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.     

Measurement and evaluation of the thermal diffusivity of two-layered materials

Transient methods, such as those with pulse- or step-wise heating, have often been used to measure thermal diffusivity of various materials including layered composite materials. The aim of the present study is to investigate effects of various parameters on the measurement of thermal diffusivity when the transient methods are applied. Mainly a two-layered material in the pulsewise heating method is considered because of its simplicity and usefulness in identifying and determining the effects of the parameters. First, it has been shown that there exists a special condition for determining the thermal diffusivity of a component in the two-layered material whose other relevant thermophysical properties are known. Second, it has been shown that the thickness of the laserbeam absorption layer, which inevitably makes sample material into the twolayered material, may cause a relatively large error when the thermal diffusivity of the base material is high. Finally, it has been derived a definite relation between the apparent thermal diffusivity obtained from the temperature response and the mean thermal diffusivity, which has a physical meaning related to the thermal resistance.     

Temperature dependence of thermal diffusivity measured by photothermal radiometry

Thermal diffusivity is generally measured by impulse or modulated flux methods; the temperature distribution inside the sample is measured by thermocouples. The nonintrusive photothermal techniques do not induce geometrical or thermal changes inside the sample; an indirect procedure gives the temperature variations on the sample surface. Photothermal radiometry, based on the measurement of the radiative flux emitted by the sample, is all the more accurate as the temperature is elevated. We have used this method to measure thermal diffusivities of thin and opaque solid samples at temperatures above 400 K. The temperature field is calculated by using a standard model accounting for the emitted radiative flux. The experimental apparatus is briefly described and experimental results for selected materials (nickel, stainless steel) and cast-iron samples are presented. The influence of the material structure on the thermal diffusivity is discussed.     

基于脉冲涡流热成像的面内方向性热扩散率测量

针对导电材料面内方向性热扩散率的测量,提出脉冲涡流热成像法这一新方法。该方法采用感应式脉冲线激励源,在导电试件表面形成沿一定方向的感应涡流,实现局部热激励,在非稳态条件下实现了材料面内方向热扩散率的测量;简单调节试件与线感应激励线圈的角度,就可以快速无损非接触地测量试件在垂直线圈方向上的热扩散率值。对感应线激励下面内热传导及高斯温度分布进行了分析,分别对AISI304不锈钢、纯铁、纯镍3种材料的热扩散率进行了测量,测量结果与手册值相符,偏差小于9.0%,相对扩展不确定度分别为3.18%,3.72%,3.70%。     

Measurements of the thermal diffusivity of aluminum using frequency-scanned, transient, and rate window photothermal radiometry. Theory and experiment

The thermal diffusivity of various types of aluminum has been measured, using a completely noncontact experimental configuration based on infrared photothermal radiometry. Photothermal response transients, conventional frequency scans, and pulse duration- or repetition rate-scanned rate windows have been investigated. It has been shown that the conventional frequency scan is not suitable for measurements of aluminum with a short thermal transport time such as foils, due to an extremely degraded signal-to-noise ratio (SNR). Also, it has been found that the conventional frequency scan method is less sensitive to the actual value of thermal diffusivity than the rate-window scan. The rate-window method, furthermore, gives superior SNR especially for thin metals and yields excellent agreement between the theory and the data. An advantage of the pulse duration-scanned rate window mode is that it does not require knowledge of the instrumental transfer function as an input. The transient response gives the worst SNR but is best for the physical interpretation of the photothermal signals. In addition, it has been shown that the infrared photothermal radiometric transmission mode is less sensitive to surface roughness than the reflection mode and, therefore, is preferable for thermal diffusivity measurements of aluminum and of good thermal conductors, in general.     

Evaluation of the Effective Sample Temperature in Thermal Diffusivity Measurements Using the Laser Flash Method

In the measurement of thermal diffusivity by the laser flash method, a temperature rise occurs in the sample as a pulsed laser hits on the sample surface. Due to the temperature dependence of thermal diffusivity of the sample, the thermal diffusivity corresponds to a temperature that is larger by T _eff than the temperature before laser irradiation is applied. This effective temperature rise, T _eff, has been investigated by using a numerical simulation. The results indicate that the effective temperature rise is almost equal to a maximum temperature rise, T _M, of the back surface of the sample in cases where both linear and nonlinear temperature variations of thermal diffusivity are considered.     

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.     

