Thermal Conductivity and Interfacial Thermal Resistance: Measurements of Thermally Oxidized SiO2 Films on a Silicon Wafer Using a Thermo-Reflectance Technique

This article describes the development of a method to measure the normal-to-plane thermal conductivity of a very thin electrically insulating film on a substrate. In this method, a metal film, which is deposited on the thin insulating films, is Joule heated periodically, and the ac-temperature response at the center of the metal film surface is measured by a thermo-reflectance technique. The one-dimensional thermal conduction equation of the metal/film/substrate system was solved analytically, and a simple approximate equation was derived. The thermal conductivities of the thermally oxidized SiO₂ films obtained in this study agreed with those of VAMAS TWA23 within ± 4%. In this study, an attempt was made to estimate the interfacial thermal resistance between the thermally oxidized SiO₂ film and the silicon wafer. The difference between the apparent thermal resistances of the thermally oxidized SiO₂ film with the gold film deposited by two different methods was examined. It was concluded that rf-sputtering produces a significant thermal resistance ((20 ± 4.5) × 10⁻⁹ m²·K·W⁻¹) between the gold film and the thermally oxidized SiO₂ film, but evaporation provides no significant interfacial thermal resistance (less than ± 4.5 × 10⁻⁹ m²·K·W⁻¹). The apparent interfacial thermal resistances between the thermally oxidized SiO₂ film and the silicon wafer were found to scatter significantly (± 9 × 10⁻⁹ m²·K·W⁻¹) around a very small thermal resistance (less than ± 4.5 × 10⁻⁹ m²·K·W⁻¹).     

Thermal Conductivity of a Simulated Fuel with Dissolved Fission Products

The thermal diffusivity of a simulated fuel with fission products forming a solid solution was measured using the laser-flash method in the temperature range from room temperature to 1673 K. The density and the grain size of the simulated fuel with the solid solutions used in the measurement were 10.49 g · cm⁻³ (96.9% of theoretical density) at room temperature and 9.5 μm, respectively. The diameter and thickness of the specimens were 10 and 1 mm, respectively. The thermal diffusivity decreased from 2.108 m² · s⁻¹ at room temperature to 0.626 m² · s⁻¹ at 1673 K. The thermal conductivity was calculated by combining the thermal diffusivity with the specific heat and density. The thermal conductivity of the simulated fuel with the dissolved fission products decreased from 4.973 W · m⁻¹ · K⁻¹ at 300 K to 2.02 W · m⁻¹ · K⁻¹ at 1673 K. The thermal conductivity of the simulated fuel was lower than that of UO₂ by 34.36% at 300 K and by 15.05% at 1673 K. The difference in the thermal conductivity between the simulated fuel and UO₂ was large at room temperature, and decreased with an increase in temperature. Paper presented at the Seventeenth European Conference on Thermophysical Properties, September 5–8, 2005, Bratislava, Slovak Republic.     

Application of photoacoustic and photothermal techniques for heat conduction measurements in a free-standing chemical vapor-deposited diamond film

Heat conduction in a free-standing chemical vapor-deposited polycristalline diamond film has been investigated by means of combined front and rear photoacoustic signal detection techniques and also by means of a “mirage” photothermal beam deflection technique. The results obtained with the different techniques are consistent with a value of α=(5.5±0.4)×10⁻⁴ m² · s⁻¹ for thermal diffusivity, resulting in a value ofκ=(9.8±0.7)×10² W·m⁻¹·K⁻¹ for thermal conductivity when literature values for the density and heat capacity for natural diamond are used.     

