Thermal Diffusivity Measurement of Two-Layer Optical Thin-Film Systems Using Photoacoustic Effect1

In this study, we designed and developed two-layer antireflection (AR) optical coating samples on glass substrates, using different evaporation conditions of coating rates and substrate temperatures for two dielectric materials, MgF₂ and ZnS, with different refractive indices. The through-plane thermal diffusivity of these systems was measured using the photoacoustic effect. The optical thicknesses of MgF₂ and ZnS layers were fixed at 5/4 (=514.5 nm) and , respectively, and the thermal diffusivities of the samples were obtained from the measured amplitude of the photoacoustic signals by changing the chopping frequency of the Ar⁺ laser beam. The results demonstrated that the thermal diffusivity of the sample fabricated under the conditions of 10Å·s^–1 and 150°C had the maximum value and that the results were directly related to the microstructure of the film system.     

Analysis of Two-Dimensional Effect in the Measurement of Thermal Diffusivity of Thin Films with an AC Calorimetric Method1

An ac calorimetric method for measuring the thermal diffusivity of thin-film materials has been widely applied. In the application of this method, the systematic errors caused by the heat loss effect, the edge reflection effect, etc., have been analyzed and corresponding correction methods have been developed. But when measuring films with low thermal diffusivity or with thickness comparable to the thermal diffusion length, a two-dimensional effect which will also result in a systematic error of the measurement is present. In this paper, the mechanism of two-dimensional heat conduction within a thin sample which is supplied a periodic heat flux by a chopped light beam is analyzed. A numerical analysis method is developed to study the effect of the two-dimensional heat conduction on the measured thermal diffusivity values. The relations between the measured thermal diffusivity and independent parameters such as frequency, thickness of sample, width of light spot, etc., are demonstrated to indicate the two-dimensional effect. The experimental precondition for minimizing the systematic error caused by the two-dimensional effect is determined. In addition, the analysis method presented in this paper should be useful for more difficult problems such as error estimation of the thermal diffusivity measurement of coatings or composite films.     

Thermal Diffusivity Measurement of Diamond Films1

This paper discusses the short-pulse-flash method developed for thermal diffusivity measurements on thin films. Two kinds of CVD diamond film have been prepared, and their thermal diffusivity in the perpendicular direction has been measured with this method. The measurement errors caused by the surface coating are discussed.     

应用光声技术测定薄型材料导温系数的研究

本文报导了用光声技术测试和研究薄型试样导温系数的结果,建立了该方法的理论模型,介绍了实验装置和数据处理的方法。用本装置对三种标准和亚标准试样的测试结果表明,实测值和文献推荐值相当吻合。本文的基本理论和实验方法同样也适用于其它有机、无机等薄型材料。     

Novel Transmission Open Photoacoustic Cell Configuration for Thermal Diffusivity Measurements in Liquids

In this paper the photoacoustic technique in the thermal-wave transmission configuration is applied to thermal diffusivity measurements in liquids. The one-dimensional heat diffusion problem involving three layers, and assuming surface absorption only, is solved for this goal. Linear relations among the photoacoustic amplitude (on a semi-log scale) and phase, as functions of the liquid sample thickness, are shown in each case. An analytical procedure involving linear fits to the experimental data is developed to produce two independent values for thermal diffusivity. The thermal diffusivity of three homogeneous liquids (distilled water, ethylene-glycol, and olive oil) was measured, and excellent agreement was obtained between results from both the amplitude and phase, as well as with thermal-diffusivity values reported in the literature.     

Analysis of the Photoacoustic Detector Signal for Thermal Diffusivities of Gases

A resonant and a nonresonant photoacoustic detector were used to determine thermal diffusivities of gases. With a nonresonant detector thermal diffusivities can be determined in a wide range between 10^–3 and 10^–7 m²·s^–1, whereas experiments with the resonant detector deliver thermal diffusivities in a range that is about a factor of 100 smaller. As refrigerants—HFCs, HCFCs, and hydrocarbons—are absorbents in the infrared at a wavelength of 3.39 m, their thermal diffusivity can be determined without the addition of a trace gas, particularly at pressures below 0.01 MPa. At pressures above 0.1 MPa, the addition of ammonia as a trace gas is recommended. The absorption wavelength is then 1.531 m. A simulation model for the nonresonant photoacoustic detector is presented for the design of a detector and for an extended error analysis.     

Thermal Diffusivity of Metallic Thin Films: Au, Sn, Mo, and Al/Ti Alloy

The thermal diffusivity of Au, Sn, Mo, and Al_0.97Ti_0.03 alloy thin films, which are commonly used in microelectromechanical (MEMs) system applications, is measured by two independent methods — the ac calorimetric and photothermal mirage methods. Both methods yield similar results of the thin-film thermal conductivity, but the uncertainty of the mirage technique is found to be relatively large because of the large temperature increase during the measurement. The measured thermal diffusivities of the thin films are generally lower than those of the same bulk material. Especially, the Al_0.97Ti_0.03 thin film shows a pronounced thermal conductivity drop compared with bulk Al, which is believed to be mainly due to impurity scattering. Comparison of the thermal conductivity with the electrical conductivity measured by the standard four-probe technique indicates that the relation of thermal and electrical conductivities follows the Wiedemann–Franz law for the case of Au and Sn thin films. However, the Lorentz number is significantly larger than the theoretical prediction for the case of Al_0.97Ti_0.03 and Mo thin films.     

