Thermal conductivity,heat capacity,and thermal diffusivity of selected commercial AlN substrates

The thermal transport properties of four commercially available AlN substrates have been investigated using a combination of steady-state and transient techniques. Measurements of thermal conductivity using a guarded longitudinal heat flow apparatus are in good agreement with published room temperature data (in the range 130–170 W · m^–1 · K^–1). Laser flash diffusivity measurements combined with heat capacity data yielded anomalously low results. This was determined to be an experimental effect for which a method of correction is presented. Low-temperature measurements of thermal conductivity and heat capacity are used to probe the mechanisms that limit the thermal conductivity in AlN.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

The thermal conductivity of propane

This paper presents thermal conductivity measurements of propane over the temperature range of 192–320 K, at pressures to 70 MPa, and densities to 15 mol · L^–1, using a transient line-source instrument. The precision and reproducibility of the instrument are within ±0.5%. The measurements are estimated to be accurate to ±1.5%. A correlation of the present data, together with other available data in the range 110–580 K up to 70 MPa, including the anomalous critical region, is presented. This correlation of the over 800 data points is estimated to be accurate within ±7.5%.Nomenclature a _n, b_ij, b_n, c_n Parameters of regression model - C Euler's constant (=1.781) - P Pressure, MPa (kPa) - P _cr Critical pressure, MPa - Q ₁ Heat flux per unit length, W · m^–1 - t time, s - T Temperature, K - T _cr Critical temperature, K - T ₀ Equilibrium temperature, K - T _re Reference temperature, K - T _r Reduced temperature = T/T _cr - T _TP Triple-point temperature, K Greek symbols Thermal diffusivity, m² · s^–1 - T _i Temperature corrections, K - T Temperature difference, K - T _w Temperature rise of wire between time t ₁ and time t ₂, K - T ^* Reduced temperature difference (T–T _cr)/T_cr - _corr Thermal conductivity value from correlation, W · m^–1 · K^–1 - _cr Thermal conductivity anomaly, W · m^–1 · K^–1 - _e Excess thermal conductivity, W · m^–1 · K^–1 - ^* Reduced density difference - Thermal conductivity, W^–1 · m^–1 · K^–1, mW · m^–1 · K^–1 - _bg Background thermal conductivity, W · m^–1 · K^–1 - ₀ Zero-density thermal conductivity, W · m^–1 · K^–1 - Density, mol · L^–1 - _cr Critical density, mol · L^–1 - _re Reference density, mol · L^–1 - _r Reduced density Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Thermal conductivity measurements of pacific illite sediment

Results are reported for effective thermal conductivity measurements performed in situ and in core samples of illite marine sediment. The measurements were obtained during a recent oceanographic expedition to a study site in the north central region of the Pacific Ocean. This study was undertaken in support of the U.S. Subseabed Disposal Project, the purpose of which is to investigate the scientific feasibility of using the fine-grained sediments of the sea floor as a repository for high-level nuclear waste. In situ measurements were made and 1.5-m-long hydrostatic piston cores were taken, under remote control, from a platform that was lowered to the sea floor, 5844 m below sea level. The in situ measurement of thermal conductivity was made at a nominal depth of 80 cm below the sediment surface using a specially developed, line-source, needle probe. Thermal conductivity measurements in three piston cores and one box core (obtained several kilometers from the study site) were made on shipboard using a miniature needle probe. The in situ thermal conductivity was approximately 0.91 W · m^–1 · K^–1. Values determined from the cores were within the range 0.81 to 0.89 W · m^–1 · K^–1.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Thermal conductivity of pure monoisotopic silicon

The thermal conductivity of pure monoisotopic silicon is estimated by two methods, which give similar results. One estimate, based on the observed thermal conductivity of monoisotopic germanium, yields a maximum of 66 W · cm^–1 · K^–1 at 22 K. The other estimate, based on measurements of natural silicon and on the theoretical isotope scattering rate, yields 75 W · cm^–1 · K^–1 at 22 K, an increase of only 45% over the natural crystal. These values are for crystals of approximately 0.5 cm diameter; smaller crystals yield lower values of the maximum conductivity and smaller isotope effects. Silicon cooled to liquid hydrogen temperature seems promising for high-irradiance laser mirrors. The small gain obtained by using monoisotopic silicon would be substantially greater in cases when the generated phonon distribution is athermal and weighted to higher frequencies. The effective heat transport could then be increased by as much as a factor 60 through the use of monoisotopic silicon.     