Carbon Aerogel-Based High-Temperature Thermal Insulation

Carbon aerogels, monolithic porous carbons derived via pyrolysis of porous organic precursors synthesized via the sol–gel route, are excellent materials for high-temperature thermal insulation applications both in vacuum and inert gas atmospheres. Measurements at 1773K reveal for the aerogels investigated thermal conductivities of 0.09W · m⁻¹ · K⁻¹ in vacuum and 0.12W · m⁻¹ · K⁻¹ in 0.1MPa argon atmosphere. Analysis of the different contributions to the overall thermal transport in the carbon aerogels shows that the heat transfer via the solid phase dominates the thermal conductivity even at high temperatures. This is due to the fact that the radiative heat transfer is strongly suppressed as a consequence of a high infrared extinction coefficient and the gaseous contribution is reduced since the average pore diameter of about 600nm is limiting the mean free path of the gas molecules in the pores at high temperatures. Based on the thermal conductivity data detected up to 1773K as well as specific extinction coefficients determined via infrared-optical measurements, the thermal conductivity can be extrapolated to 2773K yielding a value of only 0.14W· m⁻¹ · K⁻¹ in vacuum.     

Measurement of the Thermal Conductivity of Nanodeposited Material

The small size of nanomaterials deposited by either focused ions or electron beams has prevented the determination of reliable thermal property data by existing methods. A new method is described that uses a suspended platinum hot film to measure the thermal conductivity of a nanoscale deposition. The cross section of the Pt film needs to be as small as 50 nm × 500 nm to have sufficient sensitivity to detect the effect of the beam-induced nanodeposition. A direct current heating method is used before and after the deposition, and the change in the average temperature increase of the Pt hot film gives the thermal conductivity of the additional deposited material. In order to estimate the error introduced by the one-dimensional analytical model employed, a two-dimensional numerical simulation was conducted. It confirmed the reliability of this method for situations where the deposit extends onto the terminals by (1 μm or more. Measurements of amorphous carbon (a-C) films fabricated by electron beam induced deposition (EBID) produced thermal conductivities of 0.61 W · m⁻¹ · K⁻¹ to 0.73 W · m⁻¹ · K⁻¹ at 100 K to 340 K, values in good agreement with those of a-C thin films reported in the past.     

Analysis of Possibilities of Application of Nanofabricated Thermal Probes to Quantitative Thermal Measurements

A steady-state thermal model of the nanofabricated thermal probe was proposed. The resistive type probe working in the active mode was considered. The model is based on finite element analysis of the temperature field in the probe-sample system. Determination of the temperature distribution in this system allows calculations of relative changes in the probe electrical resistance. It is shown that the modeled probe can be used for measurements of the local thermal conductivity with the spatial resolution determined by the probe apex dimensions. The probe exhibits the maximum sensitivity to the changes in the thermal conductivity of the sample between 2 W·m⁻¹ ·K⁻¹ and 200 W·m⁻¹ ·K⁻¹. The influence of the thermal conductivity of the probe substrate on metrological characteristics of the probe as well as the thermal resistance of the probe-sample contact on the determination of the sample thermal conductivity were also analyzed. The selected results of numerical analysis were compared with data of preliminary experiments.     

Trilobal Polyimide Fiber Insulation for Cryogenic Applications

Recent measurements have shown a record-breaking low thermal conductivity λ_total of less than 0.25 × 10⁻³ W·m⁻¹·K⁻¹ at temperatures of 120 K for an evacuated sample consisting of polyimide fibers with a trilobal fiber cross section. Existing models for the heat transport in fiber insulations cannot sufficiently describe fiber insulations consisting of fibers with non-cylindrical cross sections. In this article, a modification for the model for cylindrical fibers will be presented. The modifications for the trilobal cross section of the fiber will be explained and compared to the original cylindrical model. The results of the theoretical calculations will be discussed in comparison to experimental results of measurements performed with a guarded hot-plate apparatus at temperatures in the range from 120 K to 420 K.     

