The lorenz number of graphite at very low temperatures

Holland, M. G.; Klein, Claude; Sträub, W.

doi:10.1016/0022-3697(66)90265-4

Cited by 58 publications

(27 citation statements)

References 11 publications

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“…The T 2.7 temperature dependence of the basal plane thermal conductivity of graphite agrees with experimental measurement in Ref. 20. Figure 3(b) shows the thermal conductivities above room temperature along with experimental data available for SLG and bulk graphite.…”

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confidence: 85%

Evolution of thermal properties from graphene to graphite

Alofi

Srivastava

2014

Appl. Phys. Lett.

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We report on the evolution of thermal properties from graphene to graphite as a function of layer thickness and temperature. The onset of the inter-layer compressional elastic constant C 33 and the shear elastic constant C 44 results in a large difference between the magnitudes and temperature dependencies of the specific heat and in-plane lattice thermal conductivity of bi-layer graphene (BLG) and single-layer graphene. The changes between BLG and few-layer graphene (FLG) decrease with increase in the number of layers. The cross-plane lattice thermal conductivity increases almost linearly with the number of layers in ultra-thin FLG. V C 2014 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4862319] Graphene, in addition to its remarkable electronic properties, 1 is one of the materials with the highest recorded thermal conductivity values. 2,3 It is also remarkable that compared to most layered systems, fabrication of singlelayer graphene (SLG), bi-layer graphene (BLG), and fewlayer graphene (FLG) can be achieved in a controlled manner. 4 This strongly suggests that the FLG systems can be used to understand the fundamental mechanisms and in achieving controlled alteration of thermal conductivity along and perpendicular to the growth direction. In particular, it would be interesting to ascertain the minimum amount of thermal conductivity established when a BLG is formed.Generally, the intrinsic ability of a material to conduct heat is altered as its dimensionality changes from twodimensional (2D) to three-dimensional (3D). Lateral (inplane) thermal conductivity in conventional semiconductors thin films tends to decrease with decreasing thickness. This is due to the domination of the boundary phonon scattering rate. 5 However, an opposite dependence is observed in FLG where the thermal conductivity is reduced as the number of layers increases. [6][7][8] As graphite is composed of multilayer graphene, it is natural to think that studying thermal properties of FLG will elucidate how the thermal conductivity and specific heat of graphene evolve into graphite-like results with increasing number of layers.In this work, specific heat and thermal conductivity of FLG are calculated. We used the semicontinuum model proposed by Komatsu and Nagamiya, 9 and employed the analytical expressions for phonon dispersion relations and vibrational density of states based on the derivations by Nihira and Iwata. 10 The lattice thermal conductivity tensor was calculated within the framework of Callaway's effective relaxation time theory. 11 We consider the FLG and graphite systems as an assembly of equally spaced elastic layers with compressional and shearing couplings between adjacent layers. According to the theory of elasticity, 12 the strength of the inter-layer coupling in layered materials increases as the number of layers increases. Two elastic constants, C 33 and C 44 , are used to describe the compressional and shearing couplings, respectively. These elastic constants are sensitive to the number of graphene layers, and any chan...

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confidence: 85%

Evolution of thermal properties from graphene to graphite

Alofi

Srivastava

2014

Appl. Phys. Lett.

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“…As mentioned in Introduction the highest thermal conductivity κ along the basal plane of graphite at room temperature can be exemplified with the value of 1950 W m −1 K −1 measured for an HOPG 7) and ∼ 2000 W m −1 K −1 for a single crystal of graphite (SCG) 8) .…”

Section: Thermal Conductivity and Electrical Conductivitymentioning

confidence: 59%

Thermal and electrical conductivity and magnetoresistance of graphite films prepared from aromatic polyimide films

