Thermal Expansion of a Simulated Fuel with Fission Products Forming Solid Solutions

Thermal expansions of UO₂ and a simulated fuel with fission products forming a solid solution were studied using a dilatometer in the temperature range from 298 to 1800 K. The densities of the UO₂ and the simulated fuel used in the measurements were 10.43 g · cm⁻³ (95.2% of theoretical density (TD)) and 10.35 g · cm⁻³ (95.6% of TD), respectively. The linear thermal expansion of the simulated fuel is higher than that of UO₂, and the difference between this fuel and UO₂ increases monotonically with temperature. The average linear thermal expansion coefficients of UO₂ and the simulated fuel are 1.09× 10⁻⁵ and 1.23×10⁻⁵ K⁻¹, respectively. As the temperature increases to 1800 K, the relative densities of UO₂ and the simulated fuel decrease to 95.1 and 94.7% of their initial densities at 298 K.Paper presented at the Seventh Asian Thermophysical Properties Conference, August 23–28, 2004, Hefei and Huangshan, Anhui, P. R. China.     

Thermal Expansion of Simulated Fuels with Dissolved Fission Products in a UO2 Matrix

As a part of the DUPIC (direct use of spent PWR fuel in CANDU reactors) fuel development program, the thermal expansion of simulated spent fuel pellets with dissolved fission products has been studied by using a thermo-mechanical analyzer (TMA) in the temperature range from 298 K to 1773 K to investigate the effects of fission products forming solid solutions in a UO₂ matrix on the thermal expansions. Simulated fuels with an equivalent burn-up of (30 to 120) GWd/tU were used in this study. The linear thermal expansions of the simulated fuel pellets were higher than that of UO₂, and the difference between these fuel pellets and UO₂ increased monotonically with temperature. For the temperature range from 298 K to 1773 K, the values of the average linear thermal expansion coefficients for UO₂ and simulated fuels with an equivalent burn-up of (30, 60, and 120) GWd/tU are 1.19 × 10⁻⁵ K⁻¹, 1.22 × 10⁻⁵ K⁻¹, 1.26 × 10⁻⁵ K⁻¹, and 1.32 × 10⁻⁵ K⁻¹, respectively.     

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.     

Thermal Conductivity of Simulated Fuels with Dissolved Fission Products

The thermal diffusivity of simulated fuels with dissolved fission products was measured by using the laser-flash method in the temperature range from room temperature to 1,473 K. Three kinds of simulated fuels with an equivalent burn-up of 3, 6, and 12 at% were used in the measurement. The thermal diffusivity and the thermal conductivity of the simulated fuels with the dissolved fission products decreased, as the temperature and the equivalent burn-up increased. The thermal conductivities of simulated fuels with equivalent burn-ups of 3, 6, and 12 at% were lower than that of UO₂ by 84.70, 67.17, and 44.97% at 300 K and 99.17, 89.88, and 80.56% of UO₂ at 1,473 K, respectively. The difference in the thermal conductivity between the simulated fuel and UO₂ was large at room temperature, and it decreased as the temperature increased. The thermal resistivity of the simulated fuels increased linearly with temperature up to 1,473 K.     

Effect of sintering temperature on structural and electrical properties of gadolinium doped ceria (Ce<Subscript>0·9</Subscript>Gd<Subscript>0·1</Subscript>O<Subscript>1·95</Subscript>)

Gadolinium doped ceria oxide is one of the promising materials as an electrolyte for IT-SOFCs. Ce_0·9Gd_0·1O_1·95 (GDC10) powder was prepared by solid state reaction and sintered at 1473 K, 1573 K, 1673 K and 1773 K. All samples were studied using X-ray diffraction, scanning electron micrograph and d.c. conductivity measurement. The crystallinity and surface morphology of the samples improved with sintering temperature. Further, the electrical conductivity measurement indicated that the conduction mechanism is mainly ionic. The conductivity of samples sintered at 1673 K and 1773 K at 800°C are of the order of 0·1 S-cm⁻¹. The activation energies decreased from 1·25–0·82 eV with increase in sintering temperature.     

Experimental Reconstruction of Thermal Parameters in CNT Array Multilayer Structure

The thermal conductivities, thermal diffusivity, thermal anisotropy ratio, and thermal boundary resistance for the multilayered microstructure of a carbon nanotube (CNT) array are reconstructed experimentally using the 3ω method with two different width metal heaters. The thermal impedance in the frequency domain and sensitivity coefficients are introduced to simultaneously determine the multiple thermal parameters. The thermal conductivity at 295 K is 38 W · m⁻¹ · K⁻¹ along the nanotube growth direction, and two orders of magnitude lower in the direction perpendicular to the tubes with the anisotropy ratio as large as 86. Separation of the contact and CNT array resistances is realized through circuit modeling. The measured thermal boundary resistances of the CNT array/Si substrate and insulating diamond film interfaces are 3.1 m² · K · MW⁻¹ and 18.4 m² · K · MW⁻¹, respectively. The measured thermal boundary resistance between the heater and diamond film is 0.085 m² · K · MW⁻¹ using a reference sample without a CNT array. The thermal conductivity for a CNT array already exceeds those of phase-changing thermal interface materials used in microelectronics.     

