Theory of lattice thermal conductivity: Role of low-frequency phonons

The lattice thermal conductivity arises from contributions by phonons of all frequencies. The mean free path l() is limited mainly by three-phonon interactions, and l _i()^–2 T ^–1 where is the phonon frequency, and T is the absolute temperature. Since the spectral specific heat varies as ², the spectral thermal conductivity is independent of frequency, and low frequencies play a larger role than they do in the heat content. The effect of additional scattering processes due to defects must be compared to intrinsic scattering, not just at the highest frequency, but over the full spectral range. This enhances the resistance due to grain boundaries and large obstacles, and reduces the effect of point defects. Some typical examples are discussed. The role of low-frequency phonons may be even further enhanced if longitudinal low-frequency phonons have their interaction with other phonons reduced by wave vector conservation. Such modes would then contribute substantially to the overall thermal conductivity, and this contribution would be sensitive to grain size and to large-scale defects. However, the mean free path must be consistent with ultrasonic attenuation data. This enhanced sensitivity may be observable.     

Reduction of lattice thermal conductivity by point defects at intermediate temperatures

The lattice thermal conductivity is reduced by point defects because they scatter phonons. An analytic expression can be derived only in the limit of high temperatures; at lower temperatures one must have recourse to numerical calculations. Because the conductivity is due mainly to phonons of low frequencies when point-defect scattering is strong, the high-temperature approximation can be used at temperatures above half the Debye temperature. Numerical calculations, using the Ge-Si system as an example, show that the error incurred by using the high-temperature approximation is less than 10%.     

Theory of Thermal Conduction in Thin Ceramic Films

The theory of heat conduction in ceramics by phonons, and at high temperatures also by infrared radiation, is reviewed. The phonon mean free path is limited by three-phonon interactions and by scattering of various imperfections. Point defects scatter high-frequency phonons; extended imperfections, such as inclusions, pores, and grain boundaries, affect mainly low-frequency phonons. Thermal radiation is also scattered by imperfections, but of a larger size, such as splat boundaries and large pores. Porosity also reduces the effective index of refraction. For films there are also external boundaries, cracks, and splat boundaries, depending on the method of deposition. Examples discussed are cubic zirconia, titanium oxide, and uranium oxide. Graphite and graphene sheets, with two-dimensional phonon gas, are discussed briefly.     

Thermal conductivity measurements at low temperatures

We describe briefly the experimental facilities developed for the measurement of thermal conductivity of solids in the temperature range 10K–300K. Different techniques have been used for the determination of thermal conductivity, depending on the relaxation time of the system under investigation. Measurements on stainless steel 304, using steady state and non-steady state methods are presented. Values of thermal conductivity obtained by both these methods agree to each other and are consistent with those reported earlier. Paper presented at the poster session of MRSI AGM VI, Kharagpur, 1995     

Thermal conductivity of sulfur hexafluoride

This paper reports new measurements of the thermal conductivity of sulfur hexafluoride at the nominal temperature of 27.5°C as a function of density in the range up to 200 kg · m^–3. The measurements were performed in a transient, hot-wire instrument. When combined with earlier measurements of the viscosity of the gas, they allow us to calculate the rather large contribution stemming from the internal degrees of freedom. The present measurements compare well with those in the literature. All of them suggest that the excess thermal conductivity is a unique function of density in the present range of states. An empirical correlation of our measurements can serve users in the ranges 0 < t< 100°C and 0 < < 200 kg · m^–3.     

Thermal conductivity of oxygen in the critical region

The thermal conductivity of oxygen has been measured in a broad region around the critical point by means of Rayleigh light scattering. Measurements were made on two isochores and on the saturation boundary. The results are compared with current methods of predicting the anomalous thermal conductivity in the critical region.     

Thermal conductivity of zirconia‐based ceramics for thermal barrier coating

Lowering the thermal conductivity of thermal barrier coatings used to protect blade and vane airfoils represents an important challenge for gas turbine designers and manufacturers. Dense zirconia‐based materials have been prepared by solid state reaction methods to determine their thermal properties up to 1000 °C. Partially stabilised zirconias having a thermal conductivity 40 % lower than the thermal conductivity of the most widely used system (ZrO₂‐8wt.%Y₂O₃) have been obtained.     