Study on the Spatial Resolution of Imaging Technique for Absorption Loss Measurement of Optical Coatings

The uniformity of optical coatings becomes more and more important as large diameter optical devices are widely used. Absorption loss in optical components, particularly in optical coatings, is a limiting factor in high-power laser applications. This article analyzes the main factors, which affect the spatial resolution of three techniques for surface absorption loss measurement, including the photothermal deflection technique, the surface thermal lens technique, and the photothermal detuning technique. The influence of the size of the heating and probe beam on the photothermal detuning technique is studied in detail. Experiments are conducted to study the photothermal signal of the photothermal detuning technique for absorption measurement of the optical coating point by point. The results show that the main factors, which affect the spatial resolution of imaging measurements for absorption loss of coatings, are the heating beam size and the step accuracy of the sample translation stage. The heating and probe beam sizes has a significant impact on the application of the photothermal detuning technique. Experimental result shows that the photothermal detuning technique can be used for imaging of absorption loss measurements of optical coatings. The results provide theoretical and experimental supports for further application of the photothermal detuning technique.     

Application of the Thermal Quadrupoles Method to Semitransparent Solids

In this study, the thermal quadrupoles method is extended to semitransparent layered solids. Using this method, the surface temperature of semitransparent multilayered materials is calculated as a function of the optical and thermal properties of each layer. This result eventually leads to determination of the thermal diffusivity, thermal resistance, and/or optical absorption coefficient of layered materials using photothermal techniques. The thermal quadrupoles method is applied to determine the thermal contact resistance in glass stacks.     

基于激光闪光法的立式热扩散率测量装置研究

介绍了基于激光闪光法的立式热扩散率测量装置,利用脉冲激光对样品进行均匀加热,使样品内部产生一维热流,并通过红外探测器测量样品温升信号,采用立式真空加热炉控制测量温度环境,实现室温至1600℃的热扩散率测量。用该装置测量厚度为1. 1 mm,直径为10 mm的不锈钢样品,测量结果与PTB参考数据的偏差小于1%。     

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.     

Measurement of thermal diffusivity of solids using infrared thermography

We report measurement of thermal diffusivity of solid samples by using a continuous heat source and infrared thermal imaging. In this technique, a continuous heat source is used for heating the front surface of solid specimen and a thermal camera for detecting the time dependent temperature variations at the rear surface. The advantage of this technique is that it does not require an expensive thermal camera with high acquisition rate or transient heat sources like laser or flash lamp. The time dependent heat equation is solved analytically for the given experimental boundary conditions. The incorporation of heat loss correction in the solution of heat equation provides the values of thermal diffusivity for aluminum, copper and brass, in good agreement with the literature values.     

Experimental Verification to Obtain Intrinsic Thermal Diffusivity by Laser-Flash Method

There is a need to obtain highly reliable values of thermophysical properties. The thermal conductivity of solids is often calculated from the thermal diffusivity, specific heat, and density, respectively, measured by the laser-flash method, differential scanning calorimetry, and Archimedes’ method. The laser-flash method is one of the most well-known methods for measuring the thermal diffusivity of solids above room temperature. This method is very convenient to measure the thermal diffusivity without contact in a short time. On the other hand, it is considered as an absolute reference measurement method, in particular, because only measurements of basic quantities such as time, temperature, length, and electrical quantities are required, and because the uncertainty of measurement can be analytically evaluated. However, it could be difficult in some cases to obtain reliable thermal-diffusivity values. The measurement results can indeed depend on experimental conditions; in particular, the pulse heating energy. A procedure to obtain the intrinsic thermal-diffusivity value was proposed by National Metrology Institute of Japan (NMIJ). Here, “intrinsic” means unique for the material, independent of measurement conditions. In this method, apparent thermal-diffusivity values are first measured by changing the pulse heating energy at the same test temperature. Then, the intrinsic thermal diffusivity is determined by extrapolating these apparent thermal diffusivities to a zero energy pulse. In order to verify and examine the applicability of the procedure for intrinsic thermal-diffusivity measurements, we have measured the thermal diffusivity of some materials (metals, ceramics) using the laser-flash method with this extrapolation procedure. NMIJ and Laboratoire National de Metrologie et d’essais (LNE) have laser-flash thermal-diffusivity measurement systems that are traceable to SI units. The thermal diffusivity measured by NMIJ and LNE on four materials shows good agreement, although they used different measurement systems and different analysis methods of the temperature-rise curve. Experimental verification on the procedure was carried out using the measured results. Some problems and considered solutions for laser-flash thermal-diffusivity measurements are discussed.     

