Recent years have seen a rapid growth of interest by the scientific and engineering communities in the thermal properties of materials. Heat removal has become a crucial issue for continuing progress in the electronic industry, and thermal conduction in low-dimensional structures has revealed truly intriguing features. Carbon allotropes and their derivatives occupy a unique place in terms of their ability to conduct heat. The room-temperature thermal conductivity of carbon materials span an extraordinary large range--of over five orders of magnitude--from the lowest in amorphous carbons to the highest in graphene and carbon nanotubes. Here, I review the thermal properties of carbon materials focusing on recent results for graphene, carbon nanotubes and nanostructured carbon materials with different degrees of disorder. Special attention is given to the unusual size dependence of heat conduction in two-dimensional crystals and, specifically, in graphene. I also describe the prospects of applications of graphene and carbon materials for thermal management of electronics.

Thermal properties of graphene and nanostructured carbon materials

Approximately 90 per cent of the world's power is generated by heat engines that use fossil fuel combustion as a heat source and typically operate at 30-40 per cent efficiency, such that roughly 15 terawatts of heat is lost to the environment. Thermoelectric modules could potentially convert part of this low-grade waste heat to electricity. Their efficiency depends on the thermoelectric figure of merit ZT of their material components, which is a function of the Seebeck coefficient, electrical resistivity, thermal conductivity and absolute temperature. Over the past five decades it has been challenging to increase ZT > 1, since the parameters of ZT are generally interdependent. While nanostructured thermoelectric materials can increase ZT > 1 (refs 2-4), the materials (Bi, Te, Pb, Sb, and Ag) and processes used are not often easy to scale to practically useful dimensions. Here we report the electrochemical synthesis of large-area, wafer-scale arrays of rough Si nanowires that are 20-300 nm in diameter. These nanowires have Seebeck coefficient and electrical resistivity values that are the same as doped bulk Si, but those with diameters of about 50 nm exhibit 100-fold reduction in thermal conductivity, yielding ZT = 0.6 at room temperature. For such nanowires, the lattice contribution to thermal conductivity approaches the amorphous limit for Si, which cannot be explained by current theories. Although bulk Si is a poor thermoelectric material, by greatly reducing thermal conductivity without much affecting the Seebeck coefficient and electrical resistivity, Si nanowire arrays show promise as high-performance, scalable thermoelectric materials.

Enhanced thermoelectric performance of rough silicon nanowires

Recent years witnessed a rapid growth of interest of scientific and engineering communities to thermal properties of materials. Carbon allotropes and derivatives occupy a unique place in terms of their ability to conduct heat. The room-temperature thermal conductivity of carbon materials span an extraordinary large range – of over five orders of magnitude – from the lowest in amorphous carbons to the highest in graphene and carbon nanotubes. I review thermal and thermoelectric properties of carbon materials focusing on recent results for graphene, carbon nanotubes and nanostructured carbon materials with different degrees of disorder. A special attention is given to the unusual size dependence of heat conduction in two-dimensional crystals and, specifically, in graphene. I also describe prospects of applications of graphene and carbon materials for thermal management of electronics.

Thermal Properties of Graphene, Carbon Nanotubes and Nanostructured Carbon Materials

Hundreds of different types of coatings are used to protect a variety of structural engineering materials from corrosion, wear, and erosion, and to provide lubrication and thermal insulation. Of all these, thermal barrier coatings (TBCs) have the most complex structure and must operate in the most demanding high-temperature environment of aircraft and industrial gas-turbine engines. TBCs, which comprise metal and ceramic multilayers, insulate turbine and combustor engine components from the hot gas stream, and improve the durability and energy efficiency of these engines. Improvements in TBCs will require a better understanding of the complex changes in their structure and properties that occur under operating conditions that lead to their failure. The structure, properties, and failure mechanisms of TBCs are herein reviewed, together with a discussion of current limitations and future opportunities.

