Thermal properties of carbon nanotubes and nanotube-based materials

The thermal properties of carbon nanotubes are directly related to their unique structure and small size. Because of these properties, nanotubes may prove to be an ideal material for the study of low-dimensional phonon physics, and for thermal management, both on the macro- and the micro-scale. We have begun to explore the thermal properties of nanotubes by measuring the specific heat and thermal conductivity of bulk SWNT samples. In addition, we have synthesized nanotube-based composite materials and measured their thermal conductivity. The measured specific heat of single-walled nanotubes differs from that of both 2D graphene and 3D graphite, especially at low temperatures, where 1D quantization of the phonon bandstructure is observed. The measured specific heat shows only weak effects of intertube coupling in nanotube bundling, suggesting that this coupling is weaker than expected. The thermal conductivity of nanotubes is large, even in bulk samples: aligned bundles of SWNTs show a thermal conductivity of >200 W/m K at room temperature. A linear K(T) up to approximately 40 K may be due to 1D quantization; measurement of K(T) of samples with different average nanotube diameters supports this interpretation. Nanotube–epoxy blends show significantly enhanced thermal conductivity, showing that nanotube-based composites may be useful not only for their potentially high strength, but also for their potentially high thermal conductivity. Received: 17 October 2001 / Accepted: 3 December 2001 / Published online: 4 March 2002     

Thermal conductivity and specific heat of thin-film amorphous silicon

We report the thermal conductivity and specific heat of amorphous silicon thin films measured from 5-300 K using silicon-nitride membrane-based microcalorimeters. Above 50 K the thermal conductivity of thin-film amorphous silicon agrees with values previously reported by other authors. However, our data show no plateau, with a low T suppression of the thermal conductivity that suggests that the scattering of long wavelength, low Q vibrations goes as Q2. The specific heat shows Debye-like behavior below 15 K, with theta(D) = 487 +/- 5 K, and is consistent with a very small contribution of tunneling states in amorphous silicon. Above 15 K, the specific heat deviates less from Debye behavior than does its crystalline allotrope, indicating no significant excess modes (boson peak) in amorphous silicon.     

Random-network model,density fluctuation,and thermal conductivity of glasses

A phonon scattering mechanism based on the structure of amorphous solids is proposed. Employing two adjustable parameters this mechanism accounts for the thermal conductivity of vitreous SiO₂ and GeO₂ at temperatures below 100°K.     

Some properties of the phonon spectra of transition metal disilicides VSi2, NbSi2, and TaSi2

The phonon spectra of metallic disilicides VSi₂, NbSi₂, and TaSi₂ have been studied in detail by inelastic neutron scattering at 300 K and specific heat measurements between 10 K and 250 K. The specific heat calculated from the generalised phonon density of states extracted from neutron measurements is in good agreement with the measured lattice contribution to the specific heat. The properties of the phonon spectra are discussed in relation with other data reported for these isostructural and isoelectronic disilicides.     

Nonmetallic crystals with high thermal conductivity

Nonmetallic crystals transport heat primarily by phonons at room temperature and below. There are only a few nonmetallic crystals which can be classed as high thermal conductivity solids, in the sense of having a thermal conductivity of > 1 W/cmK at 300K. Thermal conductivity measurements on natural and synthetic diamond, cubic BN, BP and AIN confirm that all of them are high thermal conductivity solids. Studies have been made of the effect on the thermal conductivity of nitrogen impurities in diamond, and oxygen impurities in AIN. The nitrogen impurities scatter phonons mostly from the strain field, the oxygen impurities scatter phonons mostly from the mass defects caused by aluminum vacancies. Pure A1N as well as pure SiC, BeO, BP and BeS conduct heat almost as well as does copper at room temperature, while pure natural and synthetic diamonds conduct heat five times better than copper.All of the nonmetallic solids that are known to possess high thermal conductivity have either the diamond-like, boron carbide, or graphite crystal structure. There are twelve different diamond-like crystals, a few boron carbide-type crystals, and two graphite structure crystals that have high thermal conductivity. Analyses of the rock-salt, fluorite, quartz, corundum and other structures show no candidates for this class. The four rules for finding crystals with high thermal conductivity are that the crystal should have (1) low atomic mass, (2) strong bonding, (3) simple crystal structure, and (4) low anharmonicity. The prime example of such a solid is diamond, which has the highest known thermal conductivity at 300K.     

