3D Anisotropic Thermal Conductivity of Exfoliated Rhenium Disulfide

ReS₂ represents a different class of 2D materials, which is characterized by low symmetry having 1D metallic chains within the planes and extremely weak interlayer bonding. Here, the thermal conductivity of single‐crystalline ReS₂ in a distorted 1T phase is determined at room temperature for the in‐plane directions parallel and perpendicular to the Re‐chains, and the through‐plane direction using time‐domain thermoreflectance. ReS₂ is prepared in the form of flakes having thicknesses of 60–450 nm by micromechanical exfoliation, and their crystalline orientations are identified by polarized Raman spectroscopy. The in‐plane thermal conductivity is higher along the Re‐chains, (70 ± 18) W m^?1 K^?1, as compared to transverse to the chains, (50 ± 13) W m^?1 K^?1. As expected from the weak interlayer bonding, the through‐plane thermal conductivity is the lowest observed to date for 2D materials, (0.55 ± 0.07) W m^?1 K^?1, resulting in a remarkably high anisotropy of (130 ± 40) and (90 ± 30) for the two in‐plane directions. The thermal conductivity and interface thermal conductance of ReS₂ are discussed relative to the other 2D materials.     

An assessment of expressions for the apparent thermal conductivity of cellular materials

Diverse expressions for the thermal conductivity of cellular materials are reviewed. Most expressions address only the conductive contribution to heat transfer; some expressions also consider the radiative contribution. Convection is considered to be negligible for cell diameters less than 4 mm. The predicted results are compared with measured conductivities for materials ranging from fine-pore foams to coarse packaging materials. The dependencies of the predicted conductivities on the material parameters which are most open to intervention are presented graphically for the various models.Nomenclature a Absorption coefficient - C _v (Jmol^–1 K^–1) Specific heat - E Emissivity - E _L Emissivity of hypothetical thin parallel layer - E ₀ Boundary surfaces emissivity - f Fraction of solid normal to heat flow - fics Fraction of total solid in struts of cell - K(m^–1) Mean extinction coefficient - k(W m^–1 K^–1) Effective thermal conductivity of foam - k _cd(W m^–1 K^–1) Conductive contribution - k _cr(W m^–1 K^–1) Convective contribution - k _g(W m^–1 K^–1) Thermal conductivity of cell gas - k _r(W m^–1 K^–1) Radiative contribution - k _s(W m^–1 K^–1) Thermal conductivity of solid - L(m) Thickness of sample - L _g(m) Diameter of cell - L _s(m) Cell-wall thickness - n Number of cell layers - r Reflection coefficient - t Transmission coefficient - T(K) Absolute temperature - T _m(K) Mean temperature - T _N Fraction of energy passing through cell wall - T ₁(K) Temperature of hot plate - T ₂(K) Temperature of cold plate - V _g Volume fraction of gas - V _w Volume fraction of total solid in the windows - w Refractive index - (m) Effective molecular diameter - (Pa s) Gas viscosity - Structural angle with respect to rise direction - (W m^–2 K^–4) Stefan constant     

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.     

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.     

The thermal conductivity of α uranium between 5 and 100 K

The thermal and electrical conductivities of uranium have been measured over the temperature range 5–100 K. Both in the as-received condition and after annealing, the thermal conductivity results show a maximum at low temperatures followed by a shallow minimum with increasing temperature. Typical values for the annealed specimen were 65 W m^–1 K^–1 at 15 K and 35 W m^–1 K^–1 at 100 K. The temperature dependence can be explained by an electronic conductivity increasing with temperature, and a significant lattice contribution which is almost constant over the temperature range 40–100 K. A small secondary peak centered at 55 K is observed associated with the -₀ phase transition.     

Thermal properties of MoSi2 and SiC whisker-reinforced MoSi2

The heat capacity, thermal conductivity and coefficient of thermal expansion of MoSi₂ and 18 vol % SiC whisker-reinforced MoSi₂ were investigated as a function of temperature. The materials were prepared by hot isostatic pressing between 1650 and 1700 °C, the hold time at temperature being 4 h. The heat capacity of MoSi₂ showed an increase from about 0.44 Wsg^–11K^–1 at room temperature to 0.53 at 700 °C. Whisker reinforcement increased heat capacity by about 10%. Thermal conductivity exhibited a decreasing trend from 0.63 Wcm^–1 K^–1 at room temperature to 0.28 Wem^–1 K^–1 at 1400°C. Whiskers reduced conductivity by about 10%. The thermal expansion coefficient increased from 7.42 °C^–1 between room temperature and 200 °C to 9.13 °C^–1 between room temperature and 1200 °C. There was a 10% decrease resulting from the whiskers. The measured data are compared with literature values. The trends in the data and their potential implications for high-temperature aerospace applications of MoSi₂ are discussed.     