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 Diffusivity and Heat of Formation of Harzburgite and Its Major Constituent Minerals

The thermal diffusivity, D, and its temperature dependence of Oman harzburgite rock and its major mineral olivine have been evaluated from the basic properties such as seismic velocities, density, and Debye temperature. The Arrhenius-type temperature dependence of the diffusivity was utilized to evaluate the heat of formation, ΔH _D. The diffusivity values, 1.80mm² · s⁻¹ and 2.1mm² · s⁻¹ obtained at room temperature for harzburgite and olivine, respectively, are consistent with available data. The diffusivity values for Oman harzburgite are overestimated by an amount of 0.27mm² · s⁻¹ relative to those of PNG harzburgite. The ΔH _D value (−2.40 kJ · mol⁻¹) for harzburgite rock of the Oman ophiolite suite is comparable with that (−2.90 kJ · mol⁻¹) of the harzburgite rock of Papua New Guinea. The disagreements in the thermal diffusivity and heat of formation values may be partly due to ignoring the effect of pyroxene in Oman harzburgite.     

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.     

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 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.     

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.     

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.     

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.     

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).     

Electrical transport in magnesium aluminate

The conductivity of MgAl₂O₄ has been measured at 1273, 1473 and 1673 K as a function of the partial pressure of oxygen ranging from 10⁵ to 10⁻¹⁴ Pa. The MgAl₂O₄ pellet, sandwiched between two platinum electrodes, was equilibrated with a flowing stream of either Ar + O₂, CO + CO₂ or Ar + H₂ + H₂O mixture of known composition. The gas mixture established a known oxygen partial pressure. All measurements were made at a frequency of 1 kHz. These measurements indicate pressure independent ionic conductivity in the range 1 to 10⁻¹⁴ Pa at 1273 K, 10⁻¹ to 10⁻¹² Pa at 1473 K and 10⁻¹ to 10⁻⁴ Pa at 1673 K. The activation energy for ionic conduction is 1·48 eV, close to that for self-diffusion of Mg²⁺ ion in MgAl₂O₄ calculated from the theoretical relation of Glyde. Using the model, the energy for cation vacancy formation and activation energy for migration are estimated.     

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.     

Thermal Expansion of Simulated Spent PWR Fuel and Simulated DUPIC Fuel

Thermal expansions of simulated spent PWR fuel and simulated DUPIC fuel were studied using a dilatometer in the temperature range from 298 to 1900 K. The densities of simulated spent PWR fuel and simulated DUPIC fuel used in the measurement were 10.28 gcm^–3 (95.4% of TD) and 10.26 gcm^–3 (95.1% of TD), respectively. The linear thermal expansions of the simulated fuels are higher than that of UO₂, and the difference between these fuels and UO₂ increases progressively with temperature. However, the difference between simulated spent PWR fuel and simulated DUPIC fuel is extremely small, less than the experimental error. For the temperature range from 298 to 1900 K, simulated spent PWR fuel and simulated DUPIC fuel have the same average linear thermal expansion coefficient of 1.39×10^–5K^–1. As the temperature increases to 1900 K, the relative densities of simulated spent PWR fuel and simulated DUPIC fuel decrease to 93.8% of initial densities at 298 K.     

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.     

A vibrating tube flow densitometer for measurements with corrosive solutions at temperatures up to 723 K and pressures up to 40 MPa

A new version of a vibrating tube flow densitometer has been designed permitting measurements of density differences between two fluids in the temperature range from 298 to 723 K and at pressures up to 40 MPa. The instrument is equipped with a Pt/Rh20 vibrating tube (1.6-mm o.d.) and a Pt/Rh10 transporting tube (1.2-mm o.d.) permitting measurements with highly corrosive liquids. The period of oscillation of the tube is about 7.5 ms, with a typical stability better than 10⁻⁴% over about a 1-h period over the entire temperature interval. The calibration constantK at room temperature is about 530 kg·m⁻³·ms⁻², with a temperature coefficient of approximately −0.13kg·m⁻³·ms⁻²·K⁻¹, and is practically pressure independent. It can be determined by calibration with a reproducibility generally better than 0.1%. The instrument was tested with NaCl(aq) solutions in the temperature range from 373 to 690 K for density differences between sample and reference liquid ranging from 200 to 2 kg·m⁻³; the corresponding errors are believed to be below 0.3 and 5%, respectively. A highly automated temperature control maintains the temperature of the tube stable to within ±0.02 K.