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

Theory of Thermal Conductivity of Solids at Low Temperatures

An incoherent particle model has been developed to calculate the phonon thermal conductivity of superlattice nanowires. This is an extension of the photon net-radiation method and Schuster–Schwarzschild approximation to dispersive acoustic phonons in a gray medium. By comparing the roughness and geometric variations of typical nanowires to the characteristic phonon wavelength (∼1 nm at 300 K), diffuse scattering and incoherent three-dimensional dispersion are justified. An isotropic sine-type (Born–von Karman) dispersion is used, which requires only the sound velocity, atomic number density, and bulk conductivity to fully describe a material. A simple picture is also given in terms of Matthiessen’s rule and three effective mean free paths. Agreement with available experimental data is poor at the smallest diameters, but good above 30 nm diameter. Compared to a conventional superlattice, calculations show that the additional sidewall scattering in a superlattice nanowire can reduce the thermal conductivity...

Theoretical phonon thermal conductivity of Si/Ge superlattice nanowires

Thermoelectric generators, capable of directly converting heat into electricity, hold great promise for tackling the ever-increasing energy sustainability issue. The thermoelectric energy conversio...

Advances in thermoelectrics

Common type I diamonds (as classified by Robertson et al) have additional absorption in the infrared and ultraviolet It is shown that the strongest absorption band in the infrared at 78 \ensuremath{\mu} and the ultraviolet absorption at 3065 A are proportional to the nitrogen concentration of the crystal A corresponding increase in lattice constant is found to be as high as 001% for a nitrogen content of 02% Concentration, X-ray, and density data suggest that nitrogen occupies a substitutional position in the diamond lattice The infrared absorption bands at 78, 83, 91, and 208 \ensuremath{\mu} are considered to be C-N molecular vibrations Several optical, electrical, and thermal properties of diamond are discussed in view of our findings

Nitrogen, a major impurity in common type I diamond

The thermal conductivity of single crystals of pure n-type germanium and of p-type germanium containing from 10$^{14}$ to 10$^{19}$ group III impurity atoms per cm$^{3}$ has been measured from 2 to 90 degrees K In some cases the readings have been extended up to room temperature Whereas the low-temperature conductivity of the pure specimens is that which one would expect from a dielectric crystal, the addition of even very small amounts of group III impurity decreases the conductivity very considerably and alters its temperature dependence It is suggested that the extra thermal resistance introduced is due to the scattering of the lattice vibrations by the electrons or holes in the impurity energy levels The theory of such scattering has been worked out by Ziman, and the experimental results are shown to be in fair agreement with this theory A pure n-type silicon single crystal and a gold-doped p-type silicon crystal show a behaviour similar to the germanium The room-temperature conductivity of germanium and silicon is 0$\cdot $64 and 1$\cdot $45 watt units respectively

T. H. Geballe

Papers

The Thermal Conductivity of Germanium and Silicon between 2 and 300 degrees K