Thermal Conductivity of Magnesium Oxide From Absolute,Steady-State Measurements

The thermal conductivity of polycrystalline magnesium oxide has been measured over the temperature range from 400 K to 1300 K using a modified guarded-hot-plate design. Three different thicknesses of specimens having 93 % of theoretical density were tested to verify the operation, accuracy, and reproducibility of our apparatus. The measured thermal conductivity ranges from 30 W · m⁻¹ · K⁻¹ down to 8 W · m⁻¹ · K⁻¹ and has an inverse-temperature functionality. The results agree well with literature values for this material.     

Thermal conductivity of calcium-doped aluminium nitride ceramics

Aluminium nitride ceramics were prepared with the addition of up to 12wt% of calcium oxide as a sintering aid. Both the oxygen and the calcium content of the samples decreased during sintering with increasing sintering temperature and soaking time. Higher amounts of calcium oxide resulted in higher thermal conductivities, with values up to 142 W m^–1 K^–1. Moderate sintering temperatures, short temperature soaking times and the use of inexpensive Ca-based sintering additives should enable the production of aluminium nitride ceramics with sufficiently high thermal conductivity at relatively low cost.     

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.     

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.     

Estimation of the unknown parameters in the melt-spinning process

The free-surface temperature history of the melt spinning of copper measured by Tenwick and Davies [3] is compared with those calculated using a thermokinetic model assuming different parameters. The heat-transfer coefficient, nucleation temperature and the crystal-growth kinetics were thus estimated for the melt spinning of copper at a wheel speed of 35 ms^–1 as follows: heat-transfer coefficient during liquid cooling stage HL=1.0 × 10⁷ W m^–2K^–1, heat-transfer coefficient after solidification finished HS=1.0 × 10⁵ W m^–2K^–1, heat-transfer coefficient during solidificationH= 1.0 x 10⁷- 1.2 x 10¹¹ (t-t _n) (W m^–2K^–1), the nucleation temperatureT _n 1233 K and the crystal-growth kinetic lawV=4.0 × 10^–3 T^1.1 (ms^–1).     

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 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.     

Anisotropic behaviors in polycrystalline Cd-doped GaSe thin films

GaSe thin films were deposited by thermal evaporation technique with Cd doping. X-ray diffraction analysis showed that Cd-doped films have polycrystalline structure with the preferred orientation along (008) direction. Temperature dependent electrical conductivity measurements were carried out in the temperature range of 100–400 K along perpendicular and parallel directions to the growth direction for the films exhibiting p-type conduction determined by hot probe technique. The room temperature conductivity values of the films were found to be as 1.5 × 10⁻⁸ and 4.9 × 10⁻¹² (Ω cm)⁻¹ due to the measurements along both perpendicular and parallel directions, respectively. The difference in the conductivity values is the indication of electrical anisotropy in the samples. Carrier conduction in the films was provided by the thermionic emission in the high temperature region (310–400 K) with almost the same activation energies in both directions. Space charge limited current analysis at different temperatures reveals the existence of two discrete sets of trap levels for both perpendicular and parallel directions. Calculated trap levels and trap concentrations are 99 meV, 3.5 × 10¹² cm⁻³ and 418 meV, 2.2 × 10⁵ cm⁻³ for perpendicular direction, 58 meV, 2.1 × 10¹⁸ cm⁻³ and 486 meV, 1.4 × 10¹² cm⁻³ for parallel direction. The differences in the values of the trap levels and concentrations for both directions confirm the existence of electrical anisotropy in Cd-doped GaSe thin films, because of the structural anisotropy between and inside the crystallites.     

Characteristics of a continuous Si-Ti-C-O fibre with low oxygen content using an organometallic polymer precursor

A continuous Si-Ti-C-O fibre with 12 wt% oxygen content, which is lower than the usual 18 wt% found in the normal fibres, was synthesized by using polytitanocarbosilane which has fewer Si-Si bonds than the usual precursor polymer. The density, tensile strength, tensile modulus and thermal conductivity were found to be 2.37 g cm^–3, 3.4±0.3 GPa, 190±10 GPa and 1.40 W m^–1 K^–1, respectively. Amongst these properties, the tensile modulus was improved by 20 GPa and the thermal conductivity had a higher value in comparison with that of the ordinary Si-Ti-C-O fibre with 18 wt% oxygen content. The Si-Ti-C-O fibre with a 12 wt% oxygen content has a better heat resistance above 1400 °C in an argon atmosphere and 1300 °C in air, than the usual fibre. About 60 and 40% of its tensile strength at room temperature were retained in air at respectively, 1500 and 1600 °C. This improved ceramic fibre is considered to be useful as a reinforcing material for advanced composites such as high-temperature ceramic matrix composites and metal matrix composites.     