http://science.sciencemag.org/content/sci/296/5566/280.full.pdf

Thermal Barrier Coatings for Gas-Turbine Engine Applications

Graphene based materials: Past, present and future

The scattering of lattice waves by static imperfections is treated by second-order perturbation theory. The transition matrix is composed of contributions due to the mass difference of lattice points, changes in the elastic constants of linkages between lattice points, and elastic strain. Point imperfections are shown to scatter as the fourth power of frequency, dislocations as the first power, and grain boundaries independently of frequency. The magnitude of the scattering cross section is estimated for a variety of lattice defects in alkali halides, for screw and edge dislocations and for grain boundaries. These results are discussed in relation to thermal conduction by the lattice at low temperatures.

https://iopscience.iop.org/article/10.1088/0370-1298/68/12/303/pdf

The Scattering of Low-Frequency Lattice Waves by Static Imperfections

Thermal Conduction in Solids

An expression is derived from perturbation theory for the lifetime of an optical phonon decaying into two acoustical phonons, and its temperature dependence. The strength of the interaction is expressed in terms of the Gr\"uneisen constant and the effect of a strain, equivalent to the instantaneous strain of an optical mode, on the frequency spectrum of a linear chain with alternating force constants. This interaction depends on the ratio of the acoustical and optical mode frequencies at the zone boundary. Fitting the theory to silicon, the optical mode at k = 0 has a calculated half-width at 300\ifmmode^\circ\else\textdegree\fi{}K of about 1.2% of its frequency. This result is compared with experimental data.

Anharmonic Decay of Optical Phonons

Publisher Summary This chapter discusses thermal conductivity and lattice vibrational modes. The heat transport by lattice waves in solids is governed by the anharmonicities of the lattice forces (which are also responsible for thermal expansion), by the various imperfections of the crystal lattice, and by the external boundaries. In the case of metallic and semi-metallic solids, the lattice component of thermal conduction is also governed by the free electrons. Not only may many different factors influence the thermal conductivity, but the processes that provide the principal sources of thermal resistance may vary from one material to another. In fact, they may vary in different temperature regions in any one material. Thus, the phenomenon of thermal conduction by lattice waves offers great diversity and provides an interesting field of study, both from a fundamental point of view, in which one desires to attain agreement between observation and the theoretical concepts, and from the more applied viewpoint in which one desires to use thermal conductivity as a tool in the study of lattice imperfections. Thermal conduction by lattice waves also occurs in metallic solids, but here the lattice conductivity is small, as a consequence of the scattering of lattice waves by conduction electrons, so that it is often overshadowed by the electronic thermal conductivity.

Thermal Conductivity and Lattice Vibrational Modes

The thermal conductivity of dense and porous yttria-stabilized zirconia (YSZ) ceramics has been measured as a function of temperature in the range 25 to 1000 °C The dense specimens were either single crystal (8 mol% YSZ) or sintered polycrystalline (3 mol% and 8 mol% YSZ) The porous specimens (3 mol% YSZ) were prepared using the “fugitive” polymer method, where different amounts of polymer spheres (of two different average sizes) were included in the starting powders before sintering This method yielded materials with uniformly distributed porosities with a tight pore-size distributions A theory has been developed to describe the thermal conductivity of dense YSZ as a function of temperature This theory considers the reduction in the intrinsic thermal conductivity due scattering of phonons by point defects (oxygen vacancies and solute) and by the “hopping” of oxygen vacancies It also considers an increase in the effective thermal conductivity at high temperatures due to radiation This theory captures the essential features of the observed thermal conductivity The Maxwell theory has been used to analyze the thermal conductivity of the porous materials An adequate agreement was found between the theory and experiment

Paul G. Klemens

Papers

The Scattering of Low-Frequency Lattice Waves by Static Imperfections

Thermal Conduction in Solids

Anharmonic Decay of Optical Phonons

Thermal Conductivity and Lattice Vibrational Modes

Thermal conductivity of dense and porous yttria-stabilized zirconia