Study of thermal conductivity and specific heat of amorphous and partially crystalline poly(ethylene terephthalate) in relation to its structure

The thermal conductivity k(T) and the specific heat of amorphous and partially crystalline polyethylene terephthalate) were measured in the intervals 1.2–40K and 1.2–10K, respectively. For a quantitative study of the relation between the thermal conductivity and the structure and degree of crystallinity of the samples their small angle X-ray scattering was measured. For T > 20 K, k(T) increases with increasing degree of crystallinity φ, whereas for T < 10 K, k(T) decreases when φ increases. Amorphous PET shows a temperature dependence of k(T) which is typical for all amorphous materials. These results are compared with curves which were computed from experimental small angle structure functions using a model for phonon scattering in vitreous systems obtained by Klemens. It is shown that for T < 10 K the change in conductivity in the partially crystalline samples relative to that of the purely amorphous sample can quantitatively be explained by additional scattering of phonons from static long-range order fluctuations of the sound velocity which are due to the microscopic structure of the polymer. From a measurement of the optical extinction of the samples relative values of their thermal conductivity at 50 mK are estimated. The specific heat obeys a T³-law between 1.2 K and about 7 K and decreases linearly with φ. The Debye specific heat of the amorphous sample was computed from the sound velocities. It is only 85% of the measured value.     

Thermal properties of amorphous materials at low temperatures

Recent investigations of X-ray diffraction and electron micrograph studies reveal high density clusters separated by density deficient regions (voids) in amorphous materials. The low temperature specific heat and the thermal conductivity anomalies are explained on the basis of such a structure for amorphous materials. It is a generalisation of Debye's theory applied to most of the amorphous solids in the temperature range from 0 to 10 K. The anharmonic effects lead to the observed temperature dependence of the sound velocity. The thermal conductivity between 0 and 2 K is due to thermal diffusion, the plateau observed between 2 and 20 K is a consequence of the decrease in thermal conductivity due to three phonon processes compensated by intercluster diffusion, while beyond this range it is due to excitations within a cluster limited by the size of a cluster. Further the model predicts the coefficient of expansion about 100 times that found in the corresponding crystalline solids. An experimental verification of this result can be a good test for the model.     

Temperature dependence of thermal properties of Ag<Subscript>8</Subscript>In<Subscript>14</Subscript>Sb<Subscript>55</Subscript>Te<Subscript>23</Subscript> phase-change memory materials

The dependence of thermal properties of Ag₈In₁₄Sb₅₅Te₂₃ phase-change memory materials in crystalline and amorphous states on temperature was measured and analyzed. The results show that in the crystalline state, the thermal properties monotonically decrease with the temperature and present obvious crystalline semiconductor characteristics. The heat capacity, thermal diffusivity, and thermal conductivity decrease from 0.35 J/g K, 1.85 mm²/s, and 4.0 W/m K at 300 K to 0.025 J/g K, 1.475 mm²/s, and 0.25 W/m K at 600 K, respectively. In the amorphous state, while the dependence of thermal properties on temperature does not present significant changes, the materials retain the glass-like thermal characteristics. Within the temperature range from 320 K to 440 K, the heat capacity fluctuates between 0.27 J/g K and 0.075 J/g K, the thermal diffusivity basically maintains at 0.525 mm²/s, and the thermal conductivity decreases from 1.02 W/m K at 320 K to 0.2 W/m K at 440 K. Whether in the crystalline or amorphous state, Ag₈In₁₄Sb₅₅Te₂₃ are more thermally active than Ge₂Sb₂Te₅, that is, the Ag₈In₁₄Sb₅₅Te₂₃ composites bear stronger thermal conduction and diffusion than the Ge₂Sb₂Te₅ phase-change memory materials.     

Thermal conductivity of crystalline fullerite C60 in the simple cubic phase

The behavior of the thermal conductivity k(T) of bulk faceted fullerite C₆₀ crystals is investigated at temperatures T=8–220 K. The samples are prepared by the gas-transport method from pure C₆₀, containing less than 0.01% impurities. It is found that as the temperature decreases, the thermal conductivity of the crystal increases, reaches a maximum at T=15–20 K, and drops by a factor of ∼2, proportional to the change in the specific heat, on cooling to 8 K. The effective phonon mean free path λ _p, estimated from the thermal conductivity and known from the published values of the specific heat of fullerite, is comparable to the lattice constant of the crystal λ _p∼d=1.4 nm at temperatures T>200 K and reaches values λ_p∼50d at T<15 K, i.e., the maximum phonon ranges are limited by scattering on defects in the volume of the sample in the simple cubic phase. In the range T=25−75 K the observed temperature dependence k(T) can be described by the expression k(T)∼exp(Θ/bT), characteristic for the behavior of the thermal conductivity of perfect nonconducting crystals at temperatures below the Debye temperature Θ (Θ=80 K in fullerite), where umklapp phonon-phonon scattering processes predominate in the volume of the sample. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 8, 651–656 (25 April 1997)     