Deviation from Wiedemann–Franz Law for the Thermal Conductivity of Liquid Tin and Lead at Elevated Temperature

The thermal conductivities of tin and lead in solid and liquid states have been determined using a nonstationary hot wire method. Measurements on tin and lead were carried out over temperature ranges of 293 to 1473 K and 293 to 1373 K, respectively. The thermal conductivity of solid tin is 63.9±1.3 Wm^–1K^–1 at 293 K and decreases with an increase in temperature, with a value of 56.6±0.9 Wm^–1K^–1 at 473 K. For solid lead, the thermal conductivity is 36.1±0.6 Wm^–1K^–1 at 293 K, decreases with an increase in temperature, and has a value of 29.1±1.1 Wm^–1K^–1 at 573 K. The temperature dependences for solid tin and lead are in good agreement with those estimated from the Wiedemann–Franz law using electrical conductivity values. The thermal conductivities of liquid tin displayed a value of 25.7±1.0 Wm^–1K^–1 at 573 K, and then increased, showing a maximum value of about 30.1 Wm^–1K^–1 at 673 K. Subsequently, the thermal conductivities gradually decreased with increasing temperature and the thermal conductivity was 10.1±1.0 Wm^–1K^–1 at 1473 K. In the case of liquid lead, the same tendency, as was the case of tin, was observed. The thermal conductivities of liquid lead displayed a value of 15.4±1.2 Wm^–1K^–1 at 673 K, with a maximum value of about 15.6 Wm^–1K^–1 at 773 K and a minimum value of about 11.4±0.6 Wm^–1K^–1 at 1373 K. The temperature dependence of thermal conductivity values in both liquids is discussed from the viewpoint of the Wiedemann–Franz law. The thermal conductivities for Group 14 elements at each temperature were compared.     

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.     

Fabrication of cellular structure composite material from recycled soda-lime glass and phlogopite mica powders

A homogeneous composite material with different physical structures has been fabricated from recycled colourless soda-lime glass powders and phlogopite-type mica powders by mixing the two powder components and sintering the mixture at a temperature above 850° C for a period of 30 min or longer. The physical structure of the composite material can be fabricated into either a cellular structure consisting of both closed and open cells or a highly densified ceramic body. The cellular structure composite material is found to have a compressive strength of about 0.877 MN m^–2 and thermal conductivity values in the range of 0.290 to 0.306 W m^–1 °C^–1 when measured at temperatures in the range of 25 to 100° C. The highly densified composite material, on the other hand, is found to have a compressive strength of about 53.0 MN m^–2 and thermal conductivity values in the range of 0.198 to 0.250 W m^–1 °C^–1. The composite material, when compared with other common building materials, is found to be potential material for construction applications because of its superior mechanical and thermal properties.     

Thermoelastic stress analysis with standard thermographic equipment by means of statistical noise rejection

A statistical method of signal processing allows for the quantification of small periodic temperature changes, using a standard IR camera and short image sequences without the necessity of any synchronization device. The attenuation of the signal in a high emissivity coating such as a black paint has been quantified by means of a 1D thermal model. This same model is used to analyze the heat conduction effects on thermoelastic stress measurements. By analogy with the resolution power of optical systems, a thermal spatial resolution power is calculated. The spatial resolution appears to be limited by the heat conduction at low frequencies and by the performance of the radiometer at high frequencies.

Nomenclature

Roman letters a Thermal diffusivity (m².s^–1) - c_p Specific heat at constant pressure (J.kg^–1.K^–1) - f Frequency (Hz) - h Surface exchange coefficient (W.m^–2.K^–1) - k Thermal conductivity (W.m^–1.K^–1) - q Heat source (W.m^–3) - t Time (s) - T Instantaneous temperature (K) - T₀ Initial specimen temperature (K) Greek letters Coefficient of thermal expansion (K^–1) - = 2f - Phase difference (rd) - Density (kg.m^–3) - _kl Components of Cauchy's stress tensor (MPa)     

The structural degradation and lamellar to rod transition in the Bi-Cd eutectic during unidirectional growth

The Bi-Cd eutectic system is a prototype quasi-regular eutectic in which the bismuth-rich phase has a volume fraction of 57%. It shows a high degree of regularity but, clearly, is not a normal (regular) eutectic. Microstructural observations of unidirectionally-grown specimens show that the minor cadmium-rich phase degrades at small temperature gradients and small growth rates. However, the structural refinement resulting from rapid freezing or chemical addition is found to be analogous to that of the F/NF eutectics. A lamellar rod transition has been achieved at intermediate growth rates by adding 2.0 wt % Sn as a modifier to the eutectic alloy. However, this was accompanied by the bismuth phase showing cellular facets of the solid-liquid interface.Nomenclature G _L temperature gradient in the melt ahead of the solid/liquid interface (° C cm^–1) - G _S temperature gradient in the solid behind the solid-liquid interface (° C cm^–1) - R growth rate of solid (cm sec^–1) - S cooling rate (° C sec^–1, ° C h^–1) - K _S thermal conductivity in the solid (W m^–1 K^–1) - K _L thermal conductivity in the melt (W m^–1 K^–1) - L latent heat of fusion (J mol^–1) - T temperature difference, undercooling (° C) - K ₁ constant in Equation 2 - K ₂ constant in Equation 3 - D diffusion coefficient of solute in solid (m² sec^–1) - C solubility in solid (wt %, at %) - M molecular weight (g mol^–1) - density (g cm^–3) - interfacial energy, surface tension (J mm^–2) - R gas constant, 8.314J mol^–1 K^–1 - r radius of curvature (m) - T temperature (K) - t time (sec) - F faceted - NF non-faceted