Measurement of the thermal conductivity of molten InSb under microgravity

Thermal conductivity of molten InSb was measured on board the TEXUS-24 sounding rocket by the transient hot-wire method using the originally designed thermal conductivity measurement facility (TCMF). Measurements made through this facility were affected by natural convection on the ground. This natural convection was confirmed to be sufficiently suppressed during a microgravity environment. The thermal conductivity of molten InSb was 15.8 and 18.2 W·m^–1·K^–1 at 830 and 890 K, respectively.     

Thermal conductivity of B2O3 glass under pressure

The thermal conductivity, , of vitreous boron trioxide was measured, using a hot-wire procedure, from 170 to 570 K and under pressures of up to 1.7 GPa. The thermal conductivity at room temperature and zero pressure was found to be 0.52 W · m^–1 · K^–1. The values of the logarithmic pressure derivative, g = d(ln )/d(ln ), where is the density, were found to be 1.1 for uncompacted glass and 0.7 for glass compacted to 1.2 GPa. The variation of with temperature at constant density was approximately linear, with a positive slope of 1.38×10^–3W·m^–1·K^–2.     

Thermal Conductivity of Opacified Powder Filler Materials for Vacuum Insulations1

The thermal conductivity of powder fillings for load-bearing vacuum insulations is investigated. Different opacifiers have been tested in mixtures with perlite powder, precipitated silica, and fumed silica. Using temperature-dependent thermal conductivity measurements, the radiative thermal conductivity and the solid conductivity of the powder samples are separated. Additionally, the influence of the pressure load on the solid conductivity is studied. The thermal conductivities of silica powders with added opacifier powders (carbon black, magnetite, silicon carbide, titanium dioxide) can be as low as 0.003 W·m^–1·K^–1 if the powder boards are pressed with moderate loads. The use of microporous silica powders as filler materials allows internal gas pressures even beyond 10 hPa with only a moderate increase of the overall conductivity.     

Thermal Conductivity of Chalcogenide As<Subscript>2</Subscript>S<Subscript>3</Subscript> Thin Films

In order to investigate the photo-induced thermal property changes in chalcogenide thin films, amorphous As ₂ S ₃ thin film samples, whose thicknesses are 0.5, 1.0, 2.0, and 4.0 m, were prepared on silicon wafers by thermal evaporation. Their thermal conductivity was measured by the 3 method between room temperature and 100 °C. These measurements were repeated after the illumination of an Ar⁺ laser beam whose photon energy is consistent with the bandgap energy of As ₂ S ₃, and repeated again for annealed films at 180 °C for 1 h. The result shows that the thermal conductivities of fresh films were 0.14 to 0.27 W·m ^–1·K ^–1; however, the values increase to 0.28–0.47 W·m ^–1·K ^–1 after illumination of the sample and decrease to 0.19–0.42 W·m ^–1·K ^–1 after annealing of the sample. These changes can be explained by the change in microstructure produced from the photo-darkening and thermal annealing.     

Establishment of an empirical correlation for estimating the thermal conductivity of igneous rocks

A correlation to predict the thermal conductivity of andesitic igneous rocks is developed from measured data on drill cores from wells from the Los Azufres geothermal field, Mexico. The correlation was developed from density, porosity, and thermal conductivity. Seventeen determinations were made on drill cores extracted at varying depths from 12 wells. Thermal conductivity varied from 1.05 to 2.34 W · m^–1 · K^–1, while bulk density varied from 2050 to 2740 kg · m^–3 and grain density varied from 2610 to 2940 kg · m^–3. Total porosity varied from 1.9 to 24.7%. Two polynomial regressions, one linear and one quadratic, were tested on the thermal conductivity-times-bulk density product, with total porosity as the independent variable. The correlation coefficients and residual mean square deviations were 0.83 and 0.00491 for the linear fit and 0.87 and 0.00425 for the quadratic model, respectively. For porosities up to about 18%, both models showed very close predictions, but for larger values, the quadratic model appeared to be better and it is recommended for the porosity range from 0 to 25%. Furthermore, density and porosity may be determined from drill cuttings, which are more readily available than cores.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Measurement of the thermal conductivity of molten semiconductors

The thermal conductivity of molten InSb in the temperature range between 800 and 870 K was measured by the transient hot-wire method using a ceramic probe. The probe was fabricated from a tungsten wire printed on an alumina substrate and coated with a thin alumina layer. The thermal conductivity was found to be about 18 W· m^–·K^–at the melting point and increased moderately with increasing temperature. The thermal conductivity of alumina used as the substrate for the probe was also measured in the same temperature range.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.On leave from NEC Corporation.     