Measurement of Thermal Diffusivity of Thermal Control Coatings by the Flash Method Using Two-Layer Composite Sample1

The thermal diffusivity of brittle coatings cannot be measured by the flash method directly because of the difficulty of preparing free-standing samples. Adopting the flash method using a two-layer composite sample, it is possible to measure thermal diffusivity if the radiant pulse is well defined and good thermal contact on the interface of the composite sample can be ensured. Using an equilateral trapezoidal pulse of an Nd-glass laser measuring the dimensionless temperature history of the rear face of the sample, we determined the thermal diffusivity of thermal control coatings in the temperature range of 80 to 200°C. The results for different thicknesses of substrate showed that the thermal contact resistance of the interface can be neglected.     

Thermal Diffusivity Measurement for Titanium Thin Films on Copper Substrate by Laser Produced Plasmas

The transport properties of condensed phase materials are, in principle, dependent on the local structure and composition of the specimen. This is particularly evident near the free surface of a solid alloy specimen where the morphology, composition, and thermal diffusivity exhibit significant depth dependence, as demonstrated in an earlier study of the depth-resolved thermal diffusivity of a galvanized steel specimen. A new non-contact method was used, based on time-resolved, spectroscopic measurement of the total mass removed from the specimen surface representatively in elemental composition by a high-power laser pulse. A new study of a titanium thin film of varying thickness deposited on a copper substrate is presented. The titanium thin film is first fabricated in a vacuum and then immediately analyzed for composition and thermophysical properties in situ, both by the method of representative laser-produced plasmas (LPP). Successive ablation layers of the thin film, as exposed by LPP ablation, have revealed the dependence of the thermophysical properties on film thickness as well as on depth. The existence of a characteristic length over which the substrate influences the dynamics of thermal transport in the titanium thin film has also been observed.     

Determination of the Local Thermal Diffusivity of Inhomogeneous Samples by a Modified Laser-Flash Method

The local thermal diffusivity is of special interest for quality control of materials grown by physical vapor transport. A typical specimen of these materials consists of single crystals with sizes up to 1 mm. The conventional laser-flash method delivers only an average value of the thermal diffusivity of these polycrystalline materials. A local sensitive measurement system is desirable to determine the thermal diffusivity of single grains with diameters of 100 μm and above. In this work a modification of a standard laser-flash apparatus is presented. The key feature is the position control of the specimen in the plane perpendicular to the laser beam and the IR-detection unit. The mechanical precision of the position control is better than 100 μm. The IR-detection unit consists of a MCT-detector, a polycrystalline IR-fiber, and a system to focus on the sample surface. To study the experimental potential of the modified laser-flash method, measurements of the local thermal diffusivity of a multiphase specimen with known microscopic thermal properties are presented. The obtained results are discussed with respect to the energy profile of the laser beam and the alignment of the IR-detection unit. It is shown that the thermal diffusivity of a small specimen area with a diameter of 2 mm can be determined with an uncertainty of ±5 %. For a polycrystalline aluminum nitride (AlN) specimen with grain sizes of the order of 1 mm, a mean value for the thermal diffusivity of (72.1 ± 3.6) m² · s⁻¹ at room temperature is determined. A possible local variation of the thermal diffusivity cannot yet be observed. An improvement of the resolution is in progress. Paper presented at the Seventeenth European Conference on Thermopysical Properties, September 5–8, 2005, Bratislava, Slovak Republic.     

Thermal Diffusivity Measurement of Polyamide Mesh by Temperature Wave Analysis1

The thermal diffusivity of a polyamide mesh having plane wave structure was determined by a temperature wave analysis method developed in our laboratory. The measured thermal diffusivity of the polyamide mesh represents the combined result for the polyamide fiber part and the open space of the mesh. The polyamide mesh was measured in air and liquid paraffin conditions. Its effective thermal diffusivity was obtained as a function of the volume content of the surrounding material. A unit-cell model was applied to the polyamide mesh structure and shows good correspondence with the experimental results.     

Cu2S相变过程中热扩散系数的精确测量和解析

材料发生相变时, 其结构和物理性能可能会发生剧烈的变化。采用激光闪射法测量热扩散系数时, 激光照射样品可能会伴随有光吸收/发射现象以及温度的显著升高, 导致其测量值偏离真实值。本工作以Cu₂S为研究对象, 发现激光照射样品后, 光吸收/发射的影响很小可以忽略, 但样品温度的升高则会明显影响热扩散系数的测量。通过构建具有不同石墨层厚度的石墨/Cu₂S双层结构, 利用石墨层减弱激光照射时Cu₂S样品的温度增加幅度, 成功使热扩散系数出现显著降低的起始温度接近采用DSC测量材料发生相变的起始温度。本研究进一步建立了石墨/Cu₂S双层结构样品的热流输运模型, 从石墨/Cu₂S双层结构样品的实验测试热扩散系数中解析出了Cu₂S在相变区间的本征热扩散系数。本工作对于理解和精确表征具有相变特征的离子导体热电材料、光敏、热敏材料的热扩散系数具有重要的意义。     

