Thermal Diffusivity of Diamond Wafers Deposited with Multicathode dc Plasma-Assisted CVD

A thermal diffusivity map for diamond wafers of 10-cm diameter was obtained using a converging thermal wave technique in a nondestructive and noncontact manner. Diamond wafers were deposited by seven-cathode dc plasma-assisted chemical vapor deposition with different CH₄concentrations in pure hydrogen and applied powers of the plasma. Six cathodes were located at the apexes of a hexagon with an arm distance of 4.3 cm about a central cathode. The wafer deposited at a low-power plasma (13.47 kW) and a low concentration of CH₄(6%, by volume) shows three circular zones on the thermal diffusivity map. The thermal diffusivity shows the lowest value at the center. It increases to about 10% in a radius of 2 to 3 cm and then decreases with further increases in the radius. The optical photograph and the Raman lines of the wafer show patterns similar to those of the thermal diffusivity. These are affected by the locations of the cathodes in the deposition chamber when the plasma power is low. Diamond wafers deposited at a high-power plasma (20.58 kW) with high concentrations of methane (10%, by volume) show higher values of thermal diffusivity and better uniformity than wafers deposited at a low power and low methane concentration. A fine crack can be located on a wafer with the converging thermal wave technique.     

One-Level, Two-Point Method for Estimation of Thermal Diffusivity by the Converging Thermal-Wave Technique

The thermal diffusivity of several kinds of metal sheets was measured by the converging thermal-wave technique. This is a typical technique which can obtain the in-plane thermal diffusivity by measurement of the temperature evolution at the center of the pulsed annular laser beam when the laser beam irradiates the surface of the samples. However, the rapid temperature increase and nonlinearity of the infrared detector in the earlier part, and convection heat loss from the sample surface in the later part, of the temperature evolution can be sources of errors. In this study, when the temperature of the center reached half of the maximum, the timest ₁andt ₂, in the ascending and descending parts of the temperature evolution curve, respectively, were determined and other points,t₁andt₂, were determined by increasing the temperature to 90% of the maximum in successive increments of 10% of the maximum. By using these determined times, the variation of thermal diffusivity was investigated and compared with results from existing methods and with reference values.     

Measurements of Thermal Conductivity and Thermal Diffusivity of CVD Diamond

The thermal conductivity of natural, gem-quality diamond, which can be as high as 2500 Wm^–1 K^–1 at 25°C, is the highest of any known material. Synthetic diamond grown by chemical vapor deposition (CVD) of films up to 1 mm thick exhibits generally lower values of but under optimal growth conditions it can rival gem-quality diamond with values up to 2200 Wm^–1 K^–1. However, it is polycrystalline and exhibits a columnar microstructure. Measurements on free-standing CVD diamond, with a thickness in the range 25–400 m, reveal a strong gradient in thermal conductivity as a function of position z from the substrate surface as well as a pronounced anisotropy with respect to z. The temperature dependence of in the range 4 to 400 K has been analyzed to determine the types and numbers of phonon scattering centers as a function of z. The defect structure, and therefore the thermal conductivity, are both correlated with the microstructure. Because of the high conductivity of diamond, these samples are thermally thin. For example, laser flash data for a 25-m-thick diamond sample is expected to be virtually the same as laser flash data for a 1-m-thick fused silica sample. Several of the techniques described here for diamond are therefore applicable to much thinner samples of more ordinary material.     

A New Technique for Hydrate Thermal Diffusivity Measurements

Thermal property measurements of natural gas hydrates in various sediment mixtures are necessary to describe heat transfer to surroundings during well boring and gas production. An apparatus for measuring thermal diffusivity in various mixtures of hydrates with sediment has been constructed. The apparatus uses a new method for determining thermal diffusivity that has advantages over the von Herzen and Maxwell probe method. The new experiment is simple and inexpensive to construct and appears to be much more accurate than the ±30% reported for an earlier probe. The thermal diffusivity of ice has been measured to determine the uncertainty of the technique, i.e., within ±6% with a 95% confidence level. The thermal diffusivity for pure methane hydrate at various temperatures is reported. Paper presented at the Fifteenth Symposium on Thermophysical Properties, June 22–27, 2003, Boulder, Colorado, U.S.A.     

