Conductivity, metallic solids

The thermal conductivity of solids has a wide range of numerical values, depending upon whether the solid is a relatively good conductor of heat, such as metal, or a poor conductor, such as glass-fiber or calcium silicalc. The laUer serves as insulation. 

The value of the coefficient will depend on the mechanism by which heat is transferred, on the fluid dynamics of both the heated and the cooled fluids, on the properties of the materials through which the heat must pass, and on the geometry of the fluid paths. In solids, heat is normally transferred by conduction some materials such as metals have a high thermal conductivity, whilst others such as ceramics have a low conductivity. Transparent solids like glass also transmit radiant energy particularly in the visible part of the spectrum. 

Figure 1.5. Schematic representation of a metal electrode deposited on a 02 -conducting (left) and on a Na -conducting (right) solid electrolyte, showing the location of the metal-electrolyte double layer and of the effective double layer created at the metal/gas interface due to potential-controlled ion migration (backspillover).

The conductivity of solid salts and oxides was first investigated by M. Faraday in 1833. It was not yet known at that time that the nature of conduction in solid salts is different from that in metals. A number of fundamental studies were performed between 1914 and 1927 by Carl Tubandt in Germany and from 1923 onward by Abram Ioffe and co-workers in Russia. These studies demonstrated that a mechanism of ionic migration in the lattice over macroscopic distances is involved. It was shown that during current flow in such a solid electrolyte, electrochemical changes obeying Faraday s laws occur at the metal-electrolyte interface. 

In substitutional metallic solid solutions and in liquid alloys the experimental data have been described by Epstein and Paskin (1967) in terms of a predominant frictional force which leads to the accumulation of one species towards the anode. The relative movement of metallic ion cores in an alloy phase is related to the scattering cross-section for the conduction electrons, which in turn can be correlated with the relative resistance of the pure metals. Thus iron, which has a higher specific resistance than copper, will accumulate towards the anode in a Cu-Fe alloy. Similarly in a germanium-lithium alloy, the solute lithium atoms accumulate towards the cathode. In liquid alloys the same qualitative effect is observed, thus magnesium accumulates near the cathode in solution in bismuth, while uranium, which is in a higher Group of the Periodic Table than bismuth, accumulated near the anode in the same solvent. 

Metallic solids have metal atoms occupying the crystal lattice held together by metallic bonding. In metallic bonding, the electrons of the atoms are delocalized and free to move throughout the entire solid. This explains the electrical and thermal conductivity as well as many of the other properties of metals. 

Conductivity Metals are good conductors of electricity and heat because electrons can move freely throughout the metallic structure. This freedom of movement is not possible in solid ionic compounds, because the valence electrons are held within the individual ionic bonds in the lattice. 

The Sccmning Electron Microscope (SEM) is a standard imaging technique based on electron back-scattering from the sample surface. It analyses the surfaces of solid objects, producing images with the resolution which is about order of magnitude better than that of optical microscopy (typically 10 nm). The SEM avoids the problem of thin samples (TEM) but the SEM observation requires the deposition of a thin conductive metal film on the sample surface to prevent sample charging. 

The development of new transducing materials for DNA analysis is a key issue in the current research efforts in electrochemical-based DNA analytical devices. The use of platinum, gold, indiiun-tin oxide, copper solid amalgam, mercury and other continuous conducting metal substrates has been reported [6]. However, this chapter is focused on carbon-based materials and their properties for immobihzing DNA by simple adsorption procedures. 

A concept related to the localization vs. itineracy problem of electron states, and which has been very useful in providing a frame for the understanding of the actinide metallic bond, is the Mott-Hubbard transition. By this name one calls the transition from an itinerant, electrically conducting, metallic state to a localized, insulator s state in solids, under the effect of external, thermodynamic variables, such as temperature or pressure, the effect of which is to change the interatomic distances in the lattice. 