Determination of the Thermal Diffusivity of Edible Films

One of the most important factors in the preparation of edible films regards the choice of ingredients. Edible films are commonly prepared with single or mixed high-molecular-weight compounds like proteins and gums. In the present work, protein and gum-based edible films were prepared and their thermal diffusivity determined by photoacoustics. The films were prepared with different concentrations of four basic ingredients: whey protein concentrate, mesquite gum, sodium alginate, and -carrageenan. In single-component films, the highest thermal diffusivity was found in mesquite gum (1.97×10^–7m²s^–1), followed by sodium alginate, whey protein concentrate, and -carrageenan samples. In composed films, the highest thermal diffusivity was obtained in a ternary film made of mesquite gum, whey protein concentrate, and sodium alginate in identical parts (5.20×10^–7m²s^–1).     

Correction of Edge Effect in AC Calorimetric Method for Measuring Thermal Diffusivity of CVD Diamond Films1

In the thermal diffusivity measurement of a CVD diamond film using an ac calorimetric method, the reflection of an ac temperature wave at the edge of the film sample should be considered due to the limited length of the sample and its high thermal diffusivity, i.e., the edge effect. In this case, the measured thermal diffusivity is given as a function of frequency. The relation between the measured thermal diffusivity and the frequency is represented as an analytical expression. The real thermal diffusivity is obtained by correcting the edge effect by two means. One is an iterative method using the directly measured edge length of the sample to fit the analytical expression. The other is a parameter estimation method by which a simplex method is used to estimate the edge length and the real thermal diffusivity. Thermal diffusivities of two diamond films were measured, and data were analyzed using the above methods. The result shows that the parameter estimation method is relatively accurate and convenient in processing test data.     

用光声法测量陶瓷材料的热参量

以固体光声效应的RG理论为依据,用光声法测量了压电陶瓷材料PZT的热参量。实验结果表明:用此方法只需要测出一个量就能同时确定PZT的α、k和C的值,并且实验设备简单,速度快,是一种很有前途的测热参量方法。     

Determination of the Thermal Diffusivity of Calcium Salts of Saturated Carboxylic Acids

Calcium soaps are materials that serve a wide range of industrial applications such as softeners, detergents, plasticizers, greases, lubricants, cosmetics, and medicines. In addition, calcium salts of saturated carboxylic acids are of interest because of their presence in the staple food of Mexicans and other Central American people: the corn tortilla. Because of their wide use in industry, a knowledge of the thermal properties of the alkaline metal soaps is of great importance. In the present work, the thermal diffusivity of butyric-Ca, valeric-Ca, caprilic-Ca, undecanoic-Ca, palmitic-Ca, and stearic-Ca salts has been determined by photoacoustics. The thermal diffusivity of these salts shows a linear dependence on the number of carbons in the aliphatic chain, and was found within the range 2.60×10^–3 to 1.38×10^–2cm²s^–1, with the highest and lowest values corresponding to butyric-Ca and stearic-Ca, respectively.     

基于热成像的材料热扩散率测量方法研究

将一种基于热成像的薄片材料热扩散率测量方法的理论模型由二维拓展到三维,以适用于更大厚度材料的热扩散率测量。指出该方法适用的特征条件为:Z向空间导数值与材料表面和周围环境的温度差值为线性关系。仿真分析了传热距离与激励时间对特征条件的影响以及相关的信噪比问题,并在304不锈钢材料实测实验中依照仿真分析设置传热距离和激励时间以满足特征条件,结果显示厚度为1 mm和2 mm的不锈钢材料测量偏差均在3.0%以内,厚度为5 mm的不锈钢材料测量的偏差为4.1%,从而扩大了该测量方法的适用范围。     

激光脉冲法研究半透明PI/SiO_2薄膜的热扩散率

激光脉冲法在应用于测量对实验探测波段红外线半透明的材料热扩散率时遇到了困难。文中提出了新的解决办法:即通过对理论探测曲线进行分析,并通过在实际探测曲线上的升温幅度和特征点计算得到了热扩散率,成功地解决了这一难题。在-73℃~290℃的范围内获得了对激光和红外线都是半透明的聚酰亚胺(PI)薄膜的热扩散率,并研究了室温下PI/SiO2复合材料的热扩散率随SiO2含量的变化规律。     

Effect of the Response Delay of the Measuring System on Thermal Diffusivity Measurement Using the Flash Method1

This work investigates the effect of the response delay of a measuring system on a thermal diffusivity measurement. A model of an m th-order delay in the measuring system is introduced, and a general expression for the output of the system with temperature response as input is derived. The effect on the temperature response caused by such a system is discussed. As a practical example, a third-order measuring system is considered. The measured temperature responses of stainless steel foils are compared with those calculated with the model of a third-order delay system. Good agreement between the two results is shown.