Thermal Diffusivity by Modified ac Calorimetry Using a Modulated Laser Beam Energy Source

Modified ac calorimetry, a variation of the Angstrom method, has been shown to be a precise tool for measuring the in-plane thermal diffusivity of thin films (thickness less than 300 m) of a wide variety of materials and layered composites. The property is determined from an analysis of the decay curve of the ac temperature waves generated by irradiation of a specimen using uniform chopped light (at frequencies from 1 to 20 Hz) from a halogen lamp source. To address certain limiting factors, especially to improve the signal-to-noise ratio and to eliminate heat losses, an improved form of measurement instrument has been developed. It is based on the use of a modulated laser beam heating to provide a higher intensity energy source plus a special optical system to ensure that one-dimensional ac temperature wave propagation is obtained. Measurements can now be made using frequencies in the range of 0.01 to 10 Hz, i.e., 10 times lower than in the traditional method. The performance of the improved measurement instrument will be illustrated by results on various materials of known thermal properties such as nickel and stainless steel, proposed reference materials such as a glassy carbon and alumina, plus a comparison of results obtained on CVD diamond films used in an international round-robin series with those obtained by the traditional technique.     

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.     

Uncertainty of Thermal Diffusivity Measurements by Laser Flash Method

The laser-pulse method is a well-established nonsteady-state measurement technique for measuring the thermal diffusivity, a, of solid homogeneous isotropic opaque materials. BNM-LNE has developed its own bench based on the principle of this method in which the thermal diffusivity is identified according to the “partial time moments method.” Uncertainties of thermal diffusivity by means of this method have been calculated according to the ISO/BIPM “Guide to the Expression of Uncertainty in Measurement.” Results are presented for several cases (Armco iron, Pyroceram 9606) in the temperature range from 20 to 800°C. The relative expanded (k = 2) uncertainty of the thermal diffusivity determination is estimated to be from ±3 to ±5%, depending on the material and the temperature. Paper presented at the Fifteenth Symposium on Thermophysical Properties, June 22–27, 2003, Boulder, Colorado, U.S.A.     

Thermal Diffusivity Measurements of Liquid Silicate Melts

The effect of structure on the thermal diffusivities/conductivities for liquid silicates have been summarized based on recent experimental work carried out by the Royal Institute of Technology, Stockholm and the Tokyo Institute of Technology using the laser-flash and the hot-wire methods, respectively. In the former case, the effective thermal diffusivity was measured by a three-layer method. The relationship proposed by Mills that the thermal conductivity of silicates increases with a decrease in the ratio of NBO/T (number of non-bridging oxygens per tetrahedrally coordinated atom) has been well supported by the effective thermal diffusivity data for the liquid CaO-Al₂O₃-SiO₂ slags. However, it has been shown that for the slags having a higher CaO/Al₂O₃ ratio, the effective thermal diffusivity is roughly constant independent of the ratios of NBO/T. It has been concluded that when the silicate network is largely broken down, the phonon mean free path is not affected by the structure. It has been found by the hot-wire method that the magnitudes of thermal resistivity are in the hierarchy Li₂O-SiO₂2O-SiO₂2O-SiO₂ despite their similar values of NBO/T. It has been concluded that the ionicity of non-bridging oxygen ions is also a factor controlling the thermal conductivity of silicates as well as the number of broken bridges in the silicate network. The effective thermal diffusivity was measured for the CaO-Al₂O₃-SiO₂-FeO system to elucidate the radiation contribution to the effective thermal diffusivity. It has been found that the effective thermal diffusivity increases with an increase in FeO content. It can be considered that the strong absorption and emission within the liquid slag films caused by the Fe²⁺ ions enhances the photon heat transfer.     

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.     

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.     

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.     

A Transient Heating Technique for Measuring the Thermal Diffusivity of Metals

A transient heating technique, improving the constant-rate-heating technique for the measurements of thermal diffusivities of metals, is proposed. For a physical model of a specimen to be measured, the transient heat-conduction equation was solved with some boundary conditions, and the solution obtained was used as the principle of the present transient heating technique for determining the thermal diffusivity of the specimen. Additionally, a thermal analysis was made to satisfy a boundary condition involved in the principle, that is, the condition of radiative thermal insulation at the two end surfaces of the specimen. To verify the validity of the present technique, the thermal diffusivity of iron, whose thermophysical properties are well-known, was measured with the same apparatus as used in our previous work, and the experimental results are discussed. Moreover, thermal diffusivities of thermocouple materials, namely, constantan, chromel, and alumel, were measured by the technique in the temperature range of 360 to 680 K.     