μSR investigation of the magnetic ordering in EuAs3

We have investigated the magnetic ordering and the incommensurate-commensurate phase transition in EuAs₃ by zero-field (ZF) and longitudinal-field μSR. In the commensurate phase, stable at temperatures below T_L=10.3 K, the ZF muon signal exhibits oscillations corresponding to four muon precession frequencies the lowest of which behaves anomalously. The muon signal shows no oscillation but exponential decay in the incommensurate phase stable in temperature range from T_L≈10.3 K up to T_N≈11 K. The temperature dependence of the fitted relaxation rate shows divergence-like behaviour at the ordering temperature T_N≈11 K and also at the lock-in transition T_L≈10.3 K. The results are in qualitative agreement with those previously obtained by neutron and X-ray magnetic scattering investigations except for the anomalous temperature dependence of the lowest frequency in the commensurate phase. We propose a model for this anomalous behaviour.     

Thermal conductivity of polycrystalline CVD diamond: Experiment and theory

The temperature dependences of thermal conductivity κ of polycrystalline CVD diamond are measured in the temperature range from 5 to 410 K. The diamond sample is annealed at temperatures sequentially increasing from 1550 to 1690°C to modify the properties of the intercrystallite contacts in it. As a result of annealing, the thermal conductivity decreases strongly at temperatures below 45 K, and its temperature dependence changes from approximately quadratic to cubic. At T > 45 K, the thermal conductivity remains almost unchanged upon annealing at temperatures up to 1650°C and decreases substantially at higher annealing temperatures. The experimental data are analyzed in terms of the Callaway theory of thermal conductivity [9], which takes into account the specific role of normal phonon-phonon scattering processes. The thermal conductivity is calculated with allowance for three-phonon scattering processes, the diffuse scattering by sample boundaries, the scattering by point and extended defects, the specular scattering by crystallite boundaries, and the scattering by intercrystallite contacts. A model that reproduces the main specific features of the thermal conductivity of CVD diamond is proposed. The phonon scattering by intercrystallite contacts plays a key role in this model.     

Thermal properties of smoky quartz at very low temperatures

The existence of a distribution of low-lying energy levels associated with holes trapped at substitutional aluminium impurities is confirmed by measurements of low temperature specific heat and dielectric loss. A large linearly temperature-dependent contribution to the specific heat is observed at temperatures below 1 K, down to 30 mK. A localization temperature describing the width of the distribution of the energy levels is estimated to vary between 3 and 6 K.

We determined the thermal conductivity down to 30 mK and attribute the decrease below the boundary-scattering value to irradiation damage generally, arguing that it is not attributable to resonant scattering.     

Low temperature glassy properties of disordered crystals

Low temperature measurements of specific heat, thermal conductivity, dielectric dispersion, ultrasonic dispersion and other properties have disclosed that a variety of disordered crystals exhibit the same anomalous behavior as found in amorphous solids. The anomalies arise from localized excitations having broad spectra in both energy and equilibration time. In some disordered crystals, these spectra may be changed systematically by varying the disorder present. The physical origin of the excitations, in crystals or glasses, lacks a satisfactory theoretical explanation. It is expected that the crystalline systems will be more amenable to theoretical study. The crystalline solids found to harbor the excitations include, at this time, certain fast-ion conductors, ferroelectrics, metallic alloys, and rotationally disordered solids.     

Experimental and theoretical studies on high-temperature thermal properties of fibrous insulation

In the present paper, an experimental apparatus has been developed to measure heat transfer through high-alumina fibrous insulation for thermal protection system. Effective thermal conductivities of the fibrous insulation were measured over a wide range of temperature (300-973 K) and pressure (10⁻²-10⁵ Pa) using the developed apparatus. The specific heat and the transmittance spectra in the wavelength range of 2.5-25 μm were also measured. The spectral extinction coefficients and Rosseland mean extinction coefficients were obtained from transmittance data at various temperatures to investigate the radiative heat transfer in fibrous insulation. A one-dimensional finite volume numerical model combined radiation and conduction heat transfer was developed to predict the behavior of the effective thermal conductivity of the fibrous insulation at various temperatures and pressures. The two-flux approximation was used to model the radiation heat transfer through the insulation. The experimentally measured specific heat and Rosseland mean extinction coefficients were used in the numerical heat transfer model to calculate the effective thermal conductivity. The average deviation between the numerical results for different values of albedo of scattering and the experimental results was investigated. The numerical results for ω=1 and experimental data were compared. It was found that the calculated values corresponded with the experimental values within an average of 13.5 percent. Numerical results were consistent with experimental results through the environmental conditions under examination.     