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      

Thermal conductivity of Cu-4.5 Ti alloy

The thermal conductivity (TC) of peak aged Cu-4.5 wt% Ti alloy was measured at different temperatures and studied its variation with temperature. It was found that TC increased with increasing temperature. Phonon and electronic components of thermal conductivity were computed from the results. The alloy exhibits an electronic thermal conductivity of 46.45 W/m.K at room temperature. The phonon thermal conductivity decreased with increasing temperature from 17.6 at 0 K to 1.75 W/m.K at 298 K, which agrees with literature that the phonon component of thermal conductivity is insignificant at room temperature.     

The influence of residual gas pressure on the thermal conductivity of microsphere insulations

Experimental results of investigations of the heat exchange by residual gas in microsphere insulations are presented. The results of measurements of microsphere effective thermal conductivity versus residual gas (N₂) pressure in the pressure range of 10^–3–10⁵ Pa are also given. A sample of self-pumping microsphere insulation was prepared and its thermal parameters were tested. In comparison to the standard microsphere insulation, the self-pumping insulation yielded lower thermal conductivity results over the entire pressure range. The stability of its thermal parameters as a result of considerable gas input into the insulation volume is discussed. Measurements of temperature and pressure distributions inside the microsphere layer were performed. Plots of temperature and pressure gradients inside the layer of the microsphere insulation are presented.Nomenclature d _m Mean value of the microsphere diameter - k Apparent thermal conductivity coefficient - ¯k Average thermal conductivity coefficient - k _c Component of the heat transfer by conduction - k _g Modified gas thermal conductivity under atmospheric pressure - k _r Component of the heat transfer by radiation - k _s Thermal conductivity of the sphere material - k _gc Component of the heat conduction by gas - k _go Gas thermal conductivity under atmospheric pressure - k _gr Sphere effective conductivity - k _ss Component of the heat conduction by the solid state - K 1–(k _g/k _gr) - Kn Knudsen number - ¯L Mean free path of gas molecules - m 1–_s; porosity - m Empty volume of a single sphere - p Residual gas pressure - ¯p Average pressure - p _g Pressure measured by gauge - p ₀ Residual gas pressure above the insulation bed - r Radial coordinate - T Temperature - T _c Temperature of the cold calorimeter wall - T _g Temperature of the pressure gauge - T _H Temperature of the hot calorimeter wall - T _i Gas temperature inside the bed - T _y Constant dependent on the sort of gas - v Volume - Accommodation coefficient - Density - _a Local distance between surfaces - _s Solid fraction - Constant dependent on the sort of gas - Time measured from the initiation of insulation cooling     

Thermal conductivity and heat capacity of solid nabr under pressure

Using the transient hot-wire method, measurements were made for solid NaBr of both the thermal conductivity and the heat capacity per unit volume. The measurements were performed in the temperature range 100 to 400 K and at pressures up to 2 GPa. An adiabatic compression technique allowed the determination of the thermal expansivity as a function of pressure at room temperature. The heat capacity did not vary with pressure. Analysis of the thermal conductivity data showed that it can be described adequately by the Leibfried-Schlömann formula. For temperatures up to 400 K only acoustic modes needed to be taken into account. A small contribution of optic modes to the heat transport might be apparent at the highest temperatures.     

Thermal conductivity of inhomogeneous materials

The effective thermal conductivity is calculated from the rate of entropy production per unit volume. Thermal conductivity and the temperature field are expressed in terms of Fourier components and these are related. The rate of entropy production is then obtained in terms of the volume-averaged thermal conductivity and the Fourier components of thermal conductivity. A simple expression for the effective thermal conductivity is found. In the case of striations it leads to well-known results. The formalism is applied to solids with inhomogeneously distributed solutes. It is shown that the thermal conductivity is less than the volume-averaged thermal conductivity and that homogenization by diffusion increases the thermal conductivity. Similar results would apply to the electrical conductivity of inhomogeneous alloys.     

开孔金属泡沫有效热导率的理论分析与实验研究

采用能量守恒定律和光学厚近似法,建立了开孔金属泡沫有效热导率的计算模型,分析了温度和压力等因素对传热的影响,并应用高温真空石墨加热炉对开孔金属泡沫的有效热导率进行了实验测量.理论值与测量值基本吻合,各个测量点的平均相对误差<5%,最大相对误差低于10%.结果表明,开孔泡沫金属的有效热导率随温度和压力的增加而增大,在低温情况下(T<100℃),开孔泡沫金属内部的传热机制主要为固体导热;在高温情况下(T>400℃),辐射成为开孔泡沫金属的主导传热机制;在低压下,气体导热可以忽略不计,但随着压力的增大,气体导热加大对传热的影响.     