In conduction, heat is conducted by the transfer of energy of motion between adjacent molecules in a liquid, gas, or solid. In a gas, atoms transfer energy to one another through molecular collisions. In metallic solids, the process of energy transfer via free electrons is also important. In convection, heat is transferred by bulk transport and mixing of macroscopic fluid elements. Recall that there can be forced convection, where the fluid is forced to flow via mechanical means, or natural (free) convection, where density differences cause fluid elements to flow. Since convection is found only in fluids, we will deal with it on only a limited basis. Radiation differs from conduction and convection in that no medium is needed for its propagation. As a result, the form of Eq. (4.1) is inappropriate for describing radiative heat transfer. Radiation is... 

Thermal Properties of Metallic Solids. In the preceding sections, we saw that thermal conductivities of gases, and to some extent liquids, could be related to viscosity and heat capacity. For a solid material such as an elemental metal, the link between thermal conductivity and viscosity loses its validity, since we do not normally think in terms of solid viscosities. The connection with heat capacity is still there, however. In fact, a theoretical description of thermal conductivity in solids is derived directly from the kinetic gas theory used to develop expressions in Section 4.2.1.2. 

What is the situation inside the electrode That depends upon whether the electrode is a metal or a semiconductor. What is the most important difference between a metal and a semiconductor Operationally speaking, it is the order of magnitude of the conductivity. Metals have conductivities on the order of about 106 ohm-1 cm-1 and semiconductors, about 102-1(T9 ohm-1 cm"1. These tremendous differences in conductivity reflect predominantly the concentration of free charge carriers. In crystalline solids, the atomic nuclei are relatively fixed, and the charge carriers that drift in response to electric fields are the electrons. So the question is What determines the concentration of mobile electrons One has to take an inside look at electrons in crystalline solids. 

Some physical properties of water are shown in Table 7.2. Water has higher melting and boiling temperatures, surface tension, dielectric constant, heat capacity, thermal conductivity and heats of phase transition than similar molecules (Table 7.3). Water has a lower density than would be expected from comparison with the above molecules and has the unusual property of expansion on solidification. The thermal conductivity of ice is approximately four times greater than that of water at the same temperature and is high compared with other non-metallic solids. Likewise, the thermal dif-fusivity of ice is about nine times greater than that of water. 

The conductivity of many metal modified systems is reportedly enhanced due to various factors such as charge transfer between metal ions and the electron-rich heteroatoms, elimination of impurities, and changes in the transport number of cations and anions due to environmental changes in the solid electrolytes. Even interesting cases have been reported where a polymer film can reach the electronically conducting metallic level by cis-trans isomerization. 

The mechanism of the thermal decompn of unirradiated and of briefly preirradiated Ba azide was postulated by Mott (Ref 13) and studied by Thomas, Tompkins (Ref 20). However, on detailed examination of the photo and ionic conductivity of this salt, the latter authors found that their results did not agree with the mechanism postulated previously (Ref 21). Jacobs and Tompkins (Ref 23) in their study of the ionic conductance of solid metallic azides found that all salt obeyed the equation log k " log A... 

We may classify solids broadly into three types based on their electrical conductivity. Metals conduct electricity very well. In contrast, insulators do not. Insulators may consist of discrete small molecules, such as phosphorus triiodide, in which the energy necessary to ionize an electron from one molecule and transfer it to a second is too great to be effected under ordinary potentials.M We have seen that most ionic sefids are nonconductors. Finally, solids that contain infinite covalent bonding such as diamond and quartz are usually good insulators (but see Problem 7.5). 

Following the introduction of basic kinetic concepts, some common kinetic situations will be discussed. These will be referred to repeatedly in later chapters and include 1) diffusion, particularly chemical diffusion in different solids (metals, semiconductors, mixed conductors, ionic crystals), 2) electrical conduction in solids (giving special attention to inhomogeneous systems), 3) matter transport across phase boundaries, in particular in electrochemical systems (solid electrode/solicl electrolyte), and 4) relaxation of structure elements. 

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