Hot-Ball Method for Measuring Thermal Conductivity

This article deals with the theory and performance of a sensor for measuring thermal conductivity. The sensor, in the form of a small ball, generates heat and simultaneously measures its temperature response. An ideal model of the hollow sphere in an infinite medium furnishes a working equation of the hot-ball method. A constant heat flux through the surface of the ball generates the temperature field. The thermal conductivity of the surrounding medium is to be determined by the stabilized value of the temperature response, i.e., when the steady-state regime is attained. Error components of the sensor are discussed due to analysis of the deviations of the real hot-ball construction from the ideal model. The functionality of a set of hot balls has been tested, and the calibration for a limited range of thermal conductivities was performed. A working range of thermal conductivities of tested materials has been estimated to be from 0.06 W· m⁻¹ · K⁻¹ up to 1 W· m⁻¹ · K⁻¹.     

Measurement of the In-plane Thermal Diffusivity and Temperature-Dependent Convection Coefficient Using a Transient Fin Model and Infrared Thermography

The transient fin model introduced recently for determination of the in-plane thermal diffusivity of planar samples with the help of infrared thermography was modified so as to be applicable to poor heat conductors. The new model now includes a temperature-dependent heat loss by convective heat transfer, suitable for an experimental setup in which the sample is aligned parallel to a weak, forced air flow stabilizing otherwise the convective heat transfer. The temperature field in the sample was measured with an infrared camera while the sample was heated at one edge. The symmetric temperature field created was averaged over the central fifth of the sample to obtain one-dimensional temperature profiles, both transient and stationary, which were fitted by a numerical solution of the fin model. One of the fitting parameters was the thermal diffusivity, and with a known density and specific heat capacity, the thermal conductivity was thus determined. The test measurements with tantalum samples gave the result (57.5 ± 0.2) W · m⁻¹ · K⁻¹ in excellent agreement with the known value. The other fitting parameter was a temperature-dependent heat loss coefficient from which the lower limit for the temperature-dependent convection coefficient was determined. For the stationary state the result was (1.0 ± 0.2) W · m⁻² · K⁻¹ at the temperature of the flowing air, and its temperature dependence was found to be (0.22 ± 0.01) W ·m⁻² · K⁻².     

Simultaneous Measurements of Thermal Properties of Individual Carbon Fibers

Combining the steady-state and quasi-steady-state T type probes, the longitudinal thermal conductivity and thermal effusivity of individual mesophase pitch-based carbon fiber heat treated at 2800 °C and 1000 °C have been measured from 100 K to 300 K. The present method allows simultaneous measurements of thermal properties using the same instrument, by simply changing the applied direct current to alternating current. The specific heat is found to decrease with increasing heat-treatment temperature and to approach the value of graphite. The highly graphitized carbon fiber has a maximum thermal conductivity of 410 W · m⁻¹ · K⁻¹ at about 250 K, and its thermal diffusivity decreases with increasing temperature. Comparatively, the thermal conductivity of the fiber heat treated at 1000 °C is much smaller, with the peak shifting to high temperature due to a large defect density, and its thermal diffusivity is nearly temperature independent.     

Thermophysical Property Measurements of Liquid Gadolinium by Containerless Methods

Thermophysical properties of liquid gadolinium were measured using non-contact diagnostic techniques with an electrostatic levitator. Over the 1585 K to 1920 K temperature range, the density can be expressed as ρ(T) = 7.41 × 10³ − 0.46 (T − T _m) (kg · m⁻³) where T _m = 1585 K, yielding a volume expansion coefficient of 6.2 × 10⁻⁵ K⁻¹. In addition, the surface tension data can be fitted as γ(T) = 8.22 × 10² − 0.097(T − T _m)(10⁻³ N · m⁻¹) over the 1613 K to 1803 K span and the viscosity as η(T) = 1.7exp[1.4 × 10⁴/(RT)](10⁻³ Pa · s) over the same temperature range.     

