Thermal conductivity crystalline solids

In electrically insulating solids, heat is transferred in the form of elastic waves or phonons [1], Anything that affects the propagation of the phonons through the solid affects the thermal conductivity of the solid. In a pure crystalline ceramic, the intrinsic thermal conductivity is limited by the energy dissipated during phonon-phonon collisions or so-called Umklapp processes [15], Commonly, the intrinsic thermal conductivity of solids is described by (5). 

Molybdenum (IV) bromide is a black crystalline solid which is very sensitive to oxidation and hydrolysis it should be handled only under a dry inert atmosphere. Its solubility in bromine at 51° is ca. 3.0 g./lOOO g. of bromine, and bromine solutions were found to be nonconductors. For example, at 25° both the solvent bromine and a 0.96 X 10 3 M solution in molybdenum (IV) bromide exhibited a specific conductance of 1.3 X 10-10 ohm-1 cm.-1 At 110 to 130° in vacuo, solid molybdenum (IV) bromide decomposes quantitatively into molyb-denum(III) bromide and bromine, and because of this thermal instability it cannot be sublimed except under a bromine atmosphere. 

At a given (low) temperature and pressure a crystalline phase of some substance is thermodynamically stable vis a vis the corresponding amorphous solid. Furthermore, because of its inherent metastability, the properties of the amorphous solid depend, to some extent, on the method by which it is prepared. Just as in the cases of other substances, H20(as) is prepared by deposition of vapor on a cold substrate. In general, the temperature of the substrate must be far below the ordinary freezing point and below any possible amorphous crystal transition point. In addition, conditions for deposition must be such that the heat of condensation is removed rapidly enough that local crystallization of the deposited material is prevented. Under practical conditions this means that, since the thermal conductivity of an amorphous solid is small at low temperature, the rate of deposition must be small. 

Liquid crystal polymers (LCP) are polymers that exhibit liquid crystal characteristics either in solution (lyotropic liquid crystal) or in the melt (thermotropic liquid crystal) [Ballauf, 1989 Finkelmann, 1987 Morgan et al., 1987]. We need to define the liquid crystal state before proceeding. Crystalline solids have three-dimensional, long-range ordering of molecules. The molecules are said to be ordered or oriented with respect to their centers of mass and their molecular axes. The physical properties (e.g., refractive index, electrical conductivity, coefficient of thermal expansion) of a wide variety of crystalline substances vary in different directions. Such substances are referred to as anisotropic substances. Substances that have the same properties in all directions are referred to as isotropic substances. For example, liquids that possess no long-range molecular order in any dimension are described as isotropic. 

As with thermal conductivity, we see in this section that disorder can greatly affect the mechanism of diffusion and the magnitude of diffusivities, so that crystalline ceramics and oxide glasses will be treated separately. Finally, we will briefly describe an important topic relevant to all material classes, but especially appropriate for ceramics such as catalyst supports—namely, diffusion in porous solids. 

Ross and Andersson (1982) suggested that this behavior, which was never before reported for crystalline organic materials, was associated with the properties of glassy solids. Waite et al. (2005) measured the temperature dependence of porous methane hydrate thermal conductivity. Early work on this anomalous property led to the development of a thermal conductivity needle probe (Asher et al., 1986) as a possible means of in situ discrimination of hydrates from ice in the permafrost. 

Due to the increase in density upon solidification of semi-crystalline thermoplastics, the thermal conductivity is higher in the solid state than in the melt. In the melt state, however, the thermal conductivity of semi-crystallinepolymers reduces to that of amorphous polymers as can be seen in Fig. 2.2 [40],... 

In crystalline solids, and therefore also in highly crystalline solid polymers, the thermal conductivity is enlarged by a concerted action of the molecules. 

Polymorphism is customarily monitored by melting point or infrared spectral analysis. However, other methods, such as X-ray diffraction, thermal analytical, and solid-state Raman spectroscopy, also can be used. It is expected that the sponsor will conduct a diligent search by evaluating the drug substance recrystallized from various solvents with different properties. Either the basis for concluding that only one crystalline form exists, or comparative information regarding the respective solubilities, dissolution rates, and physical/chemical stability of each crystalline form should be provided. 