Investigations into the thermal performance of multilayer insulation (300-77 K) Part 2: Thermal analysis

Simple analytical methods have been employed for heat transfer analysis of experimental data obtained through calorimetric investigations on multilayer insulation (MLI). Sectional heat transfer analysis has shown that the effective thermal conductivity of the MLI varies from section to section of the insulation structure and it has a peak which lies between the middle and warm boundary regions of the MLI. This could be attributed to a peak in residual gas conduction in this region. The theoretical estimation of heat flux through MLI, using a simple analytical model, is also discussed in this paper. This model takes into consideration the non-linear temperature profile of the insulation. The computed heat flux using this model gives a lower (2 to 4 times) value in comparison with the heat flux estimated from calorimetric measurements. A refined model has been suggested which includes the residual gas conduction also in MLI.     

DC conductivity of amorphous-nanocrystalline silicon thin films

The direct current (DC) conductivity of amorphous-nanocrystalline Si films deposited by the plasma enhanced chemical vapour deposition method was studied as a function of the structural properties obtained by Raman spectroscopy and grazing incidence small angle X-ray scattering (GISAXS).The crystalline fraction estimated from the Raman spectra altered between 0 and 60% while the average size of the crystals varied from 2 to 7 nm, however, the size distribution was wide i.e. smaller and larger crystals were also present.GISAXS showed a signal that corresponds to “particles” with values for the gyration radius close to the average crystal sizes, between 2 and 6 nm. Samples with higher crystalline fraction had elongated “particles” that are larger when situated closer to the sample surface, which indicates a columnar structure.The DC conductivity had a nearly constant, low value up to some 30% of crystal fraction. A further increase of the crystal fraction resulted in an abrupt increase of the conductivity in a narrow interval of crystal fraction. Above this interval, conductivity was much higher and remained constant in that range. This result is in perfect agreement with the percolation threshold obtained by model calculation for a six-fold coordinated cubic lattice that appears at 32% of crystal fraction. A certain scattering of the experimental data around the predicted values was discussed as a possible consequence of the variation of the individual crystal size and shape by change of the crystal fraction and/or non-uniformity of depth distribution.     

Prediction of the thermal conductivity of polar pure liquids

Abstract

A relatively simple technique for the prediction of the thermal conductivity of polar organic fluids over the temperature range from 0° to 100°C is presented. The proposed model is basically derived via the generalized property correlation model developed by Riazi and Daubert in 1980. The method requires, as input, only normal boiling point, specific gravities and dipole moments or acentric factors for each compound of interest. Predicted thermal conductivities are compared with 93 literature data for 12 polar liquids. Average deviation between prediction and experiment is approximately within 8–12%, depending on the type of third input parameter, as opposed to 17% for the much involved method of Robins and Kingrea previously recommended.     

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.     

Thermal Conductivity of Nanofluids – Experimental and Theoretical

The thermal conductivity of nanofluids has been studied experimentally using the transient hot-wire method, and it is shown that a significant increase can be obtained. Existing methods for the prediction and correlation of the thermal conductivity are discussed. It is shown that a lot of work still needs to be done in this area.Paper presented at the Seventeenth European Conference on Thermophysical Properties, September 5–8, 2005, Bratislava, Slovak Republic.     

Thermal conductivity and heat capacity of synthetic fuel components

As part of a group contribution study on the liquid thermal conductivity of synthetic fuel components, experiments were performed to study the effects of dimethyl and ethyl-group additions to cyclohexane. A transient hot-wire apparatus was used to measure the thermal conductivity of these three fluids between ambient pressure and 10.4 MPa over a temperature range of 300 to 460 K. Thermal conductivities measured with this instrument have been assigned an accuracy of ±2% based upon a standard deviation comparison with a toluene standard established by Nieto de Castro et al. (1986). The thermal conductivities and excess thermal conductivities of the naphthenes investigated have been successfully linearized by plotting the data versus reduced density exponentiated to the power of five. By using data previously reported by Perkins (1983) and Li et al. (1984), this linear reduced density method is demonstrated for methyl, dimethyl, and ethyl additions to cyclohexane, as well as methyl and dimethyl additions to benzene. The naphthenes have been shown to have similar intercepts, with slope changes dependent upon the functional group attached to cyclohexane. The aromatics have a less pronounced slope change with additional functional groups attached to the benzene base. This instrument was also used to determine heat capacities, via the thermal diffusivity, to within ±10%.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.