Radiative heat exchange method for thermal conductivity measurement applying a perpendicular heat flow to a thin-plate sample: Principle and apparatus

To measure thermal conductivity of materials of low conductivity (0.1 to 1 W·m^–1·K^–1), a method using a specimen of small size (2×25×25 mm) has been developed. This method applies a well-defined, steady, and uniform heat flux perpendicular to the surface of a small plate sample of polymers or ceramics jointly by means of radiative heat exchange as well as by an areal heater on the sample surface and allows a reasonably rapid (5-min) measurement of thermal conductivity. This method of measuring conductivity is an absolute and direct measurement method which does not need any standard reference materials or information about heat capacity. The principle of the method has been demonstrated by constructing a measurement apparatus and measuring thermal conductivity of a few materials. The thermal conductivities of silicone rubber and Pyrex (Corning 7740) glass measured by the present method between 30 and 90°C are compared with recommended values.     

Thermal conductivity of air in the range 312 to 373 K and 0.1 to 24 MPa

We have used the transient hot-wire technique to make absolute measurements of the thermal conductivity of dry, CO₂-free air in the temperature range from 312 to 373 K and at pressures of up to 24 MPa. The precision of the data is typically ±0.1%, and the overall absolute uncertainty is thought to be less than 0.5%. The data may be expressed, within their uncertainty, by polynomials of second degree in the density. The values at zero-density agree with other reported data to within their combined uncertainties. The excess thermal conductivity as a function of density is found to be independent of the temperature in the experimental range. The excess values at the higher densities are lower than those reported in earlier work.Nomenclature Thermal conductivity, mW · m^–1 · K^–1 - Density, kg · m^–3 - C _p Specific heat capacity at constant pressure, J · kg^–1 · K^–1 - T Absolute temperature, K - q Heat input per unit wire length, W · m^–1 - t Time, s - K(=/C _p) Thermal diffusivity, m² · s^–1 - a Wire radius, m - Euler's constant (=0.5772 ) - p _c Critical pressure, MPa - T _c Critical temperature, K - _c Critical density, kg · m^–3 - R Gas constant (=8.314 J · mol^–1 · K^–1) - V _c Critical volume, m³ · mol^–1 - Z _c(=p _c V _c/RT _c) Critical compressibility factor     

An improved comparative thermal conductivity apparatus for measurements at high temperatures

An apparatus developed for the measurement of thermal conductivity of solids at temperatures from 350 to 1250 K in air, vacuum, or any other controlled atmosphere is described. It is based on the steady-state axial heat flow comparative method and can be used for measurements of conductivities in the range 1 to 100 W·m^–1·K^–1. New heat source layout gives uniform heat flux across the specimen column, improving the accuracy of the measurements. The specimen stack is fixed in a rigid frame. It incorporates convection current breakers, eliminating thermal insulation of the stack and thereby considerably increasing the ease of specimen mounting. The accuracy of measurements was assessed by measuring the thermal conductivity of approved reference materials and is found to be within ±3%. The results of measurements on nickel of known purity are also presented. Error analysis of the system shows that the determinate error leaving the uncertainty in the thermal conductivity of the reference materials, is less than ±2%.     

Thermal conductivity of ethane from 290 to 600 K at pressures up to 700 bar,including the critical region