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 condnctivity at low temperatures, the lattice absorption spectra and the possibility to change... 

To understand this effect, we need to consider the Si-Si bonding within the bulk crystalline solid. As we discussed earlier, electrons are promoted from valence to conduction bands due to thermal excitation. The valence band of the extended solid is formed from the overlap of sp hybridized orbitals residing on each Si atom. When an electron migrates from valence to conduction bands under normal circumstances, there is no directional preference. However, when a strain is introduced along a specific direction of the lattice, the energies of the hybrid orbitals along this direction are altered. 

In Solids, heal conduction is due to two effects the lattice vibrational waves induced by the vibrational motions of the molecules po.sitioned at relatively fixed positions in a periodic manner called a lattice, and the energy transported via the free flow of electrons in the solid (Fig. 1—28). The Ihermal conductivity of a solid is obtained by adding the lattice and electronic components. The relatively high thermal conductivities of pure metals arc primarily due to the electronic component. The lattice component of thermal conductivity strongly depends on the way the molecules are arranged. For example, diamond, which is a liighly ordered crystalline solid, has the highest known thermal conductivity at room temperature. 

In the case of solid crystalline oxides, thermal conductivity decreases with increasing temperature but begins to rise above 1500— 1600 °C because transmission of heat by radiation (photons) begins to take a significant part besides the conduction of heat (phonon mechanism). In completely transparent materials (the coefficient of absorption a = O), no interaction with the radiation occurs in an opaque body (a = oo) the heat is transferred by conduction alone. With translucent materials, each element of the substance absorbs some of the incident radiation, and emits simultaneously,This internal radiation mechanism of heat transmission is characteristic for glasses. At high temperatures, a considerable proportion of heat is therefore transmitted by radiation the so-called apparent thermal conductivity is a sum of true conductivity with radiation conductivity ... 

A characteristic of many solids is their crystaUine state, i.e., a crystal is a solid bounded by faces meeting in definite angles. Except in the so-called regular system of crystals (cube, octahedron, etc.), the properties of a crystalline solid, such as elasticity, thermal conductivity, refractive index, etc. are different in different directions. The application of AFM to the studies of crystal structures has been of much interest. In the following we will give a few examples of such investigations. 

Abstract Refractory oxides encompass a broad range of unary, binary, and ternary ceramic compounds that can be used in structural, insulating, and other applications. The chemical bonds that provide cohesive energy to the crystalline solids also influence properties such as thermal expansion coefficient, thermal conductivity, elastic modulus, and heat capacity. This chapter provides a historical perspective on the use of refractory oxide materials, reviews applications for refractory oxides, overviews fundamental structure-property relations, describes typical processing routes, and summarizes the properties of these materials. 

Figure 8.4 shows the thermal conductivity for quartz (crystalline Si02) and amorphous silica (a-Si02) [7]. The quartz data follows the T3 behavior at low temperature, peaks at about 10 K, and then drops with increasing temperature. As discussed before, this is the expected trend for a crystalline solid. However, amorphous silica behaves very differently. The value of the thermal conductivity is much lower than that of the crystalline sample for all values of temperature. In addition, the temperature dependence of the conductivity is also vastly different. Hence, the model proposed for crystalline solids cannot be applied for such a case. Note that the relation k = Cvtl3 is still valid although the heat capacity and the mean free path cannot be determined by relations used for crystalline solids. 

FIGURE 8,4 Thermal conductivity of quartz and glassy silica as a function of temperature [7]. The quartz thermal conductivity exhibits a T behavior at low temperature, a peak at about 10 K, then reduction at higher temperatures. This is typical of a crystalline solid. For amorphous glass the thermal conductivity increases as T2 plateaus between 1 to 10 K and then increases monotonically with temperature. Also plotted are the predictions of the Cahill-Pohl and Einstein models. The Cahill-Pohl model provides accurate predictions for temperatures higher than 50 K but cannot predict the low temperature behavior. The Einstein model predictions are much lower than the measured values. 

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