Thermophysical Properties of Multi-Walled Carbon Nanotube-Reinforced Polypropylene Composites

The thermal conductivity and thermal diffusivity of chemically surface-treated multi-walled carbon nanotube (MWCNT) reinforced polypropylene (PP) composites were measured using the 3ω method in the temperature range of 90–320 K and photoacoustic (PA) spectroscopy at room temperature, respectively. Nine kinds of samples were prepared by the melt-blending of PP resins with the addition of 0.1, 0.5, and 2.0 mass% of non-treated, nitric acid (HNO₃)-treated, and potassium hydroxide (KOH)-treated nanotube contents, and compression-molded at 180°C into about 0.5 mm thickness composite films using the hot-press. The measured thermal conductivities are in the range from 0.05 to 0.6 W ·m⁻¹·K⁻¹ and increase as the temperature increases and the CNT concentrations are increased. By the chemical treatment, the thermal conductivity of 0.5 and 2.0 mass% samples were enhanced by about a factor of two; however, the sample of 0.1 mass% did not change. This can be explained qualitatively by the effects of chemical treatment on the reinforcing ability for CNTs/polymer composites.Paper presented at the Seventh Asian Thermophysical Properties Conference, August 23–28, Hefei and Huangshan, Anhui, P. R. China.     

Density and Thermal Conductivity Measurements for Silicon Melt by Electromagnetic Levitation under a Static Magnetic Field

The density and thermal conductivity of a high-purity silicon melt were measured over a wide temperature range including the undercooled regime by non-contact techniques accompanied with electromagnetic levitation (EML) under a homogeneous and static magnetic field. The maximum undercooling of 320 K for silicon was controlled by the residual impurity in the specimen, not by the melt motion or by contamination of the material. The temperature dependence of the measured density showed a linear relation for temperature as: ρ(T) = 2.51 × 10³−0.271(T−T _m) kg · m⁻³ for 1367 K < T < 1767 K, where T _m is the melting point of silicon. A periodic heating method with a CO₂ laser was adopted for the thermal conductivity measurement of the silicon melt. The measured thermal conductivity of the melt agreed roughly with values estimated by a Wiedemann–Franz law.     

Thermal-Conductivity Characterization of Gas Diffusion Layer in Proton Exchange Membrane Fuel Cells and Electrolyzers Under Mechanical Loading

Accurate information on the temperature field and associated heat transfer rates is particularly important for proton exchange membrane fuel cells (PEMFC) and PEM electrolyzers. An important parameter in fuel cell and electrolyzer performance analysis is the effective thermal conductivity of the gas diffusion layer (GDL) which is a solid porous medium. Usually, this parameter is introduced in modeling and performance analysis without taking into account the dependence of the GDL thermal conductivity λ (in W · m⁻¹ · K⁻¹) on mechanical compression. Nevertheless, mechanical stresses arising in an operating system can change significantly the thermal conductivity and heat exchange. Metrology allowing the characterization of the GDL thermal conductivity as a function of the applied mechanical compression has been developed in this study using the transient hot-wire technique (THW). This method is the best for obtaining standard reference data in fluids, but it is rarely used for thermal-conductivity measurements in solids. The experiments provided with Quintech carbon cloth indicate a strong dependence (up to 300%) of the thermal conductivity λ on the applied mechanical load. The experiments have been provided in the pressure range 0 < p < 8 MPa which corresponds to stresses arising in fuel cells. All obtained experimental results have been fitted by the equation λ = 0.9log(12p + 17)(1 − 0.4e^−50p ) with 9% uncertainty. The obtained experimental dependence can be used for correct modeling of coupled thermo/electro-mechanical phenomena in fuel cells and electrolyzers. Special attention has been devoted to justification of the main hypotheses of the THW method and for estimation of the possible influence of the contact resistances. For this purpose, measurements with a different number of carbon cloth layers have been provided. The conducted experiments indicate the independence of the measured thermal conductivity on the number of GDL layers and, thus, justify the robustness of the developed method and apparatus for this type of application.     

