Thermal Conductivity at Low Temperatures

The velocity relevant for transport is the Fermi velocity of electrons. This is typically on the order of 106 m/s for most metals and is independent of temperature [2], The mean free path can be calculated from i = iyx where x is the mean free time between collisions. At low temperature, the electron mean free path is determined mainly by scattering due to crystal imperfections such as defects, dislocations, grain boundaries, and surfaces. Electron-phonon scattering is frozen out at low temperatures. Since the defect concentration is largely temperature independent, the mean free path is a constant in this range. Therefore, the only temperature dependence in the thermal conductivity at low temperature arises from the heat capacity which varies as C T. Under these conditions, the thermal conductivity varies linearly with temperature as shown in Fig. 8.2. The value of k, though, is sample-specific since the mean free path depends on the defect density. Figure 8.2 plots the thermal conductivities of two metals. The data are the best recommended values based on a combination of experimental and theoretical studies [3],... 

Intense research has in recent years been devoted to noncrystalline materials. It was discovered also that the majority of semiconducting boron-rich borides display several properties that resemble those of the noncrystalline solids. Among the amorphous properties are the temperature and field dependencies of electrical conductivity at low temperature, the temperature dependence of thermal conductivity at high temperatures, and the temperature dependence of the magnetic susceptibility. In addition, the boron-rich semiconductors display crystalline properties, for example, the temperature dependence of the thermal conductivity at low temperatures, the lattice absorption spectra and the possibility to change... 

Yagi, H., Yanagitani, T., Numazawa, T., Ueda, K. 2007. The physical properties of transparent Y3AI5O12 Elastic modulus at high temperature and thermal conductivity at low temperature. Ceramics International 33 711-714. 

Fiber reinforcement (glass or carbon) increases the mechanical resistance strongly and decreases the thermal expansion, whereas thermal conductivity tends to increase. Powder filling does not affect the mechanical properties very much but reduces both thermal expansion and thermal conductivity at low temperatures. These two possibilities can be used to advantage for specific problems. 

The temperature dependencies of the thermal conductivity for different materials are not the same. Some materials (BeO, Cao, MgO, SiC) have a high thermal conductivity at low temperatures (up to 10-20 W/m-K), but it diminishes with a temperature increase. Other materials (silica, zirconia) have a low conductive thermal conductivity at low temperatures (1-2 W/m K), but it increases with as the temperature increases. 

Figure 8.8 shows the lattice thermal conductivity of Au and comparison with the Debye model. It shows temperature dependence of thermal conductivity at low temperature. 

Materials with large thermal conductivity at low temperatures generally have a negative temperature coefficient—and vice versa for those with low conductivity at low temperatures. 

Callaway, J. (1959). Model for lattice thermal conductivity at low temperatures. Physical Review, 113, 1046-1051. 

The trapped radicals, most of which are presumably polymeric species, have been used to initiate graft copolymerization [127,128]. For this purpose, the irradiated polymer is brought into contact with a monomer that can diffuse into the polymer and thus reach the trapped radical sites. This reaction is assumed to lead almost exclusively to graft copolymer and to very little homopolymer since it can be conducted at low temperature, thus minimizing thermal initiation and chain transfer processes. Moreover, low-molecular weight radicals, which would initiate homopolymerization, are not expected to remain trapped at ordinary temperatures. Accordingly, irradiation at low temperatures increases the grafting yield [129]. 

In most of the studies discussed above, except for the meta-linked diamines, when the aromatic content (dianhydride and diamine chain extender), of the copolymers were increased above a certain level, the materials became insoluble and infusible 153, i79, lsi) solution to this problem with minimum sacrifice in the thermal properties of the products has been the synthesis of siloxane-amide-imides183). In this approach pyromellitic acid chloride has been utilized instead of PMDA or BTDA and the copolymers were synthesized in two steps. The first step, which involved the formation of (siloxane-amide-amic acid) intermediate was conducted at low temperatures (0-25 °C) in THF/DMAC solution. After purification of this intermediate thin films were cast on stainless steel or glass plates and imidization was obtained in high temperature ovens between 100 and 300 °C following a similar procedure that was discussed for siloxane-imide copolymers. Copolymers obtained showed good solubility in various polar solvents. DSC studies indicated the formation of two-phase morphologies. Thermogravimetric analysis showed that the thermal stability of these siloxane-amide-imide systems were comparable to those of siloxane-imide copolymers 183>. 

Unfortunately, most capacitance thermometers are not stable and must be recalibrated at every cool down. They may also present problems of heat release [95] moreover, their thermalization times at low temperatures may be long since the materials used present low thermal conductivity and high specific heat. 

The thermal conductivity of bulk silicon (148 W K m ) is dominated by phonons electronic contributions are negligible. Due to restrictions of the mean free path of phonons in the porous network the thermal conductivity of micro PS is reduced by two or three orders of magnitude at RT, compared to the bulk value. Because of the larger dimensions of its network, meso PS shows a thermal conductivity several times larger than that of micro PS, for the same value of porosity. Thermal oxidation at low temperatures (300°C) is found to decrease the thermal conductivity of meso PS by a factor of about 0.5 [Pe9]. In contrast to bulk Si the thermal conductivity of PS is found to decrease with decreasing temperature [Be21, La4, Ge9, Lyl]. 

Aluminum also has a high degree of thermal and electrical conductivity. At low temperatures, the impact strength of aluminum increases, and for this reason, aluminum is commonly used in cryogenic applications. 

Figure 2, illustrating the relationship of pore size to thermal conductivity at various temperatures, indicates that larger air spaces give better insulation at low temperatures. This principle of porosity should be considered when puffing mechanisms are being investigated. 

Thermal conductivity of ceramics depends on phase composition and spatial arrangement of the phases. It is greatly affected by porosity. The pores reduce conductivity at low temperatures unless they facilitate convective heat transfer. Heal transfer in pores by radiation becomes increasingly effective with increasing tempera-... 

Garden, R. Review of thermal conductivity data in glass. Part I Thermal conductivity at low and moderate temperatures published Inti. Commission on Glass, 1983. 

The exchange reaction is usually conducted at low temperatures (below O C), because of the thermal labihty of fhe resulting magnesium species. 

The behavior of the DC conductivity at low temperatures is an important indicator for the conduction mechanism. The thermal effects on the conductance of the P3HT—MWNT composite films are shown in Figure 12.11 and the temperature dependence of conductance can be expressed in the following formula [77] ... 

The second mode of thermal transport, solid conduction, takes place through the cell walls of the foam. Both PS and PU resins are made up of disordered (noncrystalline) materials. This structure results in a low-phonon or lattice conduction at low temperatures and the conductivity is nearly a linear, decreasing function of temperature. Figure 19 illustrates this behavior for solid PS. The heat conducted by the solid phase ° can be estimated by... 

One of the most important physical parameters of any material is its thermal conductivity (see handbook chapter Thermal Properties of Porous Silicon ). Bulk crystalline Si, the material that is widely used in today s electronics and sensors, shows moderate thermal conductivity at room temperature (Slack 1964). On the other hand, highly porous Si, which is a complex nanostructured Si material, composed of interconnected nanowires and nanocrystals, shows a much lower thermal conductivity than that of bulk crystalline Si, which depends strongly on its structure and morphology. The voids within the porous Si layer and the low dimensionality of the highly porous Si skeleton serve to inhibit thermal transport within the layer. 

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