Multidimensional Flash Diffusivity Measurements of Orthotropic Materials

A generalization of the radial flash technique is presented whereby the thermal diffusivity of an orthotropic solid is measured in directions parallel and perpendicular to the flash source. The theoretical formulation is based on a Green's function approach which assumes a general orthotropic solid with three mutually orthogonal thermal diffusivities (or conductivities). Using this approach, a solution to this problem is presented which can be used to develop solutions for arbitrary pulse waveforms and incident geometries. Analytical and numerical results are presented for two-dimensional and three-dimensional cases of finite and semiinfinite solids. Characteristic equations which describe the ratio of the temperatures at two points along a principal axis are given. The equations show excellent agreement with numerical predictions as well as experimental results. A parameter estimation approach is given which improves on the accuracy of the radial flash technique in the determination of thermal diffusivity from experimental data.     

Simultaneous Measurements of the Thermal Conductivity and Thermal Diffusivity of Molten Salts with a Transient Short-Hot-Wire Method

A transient short-hot-wire technique has been successfully used to measure the thermal conductivity and thermal diffusivity of molten salts (NaNO₃, Li₂CO₃/K₂CO₃, and Li₂CO₃/Na₂CO₃) which are highly corrosive. This method was developed from the hot-wire technique and is based on two-dimensional numerical solutions of unsteady heat conduction from a short wire with the same length-to-diameter ratio and boundary conditions as those used in the actual experiments. In the present study, the wires are coated with a pure Al₂O₃ thin film by using a sputtering apparatus. The length and radius of the hot wire and the resistance ratio of the lead terminals and the entire probe are calibrated using water and toluene with known thermophysical properties. Using such a calibrated probe, the thermal conductivity and thermal diffusivity of molten nitrate are measured within errors of 3 and 20%, respectively. Also, the thermal conductivity of the molten carbonates can be measured within an error of 5%, although the thermal diffusivity can be measured within an error of 50%.     

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.     

Thermal Diffusivity Measurements of Thermographite

This paper presents results of measurements of a graphite proposed to serve as a thermophysical property reference or standard reference material. The reported measurements contribute to a program launched in 1999 by Anter Corp. with the objective to provide a replacement for the NIST thermal property reference material RM AXM-5Q graphite whose supplies were being exhausted. Measurements of the thermal diffusivity performed on five specimens taken from different positions within a large graphite block between room temperature and 1300 K were in good mutual agreement. Measurements of NIST reference AXM-5Q graphite sample supplied to minimize effects of different contributors to a common base were also in good agreement, both with the NBS reference function established by Hust in 1984 and contributions to the NBS project from the Vinca Institute of Nuclear Sciences carried out in 1979. The influence of different data reduction techniques on the measured thermal diffusivity values is illustrated and discussed.     

Thermal Diffusivity Measurements in Edible Oils using Transient Thermal Lens

Time resolved thermal lens (TL) spectrometry is applied to the study of the thermal diffusivity of edible oils such as olive, and refined and thermally treated avocado oils. A two laser mismatched-mode experimental configuration was used, with a He–Ne laser as a probe beam and an Ar⁺ laser as the excitation one. The characteristic time constant of the transient thermal lens was obtained by fitting the experimental data to the theoretical expression for a transient thermal lens. The results showed that virgin olive oil has a higher thermal diffusivity than for refined and thermally treated avocado oils. This measured thermal property may contribute to a better understanding of the quality of edible oils, which is very important in the food industry. The thermal diffusivity results for virgin olive oil, obtained from this technique, agree with those reported in the literature.Paper presented at the Seventeenth European Conference on Thermophysical Properties, September 5-8, 2005, Bratislava, Slovak Republic.     

Measurements of the Thermal Conductivity and Thermal Diffusivity of Polymer Melts with the Short-Hot-Wire Method

In this paper, the thermal conductivity and thermal diffusivity of four kinds of polymer melts were measured by using the transient short-hot-wire method. This method was developed from the hot-wire technique and is based on two-dimensional numerical solutions of unsteady heat conduction from a wire with the same length-to-diameter ratio and boundary conditions as those in the actual experiments. The present method is particularly suitable for measurements of molten polymers where natural convection effects can be ignored due to their high viscosities. The results have shown that the present method can be used to measure the thermal conductivity and thermal diffusivity of molten polymers within uncertainties of 3 and 6%, respectively. Further, the thermal conductivity and thermal diffusivity of solidified samples were also measured and discussed.