Thermal conductivity of amorphous Teflon (AF 1600) at high pressure

The thermal conductivity, λ of amorphous Teflon AF 1600 [poly(1,3-dioxole-4,5-difluoro-2,2-bis(trifluoromethyl)-co-tetrafluoroethylene)] has been measured at pressures up to 2 GPa in the temperature range 93–392 K. At 295 K and atmospheric pressure, we obtained λ=0.116, W·m⁻¹·K⁻¹. The bulk modulus was measured up to 1.0 GPa in the temperature range 150–296 K and the combined data yielded the following values ofg=(∂ln λ ∂lnp) _r :2.8±0.2 at 296 K, 3.0±0.2 at 258 K, 3.0±0.2 at 236 K. 3.4±0.2 at 200 K. and 3.4±0.2 at 150 K.     

Influence of Spacer Systems on Heat Transfer in Evacuated Glazing

One attractive possibility to essentially improve the insulation properties of glazing is to evacuate the space between the glass panes. This eliminates heat transport due to convection between the glass panes and suppresses the thermal conductivity of the remaining low pressure filling gas atmosphere. The glass panes can be prevented from collapsing by using a matrix of spacers. These spacers, however, increase heat transfer between the glass panes. To quantify this effect, heat transfer through samples of evacuated glazing was experimentally determined. The samples were prepared with different kinds of spacer materials and spacer distances. The measurements were performed with a guarded hot-plate apparatus under steady-state conditions and at room temperature. The measuring chamber of the guarded hot plate was evacuated to < 10⁻² Pa. An external pressure load of 0.1 MPa was applied on the samples to ensure realistic system conditions. Radiative heat transfer was significantly reduced by preparing the samples with a low-ε coating on one of the glass panes. In a first step, measurements without any spacers allowed quantification of the amount of radiative heat transfer. With these data, the measurements with spacers could be corrected to separate the effect of the spacers on thermal heat transfer. The influence of the thermal conductivity of the spacer material, as well as the distance between the spacers and the spacer geometry, was experimentally investigated and showed good agreement with simulation results. For mechanically stable matrices with cylindrical spacers, experimental thermal conductance values ≤0.44W·m⁻² ·K⁻¹ were found. This shows that U _g -values of about 0.5W · m⁻² · K⁻¹ are achievable in evacuated glazing, if highly efficient low-emissivity coatings are used.     

Vacuum Insulation Panels – Exciting Thermal Properties and Most Challenging Applications

Vacuum insulation panels (VIPs) have a thermal resistance that is about a factor of 10 higher than that of equally thick conventional polystyrene boards. VIPs nowadays mostly consist of a load-bearing kernel of fumed silica. The kernel is evacuated to below 1 mbar and sealed in a high- barrier laminate, which consists of several layers of Al-coated polyethylene (PE) or polyethylene terephthalate (PET). The laminate is optimized for extremely low leakage rates for air and moisture and thus for a long service life, which is required especially for building applications. The evacuated kernel has a thermal conductivity of about 4 × 10⁻³ W · m⁻¹ · K⁻¹ at room temperature, which results mainly from solid thermal conduction along the tenuous silica backbone. A U-value of 0.2 W · m⁻² · K⁻¹ results from a thickness of 2 cm. Thus slim, yet highly insulating fa?ade constructions can be realized. As the kernel has nano-size pores, the gaseous thermal conductivity becomes noticeable only for pressures above 10 mbar. Only above 100 mbar the thermal conductivity doubles to about 8 × 10⁻³ W · m⁻¹ · K⁻¹, such a pressure could occur after several decades of usage in a middle European climate. These investigations revealed that the pressure increase is due to water vapor permeating the laminate itself, and to N₂ and O₂, which tend to penetrate the VIP via the sealed edges. An extremely important innovation is the integration of a thermo-sensor into the VIP to nondestructively measure the thermal performance in situ. A successful “self-trial” was the integration of about 100 hand-made VIPs into the new ZAE-building in Würzburg. Afterwards, several other buildings were super-insulated using VIPs within a large joint R&D project initiated and coordinated by ZAE Bayern and funded by the Bavarian Ministry of Economics in Munich. These VIPs were manufactured commercially and integrated into floorings, the gable fa?ade of an old building under protection, the roof and the facades of a terraced house as well as into an ultra-low-energy “passive house” and the slim balustrade of a hospital. The thermal reliability of these constructions was monitored using an infrared camera.Invited paper presented at the Seventh European Conference on Thermophysical Properties, September 5-8, 2005, Bratislava, Slovak Republic.     