The paper presents thermal conductivity measurements of ethane over the temperature range of 290–600 K at pressures to 700 bar including the critical region with maximum uncertainty of 0.7 to 3% obtained with a transient line source instrument. A correlation of the data is presented and used to prepare tables of recommended values that are accurate to within 2.5% in the experimental range except near saturation, and in the critical region, where the anomalous thermal conductivity values are predicted to within 5%.Nomenclature a _k , b _ij , b _k , c _i Parameters of the regression model, k=0 to n, i=0 to m, j=0 to n - P Pressure, (MPa or bar) - Q _l Heat flux per unit length (mW · m^–1) - t Time, s - T Temperature, K - T _cr Critical temperature, K - T _r Reduced temperature = T/T _cr - T _w Temperature rise of wire between times t ₁ and t ₂ K - T ^* Reduced temperature difference (T–T _cr)/T _cr - Thermal conductivity, mW · m^–1 · K^–1 - ₁ Thermal conductivity at 1 bar, mW · m^–1 · K^–1 - _bg Background thermal conductivity, mW · m^–1 · K^–1 - _cr Thermal conductivity anomaly, mW · m^–1 · K^–1 - _e Excess thermal conductivity, mW · m^–1 · K^–1 - Density, g · cm^–3 - _cr Critical density, g · cm^–3 - _r Reduced density, = / _cr - ^* Reduced density difference =(- _cr)/ _cr     

Thermal conductivity of methane

This paper reports thermal conductivity data for methane measured in the temperature range 120–400 K and pressure range 25–700 bar with a maximum uncertainty of ± 1%. A simple correlation of these data accurate to within about 3% is obtained and used to prepare a table of recommended values.Nomenclature a _k ,b _ij ,b _k Parameters of the regression model, k= 0 to n; i =0 to m; j =0 to n - P Pressure (MPa or bar) - Q _kl Heat flux per unit length (mW · m^–1) - t time (s) - T Temperature (K) - T _cr Critical temperature (K) - T _r reduced temperature (= T/T _cr) - T _w Temperature rise of wire between times t ₁ and t ₂ (deg K) - T ^* Reduced temperature difference (TT _cr)/T _cr - Thermal conductivity (mW · m^–1 · K^–1) - ₁ Thermal conductivity at 1 bar (mW · m^–1 · K^–1) - _bg Background thermal conductivity (mW · m^–1 · K^–1) - _cr Anomalous thermal conductivity (mW · m^–1 · K^–1) - _e Excess thermal conductivity (mW · m^–1 · K^–1) - Density (g · cm^–3) - _cr Critical density (g · cm^–3) - _r Reduced density (= / _cr) - ^* Reduced density difference (– _cr )/ _cr      

On the analysis of the thermal diffusivity measurement method with modulated heat input

The present paper proposes a simplified way to analyze thermal diffusivity experiments in which the phase shift is measured between the modulations of the temperatures on either face of a disk-shaped sample. The direct application of complex numbers mathematics avoids the use of the cumbersome formulae which hitherto have hampered a wider confirmation of the method and which restricted the range of the phase lag to an angle of 180°. The algorithm exposed makes it more practical to refine the analysis, which may lead to a higher accuracy and a wider use of the method. The origins of some possible errors in the calculated results are briefly reviewed.Nomenclature a Thermal diffusivity, m² · s^–1 - c Index denoting a constant part, dimensionless - c _l, c ₀ Inverse extrapolation length, m^–1 - C _p Specific heat, J · kg^–1 · K^–1 - f Modulation frequency, Hz - l Thickness of disk-shaped sample, m - Q _c Equilibrium energy per unit surface deposited on surface x=l, W · m^–2 - Q _m(t) Energy of modulation per unit surface deposited on surface x=l, W · m^–2 - Q(t) Total energy per unit surface deposited on surface x=l, W · m^–2 - q Complex energy modulation amplitude, W · m^–2 - T _l Equilibrium temperature of heated surface, K - t ₀ Equilibrium temperature of nonheated surface, K - T(x, t) Total temperature of any plane at distance x and at time t, K - T _m(x, t) Modulation temperature at any distance x and at time t, K - t Time, s - x Distance perpendicular to the specimen's surface and with the nonheated surface as the reference, m - Thermal linear expansion coefficient, dimensionless - Intermediary parameter, m^–2 - Phase difference between heated and nonheated specimen face, radian - ₀ Phase difference between energy modulation and nonheated face, radian - _l Phase difference between energy modulation and heated face, radian - Total emissivity, dimensionless - _s Spectral emissivity, dimensionless - Temperature, amplitude of modulated part argument, K - Thermal conductivity, W · m^–1 · K^–1 - Density, kg · m^–3 - Stefan-Boltzmann constant, 5.66961×10^–8W · m^–2 · K^–4 - Angular frequency=2f, s^–1     