Thermal Diffusivity Measurement of High-Conductivity Materials by Dynamic Grating Radiometry

A new apparatus based on dynamic grating radiometry (DGR) to measure the thermal diffusivity of high-conductivity materials such as graphite and diamond has been developed. In the DGR method, a sample surface is heated by interference of two pulsed laser beams, and the decay of temperature at a spot on the thermal grating is monitored by an infrared detector. In the ideal case where the grating period is much smaller than the light absorption length, the thermal diffusivity parallel to the surface can be determined from the decay constant and the grating period. This paper describes a procedure to extract the thermal diffusivity parallel to the plane while eliminating the effect of anisotropy and gives results for a preliminary measurement using Zr foil. A quadratic dependence of the time constant on fringe space has been observed in the fringe space change. Data are also presented for a 0.1-mm-thick graphite sheet. The results indicate the capability of DGR to measure anisotropic high-conductivity materials.     

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.     

Numerical estimation of the spatial resolution of thermal NDT techniques based on flash heating

In this paper we present a numerical method to quantitatively estimate the spatial resolution of a pulsed photothermal NDT system. We have simulated flash light heating applied to a delaminated plasma coated sample. The thermal parameters of the sample were chosen so that thermally the substrate material corresponds to steel and the coating layer corresponds to Cr₂O₃. The time-dependent three-dimensional diffusion equations resulting from the model were solved using Crank-Nicolson and implicit finite difference methods. Results of the calculations for different delamination sizes with different thermal contact resistances and the coating thicknesses of 50, 100, and 200 µm are presented. Also the time dependence of the sample surface temperature distribution is studied.     

Estimation of thermophysical properties of a film coated on a substrate using pulsed transient analysis

The thermophysical properties (thermal diffusivity, effusivity) of a film coated on a substrate have been measured by a pulsed transient analysis. The experimental approach is to utilize the film surface temperature decay following a heating pulse from a Q-switched Nd:glass laser. The temperature decay was measured using a HgCdTe infrared detector. Following the collection of data, a nonlinear least-squares regression was performed to estimate the optimal values of three separate thermal parameters by fitting the data to the semiinfinite substrate model solution. The model was checked systematically by analysis of the sensitivity and correlation of the three parameters, and the thermal diffusivity and effusivity ratio of the film and substrate were obtained from the optimal values of the estimated parameters.     

Measurement of laser-produced plasma impulses on molten metals for thermophysical property determination

A high-power pulsed laser excitation of a material surface generates a well-separated sequence of plasma, fluid flow, and acoustic events. When the movement of the surface due to evaporation by laser heating is kept in pace with the thermal diffusion front, the ablative mass loss from a solid surface becomes strongly correlated with the thermal diffusivity of the target matter. The other thermophysiocal properties which figure in this correlation are the mass density, heat of formation, and molecular weight. The functional relationship, which is given in this text for the first time, can be exploited to measure the thertnophysical properties. We have now extended such an approach to measurement of the thermal diffusivity of molten specimens by developing a new instrumentation for determining the ablative mass loss due to a single laser pulse. This has been accomplished by combining a facility for controlled generation of a molten specimen and a novel transducer for real-time measurement of the impulse imparted to the molten target by a laser-produced plasma plume, The transducer design, calibration, signal recovery, and method of extracting the mass loss per laser excitation are detailed by comparing the results for metallic specimens in the solid and molten state.Paper presented at the Twelfth Symposium on Tile rmophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Thermal Evaluation of Scorched Graphite-Epoxy Panels by Infrared Scanning

A simple measurement system is described for evaluating damage to graphite-epoxy panels, such as those used in high-performance aircraft. The system uses a heating laser and infrared imaging system to measure thermal performance. Thermal conductivity or diffusivity is a sensitive indicator of damage in materials, allowing this thermal measurement to show various degrees of damage in graphite-epoxy composites. Our measurements track well with heat-flux damage to graphite epoxy panels. This measurement system, including analysis software, could easily be used in the field, such as on the deck of an aircraft carrier or at remote air strips.     

Effect of radiation heat transfer on thermal diffusivity measurements

Experimental data on thermal conductivity and thermal diffusivity of a semitransparent material generally include an error due to the radiation heat transfer. This error varies in accordance with the experimental conditions such as the temperature level of the sample and the measuring method. In this paper, research on the influence of radiation heat transfer on thermal diffusivity are reviewed, and as an example, the method to correct the radiation component in the apparent thermal diffusivity measured by the stepwise heating technique is presented. The transient heat transfer by simultaneous thermal conduction and radiation in a semitransparent material is analyzed when the front surface is subjected to stepwise heating. The apparent thermal diffusivity, which includes the radiation component, is calculated for various parameters.Paper presented at the Second U.S.-Japan Joint Seminar on Thermophysical Properties, June 23, 1988, Gaithersburg, Maryland, U.S.A.