Thermal Transport Properties of Functionally Graded Carbon Aerogels

Novel graded carbon aerogels were synthesized to study the impact of different synthesis parameters on the material properties on a single sample and to test a new, locally resolved thermal-conductivity measurement technique. Two identical cylindrical aerogels with a graded structure along the main cylindrical axis were synthesized. Along the gradient with an extension of about 20 mm the densities range from 240 kg·m⁻³ to 370 kg·m⁻³ and the effective pore diameter determined via small angle X-ray scattering and SEM increase systematically from 70 nm up to 11,000 nm. One specimen was cut perpendicular to the cylinder axis into disc-shaped samples; their thermal conductivities in an argon atmosphere, as determined via a standard laser-flash technique, range from 0.06W·m⁻¹·K⁻¹ to 0.12W·m⁻¹·K⁻¹ at 600 °C. The second specimen, cut to obtain a sample with the gradient in-plane, was investigated with a spatially resolved laser-flash technique at ambient conditions. The results of the two different techniques are compared and discussed in detail.     

Design and Validation of a High-Temperature Comparative Thermal-Conductivity Measurement System

A measurement system has been designed and built for the specific application of measuring the effective thermal conductivity of a composite, nuclear-fuel compact (small cylinder) over a temperature range of 100 °C to 800 °C. Because of the composite nature of the sample as well as the need to measure samples pre- and post-irradiation, measurement must be performed on the whole compact non-destructively. No existing measurement system is capable of obtaining its thermal conductivity in a non-destructive manner. The designed apparatus is an adaptation of the guarded-comparative-longitudinal heat flow technique. The system uniquely demonstrates the use of a radiative heat sink to provide cooling which greatly simplifies the design and setup of such high-temperature systems. The design was aimed to measure thermal-conductivity values covering the expected range of effective thermal conductivity of the composite nuclear fuel from 10 W . m⁻¹ . K⁻¹ to 70 W . m⁻¹ . K⁻¹. Several materials having thermal conductivities covering this expected range have been measured for system validation, and results are presented. A comparison of the results has been made to data from existing literature. Additionally, an uncertainty analysis is presented finding an overall uncertainty in sample thermal conductivity to be 6 %, matching well with the results of the validation samples.     

Effects of Laser Irradiation on the Thermal Conductivity and Viscosity of Aqueous Multiwalled Carbon Nanotube Suspensions

The effects of KrF excimer laser irradiation (248 nm) on aqueous suspensions of multiwalled carbon nanotubes (MWCNTs) were experimentally examined. MWCNTs and sodium dodecyl sulfate were added to deionized water at a mass fraction of 0.5 %, and the suspension was ultrasonicated for 30 min. Transmission electron microscopy (TEM) images of the nanotube samples after laser irradiation indicated fractures and network disentanglement. The laser fluence affected the thermal conductivity and viscosity of the suspensions beyond a threshold of 50 mJ · cm⁻². As the irradiation time progressed at a laser fluence of 144 mJ · cm⁻², the thermal conductivity and viscosity decreased until they reached saturation. The thermal-conductivity enhancement decreased from 16 % to 5 %, and the low shear viscosity decreased dramatically to 1/200 the shear viscosity of the non-irradiated sample. Raman spectra and TEM images showed that the defects in the nanotubes increased upon laser irradiation. In conclusion, excimer laser irradiation of a suspension of MWCNTs provided an effective way to tune the heat transfer and rheological characteristics of suspensions.