Thermal Conductivity and Viscosity of Aqueous K<Subscript><Emphasis Type="Bold">2</Emphasis></Subscript>SO<Subscript><Emphasis Type="Bold">4</Emphasis></Subscript> Solutions at Temperatures from 298 to 575 K and at Pressures up to 30 MPa

The thermal conductivity of three (0.239, 0.499, and 0.782 mol·kg⁻¹) and the viscosity of four (0.0658, 0.2055, 0.3050, and 0.4070 mol·kg⁻¹) binary aqueous K₂SO₄ solutions have been measured with coaxial-cylinder (steady-state) and capillary-flow techniques, respectively. Measurements were made at pressures up to 30 MPa, and the range of temperature was 298–575 K. The total uncertainties of the thermal conductivity, viscosity, pressure, temperature, and composition measurements were estimated to be less than 2%, 1.6%, 0.05%, 30 mK, and 0.02%, respectively. The measured values of the thermal conductivity and viscosity of K₂SO₄ (aq) were compared with data and correlations reported in the literature. The reliability and accuracy of the experimental method was confirmed with measurements on pure water with well known (IAPWS standards) thermal conductivity and viscosity values (deviations, AAD, within 0.31 % and 0.52 %, respectively). The values of the viscosity A-, B-, and D-coefficients of the extended Jones–Dole equation for the relative viscosity (η/η₀) of aqueous K₂SO₄ solutions as a function of temperature were studied. The maximum of the B-coefficient near 340 K has been found. The derived values of the viscosity A- and B-coefficients were compared with results predicted by the Falkenhagen–Dole theory of electrolyte solutions and calculated with the ionic B-coefficient data. The behavior of the concentration dependence of the relative viscosity of aqueous K₂SO₄ solutions is discussed in terms of the modern theory of transport phenomena in electrolyte solutions.     

Thermal conductivity of mica at low temperatures

The thermal conductivity of muscovite and phlogopite has been measured over a temperature range of 3 to 320 K, in directions parallel and perpendicular to the cleavage planes. Both materials showed anisotropic behaviour. The room temperature values for muscovite and phlogopite, respectively, were 4.05 and 3.7 W m^–1 K^–1 for conductivity parallel to the planes, and 0.46 and 0.44 W m^–1 K^–1 perpendicular to the planes. Plots of the variation of thermal conductivity with temperature for both directions in the two materials show a gradual rise in conductivity as the temperature is lowered below room temperature. All four curves reach a peak at about the same temperature of 15 K. The peak values obtained were 12.4 and 7.25 W m^–1 K^–1 parallel to the planes, and 4.7 and 2.05 W m^–1 K^–1 perpendicular to the planes.On leave from Australian Broadcasting Commission.     

Sintering and characterization of fully dense aluminium nitride ceramics

Aluminium nitride ceramics with no sintering additives could be densified to close to theoretical density (99.6% theoretical) by pressureless sintering of tape-cast green sheets at 1900 °C for 8 h. The thermal conductivity and bending strength of the specimens were 114 Wm^–1 K^–1 and 240 MPa, respectively. The effect of Y₂O₃ additive on sinterability, thermal conductivity and microstructure of aluminium nitride ceramics was investigated. Thermal conductivity increased with increasing amount of Y₂O₃ additive, sintering temperature and holding time at the sintering temperature. Samples with a thermal conductivity up to 258 Wm^–1 K^–1 were fabricated by elimination of the grain-boundary phase.     

Kapitza resistance and thermal conductivity of Kapton in superfluid helium

We have determined simultaneously the Kapitza resistance, R_K, and the thermal conductivity, κ, of Kapton HN sheets at superfluid helium temperature in the range of 1.4–2.0 K. Five sheets of Kapton with varying thickness from 14 to 130 μm, have been tested. Steady-state measurement of the temperature difference across each sheet as a function of heat flux is achieved. For small temperature difference (10–30 mK) and heat flux density smaller than 30 W m⁻², the total thermal resistance of the sheet is determined as a function of sheet thickness and bath temperature. Our method determines with good accuracy the Kapitza resistance, R_K=(10540±444)T⁻³×10⁻⁶ K m² W⁻¹, and the thermal conductivity, κ=[(2.28±0.54)+(2.40±0.32)×T]×10⁻³ W m⁻¹ K⁻¹. Result obtained for the thermal conductivity is in good agreement with data found in literature and the Kapitza resistance’s evolution with temperature follows the theoretical cubic law.