Kaburagi

Kimura

Yoshida

et al. 2012

TANSO

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Highly crystallized graphite films were prepared from carbonized films derived from commercially available aromatic polyimide films by simple heat treatment at temperatures exceeding 3000 °C. Thermal conductivity κ along the longitudinal direction of each graphite film was measured at room temperature in air by a steady-state method. Measurements of the electrical conductivity σ along the longitudinal direction of each graphite film at room temperature the ratio of the resistivity ρ RT along the longitudinal direction of each graphite film at room temperature to that at 77 K ρ 77 K ρ RT /ρ 77 K and the maximum transverse magnetoresistance (Δρ/ρ) max at 77 K in a magnetic field of 1 T were also carried out. In these measurements commercially available graphite sheets pyrolytic graphite with high thermal conductivity and pure Cu and Al were included for comparison. Measured values of κ were corrected using the known values of κ for Cu and Al and the catalogue values of the commercially available graphite sheets and the pyrolytic graphite. The corrected values of κ for the present highly crystallized graphite films were comparable to those of the commercially available thermally conductive graphite sheets. Good correlations between κ and σ as well as those between κ and (Δρ/ρ) max and also κ and ρ RT /ρ 77 K were obtained. In all the curves of κ vs. σ κ vs. ρ RT /ρ 77 K and κ vs. (Δρ/ρ) max κ tends to saturate in the region with high κ values. The dominant conduction mechanism of phonons is considered to change from phonon scattering at the boundaries of crystallites in the region with lower κ values to phonon-phonon interaction (three-phonon process) in the region indicating saturation of κ.

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“…For the latter case of crystalline graphite, we also found our calculated thermal conductivity values to be confirmed by corresponding observations in the basal plane of highest-purity synthetic graphite [17][18][19] which are also reproduced in the figure. We would like to note that experimental data suggest that the thermal conductivity in the basal plane of graphite peaks near 100 K, similar to our nanotube results.…”

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confidence: 75%

“…At high temperatures, where the specific heat is constant, λ decreases as the phonon mean free path The calculated values are compared to the experimental data of Refs. [17] (open circles), [18] (open diamonds), and [19] (open squares) for graphite.…”

mentioning

confidence: 99%

Unusually High Thermal Conductivity in Carbon Nanotubes

Berber¹,

Savas²,

Kwon³

et al.

High Thermal Conductivity Materials

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Combining equilibrium and non-equilibrium molecular dynamics simulations with accurate carbon potentials, we determine the thermal conductivity λ of carbon nanotubes and its dependence on temperature. Our results suggest an unusually high value λ≈6, 600 W/m·K for an isolated (10, 10) nanotube at room temperature, comparable to the thermal conductivity of a hypothetical isolated graphene monolayer or diamond. Our results suggest that these high values of λ are associated with the large phonon mean free paths in these systems; substantially lower values are predicted and observed for the basal plane of bulk graphite. 61.48.+c, 66.70.+f, 63.22.+m, 68.70.+w With the continually decreasing size of electronic and micromechanical devices, there is an increasing interest in materials that conduct heat efficiently, thus preventing structural damage. The stiff sp 3 bonds, resulting in a high speed of sound, make monocrystalline diamond one of the best thermal conductors [1]. An unusually high thermal conductance should also be expected in carbon nanotubes [2,3], which are held together by even stronger sp 2 bonds. These systems, consisting of seamless and atomically perfect graphitic cylinders few nanometers in diameter, are self-supporting. The rigidity of these systems, combined with virtual absence of atomic defects or coupling to soft phonon modes of the embedding medium, should make isolated nanotubes very good candidates for efficient thermal conductors. This conjecture has been confirmed by experimental data that are consistent with a very high thermal conductivity for nanotubes [4].In the following, we will present results of molecular dynamics simulations using the Tersoff potential [5], augmented by Van der Waals interactions in graphite, for the temperature dependence of the thermal conductivity of nanotubes and other carbon allotropes. We will show that isolated nanotubes are at least as good heat conductors as high-purity diamond. Our comparison with graphitic carbon shows that inter-layer coupling reduces thermal conductivity of graphite within the basal plane by one order of magnitude with respect to the nanotube value which lies close to that for a hypothetical isolated graphene monolayer.The thermal conductivity λ of a solid along a particular direction, taken here as the z axis, is related to the heat flowing down a long rod with a temperature gradient dT /dz bywhere dQ is the energy transmitted across the area A in the time interval dt. In solids where the phonon contribution to the heat conductance dominates, λ is proportional to Cvl, the product of the heat capacity per unit volume C, the speed of sound v, and the phonon mean free path l. The latter quantity is limited by scattering from sample boundaries (related to grain sizes), point defects, and by umklapp processes. In the experiment, the strong dependence of the thermal conductivity λ on l translates into an unusual sensitivity to isotopic and other atomic defects. This is best illustrated by the reported thermal conductivity values in the ba...

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The lorenz number of graphite at very low temperatures

Cited by 58 publications

References 11 publications

Evolution of thermal properties from graphene to graphite

Evolution of thermal properties from graphene to graphite

Thermal and electrical conductivity and magnetoresistance of graphite films prepared from aromatic polyimide films

Unusually High Thermal Conductivity in Carbon Nanotubes

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