Thermal conductivity of high-porosity biocarbon preforms of beech wood

This paper reports on measurements performed in the temperature range 5–300 K for the thermal conductivity κ and electrical resistivity ρ of high-porosity (cellular pores) biocarbon preforms prepared by pyrolysis (carbonization) of beech wood in an argon flow at carbonization temperatures of 1000 and 2400°C. X-ray structure analysis of the samples has been performed at 300 K. The samples have revealed the presence of nanocrystallites making up the carbon matrices of these biocarbon preforms. Their size has been determined. For samples prepared at T _carb = 1000 and 2400°C, the nanocrystallite sizes are found to be in the ranges 12–25 and 28–60 κ(T) are determined for the samples cut along and across the tree growth direction. The thermal conductivity κ increases with increasing carbonization temperature and nanocrystallite size in the carbon matrix of the sample. Thermal conductivity measurements conducted on samples of both types have revealed an unusual temperature dependence of the phonon thermal conductivity for amorphous materials. As the temperature increases from 5 to 300 K, it first increases in proportion to T, to transfer subsequently to ∼T ^1.5 scaling. The results obtained are analyzed.     

Unusual thermal conductivity of the negative thermal expansion material, ZrW2O8

In order to investigate the relationship between negative thermal expansion and other thermal properties, the thermal conductivity of the α-phase of ZrW₂O₈ has been determined from 1.9 to 390 K. In addition, the heat capacity was measured from 1.9 to 300 K. The thermal conductivity of ZrW₂O₈ is low, glass-like and close to its theoretical minimum value. The phonon-phonon coupling of the highly anharmonic low-frequency modes which are responsible for negative thermal expansion in ZrW₂O₈ appears to be highly efficient, leading to short phonon mean free paths and exceptionally low thermal conductivity.     

Thermal diffusivity in pyrrhotite (Fe7S8)

The thermal diffusivity in a natural single crystal of pyrrhotite was measured using the periodic temperature method at temperatures of 80 K and 300 K respectively. The results are compared with those calculated from the thermal conductivity, the specific heat and the density. An estimation of the heat carriers mobility is also given.     

Thermal conductivity of the amorphous and nanocrystalline phases of the beech wood biocarbon nanocomposite

Natural composites (biocarbons) obtained by carbonization of beech wood at different carbonization temperatures T _carb in the range of 800–2400°C have been studied using X-ray diffraction. The composites consist of an amorphous matrix and nanocrystallites of graphite and graphene. The volume fractions of the amorphous and nanocrystalline phases as functions of T _carb have been determined. Temperature dependences of the phonon thermal conductivity κ(T) of the biocarbons with different temperatures T _carb (1000 and 2400°C) have been analyzed in the range of 5–300 K. It has been shown that the behavior of κ(T) of the biocarbon with T _carb = 1000°C is controlled by the amorphous phase in the range of 5–50 K and by the nanocrystalline phase in the range of 100–300 K. The character of κ(T) of the biocarbon with T _carb = 2400°C is determined by the heat transfer (scattering) in the nanocrystalline phase over the entire temperature range of 5–300 K.     

Thermal conductivity of high-porosity cellular-pore biocarbon prepared from sapele wood

This paper reports on measurements (in the temperature range T = 5–300 K) of the thermal conductivity κ(T) and electrical conductivity σ(T) of the high-porosity (～63 vol %) amorphous biocarbon preform with cellular pores, prepared by pyrolysis of sapele wood at the carbonization temperature 1000°C. The preform at 300 K was characterized using X-ray diffraction analysis. Nanocrystallites 11–30 Å in ize were shown to participate in the formation of the carbon network of sapele wood preforms. The dependences κ(T) and σ(T) were measured for the samples cut across and along empty cellular pore channels, which are aligned with the tree growth direction. Thermal conductivity measurements performed on the biocarbon sapele wood preform revealed a temperature dependence of the phonon thermal conductivity that is not typical of amorphous (and X-ray amorphous) materials. The electrical conductivity σ was found to increase with the temperature increasing from 5 to 300 K. The results obtained were analyzed.     

Specific heat studies on pristine and oxygenated iron tellurides

Specific heat studies carried out on Fe_1.1Te and oxygenated Fe_1.1Te and FeTe₂ in the range 77-300 K exhibit interesting behavior. The specific heat of the pristine sample reveals a well known structural transition associated with antiferromagnetic ordering near 67 K with a small thermal hysteresis of ∼1 K. Contrastingly, the oxygenated samples exhibit a phase transition with a very large thermal hysteresis of ∼100 K. The specific heat transition observed at the 150 and 260 K regions in the oxygenated Fe_1.1Te sample could not be captured by the magnetization measurements indicating that specific heat transitions seen in oxygenated samples may not be of magnetic origin.