Photothermal gas analyzer for simultaneous measurements of thermal diffusivity and thermal effusivity

In this paper, we describe a new, simple, and fast photothermal method for simultaneous measurements of two important gas thermal properties: thermal diffusivity and thermal effusivity. The method consists essentially in combining a photoacoustic cell and a thermal wave pyroelectric cell enclosed in a single compact gas analyzer. The photoacoustic cell is kept filled with synthetic air and sealed. The pyroelectric cell is also filled with synthetic air, and after some warm up time, the synthetic air is exchanged to the gas of interest. It is shown that the analysis of the transient and saturation signals of both photoacoustic and pyroelectric cells is capable of measuring the thermal properties with an accuracy of 3%. This particular capability of performing simultaneously the measurements of thermal diffusivity and thermal effusivity allows us to carry on the complete characterization of the thermal properties of gases.     

Adaptive ultrasonic measurement of blood vessel diameter and wall thickness: theory and experimental results

An adaptive ultrasonic technique for measuring blood vessel diameter and wall thickness is presented. This technique allows one to use a target-specific transmitted waveform/receiver filter to obtain a larger signal-to-noise ratio (SNR) in the received signal than conventional techniques. Generally, SNR of a received wave increases as the intensity of the transmit wave increases; however, because of the FDA limitations placed on the amount of transmit energy, it is important to be able to make the most efficient use of the energy that is available to obtain the best possible SNR in the received signal. Adaptive ultrasonic measurement makes the most efficient use of the energy that is available by placing the maximum amount of energy in the largest target scattering mode. This results in more energy backscatter from a given target, which leads to a higher SNR in the received waveform. Computer simulations of adaptive ultrasonic measurement of blood vessel diameter show that for a SNR of 0 dB in the transmitted waveform, the standard deviation of the diameter measurements for a custom-designed transmitted waveform is about two orders of magnitude less than the standard deviation of the diameter measurements using more conventional waveforms. Diameter and wall thickness measurement experiments were performed on a latex tube and a bovine blood vessel using both custom-made and conventionally used transmitted waveforms. Results show that the adaptively designed waveform gives a smaller uncertainty in the measurements. The adaptive ultrasonic blood vessel diameter and wall thickness measuring technique has potential applications in examining vessels which are either too deep inside the body or too small for conventional techniques to be used, because of the low SNR in the received signal.     

Measurement of the Thermal Conductivity of Si and GaAs Wafers Using the Photothermal Displacement Technique

Thermal conductivity and thermal diffusivity of Si and GaAs wafers were measured using the photothermal displacement technique, and the temperature dependence of these two quantities was investigated. Thermal diffusivity was obtained from the phase difference between the heating source and the signal, and thermal conductivity was determined from the maximum value of the signal amplitude in the temperature range 80 to 300 K. It was verified that an increase in doping concentration gives rise to a decrease in thermal conductivity at low temperatures. The experimental results obtained on samples with different types and doping concentrations are consistent with those expected from theoretical considerations.     

A review of factors influencing defect detection in infrared thermography: Applications to coated materials

Infrared thermography is a technique that is used to nondestructively inspect parts for the presence of subsurface defects. The technique normally consists of applying heat to one surface of the part and observing the thermal response, using heat-sensing devices such as infrared cameras, as the part cools. Internal defects such as voids modify the thermal response and produce local hot or cold spots on the specimen surface. For the detection of subsurface defects, the sensitivity of the technique to different parameters such as defect depth, material properties, and heating methods has not been established due in part to the complex nature of the heat/flaw interaction. A finite element model is used here to examine the influence of these parameters on defect dectability. The model shows that the defect detectability decreases with increasing defect depth beneath the surface, and that the technique is most sensitive to the inspection of low thermal diffusivity coatings bonded to high thermal diffusivity substrates. The results also show that the heat pulse duration should be made as short as possible to maximize defect detectability.     

Photothermal Investigations of De-Emulsification of Fat/Water-Based Pasty Materials: Margarine

In this work a fat/water-based emulsion pasty system, margarine, is studied from the point of view of its photothermal response at temperatures of the sample near and across the temperature region at which the emulsion breaks apart. The emulsion decay has also been observed at a fixed sample temperature through the temporal behavior of its photothermal response. For these studies, two different frequency-dependent photothermal experimental techniques have been used: photo-pyroelectric detection schemes, as well as infrared radiometry. Whereas the photo-pyroelectric technique has been applied to extract integral thermal information, the photothermal infrared radiometry has been used to explore aspects concerning the sample's thermal depth profile.